Finite Group Databasebeta

← #35197363

Subgroups — #35197363

Order 20224.

7066 conjugacy classes of subgroups.

The subgroup lattice has 2024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777511C211yesmaximal, characteristic, complemented
2#23777506C213yesmaximal, complemented
3#23777502C211yesmaximal, characteristic, complemented
4#23777499C213yesmaximal, complemented
5#23777485C211yesmaximal, characteristic, complemented
6#23777484C213yesmaximal, complemented
7#23777481C213yesmaximal, complemented
8#23777476C211yesmaximal, characteristic, complemented
9#23777407C211yesmaximal, characteristic, complemented
10#23777404C213yesmaximal, complemented
11#23777400C211yesmaximal, characteristic, complemented
12#23777399C213yesmaximal, complemented
13#23777394C211yesmaximal, characteristic, complemented
14#23777391C213yesmaximal, complemented
15#23777388C213yesmaximal, complemented
16#23777253C213yesmaximal, complemented
17#23777246C213yesmaximal, complemented
18#23777207C211yesmaximal, characteristic, complemented
19#23777170C211yesmaximal, characteristic, complemented
20#23777108C213yesmaximal, complemented
21#23777100C213yesmaximal, complemented
22#23777057C211yesmaximal, characteristic, complemented
23#23777057C211yesmaximal, characteristic, complemented
24#23776821C213yesmaximal, complemented
25#23776820C213yesmaximal, complemented
26#23776791C213yesmaximal, complemented
27#23776783C213yesmaximal, complemented
28C4×#14579209C211yesmaximal, characteristic, complemented
29#23776609C211yesmaximal, characteristic, complemented
30#520×D79C211yesmaximal, characteristic, complemented
31C79×#3516C211yesmaximal, characteristic, complemented
32C2×#14579209C2211yescharacteristic
33C2×#14579209C2211yescharacteristic
34C2×#41×D79C2211yescharacteristic
35#19099298C2213yescomplemented
36#19099298C2213yescomplemented
37#19099297C2216yescomplemented
38#19099296C2216yescomplemented
39#19099295C2213yescomplemented
40#19099295C2213yescomplemented
41Q8×Dic158C2211yescharacteristic, complemented
42#19099293C2213yescomplemented
43#19099291C2213yescomplemented
44#19099290C2213yescomplemented
45#19099290C2213yescomplemented
46#19099289C2211yescharacteristic, complemented
47#19099289C2211yescharacteristic, complemented
48#19099287C2213yescomplemented
49#19099280C2216yescomplemented
50#19099277C2213yescomplemented
51#19099276C2216yescomplemented
52#19099276C2213yescomplemented
53#19099273C2213yescomplemented
54#19099271C2213yescomplemented
55#19099271C2213yescomplemented
56#19099269C2216yescomplemented
57#19099267C2216yescomplemented
58#19099266C2213yescomplemented
59#19099266C2213yescomplemented
60#19099264C2216yescomplemented
61#19099264C2216yescomplemented
62#19099264C2216yescomplemented
63#19099263C2213yescomplemented
64#19099262C2216yescomplemented
65#19099261C2213yescomplemented
66#19099259C2213yescomplemented
67#19099259C2213yescomplemented
68#19099257C2213yescomplemented
69#19099255C2213yescomplemented
70#19099254C2213yescomplemented
71#19099247C2213yescomplemented
72#19099246C2216yescomplemented
73#19099245C2216yescomplemented
74#19099235C2211yescharacteristic
75#19099235C2211yescharacteristic
76#19099235C2211yescharacteristic, complemented
77#19099235C2213yescomplemented
78#19099234C2213yes—
79#19099234C2213yes—
80#19099234C2213yescomplemented
81#19099234C2213yescomplemented
82#19099232C2211yescharacteristic
83#19099232C2211yescharacteristic
84#19099231C2213yes—
85#19099231C2213yes—
86#19099231C2216yescomplemented
87#19099228C2213yescomplemented
88#19099224C2211yescharacteristic
89#19099224C2211yescharacteristic
90#19099224C2211yescharacteristic, complemented
91#19099224C2211yescharacteristic, complemented
92#19099223C2213yes—
93#19099223C2213yes—
94#19099223C2213yescomplemented
95#19099223C2213yescomplemented
96#19099221C2213yes—
97#19099221C2213yes—
98#19099217C2213yescomplemented
99#19099216C2213yescomplemented
100#19099215C2216yescomplemented
101#19099215C2216yescomplemented
102#19099214C2213yescomplemented
103#19099214C2213yescomplemented
104#19099214C2213yescomplemented
105#19099213C2213yescomplemented
106#19099211C2216yescomplemented
107#19099193C2213yes—
108#19099190C2213yes—
109#19099186C2213yescomplemented
110#19099186C2213yescomplemented
111#19099186C2213yescomplemented
112#19099185C2213yescomplemented
113#19099185C2213yescomplemented
114#19099185C2213yescomplemented
115#19099183C2213yescomplemented
116#19099183C2216yescomplemented
117#19099182C2213yescomplemented
118#19099181C2213yescomplemented
119#19099179C2213yescomplemented
120#19099179C2216yescomplemented
121#19099177C2213yescomplemented
122#19099174C2213yescomplemented
123#19099172C2213yescomplemented
124#19099170C2213yescomplemented
125#19099169C2213yescomplemented
126#19099169C2213yescomplemented
127#19099168C2213yescomplemented
128#19099168C2213yescomplemented
129#19099166C2213yescomplemented
130#19099165C2213yescomplemented
131#19099165C2216yescomplemented
132#19099165C2216yescomplemented
133#19099164C2213yescomplemented
134#19099163C2213yescomplemented
135#19099161C2213yes—
136#19099161C2216yes—
137#19099159C2213yes—
138#19099156C2211yescharacteristic
139#19099154C2213yes—
140#19099152C2213yes—
141#19099152C2216yes—
142#19099152C2216yes—
143#19099149C2213yes—
144#19099147C2213yes—
145#19099145C2213yes—
146#19099143C2213yes—
147#19099143C2213yes—
148#19099131C2213yes—
149#19099131C2213yes—
150#19099129C2213yes—
151#19099129C2213yes—
152#19099119C2213yes—
153#19099117C2213yes—
154#19099114C2213yes—
155#19099114C2213yescomplemented
156#19099113C2213yescomplemented
157#19099112C2216yescomplemented
158#19099110C2213yes—
159#19099110C2216yescomplemented
160#19099110C2213yescomplemented
161#19099108C2213yescomplemented
162#19099100C2213yescomplemented
163#19099100C2213yescomplemented
164#19099099C2213yescomplemented
165#19099098C2216yescomplemented
166#19099098C2216yescomplemented
167#19099097C2213yescomplemented
168#19099096C2216yescomplemented
169#19099096C2216yescomplemented
170#19099096C2216yescomplemented
171#19099095C2213yescomplemented
172#19099093C2213yescomplemented
173#19099093C2213yescomplemented
174#19099092C2213yescomplemented
175#19099091C2213yescomplemented
176#19099091C2213yescomplemented
177#19099091C2216yescomplemented
178#19099076C2213yes—
179#19099076C2213yes—
180#19099076C2216yes—
181#19099075C2216yes—
182#19099072C2213yes—
183#19099072C2213yes—
184#19099072C2216yes—
185#19099071C2216yes—
186#19099046C2211yescharacteristic
187#19099045C2213yes—
188#19099045C2211yescharacteristic
189#19099045C2211yescharacteristic
190#19099045C2213yes—
191#19099045C2211yescharacteristic, complemented
192#19099045C2211yescharacteristic, complemented
193#19099044C2213yes—
194#19099044C2213yes—
195#19099044C2213yescomplemented
196#19099043C2213yes—
197#19099043C2213yes—
198#19099043C2213yescomplemented
199#19099042C2213yes—
200#19099042C2213yes—
201#19099041C2211yescharacteristic, complemented
202#19099039C2211yescharacteristic
203#19099039C2211yescharacteristic
204#19099039C2213yescomplemented
205#19099039C2213yescomplemented
206C4×#11929625C2213yes—
207C4×#11929625C2213yes—
208C4×#11929625C2211yescharacteristic, complemented
209C4×#11929625C2211yescharacteristic, complemented
210C4×#11929624C2213yes—
211C4×#11929624C2213yescomplemented
212#19099031C2213yes—
213#19099031C2213yescomplemented
214C2×Q8×Dic79C2211yescharacteristic, complemented
215C4×Q8×D79C2211yescharacteristic
216C4×Q8×D79C2211yescharacteristic
217C4×Q8×D79C2213yescomplemented
218C4×Q8×D79C2213yescomplemented
219C4×D4×D79C2213yes—
220C4×D4×D79C2213yes—
221#117×D79C2213yes—
222C2×C4⋊C4×D79C2213yes—
223#557×C79C2211yescharacteristic, complemented
224#556×C79C2213yescomplemented
225#554×C79C2213yescomplemented
226#553×C79C2213yescomplemented
227#552×C79C2213yescomplemented
228D4×Q8×C79C2211yescharacteristic, complemented
229#548×C79C2211yescharacteristic
230#548×C79C2211yescharacteristic
231#542×C79C2213yescomplemented
232#541×C79C2213yescomplemented
233#529×C79C2213yescomplemented
234#529×C79C2213yescomplemented
235#520×C79C2211yescharacteristic
236#519×C79C2211yescharacteristic, complemented
237C2×C4×Q8×C79C2211yescharacteristic, complemented
238#14579209—28no—
239#14579209—28no—
240C2×#11929625C2313yes—
241C2×#11929625C2313yes—
242C2×#11929625C2311yescharacteristic
243C2×#11929625C2311yescharacteristic
244C2×#11929625C2311yescharacteristic
245C2×#11929625C2316yes—
246C2×#11929624C2313yes—
247C2×#11929624C2313yes—
248C2×#11929624C2313yes—
249C2×#11929624C2313yes—
250C2×#11929624C2313yes—
251C2×#11929624C2316yes—
252C2×#11929624C2316yes—
253C2×#11929623C2313yes—
254C2×#11929623C2316yes—
255#41×D79—28no—
256C2×Q8×D79C2313yes—
257C2×Q8×D79C2313yes—
258C2×Q8×D79C2311yescharacteristic
259C2×D4×D79C2313yes—
260C22×C4×D79C2313yes—
261C22×C4×D79C2316yes—
262#14579161C2313yes—
263#14579160C2313yes—
264#14579160C2313yes—
265#14579160C2316yes—
266#14579160C2313yes—
267#14579160C2313yes—
268#14579160C2313yes—
269#14579160C2313yes—
270#14579159C2313yes—
271#14579159C2316yes—
272#14579158C2313yes—
273#14579158C2313yes—
274#14579158C2313yes—
275#14579157C2313yes—
276#14579157C2313yes—
277#14579157C2316yes—
278#14579157C2316yes—
279#14579157C2313yes—
280#14579156C2313yes—
281#14579156C2313yes—
282#14579156C2313yes—
283#14579156C2316yes—
284#14579156C2316yes—
285#14579156C2313yes—
286#14579156C2313yes—
287#14579156C2313yes—
288#14579156C2316yes—
289#14579155C2313yes—
290#14579155C2313yes—
291#14579155C2316yes—
292#14579154C2313yes—
293#14579154C2313yes—
294#14579154C2313yes—
295#14579154C2311yescharacteristic
296#14579154C2311yescharacteristic
297#14579154C2313yes—
298#14579153C2313yes—
299#14579153C2313yes—
300#14579153C2313yes—
301#14579152C2313yes—
302#14579152C2311yescharacteristic
303#14579152C2313yes—
304#14579152C2313yes—
305#14579151C2311yescharacteristic
306#14579151C2313yes—
307#14579151C2313yes—
308#14579151C2313yes—
309#14579151C2316yes—
310#14579151C2313yes—
311#14579151C2313yes—
312#14579151C2316yes—
313#14579151C2316yes—
314#14579150C2313yes—
315#14579150C2313yes—
316#14579150C2313yes—
317#14579150C2313yes—
318#14579150C2313yes—
319#14579149C2316yes—
320#14579149C2313yes—
321#14579149C2316yes—
322#14579148C2313yes—
323#14579147C2313yes—
324#14579147C2313yes—
325#14579147C2313yes—
326#14579147C2313yes—
327#14579147C2316yes—
328#14579147C2316yes—
329#14579147C2313yes—
330#14579147C2316yes—
331#14579147C2313yes—
332#14579147C2316yes—
333#14579146C2313yes—
334#14579146C2316yes—
335#14579146C2313yes—
336#14579146C2316yes—
337#14579146C2313yes—
338#14579146C2313yes—
339#14579146C2313yes—
340#14579146C2313yes—
341#14579146C2316yes—
342#14579146C2316yes—
343#14579146C2316yes—
344#14579146C2316yes—
345#14579146C2316yes—
346#14579145C2313yes—
347#14579145C2313yes—
348#14579145C2316yes—
349#14579145C2316yes—
350#14579144C2313yes—
351#14579144C2313yes—
352#14579144C2316yes—
353#14579143C2313yes—
354#14579143C2316yes—
355#14579143C2313yes—
356#14579143C2316yes—
357#14579143C2311yescharacteristic
358#14579143C2313yes—
359#14579143C2311yescharacteristic
360#14579143C2313yes—
361#14579143C2316yes—
362#14579142C2313yes—
363#14579142C2311yescharacteristic
364#14579141C2313yes—
365#14579141C2313yes—
366#14579141C2316yes—
367#14579141C2316yes—
368#14579140C2311yescharacteristic
369#14579139C2316yes—
370#14579139C2316yes—
371#14579139C2313yes—
372#14579139C2311yescharacteristic
373#14579139C2316yes—
374#14579139C2313yes—
375#14579139C2313yes—
376#14579139C2316yes—
377#14579139C2313yes—
378#14579139C2313yes—
379#14579139C2316yes—
380#14579138C2313yes—
381#14579138C2311yescharacteristic
382#14579138C2313yes—
383#14579138C2313yes—
384#14579138C2316yes—
385#14579137C2313yes—
386#14579137C2313yes—
387#14579137C2313yes—
388#14579137C2313yes—
389#14579137C2313yes—
390#14579137C2313yes—
391#14579136C2316yes—
392#14579136C2313yes—
393#14579136C2313yes—
394#14579136C2313yes—
395#14579136C2316yes—
396#14579136C2313yes—
397#14579136C2316yes—
398#14579136C2316yes—
399#14579136C2313yes—
400#14579136C2313yes—
401#14579136C2313yes—
402#14579136C2313yes—
403#14579135C2313yes—
404#14579135C2313yes—
405#14579135C2313yes—
406#14579135C2316yes—
407#14579135C2313yes—
408#14579135C2313yes—
409#14579135C2313yes—
410#14579135C2313yes—
411#14579134C2313yes—
412#14579134C2313yes—
413#14579134C2316yes—
414#14579134C2316yes—
415#14579134C2313yes—
416#14579134C2313yes—
417#14579134C2316yes—
418#14579134C2316yes—
419#14579134C2316yes—
420#14579134C2313yes—
421#14579134C2313yes—
422#14579134C2316yes—
423#14579134C2316yes—
424#14579134C2316yes—
425#14579134C2316yes—
426#14579133C2313yes—
427#14579133C2313yes—
428#14579133C2313yes—
429#14579133C2313yes—
430#14579133C2316yes—
431#14579132C2311yescharacteristic
432#14579132C2313yes—
433#14579132C2313yes—
434#14579132C2313yes—
435#14579131C2313yes—
436#14579131C2313yes—
437#14579131C2316yes—
438#14579131C2316yes—
439#14579129C2313yes—
440#14579129C2313yes—
441Q8×Dic79C2313yes—
442Q8×Dic79C2313yes—
443Q8×Dic79C2311yescharacteristic
444Q8×Dic79C2311yescharacteristic
445Q8×Dic79C2311yescharacteristic
446Q8×Dic79C2313yes—
447Q8×Dic79C2313yes—
448Q8×Dic79C2311yescharacteristic
449C4×Dic158C2313yes—
450C4×Dic158C2313yes—
451C4×Dic158C2313yes—
452C4×Dic158C2313yes—
453C4×Dic158C2313yes—
454C4×Dic158C2313yes—
455C4×Dic158C2316yes—
456C4×Dic158C2313yes—
457C4×Dic158C2313yes—
458C4×Dic158C2313yes—
459#14579126C2313yes—
460#14579126C2313yes—
461#14579126C2313yes—
462#14579126C2313yes—
463#14579126C2313yes—
464#14579126C2316yes—
465#14579126C2316yes—
466#14579126C2313yes—
467#14579126C2316yes—
468C4×D316C2313yes—
469C4×D316C2313yes—
470C4×D316C2316yes—
471C4×D316C2313yes—
472C4×D316C2313yes—
473C4×D316C2313yes—
474C4×D316C2313yes—
475C4×D316C2313yes—
476C4×D316C2313yes—
477C4×D316C2313yes—
478C4×D316C2313yes—
479C4×D316C2313yes—
480C4×D316C2316yes—
481C4×D316C2316yes—
482D4×Dic79C2313yes—
483D4×Dic79C2313yes—
484#14579123C2313yes—
485#14579123C2313yes—
486#14579123C2316yes—
487#14579123C2313yes—
488#14579123C2313yes—
489#14579123C2313yes—
490#14579123C2313yes—
491#14579123C2313yes—
492#14579123C2313yes—
493#14579123C2316yes—
494#14579123C2316yes—
495#14579123C2316yes—
496#14579123C2316yes—
497#14579123C2316yes—
498C4×C22⋊D79C2313yes—
499C4×C22⋊D79C2311yescharacteristic
500C4×C22⋊D79C2313yes—
501C4×C22⋊D79C2313yes—
502C4×C22⋊D79C2316yes—
503C4×C22⋊D79C2313yes—
504C4×C22⋊D79C2313yes—
505C4×C22⋊D79C2313yes—
506C4×C22⋊D79C2313yes—
507C4×C22⋊D79C2316yes—
508C4×C22⋊D79C2316yes—
509C4×C22⋊D79C2313yes—
510C4×C22⋊D79C2313yes—
511C4×C22⋊D79C2316yes—
512(C22⋊D79)⋊C4C2313yes—
513(C22⋊D79)⋊C4C2311yescharacteristic
514(C22⋊D79)⋊C4C2313yes—
515(C22⋊D79)⋊C4C2313yes—
516(C22⋊D79)⋊C4C2316yes—
517(C22⋊D79)⋊C4C2316yes—
518(C22⋊D79)⋊C4C2316yes—
519(C22⋊D79)⋊C4C2316yes—
520(C22⋊D79)⋊C4C2316yes—
521(C22⋊D79)⋊C4C2316yes—
522(C22⋊D79)⋊C4C2316yes—
523(C22⋊D79)⋊C4C2316yes—
524#14579120C2313yes—
525#14579120C2313yes—
526#14579120C2313yes—
527#14579119C2313yes—
528#14579119C2316yes—
529#14579119C2316yes—
530#14579119C2313yes—
531#14579119C2313yes—
532#14579119C2313yes—
533#14579119C2316yes—
534#14579119C2313yes—
535#14579119C2313yes—
536#14579118C2313yes—
537#14579118C2313yes—
538#14579118C2313yes—
539#14579118C2313yes—
540#14579118C2313yes—
541#14579118C2313yes—
542#14579118C2316yes—
543#14579118C2316yes—
544#14579118C2316yes—
545#14579117C2313yes—
546#14579117C2313yes—
547#14579117C2316yes—
548C2×C4⋊Dic79C2313yes—
549C2×C4⋊Dic79C2313yes—
550C2×Dic79⋊C4C2316yes—
551C4⋊C4×D79C2313yes—
552C4⋊C4×D79C2313yes—
553C4⋊C4×D79C2311yescharacteristic
554C4⋊C4×D79C2316yes—
555C4⋊C4×D79C2313yes—
556C4⋊C4×D79C2313yes—
557C4⋊C4×D79C2313yes—
558C4⋊C4×D79C2316yes—
559C4⋊C4×D79C2316yes—
560C4⋊C4×D79C2313yes—
561C4⋊C4×D79C2313yes—
562C22⋊C4×D79C2313yes—
563C22⋊C4×D79C2313yes—
564C2×C4×Dic79C2313yes—
565C42×D79C2313yes—
566C42×D79C2313yes—
567C42×D79C2313yes—
568C42×D79C2316yes—
569C42×D79C2313yes—
570C42×D79C2316yes—
571C2×#41×C79C2311yescharacteristic
572C22×Q8×C79C2311yescharacteristic
573C22×Q8×C79C2311yescharacteristic
574C4⋊Q8×C79C2313yes—
575C4⋊Q8×C79C2313yes—
576#126×C79C2313yes—
577#126×C79C2316yes—
578#126×C79C2316yes—
579#126×C79C2313yes—
580#125×C79C2313yes—
581#125×C79C2316yes—
582#125×C79C2313yes—
583#125×C79C2313yes—
584#124×C79C2313yes—
585#124×C79C2313yes—
586#124×C79C2313yes—
587#123×C79C2313yes—
588#123×C79C2311yescharacteristic
589#123×C79C2316yes—
590C22⋊Q8×C79C2313yes—
591C22⋊Q8×C79C2313yes—
592C22⋊Q8×C79C2313yes—
593C22⋊Q8×C79C2316yes—
594C22⋊Q8×C79C2313yes—
595C22⋊Q8×C79C2313yes—
596#121×C79C2313yes—
597#121×C79C2313yes—
598#121×C79C2313yes—
599C4×Q8×C79C2313yes—
600C4×Q8×C79C2313yes—
601C4×Q8×C79C2311yescharacteristic
602C4×Q8×C79C2311yescharacteristic
603C4×Q8×C79C2313yes—
604C4×Q8×C79C2311yescharacteristic
605C4×Q8×C79C2311yescharacteristic
606C4×Q8×C79C2313yes—
607C4×Q8×C79C2313yes—
608C4×D4×C79C2313yes—
609C4×D4×C79C2313yes—
610C4×D4×C79C2313yes—
611C4×D4×C79C2313yes—
612C4×D4×C79C2313yes—
613C4×D4×C79C2316yes—
614#117×C79C2313yes—
615#117×C79C2313yes—
616#117×C79C2313yes—
617#117×C79C2316yes—
618C2×C4⋊C4×C79C2313yes—
619C2×C4⋊C4×C79C2313yes—
620C2×C42×C79C2313yes—
621C23×D79C2413yes—
622#11929625—212no—
623#11929625—212no—
624#11929625—24no—
625#11929625—24no—
626#11929625—24no—
627#11929625—86no—
628#11929624—212no—
629#11929624—212no—
630#11929624—212no—
631#11929624—212no—
632#11929624—212no—
633#11929624—86no—
634#11929624—86no—
635#11929623—212no—
636#11929623—86no—
637C2×Dic158C2413yes—
638C2×Dic158C2413yes—
639C2×Dic158C2416yes—
640C2×Dic158C2413yes—
641C2×Dic158C2413yes—
642C2×Dic158C2411yescharacteristic
643C2×Dic158C2413yes—
644Q8×D79—212no—
645Q8×D79—212no—
646Q8×D79#4118yescomplemented
647C2×D316C2413yes—
648C2×D316C2413yes—
649C2×D316C2413yes—
650C2×D316C2413yes—
651C2×D316C2413yes—
652C2×D316C2416yes—
653C2×D316C2416yes—
654C2×D316C2413yes—
655C2×D316C2416yes—
656C2×D316C2413yes—
657C2×D316C2413yes—
658C2×C22⋊D79C2416yes—
659C2×C22⋊D79C2411yescharacteristic
660C2×C22⋊D79C2413yes—
661C2×C22⋊D79C2411yescharacteristic
662C2×C22⋊D79C2413yes—
663C2×C22⋊D79C2413yes—
664C2×C22⋊D79C2416yes—
665C2×C22⋊D79C2413yes—
666C2×C22⋊D79C2413yes—
667C2×C22⋊D79C2413yes—
668C2×C22⋊D79C2413yes—
669C2×C22⋊D79C2416yes—
670C2×C22⋊D79C2413yes—
671D4×D79—212no—
672C22×Dic79C2413yes—
673C22×Dic79C2413yes—
674C22×Dic79C2416yes—
675C22×Dic79C2411yescharacteristic
676C2×C4×D79—212no—
677C2×C4×D79—86no—
678C2×C4×D79C2416yes—
679C2×C4×D79C2416yes—
680C2×C4×D79C2413yes—
681C2×C4×D79C2413yes—
682C2×C4×D79C2413yes—
683C2×C4×D79C2413yes—
684C2×C4×D79C2411yescharacteristic
685C2×C4×D79C2416yes—
686C2×C4×D79C2416yes—
687C2×C4×D79C2413yes—
688C2×C4×D79C2416yes—
689C2×C4×D79C2413yes—
690C2×C4×D79C2416yes—
691C2×C4×D79C2411yescharacteristic
692C2×C4×D79C2411yescharacteristic
693C2×C4×D79C2413yes—
694C2×C4×D79C2413yes—
695C2×C4×D79C2413yes—
696C2×C4×D79C2413yes—
697C2×C4×D79C2413yes—
698C4⋊Dic79C2413yes—
699C4⋊Dic79C2413yes—
700C4⋊Dic79C2413yes—
701C4⋊Dic79C2413yes—
702C4⋊Dic79C2413yes—
703C4⋊Dic79C2416yes—
704C4⋊Dic79C2411yescharacteristic
705C4⋊Dic79C2413yes—
706C4⋊Dic79C2413yes—
707C4⋊Dic79C2413yes—
708C4⋊Dic79C2411yescharacteristic
709C4⋊Dic79C2411yescharacteristic
710C4⋊Dic79C2411yescharacteristic
711C4⋊Dic79C2413yes—
712C4⋊Dic79C2413yes—
713Dic79⋊C4C2416yes—
714Dic79⋊C4C2413yes—
715Dic79⋊C4C2413yes—
716Dic79⋊C4C2416yes—
717Dic79⋊C4C2413yes—
718Dic79⋊C4C2413yes—
719Dic79⋊C4C2413yes—
720Dic79⋊C4C2413yes—
721Dic79⋊C4C2411yescharacteristic
722Dic79⋊C4C2411yescharacteristic
723Dic79⋊C4C2413yes—
724Dic79⋊C4C2416yes—
725Dic79⋊C4C2413yes—
726Dic79⋊C4C2411yescharacteristic
727Dic79⋊C4C2413yes—
728Dic79⋊C4C2411yescharacteristic
729Dic79⋊C4C2413yes—
730Dic79⋊C4C2413yes—
731Dic79⋊C4C2413yes—
732Dic79⋊C4C2413yes—
733Dic79⋊C4C2413yes—
734Dic79⋊C4C2416yes—
735Dic79⋊C4C2411yescharacteristic
736Dic79⋊C4C2411yescharacteristic
737Dic79⋊C4C2413yes—
738Dic79⋊C4C2413yes—
739Dic79⋊C4C2411yescharacteristic
740Dic79⋊C4C2411yescharacteristic
741C22⋊Dic79C2413yes—
742C22⋊Dic79C2413yes—
743C22⋊Dic79C2413yes—
744C22⋊Dic79C2411yescharacteristic
745C22⋊Dic79C2413yes—
746C22⋊Dic79C2413yes—
747C22⋊Dic79C2411yescharacteristic
748C22⋊Dic79C2411yescharacteristic
749C22⋊Dic79C2411yescharacteristic
750C22⋊Dic79C2411yescharacteristic
751(C2×D79)⋊C4C2413yes—
752(C2×D79)⋊C4C2413yes—
753(C2×D79)⋊C4C2413yes—
754(C2×D79)⋊C4C2413yes—
755(C2×D79)⋊C4C2411yescharacteristic
756(C2×D79)⋊C4C2413yes—
757(C2×D79)⋊C4C2411yescharacteristic
758(C2×D79)⋊C4C2413yes—
759(C2×D79)⋊C4C2413yes—
760(C2×D79)⋊C4C2413yes—
761(C2×D79)⋊C4C2416yes—
762(C2×D79)⋊C4C2413yes—
763(C2×D79)⋊C4C2413yes—
764(C2×D79)⋊C4C2413yes—
765(C2×D79)⋊C4C2416yes—
766(C2×D79)⋊C4C2416yes—
767(C2×D79)⋊C4C2413yes—
768(C2×D79)⋊C4C2413yes—
769(C2×D79)⋊C4C2413yes—
770(C2×D79)⋊C4C2416yes—
771(C2×D79)⋊C4C2416yes—
772(C2×D79)⋊C4C2416yes—
773(C2×D79)⋊C4C2413yes—
774(C2×D79)⋊C4C2413yes—
775(C2×D79)⋊C4C2413yes—
776(C2×D79)⋊C4C2413yes—
777(C2×D79)⋊C4C2413yes—
778(C2×D79)⋊C4C2413yes—
779(C2×D79)⋊C4C2413yes—
780(C2×D79)⋊C4C2413yes—
781C4×Dic79C2413yes—
782C4×Dic79C2413yes—
783C4×Dic79C2411yescharacteristic
784C4×Dic79C2411yescharacteristic
785C4×Dic79C2413yes—
786C4×Dic79C2413yes—
787C4×Dic79C2413yes—
788C4×Dic79C2416yes—
789C4×Dic79C2413yes—
790C4×Dic79C2413yes—
791C4×Dic79C2413yes—
792C4×Dic79C2413yes—
793C4×Dic79C2413yes—
794C4×Dic79C2416yes—
795C4×Dic79C2416yes—
796C4×Dic79C2413yes—
797C4×Dic79C2413yes—
798#41×C79—24no—
799C2×Q8×C79—24no—
800C2×Q8×C79—24no—
801C2×Q8×C79C2413yes—
802C2×Q8×C79C2413yes—
803C2×Q8×C79C2413yes—
804C2×Q8×C79C2411yescharacteristic
805C2×D4×C79C2413yes—
806C2×D4×C79C2413yes—
807C2×D4×C79C2413yes—
808C2×D4×C79C2411yescharacteristic
809C22×C4×C79C2413yes—
810C22×C4×C79C2413yes—
811C22×C4×C79C2413yes—
812C22×C4×C79C2413yes—
813C22×C4×C79C2416yes—
814C22×C4×C79C2411yescharacteristic
815C4⋊C4×C79C2413yes—
816C4⋊C4×C79C2413yes—
817C4⋊C4×C79C2413yes—
818C4⋊C4×C79C2413yes—
819C4⋊C4×C79C2416yes—
820C4⋊C4×C79C2411yescharacteristic
821C4⋊C4×C79C2413yes—
822C4⋊C4×C79C2413yes—
823C4⋊C4×C79C2413yes—
824C4⋊C4×C79C2413yes—
825C4⋊C4×C79C2416yes—
826C4⋊C4×C79C2413yes—
827C4⋊C4×C79C2413yes—
828C4⋊C4×C79C2416yes—
829C4⋊C4×C79C2413yes—
830C4⋊C4×C79C2411yescharacteristic
831C4⋊C4×C79C2413yes—
832C22⋊C4×C79C2413yes—
833C22⋊C4×C79C2411yescharacteristic
834C22⋊C4×C79C2413yes—
835C22⋊C4×C79C2413yes—
836C22⋊C4×C79C2413yes—
837C22⋊C4×C79C2416yes—
838C22⋊C4×C79C2411yescharacteristic
839C22⋊C4×C79C2413yes—
840C22⋊C4×C79C2411yescharacteristic
841C22⋊C4×C79C2416yes—
842C22⋊C4×C79C2413yes—
843C22⋊C4×C79C2413yes—
844C42×C79C2413yes—
845C42×C79C2413yes—
846C42×C79C2413yes—
847C42×C79C2413yes—
848C42×C79C2416yes—
849C42×C79C2413yes—
850C42×C79C2413yes—
851C23×C79C2511yescharacteristic
852C23×C79C2513yes—
853C23×C79C2511yescharacteristic
854C22×D79—26no—
855C22×D79—43no—
856C22×D79—43no—
857C22×D79C2513yes—
858C22×D79C2513yes—
859C22×D79C2513yes—
860C22×D79C2511yescharacteristic
861Q8×C79—26no—
862Q8×C79—26no—
863Q8×C79—43no—
864Q8×C79C2×#4114yes—
865D4×C79—26no—
866D4×C79—43no—
867D4×C79—43no—
868D4×C79—41no—
869C2×C4×C79—26no—
870C2×C4×C79—26no—
871C2×C4×C79—26no—
872C2×C4×C79—46no—
873C2×C4×C79—43no—
874C2×C4×C79—41no—
875C2×C4×C79C2511yescharacteristic
876C2×C4×C79C2513yes—
877C2×C4×C79C2511yescharacteristic
878C2×C4×C79C2513yes—
879C2×C4×C79C2513yes—
880C2×C4×C79C2513yes—
881C2×C4×C79C2513yes—
882C2×C4×C79C2513yes—
883C2×C4×C79C2511yescharacteristic
884C2×C4×C79C2511yescharacteristic
885C2×C4×C79C2511yescharacteristic
886C2×C4×C79C2513yes—
887C22⋊D79—22no—
888C22⋊D79—22no—
889C22⋊D79—212no—
890C22⋊D79—26no—
891C22⋊D79—26no—
892C22⋊D79—46no—
893C22⋊D79—43no—
894C22⋊D79—43no—
895C22⋊D79—43no—
896C22⋊D79—46no—
897C22⋊D79—43no—
898C22⋊D79—43no—
899C22⋊D79—43no—
900C2×Dic79—26no—
901C2×Dic79—46no—
902C2×Dic79—41no—
903C2×Dic79—43no—
904C2×Dic79C2511yescharacteristic
905C2×Dic79C2511yescharacteristic
906C2×Dic79C2511yescharacteristic
907C2×Dic79C2513yes—
908C2×Dic79C2513yes—
909C2×Dic79C2511yescharacteristic
910C2×Dic79C2511yescharacteristic
911C2×Dic79C2513yes—
912C2×Dic79C2511yescharacteristic
913C2×Dic79C2513yes—
914C2×Dic79C2511yescharacteristic
915C2×Dic79C2513yes—
916D316—26no—
917D316—26no—
918D316—26no—
919D316—26no—
920D316—26no—
921D316—43no—
922D316—46no—
923D316—43no—
924D316—46no—
925D316—46no—
926D316—43no—
927C4×D79—22no—
928C4×D79—26no—
929C4×D79—26no—
930C4×D79—26no—
931C4×D79—26no—
932C4×D79—212no—
933C4×D79—212no—
934C4×D79—43no—
935C4×D79—43no—
936C4×D79—46no—
937C4×D79—46no—
938C4×D79—43no—
939C4×D79—41no—
940C4×D79—41no—
941C4×D79—43no—
942C4×D79—46no—
943C4×D79—43no—
944C4×D79—46no—
945C4×D79—43no—
946C4×D79C2×#41112yes—
947Dic158—26no—
948Dic158—26no—
949Dic158—43no—
950Dic158—41no—
951Dic158—46no—
952Dic158—43no—
953Dic158C2×#41112yes—
954C22×C79—21no—
955C22×C79—21no—
956C22×C79—23no—
957C22×C79—21no—
958C22×C79—23no—
959C22×C79—21no—
960C22×C79—23no—
961C22×C79—21no—
962C22×C79—21no—
963C22×C79C2611yescharacteristic
964C2×D79—21no—
965C2×D79—21no—
966C2×D79—23no—
967C2×D79—23no—
968C2×D79—23no—
969C2×D79—23no—
970C2×D79—23no—
971C2×D79—23no—
972C2×D79—23no—
973C2×D79—23no—
974C2×D79—23no—
975C2×D79—412no—
976C2×D79C22×#4112yes—
977C4×C79—21no—
978C4×C79—23no—
979C4×C79—23no—
980C4×C79—23no—
981C4×C79—23no—
982C4×C79—23no—
983C4×C79—21no—
984C4×C79—21no—
985C4×C79—21no—
986C4×C79—23no—
987C4×C79—21no—
988C4×C79C22×#4116yes—
989Dic79—21no—
990Dic79—21no—
991Dic79—21no—
992Dic79—21no—
993Dic79—23no—
994Dic79—23no—
995Dic79—23no—
996Dic79—23no—
997Dic79—21no—
998Dic79—21no—
999Dic79—21no—
1000Dic79C22×#4116yes—
1001#62851—791nomaximal, Sylow
1002C2×C79—43no—
1003C2×C79—41no—
1004C2×C79—41no—
1005C2×C79C23×#4111yescharacteristic
1006C2×C79H(7,𝔽2)11yescharacteristic
1007C2×C792−1+611yescharacteristic
1008D79—22no—
1009D79—43no—
1010D79—43no—
1011D79—43no—
1012#3524—793no—
1013#3524—791no—
1014#3524—793no—
1015#3524—791no—
1016#3522—793no—
1017#3522—791no—
1018#3522—793no—
1019#3522—791no—
1020#3517—791no—
1021#3517—793no—
1022#3517—793no—
1023#3517—791no—
1024#3516—793no—
1025#3516—791no—
1026#3516—793no—
1027#3516D7911yescharacteristic, complemented
1028#3506—793no—
1029#3506—793no—
1030#3502—791no—
1031#3497—791no—
1032#3492—793no—
1033#3492—793no—
1034#3487—791no—
1035#3487—791no—
1036#3460—793no—
1037#3460—793no—
1038#3455—793no—
1039#3455—793no—
1040C4×2−1+4—791no—
1041C4×2−1+4—791no—
1042C2×#520—791no—
1043C79#6285111yescharacteristic, complemented, Sylow
1044C2×2−1+4—791no—
1045C2×2−1+4—791no—
1046C22×#41—791no—
1047#559—793no—
1048#559—793no—
1049#559—796no—
1050#559—793no—
1051#559—793no—
1052#559—796no—
1053Q82—793no—
1054Q82—791no—
1055#557—793no—
1056#557—793no—
1057#557—791no—
1058#557—791no—
1059#557—793no—
1060#557C2×D7911yescharacteristic, complemented
1061#556—793no—
1062#556—796no—
1063#556C2×D7913yescomplemented
1064#555—793no—
1065#555—793no—
1066#555—796no—
1067#554—796no—
1068#554—796no—
1069#554—793no—
1070#554—793no—
1071#554—793no—
1072#554C2×D7913yescomplemented
1073#553—796no—
1074#553—796no—
1075#553—796no—
1076#553—793no—
1077#553—793no—
1078#553—793no—
1079#553—793no—
1080#553—796no—
1081#553—793no—
1082#553—793no—
1083#553—793no—
1084#553C2×D7913yescomplemented
1085#552—796no—
1086#552—793no—
1087#552—793no—
1088#552—793no—
1089#552—796no—
1090#552C2×D7913yescomplemented
1091#550—791no—
1092#550—791no—
1093#550—793no—
1094#550—793no—
1095#550—796no—
1096#550—791no—
1097#550—791no—
1098#550—791no—
1099#550—793no—
1100#550—793no—
1101#550—793no—
1102#550—793no—
1103#550—793no—
1104D4×Q8—793no—
1105D4×Q8C2×D7911yescharacteristic, complemented
1106#548—791no—
1107#548—791no—
1108#548—791no—
1109#548—791no—
1110#548—793no—
1111#548—793no—
1112#548—793no—
1113#548—793no—
1114#548—793no—
1115#548—793no—
1116#548C2×D7911yescharacteristic
1117#548C2×D7911yescharacteristic
1118#547—793no—
1119#547—796no—
1120#547—796no—
1121#547—796no—
1122#547—793no—
1123#547—793no—
1124#547—793no—
1125#547—793no—
1126#547—793no—
1127#544—793no—
1128#544—793no—
1129#542—793no—
1130#542—796no—
1131#542—793no—
1132#542—793no—
1133#542—793no—
1134#542—793no—
1135#542—796no—
1136#542—793no—
1137#542—793no—
1138#542—793no—
1139#542—793no—
1140#542—793no—
1141#542—793no—
1142#542C2×D7913yescomplemented
1143#541—793no—
1144#541—793no—
1145#541—793no—
1146#541C2×D7913yescomplemented
1147#540—793no—
1148#540—793no—
1149#540—793no—
1150#540—796no—
1151#540—796no—
1152#540—793no—
1153#540—793no—
1154#540—793no—
1155#540—793no—
1156#540—793no—
1157#539—793no—
1158#539—793no—
1159#539—796no—
1160#539—791no—
1161#539—793no—
1162#538—796no—
1163#538—796no—
1164#538—793no—
1165#538—793no—
1166#538—793no—
1167#538—793no—
1168#537—793no—
1169#537—793no—
1170#535—793no—
1171#535—793no—
1172#535—793no—
1173#535—793no—
1174#533—793no—
1175#533—793no—
1176#532—793no—
1177#532—793no—
1178#532—796no—
1179#532—793no—
1180#532—793no—
1181#532—796no—
1182#532—793no—
1183#532—793no—
1184#529—796no—
1185#529—796no—
1186#529—796no—
1187#529—796no—
1188#529—796no—
1189#529—793no—
1190#529—793no—
1191#529—793no—
1192#529—793no—
1193#529—793no—
1194#529—793no—
1195#529—793no—
1196#529—793no—
1197#529—793no—
1198#529—796no—
1199#529—793no—
1200#529C2×D7913yescomplemented
1201#529C2×D7913yescomplemented
1202#525—796no—
1203#525—793no—
1204#525—793no—
1205#525—796no—
1206#525—793no—
1207#525—793no—
1208#525—796no—
1209#525—796no—
1210#520—791no—
1211#520—791no—
1212#520—791no—
1213#520—793no—
1214#520—793no—
1215#520—791no—
1216#520—791no—
1217#520—793no—
1218#520—793no—
1219#520—793no—
1220#520—793no—
1221#520—793no—
1222#520—793no—
1223#520—793no—
1224#520—793no—
1225#520C2×D7911yescharacteristic
1226#519—791no—
1227#519—791no—
1228#519—791no—
1229#519—793no—
1230#519—793no—
1231#519C2×D7911yescharacteristic, complemented
1232C4×#41—793no—
1233C4×#41—793no—
1234C4×#41—791no—
1235C4×#41—791no—
1236C4×#41—793no—
1237C4×#41—793no—
1238C4×#41—793no—
1239C4×#41—793no—
1240C2×C4×Q8—791no—
1241C2×C4×Q8—791no—
1242C2×C4×Q8—791no—
1243C2×C4×Q8—793no—
1244C2×C4×Q8—793no—
1245C2×C4×Q8C2×D7911yescharacteristic, complemented
1246C2×C4×D4—793no—
1247C2×C4×D4—793no—
1248C2×#117—793no—
1249C22×C4⋊C4—793no—
12502−1+4—1588no—
12512−1+4—1588no—
1252C2×#41—796no—
1253C2×#41—793no—
1254C2×#41—793no—
1255C2×#41—791no—
1256C2×#41—791no—
1257C2×#41—791no—
1258C2×#41—796no—
1259C2×#41—793no—
1260C2×#41—796no—
1261C2×#41—796no—
1262C2×#41—793no—
1263C2×#41—793no—
1264C2×#41—793no—
1265C2×#41—793no—
1266C2×#41—793no—
1267C2×#41—1588no—
1268C2×#41C22×D7911yescharacteristic
1269C22×Q8—791no—
1270C22×Q8—793no—
1271C22×Q8—793no—
1272C22×Q8C22×D7911yescharacteristic
1273C22×Q8C22×D7911yescharacteristic
1274C22×D4—793no—
1275C23×C4—796no—
1276C23×C4—793no—
1277C4⋊Q8—796no—
1278C4⋊Q8—793no—
1279C4⋊Q8—793no—
1280C4⋊Q8—796no—
1281C4⋊Q8—793no—
1282C4⋊Q8—793no—
1283C4⋊Q8—793no—
1284C4⋊Q8—793no—
1285C4⋊Q8—793no—
1286C4⋊Q8—793no—
1287C4⋊Q8C22×D7913yes—
1288C4⋊Q8C22×D7913yes—
1289#127—793no—
1290#127—793no—
1291#127—796no—
1292#127—796no—
1293#127—793no—
1294#127—793no—
1295#127—793no—
1296#127—793no—
1297#126—793no—
1298#126—796no—
1299#126—793no—
1300#126—793no—
1301#126—796no—
1302#126—793no—
1303#126—793no—
1304#126—796no—
1305#126—793no—
1306#126—793no—
1307#126—793no—
1308#126—791no—
1309#126—791no—
1310#126—793no—
1311#126—793no—
1312#126—793no—
1313#126—793no—
1314#126—796no—
1315#126C22×D7916yes—
1316#126C22×D7916yes—
1317#126C22×D7913yes—
1318#126C22×D7913yes—
1319#125—793no—
1320#125—791no—
1321#125—791no—
1322#125—793no—
1323#125—796no—
1324#125—793no—
1325#125—793no—
1326#125—796no—
1327#125—796no—
1328#125—793no—
1329#125—793no—
1330#125—793no—
1331#125—793no—
1332#125—793no—
1333#125—793no—
1334#125—793no—
1335#125C22×D7913yes—
1336#125C22×D7916yes—
1337#125C22×D7913yes—
1338#125C22×D7913yes—
1339#124—793no—
1340#124—793no—
1341#124—793no—
1342#124—793no—
1343#124—793no—
1344#124—793no—
1345#124—796no—
1346#124—793no—
1347#124—793no—
1348#124—796no—
1349#124—796no—
1350#124—796no—
1351#124—793no—
1352#124—793no—
1353#124—793no—
1354#124—793no—
1355#124—796no—
1356#124—796no—
1357#124—793no—
1358#124C22×D7913yes—
1359#124C22×D7913yes—
1360#124C22×D7913yes—
1361#123—791no—
1362#123—793no—
1363#123—796no—
1364#123—793no—
1365#123—793no—
1366#123—793no—
1367#123—793no—
1368#123—796no—
1369#123—796no—
1370#123—796no—
1371#123—793no—
1372#123—796no—
1373#123—793no—
1374#123—793no—
1375#123—793no—
1376#123—796no—
1377#123—796no—
1378#123—796no—
1379#123—791no—
1380#123—791no—
1381#123—796no—
1382#123—796no—
1383#123—796no—
1384#123—796no—
1385#123—793no—
1386#123—793no—
1387#123—793no—
1388#123—796no—
1389#123—793no—
1390#123—793no—
1391#123—793no—
1392#123C22×D7916yes—
1393#123C22×D7913yes—
1394#123C22×D7911yescharacteristic
1395C22⋊Q8—793no—
1396C22⋊Q8—793no—
1397C22⋊Q8—793no—
1398C22⋊Q8—793no—
1399C22⋊Q8—793no—
1400C22⋊Q8—793no—
1401C22⋊Q8—791no—
1402C22⋊Q8—796no—
1403C22⋊Q8—793no—
1404C22⋊Q8—793no—
1405C22⋊Q8—793no—
1406C22⋊Q8—796no—
1407C22⋊Q8—796no—
1408C22⋊Q8—793no—
1409C22⋊Q8—793no—
1410C22⋊Q8—796no—
1411C22⋊Q8—796no—
1412C22⋊Q8—796no—
1413C22⋊Q8—793no—
1414C22⋊Q8—796no—
1415C22⋊Q8—793no—
1416C22⋊Q8—791no—
1417C22⋊Q8—793no—
1418C22⋊Q8—793no—
1419C22⋊Q8—796no—
1420C22⋊Q8—791no—
1421C22⋊Q8—793no—
1422C22⋊Q8C22×D7913yes—
1423C22⋊Q8C22×D7913yes—
1424C22⋊Q8C22×D7916yes—
1425C22⋊Q8C22×D7913yes—
1426C22⋊Q8C22×D7913yes—
1427C22⋊Q8C22×D7913yes—
1428#121—796no—
1429#121—793no—
1430#121—793no—
1431#121—793no—
1432#121—793no—
1433#121—793no—
1434#121—793no—
1435#121—791no—
1436#121—793no—
1437#121—796no—
1438#121—793no—
1439#121—793no—
1440#121—793no—
1441#121—793no—
1442#121—793no—
1443#121—793no—
1444#121—793no—
1445#121—796no—
1446#121—796no—
1447#121—793no—
1448#121—793no—
1449#121—796no—
1450#121—793no—
1451#121—796no—
1452#121—793no—
1453#121—793no—
1454#121—793no—
1455#121—793no—
1456#121—793no—
1457#121—793no—
1458#121—793no—
1459#121—796no—
1460#121—793no—
1461#121—793no—
1462#121—793no—
1463#121—796no—
1464#121—796no—
1465#121—796no—
1466#121—796no—
1467#121—793no—
1468#121—796no—
1469#121—796no—
1470#121—796no—
1471#121—796no—
1472#121C22×D7913yes—
1473#121C22×D7913yes—
1474#121C22×D7913yes—
1475#120—793no—
1476#120—793no—
1477#120—793no—
1478#120—796no—
1479#120—796no—
1480#120—793no—
1481C4×Q8—791no—
1482C4×Q8—793no—
1483C4×Q8—791no—
1484C4×Q8—793no—
1485C4×Q8—793no—
1486C4×Q8—791no—
1487C4×Q8—793no—
1488C4×Q8—791no—
1489C4×Q8—793no—
1490C4×Q8—793no—
1491C4×Q8—793no—
1492C4×Q8—796no—
1493C4×Q8—793no—
1494C4×Q8—793no—
1495C4×Q8—793no—
1496C4×Q8—796no—
1497C4×Q8—796no—
1498C4×Q8—793no—
1499C4×Q8—793no—
1500C4×Q8—793no—
1501C4×Q8—796no—
1502C4×Q8—793no—
1503C4×Q8—793no—
1504C4×Q8—793no—
1505C4×Q8—793no—
1506C4×Q8—793no—
1507C4×Q8—793no—
1508C4×Q8C22×D7911yescharacteristic
1509C4×Q8C22×D7913yes—
1510C4×Q8C22×D7913yes—
1511C4×Q8C22×D7911yescharacteristic
1512C4×Q8C22×D7911yescharacteristic
1513C4×Q8C22×D7913yes—
1514C4×Q8C22×D7913yes—
1515C4×Q8C22×D7911yescharacteristic
1516C4×Q8C22×D7913yes—
1517C4×D4—793no—
1518C4×D4—793no—
1519C4×D4—796no—
1520C4×D4—796no—
1521C4×D4—791no—
1522C4×D4—793no—
1523C4×D4—793no—
1524C4×D4—793no—
1525C4×D4—796no—
1526C4×D4—793no—
1527C4×D4—793no—
1528C4×D4—793no—
1529C4×D4—793no—
1530C4×D4—796no—
1531C4×D4—793no—
1532C4×D4—793no—
1533C4×D4—793no—
1534C4×D4—793no—
1535C4×D4—793no—
1536C4×D4—793no—
1537C4×D4—793no—
1538C4×D4—796no—
1539C4×D4—793no—
1540C4×D4—793no—
1541C4×D4—793no—
1542C4×D4—796no—
1543C4×D4—796no—
1544C4×D4—796no—
1545C4×D4—796no—
1546C4×D4—796no—
1547C4×D4—796no—
1548C4×D4—796no—
1549C4×D4—791no—
1550C4×D4—793no—
1551C4×D4—793no—
1552C4×D4—793no—
1553C4×D4—796no—
1554C4×D4—796no—
1555C4×D4—796no—
1556C4×D4—796no—
1557C4×D4—796no—
1558C4×D4—796no—
1559C4×D4—793no—
1560C4×D4—793no—
1561C4×D4—793no—
1562C4×D4—793no—
1563C4×D4—796no—
1564C4×D4—793no—
1565C4×D4—793no—
1566C4×D4—793no—
1567C4×D4—793no—
1568C4×D4—793no—
1569C4×D4—793no—
1570C4×D4—796no—
1571C4×D4—796no—
1572C4×D4—793no—
1573C4×D4C22×D7913yes—
1574C4×D4C22×D7913yes—
1575C4×D4C22×D7913yes—
1576C4×D4C22×D7913yes—
1577C4×D4C22×D7916yes—
1578C4×D4C22×D7913yes—
1579#117—793no—
1580#117—793no—
1581#117—793no—
1582#117—793no—
1583#117—793no—
1584#117—793no—
1585#117—793no—
1586#117—796no—
1587#117—796no—
1588#117—793no—
1589#117—793no—
1590#117—796no—
1591#117—793no—
1592#117—793no—
1593#117—796no—
1594#117—793no—
1595#117—793no—
1596#117—793no—
1597#117—793no—
1598#117—793no—
1599#117—793no—
1600#117—796no—
1601#117—796no—
1602#117—796no—
1603#117C22×D7913yes—
1604#117C22×D7913yes—
1605#117C22×D7913yes—
1606#117C22×D7916yes—
1607C2×C4⋊C4—796no—
1608C2×C4⋊C4—793no—
1609C2×C4⋊C4—793no—
1610C2×C4⋊C4—793no—
1611C2×C4⋊C4—793no—
1612C2×C4⋊C4—793no—
1613C2×C4⋊C4—796no—
1614C2×C4⋊C4—793no—
1615C2×C4⋊C4—793no—
1616C2×C4⋊C4—791no—
1617C2×C4⋊C4—796no—
1618C2×C4⋊C4—796no—
1619C2×C4⋊C4—793no—
1620C2×C4⋊C4—793no—
1621C2×C4⋊C4C22×D7913yes—
1622C2×C4⋊C4C22×D7913yes—
1623C2×C22⋊C4—793no—
1624C2×C22⋊C4—793no—
1625C2×C42—793no—
1626C2×C42—793no—
1627C2×C42—793no—
1628C2×C42—793no—
1629C2×C42—796no—
1630C2×C42—796no—
1631C2×C42—793no—
1632C2×C42C22×D7913yes—
1633C24—793no—
1634#41—24no—
1635#41—6326no—
1636#41—6326no—
1637#41—6326no—
1638#41—6326no—
1639#41—15812no—
1640#41—15812no—
1641#41—15812no—
1642#41—15812no—
1643#41—15812no—
1644#41—15812no—
1645#41—15812no—
1646#41—15812no—
1647#41—1584no—
1648#41—1584no—
1649#41—1584no—
1650C2×Q8—24no—
1651C2×Q8—24no—
1652C2×Q8—798no—
1653C2×Q8—793no—
1654C2×Q8—791no—
1655C2×Q8—793no—
1656C2×Q8—796no—
1657C2×Q8—793no—
1658C2×Q8—793no—
1659C2×Q8—793no—
1660C2×Q8—15812no—
1661C2×Q8—15812no—
1662C2×Q8C23×D7913yes—
1663C2×Q8C23×D7913yes—
1664C2×Q8C23×D7913yes—
1665C2×Q8C23×D7911yescharacteristic
1666C2×D4—793no—
1667C2×D4—796no—
1668C2×D4—793no—
1669C2×D4—793no—
1670C2×D4—796no—
1671C2×D4—793no—
1672C2×D4—793no—
1673C2×D4—793no—
1674C2×D4—791no—
1675C2×D4—791no—
1676C2×D4—796no—
1677C2×D4—793no—
1678C2×D4—793no—
1679C2×D4—796no—
1680C2×D4—793no—
1681C2×D4—793no—
1682C2×D4—796no—
1683C2×D4—793no—
1684C2×D4—796no—
1685C2×D4—793no—
1686C2×D4—793no—
1687C2×D4—793no—
1688C2×D4—793no—
1689C2×D4—793no—
1690C2×D4—15812no—
1691C2×D4C23×D7913yes—
1692C2×D4C23×D7913yes—
1693C2×D4C23×D7911yescharacteristic
1694C2×D4C23×D7913yes—
1695C22×C4—791no—
1696C22×C4—793no—
1697C22×C4—796no—
1698C22×C4—791no—
1699C22×C4—791no—
1700C22×C4—793no—
1701C22×C4—793no—
1702C22×C4—793no—
1703C22×C4—793no—
1704C22×C4—796no—
1705C22×C4—793no—
1706C22×C4—796no—
1707C22×C4—793no—
1708C22×C4—796no—
1709C22×C4—796no—
1710C22×C4—793no—
1711C22×C4—793no—
1712C22×C4—796no—
1713C22×C4—796no—
1714C22×C4—793no—
1715C22×C4—793no—
1716C22×C4—791no—
1717C22×C4—793no—
1718C22×C4—793no—
1719C22×C4—6326no—
1720C22×C4—15812no—
1721C22×C4C23×D7913yes—
1722C22×C4C23×D7913yes—
1723C22×C4C23×D7913yes—
1724C22×C4C23×D7911yescharacteristic
1725C22×C4C23×D7913yes—
1726C22×C4C23×D7916yes—
1727C4⋊C4—796no—
1728C4⋊C4—793no—
1729C4⋊C4—793no—
1730C4⋊C4—796no—
1731C4⋊C4—793no—
1732C4⋊C4—793no—
1733C4⋊C4—793no—
1734C4⋊C4—793no—
1735C4⋊C4—791no—
1736C4⋊C4—791no—
1737C4⋊C4—793no—
1738C4⋊C4—793no—
1739C4⋊C4—791no—
1740C4⋊C4—791no—
1741C4⋊C4—793no—
1742C4⋊C4—793no—
1743C4⋊C4—796no—
1744C4⋊C4—791no—
1745C4⋊C4—793no—
1746C4⋊C4—791no—
1747C4⋊C4—793no—
1748C4⋊C4—796no—
1749C4⋊C4—793no—
1750C4⋊C4—793no—
1751C4⋊C4—793no—
1752C4⋊C4—791no—
1753C4⋊C4—793no—
1754C4⋊C4—791no—
1755C4⋊C4—793no—
1756C4⋊C4—793no—
1757C4⋊C4—793no—
1758C4⋊C4—793no—
1759C4⋊C4—793no—
1760C4⋊C4—796no—
1761C4⋊C4—791no—
1762C4⋊C4—793no—
1763C4⋊C4—793no—
1764C4⋊C4—793no—
1765C4⋊C4—791no—
1766C4⋊C4—791no—
1767C4⋊C4—791no—
1768C4⋊C4—793no—
1769C4⋊C4—793no—
1770C4⋊C4C23×D7913yes—
1771C4⋊C4C23×D7913yes—
1772C4⋊C4C23×D7913yes—
1773C4⋊C4C23×D7913yes—
1774C4⋊C4C23×D7913yes—
1775C4⋊C4C23×D7916yes—
1776C4⋊C4C23×D7911yescharacteristic
1777C4⋊C4C23×D7913yes—
1778C4⋊C4C23×D7913yes—
1779C4⋊C4C23×D7916yes—
1780C4⋊C4C23×D7913yes—
1781C4⋊C4C23×D7913yes—
1782C4⋊C4C23×D7913yes—
1783C4⋊C4C23×D7913yes—
1784C4⋊C4C23×D7916yes—
1785C4⋊C4C23×D7913yes—
1786C4⋊C4C23×D7911yescharacteristic
1787C22⋊C4—793no—
1788C22⋊C4—793no—
1789C22⋊C4—793no—
1790C22⋊C4—791no—
1791C22⋊C4—793no—
1792C22⋊C4—793no—
1793C22⋊C4—791no—
1794C22⋊C4—791no—
1795C22⋊C4—791no—
1796C22⋊C4—791no—
1797C22⋊C4—793no—
1798C22⋊C4—793no—
1799C22⋊C4—793no—
1800C22⋊C4—793no—
1801C22⋊C4—793no—
1802C22⋊C4—791no—
1803C22⋊C4—793no—
1804C22⋊C4—791no—
1805C22⋊C4—793no—
1806C22⋊C4—796no—
1807C22⋊C4—796no—
1808C22⋊C4—793no—
1809C22⋊C4—793no—
1810C22⋊C4—793no—
1811C22⋊C4—796no—
1812C22⋊C4—793no—
1813C22⋊C4—793no—
1814C22⋊C4—793no—
1815C22⋊C4—796no—
1816C22⋊C4—793no—
1817C22⋊C4—793no—
1818C22⋊C4—793no—
1819C22⋊C4—793no—
1820C22⋊C4—793no—
1821C22⋊C4—796no—
1822C22⋊C4—796no—
1823C22⋊C4—793no—
1824C22⋊C4—793no—
1825C22⋊C4—793no—
1826C22⋊C4—793no—
1827C22⋊C4C23×D7913yes—
1828C22⋊C4C23×D7913yes—
1829C22⋊C4C23×D7916yes—
1830C22⋊C4C23×D7911yescharacteristic
1831C22⋊C4C23×D7913yes—
1832C22⋊C4C23×D7913yes—
1833C22⋊C4C23×D7913yes—
1834C22⋊C4C23×D7916yes—
1835C22⋊C4C23×D7913yes—
1836C22⋊C4C23×D7911yescharacteristic
1837C22⋊C4C23×D7911yescharacteristic
1838C22⋊C4C23×D7913yes—
1839C42—793no—
1840C42—793no—
1841C42—793no—
1842C42—791no—
1843C42—793no—
1844C42—791no—
1845C42—796no—
1846C42—793no—
1847C42—793no—
1848C42—793no—
1849C42—793no—
1850C42—793no—
1851C42—793no—
1852C42—796no—
1853C42—796no—
1854C42—793no—
1855C42—793no—
1856C42C23×D7913yes—
1857C42C23×D7913yes—
1858C42C23×D7916yes—
1859C42C23×D7913yes—
1860C42C23×D7913yes—
1861C42C23×D7913yes—
1862C42C23×D7913yes—
1863C23—3163no—
1864C23—3163no—
1865C23—791no—
1866C23—793no—
1867C23—793no—
1868C23—793no—
1869C23—1586no—
1870C23C24×D7911yescharacteristic
1871C23C24×D7913yes—
1872C23C24×D7911yescharacteristic
1873Q8—26no—
1874Q8—26no—
1875Q8—43no—
1876Q8—3163no—
1877Q8—3166no—
1878Q8—3161no—
1879Q8—3163no—
1880Q8—7912no—
1881Q8—1586no—
1882Q8—1586no—
1883Q8#41×D7914yes—
1884D4—26no—
1885D4—41no—
1886D4—43no—
1887D4—43no—
1888D4—3166no—
1889D4—3166no—
1890D4—3163no—
1891D4—3163no—
1892D4—3163no—
1893D4—3166no—
1894D4—3163no—
1895D4—3166no—
1896D4—3163no—
1897D4—3163no—
1898D4—3163no—
1899D4—3163no—
1900D4—3166no—
1901D4—3163no—
1902D4—1586no—
1903D4—1586no—
1904D4—15812no—
1905D4—1586no—
1906D4—1586no—
1907D4—1582no—
1908D4—1582no—
1909D4—1586no—
1910D4—1586no—
1911D4—1586no—
1912C2×C4—26no—
1913C2×C4—26no—
1914C2×C4—26no—
1915C2×C4—46no—
1916C2×C4—41no—
1917C2×C4—43no—
1918C2×C4—3163no—
1919C2×C4—3163no—
1920C2×C4—3166no—
1921C2×C4—3166no—
1922C2×C4—3163no—
1923C2×C4—3166no—
1924C2×C4—3166no—
1925C2×C4—3163no—
1926C2×C4—3161no—
1927C2×C4—3163no—
1928C2×C4—3161no—
1929C2×C4—3163no—
1930C2×C4—3166no—
1931C2×C4—3163no—
1932C2×C4—3161no—
1933C2×C4—793no—
1934C2×C4—7912no—
1935C2×C4—791no—
1936C2×C4—791no—
1937C2×C4—793no—
1938C2×C4—791no—
1939C2×C4—793no—
1940C2×C4—791no—
1941C2×C4—791no—
1942C2×C4—791no—
1943C2×C4—793no—
1944C2×C4—793no—
1945C2×C4—791no—
1946C2×C4—1586no—
1947C2×C4—15812no—
1948C2×C4—15812no—
1949C2×C4—1582no—
1950C2×C4—1586no—
1951C2×C4—1586no—
1952C2×C4—1586no—
1953C2×C4—1586no—
1954C2×C4C24×D7911yescharacteristic
1955C2×C4C24×D7913yes—
1956C2×C4C24×D7911yescharacteristic
1957C2×C4C24×D7913yes—
1958C2×C4C24×D7913yes—
1959C2×C4C24×D7913yes—
1960C2×C4C24×D7913yes—
1961C2×C4C24×D7911yescharacteristic
1962C2×C4C24×D7913yes—
1963C2×C4C24×D7911yescharacteristic
1964C2×C4C24×D7911yescharacteristic
1965C2×C4C24×D7913yes—
1966C22—21no—
1967C22—21no—
1968C22—23no—
1969C22—21no—
1970C22—23no—
1971C22—21no—
1972C22—21no—
1973C22—21no—
1974C22—23no—
1975C22—31612no—
1976C22—792no—
1977C22—1583no—
1978C22—1583no—
1979C22—1583no—
1980C22—1583no—
1981C22—1583no—
1982C22—1583no—
1983C22—1583no—
1984C22—1583no—
1985C22—1583no—
1986C22—1581no—
1987C22—1581no—
1988C22C25×D7911yescharacteristic
1989C4—21no—
1990C4—23no—
1991C4—23no—
1992C4—23no—
1993C4—23no—
1994C4—23no—
1995C4—21no—
1996C4—21no—
1997C4—21no—
1998C4—21no—
1999C4—23no—
2000C4—796no—
2001C4—1581no—
2002C4—1581no—
2003C4—1581no—
2004C4—1583no—
2005C4—1583no—
2006C4—1581no—
2007C4—1583no—
2008C4—1581no—
2009C4—1583no—
2010C4—1581no—
2011C4—1581no—
2012C4C2×#41×D7916yes—
2013C2—43no—
2014C2—41no—
2015C2—41no—
2016C2—3163no—
2017C2—3163no—
2018C2—3163no—
2019C2—1582no—
2020C2C22×#41×D7911yescharacteristic
2021C2#2377821111yescharacteristic
2022C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3516C2
hypercenter#3516D79
hypocenterC79#62851
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3516

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777511C2semidirect
2. #23777506C2semidirect
3. #23777502C2semidirect
4. #23777499C2semidirect
5. #23777485C2semidirect
6. #23777484C2semidirect
7. #23777481C2semidirect
8. #23777476C2semidirect
9. #23777407C2semidirect
10. #23777404C2semidirect
11. #23777400C2semidirect
12. #23777399C2semidirect
13. #23777394C2semidirect
14. #23777391C2semidirect
15. #23777388C2semidirect
16. #23777253C2semidirect
17. #23777246C2semidirect
18. #23777207C2semidirect
19. #23777170C2semidirect
20. #23777108C2semidirect
21. #23777100C2semidirect
22. #23777057C2semidirect
23. #23777057C2semidirect
24. #23776821C2semidirect
25. #23776820C2semidirect
26. #23776791C2semidirect
27. #23776783C2semidirect
28. C4×#14579209C2semidirect
29. #23776609C2semidirect
30. #520×D79C2semidirect
31. C79×#3516C2semidirect
35. #19099298C22semidirect
36. #19099298C22semidirect
37. #19099297C22semidirect
38. #19099296C22semidirect
39. #19099295C22semidirect
40. #19099295C22semidirect
41. Q8×Dic158C22semidirect
42. #19099293C22semidirect
43. #19099291C22semidirect
44. #19099290C22semidirect
45. #19099290C22semidirect
46. #19099289C22semidirect
47. #19099289C22semidirect
48. #19099287C22semidirect
49. #19099280C22semidirect
50. #19099277C22semidirect
51. #19099276C22semidirect
52. #19099276C22semidirect
53. #19099273C22semidirect
54. #19099271C22semidirect
55. #19099271C22semidirect
56. #19099269C22semidirect
57. #19099267C22semidirect
58. #19099266C22semidirect
59. #19099266C22semidirect
60. #19099264C22semidirect
61. #19099264C22semidirect
62. #19099264C22semidirect
63. #19099263C22semidirect
64. #19099262C22semidirect
65. #19099261C22semidirect
66. #19099259C22semidirect
67. #19099259C22semidirect
68. #19099257C22semidirect
69. #19099255C22semidirect
70. #19099254C22semidirect
71. #19099247C22semidirect
72. #19099246C22semidirect
73. #19099245C22semidirect
76. #19099235C22semidirect
77. #19099235C22semidirect
80. #19099234C22semidirect
81. #19099234C22semidirect
86. #19099231C22semidirect
87. #19099228C22semidirect
90. #19099224C22semidirect
91. #19099224C22semidirect
94. #19099223C22semidirect
95. #19099223C22semidirect
98. #19099217C22semidirect
99. #19099216C22semidirect
100. #19099215C22semidirect
101. #19099215C22semidirect
102. #19099214C22semidirect
103. #19099214C22semidirect
104. #19099214C22semidirect
105. #19099213C22semidirect
106. #19099211C22semidirect
109. #19099186C22semidirect
110. #19099186C22semidirect
111. #19099186C22semidirect
112. #19099185C22semidirect
113. #19099185C22semidirect
114. #19099185C22semidirect
115. #19099183C22semidirect
116. #19099183C22semidirect
117. #19099182C22semidirect
118. #19099181C22semidirect
119. #19099179C22semidirect
120. #19099179C22semidirect
121. #19099177C22semidirect
122. #19099174C22semidirect
123. #19099172C22semidirect
124. #19099170C22semidirect
125. #19099169C22semidirect
126. #19099169C22semidirect
127. #19099168C22semidirect
128. #19099168C22semidirect
129. #19099166C22semidirect
130. #19099165C22semidirect
131. #19099165C22semidirect
132. #19099165C22semidirect
133. #19099164C22semidirect
134. #19099163C22semidirect
155. #19099114C22semidirect
156. #19099113C22semidirect
157. #19099112C22semidirect
159. #19099110C22semidirect
160. #19099110C22semidirect
161. #19099108C22semidirect
162. #19099100C22semidirect
163. #19099100C22semidirect
164. #19099099C22semidirect
165. #19099098C22semidirect
166. #19099098C22semidirect
167. #19099097C22semidirect
168. #19099096C22semidirect
169. #19099096C22semidirect
170. #19099096C22semidirect
171. #19099095C22semidirect
172. #19099093C22semidirect
173. #19099093C22semidirect
174. #19099092C22semidirect
175. #19099091C22semidirect
176. #19099091C22semidirect
177. #19099091C22semidirect
191. #19099045C22semidirect
192. #19099045C22semidirect
195. #19099044C22semidirect
198. #19099043C22semidirect
201. #19099041C22semidirect
204. #19099039C22semidirect
205. #19099039C22semidirect
208. C4×#11929625C22semidirect
209. C4×#11929625C22semidirect
211. C4×#11929624C22semidirect
213. #19099031C22semidirect
214. C2×Q8×Dic79C22semidirect
217. C4×Q8×D79C22semidirect
218. C4×Q8×D79C22semidirect
223. #557×C79C22semidirect
224. #556×C79C22semidirect
225. #554×C79C22semidirect
226. #553×C79C22semidirect
227. #552×C79C22semidirect
228. D4×Q8×C79C22semidirect
231. #542×C79C22semidirect
232. #541×C79C22semidirect
233. #529×C79C22semidirect
234. #529×C79C22semidirect
236. #519×C79C22semidirect
237. C2×C4×Q8×C79C22semidirect
646. Q8×D79#41semidirect
1027. #3516D79semidirect
1043. C79#62851semidirect
1060. #557C2×D79semidirect
1063. #556C2×D79semidirect
1072. #554C2×D79semidirect
1084. #553C2×D79semidirect
1090. #552C2×D79semidirect
1105. D4×Q8C2×D79semidirect
1142. #542C2×D79semidirect
1146. #541C2×D79semidirect
1200. #529C2×D79semidirect
1201. #529C2×D79semidirect
1231. #519C2×D79semidirect
1245. C2×C4×Q8C2×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237775112
#237775062
#237775022
#237774992
#237774852
#237774842
#237774812
#237774762
#237774072
#237774042
#237774002
#237773992
#237773942
#237773912
#237773882
#237772532
#237772462
#237772072
#237771702
#237771082
#237771002
#237770572
#237768212
#237768202
#237767912
#237767832
C4×#145792092
#237766092
#520×D792
C79×#35162
#6285179