Finite Group Databasebeta

← #35197193

Subgroups — #35197193

Order 20224.

7148 conjugacy classes of subgroups.

The subgroup lattice has 1792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777967C214yesmaximal, complemented
2#23777935C214yesmaximal, complemented
3#23777863C214yesmaximal, complemented
4#23777807C212yesmaximal, complemented
5#23777799C212yesmaximal, complemented
6#23777790C212yesmaximal, complemented
7#23777785C212yesmaximal, complemented
8#23777626C214yesmaximal, complemented
9#23777484C214yesmaximal, complemented
10#23777443C214yesmaximal, complemented
11#23777308C214yesmaximal, complemented
12#23777308C212yesmaximal, complemented
13#23777271C212yesmaximal, complemented
14#23777263C212yesmaximal, complemented
15#23777254C211yesmaximal, characteristic, complemented
16#23777252C211yesmaximal, characteristic, complemented
17#23777215C212yesmaximal, complemented
18#23777201C211yesmaximal, characteristic, complemented
19#23777184C212yesmaximal, complemented
20#23777170C212yesmaximal, complemented
21#23777138C212yesmaximal, complemented
22#23777125C212yesmaximal, complemented
23#23777076C214yesmaximal, complemented
24#23776697C211yesmaximal, characteristic, complemented
25#533×D79C211yesmaximal, characteristic, complemented
26C2×#19099110C211yesmaximal, characteristic, complemented
27C79×#3501C211yesmaximal, characteristic, complemented
28C2×#14579209C2214yescomplemented
29C22×#11929624C2212yes—
30#19099314C2218yescomplemented
31#19099309C2218yescomplemented
32#19099309C2218yescomplemented
33#19099309C2218yescomplemented
34#19099298C2214yescomplemented
35#19099296C2214yescomplemented
36#19099296C2214yescomplemented
37#19099296C2214yescomplemented
38#19099293C2214yescomplemented
39#19099290C2214yescomplemented
40#19099286C2212yescomplemented
41#19099284C2214yescomplemented
42#19099284C2218yescomplemented
43#19099283C2212yescomplemented
44#19099279C2214yescomplemented
45#19099279C2212yescomplemented
46#19099278C2214yescomplemented
47#19099278C2212yescomplemented
48#19099274C2212yescomplemented
49#19099273C2214yescomplemented
50#19099273C2212yescomplemented
51#19099269C2214yescomplemented
52#19099269C2214yescomplemented
53#19099267C2218yes—
54#19099266C2214yescomplemented
55#19099266C2214yescomplemented
56#19099266C2214yescomplemented
57#19099263C2214yescomplemented
58#19099263C2214yescomplemented
59#19099263C2214yescomplemented
60#19099248C2214yescomplemented
61#19099247C2214yescomplemented
62#19099240C2218yes—
63#19099239C2218yes—
64#19099235C2212yescomplemented
65#19099234C2212yescomplemented
66#19099234C2214yescomplemented
67#19099234C2214yescomplemented
68Q8×D316C2212yescomplemented
69#19099228C2212yescomplemented
70#19099228C2214yescomplemented
71Q8×C22⋊D79C2214yescomplemented
72#19099226C2218yes—
73#19099224C2214yescomplemented
74#19099223C2218yescomplemented
75#19099223C2218yescomplemented
76#19099223C2218yescomplemented
77#19099223C2214yescomplemented
78#19099218C2214yescomplemented
79#19099218C2212yescomplemented
80#19099216C2214yescomplemented
81#19099216C2212yescomplemented
82#19099215C2214yescomplemented
83#19099215C2218yescomplemented
84#19099215C2218yescomplemented
85#19099214C2214yescomplemented
86#19099214C2218yescomplemented
87#19099214C2218yescomplemented
88#19099204C2218yes—
89#19099203C2218yes—
90#19099203C2218yes—
91#19099203C2218yes—
92#19099193C2214yescomplemented
93#19099191C2212yes—
94#19099190C2214yescomplemented
95#19099188C2214yes—
96#19099187C2214yescomplemented
97#19099186C2218yescomplemented
98#19099183C2218yescomplemented
99#19099183C2218yescomplemented
100#19099183C2218yescomplemented
101#19099183C2218yescomplemented
102#19099178C2214yescomplemented
103#19099169C2214yescomplemented
104#19099164C2214yescomplemented
105#19099164C2214yescomplemented
106#19099164C2214yescomplemented
107#19099160C2218yescomplemented
108#19099159C2218yescomplemented
109#19099159C2218yescomplemented
110#19099153C2214yes—
111#19099151C2214yes—
112#19099144C2214yescomplemented
113#19099143C2218yescomplemented
114#19099143C2214yescomplemented
115#19099143C2214yescomplemented
116#19099143C2218yescomplemented
117#19099137C2214yescomplemented
118#19099136C2214yescomplemented
119#19099136C2214yescomplemented
120#19099136C2218yescomplemented
121#19099132C2212yes—
122#19099130C2212yes—
123#19099120C2211yescharacteristic
124#19099119C2212yescomplemented
125#19099119C2214yescomplemented
126#19099118C2211yescharacteristic, complemented
127#19099118C2211yescharacteristic, complemented
128#19099118C2211yescharacteristic, complemented
129#19099118C2211yescharacteristic, complemented
130#19099117C2212yescomplemented
131#19099117C2212yescomplemented
132#19099116C2212yes—
133#19099115C2212yes—
134#19099115C2212yes—
135#19099114C2211yescharacteristic, complemented
136#19099114C2214yescomplemented
137#19099114C2211yescharacteristic, complemented
138#19099113C2211yescharacteristic
139#19099110C2212yes—
140#19099110C2212yes—
141#19099110C2212yes—
142#19099110C2212yes—
143#19099110C2212yes—
144#19099110C2212yes—
145#19099110C2212yes—
146#19099110C2212yes—
147#19099110C2214yescomplemented
148#19099110C2214yescomplemented
149#19099110C2214yescomplemented
150C2×#14579160C2211yescharacteristic
151C4⋊Q8×D79C2211yescharacteristic, complemented
152C4⋊Q8×D79C2214yescomplemented
153C4⋊Q8×D79C2211yescharacteristic, complemented
154C2×#14579157C2211yescharacteristic
155#19099100C2212yescomplemented
156#19099100C2212yescomplemented
157#19099099C2212yes—
158#19099099C2212yes—
159#19099098C2212yescomplemented
160#19099098C2214yescomplemented
161#19099098C2212yescomplemented
162#19099095C2214yescomplemented
163#125×D79C2212yescomplemented
164C2×#14579147C2212yes—
165#19099076C2212yes—
166#19099076C2214yes—
167#19099076C2212yes—
168#19099075C2212yes—
169#19099074C2214yes—
170C22⋊Q8×D79C2212yes—
171C22⋊Q8×D79C2214yes—
172C22⋊Q8×D79C2212yes—
173C2×#14579136C2211yescharacteristic
174C2×#14579134C2212yes—
175C2×#14579132C2211yescharacteristic
176#19099044C2212yes—
177#19099044C2214yescomplemented
178#19099044C2218yescomplemented
179#19099043C2212yes—
180#19099037C2212yes—
181C4×#11929625C2212yescomplemented
182C4×#11929625C2212yescomplemented
183#19099031C2212yes—
184C4×Q8×D79C2212yescomplemented
185C4×Q8×D79C2212yescomplemented
186C2×C4×D316C2211yescharacteristic
187C2×C4×C22⋊D79C2212yes—
188#117×D79C2212yes—
189C2×C42×D79C2211yescharacteristic
190#554×C79C2212yescomplemented
191#554×C79C2214yescomplemented
192#554×C79C2212yescomplemented
193#554×C79C2214yescomplemented
194D4×Q8×C79C2212yescomplemented
195D4×Q8×C79C2212yescomplemented
196#544×C79C2212yes—
197#543×C79C2214yes—
198#533×C79C2211yescharacteristic
199#533×C79C2211yescharacteristic
200C2×C22⋊Q8×C79C2214yes—
201#518×C79C2212yes—
202C2×C4×D4×C79C2211yescharacteristic
203#14579209—416no—
204C2×#11929625C2312yes—
205C2×#11929625C2318yes—
206C2×#11929625C2314yes—
207C2×#11929625C2312yes—
208C2×#11929624—48no—
209C2×#11929624C2314yes—
210C2×#11929624C2312yes—
211C2×#11929624C2314yes—
212C2×#11929624C2318yes—
213C2×#11929624C2318yes—
214C2×#11929624C2314yes—
215C2×#11929624C2318yes—
216C2×#11929624C2314yes—
217C2×#11929624C2314yes—
218C22×Dic158C2312yes—
219C2×Q8×D79C2312yes—
220C2×Q8×D79C2318yes—
221C2×Q8×D79C2314yes—
222C2×Q8×D79C2312yes—
223C22×D316C2311yescharacteristic
224C22×D316C2312yes—
225C22×C22⋊D79C2312yes—
226C22×C22⋊D79C2312yes—
227C22×C22⋊D79C2312yes—
228C22×C4×D79C2311yescharacteristic
229C22×C4×D79C2311yescharacteristic
230C22×C4×D79C2311yescharacteristic
231C22×C4×D79C2312yes—
232#14579161C2314yes—
233#14579161C2311yescharacteristic
234#14579161C2311yescharacteristic
235#14579161C2311yescharacteristic
236#14579160C2312yes—
237#14579160C2318yes—
238#14579160C2318yes—
239#14579160C2314yes—
240#14579160C2312yes—
241#14579160C2312yes—
242#14579160C2312yes—
243#14579160C2312yes—
244#14579160C2312yes—
245#14579160C2312yes—
246#14579160C2312yes—
247#14579159C2318yes—
248#14579159C2312yes—
249#14579159C2318yes—
250#14579159C2312yes—
251#14579158C2314yes—
252#14579158C2311yescharacteristic
253#14579157C2312yes—
254#14579157C2314yes—
255#14579157C2312yes—
256#14579157C2312yes—
257#14579157C2312yes—
258#14579156C2318yes—
259#14579156C2314yes—
260#14579156C2318yes—
261#14579156C2314yes—
262#14579156C2318yes—
263#14579154C2318yes—
264#14579154C2318yes—
265#14579154C2318yes—
266#14579153C2314yes—
267#14579153C2312yes—
268#14579152C2312yes—
269#14579152C2312yes—
270#14579152C2314yes—
271#14579152C2312yes—
272#14579152C2312yes—
273#14579151C2314yes—
274#14579151C2318yes—
275#14579151C2318yes—
276#14579151C2314yes—
277#14579150C2318yes—
278#14579150C2318yes—
279#14579150C2318yes—
280#14579150C2312yes—
281#14579150C2312yes—
282#14579149C2314yes—
283#14579149C2312yes—
284#14579148C2314yes—
285#14579147C2314yes—
286#14579147C2318yes—
287#14579147C2318yes—
288#14579147C2318yes—
289#14579147C2314yes—
290#14579147C2318yes—
291#14579147C2318yes—
292#14579147C2314yes—
293#14579147C2314yes—
294#14579146C2318yes—
295#14579146C2318yes—
296#14579146C2318yes—
297#14579146C2318yes—
298#14579146C2318yes—
299#14579146C2318yes—
300#14579146C2314yes—
301#14579146C2314yes—
302#14579145C2314yes—
303#14579144C2318yes—
304#14579144C2318yes—
305#14579144C2318yes—
306#14579144C2318yes—
307#14579144C2318yes—
308#14579143C2318yes—
309#14579143C2318yes—
310#14579143C2318yes—
311#14579143C2318yes—
312#14579143C2318yes—
313#14579141C2312yes—
314#14579141C2314yes—
315#14579141C2318yes—
316#14579141C2318yes—
317#14579141C2312yes—
318#14579141C2312yes—
319#14579141C2312yes—
320#14579140C2314yes—
321#14579140C2318yes—
322#14579140C2312yes—
323#14579140C2312yes—
324#14579139C2314yes—
325#14579139C2318yes—
326#14579139C2318yes—
327#14579139C2318yes—
328#14579139C2318yes—
329#14579139C2318yes—
330#14579139C2318yes—
331#14579139C2318yes—
332#14579139C2314yes—
333#14579138C2318yes—
334#14579138C2314yes—
335#14579138C2314yes—
336#14579137C2312yes—
337#14579137C2314yes—
338#14579137C2318yes—
339#14579137C2312yes—
340#14579137C2314yes—
341#14579137C2318yes—
342#14579137C2318yes—
343#14579137C2312yes—
344#14579137C2312yes—
345#14579136C2312yes—
346#14579136C2312yes—
347#14579136C2318yes—
348#14579136C2318yes—
349#14579136C2318yes—
350#14579136C2318yes—
351#14579136C2314yes—
352#14579136C2312yes—
353#14579136C2314yes—
354#14579136C2314yes—
355#14579136C2312yes—
356#14579136C2312yes—
357#14579136C2312yes—
358#14579136C2312yes—
359#14579136C2312yes—
360#14579135C2314yes—
361#14579135C2318yes—
362#14579135C2318yes—
363#14579135C2318yes—
364#14579135C2312yes—
365#14579135C2312yes—
366#14579134C2318yes—
367#14579134C2314yes—
368#14579134C2318yes—
369#14579134C2314yes—
370#14579134C2318yes—
371#14579134C2318yes—
372#14579134C2318yes—
373#14579134C2318yes—
374#14579134C2318yes—
375#14579134C2314yes—
376#14579134C2314yes—
377#14579132C2312yes—
378#14579132C2314yes—
379#14579132C2314yes—
380#14579132C2312yes—
381#14579132C2312yes—
382#14579132C2312yes—
383#14579131C2318yes—
384#14579131C2314yes—
385#14579130C2318yes—
386Q8×Dic79C2312yes—
387Q8×Dic79C2312yes—
388Q8×Dic79C2312yes—
389Q8×Dic79C2312yes—
390C4×Dic158C2314yes—
391C4×Dic158C2312yes—
392C4×Dic158C2314yes—
393C4×Dic158C2314yes—
394C4×Dic158C2312yes—
395#14579126C2312yes—
396#14579126C2314yes—
397#14579126C2318yes—
398#14579126C2318yes—
399#14579126C2314yes—
400#14579126C2312yes—
401#14579126C2314yes—
402#14579126C2312yes—
403#14579126C2312yes—
404C4×D316C2314yes—
405C4×D316C2314yes—
406C4×D316C2314yes—
407C4×D316C2314yes—
408C4×D316C2312yes—
409C4×D316C2312yes—
410C4×D316C2312yes—
411C4×D316C2312yes—
412C4×D316C2314yes—
413C4×D316C2312yes—
414C4×D316C2312yes—
415#14579123C2318yes—
416#14579123C2318yes—
417#14579123C2314yes—
418#14579123C2314yes—
419#14579123C2318yes—
420#14579123C2314yes—
421#14579123C2312yes—
422#14579123C2314yes—
423#14579123C2314yes—
424#14579123C2312yes—
425#14579123C2312yes—
426#14579123C2312yes—
427C4×C22⋊D79C2318yes—
428C4×C22⋊D79C2314yes—
429C4×C22⋊D79C2318yes—
430C4×C22⋊D79C2318yes—
431C4×C22⋊D79C2314yes—
432C4×C22⋊D79C2318yes—
433C4×C22⋊D79C2318yes—
434C4×C22⋊D79C2318yes—
435C4×C22⋊D79C2314yes—
436C4×C22⋊D79C2314yes—
437(C22⋊D79)⋊C4C2318yes—
438(C22⋊D79)⋊C4C2314yes—
439(C22⋊D79)⋊C4C2314yes—
440#14579120C2314yes—
441#14579120C2318yes—
442#14579120C2312yes—
443#14579119C2314yes—
444#14579119C2312yes—
445#14579119C2314yes—
446#14579119C2312yes—
447#14579119C2314yes—
448#14579119C2318yes—
449#14579119C2314yes—
450#14579119C2314yes—
451#14579119C2312yes—
452#14579119C2312yes—
453#14579118C2314yes—
454#14579118C2314yes—
455#14579117C2314yes—
456C2×C4⋊Dic79C2311yescharacteristic
457C2×Dic79⋊C4C2312yes—
458C4⋊C4×D79C2314yes—
459C4⋊C4×D79C2312yes—
460C4⋊C4×D79C2314yes—
461C4⋊C4×D79C2318yes—
462C4⋊C4×D79C2318yes—
463C4⋊C4×D79C2314yes—
464C4⋊C4×D79C2314yes—
465C4⋊C4×D79C2314yes—
466C4⋊C4×D79C2312yes—
467C4⋊C4×D79C2312yes—
468C4⋊C4×D79C2312yes—
469C2×C22⋊Dic79C2312yes—
470C2×(C2×D79)⋊C4C2312yes—
471C2×(C2×D79)⋊C4C2312yes—
472C22⋊C4×D79C2318yes—
473C22⋊C4×D79C2314yes—
474C2×C4×Dic79C2311yescharacteristic
475C2×C4×Dic79C2311yescharacteristic
476C2×C4×Dic79C2311yescharacteristic
477C42×D79C2311yescharacteristic
478C42×D79C2311yescharacteristic
479C42×D79C2311yescharacteristic
480C42×D79C2311yescharacteristic
481C42×D79C2311yescharacteristic
482C42×D79C2311yescharacteristic
483C42×D79C2311yescharacteristic
484C42×D79C2311yescharacteristic
485C42×D79C2314yes—
486C42×D79C2314yes—
487C22×Q8×C79C2314yes—
488C22×D4×C79C2311yescharacteristic
489C23×C4×C79C2312yes—
490C4⋊Q8×C79C2314yes—
491C4⋊Q8×C79C2314yes—
492C4⋊Q8×C79C2311yescharacteristic
493C4⋊Q8×C79C2311yescharacteristic
494C4⋊Q8×C79C2311yescharacteristic
495C4⋊Q8×C79C2311yescharacteristic
496#125×C79C2314yes—
497#125×C79C2314yes—
498#125×C79C2312yes—
499#125×C79C2312yes—
500C22⋊Q8×C79C2314yes—
501C22⋊Q8×C79C2314yes—
502C22⋊Q8×C79C2318yes—
503C22⋊Q8×C79C2318yes—
504C22⋊Q8×C79C2318yes—
505C22⋊Q8×C79C2312yes—
506C22⋊Q8×C79C2318yes—
507C22⋊Q8×C79C2318yes—
508C22⋊Q8×C79C2312yes—
509C22⋊Q8×C79C2318yes—
510C22⋊Q8×C79C2312yes—
511C22⋊Q8×C79C2312yes—
512C4×Q8×C79C2312yes—
513C4×Q8×C79C2312yes—
514C4×Q8×C79C2312yes—
515C4×Q8×C79C2312yes—
516C4×D4×C79C2314yes—
517C4×D4×C79C2314yes—
518C4×D4×C79C2314yes—
519C4×D4×C79C2314yes—
520C4×D4×C79C2312yes—
521C4×D4×C79C2312yes—
522C4×D4×C79C2312yes—
523C4×D4×C79C2312yes—
524#117×C79C2312yes—
525#117×C79C2312yes—
526C2×C4⋊C4×C79C2314yes—
527C2×C4⋊C4×C79C2318yes—
528C2×C4⋊C4×C79C2311yescharacteristic
529C2×C22⋊C4×C79C2312yes—
530C2×C22⋊C4×C79C2318yes—
531C2×C42×C79C2311yescharacteristic
532C23×D79C2411yescharacteristic
533C23×D79C2412yes—
534#11929625—28no—
535#11929625—48no—
536#11929625—44no—
537#11929625—416no—
538#11929624—216no—
539#11929624—28no—
540#11929624—48no—
541#11929624—416no—
542#11929624—416no—
543#11929624—48no—
544#11929624—416no—
545#11929624—48no—
546#11929624—48no—
547C2×Dic158—44no—
548C2×Dic158C2414yes—
549C2×Dic158C2412yes—
550C2×Dic158C2414yes—
551C2×Dic158C2414yes—
552C2×Dic158C2412yes—
553C2×Dic158C2418yes—
554C2×Dic158C2412yes—
555C2×Dic158C2414yes—
556Q8×D79—28no—
557Q8×D79—48no—
558Q8×D79—44no—
559Q8×D79—416no—
560C2×D316—24no—
561C2×D316—44no—
562C2×D316C2414yes—
563C2×D316C2412yes—
564C2×D316C2414yes—
565C2×D316C2412yes—
566C2×D316C2412yes—
567C2×D316C2412yes—
568C2×D316C2414yes—
569C2×D316C2418yes—
570C2×D316C2418yes—
571C2×D316C2414yes—
572C2×D316C2412yes—
573C2×C22⋊D79—44no—
574C2×C22⋊D79—44no—
575C2×C22⋊D79—44no—
576C2×C22⋊D79C2414yes—
577C2×C22⋊D79C2414yes—
578C2×C22⋊D79C2414yes—
579C2×C22⋊D79C2414yes—
580C2×C22⋊D79C2418yes—
581C2×C22⋊D79C2414yes—
582C2×C22⋊D79C2414yes—
583C2×C22⋊D79C2418yes—
584C2×C22⋊D79C2414yes—
585C22×Dic79C2411yescharacteristic
586C22×Dic79C2411yescharacteristic
587C22×Dic79C2411yescharacteristic
588C22×Dic79C2412yes—
589C2×C4×D79—24no—
590C2×C4×D79—24no—
591C2×C4×D79—44no—
592C2×C4×D79—42no—
593C2×C4×D79C2414yes—
594C2×C4×D79C2411yescharacteristic
595C2×C4×D79C2414yes—
596C2×C4×D79C2414yes—
597C2×C4×D79C2411yescharacteristic
598C2×C4×D79C2411yescharacteristic
599C2×C4×D79C2411yescharacteristic
600C2×C4×D79C2414yes—
601C2×C4×D79C2414yes—
602C2×C4×D79C2411yescharacteristic
603C2×C4×D79C2411yescharacteristic
604C2×C4×D79C2411yescharacteristic
605C2×C4×D79C2411yescharacteristic
606C2×C4×D79C2411yescharacteristic
607C2×C4×D79C2418yes—
608C2×C4×D79C2418yes—
609C2×C4×D79C2418yes—
610C2×C4×D79C2414yes—
611C2×C4×D79C2414yes—
612C2×C4×D79C2418yes—
613C2×C4×D79C2411yescharacteristic
614C2×C4×D79C2411yescharacteristic
615C2×C4×D79C2411yescharacteristic
616C4⋊Dic79C2412yes—
617C4⋊Dic79C2412yes—
618C4⋊Dic79C2412yes—
619C4⋊Dic79C2418yes—
620C4⋊Dic79C2412yes—
621C4⋊Dic79C2414yes—
622C4⋊Dic79C2414yes—
623C4⋊Dic79C2412yes—
624C4⋊Dic79C2412yes—
625C4⋊Dic79C2412yes—
626C4⋊Dic79C2414yes—
627C4⋊Dic79C2412yes—
628C4⋊Dic79C2414yes—
629Dic79⋊C4C2414yes—
630Dic79⋊C4C2414yes—
631Dic79⋊C4C2414yes—
632Dic79⋊C4C2414yes—
633Dic79⋊C4C2414yes—
634Dic79⋊C4C2418yes—
635Dic79⋊C4C2414yes—
636Dic79⋊C4C2418yes—
637Dic79⋊C4C2418yes—
638Dic79⋊C4C2418yes—
639Dic79⋊C4C2414yes—
640Dic79⋊C4C2414yes—
641Dic79⋊C4C2414yes—
642Dic79⋊C4C2414yes—
643Dic79⋊C4C2414yes—
644Dic79⋊C4C2414yes—
645C22⋊Dic79C2414yes—
646C22⋊Dic79C2414yes—
647C22⋊Dic79C2414yes—
648C22⋊Dic79C2418yes—
649C22⋊Dic79C2418yes—
650(C2×D79)⋊C4C2414yes—
651(C2×D79)⋊C4C2414yes—
652(C2×D79)⋊C4C2418yes—
653(C2×D79)⋊C4C2418yes—
654(C2×D79)⋊C4C2414yes—
655(C2×D79)⋊C4C2414yes—
656(C2×D79)⋊C4C2414yes—
657(C2×D79)⋊C4C2414yes—
658(C2×D79)⋊C4C2414yes—
659(C2×D79)⋊C4C2414yes—
660(C2×D79)⋊C4C2418yes—
661(C2×D79)⋊C4C2414yes—
662(C2×D79)⋊C4C2414yes—
663(C2×D79)⋊C4C2414yes—
664(C2×D79)⋊C4C2418yes—
665(C2×D79)⋊C4C2418yes—
666(C2×D79)⋊C4C2418yes—
667(C2×D79)⋊C4C2414yes—
668(C2×D79)⋊C4C2414yes—
669(C2×D79)⋊C4C2414yes—
670C4×Dic79C2411yescharacteristic
671C4×Dic79C2411yescharacteristic
672C4×Dic79C2411yescharacteristic
673C4×Dic79C2411yescharacteristic
674C4×Dic79C2411yescharacteristic
675C4×Dic79C2411yescharacteristic
676C4×Dic79C2411yescharacteristic
677C4×Dic79C2411yescharacteristic
678C4×Dic79C2411yescharacteristic
679C4×Dic79C2411yescharacteristic
680C4×Dic79C2411yescharacteristic
681C4×Dic79C2411yescharacteristic
682C4×Dic79C2414yes—
683C4×Dic79C2414yes—
684C4×Dic79C2414yes—
685C4×Dic79C2414yes—
686C4×Dic79C2414yes—
687C4×Dic79C2418yes—
688C4×Dic79C2418yes—
689C24×C79C2412yes—
690C2×Q8×C79—48no—
691C2×Q8×C79C2412yes—
692C2×Q8×C79C2412yes—
693C2×Q8×C79C2418yes—
694C2×Q8×C79C2412yes—
695C2×Q8×C79C2412yes—
696C2×D4×C79—24no—
697C2×D4×C79C2412yes—
698C2×D4×C79C2412yes—
699C22×C4×C79—44no—
700C22×C4×C79C2414yes—
701C22×C4×C79C2411yescharacteristic
702C22×C4×C79C2412yes—
703C22×C4×C79C2418yes—
704C22×C4×C79C2414yes—
705C22×C4×C79C2418yes—
706C22×C4×C79C2411yescharacteristic
707C22×C4×C79C2411yescharacteristic
708C4⋊C4×C79C2414yes—
709C4⋊C4×C79C2414yes—
710C4⋊C4×C79C2412yes—
711C4⋊C4×C79C2412yes—
712C4⋊C4×C79C2412yes—
713C4⋊C4×C79C2412yes—
714C4⋊C4×C79C2418yes—
715C4⋊C4×C79C2418yes—
716C4⋊C4×C79C2418yes—
717C4⋊C4×C79C2412yes—
718C4⋊C4×C79C2412yes—
719C4⋊C4×C79C2412yes—
720C4⋊C4×C79C2412yes—
721C4⋊C4×C79C2414yes—
722C4⋊C4×C79C2414yes—
723C4⋊C4×C79C2412yes—
724C4⋊C4×C79C2412yes—
725C22⋊C4×C79C2414yes—
726C22⋊C4×C79C2414yes—
727C22⋊C4×C79C2414yes—
728C22⋊C4×C79C2418yes—
729C22⋊C4×C79C2418yes—
730C22⋊C4×C79C2414yes—
731C42×C79C2411yescharacteristic
732C42×C79C2411yescharacteristic
733C42×C79C2411yescharacteristic
734C42×C79C2411yescharacteristic
735C42×C79C2414yes—
736C42×C79C2414yes—
737C23×C79—24no—
738C23×C79—42no—
739C23×C79—42no—
740C23×C79C2514yes—
741C23×C79C2511yescharacteristic
742C22×D79—22no—
743C22×D79—24no—
744C22×D79—22no—
745C22×D79—41no—
746C22×D79—42no—
747C22×D79—42no—
748C22×D79C2514yes—
749C22×D79C2511yescharacteristic
750C22×D79C2514yes—
751C22×D79C2511yescharacteristic
752Q8×C79—24no—
753Q8×C79—24no—
754Q8×C79—48no—
755Q8×C79—42no—
756Q8×C79—42no—
757D4×C79—24no—
758D4×C79—24no—
759C2×C4×C79—22no—
760C2×C4×C79—28no—
761C2×C4×C79—41no—
762C2×C4×C79—42no—
763C2×C4×C79—44no—
764C2×C4×C79—48no—
765C2×C4×C79—48no—
766C2×C4×C792−1+414yescomplemented
767C2×C4×C79C2514yes—
768C2×C4×C79C2511yescharacteristic
769C2×C4×C79C2511yescharacteristic
770C2×C4×C79C2511yescharacteristic
771C2×C4×C79C2514yes—
772C2×C4×C79C2514yes—
773C2×C4×C79C2514yes—
774C2×C4×C79C2514yes—
775C2×C4×C79C2511yescharacteristic
776C2×C4×C79C2511yescharacteristic
777C2×C4×C79C2511yescharacteristic
778C22⋊D79—28no—
779C22⋊D79—28no—
780C22⋊D79—28no—
781C22⋊D79—28no—
782C22⋊D79—44no—
783C22⋊D79—44no—
784C22⋊D79—44no—
785C22⋊D79—48no—
786C22⋊D79—48no—
787C2×Dic79—22no—
788C2×Dic79—22no—
789C2×Dic79—22no—
790C2×Dic79—42no—
791C2×Dic79C2511yescharacteristic
792C2×Dic79C2514yes—
793C2×Dic79C2511yescharacteristic
794C2×Dic79C2514yes—
795C2×Dic79C2511yescharacteristic
796C2×Dic79C2511yescharacteristic
797C2×Dic79C2514yes—
798C2×Dic79C2514yes—
799C2×Dic79C2511yescharacteristic
800C2×Dic79C2511yescharacteristic
801D316—28no—
802D316—28no—
803D316—24no—
804D316—24no—
805D316—24no—
806D316—24no—
807D316—44no—
808D316—48no—
809D316—48no—
810D316—44no—
811D316—42no—
812C4×D79—22no—
813C4×D79—28no—
814C4×D79—22no—
815C4×D79—28no—
816C4×D79—22no—
817C4×D79—22no—
818C4×D79—22no—
819C4×D79—22no—
820C4×D79—28no—
821C4×D79—22no—
822C4×D79—28no—
823C4×D79—22no—
824C4×D79—22no—
825C4×D79—28no—
826C4×D79—41no—
827C4×D79—41no—
828C4×D79—44no—
829C4×D79—44no—
830C4×D79—48no—
831C4×D79—48no—
832C4×D79—48no—
833C4×D79—48no—
834C4×D79H(5,𝔽2)14yes—
835Dic158—24no—
836Dic158—24no—
837Dic158—28no—
838Dic158—28no—
839Dic158—28no—
840Dic158—48no—
841Dic158—42no—
842Dic158—44no—
843C22×C79—21no—
844C22×C79—21no—
845C22×C79—24no—
846C22×C79—24no—
847C22×C79—24no—
848C22×C79—84no—
849C22×C79C2×2−1+412yes—
850C22×C79C2611yescharacteristic
851C2×D79—21no—
852C2×D79—21no—
853C2×D79—24no—
854C2×D79—21no—
855C2×D79—24no—
856C2×D79—24no—
857C2×D79—21no—
858C2×D79—24no—
859C2×D79—24no—
860C2×D79—24no—
861C2×D79—21no—
862C2×D79—44no—
863C2×D79—84no—
864C2×D79C2×H(5,𝔽2)12yes—
865C4×C79—21no—
866C4×C79—24no—
867C4×C79—24no—
868C4×C79—24no—
869C4×C79—24no—
870C4×C79—24no—
871C4×C79—21no—
872C4×C79—21no—
873C4×C79C2×H(5,𝔽2)12yes—
874C4×C79C2×2−1+412yes—
875C4×C79C2×2−1+412yes—
876Dic79—24no—
877Dic79—21no—
878Dic79—24no—
879Dic79—24no—
880Dic79—21no—
881Dic79—21no—
882Dic79—21no—
883Dic79—24no—
884Dic79C2×H(5,𝔽2)12yes—
885Dic79#58512yes—
886#62835—791nomaximal, Sylow
887C2×C79—22no—
888C2×C79—44no—
889C2×C79C22×H(5,𝔽2)11yescharacteristic
890C2×C79C22×2−1+411yescharacteristic
891C2×C79C2×#58511yescharacteristic
892D79—22no—
893D79—44no—
894D79—41no—
895D79—44no—
896#3561—794no—
897#3559—794no—
898#3554—794no—
899#3550—792no—
900#3548—792no—
901#3547—792no—
902#3547—792no—
903#3536—794no—
904#3522—794no—
905#3520—794no—
906#3511—792no—
907#3511—794no—
908#3508—792no—
909#3507—792no—
910#3506—791no—
911#3506—791no—
912#3503—792no—
913#3501—791no—
914#3501D7911yescharacteristic, complemented
915#3499—792no—
916#3497—792no—
917#3494—792no—
918#3494—792no—
919#3489—794no—
920#3444—791no—
921C2×#533—791no—
922C2×#532—791no—
923C79#6283511yescharacteristic, complemented, Sylow
924C2×2−1+4—794no—
925C22×#41—792no—
926#563—798no—
927#562—798no—
928#562—798no—
929#562—798no—
930#559—794no—
931#559—794no—
932#559—794no—
933#559—794no—
934Q82—794no—
935#557—794no—
936#556—798no—
937#556—794no—
938#556—792no—
939#556—792no—
940#555—794no—
941#555—792no—
942#555—794no—
943#555—792no—
944#554—792no—
945#554—794no—
946#554—794no—
947#554—798no—
948#554—792no—
949#554—794no—
950#554C2×D7912yescomplemented
951#554C2×D7912yescomplemented
952#554C2×D7914yescomplemented
953#554C2×D7914yescomplemented
954#553—794no—
955#553—794no—
956#553—794no—
957#553—794no—
958#553—794no—
959#553—794no—
960#552—794no—
961#552—794no—
962#551—798no—
963#551—798no—
964#550—792no—
965#550—792no—
966#550—794no—
967#550—794no—
968D4×Q8—794no—
969D4×Q8—792no—
970D4×Q8—794no—
971D4×Q8—798no—
972D4×Q8—792no—
973D4×Q8C2×D7912yescomplemented
974D4×Q8C2×D7912yescomplemented
975#548—794no—
976#548—798no—
977#548—798no—
978#548—794no—
979#548—798no—
980#547—794no—
981#547—792no—
982#547—798no—
983#547—794no—
984#547—798no—
985#547—794no—
986#547—792no—
987#547—798no—
988#547—798no—
989#547—794no—
990#546—798no—
991#546—798no—
992#546—798no—
993#546—798no—
994#544—794no—
995#544—794no—
996#544—792no—
997#544C2×D7912yes—
998#543—794no—
999#543C2×D7914yes—
1000#542—794no—
1001#542—798no—
1002#542—798no—
1003#542—798no—
1004#542—798no—
1005#542—798no—
1006#542—794no—
1007#540—794no—
1008#540—794no—
1009#540—794no—
1010#540—794no—
1011#539—798no—
1012#539—798no—
1013#539—798no—
1014#538—794no—
1015#538—794no—
1016#537—794no—
1017#537—794no—
1018#537—798no—
1019#537—798no—
1020#537—794no—
1021#536—794no—
1022#536—794no—
1023#536—794no—
1024#536—798no—
1025#535—792no—
1026#535—792no—
1027#533—791no—
1028#533—791no—
1029#533—791no—
1030#533—791no—
1031#533—792no—
1032#533—794no—
1033#533—792no—
1034#533—792no—
1035#533—792no—
1036#533—792no—
1037#533—792no—
1038#533—791no—
1039#533C2×D7911yescharacteristic
1040#533C2×D7911yescharacteristic
1041#532—791no—
1042#532—791no—
1043#532—794no—
1044#532—792no—
1045#532—792no—
1046#532—792no—
1047#532—792no—
1048#532—792no—
1049#532—792no—
1050#532—792no—
1051#532—792no—
1052#532—794no—
1053#532—794no—
1054#532—794no—
1055#532—791no—
1056C2×C4⋊Q8—791no—
1057C2×C4⋊Q8—791no—
1058C2×C4⋊Q8—794no—
1059C2×C4⋊Q8—791no—
1060C2×#127—791no—
1061#529—792no—
1062#529—792no—
1063#529—794no—
1064#529—792no—
1065#529—792no—
1066#529—792no—
1067#529—792no—
1068#529—794no—
1069C2×#125—792no—
1070C2×#124—792no—
1071#525—794no—
1072#525—792no—
1073#525—792no—
1074#525—794no—
1075#525—792no—
1076C2×C22⋊Q8—792no—
1077C2×C22⋊Q8—792no—
1078C2×C22⋊Q8—794no—
1079C2×C22⋊Q8C2×D7914yes—
1080C2×#121—791no—
1081C2×#121—791no—
1082C2×#121—792no—
1083#520—792no—
1084#520—794no—
1085#520—792no—
1086#520—798no—
1087#518—792no—
1088#518C2×D7912yes—
1089C4×#41—792no—
1090C4×#41—792no—
1091C4×#41—792no—
1092C2×C4×Q8—792no—
1093C2×C4×Q8—792no—
1094C2×C4×D4—792no—
1095C2×C4×D4—791no—
1096C2×C4×D4C2×D7911yescharacteristic
1097C2×#117—792no—
1098C22×C42—791no—
10992−1+4—31616no—
1100C2×#41—3168no—
1101C2×#41—792no—
1102C2×#41—794no—
1103C2×#41—798no—
1104C2×#41—792no—
1105C2×#41—798no—
1106C2×#41—794no—
1107C2×#41—794no—
1108C2×#41—794no—
1109C2×#41—794no—
1110C2×#41—798no—
1111C2×#41—798no—
1112C2×#41—792no—
1113C2×#41—794no—
1114C22×Q8—792no—
1115C22×Q8—794no—
1116C22×Q8—798no—
1117C22×Q8—792no—
1118C22×Q8—792no—
1119C22×Q8C22×D7914yes—
1120C22×D4—792no—
1121C22×D4—792no—
1122C22×D4—792no—
1123C22×D4—792no—
1124C22×D4—791no—
1125C22×D4C22×D7911yescharacteristic
1126C23×C4—792no—
1127C23×C4—791no—
1128C23×C4—791no—
1129C23×C4—791no—
1130C23×C4C22×D7912yes—
1131C4⋊Q8—792no—
1132C4⋊Q8—792no—
1133C4⋊Q8—798no—
1134C4⋊Q8—798no—
1135C4⋊Q8—792no—
1136C4⋊Q8—792no—
1137C4⋊Q8—792no—
1138C4⋊Q8—792no—
1139C4⋊Q8—792no—
1140C4⋊Q8—792no—
1141C4⋊Q8—792no—
1142C4⋊Q8—792no—
1143C4⋊Q8—798no—
1144C4⋊Q8—794no—
1145C4⋊Q8—798no—
1146C4⋊Q8—791no—
1147C4⋊Q8—791no—
1148C4⋊Q8—794no—
1149C4⋊Q8—791no—
1150C4⋊Q8C22×D7911yescharacteristic
1151C4⋊Q8C22×D7911yescharacteristic
1152C4⋊Q8C22×D7914yes—
1153C4⋊Q8C22×D7911yescharacteristic
1154C4⋊Q8C22×D7911yescharacteristic
1155C4⋊Q8C22×D7914yes—
1156#127—792no—
1157#127—792no—
1158#127—792no—
1159#127—792no—
1160#127—794no—
1161#127—791no—
1162#127—794no—
1163#126—794no—
1164#126—794no—
1165#126—798no—
1166#126—798no—
1167#126—798no—
1168#126—798no—
1169#126—798no—
1170#126—798no—
1171#125—794no—
1172#125—792no—
1173#125—792no—
1174#125—794no—
1175#125—792no—
1176#125—792no—
1177#125—794no—
1178#125—798no—
1179#125—798no—
1180#125—792no—
1181#125—794no—
1182#125C22×D7912yes—
1183#125C22×D7912yes—
1184#125C22×D7914yes—
1185#125C22×D7914yes—
1186#124—792no—
1187#124—792no—
1188#124—798no—
1189#124—798no—
1190#124—798no—
1191#124—794no—
1192#124—794no—
1193#124—794no—
1194#124—794no—
1195#124—794no—
1196#124—798no—
1197#124—798no—
1198#124—798no—
1199#124—798no—
1200#124—798no—
1201#124—792no—
1202#124—794no—
1203#123—798no—
1204#123—798no—
1205#123—798no—
1206#123—798no—
1207#123—798no—
1208#123—794no—
1209#123—794no—
1210#123—798no—
1211#123—798no—
1212#123—798no—
1213#123—798no—
1214#123—798no—
1215#123—798no—
1216#123—794no—
1217#123—798no—
1218#123—798no—
1219#123—798no—
1220#123—798no—
1221#123—798no—
1222C22⋊Q8—792no—
1223C22⋊Q8—792no—
1224C22⋊Q8—794no—
1225C22⋊Q8—792no—
1226C22⋊Q8—792no—
1227C22⋊Q8—794no—
1228C22⋊Q8—798no—
1229C22⋊Q8—798no—
1230C22⋊Q8—798no—
1231C22⋊Q8—792no—
1232C22⋊Q8—792no—
1233C22⋊Q8—794no—
1234C22⋊Q8—798no—
1235C22⋊Q8—792no—
1236C22⋊Q8—794no—
1237C22⋊Q8—794no—
1238C22⋊Q8—792no—
1239C22⋊Q8—794no—
1240C22⋊Q8—798no—
1241C22⋊Q8—792no—
1242C22⋊Q8—792no—
1243C22⋊Q8—798no—
1244C22⋊Q8—798no—
1245C22⋊Q8—798no—
1246C22⋊Q8—798no—
1247C22⋊Q8—798no—
1248C22⋊Q8—798no—
1249C22⋊Q8—798no—
1250C22⋊Q8—798no—
1251C22⋊Q8—794no—
1252C22⋊Q8—794no—
1253C22⋊Q8—798no—
1254C22⋊Q8C22×D7912yes—
1255C22⋊Q8C22×D7912yes—
1256C22⋊Q8C22×D7912yes—
1257C22⋊Q8C22×D7914yes—
1258C22⋊Q8C22×D7914yes—
1259C22⋊Q8C22×D7918yes—
1260C22⋊Q8C22×D7918yes—
1261C22⋊Q8C22×D7912yes—
1262C22⋊Q8C22×D7918yes—
1263C22⋊Q8C22×D7918yes—
1264C22⋊Q8C22×D7918yes—
1265C22⋊Q8C22×D7918yes—
1266#121—792no—
1267#121—792no—
1268#121—792no—
1269#121—792no—
1270#121—794no—
1271#121—794no—
1272#121—792no—
1273#121—792no—
1274#121—794no—
1275#121—798no—
1276#121—798no—
1277#121—798no—
1278#121—792no—
1279#121—792no—
1280#121—792no—
1281#121—792no—
1282#121—792no—
1283#121—792no—
1284#121—792no—
1285#121—792no—
1286#121—794no—
1287#121—794no—
1288#121—794no—
1289#121—798no—
1290#121—798no—
1291#121—798no—
1292#121—798no—
1293#121—794no—
1294#121—794no—
1295#121—794no—
1296#121—794no—
1297#121—798no—
1298#121—798no—
1299#121—798no—
1300#121—798no—
1301#121—798no—
1302#121—798no—
1303#121—798no—
1304#120—798no—
1305#120—794no—
1306#120—798no—
1307C4×Q8—792no—
1308C4×Q8—792no—
1309C4×Q8—792no—
1310C4×Q8—792no—
1311C4×Q8—794no—
1312C4×Q8—792no—
1313C4×Q8—792no—
1314C4×Q8—794no—
1315C4×Q8—792no—
1316C4×Q8—792no—
1317C4×Q8—794no—
1318C4×Q8—798no—
1319C4×Q8—798no—
1320C4×Q8—792no—
1321C4×Q8—794no—
1322C4×Q8—794no—
1323C4×Q8—792no—
1324C4×Q8—794no—
1325C4×Q8C22×D7912yes—
1326C4×Q8C22×D7912yes—
1327C4×Q8C22×D7912yes—
1328C4×Q8C22×D7912yes—
1329C4×D4—794no—
1330C4×D4—794no—
1331C4×D4—794no—
1332C4×D4—794no—
1333C4×D4—798no—
1334C4×D4—798no—
1335C4×D4—798no—
1336C4×D4—798no—
1337C4×D4—798no—
1338C4×D4—798no—
1339C4×D4—794no—
1340C4×D4—794no—
1341C4×D4—792no—
1342C4×D4—792no—
1343C4×D4—792no—
1344C4×D4—792no—
1345C4×D4—794no—
1346C4×D4—794no—
1347C4×D4—798no—
1348C4×D4—798no—
1349C4×D4—794no—
1350C4×D4—798no—
1351C4×D4—794no—
1352C4×D4—794no—
1353C4×D4—798no—
1354C4×D4—792no—
1355C4×D4—792no—
1356C4×D4—792no—
1357C4×D4—792no—
1358C4×D4—794no—
1359C4×D4—794no—
1360C4×D4—792no—
1361C4×D4—792no—
1362C4×D4—794no—
1363C4×D4—794no—
1364C4×D4—794no—
1365C4×D4C22×D7912yes—
1366C4×D4C22×D7912yes—
1367C4×D4C22×D7912yes—
1368C4×D4C22×D7912yes—
1369C4×D4C22×D7914yes—
1370C4×D4C22×D7914yes—
1371C4×D4C22×D7914yes—
1372C4×D4C22×D7914yes—
1373#117—792no—
1374#117—794no—
1375#117—798no—
1376#117—792no—
1377#117—792no—
1378#117—792no—
1379#117—794no—
1380#117—792no—
1381#117—794no—
1382#117—794no—
1383#117—798no—
1384#117—794no—
1385#117—794no—
1386#117—794no—
1387#117—794no—
1388#117—794no—
1389#117C22×D7912yes—
1390#117C22×D7912yes—
1391C2×C4⋊C4—791no—
1392C2×C4⋊C4—792no—
1393C2×C4⋊C4—792no—
1394C2×C4⋊C4—792no—
1395C2×C4⋊C4—792no—
1396C2×C4⋊C4—794no—
1397C2×C4⋊C4—794no—
1398C2×C4⋊C4—792no—
1399C2×C4⋊C4—794no—
1400C2×C4⋊C4—798no—
1401C2×C4⋊C4—798no—
1402C2×C4⋊C4—794no—
1403C2×C4⋊C4—794no—
1404C2×C4⋊C4C22×D7911yescharacteristic
1405C2×C4⋊C4C22×D7914yes—
1406C2×C4⋊C4C22×D7918yes—
1407C2×C22⋊C4—792no—
1408C2×C22⋊C4—792no—
1409C2×C22⋊C4—792no—
1410C2×C22⋊C4—794no—
1411C2×C22⋊C4—798no—
1412C2×C22⋊C4C22×D7912yes—
1413C2×C22⋊C4C22×D7918yes—
1414C2×C42—791no—
1415C2×C42—791no—
1416C2×C42—791no—
1417C2×C42—794no—
1418C2×C42—791no—
1419C2×C42—791no—
1420C2×C42—794no—
1421C2×C42—791no—
1422C2×C42—791no—
1423C2×C42—791no—
1424C2×C42—791no—
1425C2×C42—791no—
1426C2×C42—791no—
1427C2×C42C22×D7911yescharacteristic
1428C24—792no—
1429C24—791no—
1430C24C23×D7912yes—
1431#41—3168no—
1432#41—3168no—
1433#41—3168no—
1434#41—31616no—
1435#41—31616no—
1436#41—3168no—
1437#41—31616no—
1438#41—3168no—
1439#41—31616no—
1440#41—3164no—
1441#41—15816no—
1442#41—1588no—
1443#41—1588no—
1444C2×Q8—48no—
1445C2×Q8—3164no—
1446C2×Q8—3168no—
1447C2×Q8—3164no—
1448C2×Q8—31616no—
1449C2×Q8—792no—
1450C2×Q8—798no—
1451C2×Q8—794no—
1452C2×Q8—792no—
1453C2×Q8—794no—
1454C2×Q8—792no—
1455C2×Q8—794no—
1456C2×Q8—794no—
1457C2×Q8—1588no—
1458C2×Q8C23×D7912yes—
1459C2×Q8C23×D7912yes—
1460C2×Q8C23×D7912yes—
1461C2×Q8C23×D7912yes—
1462C2×Q8C23×D7918yes—
1463C2×D4—24no—
1464C2×D4—3164no—
1465C2×D4—3164no—
1466C2×D4—3164no—
1467C2×D4—3164no—
1468C2×D4—798no—
1469C2×D4—794no—
1470C2×D4—798no—
1471C2×D4—794no—
1472C2×D4—794no—
1473C2×D4—794no—
1474C2×D4—794no—
1475C2×D4—794no—
1476C2×D4—794no—
1477C2×D4—794no—
1478C2×D4—798no—
1479C2×D4—792no—
1480C2×D4—798no—
1481C2×D4—794no—
1482C2×D4—792no—
1483C2×D4—792no—
1484C2×D4—792no—
1485C2×D4—794no—
1486C2×D4—794no—
1487C2×D4—792no—
1488C2×D4—1584no—
1489C2×D4C23×D7912yes—
1490C2×D4C23×D7912yes—
1491C22×C4—44no—
1492C22×C4—3164no—
1493C22×C4—3162no—
1494C22×C4—792no—
1495C22×C4—791no—
1496C22×C4—791no—
1497C22×C4—794no—
1498C22×C4—798no—
1499C22×C4—798no—
1500C22×C4—794no—
1501C22×C4—798no—
1502C22×C4—798no—
1503C22×C4—791no—
1504C22×C4—791no—
1505C22×C4—791no—
1506C22×C4—791no—
1507C22×C4—791no—
1508C22×C4—791no—
1509C22×C4—791no—
1510C22×C4—791no—
1511C22×C4—791no—
1512C22×C4—791no—
1513C22×C4—791no—
1514C22×C4—791no—
1515C22×C4—791no—
1516C22×C4—794no—
1517C22×C4—794no—
1518C22×C4—794no—
1519C22×C4—794no—
1520C22×C4—794no—
1521C22×C4—1584no—
1522C22×C4—1584no—
1523C22×C4C23×D7911yescharacteristic
1524C22×C4C23×D7914yes—
1525C22×C4C23×D7911yescharacteristic
1526C22×C4C23×D7912yes—
1527C22×C4C23×D7918yes—
1528C22×C4C23×D7918yes—
1529C22×C4C23×D7914yes—
1530C22×C4C23×D7911yescharacteristic
1531C4⋊C4—794no—
1532C4⋊C4—794no—
1533C4⋊C4—794no—
1534C4⋊C4—794no—
1535C4⋊C4—794no—
1536C4⋊C4—794no—
1537C4⋊C4—794no—
1538C4⋊C4—798no—
1539C4⋊C4—798no—
1540C4⋊C4—798no—
1541C4⋊C4—798no—
1542C4⋊C4—794no—
1543C4⋊C4—794no—
1544C4⋊C4—794no—
1545C4⋊C4—794no—
1546C4⋊C4—794no—
1547C4⋊C4—792no—
1548C4⋊C4—792no—
1549C4⋊C4—792no—
1550C4⋊C4—798no—
1551C4⋊C4—792no—
1552C4⋊C4—792no—
1553C4⋊C4—794no—
1554C4⋊C4—794no—
1555C4⋊C4—792no—
1556C4⋊C4—792no—
1557C4⋊C4—794no—
1558C4⋊C4—792no—
1559C4⋊C4—794no—
1560C4⋊C4C23×D7912yes—
1561C4⋊C4C23×D7912yes—
1562C4⋊C4C23×D7914yes—
1563C4⋊C4C23×D7912yes—
1564C4⋊C4C23×D7912yes—
1565C4⋊C4C23×D7914yes—
1566C4⋊C4C23×D7918yes—
1567C4⋊C4C23×D7912yes—
1568C4⋊C4C23×D7914yes—
1569C4⋊C4C23×D7912yes—
1570C4⋊C4C23×D7912yes—
1571C4⋊C4C23×D7918yes—
1572C4⋊C4C23×D7918yes—
1573C4⋊C4C23×D7912yes—
1574C4⋊C4C23×D7914yes—
1575C4⋊C4C23×D7912yes—
1576C4⋊C4C23×D7912yes—
1577C22⋊C4—794no—
1578C22⋊C4—794no—
1579C22⋊C4—794no—
1580C22⋊C4—798no—
1581C22⋊C4—798no—
1582C22⋊C4—794no—
1583C22⋊C4—794no—
1584C22⋊C4—794no—
1585C22⋊C4—794no—
1586C22⋊C4—798no—
1587C22⋊C4—798no—
1588C22⋊C4—794no—
1589C22⋊C4—794no—
1590C22⋊C4—794no—
1591C22⋊C4—794no—
1592C22⋊C4—794no—
1593C22⋊C4—798no—
1594C22⋊C4—798no—
1595C22⋊C4—794no—
1596C22⋊C4—794no—
1597C22⋊C4—794no—
1598C22⋊C4—798no—
1599C22⋊C4—798no—
1600C22⋊C4—794no—
1601C22⋊C4—794no—
1602C22⋊C4C23×D7914yes—
1603C22⋊C4C23×D7914yes—
1604C22⋊C4C23×D7914yes—
1605C22⋊C4C23×D7918yes—
1606C22⋊C4C23×D7918yes—
1607C22⋊C4C23×D7914yes—
1608C42—791no—
1609C42—791no—
1610C42—791no—
1611C42—791no—
1612C42—791no—
1613C42—791no—
1614C42—791no—
1615C42—791no—
1616C42—791no—
1617C42—791no—
1618C42—791no—
1619C42—791no—
1620C42—794no—
1621C42—794no—
1622C42—794no—
1623C42—794no—
1624C42—794no—
1625C42—798no—
1626C42—798no—
1627C42C23×D7911yescharacteristic
1628C42C23×D7911yescharacteristic
1629C42C23×D7911yescharacteristic
1630C42C23×D7911yescharacteristic
1631C42C23×D7914yes—
1632C42C23×D7914yes—
1633C23—24no—
1634C23—42no—
1635C23—42no—
1636C23—3161no—
1637C23—3162no—
1638C23—3162no—
1639C23—791no—
1640C23—794no—
1641C23—791no—
1642C23—794no—
1643C23—1582no—
1644C23—1582no—
1645C23—1584no—
1646C23C24×D7914yes—
1647C23C24×D7911yescharacteristic
1648Q8—24no—
1649Q8—24no—
1650Q8—48no—
1651Q8—42no—
1652Q8—42no—
1653Q8—3168no—
1654Q8—3164no—
1655Q8—3162no—
1656Q8—1588no—
1657Q8—1588no—
1658Q8—1588no—
1659Q8—1584no—
1660Q8—1584no—
1661D4—24no—
1662D4—24no—
1663D4—3164no—
1664D4—3168no—
1665D4—3164no—
1666D4—3168no—
1667D4—3162no—
1668D4—3164no—
1669D4—3164no—
1670D4—3164no—
1671D4—3168no—
1672D4—3168no—
1673D4—1588no—
1674D4—1588no—
1675D4—1588no—
1676D4—1588no—
1677D4—1588no—
1678D4—1588no—
1679D4—1584no—
1680D4—1584no—
1681D4—1584no—
1682D4—1584no—
1683C2×C4—22no—
1684C2×C4—28no—
1685C2×C4—42no—
1686C2×C4—44no—
1687C2×C4—41no—
1688C2×C4—48no—
1689C2×C4—48no—
1690C2×C4—3164no—
1691C2×C4—3161no—
1692C2×C4—3161no—
1693C2×C4—3168no—
1694C2×C4—3168no—
1695C2×C4—3168no—
1696C2×C4—3164no—
1697C2×C4—3168no—
1698C2×C4—3162no—
1699C2×C4—791no—
1700C2×C4—791no—
1701C2×C4—794no—
1702C2×C4—791no—
1703C2×C4—794no—
1704C2×C4—791no—
1705C2×C4—794no—
1706C2×C4—791no—
1707C2×C4—791no—
1708C2×C4—794no—
1709C2×C4—794no—
1710C2×C4—1582no—
1711C2×C4—1582no—
1712C2×C4—1582no—
1713C2×C4—1588no—
1714C2×C4—1588no—
1715C2×C4—1582no—
1716C2×C4—1588no—
1717C2×C4—1582no—
1718C2×C4—1582no—
1719C2×C4—1582no—
1720C2×C4—1588no—
1721C2×C4—1582no—
1722C2×C4—1582no—
1723C2×C4—1582no—
1724C2×C4—1582no—
1725C2×C4—1582no—
1726C2×C4—1588no—
1727C2×C4#1457920914yescomplemented
1728C2×C4C24×D7914yes—
1729C2×C4C24×D7911yescharacteristic
1730C2×C4C24×D7911yescharacteristic
1731C2×C4C24×D7911yescharacteristic
1732C2×C4C24×D7914yes—
1733C2×C4C24×D7914yes—
1734C2×C4C24×D7914yes—
1735C2×C4C24×D7914yes—
1736C2×C4C24×D7911yescharacteristic
1737C2×C4C24×D7911yescharacteristic
1738C2×C4C24×D7911yescharacteristic
1739C22—21no—
1740C22—21no—
1741C22—24no—
1742C22—24no—
1743C22—24no—
1744C22—84no—
1745C22—3164no—
1746C22—792no—
1747C22—6324no—
1748C22—1584no—
1749C22—1584no—
1750C22—1581no—
1751C22—1581no—
1752C22—1584no—
1753C22—1584no—
1754C22—1584no—
1755C22—1581no—
1756C22—1584no—
1757C22—1581no—
1758C22—1581no—
1759C22C2×#1457920912yes—
1760C22C25×D7911yescharacteristic
1761C4—21no—
1762C4—24no—
1763C4—24no—
1764C4—24no—
1765C4—24no—
1766C4—24no—
1767C4—21no—
1768C4—21no—
1769C4—792no—
1770C4—792no—
1771C4—1584no—
1772C4—1584no—
1773C4—1581no—
1774C4—1581no—
1775C4—1581no—
1776C4—1584no—
1777C4—1584no—
1778C4—1581no—
1779C4H(5,𝔽2)×D7912yes—
1780C4C2×#1457920912yes—
1781C4C2×#1457920912yes—
1782C2—22no—
1783C2—44no—
1784C2—3161no—
1785C2—3164no—
1786C2—3164no—
1787C2—1582no—
1788C2C2×H(5,𝔽2)×D7911yescharacteristic
1789C2C22×#1457920911yescharacteristic
1790C2#585×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3501C2
hypercenter#3501D79
hypocenterC79#62835
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #23777967C2semidirect
2. #23777935C2semidirect
3. #23777863C2semidirect
4. #23777807C2semidirect
5. #23777799C2semidirect
6. #23777790C2semidirect
7. #23777785C2semidirect
8. #23777626C2semidirect
9. #23777484C2semidirect
10. #23777443C2semidirect
11. #23777308C2semidirect
12. #23777308C2semidirect
13. #23777271C2semidirect
14. #23777263C2semidirect
15. #23777254C2semidirect
16. #23777252C2semidirect
17. #23777215C2semidirect
18. #23777201C2semidirect
19. #23777184C2semidirect
20. #23777170C2semidirect
21. #23777138C2semidirect
22. #23777125C2semidirect
23. #23777076C2semidirect
24. #23776697C2semidirect
25. #533×D79C2semidirect
26. C2×#19099110C2semidirect
27. C79×#3501C2semidirect
28. C2×#14579209C22semidirect
30. #19099314C22semidirect
31. #19099309C22semidirect
32. #19099309C22semidirect
33. #19099309C22semidirect
34. #19099298C22semidirect
35. #19099296C22semidirect
36. #19099296C22semidirect
37. #19099296C22semidirect
38. #19099293C22semidirect
39. #19099290C22semidirect
40. #19099286C22semidirect
41. #19099284C22semidirect
42. #19099284C22semidirect
43. #19099283C22semidirect
44. #19099279C22semidirect
45. #19099279C22semidirect
46. #19099278C22semidirect
47. #19099278C22semidirect
48. #19099274C22semidirect
49. #19099273C22semidirect
50. #19099273C22semidirect
51. #19099269C22semidirect
52. #19099269C22semidirect
54. #19099266C22semidirect
55. #19099266C22semidirect
56. #19099266C22semidirect
57. #19099263C22semidirect
58. #19099263C22semidirect
59. #19099263C22semidirect
60. #19099248C22semidirect
61. #19099247C22semidirect
64. #19099235C22semidirect
65. #19099234C22semidirect
66. #19099234C22semidirect
67. #19099234C22semidirect
68. Q8×D316C22semidirect
69. #19099228C22semidirect
70. #19099228C22semidirect
71. Q8×C22⋊D79C22semidirect
73. #19099224C22semidirect
74. #19099223C22semidirect
75. #19099223C22semidirect
76. #19099223C22semidirect
77. #19099223C22semidirect
78. #19099218C22semidirect
79. #19099218C22semidirect
80. #19099216C22semidirect
81. #19099216C22semidirect
82. #19099215C22semidirect
83. #19099215C22semidirect
84. #19099215C22semidirect
85. #19099214C22semidirect
86. #19099214C22semidirect
87. #19099214C22semidirect
92. #19099193C22semidirect
94. #19099190C22semidirect
96. #19099187C22semidirect
97. #19099186C22semidirect
98. #19099183C22semidirect
99. #19099183C22semidirect
100. #19099183C22semidirect
101. #19099183C22semidirect
102. #19099178C22semidirect
103. #19099169C22semidirect
104. #19099164C22semidirect
105. #19099164C22semidirect
106. #19099164C22semidirect
107. #19099160C22semidirect
108. #19099159C22semidirect
109. #19099159C22semidirect
112. #19099144C22semidirect
113. #19099143C22semidirect
114. #19099143C22semidirect
115. #19099143C22semidirect
116. #19099143C22semidirect
117. #19099137C22semidirect
118. #19099136C22semidirect
119. #19099136C22semidirect
120. #19099136C22semidirect
124. #19099119C22semidirect
125. #19099119C22semidirect
126. #19099118C22semidirect
127. #19099118C22semidirect
128. #19099118C22semidirect
129. #19099118C22semidirect
130. #19099117C22semidirect
131. #19099117C22semidirect
135. #19099114C22semidirect
136. #19099114C22semidirect
137. #19099114C22semidirect
147. #19099110C22semidirect
148. #19099110C22semidirect
149. #19099110C22semidirect
151. C4⋊Q8×D79C22semidirect
152. C4⋊Q8×D79C22semidirect
153. C4⋊Q8×D79C22semidirect
155. #19099100C22semidirect
156. #19099100C22semidirect
159. #19099098C22semidirect
160. #19099098C22semidirect
161. #19099098C22semidirect
162. #19099095C22semidirect
163. #125×D79C22semidirect
177. #19099044C22semidirect
178. #19099044C22semidirect
181. C4×#11929625C22semidirect
182. C4×#11929625C22semidirect
184. C4×Q8×D79C22semidirect
185. C4×Q8×D79C22semidirect
190. #554×C79C22semidirect
191. #554×C79C22semidirect
192. #554×C79C22semidirect
193. #554×C79C22semidirect
194. D4×Q8×C79C22semidirect
195. D4×Q8×C79C22semidirect
766. C2×C4×C792−1+4semidirect
914. #3501D79semidirect
923. C79#62835semidirect
950. #554C2×D79semidirect
951. #554C2×D79semidirect
952. #554C2×D79semidirect
953. #554C2×D79semidirect
973. D4×Q8C2×D79semidirect
974. D4×Q8C2×D79semidirect
1727. C2×C4#14579209semidirect

Maximal subgroups

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

subgroupindex
#237779672
#237779352
#237778632
#237778072
#237777992
#237777902
#237777852
#237776262
#237774842
#237774432
#237773082
#237772712
#237772632
#237772542
#237772522
#237772152
#237772012
#237771842
#237771702
#237771382
#237771252
#237770762
#237766972
#533×D792
C2×#190991102
C79×#35012
#6283579