Finite Group Databasebeta

← #35197200

Subgroups — #35197200

Order 20224.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777993C214yesmaximal, complemented
2#23777982C214yesmaximal, complemented
3#23777866C214yesmaximal, complemented
4#23777767C214yesmaximal, complemented
5#23777711C218yesmaximal, complemented
6#23777405C214yesmaximal, complemented
7#23777358C214yesmaximal, complemented
8#23777332C218yesmaximal, complemented
9#23777310C214yesmaximal, complemented
10#23777299C211yesmaximal, characteristic, complemented
11#23777291C211yesmaximal, characteristic, complemented
12#23777285C211yesmaximal, characteristic, complemented
13#23777271C211yesmaximal, characteristic, complemented
14#23777268C214yesmaximal, complemented
15#23777189C211yesmaximal, characteristic, complemented
16#23777188C211yesmaximal, characteristic, complemented
17#23777182C211yesmaximal, characteristic, complemented
18#23777174C211yesmaximal, characteristic, complemented
19#23777058C211yesmaximal, characteristic, complemented
20#23777054C211yesmaximal, characteristic, complemented
21#23777042C211yesmaximal, characteristic, complemented
22#23776692C211yesmaximal, characteristic, complemented
23#23776692C211yesmaximal, characteristic, complemented
24C2×#19099109C211yesmaximal, characteristic, complemented
25C79×#3485C211yesmaximal, characteristic, complemented
26C2×#14579209C2211yescharacteristic, complemented
27C2×#14579208C2211yescharacteristic, complemented
28C2×#14579207C2211yescharacteristic
29C22×#11929624C2211yescharacteristic, complemented
30#19099310C2218yescomplemented
31#19099308C2218yescomplemented
32#19099302C2218yescomplemented
33#19099301C2218yescomplemented
34#19099297C2218yescomplemented
35#19099296C2214yescomplemented
36#19099296C2214yescomplemented
37#19099295C2214yescomplemented
38#19099288C2214yescomplemented
39#19099287C2214yescomplemented
40#19099283C2214yescomplemented
41#19099282C2214yescomplemented
42#19099277C2218yescomplemented
43#19099268C2218yescomplemented
44#19099261C2218yescomplemented
45#19099258C2218yescomplemented
46#19099258C2218yescomplemented
47#19099258C2218yescomplemented
48#19099250C2218yescomplemented
49#19099241C2218yescomplemented
50#19099239C2218yescomplemented
51#19099239C2218yescomplemented
52#19099236C2218yescomplemented
53#19099234C2214yescomplemented
54#19099234C2214yescomplemented
55#19099232C2214yescomplemented
56#19099232C2214yescomplemented
57#19099232C2214yescomplemented
58#19099231C2214yescomplemented
59#19099231C2218yescomplemented
60#19099226C2214yescomplemented
61#19099223C2214yescomplemented
62#19099223C2214yescomplemented
63#19099222C2214yescomplemented
64#19099220C2214yescomplemented
65#19099220C2214yescomplemented
66#19099220C2214yescomplemented
67#19099218C2214yescomplemented
68#19099215C2214yescomplemented
69#19099215C2214yescomplemented
70#19099211C2218yescomplemented
71#19099210C2214yescomplemented
72#19099209C2214yescomplemented
73#19099207C2218yescomplemented
74#19099207C2214yescomplemented
75#19099205C2218yescomplemented
76#19099204C2214yescomplemented
77#19099203C2218yescomplemented
78#19099203C2218yescomplemented
79#19099200C2218yescomplemented
80D4×C22⋊D79C2218yes—
81D4×C22⋊D79C2214yescomplemented
82#19099186C2214yescomplemented
83#19099181C2218yescomplemented
84#19099181C2218yescomplemented
85#19099178C2214yescomplemented
86#19099173C2214yescomplemented
87#19099166C2218yescomplemented
88#19099165C2218yescomplemented
89#19099165C2218yescomplemented
90#19099164C2214yescomplemented
91#19099163C2218yescomplemented
92#19099160C2218yescomplemented
93#19099156C2218yescomplemented
94#19099151C2218yescomplemented
95#19099149C2218yescomplemented
96#19099148C2218yescomplemented
97#19099145C2218yescomplemented
98#19099142C2218yescomplemented
99#19099139C2211yescharacteristic, complemented
100#19099138C2212yescomplemented
101#19099138C2212yescomplemented
102#19099134C2211yescharacteristic
103#19099134C2212yescomplemented
104#19099133C2212yescomplemented
105#19099132C2211yescharacteristic, complemented
106#19099131C2212yescomplemented
107#19099130C2211yescharacteristic
108#19099130C2211yescharacteristic, complemented
109#19099130C2214yescomplemented
110#19099130C2212yescomplemented
111#19099130C2212yescomplemented
112#19099128C2214yescomplemented
113#19099128C2218yescomplemented
114#19099127C2211yescharacteristic
115#19099127C2212yescomplemented
116#19099123C2214yescomplemented
117#19099116C2211yescharacteristic, complemented
118#19099116C2211yescharacteristic, complemented
119#19099115C2214yescomplemented
120#19099115C2212yescomplemented
121#19099115C2212yescomplemented
122#19099114C2212yescomplemented
123#19099112C2212yescomplemented
124#19099110C2214yescomplemented
125#19099109C2211yescharacteristic
126#19099109C2211yescharacteristic
127#19099109C2212yescomplemented
128#19099109C2214yescomplemented
129#19099109C2214yescomplemented
130#19099109C2214yescomplemented
131#19099109C2212yescomplemented
132#19099109C2214yescomplemented
133#19099108C2212yescomplemented
134#19099108C2212yescomplemented
135C2×#14579159C2211yescharacteristic, complemented
136C4⋊Q8×D79C2212yescomplemented
137C2×#14579157C2211yescharacteristic
138C2×#14579157C2212yescomplemented
139#19099099C2214yescomplemented
140#19099099C2212yescomplemented
141#19099099C2212yescomplemented
142#19099095C2214yescomplemented
143#19099094C2212yescomplemented
144#19099094C2212yescomplemented
145#19099093C2214yescomplemented
146#19099093C2214yescomplemented
147#19099090C2214yescomplemented
148#19099090C2214yescomplemented
149C2×#14579150C2211yescharacteristic, complemented
150C2×#14579148C2211yescharacteristic, complemented
151C2×#14579148C2212yescomplemented
152#124×D79C2212yescomplemented
153#19099074C2211yescharacteristic, complemented
154#19099074C2211yescharacteristic, complemented
155#19099074C2214yescomplemented
156#19099071C2214yescomplemented
157#19099069C2214yescomplemented
158#19099069C2214yescomplemented
159#123×D79C2214yescomplemented
160C2×#14579133C2214yescomplemented
161#19099044C2218yescomplemented
162#19099041C2211yescharacteristic, complemented
163#19099040C2211yescharacteristic, complemented
164#19099037C2211yescharacteristic, complemented
165#19099036C2218yescomplemented
166#41×Dic79C2211yescharacteristic
167#41×Dic79C2211yescharacteristic, complemented
168#19099031C2211yescharacteristic, complemented
169#19099031C2211yescharacteristic, complemented
170C4×#11929623C2214yescomplemented
171C4×#11929623C2214yescomplemented
172C2×C4×C22⋊D79C2214yescomplemented
173C22×C4×Dic79C2211yescharacteristic, complemented
174C2×H(5,𝔽2)×C79C2211yescharacteristic
175C22×#41×C79C2211yescharacteristic, complemented
176#547×C79C2214yescomplemented
177#547×C79C2214yescomplemented
178#546×C79C2214yescomplemented
179#546×C79C2214yescomplemented
180#536×C79C2211yescharacteristic
181#536×C79C2211yescharacteristic, complemented
182#534×C79C2214yescomplemented
183#525×C79C2211yescharacteristic
184#525×C79C2211yescharacteristic, complemented
185C2×#123×C79C2214yescomplemented
186#518×C79C2211yescharacteristic, complemented
187#14579209—44no—
188#14579208—44no—
189#14579207—44no—
190C2×#11929625C2312yes—
191C2×#11929625C2312yes—
192C2×#11929625C2312yes—
193C2×#11929624—44no—
194C2×#11929624C2311yescharacteristic
195C2×#11929624C2311yescharacteristic
196C2×#11929624C2312yes—
197C2×#11929624C2312yes—
198C2×#11929624C2314yes—
199C2×#11929624C2318yes—
200C2×#11929624C2314yes—
201C2×#11929624C2314yes—
202C2×#11929623C2314yes—
203C2×#11929623C2312yes—
204C2×#11929623C2314yes—
205C2×#11929623C2314yes—
206C22×Dic158C2311yescharacteristic
207C22×Dic158C2312yes—
208C2×Q8×D79C2312yes—
209C2×Q8×D79C2312yes—
210C2×Q8×D79C2312yes—
211C22×D316C2311yescharacteristic
212C22×D316C2312yes—
213C22×C22⋊D79C2314yes—
214C22×C22⋊D79C2318yes—
215C22×C22⋊D79C2312yes—
216C2×D4×D79C2314yes—
217C2×D4×D79C2312yes—
218C23×Dic79C2312yes—
219C22×C4×D79C2312yes—
220#14579161C2312yes—
221#14579160C2312yes—
222#14579160C2318yes—
223#14579160C2312yes—
224#14579159C2311yescharacteristic
225#14579159C2312yes—
226#14579159C2312yes—
227#14579159C2314yes—
228#14579159C2311yescharacteristic
229#14579159C2312yes—
230#14579158C2312yes—
231#14579157C2318yes—
232#14579157C2312yes—
233#14579157C2318yes—
234#14579157C2318yes—
235#14579157C2314yes—
236#14579157C2312yes—
237#14579157C2312yes—
238#14579157C2312yes—
239#14579157C2312yes—
240#14579157C2311yescharacteristic
241#14579157C2311yescharacteristic
242#14579156C2318yes—
243#14579156C2314yes—
244#14579156C2318yes—
245#14579156C2314yes—
246#14579154C2318yes—
247#14579154C2318yes—
248#14579154C2318yes—
249#14579154C2314yes—
250#14579154C2318yes—
251#14579154C2314yes—
252#14579152C2318yes—
253#14579152C2312yes—
254#14579152C2312yes—
255#14579151C2314yes—
256#14579151C2318yes—
257#14579151C2318yes—
258#14579151C2314yes—
259#14579150C2311yescharacteristic
260#14579150C2312yes—
261#14579150C2314yes—
262#14579150C2312yes—
263#14579150C2312yes—
264#14579150C2311yescharacteristic
265#14579149C2312yes—
266#14579149C2312yes—
267#14579148C2318yes—
268#14579148C2318yes—
269#14579148C2312yes—
270#14579148C2314yes—
271#14579148C2312yes—
272#14579148C2312yes—
273#14579148C2312yes—
274#14579148C2311yescharacteristic
275#14579148C2312yes—
276#14579148C2311yescharacteristic
277#14579147C2318yes—
278#14579147C2318yes—
279#14579147C2314yes—
280#14579147C2318yes—
281#14579147C2318yes—
282#14579147C2318yes—
283#14579147C2314yes—
284#14579146C2318yes—
285#14579146C2318yes—
286#14579146C2318yes—
287#14579145C2314yes—
288#14579145C2314yes—
289#14579145C2318yes—
290#14579145C2314yes—
291#14579144C2318yes—
292#14579144C2318yes—
293#14579144C2312yes—
294#14579144C2312yes—
295#14579143C2318yes—
296#14579143C2318yes—
297#14579143C2318yes—
298#14579143C2318yes—
299#14579143C2318yes—
300#14579143C2318yes—
301#14579142C2314yes—
302#14579142C2318yes—
303#14579142C2314yes—
304#14579142C2314yes—
305#14579141C2314yes—
306#14579141C2318yes—
307#14579140C2318yes—
308#14579140C2318yes—
309#14579140C2318yes—
310#14579140C2314yes—
311#14579140C2312yes—
312#14579140C2312yes—
313#14579139C2318yes—
314#14579139C2318yes—
315#14579139C2318yes—
316#14579138C2314yes—
317#14579138C2318yes—
318#14579138C2318yes—
319#14579138C2314yes—
320#14579138C2314yes—
321#14579138C2314yes—
322#14579136C2314yes—
323#14579136C2318yes—
324#14579135C2318yes—
325#14579135C2318yes—
326#14579135C2318yes—
327#14579135C2314yes—
328#14579135C2312yes—
329#14579135C2312yes—
330#14579134C2318yes—
331#14579134C2318yes—
332#14579134C2318yes—
333#14579134C2318yes—
334#14579134C2318yes—
335#14579134C2318yes—
336#14579134C2318yes—
337#14579133C2318yes—
338#14579133C2318yes—
339#14579133C2318yes—
340#14579133C2318yes—
341#14579133C2314yes—
342#14579133C2318yes—
343#14579133C2314yes—
344#14579133C2318yes—
345#14579133C2314yes—
346#14579133C2314yes—
347#14579133C2318yes—
348#14579132C2318yes—
349#14579132C2318yes—
350#14579132C2318yes—
351#14579132C2318yes—
352#14579132C2318yes—
353#14579132C2314yes—
354#14579132C2314yes—
355#14579131C2318yes—
356#14579131C2314yes—
357#14579130C2318yes—
358#14579130C2318yes—
359#14579130C2314yes—
360#14579130C2314yes—
361#14579130C2312yes—
362#14579130C2312yes—
363#14579129C2318yes—
364#14579129C2318yes—
365#14579129C2314yes—
366Q8×Dic79C2314yes—
367Q8×Dic79C2314yes—
368Q8×Dic79C2312yes—
369Q8×Dic79C2312yes—
370C4×Dic158C2314yes—
371C4×Dic158C2314yes—
372C4×Dic158C2314yes—
373#14579126C2314yes—
374#14579126C2314yes—
375#14579126C2318yes—
376#14579126C2312yes—
377#14579126C2312yes—
378#14579126C2314yes—
379C4×D316C2314yes—
380D4×Dic79C2314yes—
381D4×Dic79C2314yes—
382D4×Dic79C2312yes—
383D4×Dic79C2314yes—
384D4×Dic79C2314yes—
385D4×Dic79C2312yes—
386#14579123C2318yes—
387#14579123C2318yes—
388#14579123C2314yes—
389#14579123C2312yes—
390#14579123C2312yes—
391C4×C22⋊D79C2318yes—
392C4×C22⋊D79C2318yes—
393C4×C22⋊D79C2318yes—
394C4×C22⋊D79C2318yes—
395C4×C22⋊D79C2318yes—
396C4×C22⋊D79C2318yes—
397C4×C22⋊D79C2318yes—
398C4×C22⋊D79C2318yes—
399C4×C22⋊D79C2314yes—
400C4×C22⋊D79C2318yes—
401C4×C22⋊D79C2314yes—
402C4×C22⋊D79C2314yes—
403C4×C22⋊D79C2314yes—
404C4×C22⋊D79C2318yes—
405(C22⋊D79)⋊C4C2314yes—
406(C22⋊D79)⋊C4C2318yes—
407(C22⋊D79)⋊C4C2318yes—
408(C22⋊D79)⋊C4C2318yes—
409(C22⋊D79)⋊C4C2314yes—
410(C22⋊D79)⋊C4C2314yes—
411(C22⋊D79)⋊C4C2314yes—
412(C22⋊D79)⋊C4C2314yes—
413(C22⋊D79)⋊C4C2314yes—
414#14579120C2318yes—
415#14579120C2312yes—
416#14579120C2312yes—
417#14579120C2314yes—
418#14579120C2311yescharacteristic
419#14579120C2311yescharacteristic
420#14579119C2314yes—
421#14579119C2318yes—
422#14579119C2314yes—
423#14579118C2312yes—
424#14579118C2312yes—
425#14579117C2314yes—
426#14579117C2314yes—
427#14579117C2314yes—
428#14579117C2314yes—
429#14579117C2318yes—
430#14579117C2314yes—
431C2×Dic79⋊C4C2314yes—
432C4⋊C4×D79C2318yes—
433C4⋊C4×D79C2318yes—
434C2×C22⋊Dic79C2318yes—
435C2×C22⋊Dic79C2314yes—
436C2×(C2×D79)⋊C4C2314yes—
437C22⋊C4×D79C2318yes—
438C22⋊C4×D79C2318yes—
439C22⋊C4×D79C2314yes—
440C2×C4×Dic79C2312yes—
441C2×C4×Dic79C2312yes—
442C2×C4×Dic79C2312yes—
443C2×C4×Dic79C2311yescharacteristic
444C2×C4×Dic79C2311yescharacteristic
445C2×C4×Dic79C2312yes—
446C2×C4×Dic79C2312yes—
447C2×C4×Dic79C2312yes—
448C2×C4×Dic79C2312yes—
449C42×D79C2312yes—
450C42×D79C2312yes—
451H(5,𝔽2)×C79—44no—
452C2×#41×C79—44no—
453C2×#41×C79C2311yescharacteristic
454C2×#41×C79C2311yescharacteristic
455C2×#41×C79C2312yes—
456C2×#41×C79C2314yes—
457C2×#41×C79C2314yes—
458C2×#41×C79C2312yes—
459C22×Q8×C79C2311yescharacteristic
460C22×D4×C79C2311yescharacteristic
461C22×D4×C79C2314yes—
462C22×D4×C79C2312yes—
463C22×D4×C79C2312yes—
464C22×D4×C79C2312yes—
465C23×C4×C79C2311yescharacteristic
466C23×C4×C79C2312yes—
467C4⋊Q8×C79C2312yes—
468C4⋊Q8×C79C2312yes—
469#124×C79C2312yes—
470#124×C79C2312yes—
471#123×C79C2318yes—
472#123×C79C2318yes—
473#123×C79C2318yes—
474#123×C79C2314yes—
475#123×C79C2314yes—
476#123×C79C2312yes—
477#123×C79C2312yes—
478C22⋊Q8×C79C2314yes—
479C22⋊Q8×C79C2314yes—
480C22⋊Q8×C79C2312yes—
481C22⋊Q8×C79C2312yes—
482#121×C79C2318yes—
483#121×C79C2318yes—
484#121×C79C2312yes—
485#121×C79C2312yes—
486#120×C79C2318yes—
487#120×C79C2312yes—
488#120×C79C2312yes—
489C4×D4×C79C2314yes—
490C4×D4×C79C2314yes—
491C4×D4×C79C2314yes—
492C4×D4×C79C2314yes—
493#117×C79C2311yescharacteristic
494#117×C79C2311yescharacteristic
495C2×C4⋊C4×C79C2318yes—
496C2×C22⋊C4×C79C2318yes—
497C2×C22⋊C4×C79C2314yes—
498C23×D79C2412yes—
499C23×D79C2414yes—
500#11929625—44no—
501#11929625—44no—
502#11929625—44no—
503#11929624—24no—
504#11929624—24no—
505#11929624—48no—
506#11929624—416no—
507#11929624—48no—
508#11929624—48no—
509#11929624—44no—
510#11929624—44no—
511#11929623—48no—
512#11929623—48no—
513#11929623—44no—
514#11929623—48no—
515C2×Dic158—24no—
516C2×Dic158—44no—
517C2×Dic158C2411yescharacteristic
518C2×Dic158C2411yescharacteristic
519C2×Dic158C2412yes—
520C2×Dic158C2412yes—
521C2×Dic158C2414yes—
522C2×Dic158C2414yes—
523C2×Dic158C2414yes—
524C2×Dic158C2414yes—
525Q8×D79—44no—
526Q8×D79—44no—
527Q8×D79—44no—
528C2×D316—24no—
529C2×D316—44no—
530C2×D316C2411yescharacteristic
531C2×D316C2412yes—
532C2×D316C2412yes—
533C2×D316C2411yescharacteristic
534C2×D316C2414yes—
535C2×D316C2418yes—
536C2×D316C2414yes—
537C2×C22⋊D79—416no—
538C2×C22⋊D79—48no—
539C2×C22⋊D79—44no—
540C2×C22⋊D79C2412yes—
541C2×C22⋊D79C2414yes—
542C2×C22⋊D79C2412yes—
543C2×C22⋊D79C2418yes—
544C2×C22⋊D79C2414yes—
545C2×C22⋊D79C2414yes—
546C2×C22⋊D79C2414yes—
547C2×C22⋊D79C2414yes—
548C2×C22⋊D79C2418yes—
549C2×C22⋊D79C2418yes—
550C2×C22⋊D79C2414yes—
551C2×C22⋊D79C2418yes—
552C2×C22⋊D79C2418yes—
553C2×C22⋊D79C2418yes—
554D4×D79—48no—
555D4×D79—44no—
556C22×Dic79—44no—
557C22×Dic79C2412yes—
558C22×Dic79C2412yes—
559C22×Dic79C2412yes—
560C22×Dic79C2414yes—
561C22×Dic79C2412yes—
562C22×Dic79C2414yes—
563C22×Dic79C2414yes—
564C22×Dic79C2412yes—
565C22×Dic79C2412yes—
566C22×Dic79C2412yes—
567C2×C4×D79—44no—
568C2×C4×D79C2412yes—
569C2×C4×D79C2412yes—
570C2×C4×D79C2414yes—
571C2×C4×D79C2414yes—
572C2×C4×D79C2414yes—
573C2×C4×D79C2414yes—
574C2×C4×D79C2414yes—
575C2×C4×D79C2418yes—
576C2×C4×D79C2414yes—
577C2×C4×D79C2418yes—
578C4⋊Dic79C2418yes—
579C4⋊Dic79C2414yes—
580C4⋊Dic79C2414yes—
581C4⋊Dic79C2412yes—
582C4⋊Dic79C2412yes—
583C4⋊Dic79C2414yes—
584C4⋊Dic79C2414yes—
585C4⋊Dic79C2418yes—
586Dic79⋊C4C2414yes—
587Dic79⋊C4C2414yes—
588Dic79⋊C4C2418yes—
589Dic79⋊C4C2418yes—
590Dic79⋊C4C2418yes—
591Dic79⋊C4C2414yes—
592Dic79⋊C4C2414yes—
593Dic79⋊C4C2414yes—
594Dic79⋊C4C2414yes—
595Dic79⋊C4C2414yes—
596Dic79⋊C4C2414yes—
597Dic79⋊C4C2418yes—
598Dic79⋊C4C2414yes—
599Dic79⋊C4C2414yes—
600C22⋊Dic79C2414yes—
601C22⋊Dic79C2412yes—
602C22⋊Dic79C2418yes—
603C22⋊Dic79C2418yes—
604C22⋊Dic79C2418yes—
605C22⋊Dic79C2418yes—
606C22⋊Dic79C2412yes—
607C22⋊Dic79C2414yes—
608C22⋊Dic79C2414yes—
609C22⋊Dic79C2414yes—
610C22⋊Dic79C2418yes—
611C22⋊Dic79C2414yes—
612C22⋊Dic79C2414yes—
613(C2×D79)⋊C4C2414yes—
614(C2×D79)⋊C4C2418yes—
615(C2×D79)⋊C4C2418yes—
616(C2×D79)⋊C4C2418yes—
617(C2×D79)⋊C4C2418yes—
618(C2×D79)⋊C4C2418yes—
619(C2×D79)⋊C4C2414yes—
620(C2×D79)⋊C4C2414yes—
621(C2×D79)⋊C4C2414yes—
622(C2×D79)⋊C4C2414yes—
623(C2×D79)⋊C4C2414yes—
624(C2×D79)⋊C4C2418yes—
625C4×Dic79C2411yescharacteristic
626C4×Dic79C2411yescharacteristic
627C4×Dic79C2414yes—
628C4×Dic79C2414yes—
629C4×Dic79C2412yes—
630C4×Dic79C2412yes—
631C4×Dic79C2411yescharacteristic
632C4×Dic79C2411yescharacteristic
633C4×Dic79C2412yes—
634C4×Dic79C2412yes—
635C4×Dic79C2412yes—
636C4×Dic79C2412yes—
637C4×Dic79C2414yes—
638C4×Dic79C2414yes—
639C4×Dic79C2412yes—
640C4×Dic79C2412yes—
641C4×Dic79C2418yes—
642C4×Dic79C2418yes—
643C24×C79C2412yes—
644C24×C79C2411yescharacteristic
645C24×C79C2414yes—
646#41×C79—24no—
647#41×C79—24no—
648#41×C79—48no—
649#41×C79—48no—
650#41×C79—44no—
651#41×C79—44no—
652C2×Q8×C79—24no—
653C2×Q8×C79C2411yescharacteristic
654C2×Q8×C79C2412yes—
655C2×Q8×C79C2412yes—
656C2×Q8×C79C2411yescharacteristic
657C2×D4×C79—24no—
658C2×D4×C79—44no—
659C2×D4×C79—44no—
660C2×D4×C79—44no—
661C2×D4×C79—48no—
662C2×D4×C79C2412yes—
663C2×D4×C79C2411yescharacteristic
664C2×D4×C79C2412yes—
665C2×D4×C79C2412yes—
666C2×D4×C79C2412yes—
667C2×D4×C79C2411yescharacteristic
668C2×D4×C79C2414yes—
669C2×D4×C79C2414yes—
670C2×D4×C79C2418yes—
671C2×D4×C79C2414yes—
672C2×D4×C79C2414yes—
673C22×C4×C79—24no—
674C22×C4×C79—44no—
675C22×C4×C79C2412yes—
676C22×C4×C79C2412yes—
677C22×C4×C79C2412yes—
678C22×C4×C79C2412yes—
679C22×C4×C79C2412yes—
680C22×C4×C79C2411yescharacteristic
681C22×C4×C79C2418yes—
682C22×C4×C79C2418yes—
683C22×C4×C79C2414yes—
684C22×C4×C79C2411yescharacteristic
685C4⋊C4×C79C2414yes—
686C4⋊C4×C79C2414yes—
687C4⋊C4×C79C2418yes—
688C4⋊C4×C79C2418yes—
689C4⋊C4×C79C2412yes—
690C4⋊C4×C79C2412yes—
691C22⋊C4×C79C2412yes—
692C22⋊C4×C79C2412yes—
693C22⋊C4×C79C2414yes—
694C22⋊C4×C79C2414yes—
695C22⋊C4×C79C2418yes—
696C22⋊C4×C79C2418yes—
697C22⋊C4×C79C2418yes—
698C22⋊C4×C79C2414yes—
699C22⋊C4×C79C2414yes—
700C42×C79C2412yes—
701C42×C79C2412yes—
702C23×C79—22no—
703C23×C79—24no—
704C23×C79—42no—
705C23×C79—44no—
706C23×C79—48no—
707C23×C79—44no—
708C23×C79C2512yes—
709C23×C79C2514yes—
710C23×C79C2512yes—
711C23×C79C2512yes—
712C23×C79C2511yescharacteristic
713C22×D79—24no—
714C22×D79—44no—
715C22×D79—44no—
716C22×D79—48no—
717C22×D79C2512yes—
718C22×D79C2514yes—
719C22×D79C2512yes—
720Q8×C79—22no—
721Q8×C79—24no—
722Q8×C79—24no—
723Q8×C79—22no—
724D4×C79—24no—
725D4×C79—24no—
726D4×C79—22no—
727D4×C79—22no—
728D4×C79—24no—
729D4×C79—24no—
730D4×C79—44no—
731D4×C79—44no—
732D4×C79—44no—
733D4×C79—44no—
734D4×C79—48no—
735C2×C4×C79—22no—
736C2×C4×C79—24no—
737C2×C4×C79—24no—
738C2×C4×C79—24no—
739C2×C4×C79—24no—
740C2×C4×C79—24no—
741C2×C4×C79—48no—
742C2×C4×C79—48no—
743C2×C4×C79—44no—
744C2×C4×C79H(5,𝔽2)14yes—
745C2×C4×C79C2512yes—
746C2×C4×C79C2514yes—
747C2×C4×C79C2512yes—
748C2×C4×C79C2514yes—
749C2×C4×C79C2512yes—
750C2×C4×C79C2514yes—
751C2×C4×C79C2511yescharacteristic
752C2×C4×C79C2511yescharacteristic
753C22⋊D79—24no—
754C22⋊D79—24no—
755C22⋊D79—28no—
756C22⋊D79—216no—
757C22⋊D79—44no—
758C22⋊D79—48no—
759C22⋊D79—48no—
760C22⋊D79—48no—
761C22⋊D79—48no—
762C22⋊D79—44no—
763C22⋊D79—44no—
764C22⋊D79—44no—
765C22⋊D79—44no—
766C22⋊D79—48no—
767C2×Dic79—24no—
768C2×Dic79—24no—
769C2×Dic79—24no—
770C2×Dic79—24no—
771C2×Dic79—28no—
772C2×Dic79—42no—
773C2×Dic79—42no—
774C2×Dic79—42no—
775C2×Dic79—44no—
776C2×Dic79—44no—
777C2×Dic79C2512yes—
778C2×Dic79C2514yes—
779C2×Dic79C2512yes—
780C2×Dic79C2512yes—
781C2×Dic79C2514yes—
782C2×Dic79C2512yes—
783C2×Dic79C2514yes—
784C2×Dic79C2512yes—
785C2×Dic79C2512yes—
786D316—24no—
787D316—24no—
788D316—22no—
789D316—22no—
790D316—44no—
791D316—48no—
792D316—44no—
793C4×D79—24no—
794C4×D79—24no—
795C4×D79—28no—
796C4×D79—48no—
797C4×D79—44no—
798C4×D79—44no—
799C4×D79—44no—
800C4×D79—44no—
801C4×D79—44no—
802C4×D79—48no—
803Dic158—22no—
804Dic158—22no—
805Dic158—24no—
806Dic158—24no—
807Dic158—28no—
808Dic158—44no—
809Dic158—44no—
810Dic158—44no—
811C22×C79—22no—
812C22×C79—22no—
813C22×C79—22no—
814C22×C79—22no—
815C22×C79—24no—
816C22×C79—28no—
817C22×C79—24no—
818C22×C79—22no—
819C22×C79—22no—
820C22×C79—24no—
821C22×C79—44no—
822C22×C79—84no—
823C22×C79—164no—
824C22×C79C2×H(5,𝔽2)12yes—
825C22×C79C2611yescharacteristic
826C2×D79—22no—
827C2×D79—22no—
828C2×D79—24no—
829C2×D79—24no—
830C2×D79—28no—
831C2×D79—24no—
832C2×D79—84no—
833C2×D79—164no—
834C4×C79—22no—
835C4×C79—22no—
836C4×C79—22no—
837C4×C79—24no—
838C4×C79—24no—
839C4×C79—24no—
840C4×C79C2×H(5,𝔽2)12yes—
841C4×C79C2×H(5,𝔽2)12yes—
842Dic79—22no—
843Dic79—22no—
844Dic79—24no—
845Dic79—24no—
846Dic79—22no—
847Dic79—24no—
848Dic79—22no—
849Dic79—22no—
850Dic79#58514yes—
851#62836—791nomaximal, Sylow
852C2×C79—22no—
853C2×C79—42no—
854C2×C79—42no—
855C2×C79—44no—
856C2×C79—42no—
857C2×C79C22×H(5,𝔽2)11yescharacteristic
858C2×C79C2×#58512yes—
859D79—42no—
860D79—44no—
861D79—42no—
862#3562—794no—
863#3562—794no—
864#3554—794no—
865#3546—794no—
866#3542—798no—
867#3517—794no—
868#3514—794no—
869#3513—798no—
870#3511—794no—
871#3510—791no—
872#3510—791no—
873#3509—791no—
874#3508—794no—
875#3508—791no—
876#3500—791no—
877#3500—791no—
878#3499—791no—
879#3498—791no—
880#3487—791no—
881#3487—791no—
882#3485—791no—
883#3485D7911yescharacteristic, complemented
884#3444—791no—
885#3444—791no—
886C2×#532—791no—
887C79#6283611yescharacteristic, complemented, Sylow
888C2×2−1+4—791no—
889C2×2−1+4—791no—
890C2×H(5,𝔽2)—791no—
891C2×H(5,𝔽2)C2×D7911yescharacteristic
892C22×#41—791no—
893C22×#41C2×D7911yescharacteristic, complemented
894#562—798no—
895#562—798no—
896#560—798no—
897#560—798no—
898#559—794no—
899#559—798no—
900#559—794no—
901#559—794no—
902#557—794no—
903#556—794no—
904#556—794no—
905#556—794no—
906#555—798no—
907#554—798no—
908#553—798no—
909#553—798no—
910#553—798no—
911#553—798no—
912#552—798no—
913#551—798no—
914#551—798no—
915#551—798no—
916#551—798no—
917#550—794no—
918#550—794no—
919#550—794no—
920#550—794no—
921#550—798no—
922#550—794no—
923#550—794no—
924D4×Q8—794no—
925#548—794no—
926#548—794no—
927#548—794no—
928#548—794no—
929#548—794no—
930#548—794no—
931#547—798no—
932#547—794no—
933#547—794no—
934#547—794no—
935#547C2×D7914yescomplemented
936#547C2×D7914yescomplemented
937#546—794no—
938#546—798no—
939#546—798no—
940#546—794no—
941#546—794no—
942#546—798no—
943#546—794no—
944#546—798no—
945#546—798no—
946#546C2×D7914yescomplemented
947#546C2×D7914yescomplemented
948D42—798no—
949D42—794no—
950#542—798no—
951#542—798no—
952#542—794no—
953#542—794no—
954#541—794no—
955#540—798no—
956#540—798no—
957#540—798no—
958#540—798no—
959#540—794no—
960#539—798no—
961#539—798no—
962#538—798no—
963#538—798no—
964#538—798no—
965#538—798no—
966#537—798no—
967#536—791no—
968#536—792no—
969#536—792no—
970#536—792no—
971#536—792no—
972#536—791no—
973#536C2×D7911yescharacteristic
974#536C2×D7911yescharacteristic, complemented
975#535—791no—
976#535—792no—
977#535—791no—
978#535—791no—
979#535—794no—
980#535—792no—
981#535—792no—
982#535—792no—
983#535—794no—
984#535—798no—
985#535—791no—
986#534—794no—
987#534C2×D7914yescomplemented
988#533—792no—
989#533—792no—
990#533—794no—
991#533—791no—
992#533—791no—
993#532—794no—
994#532—794no—
995#532—794no—
996#532—794no—
997#532—791no—
998#532—791no—
999#532—792no—
1000#532—792no—
1001#532—792no—
1002#532—792no—
1003#532—792no—
1004#532—792no—
1005#532—794no—
1006C2×C4⋊Q8—791no—
1007C2×C4⋊Q8—792no—
1008C2×#127—791no—
1009C2×#127—792no—
1010#529—794no—
1011#529—794no—
1012#529—792no—
1013#529—792no—
1014#529—794no—
1015#529—792no—
1016#529—792no—
1017#529—794no—
1018#529—794no—
1019#529—794no—
1020C2×#124—791no—
1021C2×#124—791no—
1022C2×#124—792no—
1023C2×#124—792no—
1024#525—791no—
1025#525—791no—
1026#525—794no—
1027#525—794no—
1028#525—794no—
1029#525—794no—
1030#525C2×D7911yescharacteristic
1031#525C2×D7911yescharacteristic, complemented
1032C2×#123—794no—
1033C2×#123C2×D7914yescomplemented
1034C2×#121—794no—
1035#520—798no—
1036#519—791no—
1037#519—791no—
1038#518—791no—
1039#518—798no—
1040#518C2×D7911yescharacteristic, complemented
1041C4×#41—791no—
1042C4×#41—791no—
1043C4×#41—794no—
1044C4×#41—794no—
1045C4×#41—791no—
1046C4×#41—791no—
1047C2×C4×D4—794no—
1048C22×C42—791no—
10492−1+4—3164no—
10502−1+4—3164no—
1051H(5,𝔽2)—44no—
1052H(5,𝔽2)—3164no—
1053C2×#41—44no—
1054C2×#41—3164no—
1055C2×#41—792no—
1056C2×#41—792no—
1057C2×#41—792no—
1058C2×#41—794no—
1059C2×#41—794no—
1060C2×#41—794no—
1061C2×#41—792no—
1062C2×#41—798no—
1063C2×#41—794no—
1064C2×#41—794no—
1065C2×#41—794no—
1066C2×#41—792no—
1067C2×#41—792no—
1068C2×#41—791no—
1069C2×#41—791no—
1070C2×#41C22×D7911yescharacteristic
1071C2×#41C22×D7911yescharacteristic
1072C2×#41C22×D7914yes—
1073C2×#41C22×D7914yes—
1074C2×#41C22×D7912yes—
1075C2×#41C22×D7912yes—
1076C22×Q8—792no—
1077C22×Q8—792no—
1078C22×Q8—792no—
1079C22×Q8—792no—
1080C22×Q8—791no—
1081C22×Q8C22×D7911yescharacteristic
1082C22×D4—794no—
1083C22×D4—798no—
1084C22×D4—792no—
1085C22×D4—794no—
1086C22×D4—792no—
1087C22×D4—792no—
1088C22×D4—791no—
1089C22×D4C22×D7911yescharacteristic
1090C22×D4C22×D7912yes—
1091C22×D4C22×D7914yes—
1092C22×D4C22×D7912yes—
1093C22×D4C22×D7912yes—
1094C23×C4—792no—
1095C23×C4—792no—
1096C23×C4C22×D7911yescharacteristic
1097C23×C4C22×D7912yes—
1098C4⋊Q8—791no—
1099C4⋊Q8—792no—
1100C4⋊Q8—792no—
1101C4⋊Q8—794no—
1102C4⋊Q8—791no—
1103C4⋊Q8—792no—
1104C4⋊Q8—798no—
1105C4⋊Q8—792no—
1106C4⋊Q8—792no—
1107C4⋊Q8—792no—
1108C4⋊Q8C22×D7912yes—
1109C4⋊Q8C22×D7912yes—
1110#127—791no—
1111#127—792no—
1112#127—792no—
1113#127—794no—
1114#127—792no—
1115#127—792no—
1116#127—798no—
1117#127—791no—
1118#127—792no—
1119#127—798no—
1120#127—798no—
1121#127—792no—
1122#126—794no—
1123#126—794no—
1124#126—798no—
1125#126—798no—
1126#126—794no—
1127#126—794no—
1128#126—798no—
1129#126—798no—
1130#126—798no—
1131#126—798no—
1132#125—792no—
1133#125—794no—
1134#125—792no—
1135#125—794no—
1136#125—798no—
1137#125—798no—
1138#125—798no—
1139#124—792no—
1140#124—792no—
1141#124—794no—
1142#124—791no—
1143#124—791no—
1144#124—792no—
1145#124—791no—
1146#124—792no—
1147#124—792no—
1148#124—794no—
1149#124—792no—
1150#124—792no—
1151#124—798no—
1152#124—791no—
1153#124—792no—
1154#124—798no—
1155#124—798no—
1156#124—794no—
1157#124—794no—
1158#124—798no—
1159#124—798no—
1160#124—798no—
1161#124—798no—
1162#124—792no—
1163#124—792no—
1164#124C22×D7912yes—
1165#124C22×D7912yes—
1166#123—794no—
1167#123—794no—
1168#123—794no—
1169#123—798no—
1170#123—792no—
1171#123—792no—
1172#123—798no—
1173#123—798no—
1174#123—798no—
1175#123—798no—
1176#123—798no—
1177#123—794no—
1178#123—798no—
1179#123—794no—
1180#123—794no—
1181#123—798no—
1182#123—798no—
1183#123—798no—
1184#123—798no—
1185#123—798no—
1186#123—798no—
1187#123C22×D7912yes—
1188#123C22×D7912yes—
1189#123C22×D7914yes—
1190#123C22×D7914yes—
1191#123C22×D7918yes—
1192#123C22×D7918yes—
1193#123C22×D7918yes—
1194C22⋊Q8—792no—
1195C22⋊Q8—792no—
1196C22⋊Q8—798no—
1197C22⋊Q8—794no—
1198C22⋊Q8—798no—
1199C22⋊Q8—798no—
1200C22⋊Q8—798no—
1201C22⋊Q8—794no—
1202C22⋊Q8—798no—
1203C22⋊Q8—798no—
1204C22⋊Q8—798no—
1205C22⋊Q8—794no—
1206C22⋊Q8—794no—
1207C22⋊Q8—794no—
1208C22⋊Q8—794no—
1209C22⋊Q8—798no—
1210C22⋊Q8—798no—
1211C22⋊Q8C22×D7912yes—
1212C22⋊Q8C22×D7912yes—
1213C22⋊Q8C22×D7914yes—
1214C22⋊Q8C22×D7914yes—
1215#121—798no—
1216#121—798no—
1217#121—798no—
1218#121—798no—
1219#121—794no—
1220#121—794no—
1221#121—794no—
1222#121—794no—
1223#121—794no—
1224#121—794no—
1225#121—798no—
1226#121—798no—
1227#121—798no—
1228#121—798no—
1229#121—798no—
1230#121—798no—
1231#121—798no—
1232#121—798no—
1233#121—792no—
1234#121—792no—
1235#121—798no—
1236#121—794no—
1237#121—798no—
1238#121—798no—
1239#121—794no—
1240#121—798no—
1241#121—798no—
1242#121—798no—
1243#121—798no—
1244#121—798no—
1245#121—798no—
1246#121—798no—
1247#121—798no—
1248#121C22×D7912yes—
1249#121C22×D7912yes—
1250#121C22×D7918yes—
1251#121C22×D7918yes—
1252#120—792no—
1253#120—792no—
1254#120—794no—
1255#120—794no—
1256#120—798no—
1257#120—798no—
1258#120—794no—
1259#120—798no—
1260#120—798no—
1261#120—794no—
1262#120—798no—
1263#120C22×D7912yes—
1264#120C22×D7912yes—
1265#120C22×D7918yes—
1266C4×Q8—792no—
1267C4×Q8—792no—
1268C4×Q8—794no—
1269C4×Q8—794no—
1270C4×Q8—794no—
1271C4×Q8—792no—
1272C4×Q8—792no—
1273C4×Q8—794no—
1274C4×Q8—794no—
1275C4×Q8—798no—
1276C4×Q8—794no—
1277C4×Q8—794no—
1278C4×Q8—794no—
1279C4×D4—794no—
1280C4×D4—794no—
1281C4×D4—794no—
1282C4×D4—794no—
1283C4×D4—792no—
1284C4×D4—792no—
1285C4×D4—798no—
1286C4×D4—798no—
1287C4×D4—798no—
1288C4×D4—798no—
1289C4×D4—794no—
1290C4×D4—794no—
1291C4×D4—794no—
1292C4×D4—794no—
1293C4×D4—798no—
1294C4×D4—798no—
1295C4×D4—798no—
1296C4×D4—798no—
1297C4×D4—798no—
1298C4×D4—798no—
1299C4×D4—792no—
1300C4×D4—792no—
1301C4×D4—794no—
1302C4×D4—798no—
1303C4×D4—798no—
1304C4×D4—794no—
1305C4×D4—794no—
1306C4×D4—794no—
1307C4×D4—794no—
1308C4×D4—794no—
1309C4×D4—794no—
1310C4×D4—798no—
1311C4×D4—798no—
1312C4×D4—798no—
1313C4×D4—794no—
1314C4×D4C22×D7914yes—
1315C4×D4C22×D7914yes—
1316C4×D4C22×D7914yes—
1317C4×D4C22×D7914yes—
1318#117—791no—
1319#117—791no—
1320#117—792no—
1321#117—792no—
1322#117—794no—
1323#117—798no—
1324#117—794no—
1325#117—794no—
1326#117—798no—
1327#117—794no—
1328#117—794no—
1329#117—794no—
1330#117—794no—
1331#117—798no—
1332#117—794no—
1333#117—792no—
1334#117—792no—
1335#117C22×D7911yescharacteristic
1336#117C22×D7911yescharacteristic
1337C2×C4⋊C4—794no—
1338C2×C4⋊C4—798no—
1339C2×C4⋊C4—798no—
1340C2×C4⋊C4C22×D7918yes—
1341C2×C22⋊C4—794no—
1342C2×C22⋊C4—798no—
1343C2×C22⋊C4—794no—
1344C2×C22⋊C4—794no—
1345C2×C22⋊C4—798no—
1346C2×C22⋊C4—798no—
1347C2×C22⋊C4C22×D7918yes—
1348C2×C22⋊C4C22×D7914yes—
1349C2×C42—792no—
1350C2×C42—792no—
1351C2×C42—792no—
1352C2×C42—791no—
1353C2×C42—792no—
1354C2×C42—791no—
1355C2×C42—792no—
1356C2×C42—792no—
1357C2×C42—792no—
1358C2×C42—792no—
1359C2×C42—792no—
1360C24—794no—
1361C24—792no—
1362C24C23×D7912yes—
1363C24C23×D7911yescharacteristic
1364C24C23×D7914yes—
1365#41—24no—
1366#41—24no—
1367#41—48no—
1368#41—48no—
1369#41—44no—
1370#41—44no—
1371#41—3168no—
1372#41—3168no—
1373#41—3164no—
1374#41—3164no—
1375#41—3168no—
1376#41—31616no—
1377#41—3164no—
1378#41—3168no—
1379#41—3168no—
1380#41—3164no—
1381#41—3164no—
1382#41—3164no—
1383#41—3168no—
1384#41—1584no—
1385#41—1584no—
1386C2×Q8—24no—
1387C2×Q8—3164no—
1388C2×Q8—3164no—
1389C2×Q8—3164no—
1390C2×Q8—3164no—
1391C2×Q8—794no—
1392C2×Q8—794no—
1393C2×Q8—794no—
1394C2×Q8—794no—
1395C2×Q8—791no—
1396C2×Q8—791no—
1397C2×Q8—792no—
1398C2×Q8—792no—
1399C2×Q8—1584no—
1400C2×Q8C23×D7911yescharacteristic
1401C2×Q8C23×D7912yes—
1402C2×Q8C23×D7912yes—
1403C2×Q8C23×D7911yescharacteristic
1404C2×D4—24no—
1405C2×D4—44no—
1406C2×D4—44no—
1407C2×D4—44no—
1408C2×D4—48no—
1409C2×D4—3164no—
1410C2×D4—3168no—
1411C2×D4—3164no—
1412C2×D4—3164no—
1413C2×D4—3168no—
1414C2×D4—31616no—
1415C2×D4—794no—
1416C2×D4—794no—
1417C2×D4—798no—
1418C2×D4—798no—
1419C2×D4—798no—
1420C2×D4—798no—
1421C2×D4—794no—
1422C2×D4—794no—
1423C2×D4—794no—
1424C2×D4—798no—
1425C2×D4—798no—
1426C2×D4—794no—
1427C2×D4—792no—
1428C2×D4—792no—
1429C2×D4—798no—
1430C2×D4—794no—
1431C2×D4—794no—
1432C2×D4—791no—
1433C2×D4—792no—
1434C2×D4—792no—
1435C2×D4—791no—
1436C2×D4—1584no—
1437C2×D4C23×D7912yes—
1438C2×D4C23×D7912yes—
1439C2×D4C23×D7911yescharacteristic
1440C2×D4C23×D7911yescharacteristic
1441C2×D4C23×D7912yes—
1442C2×D4C23×D7912yes—
1443C2×D4C23×D7914yes—
1444C2×D4C23×D7914yes—
1445C2×D4C23×D7914yes—
1446C2×D4C23×D7918yes—
1447C2×D4C23×D7914yes—
1448C22×C4—24no—
1449C22×C4—44no—
1450C22×C4—3164no—
1451C22×C4—3164no—
1452C22×C4—792no—
1453C22×C4—792no—
1454C22×C4—792no—
1455C22×C4—794no—
1456C22×C4—794no—
1457C22×C4—794no—
1458C22×C4—798no—
1459C22×C4—794no—
1460C22×C4—798no—
1461C22×C4—794no—
1462C22×C4—794no—
1463C22×C4—794no—
1464C22×C4—792no—
1465C22×C4—792no—
1466C22×C4—792no—
1467C22×C4—794no—
1468C22×C4—792no—
1469C22×C4—794no—
1470C22×C4—792no—
1471C22×C4—792no—
1472C22×C4C23×D7912yes—
1473C22×C4C23×D7912yes—
1474C22×C4C23×D7911yescharacteristic
1475C22×C4C23×D7912yes—
1476C22×C4C23×D7912yes—
1477C22×C4C23×D7912yes—
1478C22×C4C23×D7918yes—
1479C22×C4C23×D7918yes—
1480C22×C4C23×D7914yes—
1481C22×C4C23×D7911yescharacteristic
1482C4⋊C4—794no—
1483C4⋊C4—798no—
1484C4⋊C4—794no—
1485C4⋊C4—798no—
1486C4⋊C4—798no—
1487C4⋊C4—794no—
1488C4⋊C4—794no—
1489C4⋊C4—794no—
1490C4⋊C4—794no—
1491C4⋊C4—794no—
1492C4⋊C4—794no—
1493C4⋊C4—794no—
1494C4⋊C4—794no—
1495C4⋊C4—798no—
1496C4⋊C4—798no—
1497C4⋊C4—794no—
1498C4⋊C4—792no—
1499C4⋊C4—792no—
1500C4⋊C4—794no—
1501C4⋊C4—794no—
1502C4⋊C4—794no—
1503C4⋊C4—798no—
1504C4⋊C4C23×D7914yes—
1505C4⋊C4C23×D7918yes—
1506C4⋊C4C23×D7914yes—
1507C4⋊C4C23×D7918yes—
1508C4⋊C4C23×D7912yes—
1509C4⋊C4C23×D7912yes—
1510C22⋊C4—794no—
1511C22⋊C4—792no—
1512C22⋊C4—798no—
1513C22⋊C4—798no—
1514C22⋊C4—798no—
1515C22⋊C4—798no—
1516C22⋊C4—792no—
1517C22⋊C4—794no—
1518C22⋊C4—798no—
1519C22⋊C4—794no—
1520C22⋊C4—794no—
1521C22⋊C4—794no—
1522C22⋊C4—794no—
1523C22⋊C4—794no—
1524C22⋊C4—798no—
1525C22⋊C4—798no—
1526C22⋊C4—798no—
1527C22⋊C4—798no—
1528C22⋊C4—798no—
1529C22⋊C4—794no—
1530C22⋊C4—794no—
1531C22⋊C4—798no—
1532C22⋊C4—794no—
1533C22⋊C4—794no—
1534C22⋊C4—794no—
1535C22⋊C4C23×D7914yes—
1536C22⋊C4C23×D7912yes—
1537C22⋊C4C23×D7918yes—
1538C22⋊C4C23×D7912yes—
1539C22⋊C4C23×D7914yes—
1540C22⋊C4C23×D7918yes—
1541C22⋊C4C23×D7918yes—
1542C22⋊C4C23×D7914yes—
1543C22⋊C4C23×D7914yes—
1544C42—791no—
1545C42—791no—
1546C42—792no—
1547C42—792no—
1548C42—791no—
1549C42—791no—
1550C42—792no—
1551C42—792no—
1552C42—792no—
1553C42—792no—
1554C42—794no—
1555C42—794no—
1556C42—794no—
1557C42—792no—
1558C42—794no—
1559C42—792no—
1560C42—798no—
1561C42—798no—
1562C42C23×D7912yes—
1563C42C23×D7912yes—
1564C23—22no—
1565C23—24no—
1566C23—42no—
1567C23—44no—
1568C23—44no—
1569C23—48no—
1570C23—3164no—
1571C23—3164no—
1572C23—3168no—
1573C23—794no—
1574C23—792no—
1575C23—792no—
1576C23—1584no—
1577C23C24×D7912yes—
1578C23C24×D7914yes—
1579C23C24×D7912yes—
1580C23C24×D7912yes—
1581C23C24×D7911yescharacteristic
1582Q8—24no—
1583Q8—24no—
1584Q8—22no—
1585Q8—22no—
1586Q8—3164no—
1587Q8—3164no—
1588Q8—3164no—
1589Q8—1588no—
1590Q8—1582no—
1591Q8—1582no—
1592Q8—1584no—
1593Q8—1584no—
1594D4—24no—
1595D4—24no—
1596D4—24no—
1597D4—24no—
1598D4—22no—
1599D4—22no—
1600D4—44no—
1601D4—44no—
1602D4—48no—
1603D4—44no—
1604D4—44no—
1605D4—3164no—
1606D4—3164no—
1607D4—3168no—
1608D4—3164no—
1609D4—3168no—
1610D4—3168no—
1611D4—3168no—
1612D4—3168no—
1613D4—3168no—
1614D4—3164no—
1615D4—3164no—
1616D4—3164no—
1617D4—3164no—
1618D4—15816no—
1619D4—1588no—
1620D4—1584no—
1621D4—1584no—
1622D4—1582no—
1623D4—1584no—
1624D4—1584no—
1625D4—1582no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—24no—
1632C2×C4—48no—
1633C2×C4—44no—
1634C2×C4—48no—
1635C2×C4—3168no—
1636C2×C4—3164no—
1637C2×C4—3164no—
1638C2×C4—3164no—
1639C2×C4—3164no—
1640C2×C4—3168no—
1641C2×C4—3164no—
1642C2×C4—3162no—
1643C2×C4—3162no—
1644C2×C4—3162no—
1645C2×C4—3164no—
1646C2×C4—3164no—
1647C2×C4—792no—
1648C2×C4—792no—
1649C2×C4—794no—
1650C2×C4—792no—
1651C2×C4—794no—
1652C2×C4—792no—
1653C2×C4—792no—
1654C2×C4—794no—
1655C2×C4—792no—
1656C2×C4—1588no—
1657C2×C4—1584no—
1658C2×C4—1584no—
1659C2×C4—1584no—
1660C2×C4—1588no—
1661C2×C4—1584no—
1662C2×C4—1584no—
1663C2×C4—1584no—
1664C2×C4#1457920614yes—
1665C2×C4C24×D7912yes—
1666C2×C4C24×D7914yes—
1667C2×C4C24×D7912yes—
1668C2×C4C24×D7914yes—
1669C2×C4C24×D7912yes—
1670C2×C4C24×D7914yes—
1671C2×C4C24×D7911yescharacteristic
1672C2×C4C24×D7911yescharacteristic
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—24no—
1678C22—28no—
1679C22—22no—
1680C22—22no—
1681C22—24no—
1682C22—24no—
1683C22—44no—
1684C22—84no—
1685C22—164no—
1686C22—6324no—
1687C22—1582no—
1688C22—1584no—
1689C22—1582no—
1690C22—1588no—
1691C22—1584no—
1692C22—1584no—
1693C22—12644no—
1694C22C2×#1457920612yes—
1695C22C25×D7911yescharacteristic
1696C4—22no—
1697C4—22no—
1698C4—22no—
1699C4—24no—
1700C4—24no—
1701C4—24no—
1702C4—794no—
1703C4—1584no—
1704C4—1582no—
1705C4—1582no—
1706C4—1582no—
1707C4—1584no—
1708C4—1582no—
1709C4—1582no—
1710C4—1584no—
1711C4C2×#1457920612yes—
1712C4C2×#1457920612yes—
1713C2—22no—
1714C2—42no—
1715C2—44no—
1716C2—42no—
1717C2—42no—
1718C2—3164no—
1719C2—3162no—
1720C2—3162no—
1721C2C22×#1457920611yescharacteristic
1722C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3485C2
hypercenter#3485D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #23777993C2semidirect
2. #23777982C2semidirect
3. #23777866C2semidirect
4. #23777767C2semidirect
5. #23777711C2semidirect
6. #23777405C2semidirect
7. #23777358C2semidirect
8. #23777332C2semidirect
9. #23777310C2semidirect
10. #23777299C2semidirect
11. #23777291C2semidirect
12. #23777285C2semidirect
13. #23777271C2semidirect
14. #23777268C2semidirect
15. #23777189C2semidirect
16. #23777188C2semidirect
17. #23777182C2semidirect
18. #23777174C2semidirect
19. #23777058C2semidirect
20. #23777054C2semidirect
21. #23777042C2semidirect
22. #23776692C2semidirect
23. #23776692C2semidirect
24. C2×#19099109C2semidirect
25. C79×#3485C2semidirect
26. C2×#14579209C22semidirect
27. C2×#14579208C22semidirect
29. C22×#11929624C22semidirect
30. #19099310C22semidirect
31. #19099308C22semidirect
32. #19099302C22semidirect
33. #19099301C22semidirect
34. #19099297C22semidirect
35. #19099296C22semidirect
36. #19099296C22semidirect
37. #19099295C22semidirect
38. #19099288C22semidirect
39. #19099287C22semidirect
40. #19099283C22semidirect
41. #19099282C22semidirect
42. #19099277C22semidirect
43. #19099268C22semidirect
44. #19099261C22semidirect
45. #19099258C22semidirect
46. #19099258C22semidirect
47. #19099258C22semidirect
48. #19099250C22semidirect
49. #19099241C22semidirect
50. #19099239C22semidirect
51. #19099239C22semidirect
52. #19099236C22semidirect
53. #19099234C22semidirect
54. #19099234C22semidirect
55. #19099232C22semidirect
56. #19099232C22semidirect
57. #19099232C22semidirect
58. #19099231C22semidirect
59. #19099231C22semidirect
60. #19099226C22semidirect
61. #19099223C22semidirect
62. #19099223C22semidirect
63. #19099222C22semidirect
64. #19099220C22semidirect
65. #19099220C22semidirect
66. #19099220C22semidirect
67. #19099218C22semidirect
68. #19099215C22semidirect
69. #19099215C22semidirect
70. #19099211C22semidirect
71. #19099210C22semidirect
72. #19099209C22semidirect
73. #19099207C22semidirect
74. #19099207C22semidirect
75. #19099205C22semidirect
76. #19099204C22semidirect
77. #19099203C22semidirect
78. #19099203C22semidirect
79. #19099200C22semidirect
81. D4×C22⋊D79C22semidirect
82. #19099186C22semidirect
83. #19099181C22semidirect
84. #19099181C22semidirect
85. #19099178C22semidirect
86. #19099173C22semidirect
87. #19099166C22semidirect
88. #19099165C22semidirect
89. #19099165C22semidirect
90. #19099164C22semidirect
91. #19099163C22semidirect
92. #19099160C22semidirect
93. #19099156C22semidirect
94. #19099151C22semidirect
95. #19099149C22semidirect
96. #19099148C22semidirect
97. #19099145C22semidirect
98. #19099142C22semidirect
99. #19099139C22semidirect
100. #19099138C22semidirect
101. #19099138C22semidirect
103. #19099134C22semidirect
104. #19099133C22semidirect
105. #19099132C22semidirect
106. #19099131C22semidirect
108. #19099130C22semidirect
109. #19099130C22semidirect
110. #19099130C22semidirect
111. #19099130C22semidirect
112. #19099128C22semidirect
113. #19099128C22semidirect
115. #19099127C22semidirect
116. #19099123C22semidirect
117. #19099116C22semidirect
118. #19099116C22semidirect
119. #19099115C22semidirect
120. #19099115C22semidirect
121. #19099115C22semidirect
122. #19099114C22semidirect
123. #19099112C22semidirect
124. #19099110C22semidirect
127. #19099109C22semidirect
128. #19099109C22semidirect
129. #19099109C22semidirect
130. #19099109C22semidirect
131. #19099109C22semidirect
132. #19099109C22semidirect
133. #19099108C22semidirect
134. #19099108C22semidirect
135. C2×#14579159C22semidirect
136. C4⋊Q8×D79C22semidirect
138. C2×#14579157C22semidirect
139. #19099099C22semidirect
140. #19099099C22semidirect
141. #19099099C22semidirect
142. #19099095C22semidirect
143. #19099094C22semidirect
144. #19099094C22semidirect
145. #19099093C22semidirect
146. #19099093C22semidirect
147. #19099090C22semidirect
148. #19099090C22semidirect
149. C2×#14579150C22semidirect
150. C2×#14579148C22semidirect
151. C2×#14579148C22semidirect
152. #124×D79C22semidirect
153. #19099074C22semidirect
154. #19099074C22semidirect
155. #19099074C22semidirect
156. #19099071C22semidirect
157. #19099069C22semidirect
158. #19099069C22semidirect
159. #123×D79C22semidirect
160. C2×#14579133C22semidirect
161. #19099044C22semidirect
162. #19099041C22semidirect
163. #19099040C22semidirect
164. #19099037C22semidirect
165. #19099036C22semidirect
167. #41×Dic79C22semidirect
168. #19099031C22semidirect
169. #19099031C22semidirect
170. C4×#11929623C22semidirect
171. C4×#11929623C22semidirect
172. C2×C4×C22⋊D79C22semidirect
173. C22×C4×Dic79C22semidirect
175. C22×#41×C79C22semidirect
176. #547×C79C22semidirect
177. #547×C79C22semidirect
178. #546×C79C22semidirect
179. #546×C79C22semidirect
181. #536×C79C22semidirect
182. #534×C79C22semidirect
184. #525×C79C22semidirect
185. C2×#123×C79C22semidirect
186. #518×C79C22semidirect
883. #3485D79semidirect
887. C79#62836semidirect
893. C22×#41C2×D79semidirect
935. #547C2×D79semidirect
936. #547C2×D79semidirect
946. #546C2×D79semidirect
947. #546C2×D79semidirect
974. #536C2×D79semidirect
987. #534C2×D79semidirect
1031. #525C2×D79semidirect
1033. C2×#123C2×D79semidirect
1040. #518C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779932
#237779822
#237778662
#237777672
#237777112
#237774052
#237773582
#237773322
#237773102
#237772992
#237772912
#237772852
#237772712
#237772682
#237771892
#237771882
#237771822
#237771742
#237770582
#237770542
#237770422
#237766922
C2×#190991092
C79×#34852
#6283679