Finite Group Databasebeta

← #35196998

Subgroups — #35196998

Order 20224.

6530 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778002C214yesmaximal, complemented
2#23777996C214yesmaximal, complemented
3#23777935C214yesmaximal, complemented
4#23777933C214yesmaximal, complemented
5#23777852C218yesmaximal, complemented
6#23777381C214yesmaximal, complemented
7#23777377C214yesmaximal, complemented
8#23777373C214yesmaximal, complemented
9#23777372C214yesmaximal, complemented
10#23777324C211yesmaximal, characteristic, complemented
11#23777322C211yesmaximal, characteristic, complemented
12#23777317C212yesmaximal, complemented
13#23777223C212yesmaximal, complemented
14#23777221C211yesmaximal, characteristic, complemented
15#23777110C212yesmaximal, complemented
16#23777108C218yesmaximal, complemented
17#23777103C212yesmaximal, complemented
18#23776697C211yesmaximal, characteristic, complemented
19#23776693C211yesmaximal, characteristic, complemented
20C2×#125×D79C211yesmaximal, characteristic, complemented
21C79×#3504C211yesmaximal, characteristic, complemented
22C79⋊#564C2218yescomplemented
23#19099314C2218yescomplemented
24#19099312C2218yescomplemented
25#19099309C2218yescomplemented
26#19099291C2214yescomplemented
27#19099290C2214yescomplemented
28#19099288C2214yescomplemented
29#19099274C2214yes—
30#19099274C2214yes—
31#19099274C2214yescomplemented
32#19099273C2214yes—
33#19099273C2214yescomplemented
34#19099271C2218yes—
35#19099269C2214yescomplemented
36#19099268C2214yes—
37#19099267C2218yes—
38#19099267C2218yes—
39#19099266C2214yes—
40#19099266C2214yes—
41#19099266C2214yescomplemented
42#19099263C2214yes—
43#19099263C2214yescomplemented
44#19099262C2218yes—
45#19099262C2218yes—
46#19099261C2218yes—
47#19099261C2214yescomplemented
48#19099259C2218yes—
49#19099257C2214yes—
50#19099257C2214yescomplemented
51#19099254C2214yes—
52#19099254C2218yes—
53#19099254C2214yescomplemented
54#19099254C2218yescomplemented
55#19099252C2214yes—
56#19099252C2214yescomplemented
57#19099251C2214yes—
58#19099251C2214yes—
59#19099251C2214yescomplemented
60#19099248C2214yescomplemented
61#19099248C2218yescomplemented
62#19099247C2218yes—
63#19099247C2218yescomplemented
64#19099245C2218yes—
65#19099245C2218yes—
66#19099245C2218yescomplemented
67#19099218C2214yes—
68#19099216C2218yes—
69#19099216C2214yes—
70#19099216C2214yes—
71#19099215C2218yes—
72#19099215C2218yes—
73#19099214C2214yes—
74#19099214C2218yes—
75#19099193C2214yescomplemented
76#19099191C2212yes—
77#19099190C2218yes—
78#19099190C2214yescomplemented
79#19099190C2214yescomplemented
80#19099176C2212yescomplemented
81#19099175C2212yescomplemented
82#19099174C2218yescomplemented
83#19099173C2218yescomplemented
84#19099172C2218yescomplemented
85#19099171C2214yescomplemented
86#19099171C2218yescomplemented
87#19099169C2212yescomplemented
88#19099168C2212yescomplemented
89#19099164C2214yescomplemented
90#19099162C2218yes—
91#19099161C2218yes—
92#19099161C2218yes—
93#19099161C2218yescomplemented
94#19099160C2218yescomplemented
95#19099159C2218yes—
96#19099159C2218yes—
97#19099159C2218yescomplemented
98#19099159C2218yescomplemented
99#19099155C2218yes—
100#19099144C2212yes—
101#19099143C2218yes—
102#19099141C2212yes—
103#19099119C2212yescomplemented
104#19099118C2212yes—
105#19099118C2214yescomplemented
106#19099117C2212yes—
107#19099116C2211yescharacteristic
108#19099114C2212yes—
109#19099113C2211yescharacteristic
110#19099110C2212yes—
111#19099109C2211yescharacteristic
112#19099100C2212yes—
113#19099100C2214yes—
114#19099100C2214yescomplemented
115#19099099C2214yes—
116#19099098C2212yes—
117#19099098C2212yes—
118#19099098C2214yescomplemented
119#19099097C2214yescomplemented
120#19099095C2212yes—
121#19099095C2214yescomplemented
122#19099093C2214yes—
123#19099091C2214yes—
124C2×#14579153C2211yescharacteristic
125C2×#14579152C2212yes—
126C2×#14579151C2214yes—
127#125×D79C2214yes—
128#125×D79C2214yes—
129#125×D79C2214yes—
130#125×D79C2214yes—
131#125×D79C2212yescomplemented
132#125×D79C2214yescomplemented
133#19099076C2218yes—
134#19099076C2214yes—
135#19099075C2212yes—
136#19099075C2211yescharacteristic
137#19099072C2218yes—
138#19099072C2214yes—
139#19099070C2211yescharacteristic
140#19099045C2218yes—
141#19099044C2212yes—
142#19099044C2218yes—
143#19099043C2212yes—
144#19099043C2212yes—
145C4×#11929625C2214yes—
146C4×#11929624C2211yescharacteristic
147C4×#11929624C2214yes—
148#19099031C2212yes—
149C2×C4⋊C4×D79C2212yes—
150C2×C4⋊C4×D79C2214yes—
151C2×C42×D79C2211yescharacteristic
152#557×C79C2214yescomplemented
153#554×C79C2218yes—
154#554×C79C2214yescomplemented
155#544×C79C2212yes—
156#544×C79C2214yescomplemented
157#533×C79C2211yescharacteristic
158#533×C79C2212yescomplemented
159C2×#125×C79C2211yescharacteristic
160C2×#125×C79C2212yescomplemented
161#520×C79C2212yes—
162C4×#41×C79C2211yescharacteristic
163C2×#11929625C2318yes—
164C2×#11929625C2314yes—
165C2×#11929624C2312yes—
166C2×#11929624C2311yescharacteristic
167C2×#11929624C2318yes—
168C2×#11929624C2314yes—
169C22×C4×D79C2311yescharacteristic
170C22×C4×D79C2312yes—
171C22×C4×D79C2314yes—
172#14579161C2311yescharacteristic
173#14579161C2314yes—
174#14579160C2318yes—
175#14579160C2312yes—
176#14579160C2314yes—
177#14579159C2311yescharacteristic
178#14579159C2318yes—
179#14579159C2318yes—
180#14579158C2311yescharacteristic
181#14579157C2311yescharacteristic
182#14579156C2318yes—
183#14579156C2318yes—
184#14579156C2314yes—
185#14579156C2318yes—
186#14579156C2314yes—
187#14579156C2318yes—
188#14579156C2318yes—
189#14579156C2318yes—
190#14579156C2314yes—
191#14579155C2318yes—
192#14579155C2318yes—
193#14579155C2318yes—
194#14579154C2318yes—
195#14579154C2318yes—
196#14579154C2318yes—
197#14579154C2314yes—
198#14579153C2318yes—
199#14579153C2312yes—
200#14579153C2318yes—
201#14579153C2314yes—
202#14579153C2314yes—
203#14579153C2312yes—
204#14579152C2318yes—
205#14579152C2318yes—
206#14579152C2314yes—
207#14579152C2318yes—
208#14579152C2314yes—
209#14579152C2314yes—
210#14579152C2314yes—
211#14579152C2314yes—
212#14579152C2314yes—
213#14579152C2312yes—
214#14579151C2318yes—
215#14579151C2318yes—
216#14579151C2318yes—
217#14579151C2318yes—
218#14579151C2318yes—
219#14579151C2318yes—
220#14579151C2318yes—
221#14579151C2318yes—
222#14579151C2318yes—
223#14579151C2318yes—
224#14579151C2318yes—
225#14579151C2318yes—
226#14579151C2318yes—
227#14579151C2314yes—
228#14579150C2314yes—
229#14579150C2311yescharacteristic
230#14579149C2312yes—
231#14579148C2311yescharacteristic
232#14579147C2314yes—
233#14579146C2318yes—
234#14579146C2318yes—
235#14579146C2318yes—
236#14579146C2318yes—
237#14579146C2318yes—
238#14579146C2318yes—
239#14579146C2318yes—
240#14579146C2318yes—
241#14579146C2318yes—
242#14579146C2314yes—
243#14579146C2314yes—
244#14579146C2314yes—
245#14579145C2314yes—
246#14579145C2312yes—
247#14579144C2318yes—
248#14579144C2318yes—
249#14579144C2318yes—
250#14579143C2318yes—
251#14579143C2318yes—
252#14579143C2318yes—
253#14579143C2318yes—
254#14579143C2314yes—
255#14579142C2312yes—
256#14579141C2314yes—
257#14579141C2314yes—
258#14579141C2318yes—
259#14579141C2318yes—
260#14579141C2312yes—
261#14579141C2312yes—
262#14579141C2312yes—
263#14579140C2314yes—
264#14579140C2318yes—
265#14579139C2318yes—
266#14579139C2318yes—
267#14579139C2318yes—
268#14579139C2318yes—
269#14579139C2314yes—
270#14579139C2318yes—
271#14579139C2318yes—
272#14579138C2318yes—
273#14579138C2314yes—
274#14579137C2314yes—
275#14579137C2318yes—
276#14579137C2314yes—
277#14579137C2318yes—
278#14579137C2318yes—
279#14579137C2318yes—
280#14579137C2318yes—
281#14579137C2318yes—
282#14579137C2312yes—
283#14579136C2314yes—
284#14579136C2318yes—
285#14579136C2318yes—
286#14579136C2314yes—
287#14579136C2314yes—
288#14579136C2312yes—
289#14579136C2312yes—
290#14579136C2312yes—
291#14579135C2314yes—
292#14579135C2318yes—
293#14579135C2318yes—
294#14579135C2314yes—
295#14579134C2314yes—
296#14579134C2318yes—
297#14579134C2318yes—
298#14579134C2318yes—
299#14579133C2318yes—
300#14579133C2314yes—
301#14579132C2314yes—
302#14579132C2312yes—
303#14579131C2314yes—
304#14579131C2312yes—
305#14579129C2312yes—
306Q8×Dic79C2314yes—
307Q8×Dic79C2318yes—
308C4×Dic158C2314yes—
309C4×Dic158C2314yes—
310C4×Dic158C2314yes—
311C4×Dic158C2312yes—
312C4×Dic158C2314yes—
313#14579126C2318yes—
314#14579126C2318yes—
315#14579126C2314yes—
316#14579126C2312yes—
317#14579126C2312yes—
318C4×D316C2314yes—
319C4×D316C2318yes—
320C4×D316C2318yes—
321C4×D316C2314yes—
322C4×D316C2314yes—
323C4×D316C2314yes—
324C4×D316C2314yes—
325C4×D316C2314yes—
326C4×D316C2314yes—
327C4×D316C2312yes—
328#14579123C2314yes—
329#14579123C2318yes—
330#14579123C2314yes—
331#14579123C2318yes—
332#14579123C2314yes—
333#14579123C2318yes—
334#14579123C2314yes—
335#14579123C2312yes—
336#14579123C2312yes—
337C4×C22⋊D79C2318yes—
338C4×C22⋊D79C2314yes—
339C4×C22⋊D79C2318yes—
340C4×C22⋊D79C2314yes—
341C4×C22⋊D79C2318yes—
342C4×C22⋊D79C2318yes—
343C4×C22⋊D79C2314yes—
344C4×C22⋊D79C2314yes—
345C4×C22⋊D79C2314yes—
346(C22⋊D79)⋊C4C2318yes—
347(C22⋊D79)⋊C4C2318yes—
348(C22⋊D79)⋊C4C2314yes—
349(C22⋊D79)⋊C4C2314yes—
350#14579120C2318yes—
351#14579120C2311yescharacteristic
352#14579120C2314yes—
353#14579119C2318yes—
354#14579119C2318yes—
355#14579119C2314yes—
356#14579119C2314yes—
357#14579119C2314yes—
358#14579119C2314yes—
359#14579119C2314yes—
360#14579119C2314yes—
361#14579118C2314yes—
362#14579118C2312yes—
363#14579118C2318yes—
364#14579118C2318yes—
365#14579118C2318yes—
366#14579118C2314yes—
367#14579118C2314yes—
368C2×C4⋊Dic79C2312yes—
369C2×C4⋊Dic79C2314yes—
370C2×Dic79⋊C4C2314yes—
371C2×Dic79⋊C4C2314yes—
372C2×Dic79⋊C4C2314yes—
373C4⋊C4×D79C2318yes—
374C4⋊C4×D79C2318yes—
375C4⋊C4×D79C2318yes—
376C4⋊C4×D79C2318yes—
377C4⋊C4×D79C2318yes—
378C4⋊C4×D79C2314yes—
379C4⋊C4×D79C2314yes—
380C4⋊C4×D79C2314yes—
381C4⋊C4×D79C2318yes—
382C4⋊C4×D79C2314yes—
383C4⋊C4×D79C2318yes—
384C4⋊C4×D79C2314yes—
385C4⋊C4×D79C2314yes—
386C4⋊C4×D79C2314yes—
387C2×C4×Dic79C2311yescharacteristic
388C2×C4×Dic79C2312yes—
389C42×D79C2312yes—
390C42×D79C2312yes—
391C42×D79C2312yes—
392C42×D79C2312yes—
393C42×D79C2314yes—
394C42×D79C2312yes—
395C2×#41×C79C2311yescharacteristic
396C4⋊Q8×C79C2318yes—
397C4⋊Q8×C79C2312yes—
398C4⋊Q8×C79C2314yes—
399C4⋊Q8×C79C2314yes—
400#125×C79C2318yes—
401#125×C79C2318yes—
402#125×C79C2312yes—
403#125×C79C2314yes—
404#125×C79C2312yes—
405#125×C79C2314yes—
406#125×C79C2311yescharacteristic
407#125×C79C2314yes—
408#125×C79C2311yescharacteristic
409C22⋊Q8×C79C2318yes—
410C22⋊Q8×C79C2318yes—
411C22⋊Q8×C79C2318yes—
412C22⋊Q8×C79C2318yes—
413C22⋊Q8×C79C2314yes—
414C4×Q8×C79C2314yes—
415C4×Q8×C79C2318yes—
416C4×Q8×C79C2312yes—
417C4×Q8×C79C2314yes—
418C4×D4×C79C2318yes—
419C4×D4×C79C2314yes—
420C4×D4×C79C2314yes—
421C4×D4×C79C2312yes—
422#117×C79C2312yes—
423#117×C79C2312yes—
424#117×C79C2311yescharacteristic
425#117×C79C2314yes—
426C2×C4⋊C4×C79C2312yes—
427C2×C4⋊C4×C79C2318yes—
428C2×C4⋊C4×C79C2314yes—
429C2×C4⋊C4×C79C2314yes—
430C2×C42×C79C2311yescharacteristic
431C2×C42×C79C2312yes—
432C23×D79C2411yescharacteristic
433#11929625—416no—
434#11929625—48no—
435#11929624—28no—
436#11929624—24no—
437#11929624—48no—
438#11929624—416no—
439C2×Dic158C2412yes—
440C2×Dic158C2411yescharacteristic
441C2×Dic158C2418yes—
442C2×Dic158C2414yes—
443C2×D316C2414yes—
444C2×D316C2414yes—
445C2×D316C2412yes—
446C2×D316C2411yescharacteristic
447C2×D316C2414yes—
448C2×D316C2414yes—
449C2×D316C2418yes—
450C2×C22⋊D79C2414yes—
451C2×C22⋊D79C2414yes—
452C2×C22⋊D79C2412yes—
453C2×C22⋊D79C2418yes—
454C2×C22⋊D79C2414yes—
455C22×Dic79C2411yescharacteristic
456C22×Dic79C2412yes—
457C22×Dic79C2414yes—
458C2×C4×D79—24no—
459C2×C4×D79—44no—
460C2×C4×D79—48no—
461C2×C4×D79C2412yes—
462C2×C4×D79C2418yes—
463C2×C4×D79C2412yes—
464C2×C4×D79C2414yes—
465C2×C4×D79C2412yes—
466C2×C4×D79C2412yes—
467C2×C4×D79C2412yes—
468C2×C4×D79C2414yes—
469C2×C4×D79C2418yes—
470C2×C4×D79C2414yes—
471C2×C4×D79C2414yes—
472C2×C4×D79C2418yes—
473C2×C4×D79C2418yes—
474C2×C4×D79C2412yes—
475C2×C4×D79C2412yes—
476C2×C4×D79C2418yes—
477C4⋊Dic79C2414yes—
478C4⋊Dic79C2414yes—
479C4⋊Dic79C2418yes—
480C4⋊Dic79C2418yes—
481C4⋊Dic79C2412yes—
482C4⋊Dic79C2414yes—
483C4⋊Dic79C2418yes—
484C4⋊Dic79C2418yes—
485C4⋊Dic79C2414yes—
486C4⋊Dic79C2414yes—
487C4⋊Dic79C2414yes—
488C4⋊Dic79C2414yes—
489Dic79⋊C4C2418yes—
490Dic79⋊C4C2418yes—
491Dic79⋊C4C2418yes—
492Dic79⋊C4C2418yes—
493Dic79⋊C4C2418yes—
494Dic79⋊C4C2418yes—
495Dic79⋊C4C2414yes—
496Dic79⋊C4C2418yes—
497Dic79⋊C4C2418yes—
498Dic79⋊C4C2418yes—
499Dic79⋊C4C2418yes—
500Dic79⋊C4C2418yes—
501Dic79⋊C4C2418yes—
502Dic79⋊C4C2414yes—
503Dic79⋊C4C2414yes—
504Dic79⋊C4C2414yes—
505Dic79⋊C4C2414yes—
506Dic79⋊C4C2414yes—
507Dic79⋊C4C2414yes—
508C22⋊Dic79C2414yes—
509C22⋊Dic79C2412yes—
510C22⋊Dic79C2418yes—
511C22⋊Dic79C2414yes—
512(C2×D79)⋊C4C2414yes—
513(C2×D79)⋊C4C2414yes—
514(C2×D79)⋊C4C2414yes—
515(C2×D79)⋊C4C2414yes—
516(C2×D79)⋊C4C2414yes—
517(C2×D79)⋊C4C2414yes—
518(C2×D79)⋊C4C2414yes—
519(C2×D79)⋊C4C2414yes—
520(C2×D79)⋊C4C2414yes—
521(C2×D79)⋊C4C2418yes—
522(C2×D79)⋊C4C2418yes—
523(C2×D79)⋊C4C2414yes—
524(C2×D79)⋊C4C2414yes—
525(C2×D79)⋊C4C2418yes—
526(C2×D79)⋊C4C2418yes—
527(C2×D79)⋊C4C2418yes—
528(C2×D79)⋊C4C2418yes—
529(C2×D79)⋊C4C2414yes—
530(C2×D79)⋊C4C2414yes—
531C4×Dic79C2411yescharacteristic
532C4×Dic79C2411yescharacteristic
533C4×Dic79C2412yes—
534C4×Dic79C2412yes—
535C4×Dic79C2412yes—
536C4×Dic79C2412yes—
537C4×Dic79C2412yes—
538C4×Dic79C2414yes—
539C4×Dic79C2414yes—
540C4×Dic79C2412yes—
541C4×Dic79C2414yes—
542C4×Dic79C2418yes—
543C4×Dic79C2418yes—
544C4×Dic79C2418yes—
545#41×C79—24no—
546C2×Q8×C79C2411yescharacteristic
547C2×Q8×C79C2418yes—
548C2×Q8×C79C2414yes—
549C2×D4×C79C2412yes—
550C2×D4×C79C2411yescharacteristic
551C22×C4×C79C2412yes—
552C22×C4×C79C2414yes—
553C22×C4×C79C2418yes—
554C22×C4×C79C2412yes—
555C22×C4×C79C2414yes—
556C22×C4×C79C2411yescharacteristic
557C4⋊C4×C79C2414yes—
558C4⋊C4×C79C2412yes—
559C4⋊C4×C79C2418yes—
560C4⋊C4×C79C2414yes—
561C4⋊C4×C79C2414yes—
562C4⋊C4×C79C2418yes—
563C4⋊C4×C79C2418yes—
564C4⋊C4×C79C2418yes—
565C4⋊C4×C79C2418yes—
566C4⋊C4×C79C2412yes—
567C4⋊C4×C79C2412yes—
568C4⋊C4×C79C2414yes—
569C4⋊C4×C79C2414yes—
570C4⋊C4×C79C2418yes—
571C4⋊C4×C79C2414yes—
572C22⋊C4×C79C2414yes—
573C22⋊C4×C79C2412yes—
574C22⋊C4×C79C2414yes—
575C22⋊C4×C79C2418yes—
576C42×C79C2411yescharacteristic
577C42×C79C2411yescharacteristic
578C42×C79C2412yes—
579C42×C79C2412yes—
580C42×C79C2414yes—
581C42×C79C2414yes—
582C42×C79C2418yes—
583C23×C79C2512yes—
584C23×C79C2511yescharacteristic
585C22×D79—22no—
586C22×D79—24no—
587C22×D79C2514yes—
588C22×D79C2512yes—
589C22×D79C2512yes—
590Q8×C79—22no—
591Q8×C79—44no—
592Q8×C79—48no—
593D4×C79—24no—
594D4×C79—22no—
595C2×C4×C79—24no—
596C2×C4×C79—42no—
597C2×C4×C79—44no—
598C2×C4×C79—44no—
599C2×C4×C79—48no—
600C2×C4×C792−1+414yes—
601C2×C4×C79C2512yes—
602C2×C4×C79C2514yes—
603C2×C4×C79C2514yes—
604C2×C4×C79C2512yes—
605C2×C4×C79C2514yes—
606C2×C4×C79C2518yes—
607C2×C4×C79C2512yes—
608C2×C4×C79C2511yescharacteristic
609C2×C4×C79C2511yescharacteristic
610C22⋊D79—28no—
611C22⋊D79—24no—
612C22⋊D79—28no—
613C22⋊D79—44no—
614C22⋊D79—48no—
615C2×Dic79—22no—
616C2×Dic79—42no—
617C2×Dic79—44no—
618C2×Dic79C2512yes—
619C2×Dic79C2514yes—
620C2×Dic79C2512yes—
621C2×Dic79C2512yes—
622C2×Dic79C2514yes—
623C2×Dic79C2512yes—
624C2×Dic79C2518yes—
625D316—28no—
626D316—28no—
627D316—28no—
628D316—24no—
629D316—22no—
630D316—48no—
631D316—44no—
632C4×D79—24no—
633C4×D79—216no—
634C4×D79—24no—
635C4×D79—24no—
636C4×D79—24no—
637C4×D79—24no—
638C4×D79—28no—
639C4×D79—42no—
640C4×D79—48no—
641C4×D79—42no—
642C4×D79—44no—
643C4×D79—48no—
644C4×D79—48no—
645C4×D79—48no—
646C4×D79—44no—
647C4×D79—44no—
648Dic158—24no—
649Dic158—22no—
650Dic158—44no—
651Dic158—48no—
652C22×C79—22no—
653C22×C79—22no—
654C22×C79—24no—
655C22×C79C2×2−1+412yes—
656C22×C79C2611yescharacteristic
657C2×D79—28no—
658C2×D79—22no—
659C2×D79—22no—
660C2×D79—24no—
661C2×D79—22no—
662C2×D79—24no—
663C2×D79—24no—
664C2×D79—24no—
665C2×D79#58514yes—
666C4×C79—22no—
667C4×C79—22no—
668C4×C79—24no—
669C4×C79—28no—
670C4×C79—24no—
671C4×C79—22no—
672C4×C79—24no—
673C4×C79C2×2−1+412yes—
674C4×C79C2×2−1+412yes—
675Dic79—24no—
676Dic79—22no—
677Dic79—22no—
678Dic79—24no—
679Dic79—22no—
680Dic79—28no—
681Dic79—22no—
682#62825—791nomaximal, Sylow
683C2×C79—22no—
684C2×C79—42no—
685C2×C79C22×2−1+411yescharacteristic
686C2×C79C2×#58512yes—
687D79—24no—
688D79—44no—
689D79—42no—
690#3563—794no—
691#3563—794no—
692#3559—794no—
693#3559—794no—
694#3553—798no—
695#3515—794no—
696#3515—794no—
697#3515—794no—
698#3515—794no—
699#3512—791no—
700#3512—792no—
701#3512—791no—
702#3504—792no—
703#3504—791no—
704#3504D7911yescharacteristic, complemented
705#3492—798no—
706#3492—792no—
707#3492—792no—
708#3444—791no—
709#3444—791no—
710C22×#125—791no—
711C79#6282511yescharacteristic, complemented, Sylow
712#564—798no—
713#563—798no—
714#563—798no—
715#562—798no—
716#557—794no—
717#557—794no—
718#557—794no—
719#557C2×D7914yescomplemented
720#554—794no—
721#554—794no—
722#554—794no—
723#554—794no—
724#554—798no—
725#554—798no—
726#554—798no—
727#554—794no—
728#554—794no—
729#554—794no—
730#554C2×D7918yes—
731#554C2×D7914yescomplemented
732#553—794no—
733#553—794no—
734#553—794no—
735#553—798no—
736#553—798no—
737#553—798no—
738#553—794no—
739#553—794no—
740#553—794no—
741#553—794no—
742#553—798no—
743#553—794no—
744#552—798no—
745#552—798no—
746#552—798no—
747#552—794no—
748#552—794no—
749#552—794no—
750#552—798no—
751#552—798no—
752#552—798no—
753#552—794no—
754#552—794no—
755#552—798no—
756#552—794no—
757#552—794no—
758#552—794no—
759#552—798no—
760#547—798no—
761#547—794no—
762#547—794no—
763#547—798no—
764#547—798no—
765#547—794no—
766#547—798no—
767#547—794no—
768#544—798no—
769#544—794no—
770#544—794no—
771#544—794no—
772#544—792no—
773#544C2×D7912yes—
774#544C2×D7914yescomplemented
775#541—798no—
776#541—798no—
777#541—792no—
778#541—798no—
779#541—794no—
780#541—798no—
781#541—792no—
782#540—792no—
783#540—794no—
784#540—792no—
785#539—798no—
786#539—798no—
787#539—798no—
788#539—798no—
789#539—798no—
790#539—798no—
791#539—798no—
792#539—798no—
793#539—798no—
794#539—798no—
795#537—792no—
796#537—798no—
797#537—792no—
798#533—792no—
799#533—794no—
800#533—792no—
801#533—792no—
802#533—791no—
803#533C2×D7911yescharacteristic
804#533C2×D7912yescomplemented
805#532—791no—
806#532—792no—
807#532—792no—
808#532—791no—
809#529—792no—
810#529—792no—
811#529—794no—
812#529—794no—
813#529—792no—
814#529—794no—
815#529—794no—
816#529—792no—
817#529—794no—
818#529—794no—
819#529—794no—
820#529—794no—
821C2×#125—794no—
822C2×#125—794no—
823C2×#125—794no—
824C2×#125—794no—
825C2×#125—794no—
826C2×#125—792no—
827C2×#125—792no—
828C2×#125—794no—
829C2×#125—791no—
830C2×#125C2×D7911yescharacteristic
831C2×#125C2×D7912yescomplemented
832#525—791no—
833#525—794no—
834#525—798no—
835#525—794no—
836#525—798no—
837#525—792no—
838#525—791no—
839#520—798no—
840#520—792no—
841#520—792no—
842#520—792no—
843#520—798no—
844#520C2×D7912yes—
845C4×#41—794no—
846C4×#41—792no—
847C4×#41—791no—
848C4×#41—794no—
849C4×#41C2×D7911yescharacteristic
850C22×C4⋊C4—792no—
851C22×C4⋊C4—794no—
852C22×C42—791no—
853C2×#41—794no—
854C2×#41—798no—
855C2×#41—794no—
856C2×#41—798no—
857C2×#41—792no—
858C2×#41—791no—
859C2×#41C22×D7911yescharacteristic
860C23×C4—794no—
861C23×C4—792no—
862C23×C4—791no—
863C4⋊Q8—791no—
864C4⋊Q8—798no—
865C4⋊Q8—798no—
866C4⋊Q8—792no—
867C4⋊Q8—794no—
868C4⋊Q8—798no—
869C4⋊Q8—791no—
870C4⋊Q8—794no—
871C4⋊Q8C22×D7912yes—
872C4⋊Q8C22×D7914yes—
873C4⋊Q8C22×D7914yes—
874C4⋊Q8C22×D7918yes—
875#127—791no—
876#127—791no—
877#126—794no—
878#126—794no—
879#126—794no—
880#126—798no—
881#126—798no—
882#126—798no—
883#126—798no—
884#126—798no—
885#126—798no—
886#126—794no—
887#126—798no—
888#126—798no—
889#126—798no—
890#126—798no—
891#126—798no—
892#126—798no—
893#125—794no—
894#125—798no—
895#125—798no—
896#125—794no—
897#125—798no—
898#125—794no—
899#125—794no—
900#125—798no—
901#125—792no—
902#125—798no—
903#125—798no—
904#125—798no—
905#125—794no—
906#125—794no—
907#125—794no—
908#125—798no—
909#125—798no—
910#125—798no—
911#125—798no—
912#125—798no—
913#125—798no—
914#125—798no—
915#125—798no—
916#125—798no—
917#125—792no—
918#125—792no—
919#125—794no—
920#125—794no—
921#125—798no—
922#125—798no—
923#125C22×D7912yes—
924#125C22×D7912yes—
925#125C22×D7914yes—
926#125C22×D7911yescharacteristic
927#125C22×D7914yes—
928#125C22×D7911yescharacteristic
929#125C22×D7918yes—
930#125C22×D7914yes—
931#125C22×D7918yes—
932#124—791no—
933#124—794no—
934#124—791no—
935#124—794no—
936#124—792no—
937#123—792no—
938#123—798no—
939#123—798no—
940#123—798no—
941#123—794no—
942#123—794no—
943#123—794no—
944#123—798no—
945#123—798no—
946#123—798no—
947#123—798no—
948#123—798no—
949#123—798no—
950#123—798no—
951#123—798no—
952#123—798no—
953#123—794no—
954#123—792no—
955#123—794no—
956#123—798no—
957#123—798no—
958#123—798no—
959#123—798no—
960C22⋊Q8—794no—
961C22⋊Q8—792no—
962C22⋊Q8—798no—
963C22⋊Q8—794no—
964C22⋊Q8—798no—
965C22⋊Q8—798no—
966C22⋊Q8—798no—
967C22⋊Q8—798no—
968C22⋊Q8—798no—
969C22⋊Q8—794no—
970C22⋊Q8—798no—
971C22⋊Q8—794no—
972C22⋊Q8—792no—
973C22⋊Q8—792no—
974C22⋊Q8—792no—
975C22⋊Q8—798no—
976C22⋊Q8—794no—
977C22⋊Q8—794no—
978C22⋊Q8—798no—
979C22⋊Q8—798no—
980C22⋊Q8—798no—
981C22⋊Q8—798no—
982C22⋊Q8—798no—
983C22⋊Q8—798no—
984C22⋊Q8—798no—
985C22⋊Q8—794no—
986C22⋊Q8—798no—
987C22⋊Q8C22×D7914yes—
988C22⋊Q8C22×D7918yes—
989C22⋊Q8C22×D7918yes—
990C22⋊Q8C22×D7918yes—
991C22⋊Q8C22×D7918yes—
992#121—792no—
993#121—794no—
994#121—798no—
995#121—794no—
996#121—794no—
997#121—798no—
998#121—794no—
999#121—798no—
1000#121—794no—
1001#121—792no—
1002#121—792no—
1003#121—792no—
1004#121—798no—
1005#121—794no—
1006#121—794no—
1007#121—798no—
1008#121—794no—
1009#121—798no—
1010#121—798no—
1011#121—798no—
1012#120—792no—
1013#120—794no—
1014#120—792no—
1015C4×Q8—794no—
1016C4×Q8—798no—
1017C4×Q8—792no—
1018C4×Q8—792no—
1019C4×Q8—794no—
1020C4×Q8—798no—
1021C4×Q8—798no—
1022C4×Q8—794no—
1023C4×Q8—792no—
1024C4×Q8—794no—
1025C4×Q8—794no—
1026C4×Q8—794no—
1027C4×Q8C22×D7914yes—
1028C4×Q8C22×D7912yes—
1029C4×Q8C22×D7918yes—
1030C4×Q8C22×D7914yes—
1031C4×D4—794no—
1032C4×D4—794no—
1033C4×D4—794no—
1034C4×D4—794no—
1035C4×D4—794no—
1036C4×D4—798no—
1037C4×D4—798no—
1038C4×D4—798no—
1039C4×D4—798no—
1040C4×D4—794no—
1041C4×D4—794no—
1042C4×D4—794no—
1043C4×D4—792no—
1044C4×D4—792no—
1045C4×D4—798no—
1046C4×D4—798no—
1047C4×D4—798no—
1048C4×D4—794no—
1049C4×D4—794no—
1050C4×D4—794no—
1051C4×D4—798no—
1052C4×D4—798no—
1053C4×D4—794no—
1054C4×D4—794no—
1055C4×D4—794no—
1056C4×D4—794no—
1057C4×D4—794no—
1058C4×D4—792no—
1059C4×D4—798no—
1060C4×D4—798no—
1061C4×D4—794no—
1062C4×D4—794no—
1063C4×D4C22×D7914yes—
1064C4×D4C22×D7912yes—
1065C4×D4C22×D7918yes—
1066C4×D4C22×D7914yes—
1067#117—791no—
1068#117—794no—
1069#117—798no—
1070#117—794no—
1071#117—794no—
1072#117—794no—
1073#117—798no—
1074#117—798no—
1075#117—794no—
1076#117—794no—
1077#117—794no—
1078#117—794no—
1079#117—794no—
1080#117—792no—
1081#117—794no—
1082#117—798no—
1083#117—798no—
1084#117—798no—
1085#117C22×D7912yes—
1086#117C22×D7911yescharacteristic
1087#117C22×D7912yes—
1088#117C22×D7914yes—
1089C2×C4⋊C4—792no—
1090C2×C4⋊C4—794no—
1091C2×C4⋊C4—794no—
1092C2×C4⋊C4—794no—
1093C2×C4⋊C4—794no—
1094C2×C4⋊C4—798no—
1095C2×C4⋊C4—798no—
1096C2×C4⋊C4—798no—
1097C2×C4⋊C4—798no—
1098C2×C4⋊C4—794no—
1099C2×C4⋊C4—794no—
1100C2×C4⋊C4—794no—
1101C2×C4⋊C4—794no—
1102C2×C4⋊C4—798no—
1103C2×C4⋊C4—798no—
1104C2×C4⋊C4—798no—
1105C2×C4⋊C4—794no—
1106C2×C4⋊C4—794no—
1107C2×C4⋊C4—794no—
1108C2×C4⋊C4C22×D7912yes—
1109C2×C4⋊C4C22×D7914yes—
1110C2×C4⋊C4C22×D7918yes—
1111C2×C4⋊C4C22×D7914yes—
1112C2×C42—791no—
1113C2×C42—792no—
1114C2×C42—794no—
1115C2×C42—792no—
1116C2×C42—792no—
1117C2×C42—792no—
1118C2×C42—792no—
1119C2×C42—792no—
1120C2×C42C22×D7912yes—
1121C2×C42C22×D7911yescharacteristic
1122C24—791no—
1123#41—24no—
1124#41—3168no—
1125#41—31616no—
1126#41—3168no—
1127#41—31616no—
1128#41—1584no—
1129#41—1588no—
1130C2×Q8—798no—
1131C2×Q8—794no—
1132C2×Q8—792no—
1133C2×Q8—791no—
1134C2×Q8C23×D7911yescharacteristic
1135C2×Q8C23×D7918yes—
1136C2×Q8C23×D7914yes—
1137C2×D4—798no—
1138C2×D4—794no—
1139C2×D4—792no—
1140C2×D4—794no—
1141C2×D4—794no—
1142C2×D4—798no—
1143C2×D4—794no—
1144C2×D4—792no—
1145C2×D4—791no—
1146C2×D4—794no—
1147C2×D4—794no—
1148C2×D4—794no—
1149C2×D4C23×D7912yes—
1150C2×D4C23×D7911yescharacteristic
1151C22×C4—3168no—
1152C22×C4—3164no—
1153C22×C4—792no—
1154C22×C4—794no—
1155C22×C4—792no—
1156C22×C4—792no—
1157C22×C4—794no—
1158C22×C4—794no—
1159C22×C4—794no—
1160C22×C4—798no—
1161C22×C4—798no—
1162C22×C4—798no—
1163C22×C4—798no—
1164C22×C4—791no—
1165C22×C4—792no—
1166C22×C4—792no—
1167C22×C4—792no—
1168C22×C4—792no—
1169C22×C4—792no—
1170C22×C4—794no—
1171C22×C4—798no—
1172C22×C4—1584no—
1173C22×C4C23×D7912yes—
1174C22×C4C23×D7912yes—
1175C22×C4C23×D7914yes—
1176C22×C4C23×D7914yes—
1177C22×C4C23×D7918yes—
1178C22×C4C23×D7911yescharacteristic
1179C4⋊C4—798no—
1180C4⋊C4—798no—
1181C4⋊C4—798no—
1182C4⋊C4—798no—
1183C4⋊C4—798no—
1184C4⋊C4—798no—
1185C4⋊C4—794no—
1186C4⋊C4—798no—
1187C4⋊C4—798no—
1188C4⋊C4—798no—
1189C4⋊C4—798no—
1190C4⋊C4—798no—
1191C4⋊C4—798no—
1192C4⋊C4—794no—
1193C4⋊C4—794no—
1194C4⋊C4—794no—
1195C4⋊C4—794no—
1196C4⋊C4—794no—
1197C4⋊C4—794no—
1198C4⋊C4—794no—
1199C4⋊C4—794no—
1200C4⋊C4—798no—
1201C4⋊C4—798no—
1202C4⋊C4—792no—
1203C4⋊C4—794no—
1204C4⋊C4—798no—
1205C4⋊C4—798no—
1206C4⋊C4—794no—
1207C4⋊C4—794no—
1208C4⋊C4—794no—
1209C4⋊C4—794no—
1210C4⋊C4C23×D7914yes—
1211C4⋊C4C23×D7918yes—
1212C4⋊C4C23×D7914yes—
1213C4⋊C4C23×D7918yes—
1214C4⋊C4C23×D7912yes—
1215C4⋊C4C23×D7914yes—
1216C4⋊C4C23×D7912yes—
1217C4⋊C4C23×D7918yes—
1218C4⋊C4C23×D7918yes—
1219C4⋊C4C23×D7912yes—
1220C4⋊C4C23×D7914yes—
1221C4⋊C4C23×D7918yes—
1222C4⋊C4C23×D7918yes—
1223C4⋊C4C23×D7914yes—
1224C4⋊C4C23×D7914yes—
1225C22⋊C4—794no—
1226C22⋊C4—792no—
1227C22⋊C4—798no—
1228C22⋊C4—794no—
1229C22⋊C4—794no—
1230C22⋊C4—794no—
1231C22⋊C4—794no—
1232C22⋊C4—794no—
1233C22⋊C4—794no—
1234C22⋊C4—794no—
1235C22⋊C4—794no—
1236C22⋊C4—794no—
1237C22⋊C4—794no—
1238C22⋊C4—794no—
1239C22⋊C4—798no—
1240C22⋊C4—798no—
1241C22⋊C4—798no—
1242C22⋊C4—798no—
1243C22⋊C4—798no—
1244C22⋊C4—798no—
1245C22⋊C4—794no—
1246C22⋊C4—794no—
1247C22⋊C4—794no—
1248C22⋊C4C23×D7914yes—
1249C22⋊C4C23×D7912yes—
1250C22⋊C4C23×D7914yes—
1251C22⋊C4C23×D7918yes—
1252C42—791no—
1253C42—792no—
1254C42—791no—
1255C42—792no—
1256C42—792no—
1257C42—792no—
1258C42—792no—
1259C42—794no—
1260C42—794no—
1261C42—794no—
1262C42—792no—
1263C42—798no—
1264C42—798no—
1265C42—798no—
1266C42C23×D7911yescharacteristic
1267C42C23×D7911yescharacteristic
1268C42C23×D7912yes—
1269C42C23×D7914yes—
1270C42C23×D7914yes—
1271C42C23×D7912yes—
1272C42C23×D7918yes—
1273C23—792no—
1274C23—794no—
1275C23—792no—
1276C23—1584no—
1277C23—1582no—
1278C23C24×D7912yes—
1279C23C24×D7911yescharacteristic
1280Q8—22no—
1281Q8—48no—
1282Q8—44no—
1283Q8—3168no—
1284Q8—3164no—
1285Q8—1584no—
1286Q8—1582no—
1287D4—24no—
1288D4—22no—
1289D4—3168no—
1290D4—3164no—
1291D4—3168no—
1292D4—3164no—
1293D4—1588no—
1294D4—1588no—
1295D4—1588no—
1296D4—1588no—
1297D4—1584no—
1298D4—1588no—
1299D4—1584no—
1300D4—1582no—
1301C2×C4—24no—
1302C2×C4—42no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—3162no—
1307C2×C4—3168no—
1308C2×C4—3162no—
1309C2×C4—3164no—
1310C2×C4—3168no—
1311C2×C4—3164no—
1312C2×C4—3168no—
1313C2×C4—3164no—
1314C2×C4—3168no—
1315C2×C4—3162no—
1316C2×C4—3164no—
1317C2×C4—792no—
1318C2×C4—792no—
1319C2×C4—794no—
1320C2×C4—792no—
1321C2×C4—794no—
1322C2×C4—792no—
1323C2×C4—798no—
1324C2×C4—1584no—
1325C2×C4—15816no—
1326C2×C4—1584no—
1327C2×C4—1582no—
1328C2×C4—1584no—
1329C2×C4—1584no—
1330C2×C4—1584no—
1331C2×C4—1588no—
1332C2×C4#1457920914yes—
1333C2×C4C24×D7912yes—
1334C2×C4C24×D7914yes—
1335C2×C4C24×D7914yes—
1336C2×C4C24×D7912yes—
1337C2×C4C24×D7914yes—
1338C2×C4C24×D7918yes—
1339C2×C4C24×D7912yes—
1340C2×C4C24×D7911yescharacteristic
1341C2×C4C24×D7911yescharacteristic
1342C22—22no—
1343C22—22no—
1344C22—24no—
1345C22—794no—
1346C22—1588no—
1347C22—1582no—
1348C22—1584no—
1349C22—1584no—
1350C22—1584no—
1351C22—1584no—
1352C22—1582no—
1353C22—1582no—
1354C22C2×#1457920912yes—
1355C22C25×D7911yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—28no—
1359C4—24no—
1360C4—24no—
1361C4—22no—
1362C4—24no—
1363C4—1582no—
1364C4—1582no—
1365C4—1584no—
1366C4—1582no—
1367C4—1588no—
1368C4—1584no—
1369C4—1582no—
1370C4C2×#1457920912yes—
1371C4C2×#1457920912yes—
1372C2—22no—
1373C2—42no—
1374C2—3164no—
1375C2—3162no—
1376C2—1584no—
1377C2C22×#1457920911yescharacteristic
1378C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3504C2
hypercenter#3504D79
hypocenterC79#62825
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #23778002C2semidirect
2. #23777996C2semidirect
3. #23777935C2semidirect
4. #23777933C2semidirect
5. #23777852C2semidirect
6. #23777381C2semidirect
7. #23777377C2semidirect
8. #23777373C2semidirect
9. #23777372C2semidirect
10. #23777324C2semidirect
11. #23777322C2semidirect
12. #23777317C2semidirect
13. #23777223C2semidirect
14. #23777221C2semidirect
15. #23777110C2semidirect
16. #23777108C2semidirect
17. #23777103C2semidirect
18. #23776697C2semidirect
19. #23776693C2semidirect
20. C2×#125×D79C2semidirect
21. C79×#3504C2semidirect
22. C79⋊#564C22semidirect
23. #19099314C22semidirect
24. #19099312C22semidirect
25. #19099309C22semidirect
26. #19099291C22semidirect
27. #19099290C22semidirect
28. #19099288C22semidirect
31. #19099274C22semidirect
33. #19099273C22semidirect
35. #19099269C22semidirect
41. #19099266C22semidirect
43. #19099263C22semidirect
47. #19099261C22semidirect
50. #19099257C22semidirect
53. #19099254C22semidirect
54. #19099254C22semidirect
56. #19099252C22semidirect
59. #19099251C22semidirect
60. #19099248C22semidirect
61. #19099248C22semidirect
63. #19099247C22semidirect
66. #19099245C22semidirect
75. #19099193C22semidirect
78. #19099190C22semidirect
79. #19099190C22semidirect
80. #19099176C22semidirect
81. #19099175C22semidirect
82. #19099174C22semidirect
83. #19099173C22semidirect
84. #19099172C22semidirect
85. #19099171C22semidirect
86. #19099171C22semidirect
87. #19099169C22semidirect
88. #19099168C22semidirect
89. #19099164C22semidirect
93. #19099161C22semidirect
94. #19099160C22semidirect
97. #19099159C22semidirect
98. #19099159C22semidirect
103. #19099119C22semidirect
105. #19099118C22semidirect
114. #19099100C22semidirect
118. #19099098C22semidirect
119. #19099097C22semidirect
121. #19099095C22semidirect
131. #125×D79C22semidirect
132. #125×D79C22semidirect
152. #557×C79C22semidirect
154. #554×C79C22semidirect
156. #544×C79C22semidirect
158. #533×C79C22semidirect
160. C2×#125×C79C22semidirect
704. #3504D79semidirect
711. C79#62825semidirect
719. #557C2×D79semidirect
731. #554C2×D79semidirect
774. #544C2×D79semidirect
804. #533C2×D79semidirect
831. C2×#125C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780022
#237779962
#237779352
#237779332
#237778522
#237773812
#237773772
#237773732
#237773722
#237773242
#237773222
#237773172
#237772232
#237772212
#237771102
#237771082
#237771032
#237766972
#237766932
C2×#125×D792
C79×#35042
#6282579