Finite Group Databasebeta

← #35197152

Subgroups — #35197152

Order 20224.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777840C214yesmaximal, complemented
2#23777836C214yesmaximal, complemented
3#23777834C218yesmaximal, complemented
4#23777744C211yesmaximal, characteristic, complemented
5#23777740C212yesmaximal, complemented
6#23777738C214yesmaximal, complemented
7#23777308C212yesmaximal, complemented
8#23777305C214yesmaximal, complemented
9#23777300C212yesmaximal, complemented
10#23777278C214yesmaximal, complemented
11#23777218C212yesmaximal, complemented
12#23777215C214yesmaximal, complemented
13#23777214C212yesmaximal, complemented
14#23777179C214yesmaximal, complemented
15#23777102C214yesmaximal, complemented
16#23777100C214yesmaximal, complemented
17#23777049C214yesmaximal, complemented
18#23776694C212yesmaximal, complemented
19C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
20C79×#3544C211yesmaximal, characteristic, complemented
21C2×#14579208C2214yes—
22C22×Q8×D79C2212yes—
23#19099315C2218yescomplemented
24#19099314C2218yescomplemented
25#19099313C2214yescomplemented
26#19099312C2214yescomplemented
27#19099312C2214yescomplemented
28Q8×Dic158C2212yescomplemented
29#19099293C2211yescharacteristic, complemented
30#19099293C2214yescomplemented
31#19099290C2218yescomplemented
32#19099290C2214yescomplemented
33#19099289C2214yescomplemented
34#19099284C2214yescomplemented
35#19099281C2214yescomplemented
36#19099280C2218yescomplemented
37#19099279C2211yescharacteristic, complemented
38#19099278C2212yescomplemented
39#19099275C2214yescomplemented
40#19099274C2214yes—
41#19099274C2212yescomplemented
42#19099273C2214yes—
43#19099273C2212yescomplemented
44#19099271C2214yes—
45#19099270C2212yescomplemented
46#19099269C2218yes—
47#19099268C2214yes—
48#19099267C2218yes—
49#19099267C2218yescomplemented
50#19099266C2214yes—
51#19099264C2218yes—
52#19099263C2214yes—
53#19099260C2214yes—
54#19099258C2218yes—
55#19099257C2214yes—
56#19099255C2214yes—
57#19099253C2214yes—
58#19099250C2218yes—
59#19099248C2214yes—
60#19099246C2218yes—
61D4×Dic158C2214yescomplemented
62#19099228C2218yes—
63#19099228C2218yes—
64#19099228C2214yescomplemented
65#19099226C2218yes—
66#19099226C2218yes—
67#19099226C2218yescomplemented
68#19099223C2218yes—
69#19099223C2218yes—
70#19099221C2218yes—
71#19099221C2218yes—
72#19099217C2214yes—
73#19099214C2214yes—
74#19099214C2214yescomplemented
75#19099213C2214yes—
76#19099213C2214yescomplemented
77#19099212C2218yes—
78#19099211C2218yes—
79#19099211C2218yescomplemented
80#19099193C2214yes—
81#19099193C2214yescomplemented
82#19099192C2218yescomplemented
83#19099191C2214yescomplemented
84#19099190C2214yes—
85#19099190C2218yescomplemented
86#19099190C2214yescomplemented
87#19099187C2214yescomplemented
88#19099184C2214yescomplemented
89#19099183C2218yescomplemented
90#19099182C2214yescomplemented
91#19099177C2218yescomplemented
92#19099172C2218yescomplemented
93#19099170C2218yescomplemented
94#19099161C2218yes—
95#19099159C2218yes—
96#19099156C2218yes—
97#19099154C2218yes—
98#19099143C2214yes—
99#19099142C2214yes—
100#19099137C2214yes—
101#19099136C2218yescomplemented
102#19099135C2218yes—
103#19099135C2218yes—
104#19099135C2218yescomplemented
105#19099119C2212yes—
106#19099119C2214yescomplemented
107#19099117C2212yes—
108#19099117C2214yescomplemented
109#19099116C2214yescomplemented
110#19099115C2212yes—
111#19099115C2214yescomplemented
112#19099112C2212yes—
113#19099110C2212yes—
114#19099110C2214yescomplemented
115#19099108C2212yes—
116#19099108C2214yescomplemented
117C2×#14579161C2211yescharacteristic
118C2×#14579160C2214yes—
119C2×#14579160C2214yescomplemented
120C2×#14579159C2212yes—
121C4⋊Q8×D79C2212yes—
122C4⋊Q8×D79C2214yes—
123C4⋊Q8×D79C2212yes—
124C4⋊Q8×D79C2214yes—
125C4⋊Q8×D79C2214yes—
126C4⋊Q8×D79C2214yescomplemented
127#19099098C2212yes—
128#19099097C2212yes—
129#19099096C2214yes—
130#19099096C2214yes—
131#19099092C2212yes—
132#19099091C2214yes—
133#19099090C2214yes—
134#19099076C2212yes—
135#19099075C2214yes—
136#19099073C2212yes—
137#19099072C2214yes—
138#19099071C2214yes—
139#19099071C2218yes—
140#19099070C2214yes—
141#19099045C2214yes—
142#19099044C2214yes—
143#19099043C2214yes—
144#19099042C2214yes—
145#19099040C2214yes—
146C4×#11929625C2212yes—
147#19099031C2214yes—
148C4×#11929623C2212yes—
149C4×#11929623C2214yes—
150C2×C4⋊C4×D79C2214yes—
151C2×C42×D79C2211yescharacteristic
152#563×C79C2214yescomplemented
153Q82×C79C2211yescharacteristic, complemented
154#555×C79C2211yescharacteristic, complemented
155#554×C79C2212yescomplemented
156#552×C79C2214yes—
157#547×C79C2214yes—
158#544×C79C2214yescomplemented
159#542×C79C2214yescomplemented
160#536×C79C2214yes—
161C2×C4⋊Q8×C79C2211yescharacteristic
162#529×C79C2212yes—
163#14579208—416no—
164C2×#11929625C2312yes—
165C2×#11929624C2314yes—
166C2×#11929624C2318yes—
167C2×#11929624C2314yes—
168C2×#11929623C2314yes—
169C2×#11929623C2312yes—
170C2×#11929623C2318yes—
171C2×#11929623C2318yes—
172C22×Dic158C2314yes—
173C22×Dic158C2318yes—
174C22×Dic158C2312yes—
175C2×Q8×D79—48no—
176C2×Q8×D79C2318yes—
177C2×Q8×D79C2314yes—
178C2×Q8×D79C2318yes—
179C2×Q8×D79C2314yes—
180C22×C4×D79C2312yes—
181C22×C4×D79C2311yescharacteristic
182C22×C4×D79C2314yes—
183#14579161C2314yes—
184#14579161C2314yes—
185#14579161C2312yes—
186#14579161C2312yes—
187#14579160C2318yes—
188#14579160C2318yes—
189#14579160C2314yes—
190#14579160C2318yes—
191#14579160C2314yes—
192#14579160C2318yes—
193#14579160C2318yes—
194#14579160C2318yes—
195#14579160C2314yes—
196#14579160C2314yes—
197#14579160C2318yes—
198#14579160C2314yes—
199#14579160C2314yes—
200#14579160C2312yes—
201#14579160C2312yes—
202#14579159C2314yes—
203#14579159C2314yes—
204#14579159C2314yes—
205#14579159C2314yes—
206#14579159C2318yes—
207#14579159C2314yes—
208#14579159C2314yes—
209#14579159C2312yes—
210#14579157C2312yes—
211#14579156C2318yes—
212#14579156C2318yes—
213#14579156C2318yes—
214#14579156C2314yes—
215#14579155C2318yes—
216#14579155C2314yes—
217#14579154C2318yes—
218#14579154C2318yes—
219#14579154C2318yes—
220#14579154C2314yes—
221#14579153C2318yes—
222#14579153C2314yes—
223#14579153C2312yes—
224#14579152C2318yes—
225#14579152C2318yes—
226#14579152C2314yes—
227#14579152C2314yes—
228#14579151C2318yes—
229#14579151C2318yes—
230#14579151C2318yes—
231#14579151C2318yes—
232#14579151C2314yes—
233#14579151C2318yes—
234#14579151C2314yes—
235#14579151C2318yes—
236#14579150C2314yes—
237#14579150C2314yes—
238#14579149C2312yes—
239#14579147C2314yes—
240#14579147C2318yes—
241#14579147C2314yes—
242#14579147C2318yes—
243#14579147C2318yes—
244#14579147C2318yes—
245#14579146C2318yes—
246#14579146C2318yes—
247#14579146C2314yes—
248#14579146C2314yes—
249#14579145C2318yes—
250#14579145C2318yes—
251#14579144C2314yes—
252#14579144C2318yes—
253#14579144C2318yes—
254#14579143C2318yes—
255#14579143C2318yes—
256#14579143C2314yes—
257#14579143C2314yes—
258#14579142C2318yes—
259#14579142C2318yes—
260#14579141C2318yes—
261#14579141C2314yes—
262#14579141C2318yes—
263#14579141C2312yes—
264#14579140C2318yes—
265#14579140C2314yes—
266#14579140C2312yes—
267#14579139C2318yes—
268#14579139C2318yes—
269#14579139C2318yes—
270#14579139C2318yes—
271#14579139C2318yes—
272#14579139C2318yes—
273#14579139C2318yes—
274#14579139C2318yes—
275#14579139C2318yes—
276#14579139C2314yes—
277#14579139C2314yes—
278#14579139C2314yes—
279#14579138C2318yes—
280#14579138C2318yes—
281#14579138C2318yes—
282#14579138C2318yes—
283#14579138C2318yes—
284#14579138C2318yes—
285#14579138C2318yes—
286#14579138C2314yes—
287#14579137C2318yes—
288#14579137C2318yes—
289#14579137C2318yes—
290#14579137C2314yes—
291#14579137C2318yes—
292#14579137C2312yes—
293#14579136C2318yes—
294#14579136C2314yes—
295#14579136C2312yes—
296#14579135C2314yes—
297#14579135C2312yes—
298#14579134C2318yes—
299#14579134C2318yes—
300#14579134C2318yes—
301#14579134C2314yes—
302#14579134C2314yes—
303#14579134C2314yes—
304#14579133C2318yes—
305#14579133C2314yes—
306#14579132C2318yes—
307#14579132C2314yes—
308#14579132C2312yes—
309#14579131C2314yes—
310#14579129C2314yes—
311Q8×Dic79C2314yes—
312Q8×Dic79C2312yes—
313C4×Dic158C2318yes—
314C4×Dic158C2318yes—
315C4×Dic158C2318yes—
316C4×Dic158C2314yes—
317C4×Dic158C2314yes—
318C4×Dic158C2312yes—
319#14579126C2318yes—
320#14579126C2318yes—
321#14579126C2318yes—
322#14579126C2314yes—
323#14579126C2314yes—
324#14579126C2314yes—
325#14579126C2314yes—
326#14579126C2312yes—
327C4×D316C2318yes—
328C4×D316C2318yes—
329C4×D316C2314yes—
330C4×D316C2314yes—
331C4×D316C2312yes—
332D4×Dic79C2314yes—
333D4×Dic79C2314yes—
334D4×Dic79C2312yes—
335#14579123C2318yes—
336#14579123C2318yes—
337#14579123C2314yes—
338#14579123C2312yes—
339#14579123C2314yes—
340#14579123C2314yes—
341#14579123C2314yes—
342C4×C22⋊D79C2318yes—
343C4×C22⋊D79C2318yes—
344C4×C22⋊D79C2318yes—
345C4×C22⋊D79C2314yes—
346C4×C22⋊D79C2314yes—
347C4×C22⋊D79C2314yes—
348(C22⋊D79)⋊C4C2318yes—
349(C22⋊D79)⋊C4C2318yes—
350(C22⋊D79)⋊C4C2318yes—
351(C22⋊D79)⋊C4C2314yes—
352(C22⋊D79)⋊C4C2314yes—
353(C22⋊D79)⋊C4C2314yes—
354(C22⋊D79)⋊C4C2314yes—
355(C22⋊D79)⋊C4C2314yes—
356(C22⋊D79)⋊C4C2314yes—
357(C22⋊D79)⋊C4C2314yes—
358#14579120C2314yes—
359#14579120C2314yes—
360#14579119C2314yes—
361#14579119C2314yes—
362#14579119C2312yes—
363#14579119C2314yes—
364#14579119C2312yes—
365#14579119C2314yes—
366#14579118C2314yes—
367#14579118C2314yes—
368#14579118C2318yes—
369#14579117C2314yes—
370#14579117C2314yes—
371#14579117C2318yes—
372#14579117C2318yes—
373#14579117C2314yes—
374C2×C4⋊Dic79C2314yes—
375C2×C4⋊Dic79C2314yes—
376C2×Dic79⋊C4C2318yes—
377C2×Dic79⋊C4C2318yes—
378C4⋊C4×D79C2314yes—
379C4⋊C4×D79C2314yes—
380C4⋊C4×D79C2318yes—
381C4⋊C4×D79C2318yes—
382C4⋊C4×D79C2314yes—
383C4⋊C4×D79C2314yes—
384C4⋊C4×D79C2314yes—
385C4⋊C4×D79C2318yes—
386C4⋊C4×D79C2314yes—
387C2×C4×Dic79C2312yes—
388C2×C4×Dic79C2311yescharacteristic
389C2×C4×Dic79C2314yes—
390C42×D79C2312yes—
391C42×D79C2312yes—
392C42×D79C2312yes—
393C42×D79C2312yes—
394C42×D79C2314yes—
395C2×#41×C79C2314yes—
396C22×Q8×C79C2312yes—
397C4⋊Q8×C79C2314yes—
398C4⋊Q8×C79C2314yes—
399C4⋊Q8×C79C2314yes—
400C4⋊Q8×C79C2314yes—
401C4⋊Q8×C79C2311yescharacteristic
402C4⋊Q8×C79C2311yescharacteristic
403C4⋊Q8×C79C2312yes—
404#126×C79C2318yes—
405#126×C79C2314yes—
406#125×C79C2318yes—
407#125×C79C2314yes—
408#125×C79C2312yes—
409#124×C79C2314yes—
410#124×C79C2312yes—
411#124×C79C2314yes—
412#123×C79C2318yes—
413#123×C79C2318yes—
414#123×C79C2314yes—
415C22⋊Q8×C79C2318yes—
416C22⋊Q8×C79C2314yes—
417C22⋊Q8×C79C2318yes—
418C22⋊Q8×C79C2318yes—
419C22⋊Q8×C79C2312yes—
420#121×C79C2314yes—
421#121×C79C2312yes—
422C4×Q8×C79C2312yes—
423C4×Q8×C79C2314yes—
424C4×D4×C79C2314yes—
425C4×D4×C79C2314yes—
426C4×D4×C79C2312yes—
427#117×C79C2314yes—
428#117×C79C2314yes—
429#117×C79C2314yes—
430C2×C4⋊C4×C79C2314yes—
431C2×C4⋊C4×C79C2314yes—
432C2×C42×C79C2311yescharacteristic
433C23×D79C2411yescharacteristic
434#11929625—28no—
435#11929624—216no—
436#11929624—48no—
437#11929624—416no—
438#11929623—216no—
439#11929623—28no—
440#11929623—416no—
441#11929623—416no—
442C2×Dic158—216no—
443C2×Dic158—44no—
444C2×Dic158—416no—
445C2×Dic158C2418yes—
446C2×Dic158C2414yes—
447C2×Dic158C2418yes—
448C2×Dic158C2412yes—
449C2×Dic158C2414yes—
450C2×Dic158C2414yes—
451C2×Dic158C2414yes—
452C2×Dic158C2418yes—
453C2×Dic158C2414yes—
454Q8×D79—48no—
455Q8×D79—416no—
456Q8×D79—48no—
457Q8×D79—416no—
458C2×D316C2414yes—
459C2×D316C2414yes—
460C2×D316C2412yes—
461C2×D316C2414yes—
462C2×C22⋊D79C2414yes—
463C2×C22⋊D79C2414yes—
464C2×C22⋊D79C2414yes—
465C2×C22⋊D79C2414yes—
466C2×C22⋊D79C2414yes—
467C2×C22⋊D79C2418yes—
468C22×Dic79C2414yes—
469C22×Dic79C2414yes—
470C22×Dic79C2414yes—
471C22×Dic79C2412yes—
472C22×Dic79C2418yes—
473C22×Dic79C2411yescharacteristic
474C2×C4×D79—24no—
475C2×C4×D79—28no—
476C2×C4×D79—48no—
477C2×C4×D79C2412yes—
478C2×C4×D79C2412yes—
479C2×C4×D79C2414yes—
480C2×C4×D79C2414yes—
481C2×C4×D79C2414yes—
482C2×C4×D79C2412yes—
483C2×C4×D79C2412yes—
484C2×C4×D79C2412yes—
485C2×C4×D79C2418yes—
486C2×C4×D79C2418yes—
487C2×C4×D79C2418yes—
488C2×C4×D79C2418yes—
489C2×C4×D79C2412yes—
490C4⋊Dic79C2414yes—
491C4⋊Dic79C2412yes—
492C4⋊Dic79C2414yes—
493C4⋊Dic79C2418yes—
494C4⋊Dic79C2418yes—
495C4⋊Dic79C2418yes—
496C4⋊Dic79C2412yes—
497C4⋊Dic79C2414yes—
498C4⋊Dic79C2414yes—
499C4⋊Dic79C2418yes—
500Dic79⋊C4C2418yes—
501Dic79⋊C4C2418yes—
502Dic79⋊C4C2414yes—
503Dic79⋊C4C2418yes—
504Dic79⋊C4C2418yes—
505Dic79⋊C4C2418yes—
506Dic79⋊C4C2418yes—
507Dic79⋊C4C2418yes—
508Dic79⋊C4C2418yes—
509Dic79⋊C4C2414yes—
510Dic79⋊C4C2414yes—
511Dic79⋊C4C2414yes—
512Dic79⋊C4C2414yes—
513Dic79⋊C4C2414yes—
514Dic79⋊C4C2414yes—
515Dic79⋊C4C2414yes—
516Dic79⋊C4C2418yes—
517Dic79⋊C4C2418yes—
518Dic79⋊C4C2414yes—
519Dic79⋊C4C2414yes—
520C22⋊Dic79C2414yes—
521C22⋊Dic79C2418yes—
522C22⋊Dic79C2414yes—
523C22⋊Dic79C2414yes—
524C22⋊Dic79C2418yes—
525(C2×D79)⋊C4C2414yes—
526(C2×D79)⋊C4C2414yes—
527(C2×D79)⋊C4C2414yes—
528(C2×D79)⋊C4C2414yes—
529(C2×D79)⋊C4C2418yes—
530(C2×D79)⋊C4C2418yes—
531(C2×D79)⋊C4C2414yes—
532(C2×D79)⋊C4C2414yes—
533(C2×D79)⋊C4C2414yes—
534(C2×D79)⋊C4C2418yes—
535(C2×D79)⋊C4C2414yes—
536(C2×D79)⋊C4C2418yes—
537(C2×D79)⋊C4C2414yes—
538(C2×D79)⋊C4C2414yes—
539C4×Dic79C2412yes—
540C4×Dic79C2412yes—
541C4×Dic79C2412yes—
542C4×Dic79C2411yescharacteristic
543C4×Dic79C2412yes—
544C4×Dic79C2412yes—
545C4×Dic79C2411yescharacteristic
546C4×Dic79C2414yes—
547C4×Dic79C2414yes—
548C4×Dic79C2414yes—
549C4×Dic79C2414yes—
550C4×Dic79C2414yes—
551C4×Dic79C2418yes—
552C4×Dic79C2414yes—
553C4×Dic79C2418yes—
554C4×Dic79C2414yes—
555#41×C79—48no—
556C2×Q8×C79—44no—
557C2×Q8×C79C2412yes—
558C2×Q8×C79C2412yes—
559C2×Q8×C79C2414yes—
560C2×Q8×C79C2414yes—
561C2×Q8×C79C2412yes—
562C2×D4×C79C2414yes—
563C2×D4×C79C2412yes—
564C2×D4×C79C2414yes—
565C22×C4×C79C2411yescharacteristic
566C22×C4×C79C2414yes—
567C22×C4×C79C2414yes—
568C22×C4×C79C2412yes—
569C22×C4×C79C2418yes—
570C4⋊C4×C79C2414yes—
571C4⋊C4×C79C2412yes—
572C4⋊C4×C79C2414yes—
573C4⋊C4×C79C2418yes—
574C4⋊C4×C79C2418yes—
575C4⋊C4×C79C2412yes—
576C4⋊C4×C79C2418yes—
577C4⋊C4×C79C2414yes—
578C4⋊C4×C79C2414yes—
579C4⋊C4×C79C2414yes—
580C4⋊C4×C79C2414yes—
581C4⋊C4×C79C2418yes—
582C22⋊C4×C79C2414yes—
583C22⋊C4×C79C2414yes—
584C22⋊C4×C79C2418yes—
585C22⋊C4×C79C2414yes—
586C22⋊C4×C79C2418yes—
587C22⋊C4×C79C2414yes—
588C22⋊C4×C79C2414yes—
589C42×C79C2412yes—
590C42×C79C2411yescharacteristic
591C42×C79C2411yescharacteristic
592C42×C79C2414yes—
593C42×C79C2414yes—
594C42×C79C2414yes—
595C23×C79C2514yes—
596C23×C79C2511yescharacteristic
597C22×D79—22no—
598C22×D79—24no—
599C22×D79C2514yes—
600C22×D79C2512yes—
601Q8×C79—24no—
602Q8×C79—42no—
603Q8×C79—44no—
604Q8×C79—42no—
605Q8×C79—44no—
606D4×C79—28no—
607D4×C79—24no—
608D4×C79—44no—
609C2×C4×C79—22no—
610C2×C4×C79—28no—
611C2×C4×C79—24no—
612C2×C4×C79—28no—
613C2×C4×C79—48no—
614C2×C4×C79C2514yes—
615C2×C4×C79C2514yes—
616C2×C4×C79C2512yes—
617C2×C4×C79C2511yescharacteristic
618C2×C4×C79C2511yescharacteristic
619C2×C4×C79C2514yes—
620C2×C4×C79C2514yes—
621C2×C4×C79C2514yes—
622C2×C4×C79C2512yes—
623C22⋊D79—28no—
624C22⋊D79—28no—
625C22⋊D79—28no—
626C22⋊D79—28no—
627C22⋊D79—28no—
628C22⋊D79—48no—
629C2×Dic79—28no—
630C2×Dic79—28no—
631C2×Dic79—24no—
632C2×Dic79—28no—
633C2×Dic79—48no—
634C2×Dic79H(5,𝔽2)14yes—
635C2×Dic79C2514yes—
636C2×Dic79C2514yes—
637C2×Dic79C2512yes—
638C2×Dic79C2514yes—
639C2×Dic79C2518yes—
640C2×Dic79C2512yes—
641C2×Dic79C2512yes—
642D316—28no—
643D316—28no—
644D316—24no—
645D316—44no—
646C4×D79—24no—
647C4×D79—24no—
648C4×D79—28no—
649C4×D79—24no—
650C4×D79—24no—
651C4×D79—28no—
652C4×D79—24no—
653C4×D79—28no—
654C4×D79—48no—
655C4×D79—48no—
656C4×D79—48no—
657C4×D79—48no—
658C4×D792−1+418yescomplemented
659Dic158—24no—
660Dic158—216no—
661Dic158—216no—
662Dic158—28no—
663Dic158—28no—
664Dic158—44no—
665Dic158—44no—
666Dic158—48no—
667Dic158—44no—
668C22×C79—22no—
669C22×C79—24no—
670C22×C79—24no—
671C22×C79—24no—
672C22×C79C2×H(5,𝔽2)12yes—
673C22×C79C2611yescharacteristic
674C2×D79—28no—
675C2×D79—22no—
676C2×D79—22no—
677C2×D79—24no—
678C2×D79—24no—
679C2×D79—24no—
680C2×D79C2×2−1+414yes—
681C4×C79—24no—
682C4×C79—24no—
683C4×C79—21no—
684C4×C79—21no—
685C4×C79—24no—
686C4×C79—24no—
687C4×C79—22no—
688C4×C79—24no—
689C4×C79C2×2−1+414yes—
690Dic79—24no—
691Dic79—28no—
692Dic79—24no—
693Dic79—24no—
694Dic79—22no—
695Dic79C2×H(5,𝔽2)14yes—
696Dic79C2×2−1+414yes—
697#62833—791nomaximal, Sylow
698C2×C79—22no—
699C2×C79—44no—
700C2×C79C22×H(5,𝔽2)11yescharacteristic
701C2×C79C22×2−1+412yes—
702D79—24no—
703D79—44no—
704#3552—798no—
705#3552—794no—
706#3552—794no—
707#3544—794no—
708#3544—791no—
709#3544—792no—
710#3544D7911yescharacteristic, complemented
711#3511—792no—
712#3511—792no—
713#3511—794no—
714#3509—794no—
715#3503—792no—
716#3503—792no—
717#3503—794no—
718#3499—794no—
719#3492—794no—
720#3492—794no—
721#3486—794no—
722#3444—792no—
723C22×C4⋊Q8—791no—
724C79#6283311yescharacteristic, complemented, Sylow
725C2×2−1+4—794no—
726C23×Q8—792no—
727#563—794no—
728#563—794no—
729#563—798no—
730#563—794no—
731#563—798no—
732#563C2×D7914yescomplemented
733Q82—794no—
734Q82—791no—
735Q82—792no—
736Q82C2×D7911yescharacteristic, complemented
737#557—798no—
738#557—794no—
739#557—794no—
740#556—798no—
741#556—794no—
742#556—794no—
743#555—791no—
744#555—794no—
745#555—792no—
746#555C2×D7911yescharacteristic, complemented
747#554—794no—
748#554—792no—
749#554—798no—
750#554—798no—
751#554—798no—
752#554—794no—
753#554—794no—
754#554—792no—
755#554—792no—
756#554—794no—
757#554C2×D7912yescomplemented
758#553—798no—
759#553—794no—
760#553—798no—
761#553—794no—
762#553—794no—
763#553—794no—
764#552—798no—
765#552—794no—
766#552—794no—
767#552—798no—
768#552—794no—
769#552C2×D7914yes—
770D4×Q8—798no—
771D4×Q8—798no—
772D4×Q8—794no—
773D4×Q8—798no—
774D4×Q8—798no—
775D4×Q8—798no—
776D4×Q8—794no—
777#548—798no—
778#548—798no—
779#548—798no—
780#548—798no—
781#547—798no—
782#547—798no—
783#547—798no—
784#547—794no—
785#547—794no—
786#547—794no—
787#547—794no—
788#547—794no—
789#547C2×D7914yes—
790#544—794no—
791#544—798no—
792#544—794no—
793#544—794no—
794#544—794no—
795#544—798no—
796#544—794no—
797#544C2×D7914yescomplemented
798#542—794no—
799#542—798no—
800#542—794no—
801#542—798no—
802#542—794no—
803#542C2×D7914yescomplemented
804#541—798no—
805#541—798no—
806#539—798no—
807#539—798no—
808#539—798no—
809#539—798no—
810#537—794no—
811#537—794no—
812#536—794no—
813#536—798no—
814#536—798no—
815#536—798no—
816#536—798no—
817#536C2×D7914yes—
818#533—792no—
819#533—794no—
820#533—792no—
821#533—794no—
822#533—792no—
823#533—794no—
824#533—794no—
825#532—792no—
826#532—792no—
827#532—794no—
828#532—792no—
829#532—794no—
830C2×C4⋊Q8—792no—
831C2×C4⋊Q8—792no—
832C2×C4⋊Q8—792no—
833C2×C4⋊Q8—794no—
834C2×C4⋊Q8—794no—
835C2×C4⋊Q8—794no—
836C2×C4⋊Q8—794no—
837C2×C4⋊Q8—794no—
838C2×C4⋊Q8—794no—
839C2×C4⋊Q8—791no—
840C2×C4⋊Q8C2×D7911yescharacteristic
841#529—794no—
842#529—794no—
843#529—792no—
844#529—792no—
845#529—794no—
846#529—794no—
847#529—792no—
848#529C2×D7912yes—
849#525—794no—
850#525—794no—
851#525—798no—
852#525—792no—
853#525—792no—
854#525—794no—
855#525—794no—
856#520—794no—
857#520—794no—
858#520—794no—
859#520—794no—
860#519—794no—
861C4×#41—792no—
862C4×#41—794no—
863C4×#41—792no—
864C4×#41—794no—
865C22×C4⋊C4—794no—
866C22×C42—791no—
8672−1+4—31616no—
868C2×#41—792no—
869C2×#41—798no—
870C2×#41—798no—
871C2×#41—792no—
872C2×#41—794no—
873C2×#41—794no—
874C2×#41—798no—
875C2×#41—794no—
876C2×#41C22×D7914yes—
877C22×Q8—3168no—
878C22×Q8—794no—
879C22×Q8—798no—
880C22×Q8—794no—
881C22×Q8—798no—
882C22×Q8—792no—
883C22×Q8—798no—
884C22×Q8—794no—
885C22×Q8C22×D7912yes—
886C23×C4—794no—
887C23×C4—792no—
888C23×C4—791no—
889C4⋊Q8—794no—
890C4⋊Q8—794no—
891C4⋊Q8—794no—
892C4⋊Q8—794no—
893C4⋊Q8—798no—
894C4⋊Q8—792no—
895C4⋊Q8—794no—
896C4⋊Q8—794no—
897C4⋊Q8—794no—
898C4⋊Q8—792no—
899C4⋊Q8—794no—
900C4⋊Q8—798no—
901C4⋊Q8—798no—
902C4⋊Q8—794no—
903C4⋊Q8—794no—
904C4⋊Q8—798no—
905C4⋊Q8—798no—
906C4⋊Q8—798no—
907C4⋊Q8—794no—
908C4⋊Q8—794no—
909C4⋊Q8—792no—
910C4⋊Q8—798no—
911C4⋊Q8—798no—
912C4⋊Q8—794no—
913C4⋊Q8—792no—
914C4⋊Q8—792no—
915C4⋊Q8—794no—
916C4⋊Q8C22×D7914yes—
917C4⋊Q8C22×D7911yescharacteristic
918C4⋊Q8C22×D7911yescharacteristic
919C4⋊Q8C22×D7912yes—
920C4⋊Q8C22×D7914yes—
921C4⋊Q8C22×D7914yes—
922C4⋊Q8C22×D7914yes—
923#127—792no—
924#126—794no—
925#126—798no—
926#126—798no—
927#126—798no—
928#126—794no—
929#126—798no—
930#126—798no—
931#126—798no—
932#126—794no—
933#126—798no—
934#126C22×D7914yes—
935#126C22×D7918yes—
936#125—794no—
937#125—794no—
938#125—798no—
939#125—798no—
940#125—794no—
941#125—794no—
942#125—798no—
943#125—798no—
944#125—798no—
945#125—798no—
946#125—798no—
947#125—798no—
948#125—792no—
949#125—794no—
950#125—798no—
951#125C22×D7912yes—
952#125C22×D7914yes—
953#125C22×D7918yes—
954#124—794no—
955#124—794no—
956#124—794no—
957#124—794no—
958#124—798no—
959#124—798no—
960#124—798no—
961#124—798no—
962#124—792no—
963#124C22×D7912yes—
964#124C22×D7914yes—
965#124C22×D7914yes—
966#123—798no—
967#123—798no—
968#123—794no—
969#123—798no—
970#123—798no—
971#123—794no—
972#123—794no—
973#123—798no—
974#123—798no—
975#123—794no—
976#123—794no—
977#123—798no—
978#123—798no—
979#123—798no—
980#123—798no—
981#123C22×D7914yes—
982#123C22×D7918yes—
983#123C22×D7918yes—
984C22⋊Q8—792no—
985C22⋊Q8—798no—
986C22⋊Q8—794no—
987C22⋊Q8—798no—
988C22⋊Q8—798no—
989C22⋊Q8—798no—
990C22⋊Q8—792no—
991C22⋊Q8—794no—
992C22⋊Q8—798no—
993C22⋊Q8—794no—
994C22⋊Q8—794no—
995C22⋊Q8—794no—
996C22⋊Q8—792no—
997C22⋊Q8—798no—
998C22⋊Q8—798no—
999C22⋊Q8—798no—
1000C22⋊Q8—798no—
1001C22⋊Q8—798no—
1002C22⋊Q8—798no—
1003C22⋊Q8—794no—
1004C22⋊Q8—798no—
1005C22⋊Q8—798no—
1006C22⋊Q8—798no—
1007C22⋊Q8—798no—
1008C22⋊Q8—798no—
1009C22⋊Q8—794no—
1010C22⋊Q8—798no—
1011C22⋊Q8—798no—
1012C22⋊Q8—798no—
1013C22⋊Q8—798no—
1014C22⋊Q8—798no—
1015C22⋊Q8—798no—
1016C22⋊Q8—798no—
1017C22⋊Q8C22×D7912yes—
1018C22⋊Q8C22×D7914yes—
1019C22⋊Q8C22×D7918yes—
1020C22⋊Q8C22×D7918yes—
1021C22⋊Q8C22×D7918yes—
1022#121—794no—
1023#121—792no—
1024#121—798no—
1025#121—794no—
1026#121—798no—
1027#121—792no—
1028#121—794no—
1029#121—792no—
1030#121—798no—
1031#121—794no—
1032#121—794no—
1033#121—794no—
1034#121—794no—
1035#121—798no—
1036#121—798no—
1037#121—798no—
1038#121C22×D7912yes—
1039#121C22×D7914yes—
1040#120—794no—
1041#120—794no—
1042C4×Q8—792no—
1043C4×Q8—794no—
1044C4×Q8—794no—
1045C4×Q8—794no—
1046C4×Q8—794no—
1047C4×Q8—792no—
1048C4×Q8—798no—
1049C4×Q8—798no—
1050C4×Q8—798no—
1051C4×Q8—794no—
1052C4×Q8—794no—
1053C4×Q8—792no—
1054C4×Q8—798no—
1055C4×Q8—798no—
1056C4×Q8—798no—
1057C4×Q8—794no—
1058C4×Q8C22×D7912yes—
1059C4×Q8C22×D7914yes—
1060C4×D4—794no—
1061C4×D4—792no—
1062C4×D4—794no—
1063C4×D4—794no—
1064C4×D4—794no—
1065C4×D4—794no—
1066C4×D4—798no—
1067C4×D4—798no—
1068C4×D4—798no—
1069C4×D4—794no—
1070C4×D4—794no—
1071C4×D4—794no—
1072C4×D4—792no—
1073C4×D4—798no—
1074C4×D4—798no—
1075C4×D4—794no—
1076C4×D4—794no—
1077C4×D4—794no—
1078C4×D4—794no—
1079C4×D4—794no—
1080C4×D4—794no—
1081C4×D4—794no—
1082C4×D4—794no—
1083C4×D4—798no—
1084C4×D4—798no—
1085C4×D4—798no—
1086C4×D4—794no—
1087C4×D4—792no—
1088C4×D4—798no—
1089C4×D4—798no—
1090C4×D4—794no—
1091C4×D4C22×D7914yes—
1092C4×D4C22×D7912yes—
1093C4×D4C22×D7914yes—
1094#117—794no—
1095#117—794no—
1096#117—792no—
1097#117—792no—
1098#117—794no—
1099#117—794no—
1100#117—794no—
1101#117—794no—
1102#117—794no—
1103#117—794no—
1104#117—794no—
1105#117—798no—
1106#117—798no—
1107#117—794no—
1108#117—794no—
1109#117—798no—
1110#117C22×D7914yes—
1111#117C22×D7914yes—
1112#117C22×D7914yes—
1113C2×C4⋊C4—798no—
1114C2×C4⋊C4—794no—
1115C2×C4⋊C4—798no—
1116C2×C4⋊C4—794no—
1117C2×C4⋊C4—794no—
1118C2×C4⋊C4—794no—
1119C2×C4⋊C4—798no—
1120C2×C4⋊C4—798no—
1121C2×C4⋊C4—794no—
1122C2×C4⋊C4—794no—
1123C2×C4⋊C4—798no—
1124C2×C4⋊C4—794no—
1125C2×C4⋊C4—794no—
1126C2×C4⋊C4C22×D7914yes—
1127C2×C4⋊C4C22×D7914yes—
1128C2×C42—794no—
1129C2×C42—792no—
1130C2×C42—791no—
1131C2×C42—794no—
1132C2×C42—792no—
1133C2×C42—792no—
1134C2×C42—792no—
1135C2×C42—792no—
1136C2×C42C22×D7911yescharacteristic
1137C24—791no—
1138#41—48no—
1139#41—3168no—
1140#41—31616no—
1141#41—31616no—
1142#41—31616no—
1143#41—15816no—
1144#41—1588no—
1145#41—15816no—
1146#41—1588no—
1147C2×Q8—44no—
1148C2×Q8—3164no—
1149C2×Q8—31616no—
1150C2×Q8—3168no—
1151C2×Q8—31616no—
1152C2×Q8—3168no—
1153C2×Q8—31616no—
1154C2×Q8—794no—
1155C2×Q8—798no—
1156C2×Q8—794no—
1157C2×Q8—794no—
1158C2×Q8—794no—
1159C2×Q8—792no—
1160C2×Q8—798no—
1161C2×Q8—794no—
1162C2×Q8—798no—
1163C2×Q8—15816no—
1164C2×Q8C23×D7912yes—
1165C2×Q8C23×D7914yes—
1166C2×Q8C23×D7912yes—
1167C2×Q8C23×D7914yes—
1168C2×Q8C23×D7912yes—
1169C2×D4—798no—
1170C2×D4—794no—
1171C2×D4—794no—
1172C2×D4—794no—
1173C2×D4—794no—
1174C2×D4—794no—
1175C2×D4—794no—
1176C2×D4—794no—
1177C2×D4—794no—
1178C2×D4—792no—
1179C2×D4C23×D7912yes—
1180C2×D4C23×D7914yes—
1181C2×D4C23×D7914yes—
1182C22×C4—3168no—
1183C22×C4—798no—
1184C22×C4—798no—
1185C22×C4—798no—
1186C22×C4—798no—
1187C22×C4—798no—
1188C22×C4—791no—
1189C22×C4—792no—
1190C22×C4—792no—
1191C22×C4—794no—
1192C22×C4—794no—
1193C22×C4—794no—
1194C22×C4—792no—
1195C22×C4—792no—
1196C22×C4—792no—
1197C22×C4—792no—
1198C22×C4—792no—
1199C22×C4—794no—
1200C22×C4—794no—
1201C22×C4—794no—
1202C22×C4—1588no—
1203C22×C4—1584no—
1204C22×C4C23×D7912yes—
1205C22×C4C23×D7911yescharacteristic
1206C22×C4C23×D7914yes—
1207C22×C4C23×D7914yes—
1208C22×C4C23×D7918yes—
1209C4⋊C4—798no—
1210C4⋊C4—794no—
1211C4⋊C4—798no—
1212C4⋊C4—798no—
1213C4⋊C4—798no—
1214C4⋊C4—798no—
1215C4⋊C4—798no—
1216C4⋊C4—798no—
1217C4⋊C4—798no—
1218C4⋊C4—794no—
1219C4⋊C4—794no—
1220C4⋊C4—794no—
1221C4⋊C4—794no—
1222C4⋊C4—794no—
1223C4⋊C4—794no—
1224C4⋊C4—794no—
1225C4⋊C4—794no—
1226C4⋊C4—794no—
1227C4⋊C4—798no—
1228C4⋊C4—798no—
1229C4⋊C4—794no—
1230C4⋊C4—792no—
1231C4⋊C4—794no—
1232C4⋊C4—798no—
1233C4⋊C4—798no—
1234C4⋊C4—798no—
1235C4⋊C4—792no—
1236C4⋊C4—794no—
1237C4⋊C4—794no—
1238C4⋊C4—798no—
1239C4⋊C4C23×D7914yes—
1240C4⋊C4C23×D7912yes—
1241C4⋊C4C23×D7914yes—
1242C4⋊C4C23×D7918yes—
1243C4⋊C4C23×D7918yes—
1244C4⋊C4C23×D7918yes—
1245C4⋊C4C23×D7912yes—
1246C4⋊C4C23×D7914yes—
1247C4⋊C4C23×D7914yes—
1248C4⋊C4C23×D7914yes—
1249C4⋊C4C23×D7914yes—
1250C4⋊C4C23×D7918yes—
1251C22⋊C4—794no—
1252C22⋊C4—798no—
1253C22⋊C4—798no—
1254C22⋊C4—794no—
1255C22⋊C4—794no—
1256C22⋊C4—794no—
1257C22⋊C4—794no—
1258C22⋊C4—794no—
1259C22⋊C4—794no—
1260C22⋊C4—798no—
1261C22⋊C4—798no—
1262C22⋊C4—798no—
1263C22⋊C4—798no—
1264C22⋊C4—794no—
1265C22⋊C4—794no—
1266C22⋊C4—794no—
1267C22⋊C4—794no—
1268C22⋊C4—794no—
1269C22⋊C4—794no—
1270C22⋊C4C23×D7914yes—
1271C22⋊C4C23×D7918yes—
1272C22⋊C4C23×D7914yes—
1273C22⋊C4C23×D7914yes—
1274C22⋊C4C23×D7918yes—
1275C22⋊C4C23×D7914yes—
1276C22⋊C4C23×D7914yes—
1277C42—792no—
1278C42—792no—
1279C42—792no—
1280C42—791no—
1281C42—792no—
1282C42—792no—
1283C42—791no—
1284C42—794no—
1285C42—794no—
1286C42—794no—
1287C42—794no—
1288C42—794no—
1289C42—794no—
1290C42—794no—
1291C42—798no—
1292C42—798no—
1293C42C23×D7912yes—
1294C42C23×D7911yescharacteristic
1295C42C23×D7911yescharacteristic
1296C42C23×D7914yes—
1297C42C23×D7914yes—
1298C42C23×D7914yes—
1299C23—792no—
1300C23—794no—
1301C23—1584no—
1302C23—1582no—
1303C23C24×D7914yes—
1304C23C24×D7911yescharacteristic
1305Q8—24no—
1306Q8—42no—
1307Q8—44no—
1308Q8—42no—
1309Q8—44no—
1310Q8—3164no—
1311Q8—3164no—
1312Q8—3164no—
1313Q8—3168no—
1314Q8—1588no—
1315Q8—15816no—
1316Q8—15816no—
1317Q8—1588no—
1318Q8—1584no—
1319D4—28no—
1320D4—24no—
1321D4—44no—
1322D4—3164no—
1323D4—3168no—
1324D4—1588no—
1325D4—1588no—
1326D4—1588no—
1327D4—1588no—
1328D4—1588no—
1329D4—1588no—
1330D4—1588no—
1331D4—1584no—
1332C2×C4—28no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—28no—
1336C2×C4—48no—
1337C2×C4—3168no—
1338C2×C4—3168no—
1339C2×C4—3168no—
1340C2×C4—3168no—
1341C2×C4—3168no—
1342C2×C4—794no—
1343C2×C4—792no—
1344C2×C4—792no—
1345C2×C4—798no—
1346C2×C4—794no—
1347C2×C4—794no—
1348C2×C4—792no—
1349C2×C4—798no—
1350C2×C4—794no—
1351C2×C4—1584no—
1352C2×C4—1584no—
1353C2×C4—1584no—
1354C2×C4—1588no—
1355C2×C4—1588no—
1356C2×C4—1584no—
1357C2×C4—1584no—
1358C2×C4—1588no—
1359C2×C4—1588no—
1360C2×C4—1588no—
1361C2×C4—1584no—
1362C2×C4—1588no—
1363C2×C4C24×D7914yes—
1364C2×C4C24×D7914yes—
1365C2×C4C24×D7912yes—
1366C2×C4C24×D7911yescharacteristic
1367C2×C4C24×D7911yescharacteristic
1368C2×C4C24×D7914yes—
1369C2×C4C24×D7914yes—
1370C2×C4C24×D7914yes—
1371C2×C4C24×D7912yes—
1372C22—22no—
1373C22—24no—
1374C22—24no—
1375C22—24no—
1376C22—794no—
1377C22—1588no—
1378C22—1584no—
1379C22—1584no—
1380C22—1584no—
1381C22—1582no—
1382C22—1582no—
1383C22H(5,𝔽2)×D7912yes—
1384C22C25×D7911yescharacteristic
1385C4—24no—
1386C4—24no—
1387C4—21no—
1388C4—21no—
1389C4—24no—
1390C4—22no—
1391C4—24no—
1392C4—24no—
1393C4—794no—
1394C4—794no—
1395C4—1588no—
1396C4—1584no—
1397C4—1582no—
1398C4—1584no—
1399C4—1584no—
1400C42−1+4×D7914yes—
1401C2—22no—
1402C2—44no—
1403C2—3164no—
1404C2—1584no—
1405C2C2×H(5,𝔽2)×D7911yescharacteristic
1406C2C2×2−1+4×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3544C2
hypercenter#3544D79
hypocenterC79#62833
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3544

Complements

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

NH ≅ G/Ntype
1. #23777840C2semidirect
2. #23777836C2semidirect
3. #23777834C2semidirect
4. #23777744C2semidirect
5. #23777740C2semidirect
6. #23777738C2semidirect
7. #23777308C2semidirect
8. #23777305C2semidirect
9. #23777300C2semidirect
10. #23777278C2semidirect
11. #23777218C2semidirect
12. #23777215C2semidirect
13. #23777214C2semidirect
14. #23777179C2semidirect
15. #23777102C2semidirect
16. #23777100C2semidirect
17. #23777049C2semidirect
18. #23776694C2semidirect
19. C2×C4⋊Q8×D79C2semidirect
20. C79×#3544C2semidirect
23. #19099315C22semidirect
24. #19099314C22semidirect
25. #19099313C22semidirect
26. #19099312C22semidirect
27. #19099312C22semidirect
28. Q8×Dic158C22semidirect
29. #19099293C22semidirect
30. #19099293C22semidirect
31. #19099290C22semidirect
32. #19099290C22semidirect
33. #19099289C22semidirect
34. #19099284C22semidirect
35. #19099281C22semidirect
36. #19099280C22semidirect
37. #19099279C22semidirect
38. #19099278C22semidirect
39. #19099275C22semidirect
41. #19099274C22semidirect
43. #19099273C22semidirect
45. #19099270C22semidirect
49. #19099267C22semidirect
61. D4×Dic158C22semidirect
64. #19099228C22semidirect
67. #19099226C22semidirect
74. #19099214C22semidirect
76. #19099213C22semidirect
79. #19099211C22semidirect
81. #19099193C22semidirect
82. #19099192C22semidirect
83. #19099191C22semidirect
85. #19099190C22semidirect
86. #19099190C22semidirect
87. #19099187C22semidirect
88. #19099184C22semidirect
89. #19099183C22semidirect
90. #19099182C22semidirect
91. #19099177C22semidirect
92. #19099172C22semidirect
93. #19099170C22semidirect
101. #19099136C22semidirect
104. #19099135C22semidirect
106. #19099119C22semidirect
108. #19099117C22semidirect
109. #19099116C22semidirect
111. #19099115C22semidirect
114. #19099110C22semidirect
116. #19099108C22semidirect
119. C2×#14579160C22semidirect
126. C4⋊Q8×D79C22semidirect
152. #563×C79C22semidirect
153. Q82×C79C22semidirect
154. #555×C79C22semidirect
155. #554×C79C22semidirect
158. #544×C79C22semidirect
159. #542×C79C22semidirect
658. C4×D792−1+4semidirect
710. #3544D79semidirect
724. C79#62833semidirect
732. #563C2×D79semidirect
736. Q82C2×D79semidirect
746. #555C2×D79semidirect
757. #554C2×D79semidirect
797. #544C2×D79semidirect
803. #542C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237778402
#237778362
#237778342
#237777442
#237777402
#237777382
#237773082
#237773052
#237773002
#237772782
#237772182
#237772152
#237772142
#237771792
#237771022
#237771002
#237770492
#237766942
C2×C4⋊Q8×D792
C79×#35442
#6283379