Finite Group Databasebeta

← #35197160

Subgroups — #35197160

Order 20224.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777846C214yesmaximal, complemented
2#23777844C218yesmaximal, complemented
3#23777830C214yesmaximal, complemented
4#23777742C218yesmaximal, complemented
5#23777312C214yesmaximal, complemented
6#23777304C214yesmaximal, complemented
7#23777287C211yesmaximal, characteristic, complemented
8#23777281C212yesmaximal, complemented
9#23777217C214yesmaximal, complemented
10#23777212C214yesmaximal, complemented
11#23777185C211yesmaximal, characteristic, complemented
12#23777183C211yesmaximal, characteristic, complemented
13#23777182C212yesmaximal, complemented
14#23777100C218yesmaximal, complemented
15#23777052C212yesmaximal, complemented
16#23777049C212yesmaximal, complemented
17#23776697C211yesmaximal, characteristic, complemented
18#23776693C211yesmaximal, characteristic, complemented
19C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
20C79×#3509C211yesmaximal, characteristic, complemented
21C2×#14579209C2212yes—
22C2×#14579208C2212yes—
23C22×Q8×D79C2212yes—
24#19099317C22116yescomplemented
25#19099315C22116yescomplemented
26Q8×Dic158C2218yescomplemented
27#19099292C2214yescomplemented
28#19099291C2218yescomplemented
29#19099286C2214yescomplemented
30#19099285C2218yescomplemented
31#19099276C2218yescomplemented
32#19099273C2218yes—
33#19099271C2218yes—
34#19099271C2218yescomplemented
35#19099269C22116yes—
36#19099269C2218yescomplemented
37#19099266C2218yes—
38#19099264C22116yes—
39#19099257C2218yes—
40#19099255C2218yes—
41#19099246C22116yes—
42Q8×D316C2218yes—
43Q8×D316C2218yes—
44Q8×D316C2214yescomplemented
45#19099228C2218yes—
46#19099228C2214yescomplemented
47#19099226C2218yes—
48#19099226C2218yescomplemented
49#19099225C2218yes—
50#19099225C2218yes—
51#19099223C2218yes—
52#19099221C2218yes—
53#19099217C2218yes—
54#19099217C2214yescomplemented
55#19099216C2214yescomplemented
56#19099215C2218yescomplemented
57#19099214C2218yes—
58#19099211C22116yes—
59#19099193C2218yes—
60#19099193C22116yescomplemented
61#19099193C2218yescomplemented
62#19099191C2218yescomplemented
63#19099186C2218yescomplemented
64#19099185C2218yescomplemented
65#19099179C22116yescomplemented
66#19099176C2214yescomplemented
67#19099171C2218yescomplemented
68#19099161C22116yes—
69#19099154C22116yes—
70#19099143C2218yes—
71#19099139C2212yes—
72#19099139C2212yes—
73#19099139C2218yes—
74#19099139C2214yescomplemented
75#19099138C2214yescomplemented
76#19099138C2214yescomplemented
77#19099137C2212yes—
78#19099135C2218yes—
79#19099133C2214yescomplemented
80#19099118C2212yes—
81#19099118C2214yescomplemented
82#19099117C2212yes—
83#19099117C2218yescomplemented
84#19099116C2211yescharacteristic
85#19099114C2212yes—
86#19099114C2212yescomplemented
87#19099113C2211yescharacteristic
88#19099113C2212yescomplemented
89#19099112C2214yescomplemented
90#19099110C2212yes—
91#19099109C2211yescharacteristic
92C2×#14579161C2211yescharacteristic
93C2×#14579161C2212yescomplemented
94C2×#14579160C2214yes—
95C2×#14579159C2212yes—
96C4⋊Q8×D79C2214yes—
97C4⋊Q8×D79C2214yes—
98C4⋊Q8×D79C2214yes—
99C4⋊Q8×D79C2214yes—
100C4⋊Q8×D79C2214yescomplemented
101C4⋊Q8×D79C2212yescomplemented
102#19099100C2214yes—
103#19099100C2212yes—
104#19099099C2214yes—
105#19099098C2214yes—
106#19099095C2212yes—
107#19099093C2214yes—
108#19099091C2214yes—
109#19099076C2214yes—
110#19099075C2212yes—
111#19099075C2211yescharacteristic
112#19099075C2218yes—
113#19099072C2214yes—
114#19099071C2218yes—
115#19099070C2211yescharacteristic
116#19099045C2218yes—
117#19099043C2218yes—
118#19099040C2212yes—
119C4×#11929625C2214yes—
120C4×#11929624C2211yescharacteristic
121C4×#11929624C2214yes—
122#19099031C2212yes—
123C2×C4⋊C4×D79C2214yes—
124C2×C42×D79C2211yescharacteristic
125#557×C79C2214yescomplemented
126#556×C79C2214yescomplemented
127#552×C79C2218yes—
128#541×C79C2214yescomplemented
129#536×C79C2212yes—
130#533×C79C2211yescharacteristic
131#533×C79C2214yescomplemented
132C2×C4⋊Q8×C79C2211yescharacteristic
133#519×C79C2212yes—
134C4×#41×C79C2211yescharacteristic
135#14579209—48no—
136#14579208—48no—
137C2×#11929625C2314yes—
138C2×#11929625C2314yes—
139C2×#11929625C2314yes—
140C2×#11929624C2312yes—
141C2×#11929624C2311yescharacteristic
142C2×#11929624C2314yes—
143C2×#11929624C2318yes—
144C2×#11929624C2314yes—
145C2×#11929623C2318yes—
146C2×#11929623C2314yes—
147C22×Dic158C2312yes—
148C22×Dic158C2314yes—
149C22×Dic158C2314yes—
150C2×Q8×D79—48no—
151C2×Q8×D79C2314yes—
152C2×Q8×D79C2314yes—
153C2×Q8×D79C2314yes—
154C2×Q8×D79C2318yes—
155C2×Q8×D79C2318yes—
156C22×C4×D79C2312yes—
157C22×C4×D79C2311yescharacteristic
158C22×C4×D79C2314yes—
159#14579161C2314yes—
160#14579161C23116yes—
161#14579161C2314yes—
162#14579161C2312yes—
163#14579161C2318yes—
164#14579161C2314yes—
165#14579161C2312yes—
166#14579161C2311yescharacteristic
167#14579160C2318yes—
168#14579160C2318yes—
169#14579160C2318yes—
170#14579160C23116yes—
171#14579160C23116yes—
172#14579160C2318yes—
173#14579160C2318yes—
174#14579160C2312yes—
175#14579159C2314yes—
176#14579159C2314yes—
177#14579159C2318yes—
178#14579159C2314yes—
179#14579159C2311yescharacteristic
180#14579158C2311yescharacteristic
181#14579157C2311yescharacteristic
182#14579156C23116yes—
183#14579156C23116yes—
184#14579156C2318yes—
185#14579156C2314yes—
186#14579155C23116yes—
187#14579154C2314yes—
188#14579153C23116yes—
189#14579152C23116yes—
190#14579152C2312yes—
191#14579152C2314yes—
192#14579152C2318yes—
193#14579151C23116yes—
194#14579151C23116yes—
195#14579151C2314yes—
196#14579150C2314yes—
197#14579150C2311yescharacteristic
198#14579150C2314yes—
199#14579149C2312yes—
200#14579149C2314yes—
201#14579149C2314yes—
202#14579149C23116yes—
203#14579148C2311yescharacteristic
204#14579147C2314yes—
205#14579147C23116yes—
206#14579146C23116yes—
207#14579146C23116yes—
208#14579146C2318yes—
209#14579146C2314yes—
210#14579145C2312yes—
211#14579145C2318yes—
212#14579145C2318yes—
213#14579145C2314yes—
214#14579145C23116yes—
215#14579144C2318yes—
216#14579143C2314yes—
217#14579143C23116yes—
218#14579142C2312yes—
219#14579141C2318yes—
220#14579141C2318yes—
221#14579141C23116yes—
222#14579141C23116yes—
223#14579141C23116yes—
224#14579141C23116yes—
225#14579141C2314yes—
226#14579141C2312yes—
227#14579139C23116yes—
228#14579139C23116yes—
229#14579139C23116yes—
230#14579139C23116yes—
231#14579139C23116yes—
232#14579139C2314yes—
233#14579138C23116yes—
234#14579138C23116yes—
235#14579138C2314yes—
236#14579137C2318yes—
237#14579137C2318yes—
238#14579137C2312yes—
239#14579137C2314yes—
240#14579136C23116yes—
241#14579136C2318yes—
242#14579136C2314yes—
243#14579136C2312yes—
244#14579136C2314yes—
245#14579135C2318yes—
246#14579135C2314yes—
247#14579134C23116yes—
248#14579134C23116yes—
249#14579134C2314yes—
250#14579133C2314yes—
251#14579132C2312yes—
252#14579131C2314yes—
253#14579131C2312yes—
254#14579129C2312yes—
255Q8×Dic79C2318yes—
256Q8×Dic79C2314yes—
257C4×Dic158C2318yes—
258C4×Dic158C23116yes—
259C4×Dic158C2312yes—
260C4×Dic158C2314yes—
261C4×Dic158C2314yes—
262#14579126C2318yes—
263#14579126C2314yes—
264C4×D316C23116yes—
265C4×D316C23116yes—
266C4×D316C2318yes—
267C4×D316C2312yes—
268C4×D316C2314yes—
269C4×D316C2318yes—
270C4×D316C2314yes—
271C4×D316C2314yes—
272#14579123C23116yes—
273#14579123C2318yes—
274#14579123C2314yes—
275#14579123C2318yes—
276#14579123C2314yes—
277C4×C22⋊D79C2314yes—
278C4×C22⋊D79C2314yes—
279C4×C22⋊D79C2314yes—
280C4×C22⋊D79C2314yes—
281C4×C22⋊D79C2314yes—
282(C22⋊D79)⋊C4C23116yes—
283(C22⋊D79)⋊C4C23116yes—
284(C22⋊D79)⋊C4C2318yes—
285#14579120C2311yescharacteristic
286#14579120C2314yes—
287#14579119C2318yes—
288#14579119C2314yes—
289#14579119C2318yes—
290#14579118C2312yes—
291#14579118C2314yes—
292#14579118C2314yes—
293#14579118C2314yes—
294#14579118C23116yes—
295#14579117C2318yes—
296C2×C4⋊Dic79C2318yes—
297C2×C4⋊Dic79C2314yes—
298C2×Dic79⋊C4C2318yes—
299C4⋊C4×D79C2318yes—
300C4⋊C4×D79C2318yes—
301C4⋊C4×D79C23116yes—
302C4⋊C4×D79C2318yes—
303C4⋊C4×D79C2318yes—
304C4⋊C4×D79C2318yes—
305C2×C4×Dic79C2311yescharacteristic
306C2×C4×Dic79C2312yes—
307C42×D79C2312yes—
308C42×D79C2312yes—
309C42×D79C2312yes—
310C42×D79C2312yes—
311C42×D79C2314yes—
312C42×D79C2312yes—
313C2×#41×C79C2311yescharacteristic
314C22×Q8×C79C2312yes—
315C4⋊Q8×C79C2312yes—
316C4⋊Q8×C79C2314yes—
317C4⋊Q8×C79C2314yes—
318C4⋊Q8×C79C2312yes—
319C4⋊Q8×C79C2312yes—
320#126×C79C23116yes—
321#125×C79C23116yes—
322#125×C79C2312yes—
323#125×C79C2318yes—
324#124×C79C2314yes—
325#123×C79C2318yes—
326C22⋊Q8×C79C2318yes—
327C22⋊Q8×C79C2318yes—
328C22⋊Q8×C79C2314yes—
329C4×Q8×C79C2318yes—
330C4×Q8×C79C2318yes—
331C4×Q8×C79C2318yes—
332C4×Q8×C79C2312yes—
333C4×Q8×C79C2314yes—
334C4×D4×C79C2314yes—
335C4×D4×C79C2312yes—
336#117×C79C2311yescharacteristic
337#117×C79C2318yes—
338#117×C79C2312yes—
339#117×C79C2312yes—
340#117×C79C2318yes—
341C2×C4⋊C4×C79C2314yes—
342C2×C42×C79C2311yescharacteristic
343C2×C42×C79C2312yes—
344C23×D79C2411yescharacteristic
345#11929625—216no—
346#11929625—48no—
347#11929625—48no—
348#11929624—216no—
349#11929624—28no—
350#11929624—24no—
351#11929624—416no—
352#11929624—48no—
353#11929623—416no—
354#11929623—48no—
355C2×Dic158—28no—
356C2×Dic158—48no—
357C2×Dic158—48no—
358C2×Dic158C2411yescharacteristic
359C2×Dic158C2414yes—
360C2×Dic158C2414yes—
361C2×Dic158C2412yes—
362C2×Dic158C2414yes—
363C2×Dic158C24116yes—
364C2×Dic158C2418yes—
365C2×Dic158C2418yes—
366Q8×D79—416no—
367Q8×D79—416no—
368Q8×D79—48no—
369Q8×D79—48no—
370Q8×D79—48no—
371C2×D316C2412yes—
372C2×D316C2411yescharacteristic
373C2×D316C2414yes—
374C2×D316C2418yes—
375C2×D316C2414yes—
376C2×D316C2418yes—
377C2×C22⋊D79C2414yes—
378C2×C22⋊D79C2412yes—
379C2×C22⋊D79C2414yes—
380C2×C22⋊D79C2414yes—
381C2×C22⋊D79C2418yes—
382C22×Dic79C2411yescharacteristic
383C22×Dic79C2414yes—
384C22×Dic79C2412yes—
385C22×Dic79C2418yes—
386C2×C4×D79—28no—
387C2×C4×D79—24no—
388C2×C4×D79—48no—
389C2×C4×D79C2412yes—
390C2×C4×D79C2412yes—
391C2×C4×D79C2414yes—
392C2×C4×D79C2412yes—
393C2×C4×D79C2414yes—
394C2×C4×D79C2418yes—
395C2×C4×D79C2412yes—
396C2×C4×D79C2412yes—
397C2×C4×D79C2412yes—
398C2×C4×D79C24116yes—
399C2×C4×D79C2418yes—
400C2×C4×D79C2418yes—
401C2×C4×D79C2418yes—
402C2×C4×D79C2412yes—
403C4⋊Dic79C2418yes—
404C4⋊Dic79C2414yes—
405C4⋊Dic79C2418yes—
406C4⋊Dic79C24116yes—
407C4⋊Dic79C24116yes—
408C4⋊Dic79C2418yes—
409C4⋊Dic79C2412yes—
410C4⋊Dic79C2414yes—
411C4⋊Dic79C2414yes—
412Dic79⋊C4C2414yes—
413Dic79⋊C4C24116yes—
414Dic79⋊C4C24116yes—
415Dic79⋊C4C24116yes—
416Dic79⋊C4C24116yes—
417Dic79⋊C4C2414yes—
418Dic79⋊C4C2418yes—
419Dic79⋊C4C2414yes—
420Dic79⋊C4C2414yes—
421Dic79⋊C4C2414yes—
422C22⋊Dic79C2412yes—
423C22⋊Dic79C2414yes—
424C22⋊Dic79C2414yes—
425(C2×D79)⋊C4C2418yes—
426(C2×D79)⋊C4C2414yes—
427(C2×D79)⋊C4C2414yes—
428(C2×D79)⋊C4C2414yes—
429(C2×D79)⋊C4C2414yes—
430(C2×D79)⋊C4C2414yes—
431(C2×D79)⋊C4C24116yes—
432(C2×D79)⋊C4C24116yes—
433(C2×D79)⋊C4C2418yes—
434(C2×D79)⋊C4C24116yes—
435(C2×D79)⋊C4C2418yes—
436(C2×D79)⋊C4C2418yes—
437C4×Dic79C2411yescharacteristic
438C4×Dic79C2411yescharacteristic
439C4×Dic79C2412yes—
440C4×Dic79C2412yes—
441C4×Dic79C2412yes—
442C4×Dic79C2412yes—
443C4×Dic79C2412yes—
444C4×Dic79C2414yes—
445C4×Dic79C2412yes—
446C4×Dic79C2418yes—
447C4×Dic79C24116yes—
448#41×C79—24no—
449C2×Q8×C79—28no—
450C2×Q8×C79C2411yescharacteristic
451C2×Q8×C79C2414yes—
452C2×Q8×C79C2414yes—
453C2×Q8×C79C2414yes—
454C2×D4×C79C2412yes—
455C2×D4×C79C2411yescharacteristic
456C22×C4×C79C2412yes—
457C22×C4×C79C2414yes—
458C22×C4×C79C2414yes—
459C22×C4×C79C2412yes—
460C22×C4×C79C2411yescharacteristic
461C4⋊C4×C79C2418yes—
462C4⋊C4×C79C2418yes—
463C4⋊C4×C79C2414yes—
464C4⋊C4×C79C2412yes—
465C4⋊C4×C79C2414yes—
466C4⋊C4×C79C2414yes—
467C4⋊C4×C79C24116yes—
468C4⋊C4×C79C24116yes—
469C4⋊C4×C79C2418yes—
470C22⋊C4×C79C2412yes—
471C22⋊C4×C79C2414yes—
472C22⋊C4×C79C2414yes—
473C22⋊C4×C79C24116yes—
474C42×C79C2411yescharacteristic
475C42×C79C2412yes—
476C42×C79C2411yescharacteristic
477C42×C79C2414yes—
478C42×C79C2412yes—
479C42×C79C24116yes—
480C42×C79C2414yes—
481C23×C79C2512yes—
482C23×C79C2511yescharacteristic
483C22×D79—22no—
484C22×D79—24no—
485C22×D79C2514yes—
486C22×D79C2512yes—
487C22×D79C2512yes—
488Q8×C79—22no—
489Q8×C79—28no—
490Q8×C79—28no—
491Q8×C79—28no—
492D4×C79—24no—
493D4×C79—22no—
494C2×C4×C79—28no—
495C2×C4×C79—24no—
496C2×C4×C79—24no—
497C2×C4×C79—28no—
498C2×C4×C79H(5,𝔽2)14yes—
499C2×C4×C79C2518yes—
500C2×C4×C79C2512yes—
501C2×C4×C79C2514yes—
502C2×C4×C79C2512yes—
503C2×C4×C79C2518yes—
504C2×C4×C79C2511yescharacteristic
505C2×C4×C79C2511yescharacteristic
506C2×C4×C79C2512yes—
507C22⋊D79—28no—
508C22⋊D79—24no—
509C22⋊D79—28no—
510C22⋊D79—28no—
511C22⋊D79—48no—
512C2×Dic79—22no—
513C2×Dic79—28no—
514C2×Dic79—24no—
515C2×Dic79—48no—
516C2×Dic79C2514yes—
517C2×Dic79C2512yes—
518C2×Dic79C2512yes—
519C2×Dic79C2514yes—
520C2×Dic79C2518yes—
521C2×Dic79C2512yes—
522C2×Dic79C2512yes—
523D316—28no—
524D316—216no—
525D316—24no—
526D316—22no—
527D316—28no—
528D316—48no—
529C4×D79—24no—
530C4×D79—24no—
531C4×D79—24no—
532C4×D79—28no—
533C4×D79—24no—
534C4×D79—24no—
535C4×D79—28no—
536C4×D79—24no—
537C4×D79—216no—
538C4×D79—416no—
539C4×D79—48no—
540C4×D79—48no—
541C4×D79—48no—
542C4×D792−1+418yescomplemented
543Dic158—22no—
544Dic158—28no—
545Dic158—28no—
546Dic158—24no—
547Dic158—28no—
548Dic158—416no—
549Dic158—48no—
550Dic158—48no—
551C22×C79—22no—
552C22×C79—22no—
553C22×C79—24no—
554C22×C79C2×H(5,𝔽2)12yes—
555C22×C79C2611yescharacteristic
556C2×D79—28no—
557C2×D79—22no—
558C2×D79—22no—
559C2×D79—24no—
560C2×D79—22no—
561C2×D79—24no—
562C2×D79—28no—
563C2×D79C2×2−1+414yes—
564C4×C79—22no—
565C4×C79—28no—
566C4×C79—24no—
567C4×C79—22no—
568C4×C79—28no—
569C4×C79C2×H(5,𝔽2)12yes—
570C4×C79C2×H(5,𝔽2)12yes—
571C4×C79C2×2−1+414yes—
572Dic79—22no—
573Dic79—24no—
574Dic79—28no—
575Dic79—22no—
576Dic79—24no—
577Dic79—22no—
578Dic79C2×2−1+414yes—
579#62833—791nomaximal, Sylow
580C2×C79—22no—
581C2×C79—42no—
582C2×C79C22×H(5,𝔽2)11yescharacteristic
583C2×C79C22×2−1+412yes—
584D79—24no—
585D79—44no—
586D79—42no—
587#3552—794no—
588#3552—794no—
589#3552—798no—
590#3544—798no—
591#3511—794no—
592#3511—794no—
593#3509—791no—
594#3509—792no—
595#3509D7911yescharacteristic, complemented
596#3503—794no—
597#3503—794no—
598#3499—792no—
599#3499—791no—
600#3499—791no—
601#3492—798no—
602#3486—792no—
603#3486—792no—
604#3444—791no—
605#3444—791no—
606C22×C4⋊Q8—791no—
607C79#6283311yescharacteristic, complemented, Sylow
608C2×2−1+4—792no—
609C2×2−1+4—792no—
610C23×Q8—792no—
611#563—7916no—
612#563—7916no—
613Q82—798no—
614#557—798no—
615#557—794no—
616#557C2×D7914yescomplemented
617#556—798no—
618#556—794no—
619#556C2×D7914yescomplemented
620#555—798no—
621#554—7916no—
622#554—798no—
623#554—798no—
624#554—798no—
625#554—798no—
626#553—7916no—
627#553—798no—
628#553—798no—
629#552—798no—
630#552—7916no—
631#552C2×D7918yes—
632D4×Q8—798no—
633D4×Q8—794no—
634D4×Q8—798no—
635D4×Q8—798no—
636D4×Q8—798no—
637D4×Q8—798no—
638D4×Q8—794no—
639#548—798no—
640#548—798no—
641#548—798no—
642#548—798no—
643#547—794no—
644#547—7916no—
645#547—798no—
646#547—798no—
647#547—794no—
648#547—798no—
649#544—798no—
650#544—7916no—
651#544—798no—
652#544—798no—
653#542—7916no—
654#542—798no—
655#542—798no—
656#541—794no—
657#541—798no—
658#541C2×D7914yescomplemented
659#539—7916no—
660#539—7916no—
661#537—798no—
662#536—792no—
663#536—794no—
664#536—794no—
665#536—794no—
666#536—798no—
667#536—792no—
668#536—792no—
669#536—798no—
670#536—794no—
671#536C2×D7912yes—
672#533—792no—
673#533—794no—
674#533—792no—
675#533—798no—
676#533—791no—
677#533C2×D7911yescharacteristic
678#533C2×D7914yescomplemented
679#532—791no—
680#532—792no—
681#532—792no—
682#532—794no—
683#532—792no—
684#532—791no—
685#532—792no—
686C2×C4⋊Q8—792no—
687C2×C4⋊Q8—794no—
688C2×C4⋊Q8—794no—
689C2×C4⋊Q8—794no—
690C2×C4⋊Q8—794no—
691C2×C4⋊Q8—794no—
692C2×C4⋊Q8—792no—
693C2×C4⋊Q8—794no—
694C2×C4⋊Q8—791no—
695C2×C4⋊Q8—792no—
696C2×C4⋊Q8C2×D7911yescharacteristic
697#529—794no—
698#529—794no—
699#529—794no—
700#529—792no—
701#529—794no—
702#529—792no—
703#529—794no—
704#525—791no—
705#525—798no—
706#525—794no—
707#525—794no—
708#525—792no—
709#525—791no—
710#525—798no—
711#520—798no—
712#520—798no—
713#519—792no—
714#519C2×D7912yes—
715C4×#41—794no—
716C4×#41—792no—
717C4×#41—791no—
718C4×#41—794no—
719C4×#41C2×D7911yescharacteristic
720C22×C4⋊C4—794no—
721C22×C42—791no—
7222−1+4—3168no—
7232−1+4—3168no—
724C2×#41—794no—
725C2×#41—794no—
726C2×#41—794no—
727C2×#41—798no—
728C2×#41—794no—
729C2×#41—798no—
730C2×#41—794no—
731C2×#41—794no—
732C2×#41—792no—
733C2×#41—791no—
734C2×#41C22×D7911yescharacteristic
735C22×Q8—3168no—
736C22×Q8—798no—
737C22×Q8—798no—
738C22×Q8—794no—
739C22×Q8—794no—
740C22×Q8—794no—
741C22×Q8—794no—
742C22×Q8—794no—
743C22×Q8—792no—
744C22×Q8C22×D7912yes—
745C23×C4—794no—
746C23×C4—792no—
747C23×C4—791no—
748C4⋊Q8—791no—
749C4⋊Q8—794no—
750C4⋊Q8—794no—
751C4⋊Q8—798no—
752C4⋊Q8—794no—
753C4⋊Q8—798no—
754C4⋊Q8—798no—
755C4⋊Q8—798no—
756C4⋊Q8—798no—
757C4⋊Q8—7916no—
758C4⋊Q8—798no—
759C4⋊Q8—792no—
760C4⋊Q8—7916no—
761C4⋊Q8—792no—
762C4⋊Q8—791no—
763C4⋊Q8—792no—
764C4⋊Q8—794no—
765C4⋊Q8—794no—
766C4⋊Q8—794no—
767C4⋊Q8—798no—
768C4⋊Q8—7916no—
769C4⋊Q8C22×D7912yes—
770C4⋊Q8C22×D7912yes—
771C4⋊Q8C22×D7914yes—
772C4⋊Q8C22×D7914yes—
773C4⋊Q8C22×D7912yes—
774#127—791no—
775#127—791no—
776#126—798no—
777#126—794no—
778#126—7916no—
779#126—7916no—
780#126—794no—
781#126—7916no—
782#126C22×D79116yes—
783#125—792no—
784#125—794no—
785#125—794no—
786#125—7916no—
787#125—798no—
788#125—7916no—
789#125—7916no—
790#125—7916no—
791#125C22×D7912yes—
792#125C22×D7918yes—
793#125C22×D79116yes—
794#124—791no—
795#124—794no—
796#124—794no—
797#124—791no—
798#124—794no—
799#124—7916no—
800#124—792no—
801#124—794no—
802#124—794no—
803#124—7916no—
804#124C22×D7914yes—
805#123—792no—
806#123—798no—
807#123—798no—
808#123—794no—
809#123—7916no—
810#123—7916no—
811#123—794no—
812#123—792no—
813#123—794no—
814#123—798no—
815#123—798no—
816#123—7916no—
817#123—7916no—
818#123C22×D7918yes—
819C22⋊Q8—792no—
820C22⋊Q8—794no—
821C22⋊Q8—798no—
822C22⋊Q8—798no—
823C22⋊Q8—794no—
824C22⋊Q8—792no—
825C22⋊Q8—794no—
826C22⋊Q8—7916no—
827C22⋊Q8—7916no—
828C22⋊Q8—798no—
829C22⋊Q8—798no—
830C22⋊Q8—7916no—
831C22⋊Q8—7916no—
832C22⋊Q8—7916no—
833C22⋊Q8—7916no—
834C22⋊Q8—7916no—
835C22⋊Q8—7916no—
836C22⋊Q8—7916no—
837C22⋊Q8—794no—
838C22⋊Q8—7916no—
839C22⋊Q8—7916no—
840C22⋊Q8C22×D7914yes—
841C22⋊Q8C22×D7918yes—
842C22⋊Q8C22×D7918yes—
843#121—794no—
844#121—792no—
845#121—794no—
846#121—798no—
847#121—794no—
848#121—792no—
849#121—794no—
850#121—7916no—
851#121—798no—
852#121—794no—
853#121—7916no—
854#121—7916no—
855#120—792no—
856#120—794no—
857#120—792no—
858C4×Q8—794no—
859C4×Q8—798no—
860C4×Q8—794no—
861C4×Q8—798no—
862C4×Q8—792no—
863C4×Q8—794no—
864C4×Q8—794no—
865C4×Q8—798no—
866C4×Q8—7916no—
867C4×Q8C22×D7914yes—
868C4×Q8C22×D7912yes—
869C4×Q8C22×D7918yes—
870C4×Q8C22×D7918yes—
871C4×Q8C22×D7918yes—
872C4×D4—794no—
873C4×D4—794no—
874C4×D4—794no—
875C4×D4—794no—
876C4×D4—794no—
877C4×D4—798no—
878C4×D4—794no—
879C4×D4—794no—
880C4×D4—7916no—
881C4×D4—798no—
882C4×D4—798no—
883C4×D4—7916no—
884C4×D4—7916no—
885C4×D4—798no—
886C4×D4—794no—
887C4×D4—794no—
888C4×D4—794no—
889C4×D4—792no—
890C4×D4—7916no—
891C4×D4—7916no—
892C4×D4—798no—
893C4×D4C22×D7914yes—
894C4×D4C22×D7912yes—
895#117—791no—
896#117—794no—
897#117—794no—
898#117—798no—
899#117—798no—
900#117—798no—
901#117—794no—
902#117—794no—
903#117—792no—
904#117—794no—
905#117—7916no—
906#117C22×D7912yes—
907#117C22×D7911yescharacteristic
908#117C22×D7912yes—
909#117C22×D7918yes—
910#117C22×D7918yes—
911C2×C4⋊C4—798no—
912C2×C4⋊C4—794no—
913C2×C4⋊C4—798no—
914C2×C4⋊C4—798no—
915C2×C4⋊C4—798no—
916C2×C4⋊C4—798no—
917C2×C4⋊C4—798no—
918C2×C4⋊C4—7916no—
919C2×C4⋊C4—798no—
920C2×C4⋊C4C22×D7914yes—
921C2×C42—791no—
922C2×C42—792no—
923C2×C42—794no—
924C2×C42—792no—
925C2×C42—792no—
926C2×C42—792no—
927C2×C42—792no—
928C2×C42—792no—
929C2×C42C22×D7912yes—
930C2×C42C22×D7911yescharacteristic
931C24—791no—
932#41—24no—
933#41—3168no—
934#41—31616no—
935#41—3168no—
936#41—31616no—
937#41—3168no—
938#41—3168no—
939#41—15816no—
940#41—15816no—
941#41—1588no—
942#41—1584no—
943C2×Q8—28no—
944C2×Q8—3168no—
945C2×Q8—3168no—
946C2×Q8—31616no—
947C2×Q8—31616no—
948C2×Q8—3168no—
949C2×Q8—3168no—
950C2×Q8—3168no—
951C2×Q8—798no—
952C2×Q8—798no—
953C2×Q8—7916no—
954C2×Q8—794no—
955C2×Q8—792no—
956C2×Q8—794no—
957C2×Q8—791no—
958C2×Q8—794no—
959C2×Q8—1588no—
960C2×Q8C23×D7914yes—
961C2×Q8C23×D7911yescharacteristic
962C2×Q8C23×D7914yes—
963C2×Q8C23×D7914yes—
964C2×D4—798no—
965C2×D4—794no—
966C2×D4—794no—
967C2×D4—794no—
968C2×D4—792no—
969C2×D4—798no—
970C2×D4—798no—
971C2×D4—794no—
972C2×D4—794no—
973C2×D4—792no—
974C2×D4—791no—
975C2×D4C23×D7912yes—
976C2×D4C23×D7911yescharacteristic
977C22×C4—3168no—
978C22×C4—798no—
979C22×C4—7916no—
980C22×C4—798no—
981C22×C4—798no—
982C22×C4—798no—
983C22×C4—792no—
984C22×C4—792no—
985C22×C4—791no—
986C22×C4—794no—
987C22×C4—792no—
988C22×C4—792no—
989C22×C4—792no—
990C22×C4—792no—
991C22×C4—792no—
992C22×C4—798no—
993C22×C4—794no—
994C22×C4—792no—
995C22×C4—794no—
996C22×C4—1588no—
997C22×C4—1584no—
998C22×C4C23×D7912yes—
999C22×C4C23×D7914yes—
1000C22×C4C23×D7912yes—
1001C22×C4C23×D7914yes—
1002C22×C4C23×D7911yescharacteristic
1003C4⋊C4—794no—
1004C4⋊C4—7916no—
1005C4⋊C4—7916no—
1006C4⋊C4—7916no—
1007C4⋊C4—794no—
1008C4⋊C4—794no—
1009C4⋊C4—798no—
1010C4⋊C4—794no—
1011C4⋊C4—794no—
1012C4⋊C4—7916no—
1013C4⋊C4—798no—
1014C4⋊C4—794no—
1015C4⋊C4—798no—
1016C4⋊C4—7916no—
1017C4⋊C4—7916no—
1018C4⋊C4—792no—
1019C4⋊C4—798no—
1020C4⋊C4—794no—
1021C4⋊C4—794no—
1022C4⋊C4C23×D7918yes—
1023C4⋊C4C23×D7918yes—
1024C4⋊C4C23×D79116yes—
1025C4⋊C4C23×D7914yes—
1026C4⋊C4C23×D7918yes—
1027C4⋊C4C23×D7914yes—
1028C4⋊C4C23×D7912yes—
1029C4⋊C4C23×D7914yes—
1030C4⋊C4C23×D79116yes—
1031C22⋊C4—792no—
1032C22⋊C4—794no—
1033C22⋊C4—794no—
1034C22⋊C4—794no—
1035C22⋊C4—798no—
1036C22⋊C4—794no—
1037C22⋊C4—7916no—
1038C22⋊C4—7916no—
1039C22⋊C4—7916no—
1040C22⋊C4—794no—
1041C22⋊C4—798no—
1042C22⋊C4—798no—
1043C22⋊C4—794no—
1044C22⋊C4—794no—
1045C22⋊C4—798no—
1046C22⋊C4C23×D7914yes—
1047C22⋊C4C23×D7912yes—
1048C22⋊C4C23×D79116yes—
1049C22⋊C4C23×D7914yes—
1050C42—791no—
1051C42—792no—
1052C42—791no—
1053C42—792no—
1054C42—792no—
1055C42—792no—
1056C42—792no—
1057C42—798no—
1058C42—794no—
1059C42—792no—
1060C42—7916no—
1061C42C23×D7911yescharacteristic
1062C42C23×D7911yescharacteristic
1063C42C23×D7912yes—
1064C42C23×D7914yes—
1065C42C23×D7914yes—
1066C42C23×D7912yes—
1067C42C23×D79116yes—
1068C23—792no—
1069C23—794no—
1070C23—792no—
1071C23—1584no—
1072C23—1582no—
1073C23C24×D7912yes—
1074C23C24×D7911yescharacteristic
1075Q8—28no—
1076Q8—28no—
1077Q8—22no—
1078Q8—28no—
1079Q8—31616no—
1080Q8—3168no—
1081Q8—3168no—
1082Q8—1588no—
1083Q8—1584no—
1084Q8—1582no—
1085Q8—1588no—
1086Q8—1588no—
1087D4—24no—
1088D4—22no—
1089D4—3168no—
1090D4—3168no—
1091D4—1588no—
1092D4—15816no—
1093D4—1588no—
1094D4—1588no—
1095D4—1588no—
1096D4—1584no—
1097D4—1584no—
1098D4—1582no—
1099D4—1588no—
1100C2×C4—28no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—28no—
1104C2×C4—31616no—
1105C2×C4—3168no—
1106C2×C4—3168no—
1107C2×C4—3168no—
1108C2×C4—3168no—
1109C2×C4—792no—
1110C2×C4—798no—
1111C2×C4—794no—
1112C2×C4—792no—
1113C2×C4—792no—
1114C2×C4—798no—
1115C2×C4—792no—
1116C2×C4—794no—
1117C2×C4—1584no—
1118C2×C4—15816no—
1119C2×C4—1584no—
1120C2×C4—1584no—
1121C2×C4—1588no—
1122C2×C4—1582no—
1123C2×C4—1584no—
1124C2×C4—1584no—
1125C2×C4—1584no—
1126C2×C4—1588no—
1127C2×C4—1584no—
1128C2×C4—1588no—
1129C2×C4#1457920714yes—
1130C2×C4C24×D7918yes—
1131C2×C4C24×D7912yes—
1132C2×C4C24×D7914yes—
1133C2×C4C24×D7912yes—
1134C2×C4C24×D7918yes—
1135C2×C4C24×D7911yescharacteristic
1136C2×C4C24×D7911yescharacteristic
1137C2×C4C24×D7912yes—
1138C22—22no—
1139C22—22no—
1140C22—24no—
1141C22—794no—
1142C22—1588no—
1143C22—1582no—
1144C22—1584no—
1145C22—1588no—
1146C22—1584no—
1147C22—1582no—
1148C22—1582no—
1149C22C2×#1457920712yes—
1150C22C25×D7911yescharacteristic
1151C4—22no—
1152C4—28no—
1153C4—22no—
1154C4—24no—
1155C4—28no—
1156C4—794no—
1157C4—1588no—
1158C4—1582no—
1159C4—1584no—
1160C4—1582no—
1161C4—1582no—
1162C4—1584no—
1163C4C2×#1457920712yes—
1164C4C2×#1457920712yes—
1165C42−1+4×D7914yes—
1166C2—22no—
1167C2—42no—
1168C2—3162no—
1169C2—3164no—
1170C2—1584no—
1171C2C22×#1457920711yescharacteristic
1172C2C2×2−1+4×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3509C2
hypercenter#3509D79
hypocenterC79#62833
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #23777846C2semidirect
2. #23777844C2semidirect
3. #23777830C2semidirect
4. #23777742C2semidirect
5. #23777312C2semidirect
6. #23777304C2semidirect
7. #23777287C2semidirect
8. #23777281C2semidirect
9. #23777217C2semidirect
10. #23777212C2semidirect
11. #23777185C2semidirect
12. #23777183C2semidirect
13. #23777182C2semidirect
14. #23777100C2semidirect
15. #23777052C2semidirect
16. #23777049C2semidirect
17. #23776697C2semidirect
18. #23776693C2semidirect
19. C2×C4⋊Q8×D79C2semidirect
20. C79×#3509C2semidirect
24. #19099317C22semidirect
25. #19099315C22semidirect
26. Q8×Dic158C22semidirect
27. #19099292C22semidirect
28. #19099291C22semidirect
29. #19099286C22semidirect
30. #19099285C22semidirect
31. #19099276C22semidirect
34. #19099271C22semidirect
36. #19099269C22semidirect
44. Q8×D316C22semidirect
46. #19099228C22semidirect
48. #19099226C22semidirect
54. #19099217C22semidirect
55. #19099216C22semidirect
56. #19099215C22semidirect
60. #19099193C22semidirect
61. #19099193C22semidirect
62. #19099191C22semidirect
63. #19099186C22semidirect
64. #19099185C22semidirect
65. #19099179C22semidirect
66. #19099176C22semidirect
67. #19099171C22semidirect
74. #19099139C22semidirect
75. #19099138C22semidirect
76. #19099138C22semidirect
79. #19099133C22semidirect
81. #19099118C22semidirect
83. #19099117C22semidirect
86. #19099114C22semidirect
88. #19099113C22semidirect
89. #19099112C22semidirect
93. C2×#14579161C22semidirect
100. C4⋊Q8×D79C22semidirect
101. C4⋊Q8×D79C22semidirect
125. #557×C79C22semidirect
126. #556×C79C22semidirect
128. #541×C79C22semidirect
131. #533×C79C22semidirect
542. C4×D792−1+4semidirect
595. #3509D79semidirect
607. C79#62833semidirect
616. #557C2×D79semidirect
619. #556C2×D79semidirect
658. #541C2×D79semidirect
678. #533C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237778462
#237778442
#237778302
#237777422
#237773122
#237773042
#237772872
#237772812
#237772172
#237772122
#237771852
#237771832
#237771822
#237771002
#237770522
#237770492
#237766972
#237766932
C2×C4⋊Q8×D792
C79×#35092
#6283379