Finite Group Databasebeta

← #35197210

Subgroups — #35197210

Order 20224.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777994C218yesmaximal, complemented
2#23777874C214yesmaximal, complemented
3#23777775C214yesmaximal, complemented
4#23777710C218yesmaximal, complemented
5#23777407C214yesmaximal, complemented
6#23777364C214yesmaximal, complemented
7#23777345C218yesmaximal, complemented
8#23777312C214yesmaximal, complemented
9#23777297C212yesmaximal, complemented
10#23777277C211yesmaximal, characteristic, complemented
11#23777277C214yesmaximal, complemented
12#23777189C212yesmaximal, complemented
13#23777183C211yesmaximal, characteristic, complemented
14#23777178C211yesmaximal, characteristic, complemented
15#23777059C212yesmaximal, complemented
16#23777043C212yesmaximal, complemented
17#23776697C211yesmaximal, characteristic, complemented
18#23776693C211yesmaximal, characteristic, complemented
19C2×#19099114C211yesmaximal, characteristic, complemented
20C79×#3509C211yesmaximal, characteristic, complemented
21C2×#14579209C2212yescomplemented
22C2×#14579207C2212yes—
23C22×#11929625C2212yescomplemented
24#19099311C22116yescomplemented
25#19099304C22116yescomplemented
26#19099298C2218yescomplemented
27#19099298C2218yescomplemented
28#19099298C2214yescomplemented
29#19099285C2218yescomplemented
30#19099276C2218yescomplemented
31#19099269C2218yescomplemented
32#19099266C2218yescomplemented
33#19099266C22116yescomplemented
34#19099257C2218yescomplemented
35#19099238C22116yescomplemented
36#19099237C22116yescomplemented
37#19099235C2218yescomplemented
38#19099235C2218yescomplemented
39#19099235C2214yescomplemented
40#19099235C2218yescomplemented
41#19099235C2214yescomplemented
42#19099228C2214yescomplemented
43#19099225C2218yescomplemented
44#19099225C2218yescomplemented
45#19099223C2218yescomplemented
46#19099216C2218yescomplemented
47#19099216C2214yescomplemented
48#19099215C2218yescomplemented
49#19099214C2218yescomplemented
50#19099206C2218yescomplemented
51#19099205C22116yescomplemented
52#19099204C2218yescomplemented
53#19099204C2218yescomplemented
54#19099204C2218yescomplemented
55#19099204C2218yescomplemented
56#19099204C2218yescomplemented
57D4×D316C2218yes—
58D4×D316C2214yescomplemented
59#19099186C2218yescomplemented
60#19099185C2218yescomplemented
61#19099185C2218yescomplemented
62#19099169C2218yescomplemented
63#19099169C2218yescomplemented
64#19099169C22116yescomplemented
65#19099169C2214yescomplemented
66#19099161C22116yescomplemented
67#19099152C22116yescomplemented
68#19099152C22116yescomplemented
69#19099143C2218yescomplemented
70#19099138C2214yescomplemented
71#19099138C2214yescomplemented
72#19099137C2212yescomplemented
73#19099132C2212yes—
74#19099132C2212yescomplemented
75#19099132C2218yescomplemented
76#19099132C2214yescomplemented
77#19099132C2218yescomplemented
78#19099131C2214yescomplemented
79#19099124C2218yescomplemented
80#19099118C2212yescomplemented
81#19099117C2212yescomplemented
82#19099116C2211yescharacteristic, complemented
83#19099114C2214yescomplemented
84#19099114C2214yescomplemented
85#19099114C2214yescomplemented
86#19099114C2214yescomplemented
87#19099114C2214yescomplemented
88#19099114C2212yescomplemented
89#19099114C2214yescomplemented
90#19099114C2212yescomplemented
91#19099113C2211yescharacteristic
92#19099113C2212yescomplemented
93#19099110C2212yescomplemented
94#19099109C2211yescharacteristic
95C4⋊Q8×D79C2212yescomplemented
96C2×#14579158C2211yescharacteristic
97C2×#14579158C2212yescomplemented
98#19099100C2218yescomplemented
99#19099100C2214yescomplemented
100#19099100C2212yescomplemented
101#19099099C2214yescomplemented
102#19099098C2214yescomplemented
103#19099095C2212yescomplemented
104#19099093C2214yescomplemented
105#19099091C2214yescomplemented
106C2×#14579150C2212yescomplemented
107#124×D79C2214yescomplemented
108#19099076C2214yescomplemented
109#19099075C2212yescomplemented
110#19099075C2211yescharacteristic, complemented
111#19099075C2218yescomplemented
112#19099072C2214yescomplemented
113#19099070C2211yescharacteristic
114#123×D79C2218yescomplemented
115C2×#14579136C2214yescomplemented
116#19099045C2218yescomplemented
117#19099037C2212yescomplemented
118#19099037C2218yescomplemented
119C4×#11929625C2214yescomplemented
120C4×#11929624C2214yescomplemented
121C4×#11929624C2211yescharacteristic, complemented
122#19099031C2212yescomplemented
123C2×#14579123C2214yescomplemented
124C2×C42×D79C2211yescharacteristic, complemented
125#557×C79C2214yescomplemented
126#556×C79C2214yescomplemented
127#552×C79C2218yescomplemented
128#541×C79C2214yescomplemented
129#536×C79C2212yes—
130#533×C79C2214yescomplemented
131#533×C79C2211yescharacteristic, complemented
132C2×C4⋊Q8×C79C2211yescharacteristic, complemented
133#519×C79C2212yescomplemented
134C4×#41×C79C2211yescharacteristic
135#14579209—48no—
136#14579207—48no—
137C2×#11929625—48no—
138C2×#11929625C2314yes—
139C2×#11929625C2314yes—
140C2×#11929625C2314yes—
141C2×#11929625C2318yes—
142C2×#11929625C2314yes—
143C2×#11929625C2318yes—
144C2×#11929625C2318yes—
145C2×#11929624C2312yes—
146C2×#11929624C2311yescharacteristic
147C2×#11929624C2314yes—
148C2×#11929624C2318yes—
149C2×#11929624C2314yes—
150C2×Q8×D79C2314yes—
151C2×Q8×D79C2314yes—
152C22×D316C2312yes—
153C22×D316C2314yes—
154C22×D316C2314yes—
155C22×D316C2318yes—
156C22×D316C2314yes—
157C2×D4×D79C2318yes—
158C2×D4×D79C2314yes—
159C22×C4×D79C2311yescharacteristic
160C22×C4×D79C2312yes—
161C22×C4×D79C2314yes—
162#14579161C2311yescharacteristic
163#14579160C2312yes—
164#14579160C2318yes—
165#14579159C2314yes—
166#14579159C2311yescharacteristic
167#14579158C2318yes—
168#14579158C2312yes—
169#14579158C23116yes—
170#14579158C2314yes—
171#14579158C2314yes—
172#14579158C2314yes—
173#14579158C2312yes—
174#14579158C2311yescharacteristic
175#14579157C2311yescharacteristic
176#14579156C2318yes—
177#14579156C23116yes—
178#14579156C2314yes—
179#14579155C23116yes—
180#14579154C2314yes—
181#14579152C2314yes—
182#14579152C2312yes—
183#14579151C2314yes—
184#14579150C2314yes—
185#14579150C2314yes—
186#14579150C2318yes—
187#14579150C2314yes—
188#14579150C2318yes—
189#14579150C2314yes—
190#14579150C2311yescharacteristic
191#14579149C2312yes—
192#14579149C2314yes—
193#14579149C23116yes—
194#14579149C23116yes—
195#14579149C2314yes—
196#14579148C2311yescharacteristic
197#14579147C2314yes—
198#14579147C23116yes—
199#14579146C23116yes—
200#14579146C23116yes—
201#14579146C23116yes—
202#14579146C23116yes—
203#14579146C23116yes—
204#14579146C2314yes—
205#14579146C23116yes—
206#14579146C23116yes—
207#14579146C2318yes—
208#14579145C2314yes—
209#14579145C2312yes—
210#14579144C2318yes—
211#14579143C2314yes—
212#14579143C23116yes—
213#14579142C2312yes—
214#14579141C23116yes—
215#14579141C2314yes—
216#14579141C2312yes—
217#14579139C23116yes—
218#14579139C23116yes—
219#14579139C23116yes—
220#14579139C2314yes—
221#14579138C2314yes—
222#14579137C2318yes—
223#14579137C2314yes—
224#14579137C2312yes—
225#14579136C2318yes—
226#14579136C23116yes—
227#14579136C2318yes—
228#14579136C23116yes—
229#14579136C23116yes—
230#14579136C23116yes—
231#14579136C23116yes—
232#14579136C23116yes—
233#14579136C23116yes—
234#14579136C2314yes—
235#14579136C2318yes—
236#14579136C2318yes—
237#14579136C2318yes—
238#14579136C2318yes—
239#14579136C2314yes—
240#14579136C2318yes—
241#14579136C2312yes—
242#14579136C2318yes—
243#14579135C2318yes—
244#14579135C2314yes—
245#14579134C23116yes—
246#14579134C23116yes—
247#14579134C2314yes—
248#14579133C2314yes—
249#14579132C2312yes—
250#14579131C23116yes—
251#14579131C23116yes—
252#14579131C23116yes—
253#14579131C2318yes—
254#14579131C2318yes—
255#14579131C2312yes—
256#14579131C2314yes—
257#14579129C2312yes—
258Q8×Dic79C2314yes—
259C4×Dic158C2312yes—
260C4×Dic158C2314yes—
261C4×Dic158C2314yes—
262#14579126C2314yes—
263C4×D316C23116yes—
264C4×D316C23116yes—
265C4×D316C23116yes—
266C4×D316C2318yes—
267C4×D316C2318yes—
268C4×D316C2314yes—
269C4×D316C2318yes—
270C4×D316C2312yes—
271C4×D316C2314yes—
272C4×D316C2314yes—
273#14579123C2318yes—
274#14579123C2318yes—
275#14579123C2314yes—
276#14579123C2318yes—
277#14579123C2318yes—
278#14579123C2318yes—
279#14579123C2318yes—
280#14579123C23116yes—
281#14579123C2314yes—
282#14579123C2318yes—
283#14579123C2318yes—
284C4×C22⋊D79C2314yes—
285C4×C22⋊D79C2314yes—
286C4×C22⋊D79C2314yes—
287C4×C22⋊D79C2314yes—
288C4×C22⋊D79C2314yes—
289(C22⋊D79)⋊C4C2318yes—
290#14579120C2311yescharacteristic
291#14579120C2314yes—
292#14579119C2318yes—
293#14579119C2314yes—
294#14579118C2312yes—
295#14579118C2314yes—
296#14579118C2314yes—
297#14579118C2314yes—
298#14579118C23116yes—
299C4⋊C4×D79C2318yes—
300C4⋊C4×D79C23116yes—
301C2×(C2×D79)⋊C4C2318yes—
302C22⋊C4×D79C23116yes—
303C22⋊C4×D79C23116yes—
304C22⋊C4×D79C2318yes—
305C2×C4×Dic79C2312yes—
306C2×C4×Dic79C2311yescharacteristic
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×C79C2312yes—
338#117×C79C2318yes—
339#117×C79C2312yes—
340#117×C79C2318yes—
341C2×C4⋊C4×C79C2314yes—
342C2×C42×C79C2311yescharacteristic
343C2×C42×C79C2312yes—
344C23×D79C2414yes—
345C23×D79C2411yescharacteristic
346C23×D79C2418yes—
347#11929625—416no—
348#11929625—416no—
349#11929625—48no—
350#11929625—416no—
351#11929625—48no—
352#11929625—48no—
353#11929625—48no—
354#11929624—28no—
355#11929624—24no—
356#11929624—416no—
357#11929624—48no—
358#11929624—48no—
359C2×Dic158C2411yescharacteristic
360C2×Dic158C2412yes—
361C2×Dic158C2418yes—
362C2×Dic158C2414yes—
363Q8×D79—48no—
364Q8×D79—48no—
365C2×D316—28no—
366C2×D316—48no—
367C2×D316—48no—
368C2×D316—48no—
369C2×D316—416no—
370C2×D316C2411yescharacteristic
371C2×D316C2414yes—
372C2×D316C2412yes—
373C2×D316C2414yes—
374C2×D316C2418yes—
375C2×D316C2414yes—
376C2×D316C2418yes—
377C2×D316C2414yes—
378C2×D316C24116yes—
379C2×D316C2418yes—
380C2×D316C24116yes—
381C2×D316C2418yes—
382C2×D316C2418yes—
383C2×D316C24116yes—
384C2×C22⋊D79C2412yes—
385C2×C22⋊D79C2414yes—
386C2×C22⋊D79C2414yes—
387C2×C22⋊D79C2414yes—
388C2×C22⋊D79C2418yes—
389D4×D79—416no—
390D4×D79—48no—
391C22×Dic79C2411yescharacteristic
392C22×Dic79C2412yes—
393C2×C4×D79—24no—
394C2×C4×D79—48no—
395C2×C4×D79—44no—
396C2×C4×D79C2412yes—
397C2×C4×D79C2414yes—
398C2×C4×D79C2412yes—
399C2×C4×D79C2414yes—
400C2×C4×D79C2412yes—
401C2×C4×D79C2412yes—
402C2×C4×D79C2412yes—
403C2×C4×D79C2418yes—
404C2×C4×D79C2418yes—
405C2×C4×D79C2418yes—
406C2×C4×D79C24116yes—
407C2×C4×D79C2418yes—
408C2×C4×D79C24116yes—
409C2×C4×D79C2412yes—
410C2×C4×D79C2412yes—
411C4⋊Dic79C2414yes—
412C4⋊Dic79C2418yes—
413C4⋊Dic79C2412yes—
414C4⋊Dic79C2414yes—
415C4⋊Dic79C2414yes—
416Dic79⋊C4C2414yes—
417Dic79⋊C4C24116yes—
418Dic79⋊C4C2414yes—
419Dic79⋊C4C2418yes—
420Dic79⋊C4C2414yes—
421Dic79⋊C4C2414yes—
422Dic79⋊C4C2414yes—
423C22⋊Dic79C2412yes—
424C22⋊Dic79C2414yes—
425C22⋊Dic79C2414yes—
426(C2×D79)⋊C4C2418yes—
427(C2×D79)⋊C4C24116yes—
428(C2×D79)⋊C4C24116yes—
429(C2×D79)⋊C4C24116yes—
430(C2×D79)⋊C4C24116yes—
431(C2×D79)⋊C4C24116yes—
432(C2×D79)⋊C4C2418yes—
433(C2×D79)⋊C4C2414yes—
434(C2×D79)⋊C4C2414yes—
435(C2×D79)⋊C4C2414yes—
436(C2×D79)⋊C4C2414yes—
437(C2×D79)⋊C4C2414yes—
438(C2×D79)⋊C4C24116yes—
439(C2×D79)⋊C4C2418yes—
440(C2×D79)⋊C4C2418yes—
441C4×Dic79C2411yescharacteristic
442C4×Dic79C2411yescharacteristic
443C4×Dic79C2412yes—
444C4×Dic79C2412yes—
445C4×Dic79C2412yes—
446C4×Dic79C2412yes—
447C4×Dic79C2412yes—
448C4×Dic79C2418yes—
449C4×Dic79C2412yes—
450C4×Dic79C2414yes—
451#41×C79—24no—
452C2×Q8×C79—28no—
453C2×Q8×C79C2414yes—
454C2×Q8×C79C2414yes—
455C2×Q8×C79C2411yescharacteristic
456C2×Q8×C79C2414yes—
457C2×D4×C79C2412yes—
458C2×D4×C79C2411yescharacteristic
459C22×C4×C79C2412yes—
460C22×C4×C79C2414yes—
461C22×C4×C79C2414yes—
462C22×C4×C79C2412yes—
463C22×C4×C79C2411yescharacteristic
464C4⋊C4×C79C2418yes—
465C4⋊C4×C79C2418yes—
466C4⋊C4×C79C2414yes—
467C4⋊C4×C79C2412yes—
468C4⋊C4×C79C2414yes—
469C4⋊C4×C79C2414yes—
470C4⋊C4×C79C24116yes—
471C4⋊C4×C79C24116yes—
472C4⋊C4×C79C2418yes—
473C22⋊C4×C79C2412yes—
474C22⋊C4×C79C2414yes—
475C22⋊C4×C79C2414yes—
476C22⋊C4×C79C24116yes—
477C42×C79C2411yescharacteristic
478C42×C79C2412yes—
479C42×C79C2411yescharacteristic
480C42×C79C2414yes—
481C42×C79C2412yes—
482C42×C79C24116yes—
483C42×C79C2414yes—
484C23×C79C2512yes—
485C23×C79C2511yescharacteristic
486C22×D79—22no—
487C22×D79—28no—
488C22×D79—42no—
489C22×D79—48no—
490C22×D79—48no—
491C22×D79—416no—
492C22×D79C2514yes—
493C22×D79C2518yes—
494C22×D79C2512yes—
495C22×D79C2512yes—
496Q8×C79—28no—
497Q8×C79—28no—
498Q8×C79—22no—
499Q8×C79—28no—
500D4×C79—24no—
501D4×C79—22no—
502C2×C4×C79—28no—
503C2×C4×C79—24no—
504C2×C4×C79—24no—
505C2×C4×C79—28no—
506C2×C4×C79H(5,𝔽2)14yes—
507C2×C4×C79C2512yes—
508C2×C4×C79C2518yes—
509C2×C4×C79C2514yes—
510C2×C4×C79C2518yes—
511C2×C4×C79C2512yes—
512C2×C4×C79C2511yescharacteristic
513C2×C4×C79C2511yescharacteristic
514C2×C4×C79C2512yes—
515C22⋊D79—28no—
516C22⋊D79—24no—
517C22⋊D79—48no—
518C22⋊D79—44no—
519C22⋊D79—44no—
520C2×Dic79—22no—
521C2×Dic79—42no—
522C2×Dic79C2512yes—
523C2×Dic79C2512yes—
524C2×Dic79C2512yes—
525C2×Dic79C2514yes—
526C2×Dic79C2512yes—
527C2×Dic79C2514yes—
528D316—28no—
529D316—28no—
530D316—24no—
531D316—22no—
532D316—216no—
533D316—28no—
534D316—48no—
535D316—416no—
536D316—48no—
537D316—416no—
538D316—44no—
539D316—48no—
540D316—416no—
541D316—48no—
542C4×D79—24no—
543C4×D79—24no—
544C4×D79—28no—
545C4×D79—24no—
546C4×D79—24no—
547C4×D79—24no—
548C4×D79—28no—
549C4×D79—42no—
550C4×D79—42no—
551C4×D79—416no—
552C4×D79—48no—
553C4×D79—48no—
554C4×D79—48no—
555C4×D79—416no—
556C4×D79—48no—
557Dic158—22no—
558Dic158—24no—
559Dic158—48no—
560Dic158—44no—
561C22×C79—22no—
562C22×C79—22no—
563C22×C79—24no—
564C22×C79C2×H(5,𝔽2)12yes—
565C22×C79C2611yescharacteristic
566C2×D79—24no—
567C2×D79—22no—
568C2×D79—28no—
569C2×D79—22no—
570C2×D79—22no—
571C2×D79—24no—
572C2×D79—216no—
573C2×D79—28no—
574C2×D79—22no—
575C2×D79—44no—
576C2×D79—88no—
577C2×D79—168no—
578C4×C79—22no—
579C4×C79—28no—
580C4×C79—24no—
581C4×C79—22no—
582C4×C79—28no—
583C4×C79C2×H(5,𝔽2)12yes—
584C4×C79C2×H(5,𝔽2)12yes—
585C4×C79#58514yes—
586Dic79—24no—
587Dic79—22no—
588Dic79—22no—
589Dic79—22no—
590Dic79—24no—
591Dic79—22no—
592#62836—791nomaximal, Sylow
593C2×C79—22no—
594C2×C79—42no—
595C2×C79C22×H(5,𝔽2)11yescharacteristic
596C2×C79C2×#58512yes—
597D79—42no—
598D79—42no—
599D79—48no—
600D79—44no—
601#3562—798no—
602#3554—794no—
603#3546—794no—
604#3542—798no—
605#3517—794no—
606#3514—794no—
607#3513—798no—
608#3511—794no—
609#3510—792no—
610#3509D7911yescharacteristic, complemented
611#3508—791no—
612#3508—794no—
613#3500—792no—
614#3499—791no—
615#3498—791no—
616#3487—792no—
617#3485—792no—
618#3444—791no—
619#3444—791no—
620C2×#532—791no—
621C79#6283611yescharacteristic, complemented, Sylow
622C2×2−1+4—792no—
623C2×H(5,𝔽2)—792no—
624C22×#41—792no—
625#562—7916no—
626#560—7916no—
627#559—798no—
628#559—798no—
629#559—794no—
630#557C2×D7914yescomplemented
631#556—798no—
632#556C2×D7914yescomplemented
633#555—798no—
634#554—798no—
635#553—798no—
636#553—7916no—
637#553—798no—
638#552C2×D7918yescomplemented
639#551—7916no—
640#551—7916no—
641#550—798no—
642#550—798no—
643#550—794no—
644#550—798no—
645#550—794no—
646D4×Q8—794no—
647#548—798no—
648#548—798no—
649#548—798no—
650#547—798no—
651#547—794no—
652#547—798no—
653#547—798no—
654#546—798no—
655#546—7916no—
656#546—798no—
657#546—798no—
658#546—798no—
659#546—798no—
660#546—798no—
661D42—798no—
662D42—794no—
663#542—798no—
664#542—798no—
665#542—798no—
666#541C2×D7914yescomplemented
667#540—798no—
668#540—798no—
669#540—794no—
670#540—7916no—
671#539—7916no—
672#538—7916no—
673#538—7916no—
674#537—798no—
675#536—792no—
676#536—794no—
677#536—794no—
678#536C2×D7912yes—
679#535—794no—
680#535—792no—
681#535—792no—
682#535—798no—
683#535—794no—
684#535—798no—
685#534—798no—
686#533—792no—
687#533—792no—
688#533—791no—
689#533C2×D7911yescharacteristic, complemented
690#533C2×D7914yescomplemented
691#532—791no—
692#532—794no—
693#532—794no—
694#532—794no—
695#532—794no—
696#532—792no—
697#532—792no—
698#532—794no—
699#532—794no—
700#532—792no—
701#532—791no—
702#532—792no—
703C2×C4⋊Q8—792no—
704C2×C4⋊Q8C2×D7911yescharacteristic, complemented
705C2×#127—791no—
706C2×#127—792no—
707#529—794no—
708#529—794no—
709#529—792no—
710#529—794no—
711#529—798no—
712#529—794no—
713#529—792no—
714#529—794no—
715C2×#124—792no—
716C2×#124—794no—
717#525—791no—
718#525—794no—
719#525—794no—
720#525—792no—
721#525—791no—
722#525—798no—
723C2×#123—798no—
724C2×#121—794no—
725#520—798no—
726#519C2×D7912yescomplemented
727#518—792no—
728#518—798no—
729C4×#41—794no—
730C4×#41—792no—
731C4×#41—791no—
732C4×#41—794no—
733C4×#41C2×D7911yescharacteristic
734C2×C4×D4—794no—
735C22×C42—791no—
7362−1+4—3168no—
737H(5,𝔽2)—3168no—
738C2×#41—3168no—
739C2×#41—794no—
740C2×#41—798no—
741C2×#41—798no—
742C2×#41—798no—
743C2×#41—794no—
744C2×#41—794no—
745C2×#41—794no—
746C2×#41—794no—
747C2×#41—798no—
748C2×#41—794no—
749C2×#41—791no—
750C2×#41—792no—
751C2×#41C22×D7911yescharacteristic
752C22×Q8—794no—
753C22×Q8—794no—
754C22×Q8C22×D7912yes—
755C22×D4—798no—
756C22×D4—794no—
757C22×D4—794no—
758C22×D4—798no—
759C22×D4—794no—
760C22×D4—794no—
761C22×D4—792no—
762C23×C4—794no—
763C23×C4—792no—
764C23×C4—791no—
765C4⋊Q8—794no—
766C4⋊Q8—791no—
767C4⋊Q8—798no—
768C4⋊Q8—792no—
769C4⋊Q8—791no—
770C4⋊Q8C22×D7912yes—
771C4⋊Q8C22×D7912yes—
772C4⋊Q8C22×D7914yes—
773C4⋊Q8C22×D7912yes—
774C4⋊Q8C22×D7914yes—
775#127—791no—
776#127—792no—
777#127—791no—
778#127—792no—
779#127—794no—
780#127—794no—
781#127—798no—
782#127—794no—
783#127—7916no—
784#126—798no—
785#126—794no—
786#126—7916no—
787#126—794no—
788#126—7916no—
789#126C22×D79116yes—
790#125—792no—
791#125—794no—
792#125—794no—
793#125C22×D7912yes—
794#125C22×D7918yes—
795#125C22×D79116yes—
796#124—794no—
797#124—794no—
798#124—798no—
799#124—791no—
800#124—794no—
801#124—794no—
802#124—798no—
803#124—791no—
804#124—7916no—
805#124—794no—
806#124—794no—
807#124—792no—
808#124—794no—
809#124—7916no—
810#124—7916no—
811#124C22×D7914yes—
812#123—792no—
813#123—798no—
814#123—7916no—
815#123—794no—
816#123—798no—
817#123—7916no—
818#123—7916no—
819#123—7916no—
820#123—7916no—
821#123—7916no—
822#123—7916no—
823#123—794no—
824#123—7916no—
825#123—792no—
826#123—794no—
827#123C22×D7918yes—
828C22⋊Q8—794no—
829C22⋊Q8—792no—
830C22⋊Q8—798no—
831C22⋊Q8—794no—
832C22⋊Q8—792no—
833C22⋊Q8—794no—
834C22⋊Q8—7916no—
835C22⋊Q8—7916no—
836C22⋊Q8—7916no—
837C22⋊Q8—7916no—
838C22⋊Q8—794no—
839C22⋊Q8C22×D7914yes—
840C22⋊Q8C22×D7918yes—
841C22⋊Q8C22×D7918yes—
842#121—792no—
843#121—794no—
844#121—794no—
845#121—798no—
846#121—798no—
847#121—798no—
848#121—798no—
849#121—798no—
850#121—794no—
851#121—794no—
852#121—792no—
853#121—7916no—
854#121—798no—
855#121—798no—
856#121—798no—
857#121—798no—
858#121—7916no—
859#121—7916no—
860#121—7916no—
861#121—7916no—
862#121—7916no—
863#121—7916no—
864#121—794no—
865#121—7916no—
866#121—7916no—
867#120—792no—
868#120—794no—
869#120—792no—
870#120—798no—
871#120—798no—
872#120—7916no—
873#120—7916no—
874#120—7916no—
875C4×Q8—794no—
876C4×Q8—794no—
877C4×Q8—792no—
878C4×Q8—794no—
879C4×Q8—794no—
880C4×Q8C22×D7914yes—
881C4×Q8C22×D7912yes—
882C4×Q8C22×D7918yes—
883C4×Q8C22×D7918yes—
884C4×Q8C22×D7918yes—
885C4×D4—794no—
886C4×D4—794no—
887C4×D4—794no—
888C4×D4—794no—
889C4×D4—794no—
890C4×D4—798no—
891C4×D4—798no—
892C4×D4—798no—
893C4×D4—798no—
894C4×D4—794no—
895C4×D4—798no—
896C4×D4—794no—
897C4×D4—798no—
898C4×D4—798no—
899C4×D4—798no—
900C4×D4—7916no—
901C4×D4—798no—
902C4×D4—798no—
903C4×D4—794no—
904C4×D4—794no—
905C4×D4—794no—
906C4×D4—792no—
907C4×D4—7916no—
908C4×D4—7916no—
909C4×D4—798no—
910C4×D4—7916no—
911C4×D4—798no—
912C4×D4C22×D7914yes—
913C4×D4C22×D7912yes—
914#117—791no—
915#117—794no—
916#117—794no—
917#117—798no—
918#117—794no—
919#117—794no—
920#117—794no—
921#117—792no—
922#117—7916no—
923#117C22×D7912yes—
924#117C22×D7911yescharacteristic
925#117C22×D7912yes—
926#117C22×D7918yes—
927#117C22×D7918yes—
928C2×C4⋊C4—7916no—
929C2×C4⋊C4—798no—
930C2×C4⋊C4C22×D7914yes—
931C2×C22⋊C4—798no—
932C2×C22⋊C4—798no—
933C2×C22⋊C4—7916no—
934C2×C22⋊C4—7916no—
935C2×C42—792no—
936C2×C42—791no—
937C2×C42—794no—
938C2×C42—792no—
939C2×C42—792no—
940C2×C42—792no—
941C2×C42—792no—
942C2×C42—792no—
943C2×C42C22×D7912yes—
944C2×C42C22×D7911yescharacteristic
945C24—798no—
946C24—794no—
947C24—791no—
948#41—24no—
949#41—3168no—
950#41—31616no—
951#41—3168no—
952#41—31616no—
953#41—31616no—
954#41—3168no—
955#41—31616no—
956#41—3168no—
957#41—3168no—
958#41—3168no—
959#41—1588no—
960#41—1584no—
961C2×Q8—28no—
962C2×Q8—3168no—
963C2×Q8—3168no—
964C2×Q8—794no—
965C2×Q8—798no—
966C2×Q8—791no—
967C2×Q8—792no—
968C2×Q8C23×D7914yes—
969C2×Q8C23×D7914yes—
970C2×Q8C23×D7911yescharacteristic
971C2×Q8C23×D7914yes—
972C2×D4—3168no—
973C2×D4—3168no—
974C2×D4—31616no—
975C2×D4—3168no—
976C2×D4—31616no—
977C2×D4—3168no—
978C2×D4—794no—
979C2×D4—794no—
980C2×D4—798no—
981C2×D4—792no—
982C2×D4—794no—
983C2×D4—798no—
984C2×D4—7916no—
985C2×D4—798no—
986C2×D4—7916no—
987C2×D4—794no—
988C2×D4—798no—
989C2×D4—7916no—
990C2×D4—798no—
991C2×D4—798no—
992C2×D4—794no—
993C2×D4—792no—
994C2×D4—794no—
995C2×D4—794no—
996C2×D4—791no—
997C2×D4—1588no—
998C2×D4C23×D7912yes—
999C2×D4C23×D7911yescharacteristic
1000C22×C4—3168no—
1001C22×C4—3164no—
1002C22×C4—792no—
1003C22×C4—792no—
1004C22×C4—792no—
1005C22×C4—798no—
1006C22×C4—7916no—
1007C22×C4—798no—
1008C22×C4—7916no—
1009C22×C4—798no—
1010C22×C4—798no—
1011C22×C4—791no—
1012C22×C4—792no—
1013C22×C4—792no—
1014C22×C4—792no—
1015C22×C4—792no—
1016C22×C4—794no—
1017C22×C4—792no—
1018C22×C4—794no—
1019C22×C4—1584no—
1020C22×C4C23×D7912yes—
1021C22×C4C23×D7914yes—
1022C22×C4C23×D7912yes—
1023C22×C4C23×D7914yes—
1024C22×C4C23×D7911yescharacteristic
1025C4⋊C4—794no—
1026C4⋊C4—7916no—
1027C4⋊C4—794no—
1028C4⋊C4—798no—
1029C4⋊C4—794no—
1030C4⋊C4—794no—
1031C4⋊C4—794no—
1032C4⋊C4—794no—
1033C4⋊C4—798no—
1034C4⋊C4—792no—
1035C4⋊C4—794no—
1036C4⋊C4—794no—
1037C4⋊C4C23×D7918yes—
1038C4⋊C4C23×D79116yes—
1039C4⋊C4C23×D7918yes—
1040C4⋊C4C23×D7914yes—
1041C4⋊C4C23×D7918yes—
1042C4⋊C4C23×D7914yes—
1043C4⋊C4C23×D7912yes—
1044C4⋊C4C23×D7914yes—
1045C4⋊C4C23×D79116yes—
1046C22⋊C4—792no—
1047C22⋊C4—794no—
1048C22⋊C4—794no—
1049C22⋊C4—798no—
1050C22⋊C4—7916no—
1051C22⋊C4—7916no—
1052C22⋊C4—7916no—
1053C22⋊C4—7916no—
1054C22⋊C4—7916no—
1055C22⋊C4—794no—
1056C22⋊C4—794no—
1057C22⋊C4—7916no—
1058C22⋊C4—798no—
1059C22⋊C4—798no—
1060C22⋊C4—794no—
1061C22⋊C4—798no—
1062C22⋊C4—794no—
1063C22⋊C4—794no—
1064C22⋊C4C23×D7914yes—
1065C22⋊C4C23×D79116yes—
1066C22⋊C4C23×D7912yes—
1067C22⋊C4C23×D7914yes—
1068C42—791no—
1069C42—792no—
1070C42—792no—
1071C42—791no—
1072C42—792no—
1073C42—792no—
1074C42—792no—
1075C42—798no—
1076C42—792no—
1077C42—794no—
1078C42C23×D7911yescharacteristic
1079C42C23×D7911yescharacteristic
1080C42C23×D7912yes—
1081C42C23×D7914yes—
1082C42C23×D7914yes—
1083C42C23×D7912yes—
1084C42C23×D79116yes—
1085C23—3162no—
1086C23—3168no—
1087C23—3168no—
1088C23—31616no—
1089C23—798no—
1090C23—794no—
1091C23—792no—
1092C23—792no—
1093C23—1582no—
1094C23—1588no—
1095C23C24×D7912yes—
1096C23C24×D7911yescharacteristic
1097Q8—28no—
1098Q8—28no—
1099Q8—22no—
1100Q8—28no—
1101Q8—3168no—
1102Q8—3164no—
1103Q8—1582no—
1104Q8—1584no—
1105D4—24no—
1106D4—22no—
1107D4—3168no—
1108D4—31616no—
1109D4—3168no—
1110D4—31616no—
1111D4—3168no—
1112D4—3164no—
1113D4—3168no—
1114D4—31616no—
1115D4—3168no—
1116D4—3164no—
1117D4—3164no—
1118D4—1588no—
1119D4—1584no—
1120D4—1584no—
1121D4—1588no—
1122D4—1588no—
1123D4—1582no—
1124D4—15816no—
1125D4—1588no—
1126C2×C4—28no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—28no—
1130C2×C4—31616no—
1131C2×C4—3162no—
1132C2×C4—3162no—
1133C2×C4—3168no—
1134C2×C4—3168no—
1135C2×C4—3168no—
1136C2×C4—3168no—
1137C2×C4—31616no—
1138C2×C4—3162no—
1139C2×C4—792no—
1140C2×C4—792no—
1141C2×C4—792no—
1142C2×C4—794no—
1143C2×C4—792no—
1144C2×C4—794no—
1145C2×C4—1582no—
1146C2×C4—1584no—
1147C2×C4—1584no—
1148C2×C4—1588no—
1149C2×C4—1584no—
1150C2×C4—1584no—
1151C2×C4—1584no—
1152C2×C4—1588no—
1153C2×C4#1457920714yes—
1154C2×C4C24×D7912yes—
1155C2×C4C24×D7918yes—
1156C2×C4C24×D7914yes—
1157C2×C4C24×D7918yes—
1158C2×C4C24×D7912yes—
1159C2×C4C24×D7911yescharacteristic
1160C2×C4C24×D7911yescharacteristic
1161C2×C4C24×D7912yes—
1162C22—22no—
1163C22—22no—
1164C22—24no—
1165C22—3164no—
1166C22—6328no—
1167C22—1582no—
1168C22—1588no—
1169C22—1584no—
1170C22—1582no—
1171C22—1582no—
1172C22—1582no—
1173C22—15816no—
1174C22—1588no—
1175C22—1584no—
1176C22—12648no—
1177C22C2×#1457920712yes—
1178C22C25×D7911yescharacteristic
1179C4—22no—
1180C4—28no—
1181C4—22no—
1182C4—24no—
1183C4—28no—
1184C4—1582no—
1185C4—1584no—
1186C4—1582no—
1187C4—1582no—
1188C4—1584no—
1189C4—1582no—
1190C4C2×#1457920712yes—
1191C4C2×#1457920712yes—
1192C4#1909940014yes—
1193C2—22no—
1194C2—42no—
1195C2—3162no—
1196C2—3168no—
1197C2—3164no—
1198C2—3162no—
1199C2C22×#1457920711yescharacteristic
1200C2C2×#1909940012yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3509C2
hypercenter#3509D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #23777994C2semidirect
2. #23777874C2semidirect
3. #23777775C2semidirect
4. #23777710C2semidirect
5. #23777407C2semidirect
6. #23777364C2semidirect
7. #23777345C2semidirect
8. #23777312C2semidirect
9. #23777297C2semidirect
10. #23777277C2semidirect
11. #23777277C2semidirect
12. #23777189C2semidirect
13. #23777183C2semidirect
14. #23777178C2semidirect
15. #23777059C2semidirect
16. #23777043C2semidirect
17. #23776697C2semidirect
18. #23776693C2semidirect
19. C2×#19099114C2semidirect
20. C79×#3509C2semidirect
21. C2×#14579209C22semidirect
23. C22×#11929625C22semidirect
24. #19099311C22semidirect
25. #19099304C22semidirect
26. #19099298C22semidirect
27. #19099298C22semidirect
28. #19099298C22semidirect
29. #19099285C22semidirect
30. #19099276C22semidirect
31. #19099269C22semidirect
32. #19099266C22semidirect
33. #19099266C22semidirect
34. #19099257C22semidirect
35. #19099238C22semidirect
36. #19099237C22semidirect
37. #19099235C22semidirect
38. #19099235C22semidirect
39. #19099235C22semidirect
40. #19099235C22semidirect
41. #19099235C22semidirect
42. #19099228C22semidirect
43. #19099225C22semidirect
44. #19099225C22semidirect
45. #19099223C22semidirect
46. #19099216C22semidirect
47. #19099216C22semidirect
48. #19099215C22semidirect
49. #19099214C22semidirect
50. #19099206C22semidirect
51. #19099205C22semidirect
52. #19099204C22semidirect
53. #19099204C22semidirect
54. #19099204C22semidirect
55. #19099204C22semidirect
56. #19099204C22semidirect
58. D4×D316C22semidirect
59. #19099186C22semidirect
60. #19099185C22semidirect
61. #19099185C22semidirect
62. #19099169C22semidirect
63. #19099169C22semidirect
64. #19099169C22semidirect
65. #19099169C22semidirect
66. #19099161C22semidirect
67. #19099152C22semidirect
68. #19099152C22semidirect
69. #19099143C22semidirect
70. #19099138C22semidirect
71. #19099138C22semidirect
72. #19099137C22semidirect
74. #19099132C22semidirect
75. #19099132C22semidirect
76. #19099132C22semidirect
77. #19099132C22semidirect
78. #19099131C22semidirect
79. #19099124C22semidirect
80. #19099118C22semidirect
81. #19099117C22semidirect
82. #19099116C22semidirect
83. #19099114C22semidirect
84. #19099114C22semidirect
85. #19099114C22semidirect
86. #19099114C22semidirect
87. #19099114C22semidirect
88. #19099114C22semidirect
89. #19099114C22semidirect
90. #19099114C22semidirect
92. #19099113C22semidirect
93. #19099110C22semidirect
95. C4⋊Q8×D79C22semidirect
97. C2×#14579158C22semidirect
98. #19099100C22semidirect
99. #19099100C22semidirect
100. #19099100C22semidirect
101. #19099099C22semidirect
102. #19099098C22semidirect
103. #19099095C22semidirect
104. #19099093C22semidirect
105. #19099091C22semidirect
106. C2×#14579150C22semidirect
107. #124×D79C22semidirect
108. #19099076C22semidirect
109. #19099075C22semidirect
110. #19099075C22semidirect
111. #19099075C22semidirect
112. #19099072C22semidirect
114. #123×D79C22semidirect
115. C2×#14579136C22semidirect
116. #19099045C22semidirect
117. #19099037C22semidirect
118. #19099037C22semidirect
119. C4×#11929625C22semidirect
120. C4×#11929624C22semidirect
121. C4×#11929624C22semidirect
122. #19099031C22semidirect
123. C2×#14579123C22semidirect
124. C2×C42×D79C22semidirect
125. #557×C79C22semidirect
126. #556×C79C22semidirect
127. #552×C79C22semidirect
128. #541×C79C22semidirect
130. #533×C79C22semidirect
131. #533×C79C22semidirect
132. C2×C4⋊Q8×C79C22semidirect
133. #519×C79C22semidirect
610. #3509D79semidirect
621. C79#62836semidirect
630. #557C2×D79semidirect
632. #556C2×D79semidirect
638. #552C2×D79semidirect
666. #541C2×D79semidirect
689. #533C2×D79semidirect
690. #533C2×D79semidirect
704. C2×C4⋊Q8C2×D79semidirect
726. #519C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779942
#237778742
#237777752
#237777102
#237774072
#237773642
#237773452
#237773122
#237772972
#237772772
#237771892
#237771832
#237771782
#237770592
#237770432
#237766972
#237766932
C2×#190991142
C79×#35092
#6283679