Finite Group Databasebeta

← #35201983

Subgroups — #35201983

Order 20224.

7352 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777923C213yesmaximal, complemented
2#23777916C213yesmaximal, complemented
3#23777826C216yesmaximal, complemented
4#23777805C213yesmaximal, complemented
5#23777729C216yesmaximal, complemented
6#23777724C216yesmaximal, complemented
7#23777722C216yesmaximal, complemented
8#23777717C216yesmaximal, complemented
9#23777636C216yesmaximal, complemented
10#23777539C213yesmaximal, complemented
11#23777512C212yesmaximal, complemented
12#23777501C212yesmaximal, complemented
13#23777406C211yesmaximal, characteristic, complemented
14#23777193C211yesmaximal, characteristic, complemented
15#23777177C212yesmaximal, complemented
16#23777070C212yesmaximal, complemented
17#23777068C212yesmaximal, complemented
18#23777053C212yesmaximal, complemented
19C79×#3517C211yesmaximal, characteristic, complemented
20C2×#14579208C2211yescharacteristic, complemented
21C2×#14579207C2212yescomplemented
22C2×#14579207C2211yescharacteristic, complemented
23C2×#41×D79C2212yescomplemented
24#19099317C2211yescharacteristic, complemented
25#19099315C2216yescomplemented
26#19099311C2213yescomplemented
27#19099310C2216yescomplemented
28#19099309C2216yescomplemented
29#19099307C2213yescomplemented
30#19099305C2213yescomplemented
31#19099305C2216yescomplemented
32#19099304C2216yescomplemented
33#19099303C2216yescomplemented
34#19099303C22112yescomplemented
35#19099301C2216yescomplemented
36#19099301C22112yescomplemented
37#19099298C2216yescomplemented
38#19099296C2216yescomplemented
39#19099292C2211yescharacteristic, complemented
40#19099279C2216yescomplemented
41#19099278C2216yescomplemented
42#19099278C2216yescomplemented
43#19099266C2216yescomplemented
44#19099261C2216yescomplemented
45#19099257C2216yescomplemented
46#19099251C2216yescomplemented
47#19099248C2216yescomplemented
48#19099236C22112yescomplemented
49#19099235C2211yescharacteristic, complemented
50#19099235C2212yescomplemented
51#19099234C2213yescomplemented
52#19099233C2216yescomplemented
53#19099232C2212yescomplemented
54#19099232C2212yescomplemented
55#19099231C2216yescomplemented
56#19099225C2212yescomplemented
57#19099225C2212yescomplemented
58#19099225C2212yescomplemented
59#19099222C2216yescomplemented
60#19099220C2212yescomplemented
61#19099219C2216yescomplemented
62#19099218C2213yescomplemented
63#19099210C2216yescomplemented
64#19099209C2216yescomplemented
65#19099208C2216yescomplemented
66#19099208C2216yescomplemented
67#19099208C2216yescomplemented
68#19099208C2216yescomplemented
69#19099205C22112yescomplemented
70#19099201C22112yescomplemented
71D4×D316C2216yescomplemented
72D4×D316C2216yescomplemented
73D4×D316C2216yescomplemented
74D4×D316C2216yescomplemented
75#19099198C2216yescomplemented
76#19099198C2216yescomplemented
77#19099197C2216yescomplemented
78#19099197C2216yescomplemented
79#19099197C22112yescomplemented
80#19099197C2216yescomplemented
81#19099187C2216yescomplemented
82#19099184C2216yescomplemented
83#19099169C2216yescomplemented
84#19099166C22112yescomplemented
85#19099165C22112yescomplemented
86#19099164C2216yescomplemented
87#19099164C2216yescomplemented
88#19099153C2216yescomplemented
89#19099152C22112yescomplemented
90#19099150C2216yescomplemented
91#19099146C22112yescomplemented
92#19099144C2216yescomplemented
93#19099142C2216yescomplemented
94#19099139C2213yescomplemented
95#19099132C2216yescomplemented
96#19099132C2213yescomplemented
97#19099129C2216yescomplemented
98#19099129C2216yescomplemented
99#19099129C22112yescomplemented
100#19099129C2216yescomplemented
101#19099127C22112yescomplemented
102#19099126C2216yescomplemented
103#19099126C2216yescomplemented
104#19099124C22112yescomplemented
105#19099121C22112yescomplemented
106#19099121C2216yescomplemented
107#19099121C2216yescomplemented
108#19099113C2213yescomplemented
109#19099113C2213yescomplemented
110#19099110C2216yescomplemented
111#127×D79C2216yescomplemented
112#19099100C2216yescomplemented
113#19099098C2216yescomplemented
114#19099097C2213yescomplemented
115#19099095C2216yescomplemented
116#19099091C2216yescomplemented
117C2×#14579149C2213yescomplemented
118#19099075C2216yescomplemented
119#19099073C2216yescomplemented
120#19099072C2216yescomplemented
121#19099072C2216yescomplemented
122C2×#14579136C2216yescomplemented
123#121×D79C2216yescomplemented
124#19099045C2212yescomplemented
125#19099039C2212yescomplemented
126C4×#11929625C2212yescomplemented
127#557×C79C2211yescharacteristic, complemented
128#553×C79C2216yescomplemented
129#550×C79C2212yescomplemented
130#550×C79C2211yescharacteristic, complemented
131#550×C79C2213yescomplemented
132#547×C79C2213yescomplemented
133#540×C79C2216yescomplemented
134#532×C79C2213yescomplemented
135#529×C79C2213yescomplemented
136#520×C79C2212yescomplemented
137C4×#41×C79C2211yescharacteristic, complemented
138#14579208—44no—
139#14579207—48no—
140#14579207—44no—
141C2×#11929625C2312yes—
142C2×#11929625C2312yes—
143C2×#11929624C2313yes—
144C2×#11929624C2316yes—
145C2×#11929624C2313yes—
146C2×#11929624C2316yes—
147C2×#11929624C2316yes—
148C2×#11929623C2316yes—
149C2×#11929623C2316yes—
150#41×D79—48no—
151C22×Dic158C2313yes—
152C2×Q8×D79C2312yes—
153C22×D316C2313yes—
154C22×D316C2316yes—
155C22×D316C23112yes—
156C2×D4×D79C2316yes—
157C2×D4×D79C2316yes—
158C2×D4×D79C2316yes—
159C2×D4×D79C2316yes—
160C2×D4×D79C23112yes—
161C2×D4×D79C23112yes—
162C2×D4×D79C23112yes—
163C22×C4×D79C2316yes—
164#14579161C2313yes—
165#14579161C2313yes—
166#14579160C2312yes—
167#14579158C2316yes—
168#14579158C2313yes—
169#14579158C2313yes—
170#14579157C2316yes—
171#14579157C2316yes—
172#14579157C23112yes—
173#14579157C23112yes—
174#14579157C2316yes—
175#14579156C23112yes—
176#14579156C23112yes—
177#14579156C2312yes—
178#14579156C2316yes—
179#14579156C2312yes—
180#14579155C2316yes—
181#14579154C2316yes—
182#14579153C2311yescharacteristic
183#14579152C2316yes—
184#14579152C2316yes—
185#14579151C2316yes—
186#14579150C23112yes—
187#14579150C2316yes—
188#14579149C2316yes—
189#14579149C2316yes—
190#14579149C2316yes—
191#14579149C2316yes—
192#14579149C2313yes—
193#14579149C2311yescharacteristic
194#14579149C2313yes—
195#14579148C2316yes—
196#14579147C23112yes—
197#14579147C23112yes—
198#14579147C2316yes—
199#14579147C2316yes—
200#14579147C2316yes—
201#14579146C23112yes—
202#14579146C23112yes—
203#14579146C2316yes—
204#14579146C2316yes—
205#14579146C2316yes—
206#14579146C2316yes—
207#14579146C2312yes—
208#14579145C23112yes—
209#14579145C2316yes—
210#14579145C2316yes—
211#14579144C23112yes—
212#14579144C2316yes—
213#14579143C23112yes—
214#14579143C23112yes—
215#14579143C2316yes—
216#14579143C2316yes—
217#14579143C2316yes—
218#14579141C2316yes—
219#14579141C2316yes—
220#14579141C2316yes—
221#14579141C2316yes—
222#14579141C2312yes—
223#14579140C2316yes—
224#14579140C2313yes—
225#14579139C2316yes—
226#14579139C2316yes—
227#14579139C2312yes—
228#14579138C2316yes—
229#14579138C2316yes—
230#14579137C2316yes—
231#14579136C23112yes—
232#14579136C2316yes—
233#14579136C2316yes—
234#14579136C2316yes—
235#14579136C2316yes—
236#14579136C2316yes—
237#14579136C2316yes—
238#14579136C2316yes—
239#14579136C23112yes—
240#14579136C2316yes—
241#14579136C2316yes—
242#14579136C2316yes—
243#14579135C23112yes—
244#14579135C23112yes—
245#14579135C2316yes—
246#14579135C23112yes—
247#14579135C2316yes—
248#14579135C2316yes—
249#14579135C2316yes—
250#14579135C2316yes—
251#14579135C2313yes—
252#14579134C23112yes—
253#14579134C2316yes—
254#14579134C2316yes—
255#14579134C23112yes—
256#14579134C2316yes—
257#14579134C2316yes—
258#14579134C2316yes—
259#14579133C23112yes—
260#14579133C23112yes—
261#14579133C23112yes—
262#14579133C2316yes—
263#14579133C2316yes—
264#14579132C23112yes—
265#14579132C2316yes—
266#14579132C2316yes—
267#14579132C2316yes—
268#14579132C2316yes—
269#14579131C23112yes—
270#14579131C23112yes—
271#14579131C23112yes—
272#14579131C2316yes—
273#14579131C23112yes—
274#14579131C2316yes—
275#14579131C2316yes—
276#14579131C2316yes—
277#14579131C23112yes—
278#14579129C23112yes—
279#14579129C23112yes—
280#14579129C2316yes—
281#14579129C23112yes—
282#14579129C2316yes—
283#14579129C23112yes—
284#14579129C23112yes—
285Q8×Dic79C2312yes—
286C4×Dic158C2316yes—
287C4×Dic158C2313yes—
288#14579126C2316yes—
289C4×D316C2316yes—
290C4×D316C2316yes—
291C4×D316C2316yes—
292C4×D316C2316yes—
293C4×D316C2316yes—
294C4×D316C2316yes—
295C4×D316C2316yes—
296C4×D316C2313yes—
297D4×Dic79C23112yes—
298#14579123C23112yes—
299#14579123C2316yes—
300#14579123C2316yes—
301C4×C22⋊D79C23112yes—
302C4×C22⋊D79C2316yes—
303C4×C22⋊D79C2316yes—
304C4×C22⋊D79C2316yes—
305(C22⋊D79)⋊C4C23112yes—
306#14579120C23112yes—
307#14579119C23112yes—
308#14579119C2316yes—
309#14579119C2316yes—
310#14579118C2316yes—
311#14579118C2316yes—
312C4⋊C4×D79C2316yes—
313C2×(C2×D79)⋊C4C23112yes—
314C2×(C2×D79)⋊C4C2316yes—
315C2×(C2×D79)⋊C4C2316yes—
316C22⋊C4×D79C23112yes—
317C42×D79C2316yes—
318C2×#41×C79C2311yescharacteristic
319C2×#41×C79C2312yes—
320C2×#41×C79C2316yes—
321C4⋊Q8×C79C2313yes—
322#127×C79C2313yes—
323#127×C79C2316yes—
324#126×C79C2316yes—
325#125×C79C2316yes—
326#125×C79C2311yescharacteristic
327#124×C79C2313yes—
328#123×C79C23112yes—
329#123×C79C2316yes—
330C22⋊Q8×C79C2313yes—
331#121×C79C2316yes—
332#121×C79C2316yes—
333#121×C79C23112yes—
334#121×C79C2316yes—
335#121×C79C2316yes—
336#121×C79C2313yes—
337C4×Q8×C79C2311yescharacteristic
338C4×Q8×C79C2311yescharacteristic
339C4×Q8×C79C2312yes—
340C4×Q8×C79C2313yes—
341C4×D4×C79C2316yes—
342C4×D4×C79C2313yes—
343C4×D4×C79C2316yes—
344C4×D4×C79C2316yes—
345C4×D4×C79C2316yes—
346C4×D4×C79C2313yes—
347C4×D4×C79C2313yes—
348#117×C79C2313yes—
349#117×C79C2316yes—
350C2×C4⋊C4×C79C2316yes—
351C2×C42×C79C2313yes—
352C23×D79C24112yes—
353C23×D79C2416yes—
354C23×D79C2416yes—
355#11929625—28no—
356#11929625—28no—
357#11929624—412no—
358#11929624—412no—
359#11929624—46no—
360#11929624—46no—
361#11929624—86no—
362#11929623—412no—
363#11929623—412no—
364C2×Dic158—46no—
365C2×Dic158C2416yes—
366C2×Dic158C2413yes—
367C2×Dic158C2412yes—
368C2×Dic158C2411yescharacteristic
369C2×Dic158C2413yes—
370Q8×D79—28no—
371C2×D316—412no—
372C2×D316—46no—
373C2×D316—812no—
374C2×D316C2416yes—
375C2×D316C2416yes—
376C2×D316C2411yescharacteristic
377C2×D316C2413yes—
378C2×D316C2413yes—
379C2×D316C2416yes—
380C2×D316C24112yes—
381C2×D316C2416yes—
382C2×D316C2416yes—
383C2×D316C2416yes—
384C2×D316C2416yes—
385C2×D316C2416yes—
386C2×C22⋊D79C2416yes—
387C2×C22⋊D79C24112yes—
388C2×C22⋊D79C24112yes—
389C2×C22⋊D79C2416yes—
390C2×C22⋊D79C2416yes—
391C2×C22⋊D79C2416yes—
392C2×C22⋊D79C24112yes—
393C2×C22⋊D79C2416yes—
394C2×C22⋊D79C2416yes—
395C2×C22⋊D79C2416yes—
396D4×D79—412no—
397D4×D79—412no—
398D4×D79—412no—
399D4×D79—412no—
400D4×D79—812no—
401D4×D79—812no—
402D4×D79—812no—
403C22×Dic79C2416yes—
404C22×Dic79C2416yes—
405C2×C4×D79—412no—
406C2×C4×D79C2416yes—
407C2×C4×D79C2416yes—
408C2×C4×D79C2416yes—
409C2×C4×D79C2416yes—
410C2×C4×D79C24112yes—
411C2×C4×D79C2416yes—
412C2×C4×D79C2416yes—
413C2×C4×D79C2412yes—
414C4⋊Dic79C2416yes—
415C4⋊Dic79C2416yes—
416C4⋊Dic79C2416yes—
417C4⋊Dic79C2416yes—
418C4⋊Dic79C2416yes—
419C4⋊Dic79C2412yes—
420C4⋊Dic79C2411yescharacteristic
421C4⋊Dic79C2411yescharacteristic
422Dic79⋊C4C2416yes—
423Dic79⋊C4C2412yes—
424Dic79⋊C4C2416yes—
425Dic79⋊C4C2416yes—
426Dic79⋊C4C2416yes—
427Dic79⋊C4C2412yes—
428Dic79⋊C4C2412yes—
429Dic79⋊C4C2416yes—
430C22⋊Dic79C24112yes—
431C22⋊Dic79C2416yes—
432C22⋊Dic79C2416yes—
433C22⋊Dic79C2416yes—
434(C2×D79)⋊C4C2416yes—
435(C2×D79)⋊C4C24112yes—
436(C2×D79)⋊C4C24112yes—
437(C2×D79)⋊C4C2416yes—
438(C2×D79)⋊C4C2416yes—
439(C2×D79)⋊C4C2416yes—
440(C2×D79)⋊C4C2416yes—
441(C2×D79)⋊C4C24112yes—
442(C2×D79)⋊C4C2412yes—
443(C2×D79)⋊C4C2416yes—
444(C2×D79)⋊C4C2416yes—
445(C2×D79)⋊C4C2416yes—
446(C2×D79)⋊C4C2416yes—
447(C2×D79)⋊C4C24112yes—
448(C2×D79)⋊C4C2412yes—
449(C2×D79)⋊C4C2416yes—
450(C2×D79)⋊C4C2416yes—
451(C2×D79)⋊C4C2412yes—
452(C2×D79)⋊C4C2412yes—
453(C2×D79)⋊C4C2412yes—
454C4×Dic79C2412yes—
455C4×Dic79C2416yes—
456C4×Dic79C2416yes—
457C4×Dic79C24112yes—
458#41×C79—28no—
459#41×C79—24no—
460#41×C79—86no—
461C2×Q8×C79C2413yes—
462C2×Q8×C79C2411yescharacteristic
463C2×D4×C79C2413yes—
464C2×D4×C79C2416yes—
465C2×D4×C79C2416yes—
466C2×D4×C79C2416yes—
467C2×D4×C79C2413yes—
468C2×D4×C79C24112yes—
469C22×C4×C79C2413yes—
470C22×C4×C79C2416yes—
471C22×C4×C79C2413yes—
472C22×C4×C79C2413yes—
473C22×C4×C79C24112yes—
474C4⋊C4×C79C2413yes—
475C4⋊C4×C79C2416yes—
476C4⋊C4×C79C2416yes—
477C4⋊C4×C79C2412yes—
478C4⋊C4×C79C2413yes—
479C4⋊C4×C79C2411yescharacteristic
480C4⋊C4×C79C2412yes—
481C4⋊C4×C79C2416yes—
482C4⋊C4×C79C2411yescharacteristic
483C4⋊C4×C79C2416yes—
484C22⋊C4×C79C2416yes—
485C22⋊C4×C79C2416yes—
486C22⋊C4×C79C2416yes—
487C22⋊C4×C79C2416yes—
488C22⋊C4×C79C2416yes—
489C22⋊C4×C79C2416yes—
490C42×C79C2411yescharacteristic
491C42×C79C2413yes—
492C42×C79C2413yes—
493C42×C79C2413yes—
494C42×C79C2416yes—
495C23×C79C2516yes—
496C23×C79C2513yes—
497C22×D79—46no—
498C22×D79—46no—
499C22×D79—46no—
500C22×D79—412no—
501C22×D79—46no—
502C22×D79—46no—
503C22×D79—412no—
504C22×D79—46no—
505C22×D79—412no—
506C22×D79C2516yes—
507C22×D79C2512yes—
508C22×D79C2516yes—
509Q8×C79—43no—
510Q8×C79H(5,𝔽2)14yes—
511D4×C79—212no—
512D4×C79—26no—
513D4×C79—46no—
514D4×C79—46no—
515D4×C79—412no—
516D4×C79—43no—
517C2×C4×C79—212no—
518C2×C4×C79—26no—
519C2×C4×C79—412no—
520C2×C4×C79—43no—
521C2×C4×C79—43no—
522C2×C4×C79C2516yes—
523C2×C4×C79C2512yes—
524C2×C4×C79C2511yescharacteristic
525C2×C4×C79C2511yescharacteristic
526C2×C4×C79C2513yes—
527C2×C4×C79C2513yes—
528C2×C4×C79C2511yescharacteristic
529C2×C4×C79C2512yes—
530C2×C4×C79C2513yes—
531C22⋊D79—46no—
532C22⋊D79—46no—
533C22⋊D79—46no—
534C22⋊D79—412no—
535C22⋊D79—46no—
536C22⋊D79—46no—
537C22⋊D79—46no—
538C22⋊D79—412no—
539C22⋊D79—412no—
540C22⋊D79—46no—
541C2×Dic79—46no—
542C2×Dic79—46no—
543C2×Dic79C2516yes—
544C2×Dic79C2512yes—
545C2×Dic79C2512yes—
546C2×Dic79C2516yes—
547C2×Dic79C2512yes—
548D316—212no—
549D316—212no—
550D316—46no—
551D316—46no—
552D316—412no—
553D316—43no—
554D316—46no—
555D316—46no—
556D316—46no—
557D316—46no—
558D316—41no—
559D316—43no—
560C4×D79—212no—
561C4×D79—212no—
562C4×D79—212no—
563C4×D79—42no—
564C4×D79—46no—
565C4×D79—46no—
566C4×D79—46no—
567C4×D79—412no—
568Dic158—212no—
569Dic158—43no—
570Dic158—41no—
571Dic158—42no—
572Dic158—43no—
573C22×C79—26no—
574C22×C79—23no—
575C22×C79—23no—
576C22×C79—26no—
577C22×C79—23no—
578C22×C79—26no—
579C22×C79C2611yescharacteristic
580C2×D79—22no—
581C2×D79—26no—
582C2×D79—26no—
583C2×D79—22no—
584C2×D79—26no—
585C2×D79—26no—
586C2×D79—26no—
587C2×D79—26no—
588C2×D79—22no—
589C2×D79—812no—
590C2×D79—1612no—
591C2×D79—166no—
592C4×C79—21no—
593C4×C79—22no—
594C4×C79—23no—
595C4×C79—21no—
596C4×C79—21no—
597C4×C79—26no—
598C4×C79—23no—
599C4×C79—22no—
600C4×C79C2×H(5,𝔽2)16yes—
601Dic79—22no—
602Dic79—26no—
603Dic79—22no—
604Dic79—22no—
605Dic79—26no—
606#63066—791nomaximal, Sylow
607C2×C79—46no—
608C2×C79—43no—
609C2×C79C22×H(5,𝔽2)11yescharacteristic
610C2×C79H(7,𝔽2)11yescharacteristic
611C2×C79H(7,𝔽2)11yescharacteristic
612D79—42no—
613D79—46no—
614D79—46no—
615#3558—793no—
616#3558—793no—
617#3551—796no—
618#3549—793no—
619#3543—796no—
620#3543—796no—
621#3542—796no—
622#3542—796no—
623#3537—796no—
624#3529—793no—
625#3524—792no—
626#3524—792no—
627#3517—791no—
628#3517D7911yescharacteristic, complemented
629#3500—791no—
630#3498—792no—
631#3488—792no—
632#3488—792no—
633#3487—792no—
634C79#6306611yescharacteristic, complemented, Sylow
635C2×2−1+4—791no—
636C2×H(5,𝔽2)—792no—
637C2×H(5,𝔽2)—791no—
638C22×#41—792no—
639#563—796no—
640#563—791no—
641#562—793no—
642#562—793no—
643#562—796no—
644#562—796no—
645H(3,𝔽4)—793no—
646H(3,𝔽4)—796no—
647#560—796no—
648#560—796no—
649#560—7912no—
650#560—796no—
651#560—7912no—
652#559—796no—
653#559—796no—
654#557—791no—
655#557C2×D7911yescharacteristic, complemented
656#555—796no—
657#555—796no—
658#555—796no—
659#553—796no—
660#553—796no—
661#553—796no—
662#553C2×D7916yescomplemented
663#552—796no—
664#552—796no—
665#551—7912no—
666#550—792no—
667#550—792no—
668#550—796no—
669#550—796no—
670#550—791no—
671#550—792no—
672#550—793no—
673#550C2×D7912yescomplemented
674#550C2×D7911yescharacteristic, complemented
675#550C2×D7913yescomplemented
676#548—792no—
677#548—796no—
678#548—792no—
679#548—792no—
680#548—792no—
681#548—796no—
682#547—793no—
683#547C2×D7913yescomplemented
684#546—7912no—
685#546—7912no—
686#546—796no—
687#546—796no—
688#546—796no—
689#546—796no—
690#546—796no—
691#546—796no—
692D42—796no—
693D42—796no—
694D42—796no—
695D42—796no—
696D42—796no—
697D42—7912no—
698D42—796no—
699D42—796no—
700D42—796no—
701D42—796no—
702#542—796no—
703#542—796no—
704#540—796no—
705#540—7912no—
706#540—7912no—
707#540—796no—
708#540—796no—
709#540C2×D7916yescomplemented
710#538—7912no—
711#538—796no—
712#538—796no—
713#538—7912no—
714#537—796no—
715#537—796no—
716#536—793no—
717#535—7912no—
718#535—796no—
719#535—796no—
720#535—796no—
721#535—796no—
722#535—796no—
723#535—7912no—
724#535—796no—
725#535—793no—
726#534—7912no—
727#534—7912no—
728#534—796no—
729#534—796no—
730#532—796no—
731#532—793no—
732#532—793no—
733#532C2×D7913yescomplemented
734C2×#127—796no—
735#529—796no—
736#529—796no—
737#529—796no—
738#529—796no—
739#529—793no—
740#529C2×D7913yescomplemented
741C2×#124—793no—
742#525—796no—
743#525—796no—
744#525—796no—
745#525—796no—
746C2×#121—796no—
747C2×#121—796no—
748#520—792no—
749#520C2×D7912yescomplemented
750#519—792no—
751C4×#41—792no—
752C4×#41C2×D7911yescharacteristic, complemented
7532−1+4—3164no—
754H(5,𝔽2)—3168no—
755H(5,𝔽2)—3164no—
756C2×#41—3168no—
757C2×#41—792no—
758C2×#41—792no—
759C2×#41—796no—
760C2×#41—796no—
761C2×#41—793no—
762C2×#41—796no—
763C2×#41—793no—
764C2×#41—796no—
765C2×#41—796no—
766C2×#41C22×D7911yescharacteristic
767C2×#41C22×D7912yes—
768C2×#41C22×D7916yes—
769C22×Q8—792no—
770C22×Q8—793no—
771C22×D4—796no—
772C22×D4—796no—
773C22×D4—796no—
774C22×D4—796no—
775C22×D4—7912no—
776C22×D4—7912no—
777C22×D4—7912no—
778C22×D4—796no—
779C22×D4—793no—
780C22×D4—7912no—
781C23×C4—796no—
782C4⋊Q8—792no—
783C4⋊Q8—793no—
784C4⋊Q8—793no—
785C4⋊Q8C22×D7913yes—
786#127—796no—
787#127—7912no—
788#127—796no—
789#127—796no—
790#127—7912no—
791#127—796no—
792#127—793no—
793#127—793no—
794#127C22×D7916yes—
795#127C22×D7913yes—
796#126—792no—
797#126—792no—
798#126—796no—
799#126—7912no—
800#126—7912no—
801#126—796no—
802#126—796no—
803#126C22×D7916yes—
804#125—796no—
805#125—796no—
806#125—796no—
807#125—791no—
808#125C22×D7916yes—
809#125C22×D7911yescharacteristic
810#124—796no—
811#124—7912no—
812#124—796no—
813#124—796no—
814#124—796no—
815#124—796no—
816#124—7912no—
817#124—7912no—
818#124—793no—
819#124—796no—
820#124—796no—
821#124—796no—
822#124—793no—
823#124—796no—
824#124—791no—
825#124C22×D7913yes—
826#123—796no—
827#123—7912no—
828#123—792no—
829#123—796no—
830#123—7912no—
831#123—796no—
832#123—796no—
833#123—796no—
834#123—7912no—
835#123—796no—
836#123—796no—
837#123—796no—
838#123—796no—
839#123—7912no—
840#123—796no—
841#123—7912no—
842#123—7912no—
843#123C22×D7916yes—
844#123C22×D79112yes—
845C22⋊Q8—796no—
846C22⋊Q8—796no—
847C22⋊Q8—793no—
848C22⋊Q8—792no—
849C22⋊Q8—792no—
850C22⋊Q8—796no—
851C22⋊Q8—796no—
852C22⋊Q8—796no—
853C22⋊Q8—796no—
854C22⋊Q8—796no—
855C22⋊Q8—796no—
856C22⋊Q8—796no—
857C22⋊Q8—796no—
858C22⋊Q8C22×D7913yes—
859#121—7912no—
860#121—796no—
861#121—796no—
862#121—796no—
863#121—796no—
864#121—796no—
865#121—796no—
866#121—7912no—
867#121—7912no—
868#121—7912no—
869#121—796no—
870#121—793no—
871#121—796no—
872#121—796no—
873#121—796no—
874#121—796no—
875#121—7912no—
876#121—7912no—
877#121—7912no—
878#121—796no—
879#121—7912no—
880#121—796no—
881#121—796no—
882#121—796no—
883#121—796no—
884#121—796no—
885#121—796no—
886#121—796no—
887#121—796no—
888#121—796no—
889#121—7912no—
890#121—796no—
891#121—796no—
892#121—796no—
893#121—796no—
894#121—796no—
895#121—7912no—
896#121—7912no—
897#121C22×D7916yes—
898#121C22×D7916yes—
899#121C22×D7913yes—
900#121C22×D7916yes—
901#121C22×D7916yes—
902#121C22×D79112yes—
903#120—7912no—
904#120—796no—
905#120—796no—
906#120—7912no—
907#120—7912no—
908#120—7912no—
909#120—7912no—
910#120—796no—
911#120—796no—
912#120—796no—
913#120—796no—
914#120—7912no—
915#120—7912no—
916#120—7912no—
917#120—7912no—
918#120—7912no—
919C4×Q8—792no—
920C4×Q8—796no—
921C4×Q8—796no—
922C4×Q8—793no—
923C4×Q8C22×D7912yes—
924C4×Q8C22×D7911yescharacteristic
925C4×Q8C22×D7911yescharacteristic
926C4×Q8C22×D7913yes—
927C4×D4—7912no—
928C4×D4—796no—
929C4×D4—796no—
930C4×D4—796no—
931C4×D4—7912no—
932C4×D4—796no—
933C4×D4—796no—
934C4×D4—7912no—
935C4×D4—7912no—
936C4×D4—796no—
937C4×D4—796no—
938C4×D4—796no—
939C4×D4—793no—
940C4×D4—796no—
941C4×D4—796no—
942C4×D4—796no—
943C4×D4—796no—
944C4×D4C22×D7913yes—
945C4×D4C22×D7913yes—
946C4×D4C22×D7916yes—
947C4×D4C22×D7916yes—
948C4×D4C22×D7913yes—
949C4×D4C22×D7916yes—
950C4×D4C22×D7916yes—
951#117—7912no—
952#117—796no—
953#117—796no—
954#117—7912no—
955#117—796no—
956#117—796no—
957#117C22×D7913yes—
958#117C22×D7916yes—
959C2×C4⋊C4—796no—
960C2×C4⋊C4C22×D7916yes—
961C2×C22⋊C4—7912no—
962C2×C22⋊C4—796no—
963C2×C22⋊C4—796no—
964C2×C22⋊C4—7912no—
965C2×C42—796no—
966C2×C42C22×D7913yes—
967C24—796no—
968C24—7912no—
969C24—796no—
970#41—28no—
971#41—24no—
972#41—86no—
973#41—31612no—
974#41—31612no—
975#41—3166no—
976#41—3166no—
977#41—31612no—
978#41—31612no—
979#41—6326no—
980#41—1588no—
981#41—1588no—
982C2×Q8—3166no—
983C2×Q8—793no—
984C2×Q8—792no—
985C2×Q8—793no—
986C2×Q8—791no—
987C2×Q8—796no—
988C2×Q8—1588no—
989C2×Q8C23×D7913yes—
990C2×Q8C23×D7911yescharacteristic
991C2×D4—31612no—
992C2×D4—3166no—
993C2×D4—31612no—
994C2×D4—31612no—
995C2×D4—31612no—
996C2×D4—31612no—
997C2×D4—7912no—
998C2×D4—7912no—
999C2×D4—796no—
1000C2×D4—796no—
1001C2×D4—796no—
1002C2×D4—796no—
1003C2×D4—7912no—
1004C2×D4—796no—
1005C2×D4—796no—
1006C2×D4—796no—
1007C2×D4—793no—
1008C2×D4—796no—
1009C2×D4—796no—
1010C2×D4—7912no—
1011C2×D4—796no—
1012C2×D4—796no—
1013C2×D4—796no—
1014C2×D4—791no—
1015C2×D4—793no—
1016C2×D4—796no—
1017C2×D4—796no—
1018C2×D4—796no—
1019C2×D4—63212no—
1020C2×D4—63212no—
1021C2×D4—63212no—
1022C2×D4—63212no—
1023C2×D4C23×D7916yes—
1024C2×D4C23×D7913yes—
1025C2×D4C23×D79112yes—
1026C2×D4C23×D7913yes—
1027C2×D4C23×D7916yes—
1028C2×D4C23×D7916yes—
1029C22×C4—31612no—
1030C22×C4—796no—
1031C22×C4—796no—
1032C22×C4—796no—
1033C22×C4—796no—
1034C22×C4—796no—
1035C22×C4—7912no—
1036C22×C4—792no—
1037C22×C4—796no—
1038C22×C4—796no—
1039C22×C4—796no—
1040C22×C4C23×D7913yes—
1041C22×C4C23×D7916yes—
1042C22×C4C23×D7913yes—
1043C22×C4C23×D7913yes—
1044C22×C4C23×D79112yes—
1045C4⋊C4—796no—
1046C4⋊C4—792no—
1047C4⋊C4—796no—
1048C4⋊C4—796no—
1049C4⋊C4—792no—
1050C4⋊C4—792no—
1051C4⋊C4—796no—
1052C4⋊C4—796no—
1053C4⋊C4—796no—
1054C4⋊C4—796no—
1055C4⋊C4—796no—
1056C4⋊C4—796no—
1057C4⋊C4—792no—
1058C4⋊C4—796no—
1059C4⋊C4—791no—
1060C4⋊C4—791no—
1061C4⋊C4C23×D7913yes—
1062C4⋊C4C23×D7913yes—
1063C4⋊C4C23×D7916yes—
1064C4⋊C4C23×D7916yes—
1065C4⋊C4C23×D7916yes—
1066C4⋊C4C23×D7912yes—
1067C4⋊C4C23×D7916yes—
1068C4⋊C4C23×D7912yes—
1069C4⋊C4C23×D7911yescharacteristic
1070C4⋊C4C23×D7911yescharacteristic
1071C22⋊C4—7912no—
1072C22⋊C4—796no—
1073C22⋊C4—796no—
1074C22⋊C4—796no—
1075C22⋊C4—796no—
1076C22⋊C4—796no—
1077C22⋊C4—7912no—
1078C22⋊C4—7912no—
1079C22⋊C4—796no—
1080C22⋊C4—796no—
1081C22⋊C4—796no—
1082C22⋊C4—7912no—
1083C22⋊C4—792no—
1084C22⋊C4—796no—
1085C22⋊C4—796no—
1086C22⋊C4—7912no—
1087C22⋊C4—796no—
1088C22⋊C4—796no—
1089C22⋊C4—792no—
1090C22⋊C4—792no—
1091C22⋊C4—796no—
1092C22⋊C4—796no—
1093C22⋊C4—792no—
1094C22⋊C4—792no—
1095C22⋊C4C23×D7916yes—
1096C22⋊C4C23×D7916yes—
1097C22⋊C4C23×D7916yes—
1098C22⋊C4C23×D7916yes—
1099C22⋊C4C23×D7916yes—
1100C22⋊C4C23×D7916yes—
1101C42—792no—
1102C42—796no—
1103C42—796no—
1104C42—7912no—
1105C42C23×D7916yes—
1106C42C23×D7911yescharacteristic
1107C42C23×D7913yes—
1108C42C23×D7913yes—
1109C42C23×D7913yes—
1110C23—3166no—
1111C23—3166no—
1112C23—3166no—
1113C23—3166no—
1114C23—31612no—
1115C23—31612no—
1116C23—3166no—
1117C23—3166no—
1118C23—31612no—
1119C23—796no—
1120C23—792no—
1121C23—796no—
1122C23C24×D7916yes—
1123C23C24×D7913yes—
1124Q8—43no—
1125Q8—3163no—
1126Q8—3162no—
1127Q8—3161no—
1128Q8—3163no—
1129Q8—15812no—
1130Q8#1457920714yes—
1131D4—212no—
1132D4—26no—
1133D4—46no—
1134D4—46no—
1135D4—412no—
1136D4—43no—
1137D4—3166no—
1138D4—3163no—
1139D4—3166no—
1140D4—3166no—
1141D4—31612no—
1142D4—3166no—
1143D4—3166no—
1144D4—3166no—
1145D4—3161no—
1146D4—3163no—
1147D4—3166no—
1148D4—3166no—
1149D4—3166no—
1150D4—31612no—
1151D4—3166no—
1152D4—3166no—
1153D4—31612no—
1154D4—3166no—
1155D4—31612no—
1156D4—3166no—
1157D4—15812no—
1158D4—15812no—
1159C2×C4—212no—
1160C2×C4—26no—
1161C2×C4—412no—
1162C2×C4—43no—
1163C2×C4—43no—
1164C2×C4—3162no—
1165C2×C4—3166no—
1166C2×C4—3166no—
1167C2×C4—3166no—
1168C2×C4—31612no—
1169C2×C4—3166no—
1170C2×C4—3166no—
1171C2×C4—796no—
1172C2×C4—792no—
1173C2×C4—792no—
1174C2×C4—796no—
1175C2×C4—792no—
1176C2×C4—15812no—
1177C2×C4—15812no—
1178C2×C4—15812no—
1179C2×C4C24×D7916yes—
1180C2×C4C24×D7912yes—
1181C2×C4C24×D7911yescharacteristic
1182C2×C4C24×D7911yescharacteristic
1183C2×C4C24×D7911yescharacteristic
1184C2×C4C24×D7913yes—
1185C2×C4C24×D7913yes—
1186C2×C4C24×D7912yes—
1187C2×C4C24×D7913yes—
1188C22—23no—
1189C22—26no—
1190C22—26no—
1191C22—23no—
1192C22—23no—
1193C22—26no—
1194C22—63212no—
1195C22—1582no—
1196C22—1586no—
1197C22—1586no—
1198C22—1586no—
1199C22—1582no—
1200C22—1586no—
1201C22—1586no—
1202C22—1586no—
1203C22—1582no—
1204C22—126412no—
1205C22—12646no—
1206C22C25×D7911yescharacteristic
1207C4—22no—
1208C4—21no—
1209C4—23no—
1210C4—21no—
1211C4—26no—
1212C4—21no—
1213C4—23no—
1214C4—22no—
1215C4—1582no—
1216C4—1586no—
1217C4—1582no—
1218C4—1582no—
1219C4—1586no—
1220C4C2×#1457920716yes—
1221C2—46no—
1222C2—43no—
1223C2—3162no—
1224C2—3166no—
1225C2—3166no—
1226C2C22×#1457920711yescharacteristic
1227C2#2377821011yescharacteristic
1228C2#2377821111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3517C2
hypercenter#3517D79
hypocenterC79#63066
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3517

Complements

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

NH ≅ G/Ntype
1. #23777923C2semidirect
2. #23777916C2semidirect
3. #23777826C2semidirect
4. #23777805C2semidirect
5. #23777729C2semidirect
6. #23777724C2semidirect
7. #23777722C2semidirect
8. #23777717C2semidirect
9. #23777636C2semidirect
10. #23777539C2semidirect
11. #23777512C2semidirect
12. #23777501C2semidirect
13. #23777406C2semidirect
14. #23777193C2semidirect
15. #23777177C2semidirect
16. #23777070C2semidirect
17. #23777068C2semidirect
18. #23777053C2semidirect
19. C79×#3517C2semidirect
20. C2×#14579208C22semidirect
21. C2×#14579207C22semidirect
22. C2×#14579207C22semidirect
23. C2×#41×D79C22semidirect
24. #19099317C22semidirect
25. #19099315C22semidirect
26. #19099311C22semidirect
27. #19099310C22semidirect
28. #19099309C22semidirect
29. #19099307C22semidirect
30. #19099305C22semidirect
31. #19099305C22semidirect
32. #19099304C22semidirect
33. #19099303C22semidirect
34. #19099303C22semidirect
35. #19099301C22semidirect
36. #19099301C22semidirect
37. #19099298C22semidirect
38. #19099296C22semidirect
39. #19099292C22semidirect
40. #19099279C22semidirect
41. #19099278C22semidirect
42. #19099278C22semidirect
43. #19099266C22semidirect
44. #19099261C22semidirect
45. #19099257C22semidirect
46. #19099251C22semidirect
47. #19099248C22semidirect
48. #19099236C22semidirect
49. #19099235C22semidirect
50. #19099235C22semidirect
51. #19099234C22semidirect
52. #19099233C22semidirect
53. #19099232C22semidirect
54. #19099232C22semidirect
55. #19099231C22semidirect
56. #19099225C22semidirect
57. #19099225C22semidirect
58. #19099225C22semidirect
59. #19099222C22semidirect
60. #19099220C22semidirect
61. #19099219C22semidirect
62. #19099218C22semidirect
63. #19099210C22semidirect
64. #19099209C22semidirect
65. #19099208C22semidirect
66. #19099208C22semidirect
67. #19099208C22semidirect
68. #19099208C22semidirect
69. #19099205C22semidirect
70. #19099201C22semidirect
71. D4×D316C22semidirect
72. D4×D316C22semidirect
73. D4×D316C22semidirect
74. D4×D316C22semidirect
75. #19099198C22semidirect
76. #19099198C22semidirect
77. #19099197C22semidirect
78. #19099197C22semidirect
79. #19099197C22semidirect
80. #19099197C22semidirect
81. #19099187C22semidirect
82. #19099184C22semidirect
83. #19099169C22semidirect
84. #19099166C22semidirect
85. #19099165C22semidirect
86. #19099164C22semidirect
87. #19099164C22semidirect
88. #19099153C22semidirect
89. #19099152C22semidirect
90. #19099150C22semidirect
91. #19099146C22semidirect
92. #19099144C22semidirect
93. #19099142C22semidirect
94. #19099139C22semidirect
95. #19099132C22semidirect
96. #19099132C22semidirect
97. #19099129C22semidirect
98. #19099129C22semidirect
99. #19099129C22semidirect
100. #19099129C22semidirect
101. #19099127C22semidirect
102. #19099126C22semidirect
103. #19099126C22semidirect
104. #19099124C22semidirect
105. #19099121C22semidirect
106. #19099121C22semidirect
107. #19099121C22semidirect
108. #19099113C22semidirect
109. #19099113C22semidirect
110. #19099110C22semidirect
111. #127×D79C22semidirect
112. #19099100C22semidirect
113. #19099098C22semidirect
114. #19099097C22semidirect
115. #19099095C22semidirect
116. #19099091C22semidirect
117. C2×#14579149C22semidirect
118. #19099075C22semidirect
119. #19099073C22semidirect
120. #19099072C22semidirect
121. #19099072C22semidirect
122. C2×#14579136C22semidirect
123. #121×D79C22semidirect
124. #19099045C22semidirect
125. #19099039C22semidirect
126. C4×#11929625C22semidirect
127. #557×C79C22semidirect
128. #553×C79C22semidirect
129. #550×C79C22semidirect
130. #550×C79C22semidirect
131. #550×C79C22semidirect
132. #547×C79C22semidirect
133. #540×C79C22semidirect
134. #532×C79C22semidirect
135. #529×C79C22semidirect
136. #520×C79C22semidirect
137. C4×#41×C79C22semidirect
628. #3517D79semidirect
634. C79#63066semidirect
655. #557C2×D79semidirect
662. #553C2×D79semidirect
673. #550C2×D79semidirect
674. #550C2×D79semidirect
675. #550C2×D79semidirect
683. #547C2×D79semidirect
709. #540C2×D79semidirect
733. #532C2×D79semidirect
740. #529C2×D79semidirect
749. #520C2×D79semidirect
752. C4×#41C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779232
#237779162
#237778262
#237778052
#237777292
#237777242
#237777222
#237777172
#237776362
#237775392
#237775122
#237775012
#237774062
#237771932
#237771772
#237770702
#237770682
#237770532
C79×#35172
#6306679