Finite Group Databasebeta

← #35197222

Subgroups — #35197222

Order 20224.

6428 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778008C214yesmaximal, complemented
2#23777999C214yesmaximal, complemented
3#23777893C212yesmaximal, complemented
4#23777879C218yesmaximal, complemented
5#23777809C212yesmaximal, complemented
6#23777649C211yesmaximal, characteristic, complemented
7#23777645C212yesmaximal, complemented
8#23777489C214yesmaximal, complemented
9#23777487C214yesmaximal, complemented
10#23777285C212yesmaximal, complemented
11#23777282C212yesmaximal, complemented
12#23777278C214yesmaximal, complemented
13#23777260C214yesmaximal, complemented
14#23777211C214yesmaximal, complemented
15#23777208C214yesmaximal, complemented
16#23777139C218yesmaximal, complemented
17#23776692C211yesmaximal, characteristic
18C2×#19099115C212yesmaximal, complemented
19C79×#3538C211yesmaximal, characteristic, complemented
20C79⋊#564C2218yescomplemented
21#19099316C2214yes—
22#19099316C2214yescomplemented
23#19099314C2218yes—
24#19099312C2214yescomplemented
25#19099297C2214yescomplemented
26#19099293C2214yescomplemented
27#19099293C2218yescomplemented
28#19099291C2214yescomplemented
29#19099290C2218yescomplemented
30#19099290C2218yescomplemented
31#19099290C2218yescomplemented
32#19099290C2218yescomplemented
33#19099290C2214yescomplemented
34#19099289C2214yescomplemented
35#19099288C2218yescomplemented
36#19099288C2218yescomplemented
37#19099288C2214yescomplemented
38#19099284C2214yescomplemented
39#19099284C2218yescomplemented
40#19099282C2218yes—
41#19099281C2214yescomplemented
42#19099280C2218yes—
43#19099280C2218yescomplemented
44#19099280C2218yescomplemented
45#19099272C2218yes—
46#19099267C2218yes—
47#19099267C2218yescomplemented
48#19099255C2214yes—
49#19099255C2218yes—
50#19099253C2214yes—
51#19099253C2218yes—
52#19099250C2218yes—
53#19099250C2218yes—
54#19099250C2218yes—
55#19099250C2218yescomplemented
56#19099249C2218yes—
57#19099248C2214yes—
58#19099246C2218yes—
59#19099246C2218yes—
60#19099245C2218yescomplemented
61#19099244C2214yes—
62#19099239C2218yes—
63D4×Dic158C2214yes—
64Q8×C22⋊D79C2214yes—
65Q8×C22⋊D79C2214yescomplemented
66#19099226C2214yes—
67#19099226C2214yescomplemented
68#19099194C2214yes—
69#19099192C2214yes—
70#19099192C2214yes—
71#19099192C2218yes—
72#19099192C2218yescomplemented
73#19099190C2218yescomplemented
74#19099181C2218yes—
75#19099177C2218yes—
76#19099176C2212yescomplemented
77#19099175C2212yes—
78#19099174C2212yescomplemented
79#19099174C2218yescomplemented
80#19099173C2214yes—
81#19099173C2214yescomplemented
82#19099173C2218yescomplemented
83#19099172C2218yescomplemented
84#19099172C2218yescomplemented
85#19099170C2218yes—
86#19099170C2218yes—
87#19099170C2218yescomplemented
88#19099170C2218yescomplemented
89#19099162C2214yes—
90#19099160C2214yes—
91#19099158C2214yes—
92#19099136C2214yes—
93#19099135C2218yes—
94#19099134C2212yes—
95#19099119C2212yescomplemented
96#19099117C2214yescomplemented
97#19099116C2211yescharacteristic
98#19099116C2218yes—
99#19099116C2212yescomplemented
100#19099115C2214yes—
101#19099115C2214yes—
102#19099115C2214yes—
103#19099115C2214yes—
104#19099115C2218yes—
105#19099115C2214yes—
106#19099115C2214yes—
107#19099115C2214yes—
108#19099115C2214yes—
109#19099115C2212yes—
110#19099115C2214yescomplemented
111#19099109C2211yescharacteristic
112#19099108C2212yes—
113C2×#14579160C2212yes—
114C2×#14579159C2212yes—
115C2×#14579159C2212yescomplemented
116C4⋊Q8×D79C2212yescomplemented
117#19099099C2212yes—
118#19099094C2212yes—
119#19099093C2218yes—
120#19099093C2214yes—
121#19099090C2214yes—
122#19099090C2218yes—
123C2×#14579151C2214yes—
124#19099074C2211yescharacteristic
125#19099069C2214yes—
126C2×#14579140C2212yes—
127C2×#14579138C2214yes—
128#19099042C2218yes—
129#19099041C2212yescomplemented
130#19099040C2218yes—
131#19099040C2212yescomplemented
132#19099039C2214yescomplemented
133#41×Dic79C2211yescharacteristic
134#19099031C2211yescharacteristic
135C4×#11929623C2214yes—
136C2×Q8×Dic79C2212yes—
137C2×#14579126C2214yes—
138C2×#14579126C2212yes—
139C2×#14579117C2214yes—
140C22×C4×Dic79C2211yescharacteristic
141#563×C79C2214yes—
142#552×C79C2214yes—
143#551×C79C2214yes—
144D4×Q8×C79C2214yes—
145#544×C79C2214yes—
146#541×C79C2212yes—
147#539×C79C2214yes—
148#536×C79C2212yes—
149#525×C79C2211yescharacteristic
150C2×C22⋊Q8×C79C2212yes—
151C2×#11929624C2311yescharacteristic
152C2×#11929623C2314yes—
153C22×Dic158C2314yes—
154C22×Dic158C2312yes—
155C22×Dic158C2312yes—
156C2×Q8×D79C2314yes—
157C23×Dic79C2312yes—
158#14579161C2312yes—
159#14579160C2318yes—
160#14579160C2318yes—
161#14579160C2318yes—
162#14579160C2314yes—
163#14579160C2318yes—
164#14579160C2318yes—
165#14579160C2318yes—
166#14579160C2318yes—
167#14579160C2314yes—
168#14579160C2314yes—
169#14579160C2312yes—
170#14579160C2314yes—
171#14579159C2314yes—
172#14579159C2318yes—
173#14579159C2318yes—
174#14579159C2314yes—
175#14579159C2318yes—
176#14579159C2314yes—
177#14579159C2314yes—
178#14579159C2314yes—
179#14579159C2311yescharacteristic
180#14579159C2314yes—
181#14579157C2311yescharacteristic
182#14579156C2318yes—
183#14579156C2318yes—
184#14579156C2314yes—
185#14579156C2318yes—
186#14579156C2318yes—
187#14579156C2318yes—
188#14579155C2318yes—
189#14579154C2318yes—
190#14579154C2318yes—
191#14579154C2318yes—
192#14579154C2318yes—
193#14579154C2314yes—
194#14579154C2318yes—
195#14579154C2318yes—
196#14579154C2318yes—
197#14579154C2318yes—
198#14579153C2318yes—
199#14579153C2318yes—
200#14579153C2312yes—
201#14579152C2318yes—
202#14579152C2318yes—
203#14579152C2318yes—
204#14579152C2318yes—
205#14579152C2318yes—
206#14579152C2318yes—
207#14579152C2314yes—
208#14579152C2312yes—
209#14579151C2318yes—
210#14579151C2318yes—
211#14579151C2318yes—
212#14579151C2318yes—
213#14579151C2318yes—
214#14579151C2318yes—
215#14579151C2318yes—
216#14579151C2318yes—
217#14579151C2318yes—
218#14579151C2318yes—
219#14579151C2318yes—
220#14579151C2318yes—
221#14579151C2318yes—
222#14579151C2318yes—
223#14579151C2318yes—
224#14579151C2318yes—
225#14579151C2318yes—
226#14579151C2314yes—
227#14579151C2318yes—
228#14579150C2311yescharacteristic
229#14579148C2314yes—
230#14579148C2311yescharacteristic
231#14579147C2318yes—
232#14579147C2318yes—
233#14579147C2318yes—
234#14579147C2314yes—
235#14579146C2318yes—
236#14579145C2318yes—
237#14579145C2314yes—
238#14579144C2318yes—
239#14579144C2312yes—
240#14579143C2318yes—
241#14579142C2314yes—
242#14579142C2318yes—
243#14579142C2314yes—
244#14579142C2314yes—
245#14579141C2314yes—
246#14579140C2314yes—
247#14579140C2314yes—
248#14579140C2318yes—
249#14579140C2314yes—
250#14579140C2312yes—
251#14579140C2318yes—
252#14579140C2314yes—
253#14579140C2314yes—
254#14579139C2318yes—
255#14579139C2318yes—
256#14579139C2318yes—
257#14579139C2318yes—
258#14579138C2318yes—
259#14579138C2314yes—
260#14579138C2318yes—
261#14579138C2318yes—
262#14579138C2318yes—
263#14579138C2318yes—
264#14579138C2318yes—
265#14579138C2318yes—
266#14579138C2318yes—
267#14579138C2318yes—
268#14579138C2318yes—
269#14579138C2314yes—
270#14579137C2314yes—
271#14579137C2318yes—
272#14579137C2318yes—
273#14579135C2312yes—
274#14579133C2314yes—
275#14579133C2314yes—
276#14579130C2312yes—
277Q8×Dic79C2314yes—
278Q8×Dic79C2314yes—
279Q8×Dic79C2314yes—
280Q8×Dic79C2318yes—
281Q8×Dic79C2314yes—
282Q8×Dic79C2314yes—
283Q8×Dic79C2312yes—
284C4×Dic158C2318yes—
285C4×Dic158C2318yes—
286C4×Dic158C2318yes—
287C4×Dic158C2318yes—
288C4×Dic158C2318yes—
289C4×Dic158C2318yes—
290C4×Dic158C2314yes—
291C4×Dic158C2318yes—
292C4×Dic158C2314yes—
293#14579126C2318yes—
294#14579126C2318yes—
295#14579126C2314yes—
296#14579126C2318yes—
297#14579126C2318yes—
298#14579126C2314yes—
299#14579126C2314yes—
300#14579126C2318yes—
301#14579126C2318yes—
302#14579126C2314yes—
303#14579126C2318yes—
304#14579126C2318yes—
305#14579126C2314yes—
306#14579126C2318yes—
307#14579126C2318yes—
308#14579126C2314yes—
309#14579126C2312yes—
310D4×Dic79C2318yes—
311D4×Dic79C2314yes—
312D4×Dic79C2314yes—
313D4×Dic79C2312yes—
314#14579123C2312yes—
315C4×C22⋊D79C2318yes—
316C4×C22⋊D79C2318yes—
317C4×C22⋊D79C2314yes—
318C4×C22⋊D79C2314yes—
319(C22⋊D79)⋊C4C2318yes—
320(C22⋊D79)⋊C4C2318yes—
321(C22⋊D79)⋊C4C2314yes—
322(C22⋊D79)⋊C4C2314yes—
323(C22⋊D79)⋊C4C2314yes—
324#14579120C2311yescharacteristic
325#14579120C2312yes—
326#14579120C2318yes—
327#14579120C2318yes—
328#14579120C2312yes—
329#14579119C2314yes—
330#14579119C2314yes—
331#14579119C2318yes—
332#14579118C2312yes—
333#14579118C2318yes—
334#14579118C2318yes—
335#14579117C2318yes—
336#14579117C2314yes—
337#14579117C2318yes—
338#14579117C2314yes—
339#14579117C2318yes—
340#14579117C2318yes—
341#14579117C2318yes—
342#14579117C2318yes—
343#14579117C2318yes—
344#14579117C2318yes—
345C2×C4⋊Dic79C2314yes—
346C2×C4⋊Dic79C2312yes—
347C2×Dic79⋊C4C2314yes—
348C2×Dic79⋊C4C2314yes—
349C2×Dic79⋊C4C2318yes—
350C2×Dic79⋊C4C2314yes—
351C2×Dic79⋊C4C2314yes—
352C2×Dic79⋊C4C2314yes—
353C4⋊C4×D79C2318yes—
354C2×C22⋊Dic79C2314yes—
355C2×C4×Dic79C2312yes—
356C2×C4×Dic79C2312yes—
357C2×C4×Dic79C2312yes—
358C2×C4×Dic79C2311yescharacteristic
359C2×C4×Dic79C2312yes—
360C2×C4×Dic79C2312yes—
361C2×C4×Dic79C2311yescharacteristic
362C2×C4×Dic79C2314yes—
363C2×C4×Dic79C2314yes—
364C2×C4×Dic79C2312yes—
365C42×D79C2312yes—
366C2×#41×C79C2311yescharacteristic
367C22×Q8×C79C2312yes—
368C22×Q8×C79C2312yes—
369C23×C4×C79C2311yescharacteristic
370C4⋊Q8×C79C2318yes—
371C4⋊Q8×C79C2312yes—
372C4⋊Q8×C79C2314yes—
373#126×C79C2318yes—
374#126×C79C2318yes—
375#125×C79C2318yes—
376#125×C79C2312yes—
377#125×C79C2318yes—
378#124×C79C2314yes—
379#123×C79C2314yes—
380#123×C79C2312yes—
381#123×C79C2318yes—
382#123×C79C2314yes—
383C22⋊Q8×C79C2314yes—
384C22⋊Q8×C79C2314yes—
385C22⋊Q8×C79C2318yes—
386C22⋊Q8×C79C2314yes—
387C22⋊Q8×C79C2312yes—
388C22⋊Q8×C79C2318yes—
389C22⋊Q8×C79C2314yes—
390C22⋊Q8×C79C2314yes—
391#121×C79C2312yes—
392#120×C79C2312yes—
393C4×Q8×C79C2314yes—
394C4×D4×C79C2314yes—
395C4×D4×C79C2318yes—
396#117×C79C2311yescharacteristic
397#117×C79C2318yes—
398#117×C79C2312yes—
399C2×C4⋊C4×C79C2314yes—
400C2×C4⋊C4×C79C2312yes—
401C2×C22⋊C4×C79C2314yes—
402#11929624—42no—
403#11929623—216no—
404C2×Dic158—216no—
405C2×Dic158—44no—
406C2×Dic158—44no—
407C2×Dic158C2414yes—
408C2×Dic158C2418yes—
409C2×Dic158C2418yes—
410C2×Dic158C2414yes—
411C2×Dic158C2418yes—
412C2×Dic158C2414yes—
413C2×Dic158C2414yes—
414C2×Dic158C2411yescharacteristic
415Q8×D79—48no—
416C2×D316C2411yescharacteristic
417C2×C22⋊D79C2414yes—
418C2×C22⋊D79C2414yes—
419C2×C22⋊D79C2412yes—
420C22×Dic79—28no—
421C22×Dic79C2414yes—
422C22×Dic79C2414yes—
423C22×Dic79C2412yes—
424C22×Dic79C2412yes—
425C22×Dic79C2412yes—
426C22×Dic79C2412yes—
427C22×Dic79C2412yes—
428C22×Dic79C2414yes—
429C22×Dic79C2414yes—
430C22×Dic79C2412yes—
431C2×C4×D79C2412yes—
432C2×C4×D79C2414yes—
433C2×C4×D79C2418yes—
434C4⋊Dic79C2418yes—
435C4⋊Dic79C2414yes—
436C4⋊Dic79C2418yes—
437C4⋊Dic79C2418yes—
438C4⋊Dic79C2414yes—
439C4⋊Dic79C2414yes—
440C4⋊Dic79C2414yes—
441C4⋊Dic79C2412yes—
442C4⋊Dic79C2418yes—
443C4⋊Dic79C2418yes—
444C4⋊Dic79C2418yes—
445Dic79⋊C4C2418yes—
446Dic79⋊C4C2418yes—
447Dic79⋊C4C2418yes—
448Dic79⋊C4C2418yes—
449Dic79⋊C4C2418yes—
450Dic79⋊C4C2418yes—
451Dic79⋊C4C2418yes—
452Dic79⋊C4C2418yes—
453Dic79⋊C4C2418yes—
454Dic79⋊C4C2418yes—
455Dic79⋊C4C2418yes—
456Dic79⋊C4C2418yes—
457Dic79⋊C4C2414yes—
458Dic79⋊C4C2414yes—
459Dic79⋊C4C2414yes—
460Dic79⋊C4C2414yes—
461Dic79⋊C4C2418yes—
462Dic79⋊C4C2418yes—
463Dic79⋊C4C2418yes—
464Dic79⋊C4C2418yes—
465Dic79⋊C4C2418yes—
466Dic79⋊C4C2414yes—
467Dic79⋊C4C2418yes—
468C22⋊Dic79C2418yes—
469C22⋊Dic79C2418yes—
470C22⋊Dic79C2414yes—
471C22⋊Dic79C2414yes—
472C22⋊Dic79C2414yes—
473C22⋊Dic79C2418yes—
474C22⋊Dic79C2414yes—
475C22⋊Dic79C2412yes—
476(C2×D79)⋊C4C2414yes—
477(C2×D79)⋊C4C2418yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2418yes—
480(C2×D79)⋊C4C2414yes—
481(C2×D79)⋊C4C2414yes—
482C4×Dic79C2411yescharacteristic
483C4×Dic79C2414yes—
484C4×Dic79C2412yes—
485C4×Dic79C2411yescharacteristic
486C4×Dic79C2412yes—
487C4×Dic79C2412yes—
488C4×Dic79C2412yes—
489C4×Dic79C2411yescharacteristic
490C4×Dic79C2412yes—
491C4×Dic79C2412yes—
492C4×Dic79C2411yescharacteristic
493C4×Dic79C2418yes—
494C4×Dic79C2418yes—
495C4×Dic79C2418yes—
496C4×Dic79C2418yes—
497C4×Dic79C2414yes—
498C4×Dic79C2412yes—
499C4×Dic79C2418yes—
500C4×Dic79C2418yes—
501C4×Dic79C2414yes—
502C4×Dic79C2418yes—
503C4×Dic79C2418yes—
504C24×C79C2411yescharacteristic
505#41×C79—42no—
506C2×Q8×C79—44no—
507C2×Q8×C79—44no—
508C2×Q8×C79C2414yes—
509C2×Q8×C79C2414yes—
510C2×Q8×C79C2414yes—
511C2×Q8×C79C2411yescharacteristic
512C2×D4×C79C2414yes—
513C2×D4×C79C2412yes—
514C2×D4×C79C2411yescharacteristic
515C22×C4×C79—42no—
516C22×C4×C79C2414yes—
517C22×C4×C79C2412yes—
518C22×C4×C79C2412yes—
519C22×C4×C79C2411yescharacteristic
520C22×C4×C79C2414yes—
521C22×C4×C79C2412yes—
522C22×C4×C79C2414yes—
523C22×C4×C79C2411yescharacteristic
524C4⋊C4×C79C2414yes—
525C4⋊C4×C79C2418yes—
526C4⋊C4×C79C2418yes—
527C4⋊C4×C79C2414yes—
528C4⋊C4×C79C2412yes—
529C4⋊C4×C79C2418yes—
530C4⋊C4×C79C2418yes—
531C4⋊C4×C79C2418yes—
532C4⋊C4×C79C2414yes—
533C4⋊C4×C79C2418yes—
534C22⋊C4×C79C2418yes—
535C22⋊C4×C79C2418yes—
536C22⋊C4×C79C2414yes—
537C22⋊C4×C79C2412yes—
538C22⋊C4×C79C2414yes—
539C22⋊C4×C79C2414yes—
540C22⋊C4×C79C2418yes—
541C42×C79C2414yes—
542C42×C79C2412yes—
543C42×C79C2418yes—
544C23×C79—24no—
545C23×C79—41no—
546C23×C79C2511yescharacteristic
547C23×C79C2512yes—
548C23×C79C2512yes—
549C22×D79C2512yes—
550Q8×C79—28no—
551Q8×C79—44no—
552Q8×C79—44no—
553Q8×C79—41no—
554D4×C79—28no—
555D4×C79—41no—
556D4×C79—42no—
557C2×C4×C79—28no—
558C2×C4×C79—24no—
559C2×C4×C79—24no—
560C2×C4×C79—22no—
561C2×C4×C79—42no—
562C2×C4×C79—41no—
563C2×C4×C79—44no—
564C2×C4×C79—44no—
565C2×C4×C79C2518yes—
566C2×C4×C79C2512yes—
567C2×C4×C79C2512yes—
568C2×C4×C79C2511yescharacteristic
569C2×C4×C79C2514yes—
570C2×C4×C79C2518yes—
571C2×C4×C79C2511yescharacteristic
572C22⋊D79—28no—
573C22⋊D79—28no—
574C22⋊D79—42no—
575C2×Dic79—24no—
576C2×Dic79—28no—
577C2×Dic79—24no—
578C2×Dic79—24no—
579C2×Dic79—24no—
580C2×Dic79—24no—
581C2×Dic79—28no—
582C2×Dic79—44no—
583C2×Dic79—44no—
584C2×Dic792−1+418yes—
585C2×Dic79C2512yes—
586C2×Dic79C2518yes—
587C2×Dic79C2514yes—
588C2×Dic79C2512yes—
589C2×Dic79C2512yes—
590C2×Dic79C2518yes—
591C2×Dic79C2512yes—
592C2×Dic79C2512yes—
593D316—41no—
594C4×D79—24no—
595C4×D79—28no—
596C4×D79—48no—
597Dic158—28no—
598Dic158—216no—
599Dic158—216no—
600Dic158—28no—
601Dic158—48no—
602Dic158—44no—
603Dic158—44no—
604Dic158—41no—
605C22×C79—22no—
606C22×C79—22no—
607C22×C79—24no—
608C22×C79—22no—
609C22×C79—21no—
610C22×C79—22no—
611C22×C79—44no—
612C22×C79C2×2−1+414yes—
613C22×C79C2611yescharacteristic
614C2×D79—24no—
615C2×D79—22no—
616C4×C79—28no—
617C4×C79—24no—
618C4×C79—21no—
619C4×C79—22no—
620C4×C79—22no—
621C4×C79—28no—
622C4×C79#58512yes—
623Dic79—24no—
624Dic79—28no—
625Dic79—22no—
626Dic79—22no—
627Dic79—22no—
628Dic79—28no—
629Dic79C2×2−1+414yes—
630Dic79C2×2−1+414yes—
631#62837—791nomaximal, Sylow
632C2×C79—24no—
633C2×C79—42no—
634C2×C79—41no—
635C2×C79C22×2−1+412yes—
636C2×C79C2×#58511yescharacteristic
637D79—42no—
638#3563—794no—
639#3563—794no—
640#3556—792no—
641#3555—798no—
642#3550—792no—
643#3538—791no—
644#3538—792no—
645#3538D7911yescharacteristic, complemented
646#3523—794no—
647#3523—794no—
648#3509—794no—
649#3509—792no—
650#3509—792no—
651#3507—794no—
652#3503—794no—
653#3502—794no—
654#3495—798no—
655#3444—791no—
656C2×#533—792no—
657C79#6283711yescharacteristic, complemented, Sylow
658#564—798no—
659#563—794no—
660#563—794no—
661#563—794no—
662#563—798no—
663#563C2×D7914yes—
664#559—794no—
665Q82—794no—
666Q82—798no—
667#557—798no—
668#557—798no—
669#557—794no—
670#557—798no—
671#557—798no—
672#557—798no—
673#557—798no—
674#557—794no—
675#557—794no—
676#557—794no—
677#556—798no—
678#556—798no—
679#556—798no—
680#556—798no—
681#556—798no—
682#556—794no—
683#556—794no—
684#554—798no—
685#554—798no—
686#554—798no—
687#552—798no—
688#552—798no—
689#552—798no—
690#552—798no—
691#552—798no—
692#552—798no—
693#552—798no—
694#552—794no—
695#552—798no—
696#552—794no—
697#552—798no—
698#552—798no—
699#552—794no—
700#552C2×D7914yes—
701#551—794no—
702#551—798no—
703#551C2×D7914yes—
704D4×Q8—794no—
705D4×Q8—794no—
706D4×Q8—794no—
707D4×Q8—794no—
708D4×Q8—794no—
709D4×Q8C2×D7914yes—
710#544—798no—
711#544—798no—
712#544—794no—
713#544—794no—
714#544—798no—
715#544—794no—
716#544C2×D7914yes—
717#542—798no—
718#542—798no—
719#541—792no—
720#541—798no—
721#541—798no—
722#541—798no—
723#541—798no—
724#541—798no—
725#541—798no—
726#541—798no—
727#541—792no—
728#541—794no—
729#541—794no—
730#541—798no—
731#541—792no—
732#541C2×D7912yes—
733#539—794no—
734#539—794no—
735#539—794no—
736#539C2×D7914yes—
737#536—792no—
738#536—798no—
739#536—794no—
740#536C2×D7912yes—
741#533—792no—
742#533—794no—
743#533—794no—
744#533—794no—
745#533—794no—
746#533—794no—
747#533—794no—
748#533—794no—
749#533—794no—
750#533—792no—
751#533—798no—
752#533—794no—
753#533—794no—
754#533—791no—
755#533—798no—
756#533—792no—
757#532—791no—
758#532—792no—
759C2×C4⋊Q8—792no—
760C2×C4⋊Q8—792no—
761C2×C4⋊Q8—792no—
762C2×C4⋊Q8—792no—
763#529—794no—
764#529—798no—
765#529—792no—
766#529—792no—
767#529—794no—
768#529—798no—
769C2×#125—794no—
770#525—791no—
771#525—794no—
772#525C2×D7911yescharacteristic
773C2×C22⋊Q8—792no—
774C2×C22⋊Q8—794no—
775C2×C22⋊Q8C2×D7912yes—
776#520—798no—
777#519—792no—
778#519—794no—
779#519—798no—
780#519—792no—
781C4×#41—791no—
782C4×#41—794no—
783C4×#41—791no—
784C2×C4×Q8—792no—
785C2×C4×Q8—794no—
786C2×C4×Q8—792no—
787C2×#117—794no—
788C22×C42—791no—
789C2×#41—794no—
790C2×#41—791no—
791C2×#41C22×D7911yescharacteristic
792C22×Q8—794no—
793C22×Q8—792no—
794C22×Q8—792no—
795C22×Q8—794no—
796C22×Q8C22×D7912yes—
797C22×Q8C22×D7912yes—
798C23×C4—792no—
799C23×C4C22×D7911yescharacteristic
800C4⋊Q8—794no—
801C4⋊Q8—794no—
802C4⋊Q8—794no—
803C4⋊Q8—794no—
804C4⋊Q8—794no—
805C4⋊Q8—798no—
806C4⋊Q8—791no—
807C4⋊Q8—798no—
808C4⋊Q8—794no—
809C4⋊Q8—798no—
810C4⋊Q8—794no—
811C4⋊Q8—794no—
812C4⋊Q8—794no—
813C4⋊Q8—794no—
814C4⋊Q8—798no—
815C4⋊Q8—792no—
816C4⋊Q8—798no—
817C4⋊Q8—798no—
818C4⋊Q8—798no—
819C4⋊Q8—798no—
820C4⋊Q8—798no—
821C4⋊Q8—798no—
822C4⋊Q8—792no—
823C4⋊Q8C22×D7912yes—
824C4⋊Q8C22×D7914yes—
825C4⋊Q8C22×D7918yes—
826#127—791no—
827#126—794no—
828#126—798no—
829#126—798no—
830#126—798no—
831#126—798no—
832#126—798no—
833#126—794no—
834#126—798no—
835#126—798no—
836#126—798no—
837#126—798no—
838#126—798no—
839#126—798no—
840#126—798no—
841#126—798no—
842#126—798no—
843#126C22×D7918yes—
844#126C22×D7918yes—
845#125—798no—
846#125—798no—
847#125—798no—
848#125—798no—
849#125—794no—
850#125—792no—
851#125—798no—
852#125—798no—
853#125—798no—
854#125—798no—
855#125—798no—
856#125—798no—
857#125—794no—
858#125—798no—
859#125—798no—
860#125—798no—
861#125—798no—
862#125—798no—
863#125—798no—
864#125—798no—
865#125—798no—
866#125—798no—
867#125—798no—
868#125—798no—
869#125—798no—
870#125—798no—
871#125—798no—
872#125—792no—
873#125—798no—
874#125—798no—
875#125C22×D7912yes—
876#125C22×D7918yes—
877#125C22×D7918yes—
878#124—791no—
879#124—791no—
880#124—794no—
881#124—794no—
882#124—798no—
883#124—798no—
884#124—798no—
885#124C22×D7914yes—
886#123—794no—
887#123—798no—
888#123—794no—
889#123—794no—
890#123—792no—
891#123—798no—
892#123—798no—
893#123—794no—
894#123—798no—
895#123—798no—
896#123C22×D7912yes—
897#123C22×D7918yes—
898#123C22×D7914yes—
899#123C22×D7914yes—
900C22⋊Q8—794no—
901C22⋊Q8—798no—
902C22⋊Q8—798no—
903C22⋊Q8—794no—
904C22⋊Q8—794no—
905C22⋊Q8—794no—
906C22⋊Q8—794no—
907C22⋊Q8—792no—
908C22⋊Q8—794no—
909C22⋊Q8—798no—
910C22⋊Q8—798no—
911C22⋊Q8—794no—
912C22⋊Q8—798no—
913C22⋊Q8—798no—
914C22⋊Q8—798no—
915C22⋊Q8—798no—
916C22⋊Q8—798no—
917C22⋊Q8—798no—
918C22⋊Q8—798no—
919C22⋊Q8—798no—
920C22⋊Q8—794no—
921C22⋊Q8—794no—
922C22⋊Q8—798no—
923C22⋊Q8—798no—
924C22⋊Q8—798no—
925C22⋊Q8—798no—
926C22⋊Q8—798no—
927C22⋊Q8—798no—
928C22⋊Q8C22×D7914yes—
929C22⋊Q8C22×D7914yes—
930C22⋊Q8C22×D7914yes—
931C22⋊Q8C22×D7914yes—
932C22⋊Q8C22×D7912yes—
933C22⋊Q8C22×D7914yes—
934C22⋊Q8C22×D7918yes—
935C22⋊Q8C22×D7918yes—
936#121—794no—
937#121—794no—
938#121—792no—
939#121C22×D7912yes—
940#120—792no—
941#120C22×D7912yes—
942C4×Q8—794no—
943C4×Q8—794no—
944C4×Q8—794no—
945C4×Q8—794no—
946C4×Q8—792no—
947C4×Q8—794no—
948C4×Q8—798no—
949C4×Q8—794no—
950C4×Q8—794no—
951C4×Q8—794no—
952C4×Q8—798no—
953C4×Q8—798no—
954C4×Q8—798no—
955C4×Q8—794no—
956C4×Q8—798no—
957C4×Q8—792no—
958C4×Q8—794no—
959C4×Q8—798no—
960C4×Q8—794no—
961C4×Q8—798no—
962C4×Q8—798no—
963C4×Q8—798no—
964C4×Q8—798no—
965C4×Q8—798no—
966C4×Q8—794no—
967C4×Q8—798no—
968C4×Q8—794no—
969C4×Q8—798no—
970C4×Q8—798no—
971C4×Q8—798no—
972C4×Q8—798no—
973C4×Q8—798no—
974C4×Q8—798no—
975C4×Q8C22×D7914yes—
976C4×D4—794no—
977C4×D4—794no—
978C4×D4—792no—
979C4×D4—798no—
980C4×D4—794no—
981C4×D4—794no—
982C4×D4—798no—
983C4×D4—798no—
984C4×D4—792no—
985C4×D4—794no—
986C4×D4—794no—
987C4×D4—794no—
988C4×D4—798no—
989C4×D4—798no—
990C4×D4C22×D7914yes—
991C4×D4C22×D7918yes—
992#117—792no—
993#117—791no—
994#117—798no—
995#117—792no—
996#117—798no—
997#117—794no—
998#117—798no—
999#117—794no—
1000#117—798no—
1001#117—798no—
1002#117—798no—
1003#117—798no—
1004#117—794no—
1005#117—794no—
1006#117—798no—
1007#117—798no—
1008#117—798no—
1009#117—798no—
1010#117—792no—
1011#117—798no—
1012#117—798no—
1013#117C22×D7911yescharacteristic
1014#117C22×D7912yes—
1015#117C22×D7918yes—
1016C2×C4⋊C4—794no—
1017C2×C4⋊C4—794no—
1018C2×C4⋊C4—794no—
1019C2×C4⋊C4—794no—
1020C2×C4⋊C4—794no—
1021C2×C4⋊C4—794no—
1022C2×C4⋊C4—792no—
1023C2×C4⋊C4—798no—
1024C2×C4⋊C4—798no—
1025C2×C4⋊C4C22×D7914yes—
1026C2×C4⋊C4C22×D7912yes—
1027C2×C22⋊C4—794no—
1028C2×C22⋊C4C22×D7914yes—
1029C2×C42—794no—
1030C2×C42—794no—
1031C2×C42—792no—
1032C2×C42—792no—
1033C2×C42—792no—
1034C2×C42—792no—
1035C2×C42—791no—
1036C2×C42—792no—
1037C2×C42—792no—
1038C2×C42—791no—
1039C2×C42—792no—
1040C24C23×D7911yescharacteristic
1041#41—42no—
1042#41—3162no—
1043#41—15816no—
1044C2×Q8—44no—
1045C2×Q8—44no—
1046C2×Q8—3164no—
1047C2×Q8—3164no—
1048C2×Q8—3168no—
1049C2×Q8—794no—
1050C2×Q8—798no—
1051C2×Q8—794no—
1052C2×Q8—791no—
1053C2×Q8—798no—
1054C2×Q8—798no—
1055C2×Q8—794no—
1056C2×Q8—794no—
1057C2×Q8—15816no—
1058C2×Q8C23×D7914yes—
1059C2×Q8C23×D7914yes—
1060C2×Q8C23×D7914yes—
1061C2×Q8C23×D7911yescharacteristic
1062C2×D4—792no—
1063C2×D4—794no—
1064C2×D4—794no—
1065C2×D4—791no—
1066C2×D4C23×D7914yes—
1067C2×D4C23×D7912yes—
1068C2×D4C23×D7911yescharacteristic
1069C22×C4—42no—
1070C22×C4—794no—
1071C22×C4—794no—
1072C22×C4—798no—
1073C22×C4—792no—
1074C22×C4—792no—
1075C22×C4—792no—
1076C22×C4—792no—
1077C22×C4—792no—
1078C22×C4—792no—
1079C22×C4—794no—
1080C22×C4—794no—
1081C22×C4—794no—
1082C22×C4—792no—
1083C22×C4—1588no—
1084C22×C4C23×D7912yes—
1085C22×C4C23×D7911yescharacteristic
1086C22×C4C23×D7914yes—
1087C22×C4C23×D7912yes—
1088C22×C4C23×D7912yes—
1089C22×C4C23×D7911yescharacteristic
1090C22×C4C23×D7914yes—
1091C22×C4C23×D7914yes—
1092C4⋊C4—798no—
1093C4⋊C4—798no—
1094C4⋊C4—798no—
1095C4⋊C4—798no—
1096C4⋊C4—798no—
1097C4⋊C4—798no—
1098C4⋊C4—798no—
1099C4⋊C4—798no—
1100C4⋊C4—798no—
1101C4⋊C4—798no—
1102C4⋊C4—798no—
1103C4⋊C4—798no—
1104C4⋊C4—794no—
1105C4⋊C4—794no—
1106C4⋊C4—794no—
1107C4⋊C4—794no—
1108C4⋊C4—794no—
1109C4⋊C4—798no—
1110C4⋊C4—798no—
1111C4⋊C4—798no—
1112C4⋊C4—798no—
1113C4⋊C4—798no—
1114C4⋊C4—798no—
1115C4⋊C4—794no—
1116C4⋊C4—798no—
1117C4⋊C4—798no—
1118C4⋊C4—798no—
1119C4⋊C4—794no—
1120C4⋊C4—794no—
1121C4⋊C4—792no—
1122C4⋊C4—794no—
1123C4⋊C4—798no—
1124C4⋊C4—798no—
1125C4⋊C4—798no—
1126C4⋊C4C23×D7918yes—
1127C4⋊C4C23×D7914yes—
1128C4⋊C4C23×D7918yes—
1129C4⋊C4C23×D7918yes—
1130C4⋊C4C23×D7914yes—
1131C4⋊C4C23×D7914yes—
1132C4⋊C4C23×D7918yes—
1133C4⋊C4C23×D7912yes—
1134C4⋊C4C23×D7918yes—
1135C4⋊C4C23×D7918yes—
1136C22⋊C4—798no—
1137C22⋊C4—798no—
1138C22⋊C4—794no—
1139C22⋊C4—794no—
1140C22⋊C4—794no—
1141C22⋊C4—792no—
1142C22⋊C4—794no—
1143C22⋊C4—798no—
1144C22⋊C4—794no—
1145C22⋊C4—798no—
1146C22⋊C4—794no—
1147C22⋊C4—794no—
1148C22⋊C4—798no—
1149C22⋊C4—798no—
1150C22⋊C4C23×D7918yes—
1151C22⋊C4C23×D7918yes—
1152C22⋊C4C23×D7914yes—
1153C22⋊C4C23×D7914yes—
1154C22⋊C4C23×D7914yes—
1155C22⋊C4C23×D7918yes—
1156C22⋊C4C23×D7912yes—
1157C42—791no—
1158C42—791no—
1159C42—792no—
1160C42—792no—
1161C42—792no—
1162C42—792no—
1163C42—792no—
1164C42—791no—
1165C42—792no—
1166C42—791no—
1167C42—798no—
1168C42—798no—
1169C42—794no—
1170C42—794no—
1171C42—792no—
1172C42—798no—
1173C42—798no—
1174C42—798no—
1175C42—798no—
1176C42—798no—
1177C42—794no—
1178C42—798no—
1179C42C23×D7912yes—
1180C42C23×D7918yes—
1181C42C23×D7914yes—
1182C23—24no—
1183C23—41no—
1184C23—792no—
1185C23C24×D7911yescharacteristic
1186C23C24×D7912yes—
1187C23C24×D7912yes—
1188Q8—28no—
1189Q8—44no—
1190Q8—44no—
1191Q8—41no—
1192Q8—3164no—
1193Q8—3164no—
1194Q8—3168no—
1195Q8—3161no—
1196Q8—15816no—
1197Q8—15816no—
1198Q8—1588no—
1199Q8—1588no—
1200D4—28no—
1201D4—41no—
1202D4—42no—
1203D4—3161no—
1204D4—3162no—
1205D4—1588no—
1206D4—1588no—
1207C2×C4—28no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—3168no—
1216C2×C4—3164no—
1217C2×C4—3164no—
1218C2×C4—798no—
1219C2×C4—792no—
1220C2×C4—792no—
1221C2×C4—792no—
1222C2×C4—798no—
1223C2×C4—794no—
1224C2×C4—792no—
1225C2×C4—792no—
1226C2×C4—798no—
1227C2×C4—1588no—
1228C2×C4—1584no—
1229C2×C4—1584no—
1230C2×C4—1584no—
1231C2×C4—1584no—
1232C2×C4—1588no—
1233C2×C4—1584no—
1234C2×C4—1588no—
1235C2×C4—1584no—
1236C2×C4C24×D7918yes—
1237C2×C4C24×D7912yes—
1238C2×C4C24×D7912yes—
1239C2×C4C24×D7911yescharacteristic
1240C2×C4C24×D7914yes—
1241C2×C4C24×D7918yes—
1242C2×C4C24×D7911yescharacteristic
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—24no—
1247C22—22no—
1248C22—21no—
1249C22—44no—
1250C22—1584no—
1251C22—1582no—
1252C222−1+4×D7914yes—
1253C22C25×D7911yescharacteristic
1254C4—28no—
1255C4—24no—
1256C4—21no—
1257C4—22no—
1258C4—22no—
1259C4—28no—
1260C4—794no—
1261C4—794no—
1262C4—1582no—
1263C4—1582no—
1264C4—1584no—
1265C4—1588no—
1266C4—1588no—
1267C4—1582no—
1268C4#1909939812yes—
1269C2—24no—
1270C2—41no—
1271C2—42no—
1272C2—3162no—
1273C2C2×2−1+4×D7912yes—
1274C2C2×#1909939811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3538C2
prime radical#23776692C2
hypercenter#3538D79
hypocenterC79#62837
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3538

Complements

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

NH ≅ G/Ntype
1. #23778008C2semidirect
2. #23777999C2semidirect
3. #23777893C2semidirect
4. #23777879C2semidirect
5. #23777809C2semidirect
6. #23777649C2semidirect
7. #23777645C2semidirect
8. #23777489C2semidirect
9. #23777487C2semidirect
10. #23777285C2semidirect
11. #23777282C2semidirect
12. #23777278C2semidirect
13. #23777260C2semidirect
14. #23777211C2semidirect
15. #23777208C2semidirect
16. #23777139C2semidirect
18. C2×#19099115C2semidirect
19. C79×#3538C2semidirect
20. C79⋊#564C22semidirect
22. #19099316C22semidirect
24. #19099312C22semidirect
25. #19099297C22semidirect
26. #19099293C22semidirect
27. #19099293C22semidirect
28. #19099291C22semidirect
29. #19099290C22semidirect
30. #19099290C22semidirect
31. #19099290C22semidirect
32. #19099290C22semidirect
33. #19099290C22semidirect
34. #19099289C22semidirect
35. #19099288C22semidirect
36. #19099288C22semidirect
37. #19099288C22semidirect
38. #19099284C22semidirect
39. #19099284C22semidirect
41. #19099281C22semidirect
43. #19099280C22semidirect
44. #19099280C22semidirect
47. #19099267C22semidirect
55. #19099250C22semidirect
60. #19099245C22semidirect
65. Q8×C22⋊D79C22semidirect
67. #19099226C22semidirect
72. #19099192C22semidirect
73. #19099190C22semidirect
76. #19099176C22semidirect
78. #19099174C22semidirect
79. #19099174C22semidirect
81. #19099173C22semidirect
82. #19099173C22semidirect
83. #19099172C22semidirect
84. #19099172C22semidirect
87. #19099170C22semidirect
88. #19099170C22semidirect
95. #19099119C22semidirect
96. #19099117C22semidirect
99. #19099116C22semidirect
110. #19099115C22semidirect
115. C2×#14579159C22semidirect
116. C4⋊Q8×D79C22semidirect
129. #19099041C22semidirect
131. #19099040C22semidirect
132. #19099039C22semidirect
645. #3538D79semidirect
657. C79#62837semidirect

Maximal subgroups

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

subgroupindex
#237780082
#237779992
#237778932
#237778792
#237778092
#237776492
#237776452
#237774892
#237774872
#237772852
#237772822
#237772782
#237772602
#237772112
#237772082
#237771392
#237766922
C2×#190991152
C79×#35382
#6283779