Finite Group Databasebeta

← #3550×D79 #35196073

Subgroups — #3550×D79 #35196073

Order 20224.

7074 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777814C211yesmaximal, characteristic, complemented
2#23777813C214yesmaximal, complemented
3#23777812C212yesmaximal, complemented
4#23777811C212yesmaximal, complemented
5#23777810C214yesmaximal, complemented
6#23777809C214yesmaximal, complemented
7#23777808C218yesmaximal, complemented
8#23777807C214yesmaximal, complemented
9#23777806C212yesmaximal, complemented
10#563×D79C214yesmaximal, complemented
11#559×D79C212yesmaximal, complemented
12Q82×D79C212yesmaximal, complemented
13#556×D79C214yesmaximal, complemented
14D4×Q8×D79C214yesmaximal, complemented
15#542×D79C218yesmaximal, complemented
16#536×D79C214yesmaximal, complemented
17#533×D79C212yesmaximal, complemented
18#532×D79C211yesmaximal, characteristic
19C79×#3550C211yesmaximal, characteristic, complemented
20C2×#41×D79C2212yes—
21C22×Q8×D79C2214yes—
22#19099317C2218yescomplemented
23#19099316C2218yescomplemented
24#19099315C22116yescomplemented
25#19099314C22116yescomplemented
26#19099313C2214yescomplemented
27#19099312C2218yescomplemented
28#19099299C2212yescomplemented
29#19099298C2214yescomplemented
30#19099297C2218yescomplemented
31#19099296C2218yescomplemented
32#19099295C2218yescomplemented
33Q8×Dic158C2218yescomplemented
34Q8×Dic158C2214yescomplemented
35#19099293C2212yescomplemented
36#19099293C2218yescomplemented
37#19099293C2218yescomplemented
38#19099287C2214yescomplemented
39#19099286C2214yescomplemented
40#19099285C2218yescomplemented
41#19099284C2218yescomplemented
42#19099283C2214yescomplemented
43#19099282C2218yescomplemented
44#19099281C2218yescomplemented
45#19099280C22116yescomplemented
46Q8×D316C2214yescomplemented
47D4×Dic158C2218yescomplemented
48D4×Dic158C2214yescomplemented
49#19099228C2218yescomplemented
50#19099228C2214yescomplemented
51Q8×C22⋊D79C2218yescomplemented
52#19099226C22116yescomplemented
53#19099226C2218yescomplemented
54#19099187C2218yescomplemented
55#19099186C2218yescomplemented
56#19099185C2218yescomplemented
57#19099184C2218yescomplemented
58#19099183C22116yescomplemented
59#19099182C2218yescomplemented
60#19099181C22116yescomplemented
61#19099180C2218yescomplemented
62#19099179C22116yescomplemented
63#19099178C2218yescomplemented
64#19099177C22116yescomplemented
65#19099139C2214yescomplemented
66#19099138C2218yescomplemented
67#19099137C2214yescomplemented
68#19099136C2218yescomplemented
69#19099136C2218yescomplemented
70#19099135C2218yescomplemented
71#19099135C2218yescomplemented
72#19099134C2214yescomplemented
73#19099133C2218yescomplemented
74#19099120C2212yescomplemented
75#19099119C2214yescomplemented
76#19099118C2212yescomplemented
77#19099118C2212yescomplemented
78#19099117C2214yescomplemented
79#19099117C2214yescomplemented
80#19099116C2214yescomplemented
81#19099115C2214yescomplemented
82#19099115C2214yescomplemented
83#19099114C2211yescharacteristic
84#19099113C2211yescharacteristic
85#19099112C2212yes—
86#19099111C2211yescharacteristic
87#19099110C2214yes—
88#19099109C2212yes—
89#19099108C2214yes—
90C4⋊Q8×D79C2218yes—
91C4⋊Q8×D79C2212yes—
92C4⋊Q8×D79C2211yescharacteristic
93C4⋊Q8×D79C2212yes—
94C4⋊Q8×D79C2218yes—
95#127×D79C2211yescharacteristic
96#126×D79C22116yes—
97#125×D79C2214yes—
98#124×D79C2218yes—
99#124×D79C2218yes—
100#124×D79C2212yes—
101#123×D79C2218yes—
102#123×D79C2218yes—
103C22⋊Q8×D79C2214yes—
104C22⋊Q8×D79C22116yes—
105C22⋊Q8×D79C2218yes—
106C22⋊Q8×D79C2214yes—
107#121×D79C2214yes—
108C4×Q8×D79C2218yes—
109C4×Q8×D79C2214yes—
110C4×Q8×D79C2214yes—
111C4×D4×D79C2218yes—
112C4×D4×D79C2214yes—
113#117×D79C2214yes—
114#117×D79C2214yes—
115C2×C42×D79C2211yescharacteristic
116#563×C79C2214yescomplemented
117#559×C79C2212yescomplemented
118Q82×C79C2212yescomplemented
119#556×C79C2214yescomplemented
120D4×Q8×C79C2214yescomplemented
121#542×C79C2218yescomplemented
122#536×C79C2214yescomplemented
123#533×C79C2212yescomplemented
124#532×C79C2211yescharacteristic
125C2×#11929625C2312yes—
126C2×#11929624C2312yes—
127C2×#11929624C2314yes—
128C2×#11929623C2314yes—
129C2×#11929623C2312yes—
130#41×D79—48no—
131C22×Dic158C2314yes—
132C22×Dic158C2318yes—
133C2×Q8×D79—416no—
134C2×Q8×D79C2314yes—
135C2×Q8×D79C2314yes—
136C2×Q8×D79C2318yes—
137C2×Q8×D79C2318yes—
138C2×Q8×D79C2318yes—
139C2×Q8×D79C2312yes—
140C2×D4×D79C2314yes—
141C2×D4×D79C2314yes—
142C2×D4×D79C2312yes—
143C22×C4×D79C2312yes—
144C22×C4×D79C2311yescharacteristic
145C22×C4×D79C2314yes—
146C22×C4×D79C2318yes—
147#14579161C2318yes—
148#14579161C2318yes—
149#14579161C2312yes—
150#14579161C2312yes—
151#14579161C2311yescharacteristic
152#14579160C23116yes—
153#14579160C23116yes—
154#14579160C2318yes—
155#14579160C23116yes—
156#14579160C2318yes—
157#14579160C2314yes—
158#14579160C2314yes—
159#14579160C2314yes—
160#14579160C2314yes—
161#14579160C2314yes—
162#14579159C2318yes—
163#14579159C2318yes—
164#14579159C23116yes—
165#14579159C2314yes—
166#14579159C2314yes—
167#14579159C2312yes—
168#14579158C2311yescharacteristic
169#14579157C2314yes—
170#14579157C2312yes—
171#14579156C23116yes—
172#14579156C23116yes—
173#14579156C23116yes—
174#14579155C23116yes—
175#14579154C23116yes—
176#14579154C23116yes—
177#14579154C23116yes—
178#14579153C2314yes—
179#14579152C2314yes—
180#14579152C2314yes—
181#14579151C2318yes—
182#14579151C2318yes—
183#14579150C2318yes—
184#14579150C2318yes—
185#14579150C2312yes—
186#14579149C2318yes—
187#14579149C2318yes—
188#14579149C2312yes—
189#14579148C2318yes—
190#14579148C2318yes—
191#14579148C2312yes—
192#14579147C23116yes—
193#14579147C23116yes—
194#14579147C23116yes—
195#14579147C23116yes—
196#14579147C2318yes—
197#14579146C23116yes—
198#14579146C23116yes—
199#14579145C2318yes—
200#14579145C2318yes—
201#14579144C2318yes—
202#14579144C2318yes—
203#14579143C23116yes—
204#14579143C23116yes—
205#14579142C2318yes—
206#14579142C2318yes—
207#14579141C2314yes—
208#14579141C2318yes—
209#14579141C2314yes—
210#14579141C23116yes—
211#14579140C2314yes—
212#14579140C2318yes—
213#14579140C23116yes—
214#14579140C2314yes—
215#14579139C2318yes—
216#14579139C23116yes—
217#14579139C2318yes—
218#14579139C23116yes—
219#14579139C23116yes—
220#14579138C2318yes—
221#14579138C23116yes—
222#14579138C23116yes—
223#14579138C23116yes—
224#14579138C2318yes—
225#14579137C2314yes—
226#14579137C2318yes—
227#14579137C23116yes—
228#14579137C2314yes—
229#14579136C2314yes—
230#14579135C2314yes—
231#14579134C2318yes—
232#14579133C2318yes—
233#14579132C2314yes—
234Q8×Dic79C2318yes—
235Q8×Dic79C2314yes—
236Q8×Dic79C2314yes—
237C4×Dic158C23116yes—
238C4×Dic158C2318yes—
239C4×Dic158C2318yes—
240C4×Dic158C2314yes—
241C4×Dic158C2318yes—
242C4×Dic158C2314yes—
243#14579126C2318yes—
244#14579126C23116yes—
245#14579126C2318yes—
246#14579126C2314yes—
247#14579126C2314yes—
248#14579126C2318yes—
249C4×D316C2318yes—
250C4×D316C2314yes—
251D4×Dic79C2318yes—
252D4×Dic79C2314yes—
253#14579123C2318yes—
254#14579123C2314yes—
255C4×C22⋊D79C23116yes—
256C4×C22⋊D79C2318yes—
257(C22⋊D79)⋊C4C23116yes—
258(C22⋊D79)⋊C4C2318yes—
259#14579120C2314yes—
260#14579120C2314yes—
261#14579119C2318yes—
262#14579119C2314yes—
263#14579119C2314yes—
264#14579118C2318yes—
265#14579118C2318yes—
266#14579117C2318yes—
267#14579117C2318yes—
268C4⋊C4×D79C2314yes—
269C4⋊C4×D79C2314yes—
270C4⋊C4×D79C2314yes—
271C4⋊C4×D79C2314yes—
272C4⋊C4×D79C2314yes—
273C4⋊C4×D79C2318yes—
274C4⋊C4×D79C23116yes—
275C4⋊C4×D79C2318yes—
276C22⋊C4×D79C2318yes—
277C22⋊C4×D79C2318yes—
278C22⋊C4×D79C2318yes—
279C22⋊C4×D79C23116yes—
280C2×C4×Dic79C2312yes—
281C2×C4×Dic79C2311yescharacteristic
282C42×D79C2312yes—
283C42×D79C2311yescharacteristic
284C42×D79C2311yescharacteristic
285C42×D79C2312yes—
286C42×D79C2311yescharacteristic
287C42×D79C2311yescharacteristic
288C42×D79C2318yes—
289C42×D79C2318yes—
290C2×#41×C79C2312yes—
291C22×Q8×C79C2314yes—
292C4⋊Q8×C79C2318yes—
293C4⋊Q8×C79C2318yes—
294C4⋊Q8×C79C2312yes—
295C4⋊Q8×C79C2311yescharacteristic
296C4⋊Q8×C79C2312yes—
297#127×C79C2311yescharacteristic
298#126×C79C23116yes—
299#125×C79C2314yes—
300#124×C79C2318yes—
301#124×C79C2318yes—
302#124×C79C2312yes—
303#123×C79C2318yes—
304#123×C79C2318yes—
305C22⋊Q8×C79C2314yes—
306C22⋊Q8×C79C2318yes—
307C22⋊Q8×C79C23116yes—
308C22⋊Q8×C79C2314yes—
309#121×C79C2314yes—
310C4×Q8×C79C2318yes—
311C4×Q8×C79C2314yes—
312C4×Q8×C79C2314yes—
313C4×D4×C79C2318yes—
314C4×D4×C79C2314yes—
315#117×C79C2314yes—
316#117×C79C2314yes—
317C2×C42×C79C2311yescharacteristic
318C23×D79C2414yes—
319C23×D79C2411yescharacteristic
320#11929625—44no—
321#11929624—48no—
322#11929624—44no—
323#11929623—48no—
324#11929623—44no—
325C2×Dic158—48no—
326C2×Dic158—416no—
327C2×Dic158C2418yes—
328C2×Dic158C2414yes—
329C2×Dic158C2418yes—
330C2×Dic158C2414yes—
331C2×Dic158C2418yes—
332C2×Dic158C24116yes—
333C2×Dic158C2414yes—
334C2×Dic158C2412yes—
335Q8×D79—216no—
336Q8×D79—216no—
337Q8×D79—416no—
338Q8×D79—416no—
339Q8×D79—416no—
340Q8×D79—44no—
341C2×D316C2414yes—
342C2×D316C2414yes—
343C2×D316C2412yes—
344C2×C22⋊D79C2418yes—
345C2×C22⋊D79C2414yes—
346C2×C22⋊D79C2414yes—
347C2×C22⋊D79C2414yes—
348D4×D79—216no—
349D4×D79—44no—
350D4×D79—48no—
351C22×Dic79C2414yes—
352C22×Dic79C2411yescharacteristic
353C22×Dic79C2412yes—
354C22×Dic79C2418yes—
355C2×C4×D79—216no—
356C2×C4×D79—24no—
357C2×C4×D79—28no—
358C2×C4×D79—416no—
359C2×C4×D79C2414yes—
360C2×C4×D79C2418yes—
361C2×C4×D79C2414yes—
362C2×C4×D79C2414yes—
363C2×C4×D79C2411yescharacteristic
364C2×C4×D79C2418yes—
365C2×C4×D79C2411yescharacteristic
366C2×C4×D79C2411yescharacteristic
367C2×C4×D79C2412yes—
368C2×C4×D79C2412yes—
369C2×C4×D79C2412yes—
370C2×C4×D79C24116yes—
371C2×C4×D79C2411yescharacteristic
372C2×C4×D79C2412yes—
373C4⋊Dic79C2414yes—
374C4⋊Dic79C2414yes—
375C4⋊Dic79C2414yes—
376C4⋊Dic79C2414yes—
377C4⋊Dic79C2414yes—
378C4⋊Dic79C2418yes—
379C4⋊Dic79C24116yes—
380C4⋊Dic79C2418yes—
381Dic79⋊C4C2418yes—
382Dic79⋊C4C2418yes—
383Dic79⋊C4C2418yes—
384Dic79⋊C4C2418yes—
385Dic79⋊C4C2418yes—
386Dic79⋊C4C2418yes—
387Dic79⋊C4C24116yes—
388Dic79⋊C4C24116yes—
389Dic79⋊C4C2418yes—
390Dic79⋊C4C2418yes—
391Dic79⋊C4C2418yes—
392C22⋊Dic79C2418yes—
393C22⋊Dic79C2418yes—
394C22⋊Dic79C2418yes—
395C22⋊Dic79C24116yes—
396(C2×D79)⋊C4C2418yes—
397(C2×D79)⋊C4C2418yes—
398(C2×D79)⋊C4C24116yes—
399(C2×D79)⋊C4C2418yes—
400(C2×D79)⋊C4C24116yes—
401(C2×D79)⋊C4C2418yes—
402(C2×D79)⋊C4C24116yes—
403C4×Dic79C2412yes—
404C4×Dic79C2412yes—
405C4×Dic79C2412yes—
406C4×Dic79C2411yescharacteristic
407C4×Dic79C2412yes—
408C4×Dic79C2412yes—
409C4×Dic79C2411yescharacteristic
410C4×Dic79C2418yes—
411C4×Dic79C2418yes—
412C4×Dic79C24116yes—
413C4×Dic79C2418yes—
414C4×Dic79C2418yes—
415#41×C79—44no—
416C2×Q8×C79—48no—
417C2×Q8×C79C2414yes—
418C2×Q8×C79C2414yes—
419C2×Q8×C79C2418yes—
420C2×Q8×C79C2412yes—
421C2×D4×C79C2414yes—
422C2×D4×C79C2414yes—
423C2×D4×C79C2412yes—
424C22×C4×C79C2414yes—
425C22×C4×C79C2411yescharacteristic
426C22×C4×C79C2412yes—
427C22×C4×C79C2418yes—
428C4⋊C4×C79C2414yes—
429C4⋊C4×C79C2414yes—
430C4⋊C4×C79C2414yes—
431C4⋊C4×C79C2414yes—
432C4⋊C4×C79C2414yes—
433C4⋊C4×C79C2418yes—
434C4⋊C4×C79C24116yes—
435C4⋊C4×C79C2418yes—
436C22⋊C4×C79C2418yes—
437C22⋊C4×C79C2418yes—
438C22⋊C4×C79C2418yes—
439C22⋊C4×C79C24116yes—
440C42×C79C2412yes—
441C42×C79C2411yescharacteristic
442C42×C79C2411yescharacteristic
443C42×C79C2418yes—
444C42×C79C2418yes—
445C23×C79C2511yescharacteristic
446C23×C79C2514yes—
447C22×D79—28no—
448C22×D79—22no—
449C22×D79—24no—
450C22×D79—216no—
451C22×D79C2511yescharacteristic
452C22×D79C2514yes—
453C22×D79C2511yescharacteristic
454Q8×C79—28no—
455Q8×C79—28no—
456Q8×C79—48no—
457Q8×C79—42no—
458D4×C79—28no—
459D4×C79—42no—
460D4×C79—44no—
461C2×C4×C79—28no—
462C2×C4×C79—22no—
463C2×C4×C79—24no—
464C2×C4×C79—48no—
465C2×C4×C79C2518yes—
466C2×C4×C79C2512yes—
467C2×C4×C79C2514yes—
468C2×C4×C79C2511yescharacteristic
469C2×C4×C79C2518yes—
470C2×C4×C79C2511yescharacteristic
471C2×C4×C79C2512yes—
472C22⋊D79—216no—
473C22⋊D79—44no—
474C22⋊D79—44no—
475C22⋊D79—44no—
476C2×Dic79—28no—
477C2×Dic79—22no—
478C2×Dic79—24no—
479C2×Dic79—48no—
480C2×Dic79C2518yes—
481C2×Dic79C2512yes—
482C2×Dic79C2514yes—
483C2×Dic79C2511yescharacteristic
484C2×Dic79C2518yes—
485C2×Dic79C2511yescharacteristic
486C2×Dic79C2512yes—
487D316—28no—
488D316—42no—
489D316—44no—
490C4×D79—22no—
491C4×D79—28no—
492C4×D79—216no—
493C4×D79—24no—
494C4×D79—216no—
495C4×D79—28no—
496C4×D79—22no—
497C4×D79—24no—
498C4×D79—28no—
499C4×D79—22no—
500C4×D79—24no—
501C4×D79—416no—
502C4×D79H(5,𝔽2)14yes—
503C4×D792−1+418yes—
504Dic158—28no—
505Dic158—28no—
506Dic158—216no—
507Dic158—216no—
508Dic158—416no—
509Dic158—48no—
510Dic158—44no—
511Dic158—42no—
512C22×C79—21no—
513C22×C79—24no—
514C22×C79—28no—
515C22×C79—22no—
516C22×C79C2611yescharacteristic
517C2×D79—21no—
518C2×D79—24no—
519C2×D79—28no—
520C2×D79—22no—
521C2×D79—416no—
522C2×D79—44no—
523C2×D79C2×H(5,𝔽2)12yes—
524C2×D79C2×2−1+414yes—
525C4×C79—21no—
526C4×C79—24no—
527C4×C79—28no—
528C4×C79—22no—
529C4×C79—28no—
530C4×C79C2×H(5,𝔽2)12yes—
531C4×C79C2×2−1+414yes—
532Dic79—21no—
533Dic79—24no—
534Dic79—28no—
535Dic79—28no—
536Dic79—22no—
537Dic79C2×H(5,𝔽2)12yes—
538Dic79C2×2−1+414yes—
539C2×#3550—791nomaximal, Sylow
540C2×C79—41no—
541C2×C79—44no—
542C2×C79C22×H(5,𝔽2)11yescharacteristic
543C2×C79C22×2−1+412yes—
544D79—41no—
545D79—44no—
546D79#355014yesdirect product factor
547#3550—794no—
548#3550—792no—
549#3550—792no—
550#3550—794no—
551#3550—794no—
552#3550—798no—
553#3550—794no—
554#3550—792no—
555#3550—791no—
556#3550D7911yescharacteristic, direct product factor
557C2×#563—794no—
558C2×#559—792no—
559C2×Q82—792no—
560C2×#556—794no—
561C2×D4×Q8—794no—
562C2×#542—798no—
563C2×#536—794no—
564C2×#533—792no—
565C2×#532—791no—
566C79C2×#355011yescharacteristic, complemented, Sylow
567C22×#41—792no—
568C23×Q8—794no—
569#563—798no—
570#563—7916no—
571#563—798no—
572#563—794no—
573#563—798no—
574#563—7916no—
575#563C2×D7914yescomplemented
576#559—792no—
577#559—798no—
578#559—798no—
579#559—794no—
580#559—798no—
581#559C2×D7912yescomplemented
582Q82—798no—
583Q82—798no—
584Q82—792no—
585Q82—798no—
586Q82—794no—
587Q82C2×D7912yescomplemented
588#556—794no—
589#556—7916no—
590#556—798no—
591#556—798no—
592#556—798no—
593#556—794no—
594#556—794no—
595#556—798no—
596#556C2×D7914yescomplemented
597D4×Q8—798no—
598D4×Q8—798no—
599D4×Q8—794no—
600D4×Q8—798no—
601D4×Q8—7916no—
602D4×Q8—794no—
603D4×Q8—798no—
604D4×Q8—794no—
605D4×Q8C2×D7914yescomplemented
606#542—798no—
607#542—7916no—
608#542—7916no—
609#542—798no—
610#542—7916no—
611#542—7916no—
612#542—798no—
613#542—798no—
614#542—798no—
615#542—798no—
616#542—798no—
617#542C2×D7918yescomplemented
618#536—794no—
619#536—794no—
620#536—798no—
621#536—798no—
622#536—798no—
623#536—798no—
624#536—798no—
625#536—798no—
626#536—794no—
627#536C2×D7914yescomplemented
628#533—792no—
629#533—792no—
630#533—794no—
631#533—794no—
632#533—794no—
633#533—794no—
634#533—794no—
635#533—794no—
636#533—792no—
637#533C2×D7912yescomplemented
638#532—792no—
639#532—791no—
640#532—791no—
641#532—792no—
642#532—794no—
643#532—794no—
644#532—791no—
645#532C2×D7911yescharacteristic
646C2×C4⋊Q8—791no—
647C2×C4⋊Q8—792no—
648C2×C4⋊Q8—792no—
649C2×C4⋊Q8—798no—
650C2×C4⋊Q8—798no—
651C2×#127—791no—
652C2×#126—7916no—
653C2×#125—794no—
654C2×#124—792no—
655C2×#124—798no—
656C2×#124—798no—
657C2×#123—798no—
658C2×#123—798no—
659C2×C22⋊Q8—794no—
660C2×C22⋊Q8—794no—
661C2×C22⋊Q8—798no—
662C2×C22⋊Q8—7916no—
663C2×#121—794no—
664C2×C4×Q8—794no—
665C2×C4×Q8—794no—
666C2×C4×Q8—798no—
667C2×C4×D4—794no—
668C2×C4×D4—798no—
669C2×#117—794no—
670C2×#117—794no—
671C22×C42—791no—
672C2×#41—3168no—
673C2×#41—792no—
674C2×#41—794no—
675C2×#41—792no—
676C2×#41—794no—
677C2×#41—792no—
678C2×#41C22×D7912yes—
679C22×Q8—31616no—
680C22×Q8—798no—
681C22×Q8—792no—
682C22×Q8—798no—
683C22×Q8—798no—
684C22×Q8—794no—
685C22×Q8—794no—
686C22×Q8—794no—
687C22×Q8—798no—
688C22×Q8C22×D7914yes—
689C22×D4—794no—
690C22×D4—792no—
691C22×D4—794no—
692C23×C4—798no—
693C23×C4—792no—
694C23×C4—794no—
695C23×C4—791no—
696C4⋊Q8—792no—
697C4⋊Q8—794no—
698C4⋊Q8—794no—
699C4⋊Q8—798no—
700C4⋊Q8—798no—
701C4⋊Q8—7916no—
702C4⋊Q8—794no—
703C4⋊Q8—794no—
704C4⋊Q8—794no—
705C4⋊Q8—794no—
706C4⋊Q8—794no—
707C4⋊Q8—7916no—
708C4⋊Q8—7916no—
709C4⋊Q8—7916no—
710C4⋊Q8—798no—
711C4⋊Q8—798no—
712C4⋊Q8—791no—
713C4⋊Q8—792no—
714C4⋊Q8—792no—
715C4⋊Q8—798no—
716C4⋊Q8—798no—
717C4⋊Q8C22×D7911yescharacteristic
718C4⋊Q8C22×D7912yes—
719C4⋊Q8C22×D7912yes—
720C4⋊Q8C22×D7918yes—
721C4⋊Q8C22×D7918yes—
722#127—794no—
723#127—792no—
724#127—791no—
725#127C22×D7911yescharacteristic
726#126—7916no—
727#126—7916no—
728#126—7916no—
729#126—7916no—
730#126—7916no—
731#126—7916no—
732#126—7916no—
733#126C22×D79116yes—
734#125—798no—
735#125—798no—
736#125—794no—
737#125—794no—
738#125—794no—
739#125C22×D7914yes—
740#124—792no—
741#124—798no—
742#124—798no—
743#124—792no—
744#124—798no—
745#124—798no—
746#124—798no—
747#124—7916no—
748#124—7916no—
749#124—7916no—
750#124—7916no—
751#124—792no—
752#124—798no—
753#124—798no—
754#124C22×D7912yes—
755#124C22×D7918yes—
756#124C22×D7918yes—
757#123—798no—
758#123—798no—
759#123—798no—
760#123—798no—
761#123—7916no—
762#123—7916no—
763#123—7916no—
764#123—798no—
765#123—7916no—
766#123—798no—
767#123C22×D7918yes—
768#123C22×D7918yes—
769C22⋊Q8—794no—
770C22⋊Q8—794no—
771C22⋊Q8—798no—
772C22⋊Q8—7916no—
773C22⋊Q8—794no—
774C22⋊Q8—794no—
775C22⋊Q8—798no—
776C22⋊Q8—7916no—
777C22⋊Q8—798no—
778C22⋊Q8—794no—
779C22⋊Q8—798no—
780C22⋊Q8—794no—
781C22⋊Q8—7916no—
782C22⋊Q8—798no—
783C22⋊Q8—7916no—
784C22⋊Q8—7916no—
785C22⋊Q8—7916no—
786C22⋊Q8—798no—
787C22⋊Q8—798no—
788C22⋊Q8—7916no—
789C22⋊Q8—7916no—
790C22⋊Q8—7916no—
791C22⋊Q8C22×D7914yes—
792C22⋊Q8C22×D7914yes—
793C22⋊Q8C22×D7918yes—
794C22⋊Q8C22×D79116yes—
795#121—794no—
796#121—798no—
797#121—794no—
798#121—794no—
799#121—798no—
800#121C22×D7914yes—
801C4×Q8—794no—
802C4×Q8—794no—
803C4×Q8—798no—
804C4×Q8—798no—
805C4×Q8—794no—
806C4×Q8—798no—
807C4×Q8—794no—
808C4×Q8—7916no—
809C4×Q8—798no—
810C4×Q8—798no—
811C4×Q8—794no—
812C4×Q8—798no—
813C4×Q8—794no—
814C4×Q8—7916no—
815C4×Q8—798no—
816C4×Q8C22×D7914yes—
817C4×Q8C22×D7914yes—
818C4×Q8C22×D7918yes—
819C4×D4—794no—
820C4×D4—798no—
821C4×D4—798no—
822C4×D4—7916no—
823C4×D4—794no—
824C4×D4—798no—
825C4×D4—798no—
826C4×D4—7916no—
827C4×D4—794no—
828C4×D4—798no—
829C4×D4C22×D7914yes—
830C4×D4C22×D7918yes—
831#117—794no—
832#117—794no—
833#117—794no—
834#117—794no—
835#117—798no—
836#117—798no—
837#117—798no—
838#117—798no—
839#117—798no—
840#117C22×D7914yes—
841#117C22×D7914yes—
842C2×C4⋊C4—794no—
843C2×C4⋊C4—794no—
844C2×C4⋊C4—794no—
845C2×C4⋊C4—794no—
846C2×C4⋊C4—794no—
847C2×C4⋊C4—798no—
848C2×C4⋊C4—7916no—
849C2×C4⋊C4—798no—
850C2×C22⋊C4—798no—
851C2×C22⋊C4—798no—
852C2×C22⋊C4—798no—
853C2×C22⋊C4—7916no—
854C2×C42—791no—
855C2×C42—792no—
856C2×C42—798no—
857C2×C42—798no—
858C2×C42—792no—
859C2×C42—791no—
860C2×C42—791no—
861C2×C42—791no—
862C2×C42—791no—
863C2×C42—792no—
864C2×C42C22×D7911yescharacteristic
865C24—794no—
866C24—791no—
867#41—44no—
868#41—3168no—
869#41—3164no—
870#41—3168no—
871#41—3164no—
872#41—3164no—
873C2×Q8—48no—
874C2×Q8—3168no—
875C2×Q8—31616no—
876C2×Q8—31616no—
877C2×Q8—31616no—
878C2×Q8—31616no—
879C2×Q8—3164no—
880C2×Q8—7916no—
881C2×Q8—798no—
882C2×Q8—792no—
883C2×Q8—794no—
884C2×Q8—798no—
885C2×Q8—794no—
886C2×Q8—798no—
887C2×Q8—794no—
888C2×Q8—15816no—
889C2×Q8—15816no—
890C2×Q8C23×D7914yes—
891C2×Q8C23×D7914yes—
892C2×Q8C23×D7918yes—
893C2×Q8C23×D7912yes—
894C2×D4—3164no—
895C2×D4—3168no—
896C2×D4—794no—
897C2×D4—794no—
898C2×D4—794no—
899C2×D4—798no—
900C2×D4—794no—
901C2×D4—792no—
902C2×D4—794no—
903C2×D4—15816no—
904C2×D4C23×D7914yes—
905C2×D4C23×D7914yes—
906C2×D4C23×D7912yes—
907C22×C4—31616no—
908C22×C4—798no—
909C22×C4—7916no—
910C22×C4—792no—
911C22×C4—791no—
912C22×C4—792no—
913C22×C4—791no—
914C22×C4—794no—
915C22×C4—798no—
916C22×C4—792no—
917C22×C4—794no—
918C22×C4—791no—
919C22×C4—792no—
920C22×C4—792no—
921C22×C4—791no—
922C22×C4—791no—
923C22×C4—798no—
924C22×C4—794no—
925C22×C4—794no—
926C22×C4—1588no—
927C22×C4—15816no—
928C22×C4—1584no—
929C22×C4C23×D7912yes—
930C22×C4C23×D7911yescharacteristic
931C22×C4C23×D7914yes—
932C22×C4C23×D7918yes—
933C4⋊C4—798no—
934C4⋊C4—798no—
935C4⋊C4—798no—
936C4⋊C4—798no—
937C4⋊C4—798no—
938C4⋊C4—798no—
939C4⋊C4—798no—
940C4⋊C4—7916no—
941C4⋊C4—7916no—
942C4⋊C4—798no—
943C4⋊C4—798no—
944C4⋊C4—794no—
945C4⋊C4—794no—
946C4⋊C4—794no—
947C4⋊C4—794no—
948C4⋊C4—794no—
949C4⋊C4—798no—
950C4⋊C4—7916no—
951C4⋊C4—798no—
952C4⋊C4C23×D7914yes—
953C4⋊C4C23×D7914yes—
954C4⋊C4C23×D7914yes—
955C4⋊C4C23×D7914yes—
956C4⋊C4C23×D7914yes—
957C4⋊C4C23×D7918yes—
958C4⋊C4C23×D79116yes—
959C4⋊C4C23×D7918yes—
960C22⋊C4—798no—
961C22⋊C4—798no—
962C22⋊C4—798no—
963C22⋊C4—7916no—
964C22⋊C4—798no—
965C22⋊C4—798no—
966C22⋊C4—7916no—
967C22⋊C4—798no—
968C22⋊C4—798no—
969C22⋊C4—7916no—
970C22⋊C4—7916no—
971C22⋊C4C23×D7918yes—
972C22⋊C4C23×D7918yes—
973C22⋊C4C23×D7918yes—
974C22⋊C4C23×D79116yes—
975C42—792no—
976C42—792no—
977C42—792no—
978C42—791no—
979C42—792no—
980C42—791no—
981C42—792no—
982C42—798no—
983C42—798no—
984C42—798no—
985C42—798no—
986C42—7916no—
987C42C23×D7912yes—
988C42C23×D7911yescharacteristic
989C42C23×D7911yescharacteristic
990C42C23×D7918yes—
991C42C23×D7918yes—
992C23—791no—
993C23—794no—
994C23—791no—
995C23—1588no—
996C23—1582no—
997C23—1584no—
998C23—15816no—
999C23C24×D7914yes—
1000C23C24×D7911yescharacteristic
1001Q8—28no—
1002Q8—28no—
1003Q8—48no—
1004Q8—42no—
1005Q8—3168no—
1006Q8—31616no—
1007Q8—3162no—
1008Q8—3164no—
1009Q8—15816no—
1010Q8—15816no—
1011Q8—1588no—
1012Q8—1588no—
1013D4—28no—
1014D4—42no—
1015D4—44no—
1016D4—3162no—
1017D4—3164no—
1018D4—3164no—
1019D4—3164no—
1020D4—3164no—
1021D4—15816no—
1022D4—1588no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—48no—
1027C2×C4—31616no—
1028C2×C4—3168no—
1029C2×C4—792no—
1030C2×C4—791no—
1031C2×C4—794no—
1032C2×C4—798no—
1033C2×C4—798no—
1034C2×C4—792no—
1035C2×C4—794no—
1036C2×C4—791no—
1037C2×C4—798no—
1038C2×C4—1588no—
1039C2×C4—1582no—
1040C2×C4—1584no—
1041C2×C4—15816no—
1042C2×C4—1582no—
1043C2×C4—1588no—
1044C2×C4—1584no—
1045C2×C4—15816no—
1046C2×C4—1588no—
1047C2×C4—1582no—
1048C2×C4—1584no—
1049C2×C4—1588no—
1050C2×C4—1582no—
1051C2×C4—1584no—
1052C2×C4C24×D7918yes—
1053C2×C4C24×D7912yes—
1054C2×C4C24×D7914yes—
1055C2×C4C24×D7911yescharacteristic
1056C2×C4C24×D7918yes—
1057C2×C4C24×D7911yescharacteristic
1058C2×C4C24×D7912yes—
1059C22—24no—
1060C22—21no—
1061C22—22no—
1062C22—28no—
1063C22—31616no—
1064C22—3164no—
1065C22—792no—
1066C22—794no—
1067C22—1584no—
1068C22—1581no—
1069C22—1582no—
1070C22—1588no—
1071C22C25×D7911yescharacteristic
1072C4—21no—
1073C4—24no—
1074C4—28no—
1075C4—22no—
1076C4—28no—
1077C4—792no—
1078C4—794no—
1079C4—1588no—
1080C4—1581no—
1081C4—1584no—
1082C4—1582no—
1083C4—1588no—
1084C4H(5,𝔽2)×D7912yes—
1085C42−1+4×D7914yes—
1086C2—44no—
1087C2—41no—
1088C2—3164no—
1089C2—3161no—
1090C2—794no—
1091C2C2×H(5,𝔽2)×D7911yescharacteristic
1092C2C2×2−1+4×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3550C2
prime radical#532×D79C2
hypercenter#3550D79
hypocenterC79C2×#3550
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #23777814C2semidirect
2. #23777813C2semidirect
3. #23777812C2semidirect
4. #23777811C2semidirect
5. #23777810C2semidirect
6. #23777809C2semidirect
7. #23777808C2semidirect
8. #23777807C2semidirect
9. #23777806C2semidirect
10. #563×D79C2semidirect
11. #559×D79C2semidirect
12. Q82×D79C2semidirect
13. #556×D79C2semidirect
14. D4×Q8×D79C2semidirect
15. #542×D79C2semidirect
16. #536×D79C2semidirect
17. #533×D79C2semidirect
19. C79×#3550C2semidirect
22. #19099317C22semidirect
23. #19099316C22semidirect
24. #19099315C22semidirect
25. #19099314C22semidirect
26. #19099313C22semidirect
27. #19099312C22semidirect
28. #19099299C22semidirect
29. #19099298C22semidirect
30. #19099297C22semidirect
31. #19099296C22semidirect
32. #19099295C22semidirect
33. Q8×Dic158C22semidirect
34. Q8×Dic158C22semidirect
35. #19099293C22semidirect
36. #19099293C22semidirect
37. #19099293C22semidirect
38. #19099287C22semidirect
39. #19099286C22semidirect
40. #19099285C22semidirect
41. #19099284C22semidirect
42. #19099283C22semidirect
43. #19099282C22semidirect
44. #19099281C22semidirect
45. #19099280C22semidirect
46. Q8×D316C22semidirect
47. D4×Dic158C22semidirect
48. D4×Dic158C22semidirect
49. #19099228C22semidirect
50. #19099228C22semidirect
51. Q8×C22⋊D79C22semidirect
52. #19099226C22semidirect
53. #19099226C22semidirect
54. #19099187C22semidirect
55. #19099186C22semidirect
56. #19099185C22semidirect
57. #19099184C22semidirect
58. #19099183C22semidirect
59. #19099182C22semidirect
60. #19099181C22semidirect
61. #19099180C22semidirect
62. #19099179C22semidirect
63. #19099178C22semidirect
64. #19099177C22semidirect
65. #19099139C22semidirect
66. #19099138C22semidirect
67. #19099137C22semidirect
68. #19099136C22semidirect
69. #19099136C22semidirect
70. #19099135C22semidirect
71. #19099135C22semidirect
72. #19099134C22semidirect
73. #19099133C22semidirect
74. #19099120C22semidirect
75. #19099119C22semidirect
76. #19099118C22semidirect
77. #19099118C22semidirect
78. #19099117C22semidirect
79. #19099117C22semidirect
80. #19099116C22semidirect
81. #19099115C22semidirect
82. #19099115C22semidirect
116. #563×C79C22semidirect
117. #559×C79C22semidirect
118. Q82×C79C22semidirect
119. #556×C79C22semidirect
120. D4×Q8×C79C22semidirect
121. #542×C79C22semidirect
122. #536×C79C22semidirect
123. #533×C79C22semidirect
546. D79#3550direct (N × H)
556. #3550D79direct (N × H)
566. C79C2×#3550semidirect
575. #563C2×D79semidirect
581. #559C2×D79semidirect
587. Q82C2×D79semidirect
596. #556C2×D79semidirect
605. D4×Q8C2×D79semidirect
617. #542C2×D79semidirect
627. #536C2×D79semidirect
637. #533C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237778142
#237778132
#237778122
#237778112
#237778102
#237778092
#237778082
#237778072
#237778062
#563×D792
#559×D792
Q82×D792
#556×D792
D4×Q8×D792
#542×D792
#536×D792
#533×D792
#532×D792
C79×#35502
C2×#355079