Finite Group Databasebeta

← #35196821

Subgroups — #35196821

Order 20224.

6930 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777220C218yesmaximal, complemented
2#23777214C214yesmaximal, complemented
3#23777211C214yesmaximal, complemented
4#23777208C212yesmaximal, complemented
5#23777205C212yesmaximal, complemented
6#23777203C211yesmaximal, characteristic, complemented
7#23777200C214yesmaximal, complemented
8#23777198C212yesmaximal, complemented
9#23777196C214yesmaximal, complemented
10#23776979C214yesmaximal, complemented
11#23776979C218yesmaximal, complemented
12Q8×#11929623C214yesmaximal, complemented
13#23776804C212yesmaximal, complemented
14#23776802C214yesmaximal, complemented
15C2×#19099115C214yesmaximal, complemented
16#533×D79C212yesmaximal, complemented
17#23776598C212yesmaximal
18C2×C4×#11929623C211yesmaximal, characteristic
19C79×#3501C211yesmaximal, characteristic, complemented
20C22×#11929623C2211yescharacteristic
21Q8×Dic158C2214yescomplemented
22#19099293C2214yescomplemented
23#19099293C2218yescomplemented
24#19099291C2214yescomplemented
25#19099291C2218yescomplemented
26#19099290C2218yescomplemented
27#19099290C2218yescomplemented
28#19099290C2218yescomplemented
29#19099288C2214yescomplemented
30#19099288C2218yescomplemented
31#19099272C2218yescomplemented
32#19099272C2218yescomplemented
33#19099272C2218yescomplemented
34#19099271C2218yescomplemented
35#19099271C22116yescomplemented
36#19099270C2218yescomplemented
37#19099270C2214yescomplemented
38#19099268C2218yescomplemented
39#19099268C22116yescomplemented
40#19099267C22116yescomplemented
41#19099267C22116yescomplemented
42#19099267C22116yescomplemented
43D4×Dic158C2218yescomplemented
44D4×Dic158C2214yescomplemented
45Q8×C22⋊D79C2218yescomplemented
46#19099226C2218yescomplemented
47#19099226C22116yescomplemented
48#19099194C2212yes—
49#19099193C2218yescomplemented
50#19099192C2218yes—
51#19099192C2218yes—
52#19099192C22116yescomplemented
53#19099192C22116yescomplemented
54#19099191C2214yes—
55#19099190C2218yescomplemented
56#19099189C2218yes—
57#19099189C2214yes—
58#19099188C2218yes—
59#19099120C2212yes—
60#19099119C2218yescomplemented
61#19099119C2214yescomplemented
62#19099118C2218yescomplemented
63#19099118C2212yescomplemented
64#19099118C2212yescomplemented
65#19099117C2214yescomplemented
66#19099117C2214yescomplemented
67#19099116C2214yes—
68#19099115C2214yes—
69#19099115C2218yes—
70#19099115C2218yes—
71#19099115C2214yes—
72#19099115C2218yes—
73#19099115C22116yescomplemented
74#19099115C22116yescomplemented
75#19099115C2218yescomplemented
76#19099115C2218yescomplemented
77#19099115C2218yescomplemented
78#19099115C2218yescomplemented
79C2×#14579160C2214yescomplemented
80C2×#14579159C2214yescomplemented
81C4⋊Q8×D79C2212yescomplemented
82C4⋊Q8×D79C2212yescomplemented
83C2×#14579151C2218yescomplemented
84#125×D79C2214yescomplemented
85C2×#14579140C2214yes—
86C2×#14579138C2218yes—
87C22⋊Q8×D79C2214yes—
88C22⋊Q8×D79C2214yes—
89#19099042C2218yes—
90#19099042C2218yes—
91#19099040C2214yes—
92#19099038C2212yes—
93#19099036C2218yes—
94C4×#11929623C2214yes—
95C4×#11929623C2214yes—
96C4×#11929623C2214yes—
97C4×#11929623C2214yes—
98C4×#11929623C2218yes—
99C4×#11929623C2218yes—
100C2×Q8×Dic79C2214yescomplemented
101C2×C4×Dic158C2211yescharacteristic
102C2×#14579126C2211yescharacteristic
103C2×#14579126C2218yescomplemented
104C2×#14579126C2214yescomplemented
105C4×Q8×D79C2214yescomplemented
106C4×Q8×D79C2214yescomplemented
107C2×D4×Dic79C2211yescharacteristic
108C2×C4×C22⋊D79C2212yes—
109C2×(C22⋊D79)⋊C4C2212yes—
110C2×#14579119C2211yescharacteristic
111C2×#14579117C2212yes—
112C2×#14579117C2218yes—
113#117×D79C2214yes—
114C22×C4×Dic79C2212yes—
115C2×C42×D79C2211yescharacteristic
116#554×C79C2214yescomplemented
117#554×C79C2218yescomplemented
118D4×Q8×C79C2214yescomplemented
119#544×C79C2212yes—
120#543×C79C2214yes—
121#533×C79C2212yes—
122C2×C22⋊Q8×C79C2214yes—
123#518×C79C2212yes—
124C2×C4×D4×C79C2211yescharacteristic
125C2×#11929623Q8116yescomplemented
126C2×#11929623C2314yes—
127C2×#11929623C2314yes—
128C22×Dic158C2318yes—
129C22×Dic158C2314yes—
130C22×Dic158C2311yescharacteristic
131C2×Q8×D79C2314yes—
132C2×Q8×D79C2314yes—
133C22×C22⋊D79C2312yes—
134C23×Dic79C2312yes—
135C23×Dic79C2312yes—
136C22×C4×D79C2311yescharacteristic
137C22×C4×D79C2311yescharacteristic
138C22×C4×D79C2311yescharacteristic
139#14579161C2318yes—
140#14579161C2312yes—
141#14579161C2312yes—
142#14579160C2318yes—
143#14579160C2318yes—
144#14579160C23116yes—
145#14579160C23116yes—
146#14579160C2314yes—
147#14579160C2318yes—
148#14579160C2318yes—
149#14579160C2314yes—
150#14579160C2318yes—
151#14579160C2314yes—
152#14579160C2314yes—
153#14579159C2318yes—
154#14579159C23116yes—
155#14579159C23116yes—
156#14579159C2314yes—
157#14579159C2318yes—
158#14579159C2318yes—
159#14579159C2314yes—
160#14579153C2318yes—
161#14579153C2314yes—
162#14579152C2318yes—
163#14579152C2318yes—
164#14579152C2314yes—
165#14579152C2314yes—
166#14579151C23116yes—
167#14579151C23116yes—
168#14579151C23116yes—
169#14579151C23116yes—
170#14579151C23116yes—
171#14579151C2318yes—
172#14579151C23116yes—
173#14579151C23116yes—
174#14579151C2318yes—
175#14579141C23116yes—
176#14579141C2314yes—
177#14579141C2314yes—
178#14579140C2318yes—
179#14579140C2314yes—
180#14579140C23116yes—
181#14579140C23116yes—
182#14579140C2318yes—
183#14579140C2318yes—
184#14579140C2314yes—
185#14579139C23116yes—
186#14579139C23116yes—
187#14579139C2318yes—
188#14579139C2318yes—
189#14579138C23116yes—
190#14579138C2318yes—
191#14579138C23116yes—
192#14579138C23116yes—
193#14579138C23116yes—
194#14579138C23116yes—
195#14579138C23116yes—
196#14579138C23116yes—
197#14579138C2318yes—
198#14579137C23116yes—
199#14579137C2314yes—
200#14579137C2314yes—
201Q8×Dic79C2318yes—
202Q8×Dic79C2318yes—
203Q8×Dic79C2314yes—
204Q8×Dic79C2314yes—
205Q8×Dic79C2318yes—
206C4×Dic158C2314yes—
207C4×Dic158C2318yes—
208C4×Dic158C2318yes—
209C4×Dic158C2314yes—
210C4×Dic158C2314yes—
211C4×Dic158C2314yes—
212C4×Dic158C2318yes—
213C4×Dic158C2318yes—
214#14579126C23116yes—
215#14579126C2318yes—
216#14579126C2318yes—
217#14579126C23116yes—
218#14579126C2314yes—
219#14579126C2318yes—
220#14579126C2314yes—
221#14579126C2318yes—
222#14579126C2314yes—
223#14579126C2314yes—
224#14579126C23116yes—
225#14579126C2318yes—
226#14579126C2318yes—
227#14579126C2318yes—
228D4×Dic79C2314yes—
229D4×Dic79C2318yes—
230D4×Dic79C2318yes—
231D4×Dic79C2314yes—
232C4×C22⋊D79C2318yes—
233C4×C22⋊D79C23116yes—
234C4×C22⋊D79C23116yes—
235C4×C22⋊D79C2318yes—
236(C22⋊D79)⋊C4C2318yes—
237(C22⋊D79)⋊C4C23116yes—
238(C22⋊D79)⋊C4C23116yes—
239(C22⋊D79)⋊C4C2318yes—
240#14579120C2314yes—
241#14579119C2314yes—
242#14579119C2314yes—
243#14579119C2314yes—
244#14579119C2314yes—
245#14579118C2318yes—
246#14579117C23116yes—
247#14579117C2318yes—
248#14579117C23116yes—
249#14579117C2318yes—
250#14579117C2318yes—
251#14579117C23116yes—
252C2×C4⋊Dic79C2311yescharacteristic
253C2×C4⋊Dic79C2318yes—
254C2×C4⋊Dic79C2314yes—
255C2×Dic79⋊C4C2312yes—
256C2×Dic79⋊C4C2312yes—
257C2×Dic79⋊C4C2318yes—
258C2×Dic79⋊C4C2318yes—
259C2×Dic79⋊C4C2318yes—
260C2×Dic79⋊C4C2318yes—
261C2×Dic79⋊C4C2318yes—
262C4⋊C4×D79C2314yes—
263C4⋊C4×D79C2314yes—
264C4⋊C4×D79C2314yes—
265C4⋊C4×D79C2318yes—
266C4⋊C4×D79C2318yes—
267C4⋊C4×D79C2314yes—
268C2×C22⋊Dic79C2312yes—
269C2×C22⋊Dic79C2318yes—
270C2×(C2×D79)⋊C4C2312yes—
271C22⋊C4×D79C2318yes—
272C2×C4×Dic79C2311yescharacteristic
273C2×C4×Dic79C2311yescharacteristic
274C2×C4×Dic79C2311yescharacteristic
275C2×C4×Dic79C2312yes—
276C2×C4×Dic79C2312yes—
277C2×C4×Dic79C2312yes—
278C2×C4×Dic79C2314yes—
279C2×C4×Dic79C2314yes—
280C2×C4×Dic79C2314yes—
281C2×C4×Dic79C2314yes—
282C2×C4×Dic79C2318yes—
283C2×C4×Dic79C2318yes—
284C42×D79C2312yes—
285C42×D79C2312yes—
286C42×D79C2312yes—
287C42×D79C2312yes—
288C42×D79C2318yes—
289C22×Q8×C79C2314yes—
290C22×D4×C79C2311yescharacteristic
291C23×C4×C79C2312yes—
292C4⋊Q8×C79C2318yes—
293C4⋊Q8×C79C2312yes—
294C4⋊Q8×C79C2312yes—
295#125×C79C2318yes—
296#125×C79C2314yes—
297C22⋊Q8×C79C2318yes—
298C22⋊Q8×C79C2314yes—
299C22⋊Q8×C79C23116yes—
300C22⋊Q8×C79C23116yes—
301C22⋊Q8×C79C2318yes—
302C22⋊Q8×C79C2314yes—
303C22⋊Q8×C79C2318yes—
304C4×Q8×C79C2314yes—
305C4×Q8×C79C2314yes—
306C4×D4×C79C2314yes—
307C4×D4×C79C2318yes—
308C4×D4×C79C2314yes—
309C4×D4×C79C2318yes—
310#117×C79C2314yes—
311C2×C4⋊C4×C79C2311yescharacteristic
312C2×C4⋊C4×C79C2318yes—
313C2×C4⋊C4×C79C2314yes—
314C2×C22⋊C4×C79C2312yes—
315C2×C22⋊C4×C79C2318yes—
316C2×C42×C79C2311yescharacteristic
317C23×D79C2411yescharacteristic
318#11929623C2×Q8132yescomplemented
319#11929623C2×Q8132yescomplemented
320C2×Dic158—48no—
321C2×Dic158—416no—
322C2×Dic158C2×Q818yescomplemented
323C2×Dic158C2418yes—
324C2×Dic158C2414yes—
325C2×Dic158C2414yes—
326C2×Dic158C2418yes—
327C2×Dic158C24116yes—
328C2×Dic158C2418yes—
329C2×Dic158C2414yes—
330Q8×D79—48no—
331Q8×D79—48no—
332C2×C22⋊D79C2×Q8116yescomplemented
333C2×C22⋊D79C2418yes—
334C22×Dic79—44no—
335C22×Dic79C2×Q8116yescomplemented
336C22×Dic79C2414yes—
337C22×Dic79C2411yescharacteristic
338C22×Dic79C2418yes—
339C22×Dic79C2418yes—
340C22×Dic79C2412yes—
341C22×Dic79C2411yescharacteristic
342C22×Dic79C2414yes—
343C22×Dic79C2412yes—
344C22×Dic79C2414yes—
345C22×Dic79C2414yes—
346C22×Dic79C2411yescharacteristic
347C2×C4×D79—42no—
348C2×C4×D79—42no—
349C2×C4×D79C2×Q818yescomplemented
350C2×C4×D79C2412yes—
351C2×C4×D79C2412yes—
352C2×C4×D79C2418yes—
353C2×C4×D79C2418yes—
354C2×C4×D79C2412yes—
355C2×C4×D79C2412yes—
356C2×C4×D79C2412yes—
357C2×C4×D79C2412yes—
358C4⋊Dic79C2414yes—
359C4⋊Dic79C2418yes—
360C4⋊Dic79C2414yes—
361C4⋊Dic79C2414yes—
362C4⋊Dic79C2414yes—
363C4⋊Dic79C2418yes—
364C4⋊Dic79C2414yes—
365C4⋊Dic79C24116yes—
366C4⋊Dic79C2418yes—
367Dic79⋊C4C2418yes—
368Dic79⋊C4C2418yes—
369Dic79⋊C4C2418yes—
370Dic79⋊C4C2418yes—
371Dic79⋊C4C2418yes—
372Dic79⋊C4C2418yes—
373Dic79⋊C4C2418yes—
374Dic79⋊C4C2418yes—
375Dic79⋊C4C2418yes—
376Dic79⋊C4C24116yes—
377Dic79⋊C4C24116yes—
378Dic79⋊C4C2418yes—
379Dic79⋊C4C24116yes—
380Dic79⋊C4C24116yes—
381Dic79⋊C4C24116yes—
382C22⋊Dic79C2418yes—
383C22⋊Dic79C2418yes—
384C22⋊Dic79C24116yes—
385(C2×D79)⋊C4C2418yes—
386(C2×D79)⋊C4C2418yes—
387(C2×D79)⋊C4C2418yes—
388C4×Dic79C2411yescharacteristic
389C4×Dic79C2411yescharacteristic
390C4×Dic79C2411yescharacteristic
391C4×Dic79C2411yescharacteristic
392C4×Dic79C2412yes—
393C4×Dic79C2412yes—
394C4×Dic79C2412yes—
395C4×Dic79C2412yes—
396C4×Dic79C2418yes—
397C4×Dic79C2418yes—
398C4×Dic79C2418yes—
399C4×Dic79C2414yes—
400C4×Dic79C2414yes—
401C4×Dic79C2414yes—
402C4×Dic79C2414yes—
403C4×Dic79C2414yes—
404C4×Dic79C2414yes—
405C4×Dic79C24116yes—
406C4×Dic79C24116yes—
407C24×C79C2412yes—
408C2×Q8×C79—48no—
409C2×Q8×C79C2414yes—
410C2×Q8×C79C2414yes—
411C2×Q8×C79C2418yes—
412C2×D4×C79C2×Q818yescomplemented
413C2×D4×C79C2414yes—
414C22×C4×C79—44no—
415C22×C4×C79C2414yes—
416C22×C4×C79C2411yescharacteristic
417C22×C4×C79C2418yes—
418C22×C4×C79C2411yescharacteristic
419C22×C4×C79C2418yes—
420C22×C4×C79C2412yes—
421C22×C4×C79C2414yes—
422C22×C4×C79C2411yescharacteristic
423C4⋊C4×C79C2418yes—
424C4⋊C4×C79C2414yes—
425C4⋊C4×C79C2414yes—
426C4⋊C4×C79C2418yes—
427C4⋊C4×C79C24116yes—
428C4⋊C4×C79C2414yes—
429C4⋊C4×C79C2414yes—
430C4⋊C4×C79C2418yes—
431C4⋊C4×C79C2414yes—
432C22⋊C4×C79C2418yes—
433C22⋊C4×C79C2418yes—
434C22⋊C4×C79C24116yes—
435C42×C79C2412yes—
436C42×C79C2412yes—
437C42×C79C2418yes—
438C23×C79—42no—
439C23×C79—42no—
440C23×C79C22×Q818yes—
441C23×C79C2511yescharacteristic
442C23×C79C2514yes—
443C22×D79—41no—
444C22×D79—41no—
445C22×D79C22×Q814yes—
446C22×D79C2512yes—
447Q8×C79—28no—
448Q8×C79—44no—
449Q8×C79—48no—
450D4×C79C22×Q8116yes—
451C2×C4×C79—22no—
452C2×C4×C79—28no—
453C2×C4×C79—41no—
454C2×C4×C79—48no—
455C2×C4×C79—44no—
456C2×C4×C79—42no—
457C2×C4×C79—48no—
458C2×C4×C79C22×Q814yes—
459C2×C4×C79C2511yescharacteristic
460C2×C4×C79C2514yes—
461C2×C4×C79C2518yes—
462C2×C4×C79C2518yes—
463C2×C4×C79C2512yes—
464C2×C4×C79C2512yes—
465C2×C4×C79C2511yescharacteristic
466C22⋊D79C22×Q8132yes—
467C2×Dic79—22no—
468C2×Dic79—28no—
469C2×Dic79—41no—
470C2×Dic79—42no—
471C2×Dic79—44no—
472C2×Dic79—48no—
473C2×Dic79—48no—
474C2×Dic79C22×Q814yes—
475C2×Dic79C22×Q818yes—
476C2×Dic79C22×Q8116yes—
477C2×Dic79C22×Q8116yes—
478C2×Dic79C2511yescharacteristic
479C2×Dic79C2514yes—
480C2×Dic79C2518yes—
481C2×Dic79C2518yes—
482C2×Dic79C2512yes—
483C2×Dic79C2511yescharacteristic
484C2×Dic79C2514yes—
485C2×Dic79C2511yescharacteristic
486C2×Dic79C2511yescharacteristic
487C4×D79—24no—
488C4×D79—24no—
489C4×D79—42no—
490C4×D79—42no—
491C4×D79—48no—
492C4×D79—48no—
493C4×D79C22×Q818yes—
494C4×D79C22×Q818yes—
495Dic158—28no—
496Dic158—216no—
497Dic158—44no—
498Dic158—48no—
499Dic158—48no—
500Dic158—416no—
501Dic158C22×Q8116yes—
502C22×C79—24no—
503C22×C79—21no—
504C22×C79—24no—
505C22×C79—21no—
506C22×C79—48no—
507C22×C79C23×Q818yes—
508C22×C79C23×Q812yes—
509C22×C79C2611yescharacteristic
510C2×D79—22no—
511C2×D79—22no—
512C2×D79—44no—
513C2×D79C23×Q814yes—
514C4×C79—21no—
515C4×C79—24no—
516C4×C79—28no—
517C4×C79—28no—
518C4×C79—22no—
519C4×C79C23×Q814yes—
520C4×C79#58512yes—
521Dic79—28no—
522Dic79—28no—
523Dic79—22no—
524Dic79—24no—
525Dic79—21no—
526Dic79C23×Q818yes—
527Dic79C23×Q812yes—
528Dic79C23×Q812yes—
529Dic79#58512yes—
530#62813—791nomaximal, Sylow
531C2×C79—22no—
532C2×C79—28no—
533C2×C79C24×Q811yescharacteristic
534C2×C79C2×#58511yescharacteristic
535C2×C79C2×#58511yescharacteristic
536D79—24no—
537#3504—798no—
538#3503—794no—
539#3503—794no—
540#3502—792no—
541#3502—792no—
542#3501—794no—
543#3501—794no—
544#3501—792no—
545#3501—791no—
546#3501D7911yescharacteristic, complemented
547Q8×#41—794no—
548Q8×#41—798no—
549Q8×#41—794no—
550#3458—792no—
551#3458—794no—
552C2×#533—792no—
553C2×#533—794no—
554#3428—792no—
555C2×C4×#41—791no—
556C79#6281311yescharacteristic, complemented, Sylow
557C22×#41—791no—
558Q82—798no—
559Q82—794no—
560Q82—794no—
561#557—794no—
562#557—798no—
563#557—798no—
564#557—798no—
565#557—798no—
566#557—794no—
567#557—798no—
568#554—7916no—
569#554—7916no—
570#554—7916no—
571#554—798no—
572#554—7916no—
573#554—794no—
574#554—798no—
575#554—798no—
576#554—798no—
577#554—798no—
578#554—798no—
579#554—7916no—
580#554C2×D7914yescomplemented
581#554C2×D7918yescomplemented
582D4×Q8—798no—
583D4×Q8—798no—
584D4×Q8—7916no—
585D4×Q8—798no—
586D4×Q8—794no—
587D4×Q8C2×D7914yescomplemented
588#544—798no—
589#544—798no—
590#544—798no—
591#544—798no—
592#544—7916no—
593#544—7916no—
594#544—794no—
595#544—792no—
596#544C2×D7912yes—
597#543—798no—
598#543—798no—
599#543—794no—
600#543C2×D7914yes—
601#533—792no—
602#533—792no—
603#533—798no—
604#533—794no—
605#533—798no—
606#533—794no—
607#533—794no—
608#533—798no—
609#533—798no—
610#533—798no—
611#533—798no—
612#533—798no—
613#533—798no—
614#533—798no—
615#533—7916no—
616#533—7916no—
617#533—794no—
618#533—794no—
619#533—794no—
620#533—792no—
621#533C2×D7912yes—
622C2×C4⋊Q8—794no—
623C2×C4⋊Q8—792no—
624C2×C4⋊Q8—792no—
625C2×C4⋊Q8—794no—
626C2×#125—794no—
627C2×#125—798no—
628C2×C22⋊Q8—794no—
629C2×C22⋊Q8—794no—
630C2×C22⋊Q8—794no—
631C2×C22⋊Q8—798no—
632C2×C22⋊Q8C2×D7914yes—
633#520—798no—
634#520—798no—
635#519—794no—
636#518—792no—
637#518—798no—
638#518C2×D7912yes—
639C4×#41—794no—
640C4×#41—794no—
641C4×#41—794no—
642C4×#41—794no—
643C4×#41—798no—
644C4×#41—798no—
645C2×C4×Q8—794no—
646C2×C4×Q8—794no—
647C2×C4×Q8—794no—
648C2×C4×Q8—791no—
649C2×C4×Q8—794no—
650C2×C4×Q8—798no—
651C2×C4×Q8—791no—
652C2×C4×D4—791no—
653C2×C4×D4—792no—
654C2×C4×D4—792no—
655C2×C4×D4C2×D7911yescharacteristic
656C2×#117—794no—
657C2×#117—791no—
658C2×#117—792no—
659C2×#117—798no—
660C22×C42—792no—
661C22×C42—791no—
662C2×#41—7916no—
663C2×#41—794no—
664C2×#41—794no—
665C22×Q8—794no—
666C22×Q8—794no—
667C22×Q8—794no—
668C22×Q8—798no—
669C22×Q8—791no—
670C22×Q8C22×D7914yes—
671C22×D4—792no—
672C22×D4C22×D7911yescharacteristic
673C23×C4—792no—
674C23×C4—791no—
675C23×C4—791no—
676C23×C4—792no—
677C23×C4—791no—
678C23×C4C22×D7912yes—
679C4⋊Q8—794no—
680C4⋊Q8—798no—
681C4⋊Q8—794no—
682C4⋊Q8—798no—
683C4⋊Q8—798no—
684C4⋊Q8—7916no—
685C4⋊Q8—7916no—
686C4⋊Q8—794no—
687C4⋊Q8—794no—
688C4⋊Q8—798no—
689C4⋊Q8—798no—
690C4⋊Q8—794no—
691C4⋊Q8—794no—
692C4⋊Q8—798no—
693C4⋊Q8—7916no—
694C4⋊Q8—7916no—
695C4⋊Q8—798no—
696C4⋊Q8—798no—
697C4⋊Q8—792no—
698C4⋊Q8—792no—
699C4⋊Q8—798no—
700C4⋊Q8C22×D7912yes—
701C4⋊Q8C22×D7912yes—
702C4⋊Q8C22×D7918yes—
703#125—798no—
704#125—798no—
705#125—7916no—
706#125—7916no—
707#125—7916no—
708#125—794no—
709#125—794no—
710#125—7916no—
711#125—7916no—
712#125—7916no—
713#125—7916no—
714#125—798no—
715#125—798no—
716#125—794no—
717#125—798no—
718#125C22×D7914yes—
719#125C22×D7918yes—
720C22⋊Q8—794no—
721C22⋊Q8—794no—
722C22⋊Q8—7916no—
723C22⋊Q8—794no—
724C22⋊Q8—798no—
725C22⋊Q8—794no—
726C22⋊Q8—798no—
727C22⋊Q8—798no—
728C22⋊Q8—7916no—
729C22⋊Q8—7916no—
730C22⋊Q8—798no—
731C22⋊Q8—794no—
732C22⋊Q8—798no—
733C22⋊Q8—794no—
734C22⋊Q8—7916no—
735C22⋊Q8—7916no—
736C22⋊Q8—7916no—
737C22⋊Q8—798no—
738C22⋊Q8—798no—
739C22⋊Q8—7916no—
740C22⋊Q8—7916no—
741C22⋊Q8—7916no—
742C22⋊Q8—7916no—
743C22⋊Q8—7916no—
744C22⋊Q8—7916no—
745C22⋊Q8—7916no—
746C22⋊Q8C22×D7914yes—
747C22⋊Q8C22×D7914yes—
748C22⋊Q8C22×D7918yes—
749C22⋊Q8C22×D7918yes—
750C22⋊Q8C22×D7918yes—
751C22⋊Q8C22×D79116yes—
752C22⋊Q8C22×D79116yes—
753C4×Q8—794no—
754C4×Q8—798no—
755C4×Q8—794no—
756C4×Q8—798no—
757C4×Q8—798no—
758C4×Q8—794no—
759C4×Q8—798no—
760C4×Q8—794no—
761C4×Q8—794no—
762C4×Q8—794no—
763C4×Q8—798no—
764C4×Q8—7916no—
765C4×Q8—798no—
766C4×Q8—7916no—
767C4×Q8—798no—
768C4×Q8—798no—
769C4×Q8—7916no—
770C4×Q8—798no—
771C4×Q8—798no—
772C4×Q8—794no—
773C4×Q8—794no—
774C4×Q8—798no—
775C4×Q8—794no—
776C4×Q8—798no—
777C4×Q8—794no—
778C4×Q8—798no—
779C4×Q8—798no—
780C4×Q8C22×D7914yes—
781C4×Q8C22×D7914yes—
782C4×D4—794no—
783C4×D4—794no—
784C4×D4—798no—
785C4×D4—798no—
786C4×D4—798no—
787C4×D4—798no—
788C4×D4—7916no—
789C4×D4—7916no—
790C4×D4—798no—
791C4×D4—798no—
792C4×D4—7916no—
793C4×D4—7916no—
794C4×D4C22×D7914yes—
795C4×D4C22×D7914yes—
796C4×D4C22×D7918yes—
797C4×D4C22×D7918yes—
798#117—794no—
799#117—794no—
800#117—794no—
801#117—794no—
802#117—794no—
803#117—798no—
804#117—798no—
805#117—7916no—
806#117—798no—
807#117—7916no—
808#117—7916no—
809#117—798no—
810#117C22×D7914yes—
811C2×C4⋊C4—792no—
812C2×C4⋊C4—792no—
813C2×C4⋊C4—791no—
814C2×C4⋊C4—798no—
815C2×C4⋊C4—798no—
816C2×C4⋊C4—798no—
817C2×C4⋊C4—798no—
818C2×C4⋊C4—798no—
819C2×C4⋊C4—798no—
820C2×C4⋊C4—794no—
821C2×C4⋊C4—794no—
822C2×C4⋊C4—794no—
823C2×C4⋊C4—798no—
824C2×C4⋊C4—798no—
825C2×C4⋊C4—794no—
826C2×C4⋊C4—794no—
827C2×C4⋊C4C22×D7911yescharacteristic
828C2×C4⋊C4C22×D7918yes—
829C2×C4⋊C4C22×D7914yes—
830C2×C22⋊C4—792no—
831C2×C22⋊C4—798no—
832C2×C22⋊C4—792no—
833C2×C22⋊C4—798no—
834C2×C22⋊C4C22×D7912yes—
835C2×C22⋊C4C22×D7918yes—
836C2×C42—792no—
837C2×C42—791no—
838C2×C42—798no—
839C2×C42—798no—
840C2×C42—792no—
841C2×C42—791no—
842C2×C42—792no—
843C2×C42—794no—
844C2×C42—794no—
845C2×C42—794no—
846C2×C42—794no—
847C2×C42—791no—
848C2×C42—798no—
849C2×C42—792no—
850C2×C42—792no—
851C2×C42—792no—
852C2×C42—792no—
853C2×C42C22×D7911yescharacteristic
854C24—791no—
855C24C23×D7912yes—
856#41—7932no—
857#41—7932no—
858C2×Q8—48no—
859C2×Q8—3168no—
860C2×Q8—31616no—
861C2×Q8—3168no—
862C2×Q8—3168no—
863C2×Q8—798no—
864C2×Q8—798no—
865C2×Q8—798no—
866C2×Q8—7916no—
867C2×Q8—794no—
868C2×Q8—794no—
869C2×Q8—798no—
870C2×Q8—794no—
871C2×Q8C23×D7914yes—
872C2×Q8C23×D7918yes—
873C2×Q8C23×D7914yes—
874C2×D4—7916no—
875C2×D4—798no—
876C2×D4Q8×D7918yescomplemented
877C2×D4C23×D7914yes—
878C22×C4—44no—
879C22×C4—3162no—
880C22×C4—3162no—
881C22×C4—3164no—
882C22×C4—792no—
883C22×C4—791no—
884C22×C4—794no—
885C22×C4—798no—
886C22×C4—798no—
887C22×C4—792no—
888C22×C4—792no—
889C22×C4—798no—
890C22×C4—798no—
891C22×C4—7916no—
892C22×C4—794no—
893C22×C4—791no—
894C22×C4—794no—
895C22×C4—792no—
896C22×C4—798no—
897C22×C4—792no—
898C22×C4—792no—
899C22×C4—791no—
900C22×C4—794no—
901C22×C4—792no—
902C22×C4—792no—
903C22×C4C23×D7911yescharacteristic
904C22×C4C23×D7914yes—
905C22×C4C23×D7912yes—
906C22×C4C23×D7914yes—
907C22×C4C23×D7911yescharacteristic
908C22×C4C23×D7918yes—
909C22×C4C23×D7918yes—
910C22×C4C23×D7911yescharacteristic
911C4⋊C4—798no—
912C4⋊C4—798no—
913C4⋊C4—798no—
914C4⋊C4—798no—
915C4⋊C4—798no—
916C4⋊C4—798no—
917C4⋊C4—7916no—
918C4⋊C4—7916no—
919C4⋊C4—798no—
920C4⋊C4—7916no—
921C4⋊C4—798no—
922C4⋊C4—7916no—
923C4⋊C4—798no—
924C4⋊C4—7916no—
925C4⋊C4—798no—
926C4⋊C4—798no—
927C4⋊C4—794no—
928C4⋊C4—794no—
929C4⋊C4—794no—
930C4⋊C4—794no—
931C4⋊C4—798no—
932C4⋊C4—7916no—
933C4⋊C4—798no—
934C4⋊C4—794no—
935C4⋊C4C23×D7918yes—
936C4⋊C4C23×D7914yes—
937C4⋊C4C23×D7914yes—
938C4⋊C4C23×D7914yes—
939C4⋊C4C23×D7914yes—
940C4⋊C4C23×D7918yes—
941C4⋊C4C23×D7914yes—
942C4⋊C4C23×D79116yes—
943C4⋊C4C23×D7918yes—
944C22⋊C4—798no—
945C22⋊C4—798no—
946C22⋊C4—7916no—
947C22⋊C4—798no—
948C22⋊C4—798no—
949C22⋊C4—798no—
950C22⋊C4C23×D7918yes—
951C22⋊C4C23×D7918yes—
952C22⋊C4C23×D79116yes—
953C42—791no—
954C42—791no—
955C42—791no—
956C42—791no—
957C42—794no—
958C42—798no—
959C42—798no—
960C42—792no—
961C42—794no—
962C42—792no—
963C42—794no—
964C42—794no—
965C42—792no—
966C42—794no—
967C42—794no—
968C42—792no—
969C42—7916no—
970C42—7916no—
971C42—798no—
972C42C23×D7912yes—
973C42C23×D7912yes—
974C42C23×D7918yes—
975C23—42no—
976C23—42no—
977C23—3161no—
978C23—3161no—
979C23—794no—
980C23—792no—
981C23C2×Q8×D7918yes—
982C23C24×D7911yescharacteristic
983C23C24×D7914yes—
984Q8—28no—
985Q8—48no—
986Q8—44no—
987Q8—31616no—
988Q8—3164no—
989Q8—3168no—
990Q8—3168no—
991Q8—7916no—
992Q8—15816no—
993Q8—1588no—
994D4—7932no—
995D4C2×Q8×D79116yes—
996C2×C4—22no—
997C2×C4—28no—
998C2×C4—44no—
999C2×C4—42no—
1000C2×C4—41no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—3162no—
1004C2×C4—3162no—
1005C2×C4—3168no—
1006C2×C4—3168no—
1007C2×C4—3164no—
1008C2×C4—3162no—
1009C2×C4—3161no—
1010C2×C4—3168no—
1011C2×C4—3168no—
1012C2×C4—791no—
1013C2×C4—794no—
1014C2×C4—791no—
1015C2×C4—791no—
1016C2×C4—794no—
1017C2×C4—798no—
1018C2×C4—7916no—
1019C2×C4—7916no—
1020C2×C4—798no—
1021C2×C4—798no—
1022C2×C4—791no—
1023C2×C4—798no—
1024C2×C4—794no—
1025C2×C4—798no—
1026C2×C4—792no—
1027C2×C4—1584no—
1028C2×C4—1582no—
1029C2×C4—1588no—
1030C2×C4—1584no—
1031C2×C4C2×Q8×D7914yes—
1032C2×C4C24×D7911yescharacteristic
1033C2×C4C24×D7914yes—
1034C2×C4C24×D7918yes—
1035C2×C4C24×D7918yes—
1036C2×C4C24×D7912yes—
1037C2×C4C24×D7911yescharacteristic
1038C2×C4C24×D7912yes—
1039C22—24no—
1040C22—21no—
1041C22—24no—
1042C22—21no—
1043C22—48no—
1044C22—3164no—
1045C22—794no—
1046C22—1582no—
1047C22—1582no—
1048C22C22×Q8×D7912yes—
1049C22C22×Q8×D7918yes—
1050C22C25×D7911yescharacteristic
1051C4—28no—
1052C4—22no—
1053C4—21no—
1054C4—24no—
1055C4—28no—
1056C4—792no—
1057C4—792no—
1058C4—798no—
1059C4—792no—
1060C4—1581no—
1061C4—1588no—
1062C4—1584no—
1063C4—1588no—
1064C4—1582no—
1065C4C22×Q8×D7914yes—
1066C4#1909939812yes—
1067C2—22no—
1068C2—28no—
1069C2—1584no—
1070C2C23×Q8×D7911yescharacteristic
1071C2#585×D7911yescharacteristic
1072C2C2×#1909939811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3501C2
prime radicalC22×#11929623C22
hypercenter#3501D79
hypocenterC79#62813
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #23777220C2semidirect
2. #23777214C2semidirect
3. #23777211C2semidirect
4. #23777208C2semidirect
5. #23777205C2semidirect
6. #23777203C2semidirect
7. #23777200C2semidirect
8. #23777198C2semidirect
9. #23777196C2semidirect
10. #23776979C2semidirect
11. #23776979C2semidirect
12. Q8×#11929623C2semidirect
13. #23776804C2semidirect
14. #23776802C2semidirect
15. C2×#19099115C2semidirect
16. #533×D79C2semidirect
19. C79×#3501C2semidirect
21. Q8×Dic158C22semidirect
22. #19099293C22semidirect
23. #19099293C22semidirect
24. #19099291C22semidirect
25. #19099291C22semidirect
26. #19099290C22semidirect
27. #19099290C22semidirect
28. #19099290C22semidirect
29. #19099288C22semidirect
30. #19099288C22semidirect
31. #19099272C22semidirect
32. #19099272C22semidirect
33. #19099272C22semidirect
34. #19099271C22semidirect
35. #19099271C22semidirect
36. #19099270C22semidirect
37. #19099270C22semidirect
38. #19099268C22semidirect
39. #19099268C22semidirect
40. #19099267C22semidirect
41. #19099267C22semidirect
42. #19099267C22semidirect
43. D4×Dic158C22semidirect
44. D4×Dic158C22semidirect
45. Q8×C22⋊D79C22semidirect
46. #19099226C22semidirect
47. #19099226C22semidirect
49. #19099193C22semidirect
52. #19099192C22semidirect
53. #19099192C22semidirect
55. #19099190C22semidirect
60. #19099119C22semidirect
61. #19099119C22semidirect
62. #19099118C22semidirect
63. #19099118C22semidirect
64. #19099118C22semidirect
65. #19099117C22semidirect
66. #19099117C22semidirect
73. #19099115C22semidirect
74. #19099115C22semidirect
75. #19099115C22semidirect
76. #19099115C22semidirect
77. #19099115C22semidirect
78. #19099115C22semidirect
79. C2×#14579160C22semidirect
80. C2×#14579159C22semidirect
81. C4⋊Q8×D79C22semidirect
82. C4⋊Q8×D79C22semidirect
83. C2×#14579151C22semidirect
84. #125×D79C22semidirect
100. C2×Q8×Dic79C22semidirect
103. C2×#14579126C22semidirect
104. C2×#14579126C22semidirect
105. C4×Q8×D79C22semidirect
106. C4×Q8×D79C22semidirect
116. #554×C79C22semidirect
117. #554×C79C22semidirect
118. D4×Q8×C79C22semidirect
125. C2×#11929623Q8semidirect
318. #11929623C2×Q8semidirect
319. #11929623C2×Q8semidirect
322. C2×Dic158C2×Q8semidirect
332. C2×C22⋊D79C2×Q8semidirect
335. C22×Dic79C2×Q8semidirect
349. C2×C4×D79C2×Q8semidirect
412. C2×D4×C79C2×Q8semidirect
546. #3501D79semidirect
556. C79#62813semidirect
580. #554C2×D79semidirect
581. #554C2×D79semidirect
587. D4×Q8C2×D79semidirect
876. C2×D4Q8×D79semidirect

Maximal subgroups

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

subgroupindex
#237772202
#237772142
#237772112
#237772082
#237772052
#237772032
#237772002
#237771982
#237771962
#237769792
Q8×#119296232
#237768042
#237768022
C2×#190991152
#533×D792
#237765982
C2×C4×#119296232
C79×#35012
#6281379