Finite Group Databasebeta

← C2×#23777257 #35196343

Subgroups — C2×#23777257 #35196343

Order 20224.

7130 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777257C2132yesmaximal, direct product factor
2C2×#19099299C211yesmaximal, characteristic, complemented
3C2×#19099292C211yesmaximal, characteristic, complemented
4C2×#19099291C211yesmaximal, characteristic, complemented
5C2×#19099283C212yesmaximal, complemented
6C2×#19099282C212yesmaximal, complemented
7C2×#19099282C212yesmaximal, complemented
8C2×#19099272C212yesmaximal, complemented
9C2×#19099250C214yesmaximal, complemented
10C2×#19099156C214yesmaximal, complemented
11C2×#19099133C212yesmaximal, complemented
12C2×#19099117C211yesmaximal, characteristic, complemented
13C2×#19099111C211yesmaximal, characteristic
14C2×#19099095C212yesmaximal, complemented
15C2×#19099092C212yesmaximal, complemented
16C2×#19099042C212yesmaximal, complemented
17C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
18C2×#559×C79C211yesmaximal, characteristic, complemented
19C22×#11929623C2212yes—
20C22×Q8×D79C2211yescharacteristic
21#19099299C22116yescomplemented
22#19099292C22116yescomplemented
23#19099291C22116yescomplemented
24#19099283C22132yescomplemented
25#19099282C22132yescomplemented
26#19099282C22132yescomplemented
27#19099272C22132yescomplemented
28#19099250C22164yescomplemented
29#19099156C22164yescomplemented
30#19099133C22132yescomplemented
31#19099117C22116yescomplemented
32#19099111C22116yes—
33C2×#14579161C2211yescharacteristic
34C2×#14579161C2212yes—
35C2×#14579160C2211yescharacteristic
36C2×#14579159C2211yescharacteristic
37C2×#14579159C2212yes—
38#19099095C22132yescomplemented
39#19099092C22132yescomplemented
40C2×#14579154C2214yes—
41C2×#14579154C2214yes—
42C2×#14579154C2214yes—
43C2×#14579154C2214yes—
44C2×#14579153C2212yes—
45C2×#14579152C2214yes—
46C2×#14579152C2212yes—
47C2×#14579151C2212yes—
48C2×#14579151C2214yes—
49C2×#14579148C2212yes—
50C2×#14579148C2212yes—
51C2×#14579148C2212yes—
52C2×#14579143C2214yes—
53C2×#14579143C2214yes—
54C2×#14579142C2214yes—
55C2×#14579141C2211yescharacteristic
56C2×#14579140C2214yes—
57C2×#14579139C2212yes—
58C2×#14579138C2214yes—
59C2×#14579138C2214yes—
60C2×#14579138C2214yes—
61C2×#14579137C2211yescharacteristic
62C2×#14579132C2212yes—
63C2×#14579132C2212yes—
64#19099042C22132yescomplemented
65C2×Q8×Dic79C2211yescharacteristic
66C2×Q8×Dic79C2212yes—
67C2×C4×Dic158C2212yes—
68C2×C4×Dic158C2211yescharacteristic
69C2×C4×Dic158C2212yes—
70C2×C4×Dic158C2212yes—
71C2×C4×Dic158C2212yes—
72C2×C4×Dic158C2211yescharacteristic
73C2×#14579126C2212yes—
74C2×#14579126C2211yescharacteristic
75C2×#14579126C2212yes—
76C4×Q8×D79C22116yescomplemented
77C2×D4×Dic79C2212yes—
78C2×D4×Dic79C2212yes—
79C2×D4×Dic79C2212yes—
80C2×D4×Dic79C2212yes—
81C2×C4×C22⋊D79C2214yes—
82C2×(C22⋊D79)⋊C4C2214yes—
83C2×#14579120C2214yes—
84C2×#14579118C2212yes—
85C2×#14579117C2214yes—
86C2×#14579117C2214yes—
87C22×Dic79⋊C4C2214yes—
88C2×C4⋊C4×D79C2211yescharacteristic
89C2×C4⋊C4×D79C2212yes—
90C2×C42×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92#559×C79C22116yescomplemented
93C2×#127×C79C2211yescharacteristic
94C2×#124×C79C2212yes—
95C2×#124×C79C2212yes—
96C2×#123×C79C2214yes—
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×Q8×C79C2211yescharacteristic
99C2×C4×D4×C79C2212yes—
100C2×C4×D4×C79C2212yes—
101C2×#11929623—216no—
102C2×#11929623C23116yes—
103C22×Dic158C2312yes—
104C22×Dic158C2311yescharacteristic
105C22×Dic158C2312yes—
106C22×Dic158C2311yescharacteristic
107C22×Dic158C2312yes—
108C2×Q8×D79—28no—
109C2×Q8×D79C2318yes—
110C22×C22⋊D79C2314yes—
111C23×Dic79C2314yes—
112C23×Dic79C2314yes—
113C22×C4×D79C2311yescharacteristic
114C22×C4×D79C2312yes—
115C22×C4×D79C2312yes—
116C22×C4×D79C2311yescharacteristic
117C22×C4×D79C2311yescharacteristic
118#14579161C23116yes—
119#14579161C2318yes—
120#14579160C2318yes—
121#14579159C2318yes—
122#14579159C23116yes—
123#14579154C23132yes—
124#14579154C23132yes—
125#14579154C23132yes—
126#14579154C23132yes—
127#14579153C23116yes—
128#14579152C23132yes—
129#14579152C23116yes—
130#14579151C23132yes—
131#14579151C23116yes—
132#14579148C23116yes—
133#14579148C23116yes—
134#14579148C23116yes—
135#14579143C23132yes—
136#14579143C23132yes—
137#14579142C23132yes—
138#14579141C2318yes—
139#14579140C23132yes—
140#14579139C23116yes—
141#14579138C23132yes—
142#14579138C23132yes—
143#14579138C23132yes—
144#14579137C2318yes—
145#14579132C23116yes—
146#14579132C23116yes—
147Q8×Dic79C2318yes—
148Q8×Dic79C23116yes—
149C4×Dic158C23116yes—
150C4×Dic158C2318yes—
151C4×Dic158C23116yes—
152C4×Dic158C23116yes—
153C4×Dic158C23116yes—
154C4×Dic158C2318yes—
155#14579126C23116yes—
156#14579126C2318yes—
157#14579126C23116yes—
158D4×Dic79C23116yes—
159D4×Dic79C23116yes—
160D4×Dic79C23116yes—
161D4×Dic79C23116yes—
162C4×C22⋊D79C23132yes—
163(C22⋊D79)⋊C4C23132yes—
164#14579120C23132yes—
165#14579118C23116yes—
166#14579117C23132yes—
167#14579117C23132yes—
168C2×C4⋊Dic79C2311yescharacteristic
169C2×C4⋊Dic79C2312yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2314yes—
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2314yes—
176C2×Dic79⋊C4C23132yes—
177C2×Dic79⋊C4C2312yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2314yes—
187C2×Dic79⋊C4C2312yes—
188C2×Dic79⋊C4C2312yes—
189C4⋊C4×D79C23116yes—
190C4⋊C4×D79C2318yes—
191C2×C22⋊Dic79C2314yes—
192C2×C22⋊Dic79C2314yes—
193C2×C22⋊Dic79C2314yes—
194C2×C22⋊Dic79C2314yes—
195C2×C22⋊Dic79C2314yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×C4×Dic79C2312yes—
199C2×C4×Dic79C2312yes—
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2314yes—
205C2×C4×Dic79C2314yes—
206C2×C4×Dic79C2312yes—
207C42×D79C23116yes—
208C42×D79C2318yes—
209C22×Q8×C79C2311yescharacteristic
210C22×Q8×C79C2311yescharacteristic
211C22×D4×C79C2312yes—
212C22×D4×C79C2312yes—
213C22×D4×C79C2312yes—
214C23×C4×C79C2314yes—
215#127×C79C2318yes—
216#124×C79C23116yes—
217#124×C79C23116yes—
218#123×C79C23132yes—
219C4×Q8×C79C2318yes—
220C4×Q8×C79C2318yes—
221C4×D4×C79C23116yes—
222C4×D4×C79C23116yes—
223C2×C4⋊C4×C79C2311yescharacteristic
224C2×C4⋊C4×C79C2311yescharacteristic
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2312yes—
227C2×C22⋊C4×C79C2314yes—
228C2×C22⋊C4×C79C2314yes—
229C2×C22⋊C4×C79C2314yes—
230C2×C42×C79C2312yes—
231C2×C42×C79C2312yes—
232C2×C42×C79C2311yescharacteristic
233C23×D79C2411yescharacteristic
234#11929623—264no—
235C2×Dic158—28no—
236C2×Dic158—24no—
237C2×Dic158—28no—
238C2×Dic158—24no—
239C2×Dic158—44no—
240C2×Dic158C2418yes—
241C2×Dic158C2414yes—
242C2×Dic158C2418yes—
243C2×Dic158C2414yes—
244C2×Dic158C2418yes—
245Q8×D79—232no—
246C2×C22⋊D79—216no—
247C2×C22⋊D79C24116yes—
248C22×Dic79—216no—
249C22×Dic79—48no—
250C22×Dic79C2411yescharacteristic
251C22×Dic79C2412yes—
252C22×Dic79C2412yes—
253C22×Dic79C2414yes—
254C22×Dic79C2412yes—
255C22×Dic79C24116yes—
256C22×Dic79C2411yescharacteristic
257C22×Dic79C2412yes—
258C22×Dic79C24116yes—
259C22×Dic79C2411yescharacteristic
260C2×C4×D79—28no—
261C2×C4×D79—24no—
262C2×C4×D79—44no—
263C2×C4×D79—42no—
264C2×C4×D79#4118yes—
265C2×C4×D79C2418yes—
266C2×C4×D79C2414yes—
267C2×C4×D79C2418yes—
268C2×C4×D79C2414yes—
269C2×C4×D79C2414yes—
270C4⋊Dic79C2414yes—
271C4⋊Dic79C2418yes—
272C4⋊Dic79C2418yes—
273C4⋊Dic79C24116yes—
274C4⋊Dic79C2414yes—
275C4⋊Dic79C2418yes—
276C4⋊Dic79C2418yes—
277C4⋊Dic79C24116yes—
278Dic79⋊C4C2418yes—
279Dic79⋊C4C2418yes—
280Dic79⋊C4C2418yes—
281Dic79⋊C4C2418yes—
282Dic79⋊C4C24116yes—
283Dic79⋊C4C24116yes—
284Dic79⋊C4C2418yes—
285Dic79⋊C4C2418yes—
286Dic79⋊C4C24116yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C2418yes—
289Dic79⋊C4C2418yes—
290C22⋊Dic79C24116yes—
291C22⋊Dic79C24116yes—
292C22⋊Dic79C24116yes—
293C22⋊Dic79C24116yes—
294C22⋊Dic79C24116yes—
295(C2×D79)⋊C4C2418yes—
296(C2×D79)⋊C4C2418yes—
297C4×Dic79C2418yes—
298C4×Dic79C2418yes—
299C4×Dic79C2414yes—
300C4×Dic79C2414yes—
301C4×Dic79C2418yes—
302C4×Dic79C2414yes—
303C4×Dic79C24116yes—
304C4×Dic79C24116yes—
305C4×Dic79C2418yes—
306C24×C79C2414yes—
307C2×Q8×C79—24no—
308C2×Q8×C79—24no—
309C2×Q8×C79C2414yes—
310C2×Q8×C79C2414yes—
311C2×D4×C79—28no—
312C2×D4×C79—28no—
313C2×D4×C79—44no—
314C2×D4×C79C2418yes—
315C2×D4×C79C2418yes—
316C2×D4×C79C2418yes—
317C22×C4×C79—48no—
318C22×C4×C79C2412yes—
319C22×C4×C79C2412yes—
320C22×C4×C79C2412yes—
321C22×C4×C79C2412yes—
322C22×C4×C79C2411yescharacteristic
323C22×C4×C79C24116yes—
324C22×C4×C79C2411yescharacteristic
325C22×C4×C79C2411yescharacteristic
326C4⋊C4×C79C2414yes—
327C4⋊C4×C79C2414yes—
328C4⋊C4×C79C2418yes—
329C4⋊C4×C79C2418yes—
330C22⋊C4×C79C24116yes—
331C22⋊C4×C79C24116yes—
332C22⋊C4×C79C24116yes—
333C42×C79C2418yes—
334C42×C79C2418yes—
335C42×C79C2414yes—
336C23×C79—28no—
337C23×C79—28no—
338C23×C79—28no—
339C23×C79C2518yes—
340C23×C79C2511yescharacteristic
341C22×D79—22no—
342C22×D79—22no—
343C22×D79C2×#4114yes—
344C22×D79C2512yes—
345Q8×C79—28no—
346Q8×C79—28no—
347D4×C79—216no—
348D4×C79—216no—
349D4×C79—48no—
350C2×C4×C79—24no—
351C2×C4×C79—24no—
352C2×C4×C79—24no—
353C2×C4×C79—22no—
354C2×C4×C79—24no—
355C2×C4×C79—416no—
356C2×C4×C79C2×#4114yes—
357C2×C4×C792−1+414yes—
358C2×C4×C79C2514yes—
359C2×C4×C79C2514yes—
360C2×C4×C79C2512yes—
361C2×C4×C79C2514yes—
362C2×C4×C79C2514yes—
363C2×C4×C79C2512yes—
364C2×C4×C79C2512yes—
365C22⋊D79—232no—
366C2×Dic79—24no—
367C2×Dic79—28no—
368C2×Dic79—22no—
369C2×Dic79—24no—
370C2×Dic79—24no—
371C2×Dic79—22no—
372C2×Dic79—24no—
373C2×Dic79—232no—
374C2×Dic79—416no—
375C2×Dic79C2×#4114yes—
376C2×Dic79C2512yes—
377C2×Dic79C2514yes—
378C2×Dic79C2514yes—
379C2×Dic79C2512yes—
380C2×Dic79C2514yes—
381C2×Dic79C2518yes—
382C2×Dic79C2514yes—
383C2×Dic79C2512yes—
384C4×D79—216no—
385C4×D79—28no—
386C4×D79—44no—
387C4×D79—48no—
388C4×D79C2×#41116yes—
389Dic158—28no—
390Dic158—216no—
391Dic158—28no—
392Dic158—216no—
393Dic158—48no—
394C22×C79—28no—
395C22×C79—28no—
396C22×C79—28no—
397C22×C79—416no—
398C22×C79C22×#4112yes—
399C22×C79C2×2−1+412yes—
400C22×C79#58512yes—
401C22×C79C2611yescharacteristic
402C2×D79—22no—
403C2×D79—22no—
404C2×D79—28no—
405C2×D79C22×#4114yes—
406C4×C79—24no—
407C4×C79—24no—
408C4×C79—24no—
409C4×C79—24no—
410C4×C79—22no—
411C4×C79C22×#4114yes—
412C4×C79C2×2−1+414yes—
413Dic79—28no—
414Dic79—24no—
415Dic79—24no—
416Dic79—22no—
417Dic79—22no—
418Dic79—24no—
419Dic79—24no—
420Dic79C22×#4114yes—
421C2×#3507—791nomaximal, Sylow
422C2×C79—48no—
423C2×C79#350714yescomplemented
424C2×C79C23×#4111yescharacteristic
425C2×C79C22×2−1+411yescharacteristic
426C2×C79C2×#58511yescharacteristic
427D79—24no—
428#3507—7932no—
429C2×#559—791no—
430C2×#559D7911yescharacteristic, complemented
431C2×#557—791no—
432C2×#557—791no—
433C2×#556—792no—
434C2×#556—792no—
435C2×#556—792no—
436C2×#554—792no—
437C2×#552—794no—
438C2×#539—794no—
439C2×#536—792no—
440C2×#533—791no—
441C2×#532—791no—
442C2×#529—792no—
443C2×#529—792no—
444C2×#520—792no—
445C22×C4×Q8—791no—
446C79C2×#350711yescharacteristic, complemented, Sylow
447C22×#41—792no—
448C23×Q8—791no—
449#559—7916no—
450#559C2×D79116yescomplemented
451#557—7916no—
452#557—7916no—
453#556—7932no—
454#556—7932no—
455#556—7932no—
456#554—7932no—
457#552—7964no—
458#539—7964no—
459#536—7932no—
460#533—7916no—
461#532—7916no—
462C2×C4⋊Q8—791no—
463C2×C4⋊Q8—792no—
464C2×C4⋊Q8—791no—
465C2×C4⋊Q8—791no—
466C2×C4⋊Q8—792no—
467C2×#127C2×D7911yescharacteristic
468#529—7932no—
469#529—7932no—
470C2×#126—794no—
471C2×#126—794no—
472C2×#126—794no—
473C2×#126—794no—
474C2×#125—792no—
475C2×#125—792no—
476C2×#125—794no—
477C2×#125—794no—
478C2×#125—792no—
479C2×#124—792no—
480C2×#124—792no—
481C2×#124—792no—
482C2×#124C2×D7912yes—
483C2×#124C2×D7912yes—
484C2×#123—794no—
485C2×#123—794no—
486C2×#123—794no—
487C2×#123C2×D7914yes—
488C2×C22⋊Q8—791no—
489C2×C22⋊Q8—794no—
490C2×C22⋊Q8—791no—
491C2×C22⋊Q8—792no—
492C2×C22⋊Q8—794no—
493C2×C22⋊Q8—794no—
494C2×C22⋊Q8—794no—
495C2×#121—792no—
496C2×#121—792no—
497#520—7932no—
498C2×C4×Q8—791no—
499C2×C4×Q8—792no—
500C2×C4×Q8—7916no—
501C2×C4×Q8—792no—
502C2×C4×Q8—791no—
503C2×C4×Q8—792no—
504C2×C4×Q8—792no—
505C2×C4×Q8—791no—
506C2×C4×Q8—792no—
507C2×C4×Q8—792no—
508C2×C4×Q8—792no—
509C2×C4×Q8—791no—
510C2×C4×Q8C2×D7911yescharacteristic
511C2×C4×Q8C2×D7911yescharacteristic
512C2×C4×D4—792no—
513C2×C4×D4—792no—
514C2×C4×D4—792no—
515C2×C4×D4—792no—
516C2×C4×D4—794no—
517C2×C4×D4—794no—
518C2×C4×D4C2×D7912yes—
519C2×C4×D4C2×D7912yes—
520C2×#117—794no—
521C2×#117—794no—
522C2×#117—794no—
523C2×#117—792no—
524C22×C4⋊C4—794no—
525C22×C4⋊C4—791no—
526C22×C4⋊C4—792no—
527C22×C42—792no—
528C22×C42—791no—
529C2×#41—7916no—
530C2×#41—15816no—
531C22×Q8—798no—
532C22×Q8—792no—
533C22×Q8—791no—
534C22×Q8—792no—
535C22×Q8—791no—
536C22×Q8—792no—
537C22×Q8—1588no—
538C22×Q8C22×D7911yescharacteristic
539C22×Q8C22×D7911yescharacteristic
540C22×D4—794no—
541C22×D4C22×D7912yes—
542C22×D4C22×D7912yes—
543C22×D4C22×D7912yes—
544C23×C4—794no—
545C23×C4—792no—
546C23×C4—791no—
547C23×C4—791no—
548C23×C4—794no—
549C23×C4—792no—
550C23×C4—791no—
551C23×C4C22×D7914yes—
552C4⋊Q8—798no—
553C4⋊Q8—7916no—
554C4⋊Q8—798no—
555C4⋊Q8—798no—
556C4⋊Q8—7916no—
557#127C22×D7918yes—
558#126—7932no—
559#126—7932no—
560#126—7932no—
561#126—7932no—
562#125—7916no—
563#125—7916no—
564#125—7932no—
565#125—7932no—
566#125—7916no—
567#124—7916no—
568#124—7916no—
569#124—7916no—
570#124C22×D79116yes—
571#124C22×D79116yes—
572#123—7932no—
573#123—7932no—
574#123—7932no—
575#123C22×D79132yes—
576C22⋊Q8—798no—
577C22⋊Q8—7932no—
578C22⋊Q8—798no—
579C22⋊Q8—7916no—
580C22⋊Q8—7932no—
581C22⋊Q8—7932no—
582C22⋊Q8—7932no—
583#121—7916no—
584#121—7916no—
585C4×Q8—798no—
586C4×Q8—7916no—
587C4×Q8—7916no—
588C4×Q8—798no—
589C4×Q8—7916no—
590C4×Q8—7916no—
591C4×Q8—798no—
592C4×Q8—7916no—
593C4×Q8—7916no—
594C4×Q8—7916no—
595C4×Q8—798no—
596C4×Q8C22×D7918yes—
597C4×Q8C22×D7918yes—
598C4×D4—7916no—
599C4×D4—7916no—
600C4×D4—7916no—
601C4×D4—7916no—
602C4×D4—7932no—
603C4×D4—7932no—
604C4×D4C22×D79116yes—
605C4×D4C22×D79116yes—
606#117—7932no—
607#117—7932no—
608#117—7932no—
609#117—7916no—
610C2×C4⋊C4—792no—
611C2×C4⋊C4—792no—
612C2×C4⋊C4—791no—
613C2×C4⋊C4—794no—
614C2×C4⋊C4—794no—
615C2×C4⋊C4—792no—
616C2×C4⋊C4—792no—
617C2×C4⋊C4—792no—
618C2×C4⋊C4—7932no—
619C2×C4⋊C4—792no—
620C2×C4⋊C4—792no—
621C2×C4⋊C4—792no—
622C2×C4⋊C4—794no—
623C2×C4⋊C4—794no—
624C2×C4⋊C4—791no—
625C2×C4⋊C4—792no—
626C2×C4⋊C4—792no—
627C2×C4⋊C4—792no—
628C2×C4⋊C4—794no—
629C2×C4⋊C4—794no—
630C2×C4⋊C4—792no—
631C2×C4⋊C4—798no—
632C2×C4⋊C4—7916no—
633C2×C4⋊C4C22×D7911yescharacteristic
634C2×C4⋊C4C22×D7912yes—
635C2×C4⋊C4C22×D7911yescharacteristic
636C2×C4⋊C4C22×D7912yes—
637C2×C22⋊C4—794no—
638C2×C22⋊C4—794no—
639C2×C22⋊C4—794no—
640C2×C22⋊C4—794no—
641C2×C22⋊C4—794no—
642C2×C22⋊C4—792no—
643C2×C22⋊C4—792no—
644C2×C22⋊C4C22×D7914yes—
645C2×C22⋊C4C22×D7914yes—
646C2×C22⋊C4C22×D7914yes—
647C2×C42—794no—
648C2×C42—794no—
649C2×C42—792no—
650C2×C42—792no—
651C2×C42—792no—
652C2×C42—791no—
653C2×C42—791no—
654C2×C42—792no—
655C2×C42—791no—
656C2×C42—7916no—
657C2×C42—798no—
658C2×C42C22×D7912yes—
659C2×C42C22×D7912yes—
660C2×C42C22×D7911yescharacteristic
661C24—791no—
662C24C23×D7914yes—
663#41—15864no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—3164no—
667C2×Q8—798no—
668C2×Q8—794no—
669C2×Q8—798no—
670C2×Q8—794no—
671C2×Q8—798no—
672C2×Q8—1588no—
673C2×Q8—15832no—
674C2×Q8—1584no—
675C2×Q8—1588no—
676C2×Q8—1584no—
677C2×Q8C23×D7914yes—
678C2×Q8C23×D7914yes—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—44no—
682C2×D4—7916no—
683C2×D4—15816no—
684C2×D4C23×D7918yes—
685C2×D4C23×D7918yes—
686C2×D4C23×D7918yes—
687C22×C4—48no—
688C22×C4—3164no—
689C22×C4—3162no—
690C22×C4—3168no—
691C22×C4—7916no—
692C22×C4—798no—
693C22×C4—794no—
694C22×C4—791no—
695C22×C4—798no—
696C22×C4—794no—
697C22×C4—7916no—
698C22×C4—791no—
699C22×C4—792no—
700C22×C4—792no—
701C22×C4—791no—
702C22×C4—792no—
703C22×C4—794no—
704C22×C4—792no—
705C22×C4—794no—
706C22×C4—798no—
707C22×C4—1588no—
708C22×C4—15816no—
709C22×C4—1584no—
710C22×C4C23×D7912yes—
711C22×C4C23×D7912yes—
712C22×C4C23×D7912yes—
713C22×C4C23×D7911yescharacteristic
714C22×C4C23×D7912yes—
715C22×C4C23×D79116yes—
716C22×C4C23×D7911yescharacteristic
717C22×C4C23×D7911yescharacteristic
718C4⋊C4—798no—
719C4⋊C4—798no—
720C4⋊C4—7916no—
721C4⋊C4—7916no—
722C4⋊C4—798no—
723C4⋊C4—798no—
724C4⋊C4—798no—
725C4⋊C4—798no—
726C4⋊C4—7916no—
727C4⋊C4—798no—
728C4⋊C4—7916no—
729C4⋊C4—798no—
730C4⋊C4—794no—
731C4⋊C4—798no—
732C4⋊C4—798no—
733C4⋊C4—7916no—
734C4⋊C4—794no—
735C4⋊C4—798no—
736C4⋊C4—798no—
737C4⋊C4—7916no—
738C4⋊C4C23×D7914yes—
739C4⋊C4C23×D7918yes—
740C4⋊C4C23×D7914yes—
741C4⋊C4C23×D7918yes—
742C22⋊C4—7916no—
743C22⋊C4—7916no—
744C22⋊C4—7916no—
745C22⋊C4—7916no—
746C22⋊C4—7916no—
747C22⋊C4—798no—
748C22⋊C4—798no—
749C22⋊C4C23×D79116yes—
750C22⋊C4C23×D79116yes—
751C22⋊C4C23×D79116yes—
752C42—798no—
753C42—798no—
754C42—794no—
755C42—794no—
756C42—798no—
757C42—794no—
758C42—7916no—
759C42—7916no—
760C42—798no—
761C42C23×D7918yes—
762C42C23×D7914yes—
763C42C23×D7918yes—
764C23—28no—
765C23—28no—
766C23—28no—
767C23—792no—
768C23—794no—
769C23—1582no—
770C23—1582no—
771C23C24×D7918yes—
772C23C24×D7911yescharacteristic
773Q8—28no—
774Q8—28no—
775Q8—3168no—
776Q8—15816no—
777Q8—1588no—
778Q8—1588no—
779Q8—15816no—
780D4—216no—
781D4—216no—
782D4—48no—
783D4—15832no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—416no—
790C2×C4—3168no—
791C2×C4—3164no—
792C2×C4—31616no—
793C2×C4—792no—
794C2×C4—794no—
795C2×C4—7916no—
796C2×C4—792no—
797C2×C4—794no—
798C2×C4—794no—
799C2×C4—794no—
800C2×C4—792no—
801C2×C4—798no—
802C2×C4—794no—
803C2×C4—15816no—
804C2×C4—15832no—
805C2×C4—1582no—
806C2×C4—1584no—
807C2×C4—1584no—
808C2×C4—1584no—
809C2×C4—1582no—
810C2×C4—1588no—
811C2×C4—1584no—
812C2×C4—1588no—
813C2×C4#41×D7914yes—
814C2×C4#1457920814yes—
815C2×C4C24×D7914yes—
816C2×C4C24×D7914yes—
817C2×C4C24×D7914yes—
818C2×C4C24×D7912yes—
819C2×C4C24×D7914yes—
820C2×C4C24×D7912yes—
821C2×C4C24×D7912yes—
822C22—28no—
823C22—28no—
824C22—28no—
825C22—416no—
826C22—794no—
827C22—1582no—
828C22—1582no—
829C22—1588no—
830C22C2×#41×D7912yes—
831C22C2×#1457920812yes—
832C22#1909939812yes—
833C22C25×D7911yescharacteristic
834C4—24no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—22no—
839C4—794no—
840C4—1588no—
841C4—1584no—
842C4—1582no—
843C4—1584no—
844C4—1584no—
845C4—1584no—
846C4—1582no—
847C4C2×#41×D7914yes—
848C4C2×#1457920814yes—
849C2—48no—
850C2—1584no—
851C2#2377725714yesdirect product factor
852C2C22×#41×D7911yescharacteristic
853C2C22×#1457920811yescharacteristic
854C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#559×C79C2
socleC23×C79C25
prime radicalC2×#19099111C2
hypercenterC2×#559D79
hypocenterC79C2×#3507
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #23777257C2direct (N × H)
2. C2×#19099299C2semidirect
3. C2×#19099292C2semidirect
4. C2×#19099291C2semidirect
5. C2×#19099283C2semidirect
6. C2×#19099282C2semidirect
7. C2×#19099282C2semidirect
8. C2×#19099272C2semidirect
9. C2×#19099250C2semidirect
10. C2×#19099156C2semidirect
11. C2×#19099133C2semidirect
12. C2×#19099117C2semidirect
14. C2×#19099095C2semidirect
15. C2×#19099092C2semidirect
16. C2×#19099042C2semidirect
17. C2×C4×Q8×D79C2semidirect
18. C2×#559×C79C2semidirect
21. #19099299C22semidirect
22. #19099292C22semidirect
23. #19099291C22semidirect
24. #19099283C22semidirect
25. #19099282C22semidirect
26. #19099282C22semidirect
27. #19099272C22semidirect
28. #19099250C22semidirect
29. #19099156C22semidirect
30. #19099133C22semidirect
31. #19099117C22semidirect
38. #19099095C22semidirect
39. #19099092C22semidirect
64. #19099042C22semidirect
76. C4×Q8×D79C22semidirect
92. #559×C79C22semidirect
423. C2×C79#3507semidirect
430. C2×#559D79semidirect
446. C79C2×#3507semidirect
450. #559C2×D79semidirect
851. C2#23777257direct (N × H)

Maximal subgroups

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

subgroupindex
#237772572
C2×#190992992
C2×#190992922
C2×#190992912
C2×#190992832
C2×#190992822
C2×#190992722
C2×#190992502
C2×#190991562
C2×#190991332
C2×#190991172
C2×#190991112
C2×#190990952
C2×#190990922
C2×#190990422
C2×C4×Q8×D792
C2×#559×C792
C2×#350779