Finite Group Databasebeta

← C2×#23777266 #35196350

Subgroups — C2×#23777266 #35196350

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#23777266C2132yesmaximal, direct product factor
2C2×#19099298C211yesmaximal, characteristic, complemented
3C2×#19099298C211yesmaximal, characteristic, complemented
4C2×#19099288C211yesmaximal, characteristic, complemented
5C2×#19099287C212yesmaximal, complemented
6C2×#19099285C212yesmaximal, complemented
7C2×#19099285C212yesmaximal, complemented
8C2×#19099269C212yesmaximal, complemented
9C2×#19099245C214yesmaximal, complemented
10C2×#19099161C214yesmaximal, complemented
11C2×#19099138C212yesmaximal, complemented
12C2×#19099117C211yesmaximal, characteristic, complemented
13C2×#19099114C211yesmaximal, characteristic
14C2×#19099100C212yesmaximal, complemented
15C2×#19099098C212yesmaximal, complemented
16C2×#19099045C212yesmaximal, complemented
17C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
18C2×#557×C79C211yesmaximal, characteristic, complemented
19C22×#11929625C2212yes—
20C22×Q8×D79C2211yescharacteristic
21#19099298C22116yescomplemented
22#19099298C22116yescomplemented
23#19099288C22116yescomplemented
24#19099287C22132yescomplemented
25#19099285C22132yescomplemented
26#19099285C22132yescomplemented
27#19099269C22132yescomplemented
28#19099245C22164yescomplemented
29#19099161C22164yescomplemented
30#19099138C22132yescomplemented
31#19099117C22116yescomplemented
32#19099114C22116yes—
33C2×#14579160C2211yescharacteristic
34C2×#14579159C2211yescharacteristic
35C2×#14579159C2212yes—
36C2×#14579158C2211yescharacteristic
37#19099100C22132yescomplemented
38#19099098C22132yescomplemented
39C2×#14579156C2214yes—
40C2×#14579156C2214yes—
41C2×#14579156C2214yes—
42C2×#14579155C2214yes—
43C2×#14579152C2212yes—
44C2×#14579151C2212yes—
45C2×#14579151C2214yes—
46C2×#14579150C2212yes—
47C2×#14579150C2212yes—
48C2×#14579150C2212yes—
49C2×#14579149C2212yes—
50C2×#14579149C2212yes—
51C2×#14579146C2214yes—
52C2×#14579146C2214yes—
53C2×#14579146C2214yes—
54C2×#14579146C2214yes—
55C2×#14579141C2211yescharacteristic
56C2×#14579141C2214yes—
57C2×#14579139C2214yes—
58C2×#14579139C2214yes—
59C2×#14579139C2214yes—
60C2×#14579139C2212yes—
61C2×#14579137C2211yescharacteristic
62C2×#14579136C2212yes—
63C2×#14579136C2212yes—
64#19099045C22132yescomplemented
65C2×Q8×Dic79C2211yescharacteristic
66C2×Q8×Dic79C2212yes—
67C2×C4×Dic158C2212yes—
68C2×C4×Dic158C2211yescharacteristic
69C2×C4×Dic158C2212yes—
70C2×C4×Dic158C2211yescharacteristic
71C2×#14579126C2212yes—
72C2×#14579126C2211yescharacteristic
73C2×#14579126C2212yes—
74C4×Q8×D79C22116yescomplemented
75C2×C4×D316C2214yes—
76C2×C4×D316C2212yes—
77C2×C4×D316C2212yes—
78C2×#14579123C2214yes—
79C2×#14579123C2212yes—
80C2×#14579123C2212yes—
81C2×#14579123C2212yes—
82C2×#14579123C2212yes—
83C2×#14579119C2214yes—
84C2×#14579118C2214yes—
85C2×#14579118C2212yes—
86C2×#14579118C2214yes—
87C2×C4⋊C4×D79C2211yescharacteristic
88C2×C4⋊C4×D79C2212yes—
89C2×C4⋊C4×D79C2214yes—
90C2×C42×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92#557×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×C4⋊Q8×C79C2212yes—
95C2×#125×C79C2214yes—
96C2×#125×C79C2212yes—
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×Q8×C79C2212yes—
99C2×C4×Q8×C79C2212yes—
100C2×C4×Q8×C79C2211yescharacteristic
101C2×#11929625—216no—
102C2×#11929625C23116yes—
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2312yes—
105C22×Dic158C2311yescharacteristic
106C22×Dic158C2312yes—
107C2×Q8×D79—28no—
108C2×Q8×D79C2318yes—
109C22×D316C2312yes—
110C22×D316C2314yes—
111C22×D316C2312yes—
112C22×D316C2312yes—
113C22×C4×D79C2311yescharacteristic
114C22×C4×D79C2312yes—
115C22×C4×D79C2314yes—
116C22×C4×D79C2312yes—
117C22×C4×D79C2311yescharacteristic
118C22×C4×D79C2314yes—
119C22×C4×D79C2314yes—
120C22×C4×D79C2311yescharacteristic
121#14579160C2318yes—
122#14579159C23116yes—
123#14579159C2318yes—
124#14579158C2318yes—
125#14579156C23132yes—
126#14579156C23132yes—
127#14579156C23132yes—
128#14579155C23132yes—
129#14579152C23116yes—
130#14579151C23132yes—
131#14579151C23116yes—
132#14579150C23116yes—
133#14579150C23116yes—
134#14579150C23116yes—
135#14579149C23116yes—
136#14579149C23116yes—
137#14579146C23132yes—
138#14579146C23132yes—
139#14579146C23132yes—
140#14579146C23132yes—
141#14579141C23132yes—
142#14579141C2318yes—
143#14579139C23132yes—
144#14579139C23132yes—
145#14579139C23116yes—
146#14579139C23132yes—
147#14579137C2318yes—
148#14579136C23116yes—
149#14579136C23116yes—
150Q8×Dic79C2318yes—
151Q8×Dic79C23116yes—
152C4×Dic158C23116yes—
153C4×Dic158C2318yes—
154C4×Dic158C23116yes—
155C4×Dic158C2318yes—
156#14579126C23116yes—
157#14579126C2318yes—
158#14579126C23116yes—
159C4×D316C23132yes—
160C4×D316C23116yes—
161C4×D316C23116yes—
162#14579123C23132yes—
163#14579123C23116yes—
164#14579123C23116yes—
165#14579123C23116yes—
166#14579123C23116yes—
167#14579119C23132yes—
168#14579118C23116yes—
169#14579118C23132yes—
170#14579118C23132yes—
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2314yes—
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2311yescharacteristic
176C2×Dic79⋊C4C2312yes—
177C2×Dic79⋊C4C2312yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C4⋊C4×D79C23116yes—
187C4⋊C4×D79C23132yes—
188C4⋊C4×D79C2318yes—
189C2×(C2×D79)⋊C4C2314yes—
190C2×(C2×D79)⋊C4C2312yes—
191C2×(C2×D79)⋊C4C2314yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×(C2×D79)⋊C4C2314yes—
199C2×C4×Dic79C2312yes—
200C2×C4×Dic79C2312yes—
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2314yes—
206C2×C4×Dic79C2312yes—
207C42×D79C23116yes—
208C42×D79C2318yes—
209C22×Q8×C79C2311yescharacteristic
210C22×Q8×C79C2311yescharacteristic
211C22×Q8×C79C2312yes—
212C4⋊Q8×C79C23116yes—
213C4⋊Q8×C79C2318yes—
214#125×C79C23132yes—
215#125×C79C23116yes—
216C4×Q8×C79C2318yes—
217C4×Q8×C79C23116yes—
218C4×Q8×C79C23116yes—
219C4×Q8×C79C2318yes—
220C2×C4⋊C4×C79C2311yescharacteristic
221C2×C4⋊C4×C79C2314yes—
222C2×C4⋊C4×C79C2312yes—
223C2×C4⋊C4×C79C2311yescharacteristic
224C2×C4⋊C4×C79C2312yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2314yes—
227C2×C4⋊C4×C79C2314yes—
228C2×C4⋊C4×C79C2312yes—
229C2×C42×C79C2312yes—
230C2×C42×C79C2314yes—
231C2×C42×C79C2311yescharacteristic
232C2×C42×C79C2312yes—
233C23×D79C2414yes—
234C23×D79C2411yescharacteristic
235#11929625—264no—
236C2×Dic158—28no—
237C2×Dic158—24no—
238C2×Dic158—24no—
239C2×Dic158—44no—
240C2×Dic158C2418yes—
241C2×Dic158C2414yes—
242C2×Dic158C2414yes—
243C2×Dic158C2418yes—
244Q8×D79—232no—
245C2×D316—216no—
246C2×D316—28no—
247C2×D316—28no—
248C2×D316—44no—
249C2×D316C24116yes—
250C2×D316C2418yes—
251C2×D316C2418yes—
252C2×D316C2418yes—
253C22×Dic79C2412yes—
254C22×Dic79C2411yescharacteristic
255C22×Dic79C2412yes—
256C22×Dic79C2412yes—
257C22×Dic79C2411yescharacteristic
258C22×Dic79C2412yes—
259C22×Dic79C2411yescharacteristic
260C2×C4×D79—216no—
261C2×C4×D79—28no—
262C2×C4×D79—24no—
263C2×C4×D79—44no—
264C2×C4×D79—48no—
265C2×C4×D79—48no—
266C2×C4×D79—42no—
267C2×C4×D79#4118yes—
268C2×C4×D79C2418yes—
269C2×C4×D79C24116yes—
270C2×C4×D79C2414yes—
271C2×C4×D79C2418yes—
272C2×C4×D79C2414yes—
273C2×C4×D79C24116yes—
274C2×C4×D79C24116yes—
275C2×C4×D79C2414yes—
276C4⋊Dic79C2414yes—
277C4⋊Dic79C24116yes—
278C4⋊Dic79C2418yes—
279C4⋊Dic79C2418yes—
280C4⋊Dic79C2414yes—
281Dic79⋊C4C2418yes—
282Dic79⋊C4C2418yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C2418yes—
285Dic79⋊C4C2418yes—
286Dic79⋊C4C2418yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C24116yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C2418yes—
291(C2×D79)⋊C4C24116yes—
292(C2×D79)⋊C4C2418yes—
293(C2×D79)⋊C4C24116yes—
294(C2×D79)⋊C4C2418yes—
295(C2×D79)⋊C4C24116yes—
296(C2×D79)⋊C4C24116yes—
297(C2×D79)⋊C4C24116yes—
298(C2×D79)⋊C4C24116yes—
299(C2×D79)⋊C4C24116yes—
300(C2×D79)⋊C4C24116yes—
301C4×Dic79C2418yes—
302C4×Dic79C2418yes—
303C4×Dic79C2414yes—
304C4×Dic79C2414yes—
305C4×Dic79C2418yes—
306C4×Dic79C2414yes—
307C4×Dic79C24116yes—
308C4×Dic79C2418yes—
309C2×Q8×C79—24no—
310C2×Q8×C79—28no—
311C2×Q8×C79—24no—
312C2×Q8×C79C2414yes—
313C2×Q8×C79C2418yes—
314C2×Q8×C79C2414yes—
315C22×C4×C79C2412yes—
316C22×C4×C79C2412yes—
317C22×C4×C79C2412yes—
318C22×C4×C79C2412yes—
319C22×C4×C79C2411yescharacteristic
320C22×C4×C79C2414yes—
321C22×C4×C79C2411yescharacteristic
322C22×C4×C79C2411yescharacteristic
323C4⋊C4×C79C2414yes—
324C4⋊C4×C79C24116yes—
325C4⋊C4×C79C2418yes—
326C4⋊C4×C79C2414yes—
327C4⋊C4×C79C2418yes—
328C4⋊C4×C79C2418yes—
329C4⋊C4×C79C24116yes—
330C4⋊C4×C79C24116yes—
331C4⋊C4×C79C2418yes—
332C42×C79C2418yes—
333C42×C79C24116yes—
334C42×C79C2414yes—
335C42×C79C2418yes—
336C23×C79C2511yescharacteristic
337C22×D79—22no—
338C22×D79—22no—
339C22×D79—28no—
340C22×D79—28no—
341C22×D79—28no—
342C22×D79C2×#4114yes—
343C22×D79C2518yes—
344C22×D79C2512yes—
345Q8×C79—28no—
346Q8×C79—216no—
347Q8×C79—28no—
348C2×C4×C79—28no—
349C2×C4×C79—24no—
350C2×C4×C79—24no—
351C2×C4×C79—24no—
352C2×C4×C79—24no—
353C2×C4×C79—22no—
354C2×C4×C79C2×#4114yes—
355C2×C4×C792−1+414yes—
356C2×C4×C79C2514yes—
357C2×C4×C79C2518yes—
358C2×C4×C79C2514yes—
359C2×C4×C79C2512yes—
360C2×C4×C79C2514yes—
361C2×C4×C79C2514yes—
362C2×C4×C79C2512yes—
363C2×C4×C79C2512yes—
364C2×Dic79—24no—
365C2×Dic79—22no—
366C2×Dic79—24no—
367C2×Dic79—24no—
368C2×Dic79—24no—
369C2×Dic79—22no—
370C2×Dic79C2×#4114yes—
371C2×Dic79C2512yes—
372C2×Dic79C2514yes—
373C2×Dic79C2514yes—
374C2×Dic79C2514yes—
375C2×Dic79C2512yes—
376C2×Dic79C2514yes—
377C2×Dic79C2512yes—
378D316—232no—
379D316—216no—
380D316—216no—
381D316—48no—
382C4×D79—216no—
383C4×D79—28no—
384C4×D79—232no—
385C4×D79—44no—
386C4×D79—416no—
387C4×D79—416no—
388C4×D79—48no—
389C4×D79C2×#41116yes—
390Dic158—28no—
391Dic158—28no—
392Dic158—216no—
393Dic158—48no—
394C22×C79C22×#4112yes—
395C22×C79C2×2−1+412yes—
396C22×C79#58512yes—
397C22×C79C2611yescharacteristic
398C2×D79—22no—
399C2×D79—22no—
400C2×D79—28no—
401C2×D79—28no—
402C2×D79—28no—
403C2×D79—28no—
404C2×D79—416no—
405C2×D79C22×#4114yes—
406C4×C79—24no—
407C4×C79—28no—
408C4×C79—24no—
409C4×C79—24no—
410C4×C79—24no—
411C4×C79—22no—
412C4×C79C22×#4114yes—
413C4×C79C2×2−1+414yes—
414Dic79—24no—
415Dic79—24no—
416Dic79—22no—
417Dic79—22no—
418Dic79—24no—
419Dic79—24no—
420Dic79C22×#4114yes—
421C2×#3507—791nomaximal, Sylow
422C2×C79#350714yescomplemented
423C2×C79C23×#4111yescharacteristic
424C2×C79C22×2−1+411yescharacteristic
425C2×C79C2×#58511yescharacteristic
426D79—24no—
427D79—48no—
428#3507—7932no—
429C2×#559—791no—
430C2×#559—791no—
431C2×#557—791no—
432C2×#557D7911yescharacteristic, complemented
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#559—7916no—
451#557—7916no—
452#557C2×D79116yescomplemented
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⋊Q8C2×D7911yescharacteristic
466C2×C4⋊Q8C2×D7912yes—
467C2×#127—791no—
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×#125C2×D7912yes—
478C2×#125C2×D7914yes—
479C2×#124—792no—
480C2×#124—792no—
481C2×#124—792no—
482C2×#124—792no—
483C2×#124—792no—
484C2×#123—794no—
485C2×#123—794no—
486C2×#123—794no—
487C2×#123—794no—
488C2×C22⋊Q8—791no—
489C2×C22⋊Q8—791no—
490C2×C22⋊Q8—792no—
491C2×C22⋊Q8—794no—
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—791no—
508C2×C4×Q8C2×D7911yescharacteristic
509C2×C4×Q8C2×D7912yes—
510C2×C4×Q8C2×D7912yes—
511C2×C4×Q8C2×D7911yescharacteristic
512C2×C4×D4—794no—
513C2×C4×D4—792no—
514C2×C4×D4—792no—
515C2×C4×D4—792no—
516C2×C4×D4—792no—
517C2×C4×D4—794no—
518C2×C4×D4—792no—
519C2×C4×D4—792no—
520C2×#117—794no—
521C2×#117—792no—
522C2×#117—794no—
523C2×#117—794no—
524C22×C4⋊C4—791no—
525C22×C4⋊C4—792no—
526C22×C4⋊C4—794no—
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—1588no—
537C22×Q8C22×D7911yescharacteristic
538C22×Q8C22×D7912yes—
539C22×Q8C22×D7911yescharacteristic
540C22×D4—792no—
541C22×D4—792no—
542C22×D4—794no—
543C22×D4—792no—
544C23×C4—792no—
545C23×C4—791no—
546C23×C4—794no—
547C23×C4—794no—
548C23×C4—791no—
549C23×C4—794no—
550C23×C4—792no—
551C23×C4—791no—
552C4⋊Q8—798no—
553C4⋊Q8—7916no—
554C4⋊Q8—798no—
555C4⋊Q8C22×D7918yes—
556C4⋊Q8C22×D79116yes—
557#127—798no—
558#126—7932no—
559#126—7932no—
560#126—7932no—
561#126—7932no—
562#125—7916no—
563#125—7916no—
564#125—7932no—
565#125C22×D79116yes—
566#125C22×D79132yes—
567#124—7916no—
568#124—7916no—
569#124—7916no—
570#124—7916no—
571#124—7916no—
572#123—7932no—
573#123—7932no—
574#123—7932no—
575#123—7932no—
576C22⋊Q8—798no—
577C22⋊Q8—798no—
578C22⋊Q8—7916no—
579C22⋊Q8—7932no—
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—798no—
594C4×Q8C22×D7918yes—
595C4×Q8C22×D79116yes—
596C4×Q8C22×D79116yes—
597C4×Q8C22×D7918yes—
598C4×D4—7932no—
599C4×D4—7916no—
600C4×D4—7916no—
601C4×D4—7916no—
602C4×D4—7916no—
603C4×D4—7932no—
604C4×D4—7916no—
605C4×D4—7916no—
606#117—7932no—
607#117—7916no—
608#117—7932no—
609#117—7932no—
610C2×C4⋊C4—792no—
611C2×C4⋊C4—792no—
612C2×C4⋊C4—791no—
613C2×C4⋊C4—794no—
614C2×C4⋊C4—792no—
615C2×C4⋊C4—792no—
616C2×C4⋊C4—792no—
617C2×C4⋊C4—792no—
618C2×C4⋊C4—792no—
619C2×C4⋊C4—792no—
620C2×C4⋊C4—794no—
621C2×C4⋊C4—791no—
622C2×C4⋊C4—792no—
623C2×C4⋊C4—794no—
624C2×C4⋊C4—792no—
625C2×C4⋊C4—798no—
626C2×C4⋊C4—7916no—
627C2×C4⋊C4—7932no—
628C2×C4⋊C4C22×D7911yescharacteristic
629C2×C4⋊C4C22×D7914yes—
630C2×C4⋊C4C22×D7912yes—
631C2×C4⋊C4C22×D7914yes—
632C2×C4⋊C4C22×D7911yescharacteristic
633C2×C4⋊C4C22×D7912yes—
634C2×C4⋊C4C22×D7912yes—
635C2×C4⋊C4C22×D7912yes—
636C2×C4⋊C4C22×D7914yes—
637C2×C22⋊C4—794no—
638C2×C22⋊C4—792no—
639C2×C22⋊C4—792no—
640C2×C22⋊C4—794no—
641C2×C22⋊C4—794no—
642C2×C22⋊C4—794no—
643C2×C22⋊C4—794no—
644C2×C22⋊C4—794no—
645C2×C22⋊C4—794no—
646C2×C22⋊C4—794no—
647C2×C42—794no—
648C2×C42—792no—
649C2×C42—792no—
650C2×C42—792no—
651C2×C42—791no—
652C2×C42—791no—
653C2×C42—792no—
654C2×C42—791no—
655C2×C42—7916no—
656C2×C42—798no—
657C2×C42C22×D7914yes—
658C2×C42C22×D7912yes—
659C2×C42C22×D7912yes—
660C2×C42C22×D7911yescharacteristic
661C24—791no—
662C24—794no—
663#41—15864no—
664C2×Q8—24no—
665C2×Q8—28no—
666C2×Q8—24no—
667C2×Q8—3164no—
668C2×Q8—798no—
669C2×Q8—794no—
670C2×Q8—798no—
671C2×Q8—794no—
672C2×Q8—1588no—
673C2×Q8—15832no—
674C2×Q8—1584no—
675C2×Q8—1584no—
676C2×Q8C23×D7914yes—
677C2×Q8C23×D7918yes—
678C2×Q8C23×D7914yes—
679C2×D4—3164no—
680C2×D4—798no—
681C2×D4—798no—
682C2×D4—7916no—
683C2×D4—798no—
684C2×D4—15816no—
685C2×D4—1588no—
686C2×D4—1588no—
687C22×C4—3164no—
688C22×C4—3168no—
689C22×C4—3168no—
690C22×C4—3162no—
691C22×C4—798no—
692C22×C4—794no—
693C22×C4—7916no—
694C22×C4—7916no—
695C22×C4—791no—
696C22×C4—798no—
697C22×C4—794no—
698C22×C4—791no—
699C22×C4—792no—
700C22×C4—792no—
701C22×C4—791no—
702C22×C4—792no—
703C22×C4—792no—
704C22×C4—794no—
705C22×C4—798no—
706C22×C4—7916no—
707C22×C4—15816no—
708C22×C4—1588no—
709C22×C4—1584no—
710C22×C4C23×D7912yes—
711C22×C4C23×D7912yes—
712C22×C4C23×D7914yes—
713C22×C4C23×D7911yescharacteristic
714C22×C4C23×D7912yes—
715C22×C4C23×D7912yes—
716C22×C4C23×D7911yescharacteristic
717C22×C4C23×D7911yescharacteristic
718C4⋊C4—798no—
719C4⋊C4—798no—
720C4⋊C4—798no—
721C4⋊C4—798no—
722C4⋊C4—798no—
723C4⋊C4—798no—
724C4⋊C4—7916no—
725C4⋊C4—798no—
726C4⋊C4—7916no—
727C4⋊C4—798no—
728C4⋊C4—794no—
729C4⋊C4—7916no—
730C4⋊C4—798no—
731C4⋊C4—798no—
732C4⋊C4—794no—
733C4⋊C4C23×D7914yes—
734C4⋊C4C23×D79116yes—
735C4⋊C4C23×D7918yes—
736C4⋊C4C23×D79116yes—
737C4⋊C4C23×D7914yes—
738C4⋊C4C23×D7918yes—
739C4⋊C4C23×D7918yes—
740C4⋊C4C23×D7918yes—
741C4⋊C4C23×D79116yes—
742C22⋊C4—7916no—
743C22⋊C4—798no—
744C22⋊C4—798no—
745C22⋊C4—7916no—
746C22⋊C4—7916no—
747C22⋊C4—7916no—
748C22⋊C4—7916no—
749C22⋊C4—7916no—
750C22⋊C4—7916no—
751C22⋊C4—7916no—
752C42—798no—
753C42—798no—
754C42—794no—
755C42—794no—
756C42—798no—
757C42—794no—
758C42—7916no—
759C42—798no—
760C42C23×D7918yes—
761C42C23×D7914yes—
762C42C23×D79116yes—
763C42C23×D7918yes—
764C23—792no—
765C23—794no—
766C23—798no—
767C23—1588no—
768C23—1588no—
769C23—1588no—
770C23—1582no—
771C23—1582no—
772C23C24×D7911yescharacteristic
773Q8—28no—
774Q8—28no—
775Q8—216no—
776Q8—3168no—
777Q8—15816no—
778Q8—1588no—
779Q8—1588no—
780D4—3168no—
781D4—15832no—
782D4—15816no—
783D4—15816no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—28no—
789C2×C4—24no—
790C2×C4—3168no—
791C2×C4—31616no—
792C2×C4—31616no—
793C2×C4—3164no—
794C2×C4—792no—
795C2×C4—794no—
796C2×C4—7916no—
797C2×C4—792no—
798C2×C4—794no—
799C2×C4—794no—
800C2×C4—794no—
801C2×C4—792no—
802C2×C4—794no—
803C2×C4—15832no—
804C2×C4—15816no—
805C2×C4—1582no—
806C2×C4—1584no—
807C2×C4—1584no—
808C2×C4—1584no—
809C2×C4—1582no—
810C2×C4—1584no—
811C2×C4—1588no—
812C2×C4#41×D7914yes—
813C2×C4#1457920914yes—
814C2×C4C24×D7914yes—
815C2×C4C24×D7914yes—
816C2×C4C24×D7918yes—
817C2×C4C24×D7912yes—
818C2×C4C24×D7914yes—
819C2×C4C24×D7914yes—
820C2×C4C24×D7912yes—
821C2×C4C24×D7912yes—
822C22—31616no—
823C22—794no—
824C22—1588no—
825C22—1588no—
826C22—1588no—
827C22—1582no—
828C22—1582no—
829C22—1588no—
830C22C2×#41×D7912yes—
831C22C2×#1457920912yes—
832C22#1909940012yes—
833C22C25×D7911yescharacteristic
834C4—28no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—24no—
839C4—22no—
840C4—794no—
841C4—1584no—
842C4—1582no—
843C4—1584no—
844C4—1584no—
845C4—1584no—
846C4—1582no—
847C4C2×#41×D7914yes—
848C4C2×#1457920914yes—
849C2—3168no—
850C2—1584no—
851C2#2377726614yesdirect product factor
852C2C22×#41×D7911yescharacteristic
853C2C22×#1457920911yescharacteristic
854C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#557×C79C2
socleC23×C79C25
prime radicalC2×#19099114C2
hypercenterC2×#557D79
hypocenterC79C2×#3507
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #23777266C2direct (N × H)
2. C2×#19099298C2semidirect
3. C2×#19099298C2semidirect
4. C2×#19099288C2semidirect
5. C2×#19099287C2semidirect
6. C2×#19099285C2semidirect
7. C2×#19099285C2semidirect
8. C2×#19099269C2semidirect
9. C2×#19099245C2semidirect
10. C2×#19099161C2semidirect
11. C2×#19099138C2semidirect
12. C2×#19099117C2semidirect
14. C2×#19099100C2semidirect
15. C2×#19099098C2semidirect
16. C2×#19099045C2semidirect
17. C2×C4×Q8×D79C2semidirect
18. C2×#557×C79C2semidirect
21. #19099298C22semidirect
22. #19099298C22semidirect
23. #19099288C22semidirect
24. #19099287C22semidirect
25. #19099285C22semidirect
26. #19099285C22semidirect
27. #19099269C22semidirect
28. #19099245C22semidirect
29. #19099161C22semidirect
30. #19099138C22semidirect
31. #19099117C22semidirect
37. #19099100C22semidirect
38. #19099098C22semidirect
64. #19099045C22semidirect
74. C4×Q8×D79C22semidirect
92. #557×C79C22semidirect
422. C2×C79#3507semidirect
432. C2×#557D79semidirect
446. C79C2×#3507semidirect
452. #557C2×D79semidirect
851. C2#23777266direct (N × H)

Maximal subgroups

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

subgroupindex
#237772662
C2×#190992982
C2×#190992882
C2×#190992872
C2×#190992852
C2×#190992692
C2×#190992452
C2×#190991612
C2×#190991382
C2×#190991172
C2×#190991142
C2×#190991002
C2×#190990982
C2×#190990452
C2×C4×Q8×D792
C2×#557×C792
C2×#350779