Finite Group Databasebeta

← C2×#23777255 #35196345

Subgroups — C2×#23777255 #35196345

Order 20224.

7130 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777255C2132yesmaximal, direct product factor
2C2×#19099295C212yesmaximal, complemented
3C2×#19099289C212yesmaximal, complemented
4C2×#19099287C211yesmaximal, characteristic, complemented
5C2×#19099280C214yesmaximal, complemented
6C2×#19099273C211yesmaximal, characteristic, complemented
7C2×#19099270C211yesmaximal, characteristic, complemented
8C2×#19099255C212yesmaximal, complemented
9C2×#19099252C212yesmaximal, complemented
10C2×#19099154C214yesmaximal, complemented
11C2×#19099136C212yesmaximal, complemented
12C2×#19099118C211yesmaximal, characteristic, complemented
13C2×#19099110C211yesmaximal, characteristic
14C2×#19099100C212yesmaximal, complemented
15C2×#19099092C212yesmaximal, complemented
16C2×#19099043C212yesmaximal, complemented
17C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
18C2×#556×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2212yes—
20C22×Q8×D79C2211yescharacteristic
21#19099295C22132yescomplemented
22#19099289C22132yescomplemented
23#19099287C22116yescomplemented
24#19099280C22164yescomplemented
25#19099273C22116yescomplemented
26#19099270C22116yescomplemented
27#19099255C22132yescomplemented
28#19099252C22132yescomplemented
29#19099154C22164yescomplemented
30#19099136C22132yescomplemented
31#19099118C22116yescomplemented
32#19099110C22116yes—
33C2×#14579161C2211yescharacteristic
34C2×#14579160C2211yescharacteristic
35C2×#14579160C2214yes—
36C2×#14579157C2211yescharacteristic
37#19099100C22132yescomplemented
38#19099092C22132yescomplemented
39C2×#14579156C2214yes—
40C2×#14579156C2214yes—
41C2×#14579154C2214yes—
42C2×#14579153C2214yes—
43C2×#14579153C2212yes—
44C2×#14579152C2212yes—
45C2×#14579152C2214yes—
46C2×#14579152C2212yes—
47C2×#14579150C2212yes—
48C2×#14579147C2212yes—
49C2×#14579147C2214yes—
50C2×#14579146C2214yes—
51C2×#14579145C2214yes—
52C2×#14579143C2214yes—
53C2×#14579143C2214yes—
54C2×#14579141C2212yes—
55C2×#14579141C2212yes—
56C2×#14579140C2212yes—
57C2×#14579139C2214yes—
58C2×#14579138C2214yes—
59C2×#14579137C2212yes—
60C2×#14579137C2212yes—
61C2×#14579136C2211yescharacteristic
62C2×#14579134C2212yes—
63C2×#14579132C2211yescharacteristic
64#19099043C22132yescomplemented
65C2×Q8×Dic79C2211yescharacteristic
66C2×Q8×Dic79C2212yes—
67C2×Q8×Dic79C2212yes—
68C2×C4×Dic158C2211yescharacteristic
69C2×C4×Dic158C2212yes—
70C2×C4×Dic158C2214yes—
71C2×#14579126C2211yescharacteristic
72C2×#14579126C2212yes—
73C2×#14579126C2212yes—
74C4×Q8×D79C22116yescomplemented
75C2×C4×D316C2214yes—
76C2×C4×D316C2212yes—
77C2×C4×D316C2211yescharacteristic
78C2×D4×Dic79C2212yes—
79C2×C4×C22⋊D79C2212yes—
80C2×(C22⋊D79)⋊C4C2214yes—
81C2×(C22⋊D79)⋊C4C2214yes—
82C2×#14579119C2212yes—
83C2×#14579119C2212yes—
84C2×#14579118C2214yes—
85C2×#14579117C2214yes—
86C22×C4⋊Dic79C2212yes—
87C2×C4⋊C4×D79C2211yescharacteristic
88C2×C4⋊C4×D79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C42×D79C2212yes—
91C2×C42×D79C2211yescharacteristic
92#556×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#126×C79C2214yes—
95C2×#124×C79C2212yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×Q8×C79C2212yes—
99C2×C4×D4×C79C2211yescharacteristic
100C2×#117×C79C2212yes—
101C2×#11929624—216no—
102C2×#11929624C23116yes—
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2312yes—
105C22×Dic158C2312yes—
106C22×Dic158C2312yes—
107C2×Q8×D79—28no—
108C2×Q8×D79C2318yes—
109C22×D316C2311yescharacteristic
110C22×D316C2312yes—
111C22×C22⋊D79C2312yes—
112C22×C22⋊D79C2312yes—
113C22×C22⋊D79C2312yes—
114C23×Dic79C2314yes—
115C22×C4×D79C2311yescharacteristic
116C22×C4×D79C2312yes—
117C22×C4×D79C2312yes—
118C22×C4×D79C2312yes—
119C22×C4×D79C2311yescharacteristic
120C22×C4×D79C2314yes—
121C22×C4×D79C2311yescharacteristic
122#14579161C2318yes—
123#14579160C23132yes—
124#14579160C2318yes—
125#14579157C2318yes—
126#14579156C23132yes—
127#14579156C23132yes—
128#14579154C23132yes—
129#14579153C23132yes—
130#14579153C23116yes—
131#14579152C23132yes—
132#14579152C23116yes—
133#14579152C23116yes—
134#14579150C23116yes—
135#14579147C23132yes—
136#14579147C23116yes—
137#14579146C23132yes—
138#14579145C23132yes—
139#14579143C23132yes—
140#14579143C23132yes—
141#14579141C23116yes—
142#14579141C23116yes—
143#14579140C23116yes—
144#14579139C23132yes—
145#14579138C23132yes—
146#14579137C23116yes—
147#14579137C23116yes—
148#14579136C2318yes—
149#14579134C23116yes—
150#14579132C2318yes—
151Q8×Dic79C2318yes—
152Q8×Dic79C23116yes—
153Q8×Dic79C23116yes—
154C4×Dic158C2318yes—
155C4×Dic158C23132yes—
156C4×Dic158C23116yes—
157#14579126C2318yes—
158#14579126C23116yes—
159#14579126C23116yes—
160C4×D316C23132yes—
161C4×D316C2318yes—
162C4×D316C23116yes—
163D4×Dic79C23116yes—
164C4×C22⋊D79C23116yes—
165(C22⋊D79)⋊C4C23132yes—
166(C22⋊D79)⋊C4C23132yes—
167#14579119C23116yes—
168#14579119C23116yes—
169#14579118C23132yes—
170#14579117C23132yes—
171C2×C4⋊Dic79C23116yes—
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2314yes—
176C2×C4⋊Dic79C2312yes—
177C2×C4⋊Dic79C2311yescharacteristic
178C2×C4⋊Dic79C2314yes—
179C2×C4⋊Dic79C2314yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2314yes—
187C2×Dic79⋊C4C2312yes—
188C4⋊C4×D79C23116yes—
189C4⋊C4×D79C23116yes—
190C4⋊C4×D79C2318yes—
191C2×C22⋊Dic79C2312yes—
192C2×C22⋊Dic79C2314yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×(C2×D79)⋊C4C2314yes—
199C2×C4×Dic79C2312yes—
200C2×C4×Dic79C2312yes—
201C2×C4×Dic79C2311yescharacteristic
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2314yes—
206C2×C4×Dic79C2314yes—
207C42×D79C23116yes—
208C42×D79C2318yes—
209C22×Q8×C79C2311yescharacteristic
210C22×Q8×C79C2312yes—
211C22×D4×C79C2311yescharacteristic
212C23×C4×C79C2312yes—
213C4⋊Q8×C79C2318yes—
214#126×C79C23132yes—
215#124×C79C23116yes—
216C22⋊Q8×C79C23116yes—
217C4×Q8×C79C2318yes—
218C4×Q8×C79C23116yes—
219C4×D4×C79C2318yes—
220#117×C79C23116yes—
221C2×C4⋊C4×C79C2311yescharacteristic
222C2×C4⋊C4×C79C2312yes—
223C2×C4⋊C4×C79C2311yescharacteristic
224C2×C4⋊C4×C79C2314yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2312yes—
227C2×C22⋊C4×C79C2314yes—
228C2×C22⋊C4×C79C2312yes—
229C2×C22⋊C4×C79C2314yes—
230C2×C42×C79C2314yes—
231C2×C42×C79C2311yescharacteristic
232C2×C42×C79C2312yes—
233C23×D79C2412yes—
234C23×D79C2411yescharacteristic
235#11929624—264no—
236C2×Dic158—28no—
237C2×Dic158—28no—
238C2×Dic158—24no—
239C2×Dic158—44no—
240C2×Dic158C2414yes—
241C2×Dic158C2418yes—
242C2×Dic158C2418yes—
243C2×Dic158C2418yes—
244Q8×D79—232no—
245C2×D316—28no—
246C2×D316—24no—
247C2×D316C2418yes—
248C2×D316C2414yes—
249C2×C22⋊D79—28no—
250C2×C22⋊D79—28no—
251C2×C22⋊D79—44no—
252C2×C22⋊D79C2418yes—
253C2×C22⋊D79C2418yes—
254C2×C22⋊D79C2418yes—
255C22×Dic79—48no—
256C22×Dic79C2412yes—
257C22×Dic79C2412yes—
258C22×Dic79C2414yes—
259C22×Dic79C2411yescharacteristic
260C22×Dic79C2412yes—
261C22×Dic79C2411yescharacteristic
262C22×Dic79C24116yes—
263C22×Dic79C2411yescharacteristic
264C2×C4×D79—28no—
265C2×C4×D79—28no—
266C2×C4×D79—24no—
267C2×C4×D79—44no—
268C2×C4×D79—48no—
269C2×C4×D79—42no—
270C2×C4×D79#4118yes—
271C2×C4×D79C2418yes—
272C2×C4×D79C2418yes—
273C2×C4×D79C2414yes—
274C2×C4×D79C2418yes—
275C2×C4×D79C2414yes—
276C2×C4×D79C24116yes—
277C2×C4×D79C2414yes—
278C4⋊Dic79C2414yes—
279C4⋊Dic79C2418yes—
280C4⋊Dic79C2418yes—
281C4⋊Dic79C24116yes—
282C4⋊Dic79C2418yes—
283C4⋊Dic79C2414yes—
284C4⋊Dic79C24116yes—
285C4⋊Dic79C24116yes—
286Dic79⋊C4C2418yes—
287Dic79⋊C4C24116yes—
288Dic79⋊C4C2418yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C24116yes—
291Dic79⋊C4C24116yes—
292Dic79⋊C4C24116yes—
293Dic79⋊C4C2418yes—
294C22⋊Dic79C2418yes—
295C22⋊Dic79C24116yes—
296(C2×D79)⋊C4C2418yes—
297(C2×D79)⋊C4C24116yes—
298(C2×D79)⋊C4C24116yes—
299(C2×D79)⋊C4C24116yes—
300(C2×D79)⋊C4C2418yes—
301(C2×D79)⋊C4C24116yes—
302C4×Dic79C2418yes—
303C4×Dic79C2418yes—
304C4×Dic79C2414yes—
305C4×Dic79C2418yes—
306C4×Dic79C2414yes—
307C4×Dic79C2414yes—
308C4×Dic79C24116yes—
309C4×Dic79C24116yes—
310C24×C79C2412yes—
311C2×Q8×C79—24no—
312C2×Q8×C79—28no—
313C2×Q8×C79C2414yes—
314C2×Q8×C79C2418yes—
315C2×D4×C79—24no—
316C2×D4×C79C2414yes—
317C22×C4×C79—28no—
318C22×C4×C79C2411yescharacteristic
319C22×C4×C79C2412yes—
320C22×C4×C79C2412yes—
321C22×C4×C79C2418yes—
322C22×C4×C79C2412yes—
323C22×C4×C79C2414yes—
324C22×C4×C79C2411yescharacteristic
325C22×C4×C79C2411yescharacteristic
326C4⋊C4×C79C2414yes—
327C4⋊C4×C79C2418yes—
328C4⋊C4×C79C2414yes—
329C4⋊C4×C79C24116yes—
330C4⋊C4×C79C2418yes—
331C4⋊C4×C79C2418yes—
332C22⋊C4×C79C24116yes—
333C22⋊C4×C79C2418yes—
334C22⋊C4×C79C24116yes—
335C42×C79C24116yes—
336C42×C79C2414yes—
337C42×C79C2418yes—
338C23×C79—24no—
339C23×C79—24no—
340C23×C79—24no—
341C23×C79C2514yes—
342C23×C79C2511yescharacteristic
343C22×D79—22no—
344C22×D79—22no—
345C22×D79—24no—
346C22×D79—24no—
347C22×D79—24no—
348C22×D79C2×#4114yes—
349C22×D79C2514yes—
350C22×D79C2512yes—
351Q8×C79—28no—
352Q8×C79—216no—
353D4×C79—28no—
354C2×C4×C79—24no—
355C2×C4×C79—24no—
356C2×C4×C79—28no—
357C2×C4×C79—24no—
358C2×C4×C79—22no—
359C2×C4×C79—216no—
360C2×C4×C79C2×#4114yes—
361C2×C4×C792−1+414yes—
362C2×C4×C79C2518yes—
363C2×C4×C79C2514yes—
364C2×C4×C79C2512yes—
365C2×C4×C79C2514yes—
366C2×C4×C79C2514yes—
367C2×C4×C79C2512yes—
368C2×C4×C79C2512yes—
369C22⋊D79—216no—
370C22⋊D79—216no—
371C22⋊D79—48no—
372C2×Dic79—24no—
373C2×Dic79—24no—
374C2×Dic79—22no—
375C2×Dic79—24no—
376C2×Dic79—28no—
377C2×Dic79—22no—
378C2×Dic79—416no—
379C2×Dic79C2×#4114yes—
380C2×Dic79C2512yes—
381C2×Dic79C2514yes—
382C2×Dic79C2514yes—
383C2×Dic79C2514yes—
384C2×Dic79C2512yes—
385C2×Dic79C2518yes—
386C2×Dic79C2512yes—
387D316—216no—
388D316—28no—
389C4×D79—216no—
390C4×D79—216no—
391C4×D79—28no—
392C4×D79—44no—
393C4×D79—416no—
394C4×D79—48no—
395C4×D79C2×#41116yes—
396Dic158—28no—
397Dic158—216no—
398Dic158—216no—
399Dic158—48no—
400C22×C79—24no—
401C22×C79—24no—
402C22×C79—24no—
403C22×C79—48no—
404C22×C79C22×#4112yes—
405C22×C79C2×2−1+412yes—
406C22×C79#58512yes—
407C22×C79C2611yescharacteristic
408C2×D79—22no—
409C2×D79—22no—
410C2×D79—28no—
411C2×D79—24no—
412C2×D79—24no—
413C2×D79—24no—
414C2×D79—48no—
415C2×D79C22×#4114yes—
416C4×C79—24no—
417C4×C79—24no—
418C4×C79—28no—
419C4×C79—22no—
420C4×C79—24no—
421C4×C79C22×#4114yes—
422C4×C79C2×2−1+414yes—
423Dic79—24no—
424Dic79—24no—
425Dic79—22no—
426Dic79—22no—
427Dic79—28no—
428Dic79—24no—
429Dic79C22×#4114yes—
430C2×#3507—791nomaximal, Sylow
431C2×C79—44no—
432C2×C79#350714yescomplemented
433C2×C79C23×#4111yescharacteristic
434C2×C79C22×2−1+411yescharacteristic
435C2×C79C2×#58511yescharacteristic
436D79—24no—
437D79—44no—
438#3507—7932no—
439C2×#559—792no—
440C2×#557—792no—
441C2×#556—791no—
442C2×#556—794no—
443C2×#556D7911yescharacteristic, complemented
444C2×#554—791no—
445C2×#554—791no—
446C2×#552—792no—
447C2×#552—792no—
448C2×#539—794no—
449C2×#536—792no—
450C2×#533—791no—
451C2×#532—791no—
452C2×#529—792no—
453C2×#529—792no—
454C2×#520—792no—
455C22×C4×Q8—791no—
456C79C2×#350711yescharacteristic, complemented, Sylow
457C22×#41—792no—
458C23×Q8—791no—
459#559—7932no—
460#557—7932no—
461#556—7916no—
462#556—7964no—
463#556C2×D79116yescomplemented
464#554—7916no—
465#554—7916no—
466#552—7932no—
467#552—7932no—
468#539—7964no—
469#536—7932no—
470#533—7916no—
471#532—7916no—
472C2×C4⋊Q8—791no—
473C2×C4⋊Q8—794no—
474C2×C4⋊Q8—791no—
475C2×C4⋊Q8C2×D7911yescharacteristic
476C2×#127—791no—
477#529—7932no—
478#529—7932no—
479C2×#126—794no—
480C2×#126—794no—
481C2×#126—794no—
482C2×#126C2×D7914yes—
483C2×#125—792no—
484C2×#125—792no—
485C2×#125—794no—
486C2×#125—792no—
487C2×#125—794no—
488C2×#124—792no—
489C2×#124—792no—
490C2×#124—794no—
491C2×#124C2×D7912yes—
492C2×#123—794no—
493C2×#123—794no—
494C2×#123—794no—
495C2×#123—794no—
496C2×C22⋊Q8—792no—
497C2×C22⋊Q8—792no—
498C2×C22⋊Q8—792no—
499C2×C22⋊Q8—792no—
500C2×C22⋊Q8—792no—
501C2×C22⋊Q8—794no—
502C2×C22⋊Q8—794no—
503C2×C22⋊Q8C2×D7912yes—
504C2×#121—791no—
505C2×#121—791no—
506C2×#121—792no—
507#520—7932no—
508C2×C4×Q8—791no—
509C2×C4×Q8—792no—
510C2×C4×Q8—792no—
511C2×C4×Q8—7916no—
512C2×C4×Q8—791no—
513C2×C4×Q8—792no—
514C2×C4×Q8—792no—
515C2×C4×Q8—791no—
516C2×C4×Q8—792no—
517C2×C4×Q8—794no—
518C2×C4×Q8C2×D7911yescharacteristic
519C2×C4×Q8C2×D7912yes—
520C2×C4×D4—792no—
521C2×C4×D4—792no—
522C2×C4×D4—794no—
523C2×C4×D4—794no—
524C2×C4×D4—794no—
525C2×C4×D4—792no—
526C2×C4×D4—791no—
527C2×C4×D4C2×D7911yescharacteristic
528C2×#117—792no—
529C2×#117—792no—
530C2×#117—794no—
531C2×#117—794no—
532C2×#117C2×D7912yes—
533C22×C4⋊C4—792no—
534C22×C4⋊C4—791no—
535C22×C4⋊C4—792no—
536C22×C4⋊C4—792no—
537C22×C42—792no—
538C22×C42—791no—
539C2×#41—7916no—
540C2×#41—15816no—
541C22×Q8—798no—
542C22×Q8—792no—
543C22×Q8—791no—
544C22×Q8—792no—
545C22×Q8—792no—
546C22×Q8—1588no—
547C22×Q8C22×D7912yes—
548C22×Q8C22×D7911yescharacteristic
549C22×D4—792no—
550C22×D4—792no—
551C22×D4—792no—
552C22×D4—791no—
553C22×D4—792no—
554C22×D4C22×D7911yescharacteristic
555C23×C4—794no—
556C23×C4—792no—
557C23×C4—791no—
558C23×C4—794no—
559C23×C4—791no—
560C23×C4—792no—
561C23×C4—792no—
562C23×C4—791no—
563C23×C4C22×D7912yes—
564C4⋊Q8—798no—
565C4⋊Q8—7932no—
566C4⋊Q8—798no—
567C4⋊Q8C22×D7918yes—
568#127—798no—
569#126—7932no—
570#126—7932no—
571#126—7932no—
572#126C22×D79132yes—
573#125—7916no—
574#125—7916no—
575#125—7932no—
576#125—7916no—
577#125—7932no—
578#124—7916no—
579#124—7916no—
580#124—7932no—
581#124C22×D79116yes—
582#123—7932no—
583#123—7932no—
584#123—7932no—
585#123—7932no—
586C22⋊Q8—7916no—
587C22⋊Q8—7916no—
588C22⋊Q8—7916no—
589C22⋊Q8—7916no—
590C22⋊Q8—7916no—
591C22⋊Q8—7932no—
592C22⋊Q8—7932no—
593C22⋊Q8C22×D79116yes—
594#121—798no—
595#121—798no—
596#121—7916no—
597C4×Q8—798no—
598C4×Q8—7916no—
599C4×Q8—7916no—
600C4×Q8—798no—
601C4×Q8—7916no—
602C4×Q8—7916no—
603C4×Q8—798no—
604C4×Q8—7916no—
605C4×Q8—7932no—
606C4×Q8C22×D7918yes—
607C4×Q8C22×D79116yes—
608C4×D4—7916no—
609C4×D4—7916no—
610C4×D4—7932no—
611C4×D4—7932no—
612C4×D4—7932no—
613C4×D4—7916no—
614C4×D4—798no—
615C4×D4C22×D7918yes—
616#117—7916no—
617#117—7916no—
618#117—7932no—
619#117—7932no—
620#117C22×D79116yes—
621C2×C4⋊C4—791no—
622C2×C4⋊C4—792no—
623C2×C4⋊C4—792no—
624C2×C4⋊C4—794no—
625C2×C4⋊C4—794no—
626C2×C4⋊C4—792no—
627C2×C4⋊C4—792no—
628C2×C4⋊C4—792no—
629C2×C4⋊C4—7916no—
630C2×C4⋊C4—794no—
631C2×C4⋊C4—794no—
632C2×C4⋊C4—794no—
633C2×C4⋊C4—792no—
634C2×C4⋊C4—791no—
635C2×C4⋊C4—792no—
636C2×C4⋊C4—794no—
637C2×C4⋊C4—794no—
638C2×C4⋊C4—798no—
639C2×C4⋊C4—7916no—
640C2×C4⋊C4—7916no—
641C2×C4⋊C4C22×D7911yescharacteristic
642C2×C4⋊C4C22×D7912yes—
643C2×C4⋊C4C22×D7912yes—
644C2×C4⋊C4C22×D7911yescharacteristic
645C2×C4⋊C4C22×D7912yes—
646C2×C4⋊C4C22×D7914yes—
647C2×C22⋊C4—792no—
648C2×C22⋊C4—794no—
649C2×C22⋊C4—792no—
650C2×C22⋊C4—794no—
651C2×C22⋊C4—794no—
652C2×C22⋊C4—794no—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—794no—
655C2×C22⋊C4C22×D7914yes—
656C2×C22⋊C4C22×D7914yes—
657C2×C22⋊C4C22×D7912yes—
658C2×C42—794no—
659C2×C42—792no—
660C2×C42—792no—
661C2×C42—794no—
662C2×C42—791no—
663C2×C42—792no—
664C2×C42—791no—
665C2×C42—791no—
666C2×C42—7916no—
667C2×C42—798no—
668C2×C42C22×D7914yes—
669C2×C42C22×D7911yescharacteristic
670C2×C42C22×D7912yes—
671C24—791no—
672C24—792no—
673C24C23×D7912yes—
674#41—15864no—
675C2×Q8—24no—
676C2×Q8—28no—
677C2×Q8—3164no—
678C2×Q8—798no—
679C2×Q8—794no—
680C2×Q8—798no—
681C2×Q8—798no—
682C2×Q8—1588no—
683C2×Q8—1588no—
684C2×Q8—15832no—
685C2×Q8—1584no—
686C2×Q8C23×D7918yes—
687C2×Q8C23×D7914yes—
688C2×D4—24no—
689C2×D4—3164no—
690C2×D4—798no—
691C2×D4—798no—
692C2×D4—798no—
693C2×D4—794no—
694C2×D4—798no—
695C2×D4—1588no—
696C2×D4—1588no—
697C2×D4—1588no—
698C2×D4—1584no—
699C2×D4C23×D7914yes—
700C22×C4—28no—
701C22×C4—3164no—
702C22×C4—3168no—
703C22×C4—3162no—
704C22×C4—3168no—
705C22×C4—7916no—
706C22×C4—798no—
707C22×C4—794no—
708C22×C4—7916no—
709C22×C4—791no—
710C22×C4—798no—
711C22×C4—794no—
712C22×C4—791no—
713C22×C4—792no—
714C22×C4—792no—
715C22×C4—792no—
716C22×C4—791no—
717C22×C4—794no—
718C22×C4—794no—
719C22×C4—798no—
720C22×C4—798no—
721C22×C4—1588no—
722C22×C4—1588no—
723C22×C4—1584no—
724C22×C4C23×D7918yes—
725C22×C4C23×D7914yes—
726C22×C4C23×D7912yes—
727C22×C4C23×D7912yes—
728C22×C4C23×D7911yescharacteristic
729C22×C4C23×D7912yes—
730C22×C4C23×D7911yescharacteristic
731C22×C4C23×D7911yescharacteristic
732C4⋊C4—798no—
733C4⋊C4—7916no—
734C4⋊C4—798no—
735C4⋊C4—798no—
736C4⋊C4—7916no—
737C4⋊C4—7916no—
738C4⋊C4—7916no—
739C4⋊C4—798no—
740C4⋊C4—794no—
741C4⋊C4—798no—
742C4⋊C4—7916no—
743C4⋊C4—798no—
744C4⋊C4—798no—
745C4⋊C4—794no—
746C4⋊C4—7916no—
747C4⋊C4—7916no—
748C4⋊C4C23×D7914yes—
749C4⋊C4C23×D7918yes—
750C4⋊C4C23×D7918yes—
751C4⋊C4C23×D7914yes—
752C4⋊C4C23×D7918yes—
753C4⋊C4C23×D79116yes—
754C22⋊C4—798no—
755C22⋊C4—7916no—
756C22⋊C4—798no—
757C22⋊C4—7916no—
758C22⋊C4—7916no—
759C22⋊C4—7916no—
760C22⋊C4—798no—
761C22⋊C4—7916no—
762C22⋊C4C23×D79116yes—
763C22⋊C4C23×D79116yes—
764C22⋊C4C23×D7918yes—
765C42—798no—
766C42—798no—
767C42—794no—
768C42—798no—
769C42—794no—
770C42—794no—
771C42—7916no—
772C42—7916no—
773C42C23×D7914yes—
774C42C23×D7918yes—
775C42C23×D79116yes—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—792no—
780C23—794no—
781C23—794no—
782C23—1584no—
783C23—1584no—
784C23—1584no—
785C23—1582no—
786C23—1582no—
787C23C24×D7914yes—
788C23C24×D7911yescharacteristic
789Q8—216no—
790Q8—28no—
791Q8—3168no—
792Q8—15816no—
793Q8—15816no—
794Q8—1588no—
795D4—28no—
796D4—3168no—
797D4—15816no—
798D4—15816no—
799D4—15816no—
800D4—1588no—
801C2×C4—28no—
802C2×C4—24no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—216no—
807C2×C4—3168no—
808C2×C4—31616no—
809C2×C4—3164no—
810C2×C4—31616no—
811C2×C4—792no—
812C2×C4—794no—
813C2×C4—7916no—
814C2×C4—792no—
815C2×C4—794no—
816C2×C4—794no—
817C2×C4—794no—
818C2×C4—792no—
819C2×C4—798no—
820C2×C4—15816no—
821C2×C4—1582no—
822C2×C4—1584no—
823C2×C4—1588no—
824C2×C4—1582no—
825C2×C4—1584no—
826C2×C4—1584no—
827C2×C4—1588no—
828C2×C4—15816no—
829C2×C4#41×D7914yes—
830C2×C4#1457920814yes—
831C2×C4C24×D7918yes—
832C2×C4C24×D7914yes—
833C2×C4C24×D7914yes—
834C2×C4C24×D7912yes—
835C2×C4C24×D7914yes—
836C2×C4C24×D7912yes—
837C2×C4C24×D7912yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—48no—
842C22—3168no—
843C22—794no—
844C22—1584no—
845C22—1584no—
846C22—1584no—
847C22—1582no—
848C22—1582no—
849C22—1588no—
850C22C2×#41×D7912yes—
851C22C2×#1457920812yes—
852C22#1909940012yes—
853C22C25×D7911yescharacteristic
854C4—24no—
855C4—24no—
856C4—28no—
857C4—24no—
858C4—22no—
859C4—794no—
860C4—1584no—
861C4—1584no—
862C4—1582no—
863C4—1584no—
864C4—1588no—
865C4—1582no—
866C4C2×#41×D7914yes—
867C4C2×#1457920814yes—
868C2—44no—
869C2—3164no—
870C2—1584no—
871C2#2377725514yesdirect product factor
872C2C22×#41×D7911yescharacteristic
873C2C22×#1457920811yescharacteristic
874C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#556×C79C2
socleC23×C79C25
prime radicalC2×#19099110C2
hypercenterC2×#556D79
hypocenterC79C2×#3507
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #23777255C2direct (N × H)
2. C2×#19099295C2semidirect
3. C2×#19099289C2semidirect
4. C2×#19099287C2semidirect
5. C2×#19099280C2semidirect
6. C2×#19099273C2semidirect
7. C2×#19099270C2semidirect
8. C2×#19099255C2semidirect
9. C2×#19099252C2semidirect
10. C2×#19099154C2semidirect
11. C2×#19099136C2semidirect
12. C2×#19099118C2semidirect
14. C2×#19099100C2semidirect
15. C2×#19099092C2semidirect
16. C2×#19099043C2semidirect
17. C2×C4×Q8×D79C2semidirect
18. C2×#556×C79C2semidirect
21. #19099295C22semidirect
22. #19099289C22semidirect
23. #19099287C22semidirect
24. #19099280C22semidirect
25. #19099273C22semidirect
26. #19099270C22semidirect
27. #19099255C22semidirect
28. #19099252C22semidirect
29. #19099154C22semidirect
30. #19099136C22semidirect
31. #19099118C22semidirect
37. #19099100C22semidirect
38. #19099092C22semidirect
64. #19099043C22semidirect
74. C4×Q8×D79C22semidirect
92. #556×C79C22semidirect
432. C2×C79#3507semidirect
443. C2×#556D79semidirect
456. C79C2×#3507semidirect
463. #556C2×D79semidirect
871. C2#23777255direct (N × H)

Maximal subgroups

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

subgroupindex
#237772552
C2×#190992952
C2×#190992892
C2×#190992872
C2×#190992802
C2×#190992732
C2×#190992702
C2×#190992552
C2×#190992522
C2×#190991542
C2×#190991362
C2×#190991182
C2×#190991102
C2×#190991002
C2×#190990922
C2×#190990432
C2×C4×Q8×D792
C2×#556×C792
C2×#350779