Finite Group Databasebeta

← C2×#21437962 #29496770

Subgroups — C2×#21437962 #29496770

Order 15104.

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#21437962C2132yesmaximal, direct product factor
2C2×#16838137C211yesmaximal, characteristic, complemented
3C2×#16838137C211yesmaximal, characteristic, complemented
4C2×#16838127C211yesmaximal, characteristic, complemented
5C2×#16838126C212yesmaximal, complemented
6C2×#16838124C212yesmaximal, complemented
7C2×#16838124C212yesmaximal, complemented
8C2×#16838108C212yesmaximal, complemented
9C2×#16838084C214yesmaximal, complemented
10C2×#16838000C214yesmaximal, complemented
11C2×#16837977C212yesmaximal, complemented
12C2×#16837956C211yesmaximal, characteristic, complemented
13C2×#16837953C211yesmaximal, characteristic
14C2×#16837939C212yesmaximal, complemented
15C2×#16837937C212yesmaximal, complemented
16C2×#16837884C212yesmaximal, complemented
17C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
18C2×C59×#557C211yesmaximal, characteristic, complemented
19C22×#11745689C2212yes—
20C22×Q8×D59C2211yescharacteristic
21#16838137C22116yescomplemented
22#16838137C22116yescomplemented
23#16838127C22116yescomplemented
24#16838126C22132yescomplemented
25#16838124C22132yescomplemented
26#16838124C22132yescomplemented
27#16838108C22132yescomplemented
28#16838084C22164yescomplemented
29#16838000C22164yescomplemented
30#16837977C22132yescomplemented
31#16837956C22116yescomplemented
32#16837953C22116yes—
33C2×#14273726C2211yescharacteristic
34C2×#14273725C2211yescharacteristic
35C2×#14273725C2212yes—
36C2×#14273724C2211yescharacteristic
37#16837939C22132yescomplemented
38#16837937C22132yescomplemented
39C2×#14273722C2214yes—
40C2×#14273722C2214yes—
41C2×#14273722C2214yes—
42C2×#14273721C2214yes—
43C2×#14273718C2212yes—
44C2×#14273717C2214yes—
45C2×#14273717C2212yes—
46C2×#14273716C2212yes—
47C2×#14273716C2212yes—
48C2×#14273716C2212yes—
49C2×#14273715C2212yes—
50C2×#14273715C2212yes—
51C2×#14273712C2214yes—
52C2×#14273712C2214yes—
53C2×#14273712C2214yes—
54C2×#14273712C2214yes—
55C2×#14273707C2214yes—
56C2×#14273707C2211yescharacteristic
57C2×#14273705C2212yes—
58C2×#14273705C2214yes—
59C2×#14273705C2214yes—
60C2×#14273705C2214yes—
61C2×#14273703C2211yescharacteristic
62C2×#14273702C2212yes—
63C2×#14273702C2212yes—
64#16837884C22132yescomplemented
65C2×Q8×Dic59C2211yescharacteristic
66C2×Q8×Dic59C2212yes—
67C2×C4×Dic118C2212yes—
68C2×C4×Dic118C2211yescharacteristic
69C2×C4×Dic118C2212yes—
70C2×C4×Dic118C2211yescharacteristic
71C2×#14273692C2212yes—
72C2×#14273692C2211yescharacteristic
73C2×#14273692C2212yes—
74C4×Q8×D59C22116yescomplemented
75C2×C4×D236C2214yes—
76C2×C4×D236C2212yes—
77C2×C4×D236C2212yes—
78C2×#14273689C2214yes—
79C2×#14273689C2212yes—
80C2×#14273689C2212yes—
81C2×#14273689C2212yes—
82C2×#14273689C2212yes—
83C2×#14273685C2214yes—
84C2×#14273684C2214yes—
85C2×#14273684C2212yes—
86C2×#14273684C2214yes—
87C2×C4⋊C4×D59C2212yes—
88C2×C4⋊C4×D59C2211yescharacteristic
89C2×C4⋊C4×D59C2214yes—
90C2×C42×D59C2212yes—
91C2×C42×D59C2211yescharacteristic
92C59×#557C22116yescomplemented
93C2×C4⋊Q8×C59C2211yescharacteristic
94C2×C4⋊Q8×C59C2212yes—
95C2×#125×C59C2214yes—
96C2×#125×C59C2212yes—
97C2×C4×Q8×C59C2211yescharacteristic
98C2×C4×Q8×C59C2212yes—
99C2×C4×Q8×C59C2212yes—
100C2×C4×Q8×C59C2211yescharacteristic
101C2×#11745689—216no—
102C2×#11745689C23116yes—
103C22×Dic118C2312yes—
104C22×Dic118C2311yescharacteristic
105C22×Dic118C2311yescharacteristic
106C22×Dic118C2312yes—
107C2×Q8×D59—28no—
108C2×Q8×D59C2318yes—
109C22×D236C2314yes—
110C22×D236C2312yes—
111C22×D236C2312yes—
112C22×D236C2312yes—
113C22×C4×D59C2311yescharacteristic
114C22×C4×D59C2314yes—
115C22×C4×D59C2312yes—
116C22×C4×D59C2311yescharacteristic
117C22×C4×D59C2314yes—
118C22×C4×D59C2314yes—
119C22×C4×D59C2312yes—
120C22×C4×D59C2311yescharacteristic
121#14273726C2318yes—
122#14273725C2318yes—
123#14273725C23116yes—
124#14273724C2318yes—
125#14273722C23132yes—
126#14273722C23132yes—
127#14273722C23132yes—
128#14273721C23132yes—
129#14273718C23116yes—
130#14273717C23116yes—
131#14273717C23132yes—
132#14273716C23116yes—
133#14273716C23116yes—
134#14273716C23116yes—
135#14273715C23116yes—
136#14273715C23116yes—
137#14273712C23132yes—
138#14273712C23132yes—
139#14273712C23132yes—
140#14273712C23132yes—
141#14273707C2318yes—
142#14273707C23132yes—
143#14273705C23116yes—
144#14273705C23132yes—
145#14273705C23132yes—
146#14273705C23132yes—
147#14273703C2318yes—
148#14273702C23116yes—
149#14273702C23116yes—
150Q8×Dic59C2318yes—
151Q8×Dic59C23116yes—
152C4×Dic118C23116yes—
153C4×Dic118C2318yes—
154C4×Dic118C23116yes—
155C4×Dic118C2318yes—
156#14273692C23116yes—
157#14273692C23116yes—
158#14273692C2318yes—
159C4×D236C23132yes—
160C4×D236C23116yes—
161C4×D236C23116yes—
162#14273689C23132yes—
163#14273689C23116yes—
164#14273689C23116yes—
165#14273689C23116yes—
166#14273689C23116yes—
167#14273685C23132yes—
168#14273684C23132yes—
169#14273684C23116yes—
170#14273684C23132yes—
171C2×C4⋊Dic59C2311yescharacteristic
172C2×C4⋊Dic59C2312yes—
173C2×C4⋊Dic59C2314yes—
174C2×C4⋊Dic59C2312yes—
175C2×C4⋊Dic59C2311yescharacteristic
176C2×Dic59⋊C4C2312yes—
177C2×Dic59⋊C4C2314yes—
178C2×Dic59⋊C4C2312yes—
179C2×Dic59⋊C4C2312yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2312yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2312yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2312yes—
186C4⋊C4×D59C23116yes—
187C4⋊C4×D59C23132yes—
188C4⋊C4×D59C2318yes—
189C2×(C2×D59)⋊C4C2314yes—
190C2×(C2×D59)⋊C4C2314yes—
191C2×(C2×D59)⋊C4C2312yes—
192C2×(C2×D59)⋊C4C2314yes—
193C2×(C2×D59)⋊C4C2314yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2314yes—
196C2×(C2×D59)⋊C4C2314yes—
197C2×(C2×D59)⋊C4C2314yes—
198C2×(C2×D59)⋊C4C2314yes—
199C2×C4×Dic59C2311yescharacteristic
200C2×C4×Dic59C2312yes—
201C2×C4×Dic59C2312yes—
202C2×C4×Dic59C2311yescharacteristic
203C2×C4×Dic59C2314yes—
204C2×C4×Dic59C2312yes—
205C2×C4×Dic59C2312yes—
206C2×C4×Dic59C2311yescharacteristic
207C42×D59C23116yes—
208C42×D59C2318yes—
209C22×Q8×C59C2311yescharacteristic
210C22×Q8×C59C2311yescharacteristic
211C22×Q8×C59C2312yes—
212C4⋊Q8×C59C2318yes—
213C4⋊Q8×C59C23116yes—
214#125×C59C23116yes—
215#125×C59C23132yes—
216C4×Q8×C59C23116yes—
217C4×Q8×C59C2318yes—
218C4×Q8×C59C2318yes—
219C4×Q8×C59C23116yes—
220C2×C4⋊C4×C59C2312yes—
221C2×C4⋊C4×C59C2312yes—
222C2×C4⋊C4×C59C2314yes—
223C2×C4⋊C4×C59C2312yes—
224C2×C4⋊C4×C59C2314yes—
225C2×C4⋊C4×C59C2314yes—
226C2×C4⋊C4×C59C2311yescharacteristic
227C2×C4⋊C4×C59C2312yes—
228C2×C4⋊C4×C59C2311yescharacteristic
229C2×C42×C59C2312yes—
230C2×C42×C59C2312yes—
231C2×C42×C59C2314yes—
232C2×C42×C59C2311yescharacteristic
233C23×D59C2414yes—
234C23×D59C2411yescharacteristic
235C2×Q8×C59—24no—
236C2×Q8×C59—28no—
237C2×Q8×C59—24no—
238C2×Q8×C59C2414yes—
239C2×Q8×C59C2414yes—
240C2×Q8×C59C2418yes—
241C22×C4×C59C2412yes—
242C22×C4×C59C2412yes—
243C22×C4×C59C2411yescharacteristic
244C22×C4×C59C2412yes—
245C22×C4×C59C2412yes—
246C22×C4×C59C2414yes—
247C22×C4×C59C2411yescharacteristic
248C22×C4×C59C2411yescharacteristic
249C22×Dic59C2411yescharacteristic
250C22×Dic59C2412yes—
251C22×Dic59C2412yes—
252C22×Dic59C2412yes—
253C22×Dic59C2411yescharacteristic
254C22×Dic59C2412yes—
255C22×Dic59C2411yescharacteristic
256#11745689—264no—
257Q8×D59—232no—
258C2×D236—216no—
259C2×D236—28no—
260C2×D236—28no—
261C2×D236—44no—
262C2×D236C2418yes—
263C2×D236C24116yes—
264C2×D236C2418yes—
265C2×D236C2418yes—
266C2×C4×D59—28no—
267C2×C4×D59—24no—
268C2×C4×D59—216no—
269C2×C4×D59—42no—
270C2×C4×D59—48no—
271C2×C4×D59—48no—
272C2×C4×D59—44no—
273C2×C4×D59#4118yes—
274C2×C4×D59C2414yes—
275C2×C4×D59C2418yes—
276C2×C4×D59C24116yes—
277C2×C4×D59C2418yes—
278C2×C4×D59C2414yes—
279C2×C4×D59C24116yes—
280C2×C4×D59C24116yes—
281C2×C4×D59C2414yes—
282C2×Dic118—24no—
283C2×Dic118—24no—
284C2×Dic118—28no—
285C2×Dic118—44no—
286C2×Dic118C2414yes—
287C2×Dic118C2418yes—
288C2×Dic118C2414yes—
289C2×Dic118C2418yes—
290C4⋊C4×C59C2414yes—
291C4⋊C4×C59C24116yes—
292C4⋊C4×C59C2418yes—
293C4⋊C4×C59C2414yes—
294C4⋊C4×C59C2418yes—
295C4⋊C4×C59C2418yes—
296C4⋊C4×C59C24116yes—
297C4⋊C4×C59C24116yes—
298C4⋊C4×C59C2418yes—
299C42×C59C2418yes—
300C42×C59C24116yes—
301C42×C59C2414yes—
302C42×C59C2418yes—
303(C2×D59)⋊C4C24116yes—
304(C2×D59)⋊C4C2418yes—
305(C2×D59)⋊C4C24116yes—
306(C2×D59)⋊C4C2418yes—
307(C2×D59)⋊C4C24116yes—
308(C2×D59)⋊C4C24116yes—
309(C2×D59)⋊C4C24116yes—
310(C2×D59)⋊C4C24116yes—
311(C2×D59)⋊C4C24116yes—
312(C2×D59)⋊C4C24116yes—
313C4⋊Dic59C2414yes—
314C4⋊Dic59C24116yes—
315C4⋊Dic59C2418yes—
316C4⋊Dic59C2418yes—
317C4⋊Dic59C2414yes—
318Dic59⋊C4C2418yes—
319Dic59⋊C4C2418yes—
320Dic59⋊C4C2418yes—
321Dic59⋊C4C2418yes—
322Dic59⋊C4C2418yes—
323Dic59⋊C4C2418yes—
324Dic59⋊C4C24116yes—
325Dic59⋊C4C24116yes—
326Dic59⋊C4C2418yes—
327Dic59⋊C4C2418yes—
328C4×Dic59C2418yes—
329C4×Dic59C2418yes—
330C4×Dic59C2414yes—
331C4×Dic59C2414yes—
332C4×Dic59C2418yes—
333C4×Dic59C2414yes—
334C4×Dic59C24116yes—
335C4×Dic59C2418yes—
336C23×C59C2511yescharacteristic
337C22×D59—22no—
338C22×D59—22no—
339C22×D59—28no—
340C22×D59—28no—
341C22×D59—28no—
342C22×D59C2×#4114yes—
343C22×D59C2518yes—
344C22×D59C2512yes—
345Q8×C59—28no—
346Q8×C59—216no—
347Q8×C59—28no—
348C2×C4×C59—24no—
349C2×C4×C59—28no—
350C2×C4×C59—24no—
351C2×C4×C59—24no—
352C2×C4×C59—24no—
353C2×C4×C59—22no—
354C2×C4×C59C2×#4114yes—
355C2×C4×C592−1+414yes—
356C2×C4×C59C2512yes—
357C2×C4×C59C2518yes—
358C2×C4×C59C2514yes—
359C2×C4×C59C2514yes—
360C2×C4×C59C2514yes—
361C2×C4×C59C2514yes—
362C2×C4×C59C2512yes—
363C2×C4×C59C2512yes—
364C2×Dic59—24no—
365C2×Dic59—24no—
366C2×Dic59—22no—
367C2×Dic59—22no—
368C2×Dic59—24no—
369C2×Dic59—24no—
370C2×Dic59C2×#4114yes—
371C2×Dic59C2512yes—
372C2×Dic59C2514yes—
373C2×Dic59C2514yes—
374C2×Dic59C2514yes—
375C2×Dic59C2512yes—
376C2×Dic59C2514yes—
377C2×Dic59C2512yes—
378D236—232no—
379D236—216no—
380D236—216no—
381D236—48no—
382C4×D59—216no—
383C4×D59—28no—
384C4×D59—232no—
385C4×D59—44no—
386C4×D59—416no—
387C4×D59—416no—
388C4×D59—48no—
389C4×D59C2×#41116yes—
390Dic118—28no—
391Dic118—28no—
392Dic118—216no—
393Dic118—48no—
394C2×#3507—591nomaximal, Sylow
395C22×C59C22×#4112yes—
396C22×C59C2×2−1+412yes—
397C22×C59#58512yes—
398C22×C59C2611yescharacteristic
399C2×D59—22no—
400C2×D59—22no—
401C2×D59—28no—
402C2×D59—28no—
403C2×D59—28no—
404C2×D59—28no—
405C2×D59—416no—
406C2×D59C22×#4114yes—
407C4×C59—24no—
408C4×C59—28no—
409C4×C59—24no—
410C4×C59—24no—
411C4×C59—24no—
412C4×C59—22no—
413C4×C59C22×#4114yes—
414C4×C59C2×2−1+414yes—
415Dic59—24no—
416Dic59—24no—
417Dic59—22no—
418Dic59—22no—
419Dic59—24no—
420Dic59—24no—
421Dic59C22×#4114yes—
422#3507—5932no—
423C2×#559—591no—
424C2×#559—591no—
425C2×#557—591no—
426C2×#557D5911yescharacteristic, complemented
427C2×#556—592no—
428C2×#556—592no—
429C2×#556—592no—
430C2×#554—592no—
431C2×#552—594no—
432C2×#539—594no—
433C2×#536—592no—
434C2×#533—591no—
435C2×#532—591no—
436C2×#529—592no—
437C2×#529—592no—
438C2×#520—592no—
439C22×C4×Q8—591no—
440C2×C59#350714yescomplemented
441C2×C59C23×#4111yescharacteristic
442C2×C59C22×2−1+411yescharacteristic
443C2×C59C2×#58511yescharacteristic
444D59—24no—
445D59—48no—
446C22×#41—592no—
447C23×Q8—591no—
448#559—5916no—
449#559—5916no—
450#557—5916no—
451#557C2×D59116yescomplemented
452#556—5932no—
453#556—5932no—
454#556—5932no—
455#554—5932no—
456#552—5964no—
457#539—5964no—
458#536—5932no—
459#533—5916no—
460#532—5916no—
461C2×C4⋊Q8—591no—
462C2×C4⋊Q8—592no—
463C2×C4⋊Q8—591no—
464C2×C4⋊Q8C2×D5911yescharacteristic
465C2×C4⋊Q8C2×D5912yes—
466C2×#127—591no—
467#529—5932no—
468#529—5932no—
469C2×#126—594no—
470C2×#126—594no—
471C2×#126—594no—
472C2×#126—594no—
473C2×#125—592no—
474C2×#125—594no—
475C2×#125—592no—
476C2×#125C2×D5912yes—
477C2×#125C2×D5914yes—
478C2×#124—592no—
479C2×#124—592no—
480C2×#124—592no—
481C2×#124—592no—
482C2×#124—592no—
483C2×#123—594no—
484C2×#123—594no—
485C2×#123—594no—
486C2×#123—594no—
487C2×C22⋊Q8—591no—
488C2×C22⋊Q8—592no—
489C2×C22⋊Q8—594no—
490C2×C22⋊Q8—594no—
491C2×C22⋊Q8—594no—
492C2×C22⋊Q8—591no—
493C2×C22⋊Q8—594no—
494C2×#121—592no—
495C2×#121—592no—
496#520—5932no—
497C2×C4×Q8—591no—
498C2×C4×Q8—592no—
499C2×C4×Q8—5916no—
500C2×C4×Q8—592no—
501C2×C4×Q8—591no—
502C2×C4×Q8—592no—
503C2×C4×Q8—592no—
504C2×C4×Q8—591no—
505C2×C4×Q8—592no—
506C2×C4×Q8—591no—
507C2×C4×Q8C2×D5911yescharacteristic
508C2×C4×Q8C2×D5912yes—
509C2×C4×Q8C2×D5912yes—
510C2×C4×Q8C2×D5911yescharacteristic
511C2×C4×D4—594no—
512C2×C4×D4—592no—
513C2×C4×D4—592no—
514C2×C4×D4—592no—
515C2×C4×D4—592no—
516C2×C4×D4—594no—
517C2×C4×D4—592no—
518C2×C4×D4—592no—
519C2×#117—594no—
520C2×#117—592no—
521C2×#117—594no—
522C2×#117—594no—
523C22×C4⋊C4—591no—
524C22×C4⋊C4—592no—
525C22×C4⋊C4—594no—
526C22×C42—592no—
527C22×C42—591no—
528C59C2×#350711yescharacteristic, complemented, Sylow
529C2×#41—5916no—
530C2×#41—11816no—
531C22×Q8—598no—
532C22×Q8—591no—
533C22×Q8—592no—
534C22×Q8—591no—
535C22×Q8—592no—
536C22×Q8—1188no—
537C22×Q8C22×D5911yescharacteristic
538C22×Q8C22×D5912yes—
539C22×Q8C22×D5911yescharacteristic
540C22×D4—592no—
541C22×D4—594no—
542C22×D4—592no—
543C22×D4—592no—
544C23×C4—591no—
545C23×C4—594no—
546C23×C4—592no—
547C23×C4—591no—
548C23×C4—592no—
549C23×C4—591no—
550C23×C4—594no—
551C23×C4—594no—
552C4⋊Q8—598no—
553C4⋊Q8—5916no—
554C4⋊Q8—598no—
555C4⋊Q8C22×D5918yes—
556C4⋊Q8C22×D59116yes—
557#127—598no—
558#126—5932no—
559#126—5932no—
560#126—5932no—
561#126—5932no—
562#125—5916no—
563#125—5916no—
564#125—5932no—
565#125C22×D59116yes—
566#125C22×D59132yes—
567#124—5916no—
568#124—5916no—
569#124—5916no—
570#124—5916no—
571#124—5916no—
572#123—5932no—
573#123—5932no—
574#123—5932no—
575#123—5932no—
576C22⋊Q8—598no—
577C22⋊Q8—598no—
578C22⋊Q8—5916no—
579C22⋊Q8—5932no—
580C22⋊Q8—5932no—
581C22⋊Q8—5932no—
582C22⋊Q8—5932no—
583#121—5916no—
584#121—5916no—
585C4×Q8—598no—
586C4×Q8—5916no—
587C4×Q8—5916no—
588C4×Q8—598no—
589C4×Q8—5916no—
590C4×Q8—5916no—
591C4×Q8—598no—
592C4×Q8—5916no—
593C4×Q8—598no—
594C4×Q8C22×D5918yes—
595C4×Q8C22×D59116yes—
596C4×Q8C22×D59116yes—
597C4×Q8C22×D5918yes—
598C4×D4—5932no—
599C4×D4—5916no—
600C4×D4—5916no—
601C4×D4—5916no—
602C4×D4—5916no—
603C4×D4—5932no—
604C4×D4—5916no—
605C4×D4—5916no—
606#117—5932no—
607#117—5916no—
608#117—5932no—
609#117—5932no—
610C2×C4⋊C4—592no—
611C2×C4⋊C4—592no—
612C2×C4⋊C4—591no—
613C2×C4⋊C4—594no—
614C2×C4⋊C4—592no—
615C2×C4⋊C4—592no—
616C2×C4⋊C4—592no—
617C2×C4⋊C4—592no—
618C2×C4⋊C4—592no—
619C2×C4⋊C4—592no—
620C2×C4⋊C4—594no—
621C2×C4⋊C4—591no—
622C2×C4⋊C4—592no—
623C2×C4⋊C4—594no—
624C2×C4⋊C4—592no—
625C2×C4⋊C4—598no—
626C2×C4⋊C4—5916no—
627C2×C4⋊C4—5932no—
628C2×C4⋊C4C22×D5911yescharacteristic
629C2×C4⋊C4C22×D5914yes—
630C2×C4⋊C4C22×D5912yes—
631C2×C4⋊C4C22×D5914yes—
632C2×C4⋊C4C22×D5911yescharacteristic
633C2×C4⋊C4C22×D5912yes—
634C2×C4⋊C4C22×D5912yes—
635C2×C4⋊C4C22×D5912yes—
636C2×C4⋊C4C22×D5914yes—
637C2×C22⋊C4—594no—
638C2×C22⋊C4—592no—
639C2×C22⋊C4—592no—
640C2×C22⋊C4—594no—
641C2×C22⋊C4—594no—
642C2×C22⋊C4—594no—
643C2×C22⋊C4—594no—
644C2×C22⋊C4—594no—
645C2×C22⋊C4—594no—
646C2×C22⋊C4—594no—
647C2×C42—594no—
648C2×C42—592no—
649C2×C42—592no—
650C2×C42—592no—
651C2×C42—591no—
652C2×C42—591no—
653C2×C42—592no—
654C2×C42—591no—
655C2×C42—5916no—
656C2×C42—598no—
657C2×C42C22×D5914yes—
658C2×C42C22×D5912yes—
659C2×C42C22×D5912yes—
660C2×C42C22×D5911yescharacteristic
661C24—591no—
662C24—594no—
663#41—11864no—
664C2×Q8—24no—
665C2×Q8—28no—
666C2×Q8—24no—
667C2×Q8—594no—
668C2×Q8—598no—
669C2×Q8—594no—
670C2×Q8—598no—
671C2×Q8—1188no—
672C2×Q8—11832no—
673C2×Q8—1184no—
674C2×Q8—1184no—
675C2×Q8—2364no—
676C2×Q8C23×D5914yes—
677C2×Q8C23×D5918yes—
678C2×Q8C23×D5914yes—
679C2×D4—598no—
680C2×D4—5916no—
681C2×D4—598no—
682C2×D4—598no—
683C2×D4—11816no—
684C2×D4—1188no—
685C2×D4—1188no—
686C2×D4—2364no—
687C22×C4—591no—
688C22×C4—598no—
689C22×C4—594no—
690C22×C4—591no—
691C22×C4—592no—
692C22×C4—592no—
693C22×C4—592no—
694C22×C4—591no—
695C22×C4—592no—
696C22×C4—594no—
697C22×C4—598no—
698C22×C4—5916no—
699C22×C4—598no—
700C22×C4—594no—
701C22×C4—5916no—
702C22×C4—5916no—
703C22×C4—11816no—
704C22×C4—1188no—
705C22×C4—1184no—
706C22×C4—2364no—
707C22×C4—2368no—
708C22×C4—2368no—
709C22×C4—2362no—
710C22×C4C23×D5912yes—
711C22×C4C23×D5912yes—
712C22×C4C23×D5914yes—
713C22×C4C23×D5911yescharacteristic
714C22×C4C23×D5912yes—
715C22×C4C23×D5912yes—
716C22×C4C23×D5911yescharacteristic
717C22×C4C23×D5911yescharacteristic
718C4⋊C4—598no—
719C4⋊C4—598no—
720C4⋊C4—594no—
721C4⋊C4—5916no—
722C4⋊C4—598no—
723C4⋊C4—598no—
724C4⋊C4—598no—
725C4⋊C4—598no—
726C4⋊C4—598no—
727C4⋊C4—598no—
728C4⋊C4—5916no—
729C4⋊C4—594no—
730C4⋊C4—598no—
731C4⋊C4—5916no—
732C4⋊C4—598no—
733C4⋊C4C23×D5914yes—
734C4⋊C4C23×D59116yes—
735C4⋊C4C23×D5918yes—
736C4⋊C4C23×D59116yes—
737C4⋊C4C23×D5914yes—
738C4⋊C4C23×D5918yes—
739C4⋊C4C23×D5918yes—
740C4⋊C4C23×D5918yes—
741C4⋊C4C23×D59116yes—
742C22⋊C4—5916no—
743C22⋊C4—598no—
744C22⋊C4—598no—
745C22⋊C4—5916no—
746C22⋊C4—5916no—
747C22⋊C4—5916no—
748C22⋊C4—5916no—
749C22⋊C4—5916no—
750C22⋊C4—5916no—
751C22⋊C4—5916no—
752C42—598no—
753C42—598no—
754C42—594no—
755C42—594no—
756C42—598no—
757C42—594no—
758C42—5916no—
759C42—598no—
760C42C23×D5918yes—
761C42C23×D5914yes—
762C42C23×D59116yes—
763C42C23×D5918yes—
764C23—594no—
765C23—592no—
766C23—598no—
767C23—1182no—
768C23—1182no—
769C23—1188no—
770C23—1188no—
771C23—1188no—
772C23C24×D5911yescharacteristic
773Q8—28no—
774Q8—216no—
775Q8—28no—
776Q8—11816no—
777Q8—1188no—
778Q8—1188no—
779Q8—2368no—
780D4—11832no—
781D4—11816no—
782D4—11816no—
783D4—2368no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—594no—
791C2×C4—592no—
792C2×C4—5916no—
793C2×C4—592no—
794C2×C4—594no—
795C2×C4—594no—
796C2×C4—594no—
797C2×C4—592no—
798C2×C4—594no—
799C2×C4—11832no—
800C2×C4—11816no—
801C2×C4—1184no—
802C2×C4—1182no—
803C2×C4—1184no—
804C2×C4—1184no—
805C2×C4—1184no—
806C2×C4—1182no—
807C2×C4—1188no—
808C2×C4—2368no—
809C2×C4—23616no—
810C2×C4—23616no—
811C2×C4—2364no—
812C2×C4#41×D5914yes—
813C2×C4#1427377514yes—
814C2×C4C24×D5914yes—
815C2×C4C24×D5914yes—
816C2×C4C24×D5918yes—
817C2×C4C24×D5912yes—
818C2×C4C24×D5914yes—
819C2×C4C24×D5914yes—
820C2×C4C24×D5912yes—
821C2×C4C24×D5912yes—
822C22—594no—
823C22—1188no—
824C22—1182no—
825C22—1182no—
826C22—1188no—
827C22—1188no—
828C22—1188no—
829C22—23616no—
830C22C2×#41×D5912yes—
831C22C2×#1427377512yes—
832C22#1683823912yes—
833C22C25×D5911yescharacteristic
834C4—28no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—24no—
839C4—22no—
840C4—594no—
841C4—1184no—
842C4—1182no—
843C4—1184no—
844C4—1184no—
845C4—1184no—
846C4—1182no—
847C4C2×#41×D5914yes—
848C4C2×#1427377514yes—
849C2—1184no—
850C2—2368no—
851C2#2143796214yesdirect product factor
852C2C22×#41×D5911yescharacteristic
853C2C22×#1427377511yescharacteristic
854C2C2×#1683823911yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#557C2
socleC23×C59C25
prime radicalC2×#16837953C2
hypercenterC2×#557D59
hypocenterC59C2×#3507
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #21437962C2direct (N × H)
2. C2×#16838137C2semidirect
3. C2×#16838137C2semidirect
4. C2×#16838127C2semidirect
5. C2×#16838126C2semidirect
6. C2×#16838124C2semidirect
7. C2×#16838124C2semidirect
8. C2×#16838108C2semidirect
9. C2×#16838084C2semidirect
10. C2×#16838000C2semidirect
11. C2×#16837977C2semidirect
12. C2×#16837956C2semidirect
14. C2×#16837939C2semidirect
15. C2×#16837937C2semidirect
16. C2×#16837884C2semidirect
17. C2×C4×Q8×D59C2semidirect
18. C2×C59×#557C2semidirect
21. #16838137C22semidirect
22. #16838137C22semidirect
23. #16838127C22semidirect
24. #16838126C22semidirect
25. #16838124C22semidirect
26. #16838124C22semidirect
27. #16838108C22semidirect
28. #16838084C22semidirect
29. #16838000C22semidirect
30. #16837977C22semidirect
31. #16837956C22semidirect
37. #16837939C22semidirect
38. #16837937C22semidirect
64. #16837884C22semidirect
74. C4×Q8×D59C22semidirect
92. C59×#557C22semidirect
426. C2×#557D59semidirect
440. C2×C59#3507semidirect
451. #557C2×D59semidirect
528. C59C2×#3507semidirect
851. C2#21437962direct (N × H)

Maximal subgroups

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

subgroupindex
#214379622
C2×#168381372
C2×#168381272
C2×#168381262
C2×#168381242
C2×#168381082
C2×#168380842
C2×#168380002
C2×#168379772
C2×#168379562
C2×#168379532
C2×#168379392
C2×#168379372
C2×#168378842
C2×C4×Q8×D592
C2×C59×#5572
C2×#350759