Finite Group Databasebeta

← C2×#21437959 #29496766

Subgroups — C2×#21437959 #29496766

Order 15104.

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#21437959C2132yesmaximal, direct product factor
2C2×#16838135C212yesmaximal, complemented
3C2×#16838129C212yesmaximal, complemented
4C2×#16838125C211yesmaximal, characteristic, complemented
5C2×#16838123C214yesmaximal, complemented
6C2×#16838122C211yesmaximal, characteristic, complemented
7C2×#16838113C211yesmaximal, characteristic, complemented
8C2×#16838087C212yesmaximal, complemented
9C2×#16838086C212yesmaximal, complemented
10C2×#16837998C214yesmaximal, complemented
11C2×#16837975C212yesmaximal, complemented
12C2×#16837957C211yesmaximal, characteristic, complemented
13C2×#16837949C211yesmaximal, characteristic
14C2×#16837937C212yesmaximal, complemented
15C2×#16837934C212yesmaximal, complemented
16C2×#16837883C212yesmaximal, complemented
17C2×C4×Q8×D59C211yesmaximal, characteristic, complemented
18C2×C59×#554C211yesmaximal, characteristic, complemented
19C22×#11745685C2212yes—
20C22×Q8×D59C2211yescharacteristic
21#16838135C22132yescomplemented
22#16838129C22132yescomplemented
23#16838125C22116yescomplemented
24#16838123C22164yescomplemented
25#16838122C22116yescomplemented
26#16838113C22116yescomplemented
27#16838087C22132yescomplemented
28#16838086C22132yescomplemented
29#16837998C22164yescomplemented
30#16837975C22132yescomplemented
31#16837957C22116yescomplemented
32#16837949C22116yes—
33C2×#14273727C2211yescharacteristic
34C2×#14273726C2211yescharacteristic
35C2×#14273726C2214yes—
36C2×#14273723C2211yescharacteristic
37#16837937C22132yescomplemented
38#16837934C22132yescomplemented
39C2×#14273722C2214yes—
40C2×#14273722C2214yes—
41C2×#14273720C2214yes—
42C2×#14273720C2214yes—
43C2×#14273718C2212yes—
44C2×#14273718C2212yes—
45C2×#14273717C2214yes—
46C2×#14273717C2214yes—
47C2×#14273715C2212yes—
48C2×#14273714C2212yes—
49C2×#14273713C2212yes—
50C2×#14273713C2214yes—
51C2×#14273712C2214yes—
52C2×#14273710C2214yes—
53C2×#14273709C2214yes—
54C2×#14273709C2214yes—
55C2×#14273707C2212yes—
56C2×#14273707C2212yes—
57C2×#14273706C2212yes—
58C2×#14273703C2212yes—
59C2×#14273703C2214yes—
60C2×#14273703C2212yes—
61C2×#14273702C2211yescharacteristic
62C2×#14273700C2212yes—
63C2×#14273698C2211yescharacteristic
64#16837883C22132yescomplemented
65C2×Q8×Dic59C2211yescharacteristic
66C2×Q8×Dic59C2212yes—
67C2×C4×Dic118C2211yescharacteristic
68C2×C4×Dic118C2212yes—
69C2×C4×Dic118C2212yes—
70C2×#14273692C2211yescharacteristic
71C2×#14273692C2212yes—
72C2×#14273692C2214yes—
73C2×#14273692C2212yes—
74C2×#14273692C2212yes—
75C4×Q8×D59C22116yescomplemented
76C2×C4×D236C2211yescharacteristic
77C2×#14273689C2214yes—
78C2×#14273689C2212yes—
79C2×C4×C22⋊D59C2214yes—
80C2×C4×C22⋊D59C2214yes—
81C2×C4×C22⋊D59C2212yes—
82C2×#14273686C2212yes—
83C2×#14273686C2214yes—
84C2×#14273685C2212yes—
85C2×#14273685C2212yes—
86C2×#14273685C2214yes—
87C2×C4⋊C4×D59C2212yes—
88C2×C4⋊C4×D59C2211yescharacteristic
89C2×C4⋊C4×D59C2212yes—
90C2×C42×D59C2212yes—
91C2×C42×D59C2211yescharacteristic
92C59×#554C22116yescomplemented
93C2×C4⋊Q8×C59C2211yescharacteristic
94C2×#125×C59C2212yes—
95C2×C22⋊Q8×C59C2214yes—
96C2×C22⋊Q8×C59C2212yes—
97C2×C4×Q8×C59C2211yescharacteristic
98C2×C4×D4×C59C2212yes—
99C2×C4×D4×C59C2211yescharacteristic
100C22×C4⋊C4×C59C2212yes—
101C2×#11745685—216no—
102C2×#11745685C23116yes—
103C22×Dic118C2311yescharacteristic
104C22×Dic118C2312yes—
105C22×Dic118C2312yes—
106C22×Dic118C2312yes—
107C2×Q8×D59—28no—
108C2×Q8×D59C2318yes—
109C22×D236C2312yes—
110C22×D236C2311yescharacteristic
111C22×C22⋊D59C2312yes—
112C22×C22⋊D59C2312yes—
113C22×C22⋊D59C2312yes—
114C22×C4×D59C2311yescharacteristic
115C22×C4×D59C2312yes—
116C22×C4×D59C2312yes—
117C22×C4×D59C2311yescharacteristic
118C22×C4×D59C2314yes—
119C22×C4×D59C2312yes—
120C22×C4×D59C2311yescharacteristic
121#14273727C2318yes—
122#14273726C2318yes—
123#14273726C23132yes—
124#14273723C2318yes—
125#14273722C23132yes—
126#14273722C23132yes—
127#14273720C23132yes—
128#14273720C23132yes—
129#14273718C23116yes—
130#14273718C23116yes—
131#14273717C23132yes—
132#14273717C23132yes—
133#14273715C23116yes—
134#14273714C23116yes—
135#14273713C23116yes—
136#14273713C23132yes—
137#14273712C23132yes—
138#14273710C23132yes—
139#14273709C23132yes—
140#14273709C23132yes—
141#14273707C23116yes—
142#14273707C23116yes—
143#14273706C23116yes—
144#14273703C23116yes—
145#14273703C23116yes—
146#14273703C23132yes—
147#14273702C2318yes—
148#14273700C23116yes—
149#14273698C2318yes—
150Q8×Dic59C23116yes—
151Q8×Dic59C2318yes—
152C4×Dic118C23116yes—
153C4×Dic118C2318yes—
154C4×Dic118C23116yes—
155#14273692C23116yes—
156#14273692C23116yes—
157#14273692C2318yes—
158#14273692C23116yes—
159#14273692C23132yes—
160C4×D236C2318yes—
161#14273689C23132yes—
162#14273689C23116yes—
163C4×C22⋊D59C23132yes—
164C4×C22⋊D59C23116yes—
165C4×C22⋊D59C23132yes—
166#14273686C23132yes—
167#14273686C23116yes—
168#14273685C23132yes—
169#14273685C23116yes—
170#14273685C23116yes—
171C2×C4⋊Dic59C2311yescharacteristic
172C2×C4⋊Dic59C2312yes—
173C2×C4⋊Dic59C2314yes—
174C2×C4⋊Dic59C2312yes—
175C2×C4⋊Dic59C2314yes—
176C2×C4⋊Dic59C2312yes—
177C2×C4⋊Dic59C2311yescharacteristic
178C2×Dic59⋊C4C2312yes—
179C2×Dic59⋊C4C2312yes—
180C2×Dic59⋊C4C2314yes—
181C2×Dic59⋊C4C2314yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2312yes—
186C4⋊C4×D59C23116yes—
187C4⋊C4×D59C23116yes—
188C4⋊C4×D59C2318yes—
189C2×C22⋊Dic59C2312yes—
190C2×C22⋊Dic59C2314yes—
191C2×C22⋊Dic59C2314yes—
192C2×(C2×D59)⋊C4C2312yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2314yes—
195C2×(C2×D59)⋊C4C2314yes—
196C2×(C2×D59)⋊C4C2314yes—
197C2×(C2×D59)⋊C4C2314yes—
198C2×C4×Dic59C2311yescharacteristic
199C2×C4×Dic59C2314yes—
200C2×C4×Dic59C2312yes—
201C2×C4×Dic59C2314yes—
202C2×C4×Dic59C2314yes—
203C2×C4×Dic59C2311yescharacteristic
204C2×C4×Dic59C2312yes—
205C2×C4×Dic59C2312yes—
206C2×C4×Dic59C2311yescharacteristic
207C42×D59C23116yes—
208C42×D59C2318yes—
209C22×Q8×C59C2311yescharacteristic
210C22×Q8×C59C2312yes—
211C22×D4×C59C2311yescharacteristic
212C23×C4×C59C2312yes—
213C23×C4×C59C2314yes—
214C4⋊Q8×C59C2318yes—
215#125×C59C23116yes—
216C22⋊Q8×C59C23116yes—
217C22⋊Q8×C59C23132yes—
218C4×Q8×C59C2318yes—
219C4×D4×C59C23116yes—
220C4×D4×C59C2318yes—
221C2×C4⋊C4×C59C2311yescharacteristic
222C2×C4⋊C4×C59C2312yes—
223C2×C4⋊C4×C59C2312yes—
224C2×C4⋊C4×C59C2314yes—
225C2×C4⋊C4×C59C2314yes—
226C2×C4⋊C4×C59C2312yes—
227C2×C4⋊C4×C59C2311yescharacteristic
228C2×C4⋊C4×C59C23116yes—
229C2×C22⋊C4×C59C2312yes—
230C2×C22⋊C4×C59C2314yes—
231C2×C42×C59C2312yes—
232C2×C42×C59C2311yescharacteristic
233C24×C59C2412yes—
234C23×D59C2412yes—
235C23×D59C2411yescharacteristic
236C2×Q8×C59—24no—
237C2×Q8×C59—44no—
238C2×Q8×C59C2414yes—
239C2×Q8×C59C2418yes—
240C2×D4×C59—24no—
241C2×D4×C59C2414yes—
242C22×C4×C59—28no—
243C22×C4×C59—48no—
244C22×C4×C59C2412yes—
245C22×C4×C59C2411yescharacteristic
246C22×C4×C59C2412yes—
247C22×C4×C59C2412yes—
248C22×C4×C59C2414yes—
249C22×C4×C59C2418yes—
250C22×C4×C59C24116yes—
251C22×C4×C59C2411yescharacteristic
252C22×C4×C59C2411yescharacteristic
253C2×C22⋊D59—28no—
254C2×C22⋊D59—28no—
255C2×C22⋊D59—44no—
256C2×C22⋊D59C2418yes—
257C2×C22⋊D59C2418yes—
258C2×C22⋊D59C2418yes—
259C22×Dic59C2411yescharacteristic
260C22×Dic59C2412yes—
261C22×Dic59C2414yes—
262C22×Dic59C2412yes—
263C22×Dic59C2412yes—
264C22×Dic59C2411yescharacteristic
265C22×Dic59C2411yescharacteristic
266Q8×D59—232no—
267#11745685—264no—
268C2×D236—28no—
269C2×D236—24no—
270C2×D236C2414yes—
271C2×D236C2418yes—
272C2×C4×D59—28no—
273C2×C4×D59—28no—
274C2×C4×D59—24no—
275C2×C4×D59—44no—
276C2×C4×D59—48no—
277C2×C4×D59—42no—
278C2×C4×D59#4118yes—
279C2×C4×D59C2414yes—
280C2×C4×D59C2418yes—
281C2×C4×D59C2418yes—
282C2×C4×D59C2418yes—
283C2×C4×D59C2414yes—
284C2×C4×D59C24116yes—
285C2×C4×D59C2414yes—
286C2×Dic118—24no—
287C2×Dic118—28no—
288C2×Dic118—28no—
289C2×Dic118—28no—
290C2×Dic118C2418yes—
291C2×Dic118C2418yes—
292C2×Dic118C2414yes—
293C2×Dic118C2418yes—
294C4⋊C4×C59C2414yes—
295C4⋊C4×C59C24116yes—
296C4⋊C4×C59C2418yes—
297C4⋊C4×C59C2414yes—
298C4⋊C4×C59C2418yes—
299C4⋊C4×C59C2418yes—
300C4⋊C4×C59C24116yes—
301C22⋊C4×C59C2418yes—
302C22⋊C4×C59C24116yes—
303C42×C59C2418yes—
304C42×C59C2414yes—
305C22⋊Dic59C2418yes—
306C22⋊Dic59C24116yes—
307C22⋊Dic59C24116yes—
308(C2×D59)⋊C4C2418yes—
309(C2×D59)⋊C4C24116yes—
310(C2×D59)⋊C4C24116yes—
311(C2×D59)⋊C4C24116yes—
312(C2×D59)⋊C4C24116yes—
313(C2×D59)⋊C4C2418yes—
314C4⋊Dic59C2414yes—
315C4⋊Dic59C2418yes—
316C4⋊Dic59C2418yes—
317C4⋊Dic59C24116yes—
318C4⋊Dic59C24116yes—
319C4⋊Dic59C2414yes—
320C4⋊Dic59C2418yes—
321Dic59⋊C4C2418yes—
322Dic59⋊C4C24116yes—
323Dic59⋊C4C2418yes—
324Dic59⋊C4C2418yes—
325Dic59⋊C4C2418yes—
326Dic59⋊C4C24116yes—
327Dic59⋊C4C24116yes—
328Dic59⋊C4C24116yes—
329C4×Dic59C2418yes—
330C4×Dic59C2418yes—
331C4×Dic59C2414yes—
332C4×Dic59C2418yes—
333C4×Dic59C2414yes—
334C4×Dic59C2414yes—
335C4×Dic59C24116yes—
336C4×Dic59C24116yes—
337C4×Dic59C24116yes—
338C23×C59—24no—
339C23×C59—24no—
340C23×C59—24no—
341C23×C59C2514yes—
342C23×C59C2511yescharacteristic
343C22×D59—22no—
344C22×D59—22no—
345C22×D59—24no—
346C22×D59—24no—
347C22×D59—24no—
348C22×D59C2×#4114yes—
349C22×D59C2514yes—
350C22×D59C2512yes—
351Q8×C59—28no—
352Q8×C59—48no—
353D4×C59—28no—
354C2×C4×C59—24no—
355C2×C4×C59—24no—
356C2×C4×C59—24no—
357C2×C4×C59—28no—
358C2×C4×C59—22no—
359C2×C4×C59—216no—
360C2×C4×C59—416no—
361C2×C4×C59C2×#4114yes—
362C2×C4×C592−1+414yes—
363C2×C4×C59C2514yes—
364C2×C4×C59C2514yes—
365C2×C4×C59C2512yes—
366C2×C4×C59C2518yes—
367C2×C4×C59C2514yes—
368C2×C4×C59C2512yes—
369C2×C4×C59C2512yes—
370C22⋊D59—216no—
371C22⋊D59—216no—
372C22⋊D59—48no—
373C2×Dic59—24no—
374C2×Dic59—24no—
375C2×Dic59—28no—
376C2×Dic59—22no—
377C2×Dic59—24no—
378C2×Dic59—22no—
379C2×Dic59C2×#4114yes—
380C2×Dic59C2512yes—
381C2×Dic59C2514yes—
382C2×Dic59C2518yes—
383C2×Dic59C2512yes—
384C2×Dic59C2514yes—
385C2×Dic59C2514yes—
386C2×Dic59C2512yes—
387D236—216no—
388D236—28no—
389C4×D59—216no—
390C4×D59—216no—
391C4×D59—28no—
392C4×D59—48no—
393C4×D59—416no—
394C4×D59—44no—
395C4×D59C2×#41116yes—
396Dic118—28no—
397Dic118—216no—
398Dic118—216no—
399Dic118—216no—
400C2×#3507—591nomaximal, Sylow
401C22×C59—24no—
402C22×C59—24no—
403C22×C59—24no—
404C22×C59—48no—
405C22×C59C22×#4112yes—
406C22×C59C2×2−1+412yes—
407C22×C59#58512yes—
408C22×C59C2611yescharacteristic
409C2×D59—22no—
410C2×D59—22no—
411C2×D59—28no—
412C2×D59—24no—
413C2×D59—24no—
414C2×D59—24no—
415C2×D59—48no—
416C2×D59C22×#4114yes—
417C4×C59—24no—
418C4×C59—24no—
419C4×C59—24no—
420C4×C59—28no—
421C4×C59—22no—
422C4×C59C22×#4114yes—
423C4×C59C2×2−1+414yes—
424Dic59—24no—
425Dic59—24no—
426Dic59—28no—
427Dic59—22no—
428Dic59—24no—
429Dic59—22no—
430Dic59C22×#4114yes—
431#3507—5932no—
432C2×#559—592no—
433C2×#557—592no—
434C2×#556—594no—
435C2×#556—591no—
436C2×#556—591no—
437C2×#554—591no—
438C2×#554D5911yescharacteristic, complemented
439C2×#552—592no—
440C2×#552—592no—
441C2×#539—594no—
442C2×#536—592no—
443C2×#533—591no—
444C2×#532—591no—
445C2×#529—592no—
446C2×#529—592no—
447C2×#520—592no—
448C22×C4×Q8—591no—
449C2×C59—44no—
450C2×C59#350714yescomplemented
451C2×C59C23×#4111yescharacteristic
452C2×C59C22×2−1+411yescharacteristic
453C2×C59C2×#58511yescharacteristic
454D59—24no—
455D59—44no—
456C22×#41—592no—
457C23×Q8—591no—
458#559—5932no—
459#557—5932no—
460#556—5964no—
461#556—5916no—
462#556—5916no—
463#554—5916no—
464#554C2×D59116yescomplemented
465#552—5932no—
466#552—5932no—
467#539—5964no—
468#536—5932no—
469#533—5916no—
470#532—5916no—
471C2×C4⋊Q8—591no—
472C2×C4⋊Q8—594no—
473C2×C4⋊Q8—591no—
474C2×C4⋊Q8C2×D5911yescharacteristic
475C2×#127—591no—
476#529—5932no—
477#529—5932no—
478C2×#126—594no—
479C2×#126—594no—
480C2×#126—594no—
481C2×#126—594no—
482C2×#125—594no—
483C2×#125—594no—
484C2×#125—592no—
485C2×#125—592no—
486C2×#125C2×D5912yes—
487C2×#124—592no—
488C2×#124—592no—
489C2×#124—594no—
490C2×#124—592no—
491C2×#123—594no—
492C2×#123—594no—
493C2×#123—594no—
494C2×#123—594no—
495C2×C22⋊Q8—592no—
496C2×C22⋊Q8—592no—
497C2×C22⋊Q8—594no—
498C2×C22⋊Q8—592no—
499C2×C22⋊Q8—592no—
500C2×C22⋊Q8—592no—
501C2×C22⋊Q8C2×D5912yes—
502C2×C22⋊Q8C2×D5914yes—
503C2×#121—591no—
504C2×#121—591no—
505C2×#121—592no—
506#520—5932no—
507C2×C4×Q8—591no—
508C2×C4×Q8—592no—
509C2×C4×Q8—5916no—
510C2×C4×Q8—591no—
511C2×C4×Q8—592no—
512C2×C4×Q8—594no—
513C2×C4×Q8—592no—
514C2×C4×Q8—592no—
515C2×C4×Q8—591no—
516C2×C4×Q8—592no—
517C2×C4×Q8—592no—
518C2×C4×Q8C2×D5911yescharacteristic
519C2×C4×D4—594no—
520C2×C4×D4—594no—
521C2×C4×D4—592no—
522C2×C4×D4—594no—
523C2×C4×D4—592no—
524C2×C4×D4—591no—
525C2×C4×D4C2×D5912yes—
526C2×C4×D4C2×D5911yescharacteristic
527C2×#117—592no—
528C2×#117—594no—
529C2×#117—592no—
530C2×#117—592no—
531C2×#117—594no—
532C22×C4⋊C4—591no—
533C22×C4⋊C4—592no—
534C22×C4⋊C4—592no—
535C22×C4⋊C4C2×D5912yes—
536C22×C42—592no—
537C22×C42—591no—
538C59C2×#350711yescharacteristic, complemented, Sylow
539C2×#41—5916no—
540C2×#41—11816no—
541C22×Q8—598no—
542C22×Q8—592no—
543C22×Q8—591no—
544C22×Q8—592no—
545C22×Q8—592no—
546C22×Q8—1188no—
547C22×Q8C22×D5911yescharacteristic
548C22×Q8C22×D5912yes—
549C22×D4—592no—
550C22×D4—592no—
551C22×D4—592no—
552C22×D4—591no—
553C22×D4—592no—
554C22×D4C22×D5911yescharacteristic
555C23×C4—591no—
556C23×C4—592no—
557C23×C4—592no—
558C23×C4—591no—
559C23×C4—592no—
560C23×C4—591no—
561C23×C4—594no—
562C23×C4C22×D5912yes—
563C23×C4C22×D5914yes—
564C4⋊Q8—598no—
565C4⋊Q8—5932no—
566C4⋊Q8—598no—
567C4⋊Q8C22×D5918yes—
568#127—598no—
569#126—5932no—
570#126—5932no—
571#126—5932no—
572#126—5932no—
573#125—5916no—
574#125—5916no—
575#125—5932no—
576#125—5932no—
577#125C22×D59116yes—
578#124—5916no—
579#124—5916no—
580#124—5932no—
581#124—5916no—
582#123—5932no—
583#123—5932no—
584#123—5932no—
585#123—5932no—
586C22⋊Q8—5916no—
587C22⋊Q8—5916no—
588C22⋊Q8—5932no—
589C22⋊Q8—5916no—
590C22⋊Q8—5916no—
591C22⋊Q8—5916no—
592C22⋊Q8C22×D59116yes—
593C22⋊Q8C22×D59132yes—
594#121—598no—
595#121—598no—
596#121—5916no—
597C4×Q8—598no—
598C4×Q8—5916no—
599C4×Q8—598no—
600C4×Q8—5916no—
601C4×Q8—5932no—
602C4×Q8—5916no—
603C4×Q8—5916no—
604C4×Q8—598no—
605C4×Q8—5916no—
606C4×Q8—5916no—
607C4×Q8C22×D5918yes—
608C4×D4—5932no—
609C4×D4—5932no—
610C4×D4—5916no—
611C4×D4—5932no—
612C4×D4—5916no—
613C4×D4—598no—
614C4×D4C22×D59116yes—
615C4×D4C22×D5918yes—
616#117—5916no—
617#117—5932no—
618#117—5916no—
619#117—5916no—
620#117—5932no—
621C2×C4⋊C4—591no—
622C2×C4⋊C4—592no—
623C2×C4⋊C4—594no—
624C2×C4⋊C4—592no—
625C2×C4⋊C4—592no—
626C2×C4⋊C4—592no—
627C2×C4⋊C4—592no—
628C2×C4⋊C4—594no—
629C2×C4⋊C4—594no—
630C2×C4⋊C4—591no—
631C2×C4⋊C4—592no—
632C2×C4⋊C4—594no—
633C2×C4⋊C4—594no—
634C2×C4⋊C4—594no—
635C2×C4⋊C4—592no—
636C2×C4⋊C4—598no—
637C2×C4⋊C4—5916no—
638C2×C4⋊C4—5916no—
639C2×C4⋊C4C22×D5911yescharacteristic
640C2×C4⋊C4C22×D5912yes—
641C2×C4⋊C4C22×D5912yes—
642C2×C4⋊C4C22×D5914yes—
643C2×C4⋊C4C22×D59116yes—
644C2×C4⋊C4C22×D5914yes—
645C2×C4⋊C4C22×D5912yes—
646C2×C4⋊C4C22×D5911yescharacteristic
647C2×C22⋊C4—592no—
648C2×C22⋊C4—594no—
649C2×C22⋊C4—594no—
650C2×C22⋊C4—592no—
651C2×C22⋊C4—594no—
652C2×C22⋊C4—594no—
653C2×C22⋊C4—594no—
654C2×C22⋊C4—592no—
655C2×C22⋊C4—594no—
656C2×C22⋊C4C22×D5912yes—
657C2×C22⋊C4C22×D5914yes—
658C2×C42—594no—
659C2×C42—594no—
660C2×C42—592no—
661C2×C42—592no—
662C2×C42—594no—
663C2×C42—591no—
664C2×C42—592no—
665C2×C42—591no—
666C2×C42—591no—
667C2×C42—5916no—
668C2×C42—598no—
669C2×C42C22×D5911yescharacteristic
670C2×C42C22×D5912yes—
671C24—591no—
672C24—592no—
673C24C23×D5912yes—
674#41—11864no—
675C2×Q8—24no—
676C2×Q8—44no—
677C2×Q8—598no—
678C2×Q8—594no—
679C2×Q8—598no—
680C2×Q8—598no—
681C2×Q8—1188no—
682C2×Q8—1188no—
683C2×Q8—11832no—
684C2×Q8—1184no—
685C2×Q8—1188no—
686C2×Q8C23×D5914yes—
687C2×Q8C23×D5918yes—
688C2×D4—24no—
689C2×D4—598no—
690C2×D4—598no—
691C2×D4—598no—
692C2×D4—594no—
693C2×D4—598no—
694C2×D4—1188no—
695C2×D4—1188no—
696C2×D4—1188no—
697C2×D4—1184no—
698C2×D4—2364no—
699C2×D4C23×D5914yes—
700C22×C4—28no—
701C22×C4—48no—
702C22×C4—591no—
703C22×C4—598no—
704C22×C4—594no—
705C22×C4—591no—
706C22×C4—592no—
707C22×C4—594no—
708C22×C4—592no—
709C22×C4—592no—
710C22×C4—591no—
711C22×C4—594no—
712C22×C4—598no—
713C22×C4—598no—
714C22×C4—598no—
715C22×C4—594no—
716C22×C4—5916no—
717C22×C4—1188no—
718C22×C4—1188no—
719C22×C4—1184no—
720C22×C4—2364no—
721C22×C4—2368no—
722C22×C4—2362no—
723C22×C4C23×D5918yes—
724C22×C4C23×D5912yes—
725C22×C4C23×D5912yes—
726C22×C4C23×D5911yescharacteristic
727C22×C4C23×D5912yes—
728C22×C4C23×D5914yes—
729C22×C4C23×D59116yes—
730C22×C4C23×D5911yescharacteristic
731C22×C4C23×D5911yescharacteristic
732C4⋊C4—594no—
733C4⋊C4—598no—
734C4⋊C4—5916no—
735C4⋊C4—598no—
736C4⋊C4—598no—
737C4⋊C4—598no—
738C4⋊C4—598no—
739C4⋊C4—5916no—
740C4⋊C4—5916no—
741C4⋊C4—594no—
742C4⋊C4—598no—
743C4⋊C4—5916no—
744C4⋊C4—5916no—
745C4⋊C4—5916no—
746C4⋊C4—598no—
747C4⋊C4C23×D5914yes—
748C4⋊C4C23×D5918yes—
749C4⋊C4C23×D5918yes—
750C4⋊C4C23×D59116yes—
751C4⋊C4C23×D59116yes—
752C4⋊C4C23×D5918yes—
753C4⋊C4C23×D5914yes—
754C22⋊C4—598no—
755C22⋊C4—5916no—
756C22⋊C4—5916no—
757C22⋊C4—598no—
758C22⋊C4—5916no—
759C22⋊C4—5916no—
760C22⋊C4—5916no—
761C22⋊C4—598no—
762C22⋊C4—5916no—
763C22⋊C4C23×D5918yes—
764C22⋊C4C23×D59116yes—
765C42—598no—
766C42—598no—
767C42—594no—
768C42—598no—
769C42—594no—
770C42—594no—
771C42—5916no—
772C42—5916no—
773C42—5916no—
774C42C23×D5914yes—
775C42C23×D5918yes—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—594no—
780C23—592no—
781C23—594no—
782C23—1182no—
783C23—1182no—
784C23—1184no—
785C23—1184no—
786C23—1184no—
787C23C24×D5914yes—
788C23C24×D5911yescharacteristic
789Q8—28no—
790Q8—48no—
791Q8—11816no—
792Q8—11816no—
793Q8—1188no—
794Q8—11816no—
795D4—28no—
796D4—11816no—
797D4—11816no—
798D4—11816no—
799D4—1188no—
800D4—2368no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—28no—
805C2×C4—22no—
806C2×C4—216no—
807C2×C4—416no—
808C2×C4—594no—
809C2×C4—592no—
810C2×C4—5916no—
811C2×C4—592no—
812C2×C4—594no—
813C2×C4—598no—
814C2×C4—594no—
815C2×C4—594no—
816C2×C4—592no—
817C2×C4—11816no—
818C2×C4—1184no—
819C2×C4—1184no—
820C2×C4—1182no—
821C2×C4—1188no—
822C2×C4—1184no—
823C2×C4—1182no—
824C2×C4—11816no—
825C2×C4—1188no—
826C2×C4—2368no—
827C2×C4—23616no—
828C2×C4—2364no—
829C2×C4#41×D5914yes—
830C2×C4#1427377514yes—
831C2×C4C24×D5914yes—
832C2×C4C24×D5914yes—
833C2×C4C24×D5912yes—
834C2×C4C24×D5914yes—
835C2×C4C24×D5918yes—
836C2×C4C24×D5912yes—
837C2×C4C24×D5912yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—48no—
842C22—594no—
843C22—1188no—
844C22—1182no—
845C22—1182no—
846C22—1184no—
847C22—1184no—
848C22—1184no—
849C22—2368no—
850C22C2×#41×D5912yes—
851C22C2×#1427377512yes—
852C22#1683823712yes—
853C22C25×D5911yescharacteristic
854C4—24no—
855C4—24no—
856C4—24no—
857C4—28no—
858C4—22no—
859C4—594no—
860C4—1184no—
861C4—1184no—
862C4—1182no—
863C4—1188no—
864C4—1184no—
865C4—1182no—
866C4C2×#41×D5914yes—
867C4C2×#1427377514yes—
868C2—44no—
869C2—1184no—
870C2—2364no—
871C2#2143795914yesdirect product factor
872C2C22×#41×D5911yescharacteristic
873C2C22×#1427377511yescharacteristic
874C2C2×#1683823711yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#554C2
socleC23×C59C25
prime radicalC2×#16837949C2
hypercenterC2×#554D59
hypocenterC59C2×#3507
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #21437959C2direct (N × H)
2. C2×#16838135C2semidirect
3. C2×#16838129C2semidirect
4. C2×#16838125C2semidirect
5. C2×#16838123C2semidirect
6. C2×#16838122C2semidirect
7. C2×#16838113C2semidirect
8. C2×#16838087C2semidirect
9. C2×#16838086C2semidirect
10. C2×#16837998C2semidirect
11. C2×#16837975C2semidirect
12. C2×#16837957C2semidirect
14. C2×#16837937C2semidirect
15. C2×#16837934C2semidirect
16. C2×#16837883C2semidirect
17. C2×C4×Q8×D59C2semidirect
18. C2×C59×#554C2semidirect
21. #16838135C22semidirect
22. #16838129C22semidirect
23. #16838125C22semidirect
24. #16838123C22semidirect
25. #16838122C22semidirect
26. #16838113C22semidirect
27. #16838087C22semidirect
28. #16838086C22semidirect
29. #16837998C22semidirect
30. #16837975C22semidirect
31. #16837957C22semidirect
37. #16837937C22semidirect
38. #16837934C22semidirect
64. #16837883C22semidirect
75. C4×Q8×D59C22semidirect
92. C59×#554C22semidirect
438. C2×#554D59semidirect
450. C2×C59#3507semidirect
464. #554C2×D59semidirect
538. C59C2×#3507semidirect
871. C2#21437959direct (N × H)

Maximal subgroups

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

subgroupindex
#214379592
C2×#168381352
C2×#168381292
C2×#168381252
C2×#168381232
C2×#168381222
C2×#168381132
C2×#168380872
C2×#168380862
C2×#168379982
C2×#168379752
C2×#168379572
C2×#168379492
C2×#168379372
C2×#168379342
C2×#168378832
C2×C4×Q8×D592
C2×C59×#5542
C2×#350759