Finite Group Databasebeta

← C2×#21438437 #29496372

Subgroups — C2×#21438437 #29496372

Order 15104.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438437C2132yesmaximal, direct product factor
2C2×#16838153C214yesmaximal, complemented
3C2×Q8×Dic118C211yesmaximal, characteristic, complemented
4C2×#16838117C211yesmaximal, characteristic, complemented
5C2×#16838113C211yesmaximal, characteristic, complemented
6C2×#16838090C212yesmaximal, complemented
7C2×#16838086C212yesmaximal, complemented
8C2×#16838057C212yesmaximal, complemented
9C2×#16838053C212yesmaximal, complemented
10C2×#16838033C212yesmaximal, complemented
11C2×#16838032C212yesmaximal, complemented
12C2×#16838025C212yesmaximal, complemented
13C2×#16838017C212yesmaximal, complemented
14C2×#16837975C214yesmaximal, complemented
15C2×C4⋊Q8×D59C211yesmaximal, characteristic, complemented
16C2×#16837939C211yesmaximal, characteristic, complemented
17C2×#16837934C211yesmaximal, characteristic, complemented
18C2×C59×#554C211yesmaximal, characteristic, complemented
19C22×#11745685C2214yes—
20C22×Q8×D59C2212yes—
21#16838153C22164yescomplemented
22Q8×Dic118C22116yescomplemented
23#16838117C22116yescomplemented
24#16838113C22116yescomplemented
25#16838090C22132yescomplemented
26#16838086C22132yescomplemented
27#16838057C22132yescomplemented
28#16838053C22132yescomplemented
29#16838033C22132yescomplemented
30#16838032C22132yescomplemented
31#16838025C22132yescomplemented
32#16838017C22132yescomplemented
33#16837975C22164yescomplemented
34C2×#14273727C2212yes—
35C2×#14273727C2211yescharacteristic
36C2×#14273726C2214yes—
37C2×#14273726C2212yes—
38C2×#14273726C2212yes—
39C2×#14273726C2214yes—
40C2×#14273726C2212yes—
41C2×#14273725C2212yes—
42C4⋊Q8×D59C22116yescomplemented
43#16837939C22116yescomplemented
44#16837934C22116yescomplemented
45C2×#14273722C2212yes—
46C2×#14273722C2214yes—
47C2×#14273720C2212yes—
48C2×#14273720C2214yes—
49C2×#14273718C2214yes—
50C2×#14273718C2211yescharacteristic
51C2×#14273718C2211yescharacteristic
52C2×#14273718C2212yes—
53C2×#14273717C2214yes—
54C2×#14273716C2211yescharacteristic
55C2×#14273714C2211yescharacteristic
56C2×#14273713C2214yes—
57C2×#14273713C2214yes—
58C2×#14273712C2214yes—
59C2×#14273712C2212yes—
60C2×#14273710C2214yes—
61C2×#14273709C2214yes—
62C2×#14273709C2214yes—
63C2×#14273709C2212yes—
64C2×#14273707C2212yes—
65C2×#14273707C2214yes—
66C2×#14273707C2211yescharacteristic
67C2×#14273706C2214yes—
68C2×#14273706C2214yes—
69C2×#14273705C2214yes—
70C2×#14273703C2214yes—
71C2×#14273703C2211yescharacteristic
72C2×#14273702C2211yescharacteristic
73C2×#14273701C2212yes—
74C2×#14273698C2212yes—
75C2×#14273698C2211yescharacteristic
76C2×Q8×Dic59C2212yes—
77C2×C4×Dic118C2212yes—
78C2×C4×Dic118C2211yescharacteristic
79C2×C4×D236C2212yes—
80C2×C4×D236C2211yescharacteristic
81C2×#14273689C2212yes—
82C2×C4×C22⋊D59C2212yes—
83C2×#14273686C2212yes—
84C2×#14273686C2212yes—
85C2×#14273685C2212yes—
86C2×#14273685C2214yes—
87C2×#14273684C2212yes—
88C2×C4⋊C4×D59C2212yes—
89C2×C4⋊C4×D59C2212yes—
90C2×C4⋊C4×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—416no—
102C2×#11745685C23132yes—
103C22×Dic118C2311yescharacteristic
104C22×Dic118C2314yes—
105C22×Dic118C2314yes—
106C22×Dic118C2312yes—
107C2×Q8×D59—48no—
108C2×Q8×D59C23116yes—
109C22×D236C2311yescharacteristic
110C22×D236C2312yes—
111C22×C22⋊D59C2312yes—
112C22×C22⋊D59C2314yes—
113C22×C4×D59C2311yescharacteristic
114C22×C4×D59C2312yes—
115C22×C4×D59C2311yescharacteristic
116C22×C4×D59C2311yescharacteristic
117C22×C4×D59C2314yes—
118C22×C4×D59C2314yes—
119#14273727C2318yes—
120#14273727C23116yes—
121#14273726C23132yes—
122#14273726C23116yes—
123#14273726C23116yes—
124#14273726C23132yes—
125#14273726C23116yes—
126#14273725C23116yes—
127#14273722C23116yes—
128#14273722C23132yes—
129#14273720C23116yes—
130#14273720C23132yes—
131#14273718C23132yes—
132#14273718C2318yes—
133#14273718C2318yes—
134#14273718C23116yes—
135#14273717C23132yes—
136#14273716C2318yes—
137#14273714C2318yes—
138#14273713C23132yes—
139#14273713C23132yes—
140#14273712C23116yes—
141#14273712C23132yes—
142#14273710C23132yes—
143#14273709C23132yes—
144#14273709C23116yes—
145#14273709C23132yes—
146#14273707C2318yes—
147#14273707C23132yes—
148#14273707C23116yes—
149#14273706C23132yes—
150#14273706C23132yes—
151#14273705C23132yes—
152#14273703C23132yes—
153#14273703C2318yes—
154#14273702C2318yes—
155#14273701C23116yes—
156#14273698C2318yes—
157#14273698C23116yes—
158Q8×Dic59C23116yes—
159C4×Dic118C2318yes—
160C4×Dic118C23116yes—
161C4×D236C23116yes—
162C4×D236C2318yes—
163#14273689C23116yes—
164C4×C22⋊D59C23116yes—
165#14273686C23116yes—
166#14273686C23116yes—
167#14273685C23132yes—
168#14273685C23116yes—
169#14273684C23116yes—
170C2×C4⋊Dic59C2311yescharacteristic
171C2×C4⋊Dic59C2312yes—
172C2×C4⋊Dic59C2312yes—
173C2×C4⋊Dic59C2314yes—
174C2×C4⋊Dic59C2311yescharacteristic
175C2×C4⋊Dic59C2312yes—
176C2×C4⋊Dic59C2312yes—
177C2×C4⋊Dic59C2314yes—
178C2×C4⋊Dic59C2312yes—
179C2×Dic59⋊C4C2312yes—
180C2×Dic59⋊C4C2314yes—
181C2×Dic59⋊C4C2312yes—
182C2×Dic59⋊C4C2312yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2314yes—
186C2×Dic59⋊C4C2314yes—
187C4⋊C4×D59C23116yes—
188C4⋊C4×D59C23116yes—
189C4⋊C4×D59C23116yes—
190C2×C22⋊Dic59C2312yes—
191C2×C22⋊Dic59C2314yes—
192C2×C22⋊Dic59C2312yes—
193C2×C22⋊Dic59C2312yes—
194C2×(C2×D59)⋊C4C2314yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2312yes—
197C2×(C2×D59)⋊C4C2314yes—
198C2×(C2×D59)⋊C4C2312yes—
199C2×(C2×D59)⋊C4C2312yes—
200C2×(C2×D59)⋊C4C2312yes—
201C2×(C2×D59)⋊C4C2312yes—
202C2×C4×Dic59C2314yes—
203C2×C4×Dic59C2314yes—
204C2×C4×Dic59C2311yescharacteristic
205C2×C4×Dic59C2311yescharacteristic
206C2×C4×Dic59C2312yes—
207C2×C4×Dic59C2311yescharacteristic
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×C59C23132yes—
217C22⋊Q8×C59C23116yes—
218C4×Q8×C59C2318yes—
219C4×D4×C59C2318yes—
220C4×D4×C59C23116yes—
221C2×C4⋊C4×C59C2311yescharacteristic
222C2×C4⋊C4×C59C2314yes—
223C2×C4⋊C4×C59C2314yes—
224C2×C4⋊C4×C59C2311yescharacteristic
225C2×C4⋊C4×C59C2312yes—
226C2×C4⋊C4×C59C2312yes—
227C2×C4⋊C4×C59C2312yes—
228C2×C4⋊C4×C59C23116yes—
229C2×C22⋊C4×C59C2314yes—
230C2×C22⋊C4×C59C2312yes—
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—48no—
255C2×C22⋊D59C2418yes—
256C2×C22⋊D59C24116yes—
257C22×Dic59C2412yes—
258C22×Dic59C2411yescharacteristic
259C22×Dic59C2412yes—
260C22×Dic59C2411yescharacteristic
261C22×Dic59C2411yescharacteristic
262C22×Dic59C2414yes—
263C22×Dic59C2412yes—
264Q8×D59—432no—
265#11745685—464no—
266C2×D236—28no—
267C2×D236—24no—
268C2×D236C2414yes—
269C2×D236C2418yes—
270C2×C4×D59—24no—
271C2×C4×D59—216no—
272C2×C4×D59—24no—
273C2×C4×D59—24no—
274C2×C4×D59—28no—
275C2×C4×D59—48no—
276C2×C4×D59C2414yes—
277C2×C4×D59C2414yes—
278C2×C4×D59C2414yes—
279C2×C4×D59C24116yes—
280C2×C4×D59C2418yes—
281C2×C4×D59C24116yes—
282C2×Dic118—24no—
283C2×Dic118—48no—
284C2×Dic118—44no—
285C2×Dic118—48no—
286C2×Dic118C2414yes—
287C2×Dic118C24116yes—
288C2×Dic118C24116yes—
289C2×Dic118C2418yes—
290C4⋊C4×C59C2414yes—
291C4⋊C4×C59C24116yes—
292C4⋊C4×C59C2418yes—
293C4⋊C4×C59C2414yes—
294C4⋊C4×C59C2418yes—
295C4⋊C4×C59C2418yes—
296C4⋊C4×C59C24116yes—
297C22⋊C4×C59C24116yes—
298C22⋊C4×C59C2418yes—
299C42×C59C2418yes—
300C42×C59C2414yes—
301C22⋊Dic59C2418yes—
302C22⋊Dic59C24116yes—
303C22⋊Dic59C2418yes—
304C22⋊Dic59C2418yes—
305(C2×D59)⋊C4C2418yes—
306(C2×D59)⋊C4C2418yes—
307(C2×D59)⋊C4C2418yes—
308(C2×D59)⋊C4C2418yes—
309(C2×D59)⋊C4C24116yes—
310(C2×D59)⋊C4C24116yes—
311(C2×D59)⋊C4C2418yes—
312(C2×D59)⋊C4C2418yes—
313C4⋊Dic59C2414yes—
314C4⋊Dic59C2418yes—
315C4⋊Dic59C2418yes—
316C4⋊Dic59C24116yes—
317C4⋊Dic59C2414yes—
318C4⋊Dic59C2418yes—
319C4⋊Dic59C2418yes—
320C4⋊Dic59C2418yes—
321C4⋊Dic59C24116yes—
322Dic59⋊C4C24116yes—
323Dic59⋊C4C24116yes—
324Dic59⋊C4C24116yes—
325Dic59⋊C4C2418yes—
326Dic59⋊C4C2418yes—
327Dic59⋊C4C2418yes—
328Dic59⋊C4C2418yes—
329Dic59⋊C4C24116yes—
330C4×Dic59C2414yes—
331C4×Dic59C2414yes—
332C4×Dic59C2414yes—
333C4×Dic59C24116yes—
334C4×Dic59C24116yes—
335C4×Dic59C2418yes—
336C23×C59—24no—
337C23×C59—24no—
338C23×C59—24no—
339C23×C59C2514yes—
340C23×C59C2511yescharacteristic
341C22×D59—22no—
342C22×D59—22no—
343C22×D59—24no—
344C22×D59—24no—
345C22×D59—24no—
346C22×D59H(5,𝔽2)14yes—
347C22×D59C2514yes—
348C22×D59C2512yes—
349Q8×C59—28no—
350Q8×C59—48no—
351D4×C59—28no—
352C2×C4×C59—22no—
353C2×C4×C59—24no—
354C2×C4×C59—28no—
355C2×C4×C59—24no—
356C2×C4×C59—24no—
357C2×C4×C59—216no—
358C2×C4×C59—416no—
359C2×C4×C592−1+414yes—
360C2×C4×C592−1+414yes—
361C2×C4×C59C2514yes—
362C2×C4×C59C2514yes—
363C2×C4×C59C2512yes—
364C2×C4×C59C2514yes—
365C2×C4×C59C2518yes—
366C2×C4×C59C2512yes—
367C2×C4×C59C2512yes—
368C22⋊D59—216no—
369C22⋊D59—416no—
370C2×Dic59—22no—
371C2×Dic59—28no—
372C2×Dic59—24no—
373C2×Dic59—24no—
374C2×Dic59—22no—
375C2×Dic59—22no—
376C2×Dic59—24no—
377C2×Dic59C2514yes—
378C2×Dic59C2512yes—
379C2×Dic59C2512yes—
380C2×Dic59C2514yes—
381C2×Dic59C2518yes—
382C2×Dic59C2512yes—
383C2×Dic59C2514yes—
384D236—216no—
385D236—28no—
386C4×D59—232no—
387C4×D59—28no—
388C4×D59—28no—
389C4×D59—28no—
390C4×D59—216no—
391C4×D59—416no—
392Dic118—28no—
393Dic118—416no—
394Dic118—416no—
395Dic118—48no—
396C2×#3544—591nomaximal, Sylow
397C22×C59—24no—
398C22×C59—24no—
399C22×C59—24no—
400C22×C59—48no—
401C22×C59C2×H(5,𝔽2)12yes—
402C22×C59C2×2−1+412yes—
403C22×C59C2×2−1+412yes—
404C22×C59C2611yescharacteristic
405C2×D59—22no—
406C2×D59—22no—
407C2×D59—28no—
408C2×D59—24no—
409C2×D59—24no—
410C2×D59—24no—
411C2×D59—48no—
412C2×D59C2×H(5,𝔽2)14yes—
413C4×C59—22no—
414C4×C59—24no—
415C4×C59—28no—
416C4×C59—24no—
417C4×C59—24no—
418C4×C59C2×2−1+414yes—
419C4×C59C2×2−1+414yes—
420Dic59—22no—
421Dic59—28no—
422Dic59—24no—
423Dic59—24no—
424Dic59—22no—
425Dic59—22no—
426Dic59—24no—
427#3544—5932no—
428C2×#563—594no—
429C2×Q82—591no—
430C2×#555—591no—
431C2×#554—591no—
432C2×#554D5911yescharacteristic, complemented
433C2×#552—592no—
434C2×#552—592no—
435C2×#547—592no—
436C2×#547—592no—
437C2×#544—592no—
438C2×#544—592no—
439C2×#542—592no—
440C2×#542—592no—
441C2×#536—594no—
442C22×C4⋊Q8—591no—
443C2×#529—591no—
444C2×#529—591no—
445C2×C59—44no—
446C2×C59#354414yescomplemented
447C2×C59C22×H(5,𝔽2)11yescharacteristic
448C2×C59C22×2−1+411yescharacteristic
449C2×C59C22×2−1+411yescharacteristic
450D59—24no—
451D59—44no—
452C22×#41—594no—
453C23×Q8—592no—
454#563—5964no—
455Q82—5916no—
456#555—5916no—
457#554—5916no—
458#554C2×D59116yescomplemented
459#552—5932no—
460#552—5932no—
461#547—5932no—
462#547—5932no—
463#544—5932no—
464#544—5932no—
465#542—5932no—
466#542—5932no—
467#536—5964no—
468C2×C4⋊Q8—592no—
469C2×C4⋊Q8—5916no—
470C2×C4⋊Q8—592no—
471C2×C4⋊Q8—592no—
472C2×C4⋊Q8—594no—
473C2×C4⋊Q8—594no—
474C2×C4⋊Q8—592no—
475C2×C4⋊Q8—591no—
476C2×C4⋊Q8—592no—
477C2×C4⋊Q8C2×D5911yescharacteristic
478#529—5916no—
479#529—5916no—
480C2×#126—592no—
481C2×#126—594no—
482C2×#126—592no—
483C2×#126—594no—
484C2×#125—594no—
485C2×#125—591no—
486C2×#125—591no—
487C2×#125—592no—
488C2×#125—594no—
489C2×#125C2×D5912yes—
490C2×#124—591no—
491C2×#124—591no—
492C2×#124—594no—
493C2×#124—594no—
494C2×#123—594no—
495C2×#123—592no—
496C2×#123—594no—
497C2×#123—592no—
498C2×#123—594no—
499C2×#123—594no—
500C2×C22⋊Q8—591no—
501C2×C22⋊Q8—594no—
502C2×C22⋊Q8—594no—
503C2×C22⋊Q8—594no—
504C2×C22⋊Q8—594no—
505C2×C22⋊Q8—591no—
506C2×C22⋊Q8—594no—
507C2×C22⋊Q8—592no—
508C2×C22⋊Q8C2×D5914yes—
509C2×C22⋊Q8C2×D5912yes—
510C2×#121—591no—
511C2×#121—592no—
512C2×#121—592no—
513C2×#121—591no—
514C2×C4×Q8—592no—
515C2×C4×Q8—591no—
516C2×C4×Q8—592no—
517C2×C4×Q8C2×D5911yescharacteristic
518C2×C4×D4—592no—
519C2×C4×D4—592no—
520C2×C4×D4—592no—
521C2×C4×D4—591no—
522C2×C4×D4C2×D5911yescharacteristic
523C2×C4×D4C2×D5912yes—
524C2×#117—592no—
525C2×#117—592no—
526C2×#117—594no—
527C2×#117—592no—
528C2×#117—592no—
529C22×C4⋊C4—592no—
530C22×C4⋊C4—592no—
531C22×C4⋊C4—592no—
532C22×C4⋊C4C2×D5912yes—
533C22×C42—591no—
534C59C2×#354411yescharacteristic, complemented, Sylow
535C2×#41—5932no—
536C2×#41—23616no—
537C22×Q8—5916no—
538C22×Q8—591no—
539C22×Q8—594no—
540C22×Q8—594no—
541C22×Q8—592no—
542C22×Q8—2368no—
543C22×Q8C22×D5911yescharacteristic
544C22×Q8C22×D5912yes—
545C22×D4—592no—
546C22×D4—594no—
547C22×D4—591no—
548C22×D4—592no—
549C22×D4C22×D5911yescharacteristic
550C23×C4—594no—
551C23×C4—591no—
552C23×C4—591no—
553C23×C4—592no—
554C23×C4—591no—
555C23×C4—594no—
556C23×C4C22×D5912yes—
557C23×C4C22×D5914yes—
558C4⋊Q8—5916no—
559C4⋊Q8—5916no—
560C4⋊Q8—5916no—
561C4⋊Q8—5932no—
562C4⋊Q8—5932no—
563C4⋊Q8—5916no—
564C4⋊Q8—598no—
565C4⋊Q8—5916no—
566C4⋊Q8C22×D5918yes—
567#126—5916no—
568#126—5932no—
569#126—5916no—
570#126—5932no—
571#125—598no—
572#125—598no—
573#125—5916no—
574#125—5932no—
575#125—5932no—
576#125C22×D59116yes—
577#124—598no—
578#124—598no—
579#124—5932no—
580#124—5932no—
581#123—5932no—
582#123—5916no—
583#123—5932no—
584#123—5916no—
585#123—5932no—
586#123—5932no—
587C22⋊Q8—598no—
588C22⋊Q8—5932no—
589C22⋊Q8—5932no—
590C22⋊Q8—5932no—
591C22⋊Q8—598no—
592C22⋊Q8—5932no—
593C22⋊Q8—5916no—
594C22⋊Q8—5932no—
595C22⋊Q8C22×D59132yes—
596C22⋊Q8C22×D59116yes—
597#121—598no—
598#121—5916no—
599#121—5916no—
600#121—598no—
601C4×Q8—5916no—
602C4×Q8—598no—
603C4×Q8—5916no—
604C4×Q8C22×D5918yes—
605C4×D4—5916no—
606C4×D4—5916no—
607C4×D4—5916no—
608C4×D4—598no—
609C4×D4C22×D5918yes—
610C4×D4C22×D59116yes—
611#117—5916no—
612#117—5916no—
613#117—5932no—
614#117—5916no—
615#117—5916no—
616C2×C4⋊C4—591no—
617C2×C4⋊C4—592no—
618C2×C4⋊C4—592no—
619C2×C4⋊C4—594no—
620C2×C4⋊C4—594no—
621C2×C4⋊C4—594no—
622C2×C4⋊C4—591no—
623C2×C4⋊C4—594no—
624C2×C4⋊C4—592no—
625C2×C4⋊C4—592no—
626C2×C4⋊C4—592no—
627C2×C4⋊C4—592no—
628C2×C4⋊C4—592no—
629C2×C4⋊C4—592no—
630C2×C4⋊C4—592no—
631C2×C4⋊C4—594no—
632C2×C4⋊C4—594no—
633C2×C4⋊C4—5916no—
634C2×C4⋊C4—5916no—
635C2×C4⋊C4—5916no—
636C2×C4⋊C4C22×D5912yes—
637C2×C4⋊C4C22×D5912yes—
638C2×C4⋊C4C22×D5911yescharacteristic
639C2×C4⋊C4C22×D5914yes—
640C2×C4⋊C4C22×D59116yes—
641C2×C4⋊C4C22×D5911yescharacteristic
642C2×C4⋊C4C22×D5914yes—
643C2×C4⋊C4C22×D5912yes—
644C2×C22⋊C4—592no—
645C2×C22⋊C4—594no—
646C2×C22⋊C4—592no—
647C2×C22⋊C4—592no—
648C2×C22⋊C4—592no—
649C2×C22⋊C4—592no—
650C2×C22⋊C4—592no—
651C2×C22⋊C4—594no—
652C2×C22⋊C4—592no—
653C2×C22⋊C4—594no—
654C2×C22⋊C4—592no—
655C2×C22⋊C4—592no—
656C2×C22⋊C4C22×D5914yes—
657C2×C22⋊C4C22×D5912yes—
658C2×C42—594no—
659C2×C42—591no—
660C2×C42—591no—
661C2×C42—592no—
662C2×C42—594no—
663C2×C42—591no—
664C2×C42—598no—
665C2×C42C22×D5912yes—
666C2×C42C22×D5911yescharacteristic
667C24—591no—
668C24—592no—
669C24C23×D5912yes—
670#41—23664no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—594no—
674C2×Q8—5916no—
675C2×Q8—5916no—
676C2×Q8—598no—
677C2×Q8—1184no—
678C2×Q8—2368no—
679C2×Q8—2364no—
680C2×Q8—2368no—
681C2×Q8—23632no—
682C2×Q8C23×D5914yes—
683C2×Q8C23×D5918yes—
684C2×D4—24no—
685C2×D4—598no—
686C2×D4—5916no—
687C2×D4—594no—
688C2×D4—598no—
689C2×D4—1188no—
690C2×D4—1188no—
691C2×D4—1184no—
692C2×D4—2368no—
693C2×D4C23×D5914yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—592no—
697C22×C4—591no—
698C22×C4—592no—
699C22×C4—591no—
700C22×C4—591no—
701C22×C4—594no—
702C22×C4—592no—
703C22×C4—594no—
704C22×C4—594no—
705C22×C4—594no—
706C22×C4—5916no—
707C22×C4—598no—
708C22×C4—5916no—
709C22×C4—1184no—
710C22×C4—11816no—
711C22×C4—1184no—
712C22×C4—1184no—
713C22×C4—1188no—
714C22×C4—2368no—
715C22×C4C23×D5918yes—
716C22×C4C23×D5912yes—
717C22×C4C23×D5912yes—
718C22×C4C23×D5911yescharacteristic
719C22×C4C23×D5912yes—
720C22×C4C23×D5914yes—
721C22×C4C23×D59116yes—
722C22×C4C23×D5911yescharacteristic
723C22×C4C23×D5911yescharacteristic
724C4⋊C4—594no—
725C4⋊C4—598no—
726C4⋊C4—598no—
727C4⋊C4—5916no—
728C4⋊C4—5916no—
729C4⋊C4—5916no—
730C4⋊C4—594no—
731C4⋊C4—5916no—
732C4⋊C4—598no—
733C4⋊C4—598no—
734C4⋊C4—598no—
735C4⋊C4—598no—
736C4⋊C4—598no—
737C4⋊C4—598no—
738C4⋊C4—598no—
739C4⋊C4—5916no—
740C4⋊C4—5916no—
741C4⋊C4C23×D5918yes—
742C4⋊C4C23×D5918yes—
743C4⋊C4C23×D5914yes—
744C4⋊C4C23×D59116yes—
745C4⋊C4C23×D5914yes—
746C4⋊C4C23×D59116yes—
747C4⋊C4C23×D5918yes—
748C22⋊C4—598no—
749C22⋊C4—5916no—
750C22⋊C4—598no—
751C22⋊C4—598no—
752C22⋊C4—598no—
753C22⋊C4—598no—
754C22⋊C4—598no—
755C22⋊C4—5916no—
756C22⋊C4—598no—
757C22⋊C4—5916no—
758C22⋊C4—598no—
759C22⋊C4—598no—
760C22⋊C4C23×D59116yes—
761C22⋊C4C23×D5918yes—
762C42—594no—
763C42—594no—
764C42—594no—
765C42—5916no—
766C42—598no—
767C42—5916no—
768C42C23×D5914yes—
769C42C23×D5918yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—594no—
774C23—592no—
775C23—594no—
776C23—1182no—
777C23—1182no—
778C23—1184no—
779C23—1184no—
780C23—1184no—
781C23C24×D5914yes—
782C23C24×D5911yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—1188no—
786Q8—23616no—
787Q8—2368no—
788Q8—23616no—
789D4—28no—
790D4—11816no—
791D4—11816no—
792D4—1188no—
793D4—23616no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—594no—
802C2×C4—592no—
803C2×C4—592no—
804C2×C4—594no—
805C2×C4—592no—
806C2×C4—598no—
807C2×C4—594no—
808C2×C4—1188no—
809C2×C4—11832no—
810C2×C4—1188no—
811C2×C4—1182no—
812C2×C4—1184no—
813C2×C4—1182no—
814C2×C4—1184no—
815C2×C4—1182no—
816C2×C4—1184no—
817C2×C4—1188no—
818C2×C4—1188no—
819C2×C4—11816no—
820C2×C4—23616no—
821C2×C4#1427377414yes—
822C2×C4#1427377514yes—
823C2×C4C24×D5914yes—
824C2×C4C24×D5914yes—
825C2×C4C24×D5912yes—
826C2×C4C24×D5914yes—
827C2×C4C24×D5918yes—
828C2×C4C24×D5912yes—
829C2×C4C24×D5912yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—594no—
835C22—1182no—
836C22—1182no—
837C22—1188no—
838C22—1184no—
839C22—1184no—
840C22—1184no—
841C22—2368no—
842C22H(5,𝔽2)×D5912yes—
843C22C2×#1427377412yes—
844C22C2×#1427377512yes—
845C22C25×D5911yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—1188no—
852C4—1182no—
853C4—1184no—
854C4—1182no—
855C4—1182no—
856C4—1184no—
857C4—1184no—
858C4C2×#1427377414yes—
859C4C2×#1427377514yes—
860C2—44no—
861C2—1184no—
862C2—2364no—
863C2#2143843714yesdirect product factor
864C2C2×H(5,𝔽2)×D5911yescharacteristic
865C2C22×#1427377411yescharacteristic
866C2C22×#1427377511yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#554C2
socleC23×C59C25
hypercenterC2×#554D59
hypocenterC59C2×#3544
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #21438437C2direct (N × H)
2. C2×#16838153C2semidirect
3. C2×Q8×Dic118C2semidirect
4. C2×#16838117C2semidirect
5. C2×#16838113C2semidirect
6. C2×#16838090C2semidirect
7. C2×#16838086C2semidirect
8. C2×#16838057C2semidirect
9. C2×#16838053C2semidirect
10. C2×#16838033C2semidirect
11. C2×#16838032C2semidirect
12. C2×#16838025C2semidirect
13. C2×#16838017C2semidirect
14. C2×#16837975C2semidirect
15. C2×C4⋊Q8×D59C2semidirect
16. C2×#16837939C2semidirect
17. C2×#16837934C2semidirect
18. C2×C59×#554C2semidirect
21. #16838153C22semidirect
22. Q8×Dic118C22semidirect
23. #16838117C22semidirect
24. #16838113C22semidirect
25. #16838090C22semidirect
26. #16838086C22semidirect
27. #16838057C22semidirect
28. #16838053C22semidirect
29. #16838033C22semidirect
30. #16838032C22semidirect
31. #16838025C22semidirect
32. #16838017C22semidirect
33. #16837975C22semidirect
42. C4⋊Q8×D59C22semidirect
43. #16837939C22semidirect
44. #16837934C22semidirect
92. C59×#554C22semidirect
432. C2×#554D59semidirect
446. C2×C59#3544semidirect
458. #554C2×D59semidirect
534. C59C2×#3544semidirect
863. C2#21438437direct (N × H)

Maximal subgroups

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

subgroupindex
#214384372
C2×#168381532
C2×Q8×Dic1182
C2×#168381172
C2×#168381132
C2×#168380902
C2×#168380862
C2×#168380572
C2×#168380532
C2×#168380332
C2×#168380322
C2×#168380252
C2×#168380172
C2×#168379752
C2×C4⋊Q8×D592
C2×#168379392
C2×#168379342
C2×C59×#5542
C2×#354459