Finite Group Databasebeta

← C2×#21438481 #29496392

Subgroups — C2×#21438481 #29496392

Order 15104.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438481C2132yesmaximal, direct product factor
2C2×#16838148C214yesmaximal, complemented
3C2×#16838118C212yesmaximal, complemented
4C2×#16838117C211yesmaximal, characteristic, complemented
5C2×#16838112C211yesmaximal, characteristic, complemented
6C2×#16838102C212yesmaximal, complemented
7C2×#16838086C212yesmaximal, complemented
8C2×#16838063C212yesmaximal, complemented
9C2×#16838055C211yesmaximal, characteristic, complemented
10C2×#16838029C212yesmaximal, complemented
11C2×#16838022C214yesmaximal, complemented
12C2×#16838003C212yesmaximal, complemented
13C2×#16837982C212yesmaximal, complemented
14C2×#16837976C212yesmaximal, complemented
15C2×#16837957C211yesmaximal, characteristic, complemented
16C2×#16837949C211yesmaximal, characteristic, complemented
17C2×#16837939C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C59C211yesmaximal, characteristic, complemented
19C22×#11745689C2212yes—
20C22×#11745685C2212yes—
21#16838148C22164yescomplemented
22#16838118C22132yescomplemented
23#16838117C22116yescomplemented
24#16838112C22116yescomplemented
25#16838102C22132yescomplemented
26#16838086C22132yescomplemented
27#16838063C22132yescomplemented
28#16838055C22116yescomplemented
29#16838029C22132yescomplemented
30#16838022C22164yescomplemented
31#16838003C22132yescomplemented
32#16837982C22132yescomplemented
33#16837976C22132yescomplemented
34#16837957C22116yescomplemented
35#16837949C22116yescomplemented
36C2×#14273727C2211yescharacteristic
37C2×#14273726C2211yescharacteristic
38C2×#14273725C2214yes—
39C2×#14273723C2211yescharacteristic
40#16837939C22116yescomplemented
41C2×#14273722C2212yes—
42C2×#14273720C2214yes—
43C2×#14273719C2212yes—
44C2×#14273718C2212yes—
45C2×#14273718C2211yescharacteristic
46C2×#14273717C2214yes—
47C2×#14273716C2214yes—
48C2×#14273716C2214yes—
49C2×#14273716C2211yescharacteristic
50C2×#14273713C2214yes—
51C2×#14273713C2212yes—
52C2×#14273712C2212yes—
53C2×#14273712C2214yes—
54C2×#14273710C2214yes—
55C2×#14273710C2214yes—
56C2×#14273709C2214yes—
57C2×#14273707C2212yes—
58C2×#14273705C2214yes—
59C2×#14273705C2214yes—
60C2×#14273703C2214yes—
61C2×#14273703C2212yes—
62C2×#14273703C2212yes—
63C2×#14273703C2211yescharacteristic
64C2×#14273703C2212yes—
65C2×#14273702C2212yes—
66C2×#14273702C2214yes—
67C2×#14273702C2211yescharacteristic
68C2×#14273702C2211yescharacteristic
69C2×#14273701C2214yes—
70C2×#14273701C2212yes—
71C2×#14273700C2214yes—
72C2×#14273700C2212yes—
73C2×#14273700C2214yes—
74C2×#14273698C2212yes—
75C2×#14273698C2211yescharacteristic
76C2×Q8×Dic59C2212yes—
77C2×#14273692C2212yes—
78C2×C4×D236C2212yes—
79C2×C4×D236C2211yescharacteristic
80C2×C4×D236C2211yescharacteristic
81C2×C4×D236C2212yes—
82C2×C4×C22⋊D59C2214yes—
83C2×C4×C22⋊D59C2212yes—
84C2×#14273686C2212yes—
85C2×#14273685C2214yes—
86C2×#14273685C2212yes—
87C2×#14273685C2212yes—
88C2×#14273684C2212yes—
89C2×C4⋊C4×D59C2212yes—
90C2×C4⋊C4×D59C2212yes—
91C2×C42×D59C2211yescharacteristic
92C23×Q8×C59C2212yes—
93D4×Q8×C59C22116yescomplemented
94C2×C4⋊Q8×C59C2212yes—
95C2×C4⋊Q8×C59C2211yescharacteristic
96C2×C22⋊Q8×C59C2214yes—
97C2×C22⋊Q8×C59C2212yes—
98C2×C4×Q8×C59C2211yescharacteristic
99C2×C4×D4×C59C2212yes—
100C2×C4×D4×C59C2211yescharacteristic
101C2×#11745689—48no—
102C2×#11745689C23116yes—
103C2×#11745685—48no—
104C2×#11745685C23116yes—
105C22×Dic118C2312yes—
106C22×Dic118C2312yes—
107C22×D236C2311yescharacteristic
108C22×D236C2311yescharacteristic
109C22×D236C2312yes—
110C22×D236C2314yes—
111C22×D236C2312yes—
112C22×C22⋊D59C2312yes—
113C22×C22⋊D59C2314yes—
114C22×C22⋊D59C2312yes—
115C22×C22⋊D59C2312yes—
116C22×C4×D59C2311yescharacteristic
117C22×C4×D59C2312yes—
118C22×C4×D59C2311yescharacteristic
119C22×C4×D59C2312yes—
120C22×C4×D59C2311yescharacteristic
121C22×C4×D59C2314yes—
122C22×C4×D59C2314yes—
123#14273727C2318yes—
124#14273726C2318yes—
125#14273725C23132yes—
126#14273723C2318yes—
127#14273722C23116yes—
128#14273720C23132yes—
129#14273719C23116yes—
130#14273718C2318yes—
131#14273718C23116yes—
132#14273717C23132yes—
133#14273716C23132yes—
134#14273716C2318yes—
135#14273716C23132yes—
136#14273713C23132yes—
137#14273713C23116yes—
138#14273712C23116yes—
139#14273712C23132yes—
140#14273710C23132yes—
141#14273710C23132yes—
142#14273709C23132yes—
143#14273707C23116yes—
144#14273705C23132yes—
145#14273705C23132yes—
146#14273703C23132yes—
147#14273703C2318yes—
148#14273703C23116yes—
149#14273703C23116yes—
150#14273703C23116yes—
151#14273702C23132yes—
152#14273702C2318yes—
153#14273702C2318yes—
154#14273702C23116yes—
155#14273701C23132yes—
156#14273701C23116yes—
157#14273700C23116yes—
158#14273700C23132yes—
159#14273700C23132yes—
160#14273698C2318yes—
161#14273698C23116yes—
162Q8×Dic59C23116yes—
163#14273692C23116yes—
164C4×D236C2318yes—
165C4×D236C23116yes—
166C4×D236C2318yes—
167C4×D236C23116yes—
168C4×C22⋊D59C23116yes—
169C4×C22⋊D59C23132yes—
170#14273686C23116yes—
171#14273685C23116yes—
172#14273685C23132yes—
173#14273685C23116yes—
174#14273684C23116yes—
175C2×C4⋊Dic59C2312yes—
176C2×C4⋊Dic59C2311yescharacteristic
177C2×C4⋊Dic59C2312yes—
178C2×C4⋊Dic59C2314yes—
179C2×C4⋊Dic59C2311yescharacteristic
180C2×C4⋊Dic59C2312yes—
181C2×Dic59⋊C4C2312yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2314yes—
184C2×Dic59⋊C4C2314yes—
185C2×Dic59⋊C4C2312yes—
186C2×Dic59⋊C4C2314yes—
187C2×Dic59⋊C4C2312yes—
188C4⋊C4×D59C23116yes—
189C4⋊C4×D59C23116yes—
190C2×C22⋊Dic59C2314yes—
191C2×C22⋊Dic59C2312yes—
192C2×(C2×D59)⋊C4C2312yes—
193C2×(C2×D59)⋊C4C2314yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2314yes—
197C2×(C2×D59)⋊C4C2314yes—
198C2×(C2×D59)⋊C4C2314yes—
199C2×(C2×D59)⋊C4C2312yes—
200C2×(C2×D59)⋊C4C2312yes—
201C2×(C2×D59)⋊C4C2312yes—
202C2×(C2×D59)⋊C4C2312yes—
203C2×C4×Dic59C2311yescharacteristic
204C2×C4×Dic59C2314yes—
205C2×C4×Dic59C2311yescharacteristic
206C2×C4×Dic59C2314yes—
207C2×C4×Dic59C2311yescharacteristic
208C42×D59C2318yes—
209C22×Q8×C59—48no—
210C22×Q8×C59C2311yescharacteristic
211C22×Q8×C59C2312yes—
212C22×Q8×C59C2314yes—
213C22×Q8×C59C23116yes—
214C22×D4×C59C2311yescharacteristic
215C23×C4×C59C2312yes—
216C23×C4×C59C2314yes—
217C4⋊Q8×C59C2318yes—
218C4⋊Q8×C59C23116yes—
219C22⋊Q8×C59C23132yes—
220C22⋊Q8×C59C23116yes—
221C4×Q8×C59C2318yes—
222C4×D4×C59C2318yes—
223C4×D4×C59C23116yes—
224C2×C4⋊C4×C59C2314yes—
225C2×C4⋊C4×C59C2312yes—
226C2×C4⋊C4×C59C2311yescharacteristic
227C2×C4⋊C4×C59C2311yescharacteristic
228C2×C4⋊C4×C59C2312yes—
229C2×C4⋊C4×C59C2312yes—
230C2×C22⋊C4×C59C2314yes—
231C2×C22⋊C4×C59C2312yes—
232C2×C42×C59C2312yes—
233C2×C42×C59C2311yescharacteristic
234C24×C59C2412yes—
235C23×D59C2412yes—
236C23×D59C2411yescharacteristic
237C23×D59C2412yes—
238C2×Q8×C59—24no—
239C2×Q8×C59—28no—
240C2×Q8×C59—48no—
241C2×Q8×C59—432no—
242C2×Q8×C59C2414yes—
243C2×Q8×C59C2418yes—
244C2×Q8×C59C24116yes—
245C2×D4×C59—24no—
246C2×D4×C59C2414yes—
247C22×C4×C59—28no—
248C22×C4×C59—48no—
249C22×C4×C59C2411yescharacteristic
250C22×C4×C59C2412yes—
251C22×C4×C59C2412yes—
252C22×C4×C59C2412yes—
253C22×C4×C59C2414yes—
254C22×C4×C59C2418yes—
255C22×C4×C59C24116yes—
256C22×C4×C59C2411yescharacteristic
257C22×C4×C59C2411yescharacteristic
258C2×C22⋊D59—48no—
259C2×C22⋊D59—44no—
260C2×C22⋊D59—44no—
261C2×C22⋊D59—44no—
262C2×C22⋊D59C24116yes—
263C2×C22⋊D59C2418yes—
264C2×C22⋊D59C2418yes—
265C2×C22⋊D59C2418yes—
266C22×Dic59C2411yescharacteristic
267C22×Dic59C2412yes—
268C22×Dic59C2414yes—
269C22×Dic59C2411yescharacteristic
270C22×Dic59C2411yescharacteristic
271C22×Dic59C2412yes—
272#11745689—432no—
273#11745685—432no—
274C2×D236—24no—
275C2×D236—24no—
276C2×D236—44no—
277C2×D236—44no—
278C2×D236—48no—
279C2×D236C2414yes—
280C2×D236C2414yes—
281C2×D236C2418yes—
282C2×D236C24116yes—
283C2×D236C2418yes—
284C2×C4×D59—24no—
285C2×C4×D59—28no—
286C2×C4×D59—24no—
287C2×C4×D59—28no—
288C2×C4×D59—48no—
289C2×C4×D59—42no—
290C2×C4×D59—48no—
291C2×C4×D59C2414yes—
292C2×C4×D59C2414yes—
293C2×C4×D59C2418yes—
294C2×C4×D59C2418yes—
295C2×C4×D59C2414yes—
296C2×C4×D59C24116yes—
297C2×C4×D59C24116yes—
298C2×Dic118—44no—
299C2×Dic118—44no—
300C2×Dic118C2418yes—
301C2×Dic118C2418yes—
302C4⋊C4×C59C2418yes—
303C4⋊C4×C59C2414yes—
304C4⋊C4×C59C2414yes—
305C4⋊C4×C59C2418yes—
306C4⋊C4×C59C24116yes—
307C4⋊C4×C59C2418yes—
308C22⋊C4×C59C24116yes—
309C22⋊C4×C59C2418yes—
310C42×C59C2414yes—
311C42×C59C2418yes—
312C22⋊Dic59C24116yes—
313C22⋊Dic59C2418yes—
314(C2×D59)⋊C4C2418yes—
315(C2×D59)⋊C4C2418yes—
316(C2×D59)⋊C4C2418yes—
317(C2×D59)⋊C4C24116yes—
318(C2×D59)⋊C4C24116yes—
319(C2×D59)⋊C4C24116yes—
320(C2×D59)⋊C4C2418yes—
321(C2×D59)⋊C4C2418yes—
322(C2×D59)⋊C4C24116yes—
323(C2×D59)⋊C4C2418yes—
324(C2×D59)⋊C4C2418yes—
325C4⋊Dic59C2414yes—
326C4⋊Dic59C2418yes—
327C4⋊Dic59C2418yes—
328C4⋊Dic59C2418yes—
329C4⋊Dic59C2414yes—
330C4⋊Dic59C24116yes—
331Dic59⋊C4C24116yes—
332Dic59⋊C4C24116yes—
333Dic59⋊C4C2418yes—
334Dic59⋊C4C2418yes—
335Dic59⋊C4C2418yes—
336Dic59⋊C4C24116yes—
337Dic59⋊C4C24116yes—
338C4×Dic59C2414yes—
339C4×Dic59C2414yes—
340C4×Dic59C2414yes—
341C4×Dic59C24116yes—
342C4×Dic59C24116yes—
343C23×C59—24no—
344C23×C59—24no—
345C23×C59—24no—
346C23×C59C2514yes—
347C23×C59C2511yescharacteristic
348C22×D59—24no—
349C22×D59—22no—
350C22×D59—24no—
351C22×D59—22no—
352C22×D59—24no—
353C22×D59—24no—
354C22×D59—24no—
355C22×D59—22no—
356C22×D59—24no—
357C22×D59C2514yes—
358C22×D59C2512yes—
359C22×D59C2514yes—
360Q8×C59—216no—
361Q8×C59—28no—
362Q8×C59—416no—
363D4×C59—28no—
364C2×C4×C59—24no—
365C2×C4×C59—28no—
366C2×C4×C59—24no—
367C2×C4×C59—22no—
368C2×C4×C59—24no—
369C2×C4×C59—216no—
370C2×C4×C59—416no—
371C2×C4×C59H(5,𝔽2)14yes—
372C2×C4×C592−1+414yes—
373C2×C4×C59C2514yes—
374C2×C4×C59C2518yes—
375C2×C4×C59C2512yes—
376C2×C4×C59C2514yes—
377C2×C4×C59C2514yes—
378C2×C4×C59C2512yes—
379C2×C4×C59C2512yes—
380C22⋊D59—48no—
381C22⋊D59—48no—
382C22⋊D59—416no—
383C22⋊D59—48no—
384C2×Dic59—22no—
385C2×Dic59—24no—
386C2×Dic59—22no—
387C2×Dic59—24no—
388C2×Dic59—28no—
389C2×Dic59—22no—
390C2×Dic59C2512yes—
391C2×Dic59C2512yes—
392C2×Dic59C2512yes—
393C2×Dic59C2514yes—
394C2×Dic59C2518yes—
395C2×Dic59C2514yes—
396D236—28no—
397D236—28no—
398D236—48no—
399D236—48no—
400D236—416no—
401C4×D59—28no—
402C4×D59—216no—
403C4×D59—28no—
404C4×D59—216no—
405C4×D59—416no—
406C4×D59—44no—
407C4×D59—416no—
408Dic118—48no—
409Dic118—48no—
410C2×#3547—591nomaximal, Sylow
411C22×C59—24no—
412C22×C59—24no—
413C22×C59—24no—
414C22×C59—48no—
415C22×C59C2×H(5,𝔽2)12yes—
416C22×C59C2×2−1+412yes—
417C22×C59#58512yes—
418C22×C59C2611yescharacteristic
419C2×D59—24no—
420C2×D59—22no—
421C2×D59—24no—
422C2×D59—22no—
423C2×D59—24no—
424C2×D59—24no—
425C2×D59—24no—
426C2×D59—22no—
427C2×D59—24no—
428C2×D59—48no—
429C2×D59—44no—
430C2×D59—48no—
431C4×C59—24no—
432C4×C59—28no—
433C4×C59—24no—
434C4×C59—22no—
435C4×C59—24no—
436C4×C59C2×H(5,𝔽2)14yes—
437C4×C59C2×2−1+414yes—
438Dic59—22no—
439Dic59—24no—
440Dic59—22no—
441Dic59—24no—
442Dic59—28no—
443Dic59—22no—
444#3547—5932no—
445C2×#562—594no—
446C2×#555—592no—
447C2×#555—591no—
448C2×#554—591no—
449C2×#553—592no—
450C2×#552—592no—
451C2×D4×Q8D5911yescharacteristic, complemented
452C2×#548—592no—
453C2×#547—591no—
454C2×#544—592no—
455C2×#542—594no—
456C2×#540—592no—
457C2×#537—592no—
458C2×#536—592no—
459C2×#533—591no—
460C2×#532—591no—
461C2×#529—591no—
462C2×C59—44no—
463C2×C59#354714yescomplemented
464C2×C59C22×H(5,𝔽2)11yescharacteristic
465C2×C59C22×2−1+411yescharacteristic
466C2×C59C2×#58511yescharacteristic
467D59—44no—
468D59—42no—
469D59—44no—
470C22×#41—592no—
471C22×#41—592no—
472C23×Q8C2×D5912yes—
473#562—5964no—
474#555—5932no—
475#555—5916no—
476#554—5916no—
477#553—5932no—
478#552—5932no—
479D4×Q8C2×D59116yescomplemented
480#548—5932no—
481#547—5916no—
482#544—5932no—
483#542—5964no—
484#540—5932no—
485#537—5932no—
486#536—5932no—
487#533—5916no—
488#532—5916no—
489C2×C4⋊Q8—594no—
490C2×C4⋊Q8—591no—
491C2×C4⋊Q8—591no—
492C2×C4⋊Q8C2×D5911yescharacteristic
493C2×C4⋊Q8C2×D5912yes—
494C2×#127—591no—
495#529—5916no—
496C2×#126—592no—
497C2×#126—594no—
498C2×#125—594no—
499C2×#125—591no—
500C2×#125—592no—
501C2×#125—592no—
502C2×#124—591no—
503C2×#124—594no—
504C2×#124—594no—
505C2×#124—592no—
506C2×#124—594no—
507C2×#123—594no—
508C2×#123—594no—
509C2×#123—592no—
510C2×#123—594no—
511C2×#123—594no—
512C2×C22⋊Q8—591no—
513C2×C22⋊Q8—592no—
514C2×C22⋊Q8—592no—
515C2×C22⋊Q8—592no—
516C2×C22⋊Q8—594no—
517C2×C22⋊Q8—594no—
518C2×C22⋊Q8—594no—
519C2×C22⋊Q8—592no—
520C2×C22⋊Q8C2×D5912yes—
521C2×C22⋊Q8C2×D5914yes—
522C2×#121—591no—
523C2×#121—592no—
524C2×#121—592no—
525C2×#121—594no—
526C2×#121—591no—
527C2×#121—591no—
528C2×#121—594no—
529C2×#121—592no—
530C2×#121—592no—
531C2×#121—594no—
532C2×#121—594no—
533C2×C4×Q8—592no—
534C2×C4×Q8—592no—
535C2×C4×Q8C2×D5911yescharacteristic
536C2×C4×D4—592no—
537C2×C4×D4—594no—
538C2×C4×D4—591no—
539C2×C4×D4—592no—
540C2×C4×D4—591no—
541C2×C4×D4—592no—
542C2×C4×D4C2×D5911yescharacteristic
543C2×C4×D4C2×D5912yes—
544C2×#117—592no—
545C2×#117—592no—
546C2×#117—594no—
547C2×#117—592no—
548C2×#117—592no—
549C22×C4⋊C4—592no—
550C22×C4⋊C4—592no—
551C22×C42—591no—
552C59C2×#354711yescharacteristic, complemented, Sylow
553C2×#41—5916no—
554C2×#41—5916no—
555C2×#41—2368no—
556C2×#41—2368no—
557C22×Q8—48no—
558C22×Q8—592no—
559C22×Q8—592no—
560C22×Q8C22×D5912yes—
561C22×Q8C22×D5911yescharacteristic
562C22×Q8C22×D5914yes—
563C22×Q8C22×D59116yes—
564C22×D4—594no—
565C22×D4—592no—
566C22×D4—592no—
567C22×D4—592no—
568C22×D4—591no—
569C22×D4—591no—
570C22×D4—592no—
571C22×D4—594no—
572C22×D4—592no—
573C22×D4C22×D5911yescharacteristic
574C23×C4—592no—
575C23×C4—592no—
576C23×C4—591no—
577C23×C4—591no—
578C23×C4—594no—
579C23×C4—594no—
580C23×C4—591no—
581C23×C4C22×D5912yes—
582C23×C4C22×D5914yes—
583C4⋊Q8—5932no—
584C4⋊Q8—598no—
585C4⋊Q8—598no—
586C4⋊Q8C22×D5918yes—
587C4⋊Q8C22×D59116yes—
588#127—598no—
589#126—5916no—
590#126—5932no—
591#125—598no—
592#125—5916no—
593#125—5932no—
594#125—5916no—
595#124—598no—
596#124—5932no—
597#124—5932no—
598#124—5916no—
599#124—5932no—
600#123—5932no—
601#123—5932no—
602#123—5916no—
603#123—5932no—
604#123—5932no—
605C22⋊Q8—598no—
606C22⋊Q8—5916no—
607C22⋊Q8—5916no—
608C22⋊Q8—5916no—
609C22⋊Q8—5932no—
610C22⋊Q8—5916no—
611C22⋊Q8—5932no—
612C22⋊Q8—5932no—
613C22⋊Q8C22×D59116yes—
614C22⋊Q8C22×D59132yes—
615#121—598no—
616#121—5916no—
617#121—5916no—
618#121—5932no—
619#121—598no—
620#121—598no—
621#121—5932no—
622#121—5916no—
623#121—5916no—
624#121—5932no—
625#121—5932no—
626C4×Q8—5916no—
627C4×Q8—5916no—
628C4×Q8C22×D5918yes—
629C4×D4—5916no—
630C4×D4—5932no—
631C4×D4—598no—
632C4×D4—5916no—
633C4×D4—598no—
634C4×D4—5916no—
635C4×D4C22×D5918yes—
636C4×D4C22×D59116yes—
637#117—5916no—
638#117—5916no—
639#117—5932no—
640#117—5916no—
641#117—5916no—
642C2×C4⋊C4—591no—
643C2×C4⋊C4—592no—
644C2×C4⋊C4—594no—
645C2×C4⋊C4—594no—
646C2×C4⋊C4—592no—
647C2×C4⋊C4—591no—
648C2×C4⋊C4—592no—
649C2×C4⋊C4—592no—
650C2×C4⋊C4—592no—
651C2×C4⋊C4—592no—
652C2×C4⋊C4—594no—
653C2×C4⋊C4—594no—
654C2×C4⋊C4—594no—
655C2×C4⋊C4—5916no—
656C2×C4⋊C4—5916no—
657C2×C4⋊C4C22×D5911yescharacteristic
658C2×C4⋊C4C22×D5912yes—
659C2×C4⋊C4C22×D5911yescharacteristic
660C2×C4⋊C4C22×D5914yes—
661C2×C4⋊C4C22×D5912yes—
662C2×C4⋊C4C22×D5912yes—
663C2×C22⋊C4—594no—
664C2×C22⋊C4—592no—
665C2×C22⋊C4—592no—
666C2×C22⋊C4—592no—
667C2×C22⋊C4—594no—
668C2×C22⋊C4—592no—
669C2×C22⋊C4—594no—
670C2×C22⋊C4—594no—
671C2×C22⋊C4—592no—
672C2×C22⋊C4—592no—
673C2×C22⋊C4—594no—
674C2×C22⋊C4—592no—
675C2×C22⋊C4—592no—
676C2×C22⋊C4C22×D5914yes—
677C2×C22⋊C4C22×D5912yes—
678C2×C42—594no—
679C2×C42—594no—
680C2×C42—591no—
681C2×C42—591no—
682C2×C42—591no—
683C2×C42—598no—
684C2×C42C22×D5912yes—
685C2×C42C22×D5911yescharacteristic
686C24—591no—
687C24—592no—
688C24—592no—
689C24C23×D5912yes—
690#41—23632no—
691#41—23632no—
692C2×Q8—24no—
693C2×Q8—28no—
694C2×Q8—48no—
695C2×Q8—432no—
696C2×Q8—598no—
697C2×Q8—598no—
698C2×Q8—2364no—
699C2×Q8—2364no—
700C2×Q8C23×D5918yes—
701C2×Q8C23×D5914yes—
702C2×Q8C23×D59116yes—
703C2×D4—24no—
704C2×D4—5916no—
705C2×D4—598no—
706C2×D4—598no—
707C2×D4—598no—
708C2×D4—594no—
709C2×D4—594no—
710C2×D4—598no—
711C2×D4—5916no—
712C2×D4—598no—
713C2×D4—1184no—
714C2×D4—1184no—
715C2×D4—2364no—
716C2×D4—2368no—
717C2×D4—2364no—
718C2×D4—2364no—
719C2×D4—2364no—
720C2×D4—2364no—
721C2×D4—2368no—
722C2×D4C23×D5914yes—
723C22×C4—28no—
724C22×C4—48no—
725C22×C4—591no—
726C22×C4—592no—
727C22×C4—594no—
728C22×C4—591no—
729C22×C4—591no—
730C22×C4—592no—
731C22×C4—594no—
732C22×C4—594no—
733C22×C4—598no—
734C22×C4—598no—
735C22×C4—594no—
736C22×C4—5916no—
737C22×C4—5916no—
738C22×C4—1188no—
739C22×C4—1184no—
740C22×C4—1188no—
741C22×C4—1184no—
742C22×C4—2368no—
743C22×C4—2368no—
744C22×C4—2362no—
745C22×C4C23×D5918yes—
746C22×C4C23×D5912yes—
747C22×C4C23×D5911yescharacteristic
748C22×C4C23×D5914yes—
749C22×C4C23×D5912yes—
750C22×C4C23×D5912yes—
751C22×C4C23×D59116yes—
752C22×C4C23×D5911yescharacteristic
753C22×C4C23×D5911yescharacteristic
754C4⋊C4—594no—
755C4⋊C4—598no—
756C4⋊C4—5916no—
757C4⋊C4—5916no—
758C4⋊C4—598no—
759C4⋊C4—594no—
760C4⋊C4—598no—
761C4⋊C4—598no—
762C4⋊C4—598no—
763C4⋊C4—598no—
764C4⋊C4—5916no—
765C4⋊C4—5916no—
766C4⋊C4—5916no—
767C4⋊C4C23×D5914yes—
768C4⋊C4C23×D5918yes—
769C4⋊C4C23×D5914yes—
770C4⋊C4C23×D59116yes—
771C4⋊C4C23×D5918yes—
772C4⋊C4C23×D5918yes—
773C22⋊C4—5916no—
774C22⋊C4—598no—
775C22⋊C4—598no—
776C22⋊C4—598no—
777C22⋊C4—5916no—
778C22⋊C4—598no—
779C22⋊C4—5916no—
780C22⋊C4—5916no—
781C22⋊C4—598no—
782C22⋊C4—598no—
783C22⋊C4—5916no—
784C22⋊C4—598no—
785C22⋊C4—598no—
786C22⋊C4C23×D59116yes—
787C22⋊C4C23×D5918yes—
788C42—594no—
789C42—594no—
790C42—594no—
791C42—5916no—
792C42—5916no—
793C42C23×D5914yes—
794C42C23×D5918yes—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—592no—
799C23—594no—
800C23—594no—
801C23—1184no—
802C23—1182no—
803C23—1184no—
804C23—1182no—
805C23—1184no—
806C23—1184no—
807C23—1184no—
808C23—1182no—
809C23—1184no—
810C23C24×D5914yes—
811C23C24×D5911yescharacteristic
812Q8—28no—
813Q8—216no—
814Q8—416no—
815Q8—2368no—
816Q8—2368no—
817D4—28no—
818D4—1188no—
819D4—1188no—
820D4—2368no—
821D4—2368no—
822D4—23616no—
823D4—2368no—
824D4—23616no—
825D4—2368no—
826D4—2368no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—592no—
835C2×C4—594no—
836C2×C4—598no—
837C2×C4—592no—
838C2×C4—592no—
839C2×C4—594no—
840C2×C4—1184no—
841C2×C4—1182no—
842C2×C4—1182no—
843C2×C4—1184no—
844C2×C4—1182no—
845C2×C4—1188no—
846C2×C4—11816no—
847C2×C4—1188no—
848C2×C4—1188no—
849C2×C4—11816no—
850C2×C4—23616no—
851C2×C4—2364no—
852C2×C4—23616no—
853C2×C4#1427377214yes—
854C2×C4#1427377514yes—
855C2×C4C24×D5914yes—
856C2×C4C24×D5912yes—
857C2×C4C24×D5918yes—
858C2×C4C24×D5914yes—
859C2×C4C24×D5914yes—
860C2×C4C24×D5912yes—
861C2×C4C24×D5912yes—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—48no—
866C22—1184no—
867C22—1182no—
868C22—1184no—
869C22—1182no—
870C22—1184no—
871C22—1184no—
872C22—1184no—
873C22—1182no—
874C22—1184no—
875C22—2364no—
876C22—2368no—
877C22—2368no—
878C22C2×#1427377212yes—
879C22C2×#1427377512yes—
880C22#1683823912yes—
881C22C25×D5911yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—22no—
887C4—1184no—
888C4—1182no—
889C4—1182no—
890C4—1184no—
891C4—1182no—
892C4—1188no—
893C4C2×#1427377214yes—
894C4C2×#1427377514yes—
895C2—44no—
896C2—2362no—
897C2—2364no—
898C2—2364no—
899C2#2143848114yesdirect product factor
900C2C22×#1427377211yescharacteristic
901C2C22×#1427377511yescharacteristic
902C2C2×#1683823911yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×D4×Q8×C59C2
socleC23×C59C25
hypercenterC2×D4×Q8D59
hypocenterC59C2×#3547
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #21438481C2direct (N × H)
2. C2×#16838148C2semidirect
3. C2×#16838118C2semidirect
4. C2×#16838117C2semidirect
5. C2×#16838112C2semidirect
6. C2×#16838102C2semidirect
7. C2×#16838086C2semidirect
8. C2×#16838063C2semidirect
9. C2×#16838055C2semidirect
10. C2×#16838029C2semidirect
11. C2×#16838022C2semidirect
12. C2×#16838003C2semidirect
13. C2×#16837982C2semidirect
14. C2×#16837976C2semidirect
15. C2×#16837957C2semidirect
16. C2×#16837949C2semidirect
17. C2×#16837939C2semidirect
18. C2×D4×Q8×C59C2semidirect
21. #16838148C22semidirect
22. #16838118C22semidirect
23. #16838117C22semidirect
24. #16838112C22semidirect
25. #16838102C22semidirect
26. #16838086C22semidirect
27. #16838063C22semidirect
28. #16838055C22semidirect
29. #16838029C22semidirect
30. #16838022C22semidirect
31. #16838003C22semidirect
32. #16837982C22semidirect
33. #16837976C22semidirect
34. #16837957C22semidirect
35. #16837949C22semidirect
40. #16837939C22semidirect
93. D4×Q8×C59C22semidirect
451. C2×D4×Q8D59semidirect
463. C2×C59#3547semidirect
479. D4×Q8C2×D59semidirect
552. C59C2×#3547semidirect
899. C2#21438481direct (N × H)

Maximal subgroups

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

subgroupindex
#214384812
C2×#168381482
C2×#168381182
C2×#168381172
C2×#168381122
C2×#168381022
C2×#168380862
C2×#168380632
C2×#168380552
C2×#168380292
C2×#168380222
C2×#168380032
C2×#168379822
C2×#168379762
C2×#168379572
C2×#168379492
C2×#168379392
C2×D4×Q8×C592
C2×#354759