Finite Group Databasebeta

← C2×#21438568 #29496313

Subgroups — C2×#21438568 #29496313

Order 15104.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438568C2132yesmaximal, direct product factor
2C2×#16838148C214yesmaximal, complemented
3C2×#16838137C211yesmaximal, characteristic, complemented
4C2×#16838135C212yesmaximal, complemented
5C2×#16838127C211yesmaximal, characteristic, complemented
6C2×#16838113C212yesmaximal, complemented
7C2×#16838073C211yesmaximal, characteristic, complemented
8C2×#16838063C212yesmaximal, complemented
9C2×#16838054C212yesmaximal, complemented
10C2×#16838026C212yesmaximal, complemented
11C2×#16838025C212yesmaximal, complemented
12C2×#16838003C212yesmaximal, complemented
13C2×#16837998C214yesmaximal, complemented
14C2×#16837976C212yesmaximal, complemented
15C2×#16837956C211yesmaximal, characteristic, complemented
16C2×#16837953C211yesmaximal, characteristic, complemented
17C2×#16837934C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C59C211yesmaximal, characteristic, complemented
19C22×#11745689C2212yes—
20C22×#11745685C2212yes—
21#16838148C22164yescomplemented
22#16838137C22116yescomplemented
23#16838135C22132yescomplemented
24#16838127C22116yescomplemented
25#16838113C22132yescomplemented
26#16838073C22116yescomplemented
27#16838063C22132yescomplemented
28#16838054C22132yescomplemented
29#16838026C22132yescomplemented
30#16838025C22132yescomplemented
31#16838003C22132yescomplemented
32#16837998C22164yescomplemented
33#16837976C22132yescomplemented
34#16837956C22116yescomplemented
35#16837953C22116yescomplemented
36C2×#14273726C2211yescharacteristic
37C2×#14273725C2212yes—
38C2×#14273725C2211yescharacteristic
39C2×#14273724C2211yescharacteristic
40C2×#14273723C2212yes—
41#16837934C22116yescomplemented
42C2×#14273722C2214yes—
43C2×#14273720C2212yes—
44C2×#14273718C2212yes—
45C2×#14273718C2211yescharacteristic
46C2×#14273717C2212yes—
47C2×#14273717C2214yes—
48C2×#14273716C2214yes—
49C2×#14273716C2212yes—
50C2×#14273716C2212yes—
51C2×#14273715C2212yes—
52C2×#14273714C2211yescharacteristic
53C2×#14273713C2214yes—
54C2×#14273712C2214yes—
55C2×#14273712C2214yes—
56C2×#14273710C2214yes—
57C2×#14273710C2214yes—
58C2×#14273709C2214yes—
59C2×#14273709C2214yes—
60C2×#14273709C2212yes—
61C2×#14273707C2214yes—
62C2×#14273707C2211yescharacteristic
63C2×#14273707C2211yescharacteristic
64C2×#14273705C2212yes—
65C2×#14273703C2214yes—
66C2×#14273703C2214yes—
67C2×#14273703C2214yes—
68C2×#14273703C2211yescharacteristic
69C2×#14273702C2212yes—
70C2×#14273702C2212yes—
71C2×#14273701C2214yes—
72C2×#14273701C2212yes—
73C2×#14273700C2214yes—
74C2×#14273700C2214yes—
75C2×#14273698C2211yescharacteristic
76C2×Q8×Dic59C2212yes—
77C2×C4×Dic118C2211yescharacteristic
78C2×C4×Dic118C2211yescharacteristic
79C2×C4×Dic118C2212yes—
80C2×#14273692C2212yes—
81C2×C4×D236C2212yes—
82C2×#14273689C2212yes—
83C2×#14273689C2212yes—
84C2×#14273689C2212yes—
85C2×#14273689C2212yes—
86C2×C4×C22⋊D59C2214yes—
87C2×C4×C22⋊D59C2212yes—
88C2×#14273686C2212yes—
89C2×#14273684C2212yes—
90C2×C4⋊C4×D59C2214yes—
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×Dic118C2311yescharacteristic
106C22×Dic118C2311yescharacteristic
107C22×Dic118C2312yes—
108C22×D236C2312yes—
109C22×D236C2312yes—
110C22×D236C2312yes—
111C22×D236C2314yes—
112C22×C22⋊D59C2312yes—
113C22×C22⋊D59C2314yes—
114C22×C22⋊D59C2314yes—
115C22×C4×D59C2311yescharacteristic
116C22×C4×D59C2311yescharacteristic
117C22×C4×D59C2314yes—
118C22×C4×D59C2314yes—
119C22×C4×D59C2311yescharacteristic
120C22×C4×D59C2314yes—
121#14273726C2318yes—
122#14273725C2318yes—
123#14273725C23116yes—
124#14273724C2318yes—
125#14273723C23116yes—
126#14273722C23132yes—
127#14273720C23116yes—
128#14273718C2318yes—
129#14273718C23116yes—
130#14273717C23132yes—
131#14273717C23116yes—
132#14273716C23132yes—
133#14273716C23116yes—
134#14273716C23116yes—
135#14273715C23116yes—
136#14273714C2318yes—
137#14273713C23132yes—
138#14273712C23132yes—
139#14273712C23132yes—
140#14273710C23132yes—
141#14273710C23132yes—
142#14273709C23116yes—
143#14273709C23132yes—
144#14273709C23132yes—
145#14273707C23132yes—
146#14273707C2318yes—
147#14273707C2318yes—
148#14273705C23116yes—
149#14273703C23132yes—
150#14273703C2318yes—
151#14273703C23132yes—
152#14273703C23132yes—
153#14273702C23116yes—
154#14273702C23116yes—
155#14273701C23132yes—
156#14273701C23116yes—
157#14273700C23132yes—
158#14273700C23132yes—
159#14273698C2318yes—
160Q8×Dic59C23116yes—
161C4×Dic118C2318yes—
162C4×Dic118C2318yes—
163C4×Dic118C23116yes—
164#14273692C23116yes—
165C4×D236C23116yes—
166#14273689C23116yes—
167#14273689C23116yes—
168#14273689C23116yes—
169#14273689C23116yes—
170C4×C22⋊D59C23116yes—
171C4×C22⋊D59C23132yes—
172#14273686C23116yes—
173#14273684C23116yes—
174C2×C4⋊Dic59C2311yescharacteristic
175C2×C4⋊Dic59C2311yescharacteristic
176C2×C4⋊Dic59C2314yes—
177C2×C4⋊Dic59C2312yes—
178C2×C4⋊Dic59C2312yes—
179C2×C4⋊Dic59C2312yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2314yes—
182C2×Dic59⋊C4C2312yes—
183C2×Dic59⋊C4C2312yes—
184C2×Dic59⋊C4C2312yes—
185C2×Dic59⋊C4C2312yes—
186C2×Dic59⋊C4C2314yes—
187C2×Dic59⋊C4C2312yes—
188C2×Dic59⋊C4C2312yes—
189C4⋊C4×D59C23132yes—
190C2×C22⋊Dic59C2312yes—
191C2×C22⋊Dic59C2312yes—
192C2×C22⋊Dic59C2312yes—
193C2×(C2×D59)⋊C4C2312yes—
194C2×(C2×D59)⋊C4C2314yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2314yes—
197C2×(C2×D59)⋊C4C2314yes—
198C2×(C2×D59)⋊C4C2314yes—
199C2×(C2×D59)⋊C4C2314yes—
200C2×(C2×D59)⋊C4C2312yes—
201C2×(C2×D59)⋊C4C2314yes—
202C2×C4×Dic59C2314yes—
203C2×C4×Dic59C2311yescharacteristic
204C2×C4×Dic59C2311yescharacteristic
205C2×C4×Dic59C2312yes—
206C2×C4×Dic59C2311yescharacteristic
207C2×C4×Dic59C2312yes—
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×C59C2312yes—
225C2×C4⋊C4×C59C2312yes—
226C2×C4⋊C4×C59C2312yes—
227C2×C4⋊C4×C59C2314yes—
228C2×C4⋊C4×C59C2311yescharacteristic
229C2×C4⋊C4×C59C2311yescharacteristic
230C2×C22⋊C4×C59C2312yes—
231C2×C22⋊C4×C59C2314yes—
232C2×C42×C59C2312yes—
233C2×C42×C59C2311yescharacteristic
234C24×C59C2412yes—
235C23×D59C2411yescharacteristic
236C23×D59C2414yes—
237C2×Q8×C59—24no—
238C2×Q8×C59—28no—
239C2×Q8×C59—48no—
240C2×Q8×C59—432no—
241C2×Q8×C59C2414yes—
242C2×Q8×C59C2418yes—
243C2×Q8×C59C24116yes—
244C2×D4×C59—24no—
245C2×D4×C59C2414yes—
246C22×C4×C59—28no—
247C22×C4×C59—48no—
248C22×C4×C59C2411yescharacteristic
249C22×C4×C59C2412yes—
250C22×C4×C59C2412yes—
251C22×C4×C59C2414yes—
252C22×C4×C59C2412yes—
253C22×C4×C59C2418yes—
254C22×C4×C59C24116yes—
255C22×C4×C59C2411yescharacteristic
256C22×C4×C59C2411yescharacteristic
257C2×C22⋊D59—48no—
258C2×C22⋊D59—44no—
259C2×C22⋊D59—48no—
260C2×C22⋊D59C2418yes—
261C2×C22⋊D59C24116yes—
262C2×C22⋊D59C24116yes—
263C22×Dic59C2412yes—
264C22×Dic59C2412yes—
265C22×Dic59C2411yescharacteristic
266C22×Dic59C2411yescharacteristic
267C22×Dic59C2411yescharacteristic
268C22×Dic59C2412yes—
269C22×Dic59C2412yes—
270#11745689—432no—
271#11745685—432no—
272C2×D236—28no—
273C2×D236—28no—
274C2×D236—44no—
275C2×D236—48no—
276C2×D236C2418yes—
277C2×D236C2418yes—
278C2×D236C2418yes—
279C2×D236C24116yes—
280C2×C4×D59—24no—
281C2×C4×D59—24no—
282C2×C4×D59—42no—
283C2×C4×D59—48no—
284C2×C4×D59—48no—
285C2×C4×D59—48no—
286C2×C4×D59C2414yes—
287C2×C4×D59C2414yes—
288C2×C4×D59C2414yes—
289C2×C4×D59C24116yes—
290C2×C4×D59C24116yes—
291C2×C4×D59C24116yes—
292C2×Dic118—24no—
293C2×Dic118—24no—
294C2×Dic118—44no—
295C2×Dic118C2414yes—
296C2×Dic118C2414yes—
297C2×Dic118C2418yes—
298C4⋊C4×C59C2414yes—
299C4⋊C4×C59C2418yes—
300C4⋊C4×C59C2414yes—
301C4⋊C4×C59C2418yes—
302C4⋊C4×C59C24116yes—
303C4⋊C4×C59C2418yes—
304C22⋊C4×C59C2418yes—
305C22⋊C4×C59C24116yes—
306C42×C59C2414yes—
307C42×C59C2418yes—
308C22⋊Dic59C2418yes—
309C22⋊Dic59C2418yes—
310C22⋊Dic59C2418yes—
311(C2×D59)⋊C4C2418yes—
312(C2×D59)⋊C4C2418yes—
313(C2×D59)⋊C4C24116yes—
314(C2×D59)⋊C4C2418yes—
315(C2×D59)⋊C4C24116yes—
316(C2×D59)⋊C4C24116yes—
317(C2×D59)⋊C4C24116yes—
318(C2×D59)⋊C4C24116yes—
319(C2×D59)⋊C4C24116yes—
320C4⋊Dic59C2418yes—
321C4⋊Dic59C2418yes—
322C4⋊Dic59C2418yes—
323C4⋊Dic59C2414yes—
324C4⋊Dic59C2414yes—
325C4⋊Dic59C24116yes—
326Dic59⋊C4C2418yes—
327Dic59⋊C4C24116yes—
328Dic59⋊C4C2418yes—
329Dic59⋊C4C2418yes—
330Dic59⋊C4C2418yes—
331Dic59⋊C4C24116yes—
332Dic59⋊C4C2418yes—
333Dic59⋊C4C2418yes—
334Dic59⋊C4C2418yes—
335C4×Dic59C2414yes—
336C4×Dic59C2414yes—
337C4×Dic59C2414yes—
338C4×Dic59C2418yes—
339C4×Dic59C2418yes—
340C4×Dic59C24116yes—
341C23×C59—24no—
342C23×C59—24no—
343C23×C59—24no—
344C23×C59C2514yes—
345C23×C59C2511yescharacteristic
346C22×D59—22no—
347C22×D59—28no—
348C22×D59—22no—
349C22×D59—28no—
350C22×D59—28no—
351C22×D59—22no—
352C22×D59C2512yes—
353C22×D59C2518yes—
354Q8×C59—216no—
355Q8×C59—28no—
356Q8×C59—416no—
357D4×C59—28no—
358C2×C4×C59—24no—
359C2×C4×C59—28no—
360C2×C4×C59—24no—
361C2×C4×C59—24no—
362C2×C4×C59—22no—
363C2×C4×C59—216no—
364C2×C4×C59—416no—
365C2×C4×C59H(5,𝔽2)14yes—
366C2×C4×C592−1+414yes—
367C2×C4×C59C2512yes—
368C2×C4×C59C2518yes—
369C2×C4×C59C2514yes—
370C2×C4×C59C2514yes—
371C2×C4×C59C2514yes—
372C2×C4×C59C2512yes—
373C2×C4×C59C2512yes—
374C22⋊D59—416no—
375C22⋊D59—416no—
376C22⋊D59—48no—
377C2×Dic59—24no—
378C2×Dic59—22no—
379C2×Dic59—24no—
380C2×Dic59—22no—
381C2×Dic59—22no—
382C2×Dic59—24no—
383C2×Dic59—24no—
384C2×Dic59C2514yes—
385C2×Dic59C2514yes—
386C2×Dic59C2512yes—
387C2×Dic59C2512yes—
388C2×Dic59C2512yes—
389C2×Dic59C2514yes—
390C2×Dic59C2514yes—
391D236—216no—
392D236—216no—
393D236—48no—
394D236—416no—
395C4×D59—28no—
396C4×D59—28no—
397C4×D59—44no—
398C4×D59—416no—
399C4×D59—416no—
400C4×D59—416no—
401Dic118—28no—
402Dic118—28no—
403Dic118—48no—
404C2×#3554—591nomaximal, Sylow
405C22×C59—24no—
406C22×C59—24no—
407C22×C59—24no—
408C22×C59—48no—
409C22×C59C2×H(5,𝔽2)12yes—
410C22×C59C2×2−1+412yes—
411C22×C59#58512yes—
412C22×C59C2611yescharacteristic
413C2×D59—22no—
414C2×D59—28no—
415C2×D59—22no—
416C2×D59—28no—
417C2×D59—28no—
418C2×D59—22no—
419C2×D59—44no—
420C2×D59—416no—
421C4×C59—24no—
422C4×C59—28no—
423C4×C59—24no—
424C4×C59—24no—
425C4×C59—22no—
426C4×C59C2×H(5,𝔽2)14yes—
427C4×C59C2×2−1+414yes—
428Dic59—24no—
429Dic59—22no—
430Dic59—24no—
431Dic59—22no—
432Dic59—22no—
433Dic59—24no—
434Dic59—24no—
435#3554—5932no—
436C2×#562—594no—
437C2×#559—591no—
438C2×#559—592no—
439C2×#557—591no—
440C2×#554—592no—
441C2×#550—591no—
442C2×D4×Q8D5911yescharacteristic, complemented
443C2×#548—592no—
444C2×#547—592no—
445C2×#542—592no—
446C2×#542—592no—
447C2×#540—592no—
448C2×#539—594no—
449C2×#536—592no—
450C2×#533—591no—
451C2×#532—591no—
452C2×#529—591no—
453C2×C59—44no—
454C2×C59#355414yescomplemented
455C2×C59C22×H(5,𝔽2)11yescharacteristic
456C2×C59C22×2−1+411yescharacteristic
457C2×C59C2×#58511yescharacteristic
458D59—42no—
459D59—48no—
460C22×#41—592no—
461C22×#41—592no—
462C23×Q8C2×D5912yes—
463#562—5964no—
464#559—5916no—
465#559—5932no—
466#557—5916no—
467#554—5932no—
468#550—5916no—
469D4×Q8C2×D59116yescomplemented
470#548—5932no—
471#547—5932no—
472#542—5932no—
473#542—5932no—
474#540—5932no—
475#539—5964no—
476#536—5932no—
477#533—5916no—
478#532—5916no—
479C2×C4⋊Q8—591no—
480C2×C4⋊Q8—592no—
481C2×C4⋊Q8—591no—
482C2×C4⋊Q8C2×D5911yescharacteristic
483C2×C4⋊Q8C2×D5912yes—
484C2×#127—592no—
485C2×#127—591no—
486#529—5916no—
487C2×#126—594no—
488C2×#126—592no—
489C2×#125—592no—
490C2×#125—594no—
491C2×#125—591no—
492C2×#125—592no—
493C2×#124—592no—
494C2×#124—592no—
495C2×#124—594no—
496C2×#124—591no—
497C2×#124—594no—
498C2×#124—592no—
499C2×#123—594no—
500C2×#123—594no—
501C2×#123—594no—
502C2×#123—594no—
503C2×#123—592no—
504C2×#123—594no—
505C2×#123—594no—
506C2×C22⋊Q8—591no—
507C2×C22⋊Q8—594no—
508C2×C22⋊Q8—594no—
509C2×C22⋊Q8—594no—
510C2×C22⋊Q8—592no—
511C2×C22⋊Q8—591no—
512C2×C22⋊Q8—591no—
513C2×C22⋊Q8—594no—
514C2×C22⋊Q8C2×D5914yes—
515C2×C22⋊Q8C2×D5912yes—
516C2×#121—591no—
517C2×#121—594no—
518C2×#121—592no—
519C2×#121—592no—
520C2×#121—592no—
521C2×#121—594no—
522C2×#121—594no—
523C2×C4×Q8—592no—
524C2×C4×Q8—592no—
525C2×C4×Q8—591no—
526C2×C4×Q8—591no—
527C2×C4×Q8—592no—
528C2×C4×Q8C2×D5911yescharacteristic
529C2×C4×D4—592no—
530C2×C4×D4—594no—
531C2×C4×D4—592no—
532C2×C4×D4—592no—
533C2×C4×D4—592no—
534C2×C4×D4—592no—
535C2×C4×D4—592no—
536C2×C4×D4C2×D5911yescharacteristic
537C2×C4×D4C2×D5912yes—
538C2×#117—592no—
539C2×#117—592no—
540C22×C4⋊C4—594no—
541C22×C42—591no—
542C59C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—5916no—
544C2×#41—5916no—
545C2×#41—2368no—
546C2×#41—2368no—
547C22×Q8—48no—
548C22×Q8—591no—
549C22×Q8—591no—
550C22×Q8—592no—
551C22×Q8C22×D5912yes—
552C22×Q8C22×D5911yescharacteristic
553C22×Q8C22×D5914yes—
554C22×Q8C22×D59116yes—
555C22×D4—592no—
556C22×D4—594no—
557C22×D4—594no—
558C22×D4—592no—
559C22×D4—592no—
560C22×D4—592no—
561C22×D4—594no—
562C22×D4C22×D5911yescharacteristic
563C23×C4—591no—
564C23×C4—591no—
565C23×C4—594no—
566C23×C4—594no—
567C23×C4—594no—
568C23×C4—591no—
569C23×C4C22×D5912yes—
570C23×C4C22×D5914yes—
571C4⋊Q8—598no—
572C4⋊Q8—5916no—
573C4⋊Q8—598no—
574C4⋊Q8C22×D5918yes—
575C4⋊Q8C22×D59116yes—
576#127—5916no—
577#127—598no—
578#126—5932no—
579#126—5916no—
580#125—598no—
581#125—5916no—
582#125—5932no—
583#125—5916no—
584#124—5916no—
585#124—5916no—
586#124—5932no—
587#124—598no—
588#124—5932no—
589#124—5916no—
590#123—5932no—
591#123—5932no—
592#123—5932no—
593#123—5932no—
594#123—5916no—
595#123—5932no—
596#123—5932no—
597C22⋊Q8—598no—
598C22⋊Q8—5932no—
599C22⋊Q8—5932no—
600C22⋊Q8—5932no—
601C22⋊Q8—598no—
602C22⋊Q8—598no—
603C22⋊Q8—5916no—
604C22⋊Q8—5932no—
605C22⋊Q8C22×D59132yes—
606C22⋊Q8C22×D59116yes—
607#121—598no—
608#121—5932no—
609#121—5916no—
610#121—5916no—
611#121—5916no—
612#121—5932no—
613#121—5932no—
614C4×Q8—5916no—
615C4×Q8—5916no—
616C4×Q8—598no—
617C4×Q8—598no—
618C4×Q8—5916no—
619C4×Q8C22×D5918yes—
620C4×D4—5916no—
621C4×D4—5932no—
622C4×D4—5916no—
623C4×D4—5916no—
624C4×D4—5916no—
625C4×D4—5916no—
626C4×D4—5916no—
627C4×D4C22×D5918yes—
628C4×D4C22×D59116yes—
629#117—5916no—
630#117—5916no—
631C2×C4⋊C4—592no—
632C2×C4⋊C4—592no—
633C2×C4⋊C4—594no—
634C2×C4⋊C4—592no—
635C2×C4⋊C4—592no—
636C2×C4⋊C4—592no—
637C2×C4⋊C4—592no—
638C2×C4⋊C4—591no—
639C2×C4⋊C4—592no—
640C2×C4⋊C4—591no—
641C2×C4⋊C4—592no—
642C2×C4⋊C4—594no—
643C2×C4⋊C4—592no—
644C2×C4⋊C4—594no—
645C2×C4⋊C4—592no—
646C2×C4⋊C4—5932no—
647C2×C4⋊C4C22×D5914yes—
648C2×C4⋊C4C22×D5911yescharacteristic
649C2×C4⋊C4C22×D5911yescharacteristic
650C2×C4⋊C4C22×D5912yes—
651C2×C4⋊C4C22×D5912yes—
652C2×C4⋊C4C22×D5912yes—
653C2×C22⋊C4—592no—
654C2×C22⋊C4—592no—
655C2×C22⋊C4—592no—
656C2×C22⋊C4—592no—
657C2×C22⋊C4—592no—
658C2×C22⋊C4—594no—
659C2×C22⋊C4—594no—
660C2×C22⋊C4—594no—
661C2×C22⋊C4—594no—
662C2×C22⋊C4—592no—
663C2×C22⋊C4—594no—
664C2×C22⋊C4—594no—
665C2×C22⋊C4C22×D5912yes—
666C2×C22⋊C4C22×D5914yes—
667C2×C42—591no—
668C2×C42—592no—
669C2×C42—592no—
670C2×C42—591no—
671C2×C42—591no—
672C2×C42—594no—
673C2×C42—598no—
674C2×C42C22×D5912yes—
675C2×C42C22×D5911yescharacteristic
676C24—591no—
677C24—594no—
678C24C23×D5912yes—
679#41—23632no—
680#41—23632no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—48no—
684C2×Q8—432no—
685C2×Q8—594no—
686C2×Q8—594no—
687C2×Q8—598no—
688C2×Q8—1184no—
689C2×Q8—1184no—
690C2×Q8—2364no—
691C2×Q8C23×D5918yes—
692C2×Q8C23×D5914yes—
693C2×Q8C23×D59116yes—
694C2×D4—24no—
695C2×D4—598no—
696C2×D4—5916no—
697C2×D4—5916no—
698C2×D4—598no—
699C2×D4—598no—
700C2×D4—598no—
701C2×D4—5916no—
702C2×D4—1188no—
703C2×D4—1188no—
704C2×D4—2368no—
705C2×D4—2364no—
706C2×D4—2368no—
707C2×D4—2364no—
708C2×D4—2368no—
709C2×D4C23×D5914yes—
710C22×C4—28no—
711C22×C4—48no—
712C22×C4—592no—
713C22×C4—592no—
714C22×C4—591no—
715C22×C4—591no—
716C22×C4—591no—
717C22×C4—592no—
718C22×C4—592no—
719C22×C4—594no—
720C22×C4—594no—
721C22×C4—594no—
722C22×C4—5916no—
723C22×C4—5916no—
724C22×C4—5916no—
725C22×C4—1184no—
726C22×C4—1184no—
727C22×C4—2368no—
728C22×C4—2368no—
729C22×C4—2368no—
730C22×C4—2362no—
731C22×C4C23×D5918yes—
732C22×C4C23×D5911yescharacteristic
733C22×C4C23×D5914yes—
734C22×C4C23×D5912yes—
735C22×C4C23×D5912yes—
736C22×C4C23×D5912yes—
737C22×C4C23×D59116yes—
738C22×C4C23×D5911yescharacteristic
739C22×C4C23×D5911yescharacteristic
740C4⋊C4—598no—
741C4⋊C4—598no—
742C4⋊C4—5916no—
743C4⋊C4—598no—
744C4⋊C4—598no—
745C4⋊C4—598no—
746C4⋊C4—598no—
747C4⋊C4—594no—
748C4⋊C4—598no—
749C4⋊C4—594no—
750C4⋊C4—598no—
751C4⋊C4—5916no—
752C4⋊C4—598no—
753C4⋊C4—5916no—
754C4⋊C4—598no—
755C4⋊C4C23×D59116yes—
756C4⋊C4C23×D5914yes—
757C4⋊C4C23×D5914yes—
758C4⋊C4C23×D5918yes—
759C4⋊C4C23×D5918yes—
760C4⋊C4C23×D5918yes—
761C22⋊C4—598no—
762C22⋊C4—598no—
763C22⋊C4—598no—
764C22⋊C4—598no—
765C22⋊C4—598no—
766C22⋊C4—5916no—
767C22⋊C4—5916no—
768C22⋊C4—5916no—
769C22⋊C4—5916no—
770C22⋊C4—598no—
771C22⋊C4—5916no—
772C22⋊C4—5916no—
773C22⋊C4C23×D5918yes—
774C22⋊C4C23×D59116yes—
775C42—594no—
776C42—594no—
777C42—594no—
778C42—598no—
779C42—598no—
780C42—5916no—
781C42C23×D5914yes—
782C42C23×D5918yes—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—592no—
787C23—598no—
788C23—1182no—
789C23—1188no—
790C23—1182no—
791C23—1188no—
792C23—1188no—
793C23—1182no—
794C23C24×D5914yes—
795C23C24×D5911yescharacteristic
796Q8—28no—
797Q8—216no—
798Q8—416no—
799Q8—1188no—
800Q8—1188no—
801Q8—2368no—
802D4—28no—
803D4—11816no—
804D4—11816no—
805D4—2368no—
806D4—23616no—
807D4—2368no—
808D4—23616no—
809D4—23616no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—216no—
816C2×C4—416no—
817C2×C4—594no—
818C2×C4—594no—
819C2×C4—592no—
820C2×C4—592no—
821C2×C4—592no—
822C2×C4—594no—
823C2×C4—594no—
824C2×C4—1182no—
825C2×C4—1184no—
826C2×C4—1182no—
827C2×C4—1184no—
828C2×C4—1184no—
829C2×C4—1182no—
830C2×C4—1184no—
831C2×C4—1188no—
832C2×C4—1188no—
833C2×C4—23616no—
834C2×C4—2364no—
835C2×C4—23616no—
836C2×C4—23616no—
837C2×C4#1427377214yes—
838C2×C4#1427377514yes—
839C2×C4C24×D5912yes—
840C2×C4C24×D5918yes—
841C2×C4C24×D5914yes—
842C2×C4C24×D5914yes—
843C2×C4C24×D5914yes—
844C2×C4C24×D5912yes—
845C2×C4C24×D5912yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—1182no—
851C22—1188no—
852C22—1182no—
853C22—1188no—
854C22—1188no—
855C22—1182no—
856C22—2364no—
857C22—23616no—
858C22C2×#1427377212yes—
859C22C2×#1427377512yes—
860C22#1683823912yes—
861C22C25×D5911yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—1182no—
868C4—1184no—
869C4—1182no—
870C4—1184no—
871C4—1184no—
872C4—1182no—
873C4—1184no—
874C4C2×#1427377214yes—
875C4C2×#1427377514yes—
876C2—44no—
877C2—2362no—
878C2—2368no—
879C2#2143856814yesdirect product factor
880C2C22×#1427377211yescharacteristic
881C2C22×#1427377511yescharacteristic
882C2C2×#1683823911yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×D4×Q8×C59C2
socleC23×C59C25
hypercenterC2×D4×Q8D59
hypocenterC59C2×#3554
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #21438568C2direct (N × H)
2. C2×#16838148C2semidirect
3. C2×#16838137C2semidirect
4. C2×#16838135C2semidirect
5. C2×#16838127C2semidirect
6. C2×#16838113C2semidirect
7. C2×#16838073C2semidirect
8. C2×#16838063C2semidirect
9. C2×#16838054C2semidirect
10. C2×#16838026C2semidirect
11. C2×#16838025C2semidirect
12. C2×#16838003C2semidirect
13. C2×#16837998C2semidirect
14. C2×#16837976C2semidirect
15. C2×#16837956C2semidirect
16. C2×#16837953C2semidirect
17. C2×#16837934C2semidirect
18. C2×D4×Q8×C59C2semidirect
21. #16838148C22semidirect
22. #16838137C22semidirect
23. #16838135C22semidirect
24. #16838127C22semidirect
25. #16838113C22semidirect
26. #16838073C22semidirect
27. #16838063C22semidirect
28. #16838054C22semidirect
29. #16838026C22semidirect
30. #16838025C22semidirect
31. #16838003C22semidirect
32. #16837998C22semidirect
33. #16837976C22semidirect
34. #16837956C22semidirect
35. #16837953C22semidirect
41. #16837934C22semidirect
93. D4×Q8×C59C22semidirect
442. C2×D4×Q8D59semidirect
454. C2×C59#3554semidirect
469. D4×Q8C2×D59semidirect
542. C59C2×#3554semidirect
879. C2#21438568direct (N × H)

Maximal subgroups

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

subgroupindex
#214385682
C2×#168381482
C2×#168381372
C2×#168381352
C2×#168381272
C2×#168381132
C2×#168380732
C2×#168380632
C2×#168380542
C2×#168380262
C2×#168380252
C2×#168380032
C2×#168379982
C2×#168379762
C2×#168379562
C2×#168379532
C2×#168379342
C2×D4×Q8×C592
C2×#355459