Finite Group Databasebeta

← C2×#21438073 #29496806

Subgroups — C2×#21438073 #29496806

Order 15104.

7142 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#21438073C2132yesmaximal, direct product factor
2C2×#16838112C211yesmaximal, characteristic, complemented
3C2×#16838112C211yesmaximal, characteristic, complemented
4C2×#16838105C212yesmaximal, complemented
5C2×#16838093C212yesmaximal, complemented
6C2×#16838093C212yesmaximal, complemented
7C2×#16838084C214yesmaximal, complemented
8C2×#16838055C212yesmaximal, complemented
9C2×#16838055C211yesmaximal, characteristic, complemented
10C2×#16838013C212yesmaximal, complemented
11C2×#16838000C214yesmaximal, complemented
12C2×#16837957C211yesmaximal, characteristic, complemented
13C2×#16837939C212yesmaximal, complemented
14C2×#16837939C211yesmaximal, characteristic, complemented
15C2×#125×D59C212yesmaximal, complemented
16C2×#16837884C212yesmaximal, complemented
17C2×C4×#11745689C211yesmaximal, characteristic, complemented
18C2×C59×#557C211yesmaximal, characteristic, complemented
19C22×#11745689C2211yescharacteristic
20C22×#11745689C2212yes—
21#16838112C22116yescomplemented
22#16838112C22116yescomplemented
23#16838105C22132yescomplemented
24#16838093C22132yescomplemented
25#16838093C22132yescomplemented
26#16838084C22164yescomplemented
27#16838055C22116yescomplemented
28#16838055C22132yescomplemented
29#16838013C22132yescomplemented
30#16838000C22164yescomplemented
31#16837957C22116yescomplemented
32C2×#14273727C2211yescharacteristic
33#16837939C22132yescomplemented
34#16837939C22116yescomplemented
35C2×#14273722C2214yes—
36C2×#14273722C2214yes—
37C2×#14273722C2212yes—
38C2×#14273721C2214yes—
39C2×#14273719C2212yes—
40C2×#14273719C2212yes—
41C2×#14273718C2211yescharacteristic
42C2×#14273718C2212yes—
43C2×#14273717C2214yes—
44C2×#14273717C2214yes—
45C2×#14273717C2214yes—
46#125×D59C22132yescomplemented
47C2×#14273716C2211yescharacteristic
48C2×#14273712C2212yes—
49C2×#14273712C2214yes—
50C2×#14273712C2214yes—
51C2×#14273712C2214yes—
52C2×#14273712C2214yes—
53C2×#14273707C2212yes—
54C2×#14273705C2214yes—
55C2×#14273705C2214yes—
56C2×#14273703C2212yes—
57C2×#14273703C2212yes—
58C2×#14273703C2212yes—
59C2×#14273703C2211yescharacteristic
60C2×#14273703C2212yes—
61C2×#14273702C2214yes—
62C2×#14273702C2212yes—
63C2×#14273702C2211yescharacteristic
64#16837884C22132yescomplemented
65C4×#11745689C22116yescomplemented
66C2×Q8×Dic59C2211yescharacteristic
67C2×Q8×Dic59C2212yes—
68C2×#14273692C2212yes—
69C2×C4×D236C2214yes—
70C2×C4×D236C2211yescharacteristic
71C2×C4×D236C2212yes—
72C2×C4×D236C2212yes—
73C2×C4×D236C2212yes—
74C2×C4×D236C2211yescharacteristic
75C2×C4×D236C2212yes—
76C2×#14273689C2212yes—
77C2×#14273689C2211yescharacteristic
78C2×#14273689C2214yes—
79C2×#14273685C2212yes—
80C2×#14273685C2211yescharacteristic
81C2×#14273685C2212yes—
82C2×#14273684C2212yes—
83C2×#14273684C2214yes—
84C2×#14273684C2214yes—
85C2×C4⋊C4×D59C2214yes—
86C2×C4⋊C4×D59C2212yes—
87C2×C4⋊C4×D59C2214yes—
88C2×C4⋊C4×D59C2212yes—
89C2×C4⋊C4×D59C2212yes—
90C2×C42×D59C2212yes—
91C2×C42×D59C2211yescharacteristic
92C59×#557C22116yescomplemented
93C2×C4⋊Q8×C59C2212yes—
94C2×C4⋊Q8×C59C2211yescharacteristic
95C2×#125×C59C2214yes—
96C2×#125×C59C2212yes—
97C2×C4×Q8×C59C2211yescharacteristic
98C2×C4×Q8×C59C2212yes—
99C2×C4×Q8×C59C2212yes—
100C2×C4×Q8×C59C2211yescharacteristic
101C2×#11745689—28no—
102C2×#11745689—216no—
103C2×#11745689C2318yes—
104C2×#11745689C23116yes—
105C22×Dic118C2312yes—
106C22×D236C2311yescharacteristic
107C22×D236C2312yes—
108C22×D236C2314yes—
109C22×D236C2312yes—
110C22×D236C2311yescharacteristic
111C22×C4×D59C2312yes—
112C22×C4×D59C2311yescharacteristic
113C22×C4×D59C2311yescharacteristic
114C22×C4×D59C2312yes—
115C22×C4×D59C2312yes—
116C22×C4×D59C2314yes—
117C22×C4×D59C2314yes—
118C22×C4×D59C2314yes—
119C22×C4×D59C2311yescharacteristic
120C22×C4×D59C2312yes—
121#14273727C2318yes—
122#14273722C23132yes—
123#14273722C23116yes—
124#14273722C23132yes—
125#14273721C23132yes—
126#14273719C23116yes—
127#14273719C23116yes—
128#14273718C2318yes—
129#14273718C23116yes—
130#14273717C23132yes—
131#14273717C23132yes—
132#14273717C23132yes—
133#14273716C2318yes—
134#14273712C23116yes—
135#14273712C23132yes—
136#14273712C23132yes—
137#14273712C23132yes—
138#14273712C23132yes—
139#14273707C23116yes—
140#14273705C23132yes—
141#14273705C23132yes—
142#14273703C2318yes—
143#14273703C23116yes—
144#14273703C23116yes—
145#14273703C23116yes—
146#14273703C23116yes—
147#14273702C23116yes—
148#14273702C2318yes—
149#14273702C23132yes—
150Q8×Dic59C23116yes—
151Q8×Dic59C2318yes—
152#14273692C23116yes—
153C4×D236C23132yes—
154C4×D236C23116yes—
155C4×D236C2318yes—
156C4×D236C23116yes—
157C4×D236C2318yes—
158C4×D236C23116yes—
159C4×D236C23116yes—
160#14273689C23116yes—
161#14273689C23132yes—
162#14273689C2318yes—
163#14273685C23116yes—
164#14273685C23116yes—
165#14273685C2318yes—
166#14273684C23116yes—
167#14273684C23132yes—
168#14273684C23132yes—
169C2×C4⋊Dic59C2311yescharacteristic
170C2×C4⋊Dic59C2312yes—
171C2×C4⋊Dic59C2311yescharacteristic
172C2×C4⋊Dic59C2312yes—
173C2×C4⋊Dic59C2314yes—
174C2×C4⋊Dic59C2312yes—
175C2×C4⋊Dic59C2312yes—
176C2×Dic59⋊C4C2314yes—
177C2×Dic59⋊C4C2314yes—
178C2×Dic59⋊C4C2314yes—
179C2×Dic59⋊C4C2314yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2314yes—
182C2×Dic59⋊C4C2314yes—
183C2×Dic59⋊C4C2312yes—
184C4⋊C4×D59C23132yes—
185C4⋊C4×D59C23132yes—
186C4⋊C4×D59C23116yes—
187C4⋊C4×D59C23116yes—
188C4⋊C4×D59C23116yes—
189C2×(C2×D59)⋊C4C2314yes—
190C2×(C2×D59)⋊C4C2314yes—
191C2×(C2×D59)⋊C4C2314yes—
192C2×(C2×D59)⋊C4C2312yes—
193C2×(C2×D59)⋊C4C2314yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2312yes—
197C2×(C2×D59)⋊C4C2312yes—
198C2×(C2×D59)⋊C4C2312yes—
199C2×(C2×D59)⋊C4C2312yes—
200C2×(C2×D59)⋊C4C2312yes—
201C2×C4×Dic59C2311yescharacteristic
202C2×C4×Dic59C2312yes—
203C2×C4×Dic59C2312yes—
204C2×C4×Dic59C2314yes—
205C2×C4×Dic59C2311yescharacteristic
206C2×C4×Dic59C2311yescharacteristic
207C42×D59C23116yes—
208C42×D59C2318yes—
209C22×Q8×C59C2311yescharacteristic
210C22×Q8×C59C2312yes—
211C22×Q8×C59C2311yescharacteristic
212C4⋊Q8×C59C2318yes—
213C4⋊Q8×C59C23116yes—
214#125×C59C23116yes—
215#125×C59C23132yes—
216C4×Q8×C59C23116yes—
217C4×Q8×C59C2318yes—
218C4×Q8×C59C23116yes—
219C4×Q8×C59C2318yes—
220C2×C4⋊C4×C59C2314yes—
221C2×C4⋊C4×C59C2311yescharacteristic
222C2×C4⋊C4×C59C2312yes—
223C2×C4⋊C4×C59C2312yes—
224C2×C4⋊C4×C59C2312yes—
225C2×C4⋊C4×C59C2312yes—
226C2×C4⋊C4×C59C2314yes—
227C2×C4⋊C4×C59C2314yes—
228C2×C4⋊C4×C59C2311yescharacteristic
229C2×C42×C59C2312yes—
230C2×C42×C59C2312yes—
231C2×C42×C59C2314yes—
232C2×C42×C59C2311yescharacteristic
233C23×D59C2411yescharacteristic
234C23×D59C2412yes—
235C23×D59C2412yes—
236C2×Q8×C59—28no—
237C2×Q8×C59—24no—
238C2×Q8×C59—24no—
239C2×Q8×C59C2414yes—
240C2×Q8×C59C2418yes—
241C2×Q8×C59C2414yes—
242C22×C4×C59C2412yes—
243C22×C4×C59C2412yes—
244C22×C4×C59C2411yescharacteristic
245C22×C4×C59C2412yes—
246C22×C4×C59C2412yes—
247C22×C4×C59C2414yes—
248C22×C4×C59C2411yescharacteristic
249C22×C4×C59C2411yescharacteristic
250C22×Dic59C2411yescharacteristic
251C22×Dic59C2411yescharacteristic
252C22×Dic59C2411yescharacteristic
253C22×Dic59C2412yes—
254C22×Dic59C2414yes—
255C22×Dic59C2412yes—
256#11745689—232no—
257#11745689—264no—
258C2×D236—28no—
259C2×D236—216no—
260C2×D236—24no—
261C2×D236—44no—
262C2×D236#4118yes—
263C2×D236C2418yes—
264C2×D236C24116yes—
265C2×D236C2414yes—
266C2×D236C2418yes—
267C2×D236C2414yes—
268C2×C4×D59—28no—
269C2×C4×D59—216no—
270C2×C4×D59—24no—
271C2×C4×D59—28no—
272C2×C4×D59—28no—
273C2×C4×D59—24no—
274C2×C4×D59—48no—
275C2×C4×D59—48no—
276C2×C4×D59—42no—
277C2×C4×D59—44no—
278C2×C4×D59C2418yes—
279C2×C4×D59C2418yes—
280C2×C4×D59C2414yes—
281C2×C4×D59C2414yes—
282C2×C4×D59C24116yes—
283C2×C4×D59C2418yes—
284C2×C4×D59C2418yes—
285C2×C4×D59C2414yes—
286C2×C4×D59C24116yes—
287C2×C4×D59C24116yes—
288C2×Dic118—44no—
289C2×Dic118C2418yes—
290C4⋊C4×C59C2414yes—
291C4⋊C4×C59C2414yes—
292C4⋊C4×C59C24116yes—
293C4⋊C4×C59C2418yes—
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)⋊C4C2418yes—
304(C2×D59)⋊C4C2418yes—
305(C2×D59)⋊C4C2418yes—
306(C2×D59)⋊C4C24116yes—
307(C2×D59)⋊C4C2418yes—
308(C2×D59)⋊C4C24116yes—
309(C2×D59)⋊C4C2418yes—
310(C2×D59)⋊C4C2418yes—
311(C2×D59)⋊C4C24116yes—
312(C2×D59)⋊C4C24116yes—
313(C2×D59)⋊C4C2418yes—
314(C2×D59)⋊C4C2418yes—
315C4⋊Dic59C2414yes—
316C4⋊Dic59C2418yes—
317C4⋊Dic59C2418yes—
318C4⋊Dic59C2418yes—
319C4⋊Dic59C24116yes—
320C4⋊Dic59C2414yes—
321C4⋊Dic59C2418yes—
322Dic59⋊C4C24116yes—
323Dic59⋊C4C2418yes—
324Dic59⋊C4C24116yes—
325Dic59⋊C4C24116yes—
326Dic59⋊C4C24116yes—
327Dic59⋊C4C24116yes—
328Dic59⋊C4C2418yes—
329Dic59⋊C4C24116yes—
330C4×Dic59C2414yes—
331C4×Dic59C2418yes—
332C4×Dic59C2414yes—
333C4×Dic59C2414yes—
334C4×Dic59C2418yes—
335C4×Dic59C24116yes—
336C23×C59C2511yescharacteristic
337C22×D59—24no—
338C22×D59—24no—
339C22×D59—22no—
340C22×D59—24no—
341C22×D59—22no—
342C22×D59—24no—
343C22×D59—24no—
344C22×D59—22no—
345C22×D59C2×#4118yes—
346C22×D59C2512yes—
347C22×D59C2514yes—
348C22×D59C2514yes—
349Q8×C59—28no—
350Q8×C59—216no—
351Q8×C59—28no—
352C2×C4×C59—24no—
353C2×C4×C59—28no—
354C2×C4×C59—24no—
355C2×C4×C59—22no—
356C2×C4×C59—24no—
357C2×C4×C59—24no—
358C2×C4×C59C2×#4114yes—
359C2×C4×C592−1+414yes—
360C2×C4×C59C2514yes—
361C2×C4×C59C2518yes—
362C2×C4×C59C2514yes—
363C2×C4×C59C2512yes—
364C2×C4×C59C2514yes—
365C2×C4×C59C2514yes—
366C2×C4×C59C2512yes—
367C2×C4×C59C2512yes—
368C2×Dic59—22no—
369C2×Dic59—24no—
370C2×Dic59—22no—
371C2×Dic59—24no—
372C2×Dic59—28no—
373C2×Dic59—22no—
374C2×Dic59C2512yes—
375C2×Dic59C2512yes—
376C2×Dic59C2512yes—
377C2×Dic59C2514yes—
378C2×Dic59C2518yes—
379C2×Dic59C2514yes—
380D236—216no—
381D236—232no—
382D236—28no—
383D236—48no—
384D236C2×#41116yes—
385C4×D59—216no—
386C4×D59—232no—
387C4×D59—28no—
388C4×D59—216no—
389C4×D59—216no—
390C4×D59—28no—
391C4×D59—416no—
392C4×D59—416no—
393C4×D59—44no—
394C4×D59—48no—
395Dic118—48no—
396C2×#3515—591nomaximal, Sylow
397C22×C59C22×#4112yes—
398C22×C59C2×2−1+412yes—
399C22×C59#58512yes—
400C22×C59C2611yescharacteristic
401C2×D59—24no—
402C2×D59—24no—
403C2×D59—216no—
404C2×D59—22no—
405C2×D59—24no—
406C2×D59—22no—
407C2×D59—24no—
408C2×D59—24no—
409C2×D59—22no—
410C2×D59—44no—
411C2×D59—48no—
412C2×D59C22×#4118yes—
413C4×C59—24no—
414C4×C59—28no—
415C4×C59—24no—
416C4×C59—22no—
417C4×C59—24no—
418C4×C59—24no—
419C4×C59C22×#4114yes—
420C4×C59C2×2−1+414yes—
421Dic59—22no—
422Dic59—24no—
423Dic59—22no—
424Dic59—24no—
425Dic59—28no—
426Dic59—22no—
427#3515—5932no—
428C2×#557D5911yescharacteristic, complemented
429C2×#554—591no—
430C2×#554—591no—
431C2×#553—592no—
432C2×#552—594no—
433C2×#552—592no—
434C2×#552—592no—
435C2×#547—591no—
436C2×#547—592no—
437C2×#541—592no—
438C2×#539—594no—
439C2×#533—591no—
440C2×#529—591no—
441C2×#529—592no—
442C22×#125—592no—
443C2×#520—592no—
444C2×C4×#41—591no—
445C2×C59#351514yescomplemented
446C2×C59C23×#4111yescharacteristic
447C2×C59C22×2−1+411yescharacteristic
448C2×C59C2×#58511yescharacteristic
449D59—28no—
450D59—42no—
451D59—44no—
452C22×#41—591no—
453C22×#41—592no—
454#557C2×D59116yescomplemented
455#554—5916no—
456#554—5916no—
457#553—5932no—
458#552—5964no—
459#552—5932no—
460#552—5932no—
461#547—5916no—
462#547—5932no—
463#541—5932no—
464#539—5964no—
465#533—5916no—
466C2×C4⋊Q8—591no—
467C2×C4⋊Q8C2×D5911yescharacteristic
468C2×C4⋊Q8C2×D5912yes—
469#529—5932no—
470#529—5916no—
471C2×#126—594no—
472C2×#126—592no—
473C2×#126—594no—
474C2×#126—594no—
475C2×#125—5932no—
476C2×#125—594no—
477C2×#125—594no—
478C2×#125—594no—
479C2×#125—591no—
480C2×#125—592no—
481C2×#125—592no—
482C2×#125—592no—
483C2×#125C2×D5912yes—
484C2×#125C2×D5914yes—
485C2×#124—591no—
486C2×#123—592no—
487C2×#123—594no—
488C2×#123—594no—
489C2×#123—594no—
490C2×#123—594no—
491C2×C22⋊Q8—591no—
492C2×C22⋊Q8—592no—
493C2×C22⋊Q8—592no—
494C2×C22⋊Q8—592no—
495C2×C22⋊Q8—592no—
496C2×C22⋊Q8—594no—
497C2×C22⋊Q8—594no—
498C2×C22⋊Q8—592no—
499C2×#121—592no—
500C2×#121—591no—
501C2×#121—594no—
502#520—5932no—
503C4×#41—5916no—
504C2×C4×Q8—591no—
505C2×C4×Q8—592no—
506C2×C4×Q8—592no—
507C2×C4×Q8C2×D5911yescharacteristic
508C2×C4×Q8C2×D5912yes—
509C2×C4×Q8C2×D5912yes—
510C2×C4×Q8C2×D5911yescharacteristic
511C2×C4×D4—591no—
512C2×C4×D4—592no—
513C2×C4×D4—594no—
514C2×C4×D4—591no—
515C2×C4×D4—592no—
516C2×C4×D4—594no—
517C2×C4×D4—592no—
518C2×C4×D4—592no—
519C2×C4×D4—591no—
520C2×C4×D4—592no—
521C2×#117—591no—
522C2×#117—592no—
523C2×#117—592no—
524C2×#117—592no—
525C2×#117—594no—
526C2×#117—594no—
527C22×C4⋊C4—594no—
528C22×C4⋊C4—592no—
529C22×C4⋊C4—592no—
530C22×C4⋊C4—594no—
531C22×C4⋊C4—592no—
532C22×C42—592no—
533C22×C42—591no—
534C59C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—598no—
536C2×#41—5916no—
537C2×#41—1188no—
538C2×#41—11816no—
539C22×Q8—592no—
540C22×Q8C22×D5911yescharacteristic
541C22×Q8C22×D5912yes—
542C22×Q8C22×D5911yescharacteristic
543C22×D4—591no—
544C22×D4—591no—
545C22×D4—592no—
546C22×D4—594no—
547C22×D4—592no—
548C23×C4—594no—
549C23×C4—592no—
550C23×C4—592no—
551C23×C4—592no—
552C23×C4—591no—
553C23×C4—591no—
554C23×C4—594no—
555C23×C4—592no—
556C23×C4—594no—
557C23×C4—591no—
558C4⋊Q8—598no—
559C4⋊Q8C22×D5918yes—
560C4⋊Q8C22×D59116yes—
561#126—5932no—
562#126—5916no—
563#126—5932no—
564#126—5932no—
565#125—598no—
566#125—5916no—
567#125—5932no—
568#125—5932no—
569#125—5932no—
570#125—5916no—
571#125—5916no—
572#125C22×D59116yes—
573#125C22×D59132yes—
574#124—598no—
575#123—5916no—
576#123—5932no—
577#123—5932no—
578#123—5932no—
579#123—5932no—
580C22⋊Q8—598no—
581C22⋊Q8—5916no—
582C22⋊Q8—5916no—
583C22⋊Q8—5916no—
584C22⋊Q8—5916no—
585C22⋊Q8—5916no—
586C22⋊Q8—5932no—
587C22⋊Q8—5932no—
588#121—5916no—
589#121—598no—
590#121—5932no—
591C4×Q8—598no—
592C4×Q8—5916no—
593C4×Q8—5916no—
594C4×Q8C22×D5918yes—
595C4×Q8C22×D59116yes—
596C4×Q8C22×D59116yes—
597C4×Q8C22×D5918yes—
598C4×D4—598no—
599C4×D4—5916no—
600C4×D4—5932no—
601C4×D4—598no—
602C4×D4—5916no—
603C4×D4—5932no—
604C4×D4—5916no—
605C4×D4—5916no—
606C4×D4—598no—
607C4×D4—5916no—
608#117—598no—
609#117—5916no—
610#117—5916no—
611#117—5916no—
612#117—5932no—
613#117—5932no—
614C2×C4⋊C4—594no—
615C2×C4⋊C4—592no—
616C2×C4⋊C4—591no—
617C2×C4⋊C4—592no—
618C2×C4⋊C4—592no—
619C2×C4⋊C4—594no—
620C2×C4⋊C4—592no—
621C2×C4⋊C4—594no—
622C2×C4⋊C4—594no—
623C2×C4⋊C4—594no—
624C2×C4⋊C4—594no—
625C2×C4⋊C4—592no—
626C2×C4⋊C4—591no—
627C2×C4⋊C4—592no—
628C2×C4⋊C4—594no—
629C2×C4⋊C4—5932no—
630C2×C4⋊C4—5916no—
631C2×C4⋊C4—5916no—
632C2×C4⋊C4—5932no—
633C2×C4⋊C4—5916no—
634C2×C4⋊C4C22×D5911yescharacteristic
635C2×C4⋊C4C22×D5911yescharacteristic
636C2×C4⋊C4C22×D5912yes—
637C2×C4⋊C4C22×D5914yes—
638C2×C4⋊C4C22×D5914yes—
639C2×C4⋊C4C22×D5912yes—
640C2×C4⋊C4C22×D5912yes—
641C2×C4⋊C4C22×D5912yes—
642C2×C4⋊C4C22×D5914yes—
643C2×C22⋊C4—592no—
644C2×C22⋊C4—592no—
645C2×C22⋊C4—592no—
646C2×C22⋊C4—592no—
647C2×C22⋊C4—594no—
648C2×C22⋊C4—592no—
649C2×C22⋊C4—592no—
650C2×C22⋊C4—594no—
651C2×C22⋊C4—594no—
652C2×C22⋊C4—594no—
653C2×C22⋊C4—592no—
654C2×C22⋊C4—592no—
655C2×C42—592no—
656C2×C42—591no—
657C2×C42—594no—
658C2×C42—591no—
659C2×C42—592no—
660C2×C42—591no—
661C2×C42—5916no—
662C2×C42—598no—
663C2×C42C22×D5914yes—
664C2×C42C22×D5912yes—
665C2×C42C22×D5912yes—
666C2×C42C22×D5911yescharacteristic
667C24—592no—
668C24—591no—
669C24—592no—
670#41—11832no—
671#41—11864no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—24no—
675C2×Q8—598no—
676C2×Q8—2364no—
677C2×Q8C23×D5914yes—
678C2×Q8C23×D5918yes—
679C2×Q8C23×D5914yes—
680C2×D4—598no—
681C2×D4—594no—
682C2×D4—594no—
683C2×D4—598no—
684C2×D4—5916no—
685C2×D4—598no—
686C2×D4—1188no—
687C2×D4—11816no—
688C2×D4—1184no—
689C2×D4—2364no—
690C22×C4—591no—
691C22×C4—591no—
692C22×C4—591no—
693C22×C4—592no—
694C22×C4—594no—
695C22×C4—592no—
696C22×C4—598no—
697C22×C4—598no—
698C22×C4—594no—
699C22×C4—594no—
700C22×C4—5916no—
701C22×C4—598no—
702C22×C4—598no—
703C22×C4—594no—
704C22×C4—5916no—
705C22×C4—5916no—
706C22×C4—11816no—
707C22×C4—1188no—
708C22×C4—1188no—
709C22×C4—1184no—
710C22×C4—1188no—
711C22×C4—1184no—
712C22×C4—2364no—
713C22×C4—2368no—
714C22×C4—2368no—
715C22×C4—2362no—
716C22×C4C23×D5912yes—
717C22×C4C23×D5911yescharacteristic
718C22×C4C23×D5914yes—
719C22×C4C23×D5912yes—
720C22×C4C23×D5912yes—
721C22×C4C23×D5912yes—
722C22×C4C23×D5911yescharacteristic
723C22×C4C23×D5911yescharacteristic
724C4⋊C4—5916no—
725C4⋊C4—598no—
726C4⋊C4—594no—
727C4⋊C4—598no—
728C4⋊C4—598no—
729C4⋊C4—5916no—
730C4⋊C4—598no—
731C4⋊C4—5916no—
732C4⋊C4—5916no—
733C4⋊C4—5916no—
734C4⋊C4—5916no—
735C4⋊C4—598no—
736C4⋊C4—594no—
737C4⋊C4—598no—
738C4⋊C4—5916no—
739C4⋊C4C23×D5914yes—
740C4⋊C4C23×D5914yes—
741C4⋊C4C23×D5918yes—
742C4⋊C4C23×D59116yes—
743C4⋊C4C23×D59116yes—
744C4⋊C4C23×D5918yes—
745C4⋊C4C23×D5918yes—
746C4⋊C4C23×D5918yes—
747C4⋊C4C23×D59116yes—
748C22⋊C4—598no—
749C22⋊C4—598no—
750C22⋊C4—598no—
751C22⋊C4—598no—
752C22⋊C4—5916no—
753C22⋊C4—598no—
754C22⋊C4—598no—
755C22⋊C4—5916no—
756C22⋊C4—5916no—
757C22⋊C4—5916no—
758C22⋊C4—598no—
759C22⋊C4—598no—
760C42—594no—
761C42—598no—
762C42—594no—
763C42—594no—
764C42—598no—
765C42—5916no—
766C42C23×D5918yes—
767C42C23×D5914yes—
768C42C23×D59116yes—
769C42C23×D5918yes—
770C23—598no—
771C23—594no—
772C23—592no—
773C23—594no—
774C23—1184no—
775C23—1184no—
776C23—1182no—
777C23—1184no—
778C23—1182no—
779C23—1184no—
780C23—1184no—
781C23—1182no—
782C23C24×D5911yescharacteristic
783Q8—28no—
784Q8—216no—
785Q8—28no—
786Q8—2368no—
787D4—5916no—
788D4—11816no—
789D4—11832no—
790D4—1188no—
791D4—2368no—
792C2×C4—28no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—592no—
799C2×C4—592no—
800C2×C4—592no—
801C2×C4—594no—
802C2×C4—598no—
803C2×C4—594no—
804C2×C4—11816no—
805C2×C4—11832no—
806C2×C4—1182no—
807C2×C4—1184no—
808C2×C4—1182no—
809C2×C4—1184no—
810C2×C4—1182no—
811C2×C4—1188no—
812C2×C4—1188no—
813C2×C4—11816no—
814C2×C4—11816no—
815C2×C4—1188no—
816C2×C4—2368no—
817C2×C4—23616no—
818C2×C4—23616no—
819C2×C4—2364no—
820C2×C4#41×D5914yes—
821C2×C4#1427377514yes—
822C2×C4C24×D5914yes—
823C2×C4C24×D5912yes—
824C2×C4C24×D5914yes—
825C2×C4C24×D5918yes—
826C2×C4C24×D5914yes—
827C2×C4C24×D5914yes—
828C2×C4C24×D5912yes—
829C2×C4C24×D5912yes—
830C22—598no—
831C22—11816no—
832C22—1184no—
833C22—1184no—
834C22—1182no—
835C22—1184no—
836C22—1182no—
837C22—1184no—
838C22—1184no—
839C22—1182no—
840C22—2364no—
841C22—2368no—
842C22C2×#41×D5912yes—
843C22C2×#1427377512yes—
844C22#1683823912yes—
845C22C25×D5911yescharacteristic
846C4—24no—
847C4—28no—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—22no—
852C4—1182no—
853C4—1184no—
854C4—1182no—
855C4—1184no—
856C4—1182no—
857C4—1188no—
858C4C2×#41×D5914yes—
859C4C2×#1427377514yes—
860C2—1188no—
861C2—2362no—
862C2—2364no—
863C2#2143807314yesdirect product factor
864C2C22×#41×D5911yescharacteristic
865C2C22×#1427377511yescharacteristic
866C2C2×#1683823911yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#557C2
socleC23×C59C25
hypercenterC2×#557D59
hypocenterC59C2×#3515
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #21438073C2direct (N × H)
2. C2×#16838112C2semidirect
3. C2×#16838112C2semidirect
4. C2×#16838105C2semidirect
5. C2×#16838093C2semidirect
6. C2×#16838093C2semidirect
7. C2×#16838084C2semidirect
8. C2×#16838055C2semidirect
9. C2×#16838055C2semidirect
10. C2×#16838013C2semidirect
11. C2×#16838000C2semidirect
12. C2×#16837957C2semidirect
13. C2×#16837939C2semidirect
14. C2×#16837939C2semidirect
15. C2×#125×D59C2semidirect
16. C2×#16837884C2semidirect
17. C2×C4×#11745689C2semidirect
18. C2×C59×#557C2semidirect
21. #16838112C22semidirect
22. #16838112C22semidirect
23. #16838105C22semidirect
24. #16838093C22semidirect
25. #16838093C22semidirect
26. #16838084C22semidirect
27. #16838055C22semidirect
28. #16838055C22semidirect
29. #16838013C22semidirect
30. #16838000C22semidirect
31. #16837957C22semidirect
33. #16837939C22semidirect
34. #16837939C22semidirect
46. #125×D59C22semidirect
64. #16837884C22semidirect
65. C4×#11745689C22semidirect
92. C59×#557C22semidirect
428. C2×#557D59semidirect
445. C2×C59#3515semidirect
454. #557C2×D59semidirect
534. C59C2×#3515semidirect
863. C2#21438073direct (N × H)

Maximal subgroups

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

subgroupindex
#214380732
C2×#168381122
C2×#168381052
C2×#168380932
C2×#168380842
C2×#168380552
C2×#168380132
C2×#168380002
C2×#168379572
C2×#168379392
C2×#125×D592
C2×#168378842
C2×C4×#117456892
C2×C59×#5572
C2×#351559