Finite Group Databasebeta

← C2×#21438019 #29497191

Subgroups — C2×#21438019 #29497191

Order 15104.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438019C2132yesmaximal, direct product factor
2C2×#16838105C214yesmaximal, complemented
3C2×#16838103C214yesmaximal, complemented
4C2×#16838103C214yesmaximal, complemented
5C2×#16838084C214yesmaximal, complemented
6C2×#16838013C211yesmaximal, characteristic, complemented
7C2×#16838008C211yesmaximal, characteristic, complemented
8C2×#16838007C211yesmaximal, characteristic, complemented
9C2×#16837982C212yesmaximal, complemented
10C2×#16837953C211yesmaximal, characteristic, complemented
11C2×#16837939C212yesmaximal, complemented
12C2×#16837938C212yesmaximal, complemented
13C2×#125×D59C211yesmaximal, characteristic, complemented
14C2×#16837884C212yesmaximal, complemented
15C2×#16837870C211yesmaximal, characteristic, complemented
16C2×C59×#541C211yesmaximal, characteristic, complemented
17C22×#11745689C2212yes—
18C22×#11745685C2211yescharacteristic
19#16838105C22164yescomplemented
20#16838103C22164yescomplemented
21#16838103C22164yescomplemented
22#16838084C22164yescomplemented
23#16838013C22116yescomplemented
24#16838008C22116yescomplemented
25#16838007C22116yescomplemented
26#16837982C22132yescomplemented
27#16837953C22116yescomplemented
28C2×#14273724C2211yescharacteristic
29#16837939C22132yescomplemented
30#16837938C22132yescomplemented
31C2×#14273722C2214yes—
32C2×#14273722C2214yes—
33C2×#14273722C2214yes—
34C2×#14273719C2211yescharacteristic
35C2×#14273718C2212yes—
36C2×#14273717C2214yes—
37C2×#14273717C2214yes—
38#125×D59C22116yescomplemented
39C2×#14273716C2212yes—
40C2×#14273712C2214yes—
41C2×#14273712C2214yes—
42C2×#14273712C2214yes—
43C2×#14273711C2214yes—
44C2×#14273705C2214yes—
45C2×#14273703C2212yes—
46C2×#14273702C2214yes—
47C2×#14273702C2212yes—
48C2×#14273702C2214yes—
49C2×#14273702C2214yes—
50C2×#14273701C2212yes—
51C2×#14273700C2214yes—
52C2×#14273700C2214yes—
53C2×#14273700C2214yes—
54#16837884C22132yescomplemented
55#16837870C22116yescomplemented
56C2×Q8×Dic59C2212yes—
57C2×#14273692C2212yes—
58C2×C4×D236C2212yes—
59C2×C4×D236C2214yes—
60C2×C4×D236C2214yes—
61C2×#14273689C2212yes—
62C2×#14273689C2212yes—
63C2×#14273689C2214yes—
64C2×#14273689C2214yes—
65C2×(C22⋊D59)⋊C4C2212yes—
66C2×(C22⋊D59)⋊C4C2212yes—
67C2×(C22⋊D59)⋊C4C2214yes—
68C2×#14273685C2214yes—
69C2×#14273684C2211yescharacteristic
70C2×#14273684C2211yescharacteristic
71C2×#14273684C2214yes—
72C2×#14273684C2214yes—
73C2×C4⋊C4×D59C2214yes—
74C2×C4⋊C4×D59C2212yes—
75C2×C4⋊C4×D59C2214yes—
76C22×C4×Dic59C2211yescharacteristic
77C2×C42×D59C2211yescharacteristic
78C2×C42×D59C2211yescharacteristic
79C59×#541C22116yescomplemented
80C2×C4⋊Q8×C59C2211yescharacteristic
81C2×#126×C59C2214yes—
82C2×#125×C59C2211yescharacteristic
83C2×#125×C59C2214yes—
84C2×C22⋊Q8×C59C2212yes—
85C2×C4×Q8×C59C2212yes—
86C2×#117×C59C2211yescharacteristic
87C2×#11745689—216no—
88C2×#11745689C23116yes—
89C2×#11745685—28no—
90C2×#11745685C2318yes—
91C22×Dic118C2311yescharacteristic
92C22×D236C2314yes—
93C22×D236C2312yes—
94C22×D236C2311yescharacteristic
95C22×D236C2314yes—
96C22×D236C2314yes—
97C22×C22⋊D59C2311yescharacteristic
98C22×C22⋊D59C2311yescharacteristic
99C22×C22⋊D59C2314yes—
100C23×Dic59C2312yes—
101C22×C4×D59C2314yes—
102C22×C4×D59C2311yescharacteristic
103C22×C4×D59C2314yes—
104C22×C4×D59C2314yes—
105C22×C4×D59C2312yes—
106C22×C4×D59C2314yes—
107C22×C4×D59C2312yes—
108C22×C4×D59C2311yescharacteristic
109#14273724C2318yes—
110#14273722C23132yes—
111#14273722C23132yes—
112#14273722C23132yes—
113#14273719C2318yes—
114#14273718C23116yes—
115#14273717C23132yes—
116#14273717C23132yes—
117#14273716C23116yes—
118#14273712C23132yes—
119#14273712C23132yes—
120#14273712C23132yes—
121#14273711C23132yes—
122#14273705C23132yes—
123#14273703C23116yes—
124#14273702C23116yes—
125#14273702C23132yes—
126#14273702C23132yes—
127#14273702C23132yes—
128#14273701C23116yes—
129#14273700C23132yes—
130#14273700C23132yes—
131#14273700C23132yes—
132Q8×Dic59C23116yes—
133#14273692C23116yes—
134C4×D236C23116yes—
135C4×D236C23132yes—
136C4×D236C23132yes—
137#14273689C23116yes—
138#14273689C23132yes—
139#14273689C23132yes—
140#14273689C23116yes—
141(C22⋊D59)⋊C4C23132yes—
142(C22⋊D59)⋊C4C23116yes—
143(C22⋊D59)⋊C4C23116yes—
144#14273685C23132yes—
145#14273684C23132yes—
146#14273684C2318yes—
147#14273684C23132yes—
148#14273684C2318yes—
149C2×C4⋊Dic59C2312yes—
150C2×C4⋊Dic59C2314yes—
151C2×C4⋊Dic59C2314yes—
152C2×Dic59⋊C4C2314yes—
153C2×Dic59⋊C4C2314yes—
154C2×Dic59⋊C4C2314yes—
155C2×Dic59⋊C4C2312yes—
156C2×Dic59⋊C4C2314yes—
157C2×Dic59⋊C4C2312yes—
158C4⋊C4×D59C23116yes—
159C4⋊C4×D59C23132yes—
160C4⋊C4×D59C23132yes—
161C2×(C2×D59)⋊C4C2314yes—
162C2×(C2×D59)⋊C4C2314yes—
163C2×(C2×D59)⋊C4C2314yes—
164C2×(C2×D59)⋊C4C2314yes—
165C2×(C2×D59)⋊C4C2312yes—
166C2×(C2×D59)⋊C4C2314yes—
167C2×(C2×D59)⋊C4C2314yes—
168C2×(C2×D59)⋊C4C2314yes—
169C2×(C2×D59)⋊C4C2312yes—
170C2×C4×Dic59C2311yescharacteristic
171C2×C4×Dic59C2312yes—
172C2×C4×Dic59C2314yes—
173C2×C4×Dic59C2312yes—
174C2×C4×Dic59C2312yes—
175C2×C4×Dic59C2318yes—
176C2×C4×Dic59C2311yescharacteristic
177C42×D59C2318yes—
178C42×D59C2318yes—
179C22×Q8×C59C2312yes—
180C23×C4×C59C2311yescharacteristic
181C4⋊Q8×C59C2318yes—
182#126×C59C23132yes—
183#125×C59C2318yes—
184#125×C59C23132yes—
185C22⋊Q8×C59C23116yes—
186C4×Q8×C59C23116yes—
187#117×C59C2318yes—
188C2×C4⋊C4×C59C2314yes—
189C2×C4⋊C4×C59C2314yes—
190C2×C4⋊C4×C59C2314yes—
191C2×C4⋊C4×C59C2312yes—
192C2×C4⋊C4×C59C2312yes—
193C2×C4⋊C4×C59C2314yes—
194C2×C22⋊C4×C59C2314yes—
195C2×C22⋊C4×C59C2312yes—
196C2×C42×C59C2311yescharacteristic
197C2×C42×C59C2311yescharacteristic
198C2×C42×C59C2314yes—
199C24×C59C2411yescharacteristic
200C23×D59C2414yes—
201C23×D59C2411yescharacteristic
202C23×D59C2411yescharacteristic
203C2×Q8×C59—28no—
204C2×Q8×C59C2418yes—
205C22×C4×C59—24no—
206C22×C4×C59C2412yes—
207C22×C4×C59C2412yes—
208C22×C4×C59C2414yes—
209C22×C4×C59C2414yes—
210C22×C4×C59C2411yescharacteristic
211C22×C4×C59C2414yes—
212C22×C4×C59C2411yescharacteristic
213C2×C22⋊D59—24no—
214C2×C22⋊D59—24no—
215C2×C22⋊D59—48no—
216C2×C22⋊D59C2414yes—
217C2×C22⋊D59C2414yes—
218C2×C22⋊D59C24116yes—
219C22×Dic59—44no—
220C22×Dic59C2412yes—
221C22×Dic59C2412yes—
222C22×Dic59C2411yescharacteristic
223C22×Dic59C2414yes—
224C22×Dic59C2418yes—
225C22×Dic59C2411yescharacteristic
226#11745689—264no—
227#11745685—232no—
228C2×D236—24no—
229C2×D236—216no—
230C2×D236—28no—
231C2×D236—48no—
232C2×D236—48no—
233C2×D236C2414yes—
234C2×D236C24116yes—
235C2×D236C2418yes—
236C2×D236C24116yes—
237C2×D236C24116yes—
238C2×C4×D59—24no—
239C2×C4×D59—216no—
240C2×C4×D59—44no—
241C2×C4×D59—48no—
242C2×C4×D59—44no—
243C2×C4×D59—48no—
244C2×C4×D59—48no—
245C2×C4×D59#4118yes—
246C2×C4×D59C2414yes—
247C2×C4×D59C24116yes—
248C2×C4×D59C2418yes—
249C2×C4×D59C2418yes—
250C2×C4×D59C24116yes—
251C2×C4×D59C24116yes—
252C2×C4×D59C24116yes—
253C2×C4×D59C2414yes—
254C2×Dic118—24no—
255C2×Dic118C2414yes—
256C4⋊C4×C59C2418yes—
257C4⋊C4×C59C2418yes—
258C4⋊C4×C59C24116yes—
259C4⋊C4×C59C24116yes—
260C4⋊C4×C59C24116yes—
261C4⋊C4×C59C24116yes—
262C22⋊C4×C59C2418yes—
263C22⋊C4×C59C24116yes—
264C42×C59C2414yes—
265C42×C59C2414yes—
266C42×C59C24116yes—
267(C2×D59)⋊C4C24116yes—
268(C2×D59)⋊C4C2418yes—
269(C2×D59)⋊C4C2418yes—
270(C2×D59)⋊C4C24116yes—
271(C2×D59)⋊C4C24116yes—
272(C2×D59)⋊C4C24116yes—
273(C2×D59)⋊C4C24116yes—
274(C2×D59)⋊C4C24116yes—
275(C2×D59)⋊C4C24116yes—
276C4⋊Dic59C24116yes—
277C4⋊Dic59C2418yes—
278C4⋊Dic59C24116yes—
279Dic59⋊C4C2418yes—
280Dic59⋊C4C24116yes—
281Dic59⋊C4C24116yes—
282Dic59⋊C4C24116yes—
283Dic59⋊C4C2418yes—
284Dic59⋊C4C24116yes—
285C4×Dic59C2414yes—
286C4×Dic59C2418yes—
287C4×Dic59C2418yes—
288C4×Dic59C2414yes—
289C4×Dic59C2418yes—
290C4×Dic59C24116yes—
291C23×C59—22no—
292C23×C59—24no—
293C23×C59C2512yes—
294C23×C59C2511yescharacteristic
295C22×D59—24no—
296C22×D59—28no—
297C22×D59—22no—
298C22×D59—28no—
299C22×D59—24no—
300C22×D59—28no—
301C22×D59C2×#4114yes—
302C22×D59C2518yes—
303C22×D59C2512yes—
304C22×D59C2512yes—
305Q8×C59—216no—
306C2×C4×C59—22no—
307C2×C4×C59—28no—
308C2×C4×C59—24no—
309C2×C4×C59—28no—
310C2×C4×C59—24no—
311C2×C4×C59—28no—
312C2×C4×C59C2×#4114yes—
313C2×C4×C59C2512yes—
314C2×C4×C59C2514yes—
315C2×C4×C59C2518yes—
316C2×C4×C59C2514yes—
317C2×C4×C59C2518yes—
318C2×C4×C59C2512yes—
319C22⋊D59—28no—
320C22⋊D59—28no—
321C22⋊D59—416no—
322C2×Dic59—22no—
323C2×Dic59—24no—
324C2×Dic59—24no—
325C2×Dic59—28no—
326C2×Dic59—48no—
327C2×Dic59C2×#4114yes—
328C2×Dic59C2514yes—
329C2×Dic59C2514yes—
330C2×Dic59C2512yes—
331C2×Dic59C2518yes—
332C2×Dic59C2512yes—
333D236—28no—
334D236—232no—
335D236—216no—
336D236—416no—
337D236—416no—
338C4×D59—28no—
339C4×D59—232no—
340C4×D59—48no—
341C4×D59—416no—
342C4×D59—48no—
343C4×D59—416no—
344C4×D59—416no—
345C4×D59C2×#41116yes—
346Dic118—28no—
347C2×#3512—591nomaximal, Sylow
348C22×C59—22no—
349C22×C59—24no—
350C22×C59—44no—
351C22×C59C22×#4112yes—
352C22×C59#58514yes—
353C22×C59C2611yescharacteristic
354C2×D59—24no—
355C2×D59—28no—
356C2×D59—28no—
357C2×D59—22no—
358C2×D59—28no—
359C2×D59—24no—
360C2×D59—28no—
361C2×D59—416no—
362C2×D59—44no—
363C2×D59C22×#4114yes—
364C4×C59—22no—
365C4×C59—28no—
366C4×C59—24no—
367C4×C59—28no—
368C4×C59—24no—
369C4×C59C22×#4114yes—
370Dic59—22no—
371Dic59—24no—
372Dic59—24no—
373Dic59—28no—
374Dic59C22×#4114yes—
375#3512—5932no—
376C2×#553—594no—
377C2×#553—594no—
378C2×#553—594no—
379C2×#552—594no—
380C2×#541—591no—
381C2×#541D5911yescharacteristic, complemented
382C2×#540—591no—
383C2×#540—591no—
384C2×#537—592no—
385C2×#532—591no—
386C2×#529—592no—
387C2×#529—592no—
388C22×#125—591no—
389C2×#520—592no—
390C2×C4×#41—591no—
391C2×C59—42no—
392C2×C59#351214yescomplemented
393C2×C59C23×#4111yescharacteristic
394C2×C59C2×#58512yes—
395D59—24no—
396D59—48no—
397D59—42no—
398C22×#41—592no—
399C22×#41—591no—
400#553—5964no—
401#553—5964no—
402#553—5964no—
403#552—5964no—
404#541—5916no—
405#541C2×D59116yescomplemented
406#540—5916no—
407#540—5916no—
408#537—5932no—
409#532—5916no—
410C2×C4⋊Q8C2×D5911yescharacteristic
411C2×#127—591no—
412#529—5932no—
413#529—5932no—
414C2×#126—594no—
415C2×#126—594no—
416C2×#126—594no—
417C2×#126C2×D5914yes—
418C2×#125—5916no—
419C2×#125—594no—
420C2×#125—594no—
421C2×#125—592no—
422C2×#125—591no—
423C2×#125C2×D5911yescharacteristic
424C2×#125C2×D5914yes—
425C2×#124—592no—
426C2×#123—594no—
427C2×#123—594no—
428C2×#123—594no—
429C2×#123—594no—
430C2×C22⋊Q8—592no—
431C2×C22⋊Q8—594no—
432C2×C22⋊Q8C2×D5912yes—
433C2×#121—592no—
434C2×#121—592no—
435C2×#121—594no—
436C2×#121—594no—
437C2×#121—594no—
438C2×#121—594no—
439C2×#121—594no—
440C2×#121—594no—
441#520—5932no—
442C4×#41—5916no—
443C2×C4×Q8—592no—
444C2×C4×Q8—592no—
445C2×C4×Q8C2×D5912yes—
446C2×C4×D4—592no—
447C2×C4×D4—592no—
448C2×C4×D4—594no—
449C2×C4×D4—594no—
450C2×C4×D4—592no—
451C2×C4×D4—592no—
452C2×C4×D4—594no—
453C2×C4×D4—592no—
454C2×C4×D4—594no—
455C2×C4×D4—594no—
456C2×#117—594no—
457C2×#117—591no—
458C2×#117—591no—
459C2×#117—594no—
460C2×#117—594no—
461C2×#117C2×D5911yescharacteristic
462C22×C4⋊C4—592no—
463C22×C4⋊C4—594no—
464C22×C4⋊C4—594no—
465C22×C42—591no—
466C22×C42—591no—
467C22×C42—591no—
468C59C2×#351211yescharacteristic, complemented, Sylow
469C2×#41—5916no—
470C2×#41—598no—
471C2×#41—1188no—
472C2×#41—11816no—
473C22×Q8—591no—
474C22×Q8C22×D5912yes—
475C22×D4—591no—
476C22×D4—591no—
477C22×D4—594no—
478C22×D4—591no—
479C22×D4—594no—
480C22×D4—592no—
481C22×D4—594no—
482C22×D4—594no—
483C23×C4—591no—
484C23×C4—592no—
485C23×C4—594no—
486C23×C4—591no—
487C23×C4—594no—
488C23×C4—592no—
489C23×C4—594no—
490C23×C4—594no—
491C23×C4—592no—
492C23×C4C22×D5911yescharacteristic
493C4⋊Q8C22×D5918yes—
494#127—598no—
495#126—5932no—
496#126—5932no—
497#126—5932no—
498#126C22×D59132yes—
499#125—5916no—
500#125—5932no—
501#125—5932no—
502#125—598no—
503#125C22×D5918yes—
504#125C22×D59132yes—
505#124—5916no—
506#123—5932no—
507#123—5932no—
508#123—5932no—
509#123—5932no—
510C22⋊Q8—5916no—
511C22⋊Q8—5932no—
512C22⋊Q8C22×D59116yes—
513#121—5916no—
514#121—5916no—
515#121—5932no—
516#121—5932no—
517#121—5932no—
518#121—5932no—
519#121—5932no—
520#121—5932no—
521C4×Q8—5916no—
522C4×Q8—5916no—
523C4×Q8C22×D59116yes—
524C4×D4—5916no—
525C4×D4—5916no—
526C4×D4—5932no—
527C4×D4—5932no—
528C4×D4—5916no—
529C4×D4—5916no—
530C4×D4—5932no—
531C4×D4—5916no—
532C4×D4—5932no—
533C4×D4—5932no—
534#117—5932no—
535#117—598no—
536#117—598no—
537#117—5932no—
538#117—5932no—
539#117C22×D5918yes—
540C2×C4⋊C4—592no—
541C2×C4⋊C4—594no—
542C2×C4⋊C4—594no—
543C2×C4⋊C4—594no—
544C2×C4⋊C4—592no—
545C2×C4⋊C4—594no—
546C2×C4⋊C4—594no—
547C2×C4⋊C4—592no—
548C2×C4⋊C4—594no—
549C2×C4⋊C4—5916no—
550C2×C4⋊C4—5932no—
551C2×C4⋊C4—5932no—
552C2×C4⋊C4C22×D5912yes—
553C2×C4⋊C4C22×D5914yes—
554C2×C4⋊C4C22×D5914yes—
555C2×C4⋊C4C22×D5914yes—
556C2×C4⋊C4C22×D5912yes—
557C2×C4⋊C4C22×D5914yes—
558C2×C22⋊C4—594no—
559C2×C22⋊C4—592no—
560C2×C22⋊C4—592no—
561C2×C22⋊C4—594no—
562C2×C22⋊C4—594no—
563C2×C22⋊C4—594no—
564C2×C22⋊C4—594no—
565C2×C22⋊C4—594no—
566C2×C22⋊C4—594no—
567C2×C22⋊C4C22×D5912yes—
568C2×C22⋊C4C22×D5914yes—
569C2×C42—591no—
570C2×C42—594no—
571C2×C42—592no—
572C2×C42—592no—
573C2×C42—592no—
574C2×C42—598no—
575C2×C42—591no—
576C2×C42—598no—
577C2×C42—598no—
578C2×C42C22×D5914yes—
579C2×C42C22×D5911yescharacteristic
580C2×C42C22×D5911yescharacteristic
581C24—591no—
582C24—594no—
583C24—591no—
584C24C23×D5911yescharacteristic
585#41—11832no—
586#41—11864no—
587C2×Q8—28no—
588C2×Q8—594no—
589C2×Q8—1184no—
590C2×Q8C23×D5918yes—
591C2×D4—594no—
592C2×D4—594no—
593C2×D4—5916no—
594C2×D4—594no—
595C2×D4—5916no—
596C2×D4—598no—
597C2×D4—5916no—
598C2×D4—5916no—
599C2×D4—1184no—
600C2×D4—11816no—
601C2×D4—1184no—
602C2×D4—1184no—
603C2×D4—1188no—
604C2×D4—2368no—
605C2×D4—2368no—
606C2×D4—2368no—
607C22×C4—24no—
608C22×C4—591no—
609C22×C4—598no—
610C22×C4—594no—
611C22×C4—592no—
612C22×C4—592no—
613C22×C4—591no—
614C22×C4—594no—
615C22×C4—598no—
616C22×C4—594no—
617C22×C4—5916no—
618C22×C4—598no—
619C22×C4—598no—
620C22×C4—5916no—
621C22×C4—5916no—
622C22×C4—5916no—
623C22×C4—11816no—
624C22×C4—1184no—
625C22×C4—2364no—
626C22×C4—2368no—
627C22×C4—2368no—
628C22×C4—2368no—
629C22×C4—2364no—
630C22×C4—2364no—
631C22×C4C23×D5914yes—
632C22×C4C23×D5911yescharacteristic
633C22×C4C23×D5912yes—
634C22×C4C23×D5914yes—
635C22×C4C23×D5912yes—
636C22×C4C23×D5914yes—
637C22×C4C23×D5911yescharacteristic
638C4⋊C4—598no—
639C4⋊C4—5916no—
640C4⋊C4—5916no—
641C4⋊C4—5916no—
642C4⋊C4—598no—
643C4⋊C4—5916no—
644C4⋊C4—5916no—
645C4⋊C4—598no—
646C4⋊C4—5916no—
647C4⋊C4C23×D5918yes—
648C4⋊C4C23×D59116yes—
649C4⋊C4C23×D59116yes—
650C4⋊C4C23×D59116yes—
651C4⋊C4C23×D5918yes—
652C4⋊C4C23×D59116yes—
653C22⋊C4—5916no—
654C22⋊C4—598no—
655C22⋊C4—598no—
656C22⋊C4—5916no—
657C22⋊C4—5916no—
658C22⋊C4—5916no—
659C22⋊C4—5916no—
660C22⋊C4—5916no—
661C22⋊C4—5916no—
662C22⋊C4C23×D5918yes—
663C22⋊C4C23×D59116yes—
664C42—594no—
665C42—594no—
666C42—598no—
667C42—598no—
668C42—598no—
669C42—5916no—
670C42C23×D5914yes—
671C42C23×D5914yes—
672C42C23×D59116yes—
673C23—22no—
674C23—24no—
675C23—594no—
676C23—592no—
677C23—598no—
678C23—592no—
679C23—1184no—
680C23—1188no—
681C23—1182no—
682C23—1188no—
683C23—1184no—
684C23—1188no—
685C23C24×D5912yes—
686C23C24×D5911yescharacteristic
687Q8—216no—
688Q8—1188no—
689D4—1188no—
690D4—11832no—
691D4—1188no—
692D4—1188no—
693D4—11816no—
694D4—23616no—
695D4—23616no—
696D4—23616no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—594no—
704C2×C4—592no—
705C2×C4—5916no—
706C2×C4—594no—
707C2×C4—594no—
708C2×C4—592no—
709C2×C4—598no—
710C2×C4—11832no—
711C2×C4—1182no—
712C2×C4—1184no—
713C2×C4—1184no—
714C2×C4—1188no—
715C2×C4—1188no—
716C2×C4—2368no—
717C2×C4—23616no—
718C2×C4—23616no—
719C2×C4—23616no—
720C2×C4—2368no—
721C2×C4—2368no—
722C2×C4#41×D5914yes—
723C2×C4C24×D5912yes—
724C2×C4C24×D5914yes—
725C2×C4C24×D5918yes—
726C2×C4C24×D5914yes—
727C2×C4C24×D5918yes—
728C2×C4C24×D5912yes—
729C22—22no—
730C22—24no—
731C22—44no—
732C22—594no—
733C22—1188no—
734C22—1184no—
735C22—1188no—
736C22—1182no—
737C22—1188no—
738C22—1184no—
739C22—1188no—
740C22—23616no—
741C22—2364no—
742C22C2×#41×D5912yes—
743C22#1683823914yes—
744C22C25×D5911yescharacteristic
745C4—22no—
746C4—28no—
747C4—24no—
748C4—28no—
749C4—24no—
750C4—594no—
751C4—1182no—
752C4—1184no—
753C4—1184no—
754C4—1188no—
755C4C2×#41×D5914yes—
756C2—42no—
757C2—1184no—
758C2—2368no—
759C2—2362no—
760C2#2143801914yesdirect product factor
761C2C22×#41×D5911yescharacteristic
762C2C2×#1683823912yes—
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#541C2
socleC23×C59C25
hypercenterC2×#541D59
hypocenterC59C2×#3512
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #21438019C2direct (N × H)
2. C2×#16838105C2semidirect
3. C2×#16838103C2semidirect
4. C2×#16838103C2semidirect
5. C2×#16838084C2semidirect
6. C2×#16838013C2semidirect
7. C2×#16838008C2semidirect
8. C2×#16838007C2semidirect
9. C2×#16837982C2semidirect
10. C2×#16837953C2semidirect
11. C2×#16837939C2semidirect
12. C2×#16837938C2semidirect
13. C2×#125×D59C2semidirect
14. C2×#16837884C2semidirect
15. C2×#16837870C2semidirect
16. C2×C59×#541C2semidirect
19. #16838105C22semidirect
20. #16838103C22semidirect
21. #16838103C22semidirect
22. #16838084C22semidirect
23. #16838013C22semidirect
24. #16838008C22semidirect
25. #16838007C22semidirect
26. #16837982C22semidirect
27. #16837953C22semidirect
29. #16837939C22semidirect
30. #16837938C22semidirect
38. #125×D59C22semidirect
54. #16837884C22semidirect
55. #16837870C22semidirect
79. C59×#541C22semidirect
381. C2×#541D59semidirect
392. C2×C59#3512semidirect
405. #541C2×D59semidirect
468. C59C2×#3512semidirect
760. C2#21438019direct (N × H)

Maximal subgroups

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

subgroupindex
#214380192
C2×#168381052
C2×#168381032
C2×#168380842
C2×#168380132
C2×#168380082
C2×#168380072
C2×#168379822
C2×#168379532
C2×#168379392
C2×#168379382
C2×#125×D592
C2×#168378842
C2×#168378702
C2×C59×#5412
C2×#351259