Finite Group Databasebeta

← C2×#21459738 #30588517

Subgroups — C2×#21459738 #30588517

Order 15616.

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#21459738C2132yesmaximal, direct product factor
2C2×#16840459C214yesmaximal, complemented
3C2×#16840457C214yesmaximal, complemented
4C2×#16840455C214yesmaximal, complemented
5C2×#16840449C214yesmaximal, complemented
6C2×#16840375C211yesmaximal, characteristic, complemented
7C2×#16840374C211yesmaximal, characteristic, complemented
8C2×#16840366C211yesmaximal, characteristic, complemented
9C2×#16840341C212yesmaximal, complemented
10C2×#16840310C211yesmaximal, characteristic, complemented
11C2×#16840294C212yesmaximal, complemented
12C2×#16840293C212yesmaximal, complemented
13C2×#125×D61C211yesmaximal, characteristic, complemented
14C2×#16840241C212yesmaximal, complemented
15C2×#16840230C211yesmaximal, characteristic, complemented
16C2×C61×#540C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224C2212yes—
19#16840459C22164yescomplemented
20#16840457C22164yescomplemented
21#16840455C22164yescomplemented
22#16840449C22164yescomplemented
23#16840375C22116yescomplemented
24#16840374C22116yescomplemented
25#16840366C22116yescomplemented
26#16840341C22132yescomplemented
27#16840310C22116yescomplemented
28C2×#14519777C2211yescharacteristic
29#16840294C22132yescomplemented
30#16840293C22132yescomplemented
31C2×#14519772C2214yes—
32C2×#14519770C2214yes—
33C2×#14519770C2214yes—
34C2×#14519770C2214yes—
35C2×#14519769C2211yescharacteristic
36C2×#14519768C2212yes—
37C2×#14519768C2214yes—
38C2×#14519767C2214yes—
39C2×#14519767C2214yes—
40#125×D61C22116yescomplemented
41C2×#14519764C2212yes—
42C2×#14519759C2214yes—
43C2×#14519758C2214yes—
44C2×#14519758C2214yes—
45C2×#14519757C2212yes—
46C2×#14519756C2212yes—
47C2×#14519754C2214yes—
48C2×#14519750C2214yes—
49C2×#14519749C2214yes—
50C2×#14519749C2214yes—
51C2×#14519748C2214yes—
52C2×#14519748C2212yes—
53C2×#14519748C2214yes—
54#16840241C22132yescomplemented
55#16840230C22116yescomplemented
56C2×C4×Dic122C2212yes—
57C2×#14519742C2212yes—
58C2×#14519742C2212yes—
59C2×D4×Dic61C2212yes—
60C2×D4×Dic61C2214yes—
61C2×D4×Dic61C2214yes—
62C2×#14519739C2212yes—
63C2×C4×C22⋊D61C2214yes—
64C2×C4×C22⋊D61C2214yes—
65C2×#14519737C2212yes—
66C2×#14519737C2212yes—
67C2×#14519737C2214yes—
68C2×#14519736C2214yes—
69C2×#14519734C2211yescharacteristic
70C2×#14519734C2211yescharacteristic
71C2×#14519733C2214yes—
72C2×#14519733C2214yes—
73C22×#11758196C2214yes—
74C2×C4⋊C4×D61C2212yes—
75C2×C4⋊C4×D61C2214yes—
76C22×C4×Dic61C2211yescharacteristic
77C2×C42×D61C2211yescharacteristic
78C2×C42×D61C2211yescharacteristic
79C61×#540C22116yescomplemented
80C2×#127×C61C2211yescharacteristic
81C2×#125×C61C2211yescharacteristic
82C2×#123×C61C2214yes—
83C2×#121×C61C2214yes—
84C2×#121×C61C2212yes—
85C2×C4×D4×C61C2212yes—
86C2×#117×C61C2211yescharacteristic
87C2×#11758222—28no—
88C2×#11758222C2318yes—
89C2×#11758224—216no—
90C2×#11758224C23116yes—
91C22×Dic122C2311yescharacteristic
92C22×Dic122C2312yes—
93C22×D244C2311yescharacteristic
94C22×C22⋊D61C2311yescharacteristic
95C22×C22⋊D61C2311yescharacteristic
96C22×C22⋊D61C2314yes—
97C22×C22⋊D61C2314yes—
98C23×Dic61C2314yes—
99C23×Dic61C2312yes—
100C23×Dic61C2314yes—
101C22×C4×D61C2311yescharacteristic
102C22×C4×D61C2312yes—
103C22×C4×D61C2312yes—
104C22×C4×D61C2314yes—
105C22×C4×D61C2311yescharacteristic
106#14519777C2318yes—
107#14519772C23132yes—
108#14519770C23132yes—
109#14519770C23132yes—
110#14519770C23132yes—
111#14519769C2318yes—
112#14519768C23132yes—
113#14519768C23116yes—
114#14519767C23132yes—
115#14519767C23132yes—
116#14519764C23116yes—
117#14519759C23132yes—
118#14519758C23132yes—
119#14519758C23132yes—
120#14519757C23116yes—
121#14519756C23116yes—
122#14519754C23132yes—
123#14519750C23132yes—
124#14519749C23132yes—
125#14519749C23132yes—
126#14519748C23132yes—
127#14519748C23132yes—
128#14519748C23116yes—
129C4×Dic122C23116yes—
130#14519742C23116yes—
131#14519742C23116yes—
132D4×Dic61C23132yes—
133D4×Dic61C23132yes—
134D4×Dic61C23116yes—
135#14519739C23116yes—
136C4×C22⋊D61C23132yes—
137C4×C22⋊D61C23132yes—
138#14519737C23116yes—
139#14519737C23132yes—
140#14519737C23116yes—
141#14519736C23132yes—
142#14519734C2318yes—
143#14519734C2318yes—
144#14519733C23132yes—
145#14519733C23132yes—
146C2×C4⋊Dic61C2314yes—
147C2×C4⋊Dic61C2312yes—
148C2×C4⋊Dic61C2314yes—
149C2×C4⋊Dic61C2314yes—
150C2×#11758196C23132yes—
151C2×#11758196C2314yes—
152C2×#11758196C2314yes—
153C2×#11758196C2314yes—
154C2×#11758196C2312yes—
155C2×#11758196C2314yes—
156C2×#11758196C2314yes—
157C2×#11758196C2314yes—
158C2×#11758196C2312yes—
159C4⋊C4×D61C23132yes—
160C4⋊C4×D61C23116yes—
161C2×C22⋊Dic61C2314yes—
162C2×C22⋊Dic61C2314yes—
163C2×C22⋊Dic61C2314yes—
164C2×C22⋊Dic61C2314yes—
165C2×C22⋊Dic61C2314yes—
166C2×#11758198C2312yes—
167C2×#11758198C2312yes—
168C2×#11758198C2314yes—
169C2×C4×Dic61C2311yescharacteristic
170C2×C4×Dic61C2312yes—
171C2×C4×Dic61C2312yes—
172C2×C4×Dic61C2312yes—
173C2×C4×Dic61C2311yescharacteristic
174C2×C4×Dic61C2318yes—
175C2×C4×Dic61C2314yes—
176C2×C4×Dic61C2314yes—
177C42×D61C2318yes—
178C42×D61C2318yes—
179C22×D4×C61C2312yes—
180C22×D4×C61C2314yes—
181C22×D4×C61C2314yes—
182C23×C4×C61C2311yescharacteristic
183C23×C4×C61C2314yes—
184#127×C61C2318yes—
185#125×C61C2318yes—
186#123×C61C23132yes—
187#121×C61C23132yes—
188#121×C61C23116yes—
189C4×D4×C61C23116yes—
190#117×C61C2318yes—
191C2×C4⋊C4×C61C2312yes—
192C2×C4⋊C4×C61C2314yes—
193C2×C4⋊C4×C61C2312yes—
194C2×C22⋊C4×C61C2314yes—
195C2×C22⋊C4×C61C2314yes—
196C2×C22⋊C4×C61C2312yes—
197C2×C42×C61C2311yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C24×C61C2414yes—
200C24×C61C2411yescharacteristic
201C23×D61C2411yescharacteristic
202C23×D61C2411yescharacteristic
203C2×D4×C61—28no—
204C2×D4×C61—48no—
205C2×D4×C61—48no—
206C2×D4×C61C2418yes—
207C2×D4×C61C24116yes—
208C2×D4×C61C24116yes—
209C22×C4×C61—24no—
210C22×C4×C61—48no—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2414yes—
214C22×C4×C61C2411yescharacteristic
215C22×C4×C61C2414yes—
216C22×C4×C61C24116yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—216no—
219C2×C22⋊D61—24no—
220C2×C22⋊D61—24no—
221C2×C22⋊D61—48no—
222C2×C22⋊D61C24116yes—
223C2×C22⋊D61C2414yes—
224C2×C22⋊D61C2414yes—
225C2×C22⋊D61C24116yes—
226C22×Dic61—216no—
227C22×Dic61—44no—
228C22×Dic61—48no—
229C22×Dic61C2412yes—
230C22×Dic61C2414yes—
231C22×Dic61C2411yescharacteristic
232C22×Dic61C2412yes—
233C22×Dic61C2414yes—
234C22×Dic61C24116yes—
235C22×Dic61C2418yes—
236C22×Dic61C24116yes—
237C22×Dic61C2411yescharacteristic
238#11758224—264no—
239#11758222—232no—
240C2×D244—24no—
241C2×D244C2414yes—
242C2×C4×D61—24no—
243C2×C4×D61—44no—
244C2×C4×D61—44no—
245C2×C4×D61—48no—
246C2×C4×D61#4118yes—
247C2×C4×D61C2414yes—
248C2×C4×D61C2418yes—
249C2×C4×D61C2418yes—
250C2×C4×D61C24116yes—
251C2×C4×D61C2414yes—
252C2×Dic122—28no—
253C2×Dic122—24no—
254C2×Dic122C2418yes—
255C2×Dic122C2414yes—
256C4⋊C4×C61C2418yes—
257C4⋊C4×C61C2418yes—
258C4⋊C4×C61C24116yes—
259C22⋊C4×C61C2418yes—
260C22⋊C4×C61C24116yes—
261C22⋊C4×C61C24116yes—
262C42×C61C2414yes—
263C42×C61C2414yes—
264C22⋊Dic61C24116yes—
265C22⋊Dic61C24116yes—
266C22⋊Dic61C24116yes—
267C22⋊Dic61C24116yes—
268C22⋊Dic61C24116yes—
269#11758198C2418yes—
270#11758198C2418yes—
271#11758198C24116yes—
272C4⋊Dic61C24116yes—
273C4⋊Dic61C2418yes—
274C4⋊Dic61C24116yes—
275C4⋊Dic61C24116yes—
276#11758196C24116yes—
277#11758196C24116yes—
278#11758196C24116yes—
279#11758196C2418yes—
280#11758196C24116yes—
281#11758196C24116yes—
282#11758196C24116yes—
283#11758196C2418yes—
284C4×Dic61C2414yes—
285C4×Dic61C2418yes—
286C4×Dic61C2418yes—
287C4×Dic61C2418yes—
288C4×Dic61C2414yes—
289C4×Dic61C24116yes—
290C4×Dic61C24116yes—
291C23×C61—28no—
292C23×C61—22no—
293C23×C61—28no—
294C23×C61—24no—
295C23×C61—28no—
296C23×C61C2518yes—
297C23×C61C2512yes—
298C23×C61C2511yescharacteristic
299C22×D61—24no—
300C22×D61—22no—
301C22×D61—24no—
302C22×D61C2×#4114yes—
303C22×D61C2512yes—
304C22×D61C2512yes—
305D4×C61—216no—
306D4×C61—416no—
307D4×C61—416no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—28no—
311C2×C4×C61—24no—
312C2×C4×C61—28no—
313C2×C4×C61—416no—
314C2×C4×C61C2×#4114yes—
315C2×C4×C61C2514yes—
316C2×C4×C61C2512yes—
317C2×C4×C61C2514yes—
318C2×C4×C61C2518yes—
319C2×C4×C61C2512yes—
320C22⋊D61—28no—
321C22⋊D61—232no—
322C22⋊D61—28no—
323C22⋊D61—416no—
324C2×Dic61—22no—
325C2×Dic61—28no—
326C2×Dic61—24no—
327C2×Dic61—28no—
328C2×Dic61—24no—
329C2×Dic61—232no—
330C2×Dic61—48no—
331C2×Dic61—416no—
332C2×Dic61C2×#4114yes—
333C2×Dic61C2514yes—
334C2×Dic61C2514yes—
335C2×Dic61C2518yes—
336C2×Dic61C2512yes—
337C2×Dic61C2518yes—
338C2×Dic61C2512yes—
339D244—28no—
340C4×D61—28no—
341C4×D61—48no—
342C4×D61—48no—
343C4×D61—416no—
344C4×D61C2×#41116yes—
345Dic122—216no—
346Dic122—28no—
347C2×#3512—611nomaximal, Sylow
348C22×C61—28no—
349C22×C61—22no—
350C22×C61—28no—
351C22×C61—24no—
352C22×C61—28no—
353C22×C61—416no—
354C22×C61—44no—
355C22×C61C22×#4112yes—
356C22×C61#58514yes—
357C22×C61C2611yescharacteristic
358C2×D61—24no—
359C2×D61—28no—
360C2×D61—22no—
361C2×D61—24no—
362C2×D61—44no—
363C2×D61C22×#4114yes—
364C4×C61—22no—
365C4×C61—24no—
366C4×C61—28no—
367C4×C61—24no—
368C4×C61C22×#4114yes—
369Dic61—22no—
370Dic61—28no—
371Dic61—24no—
372Dic61—28no—
373Dic61—24no—
374Dic61C22×#4114yes—
375#3512—6132no—
376C2×#553—614no—
377C2×#553—614no—
378C2×#553—614no—
379C2×#552—614no—
380C2×#541—611no—
381C2×#541—611no—
382C2×#540—611no—
383C2×#540D6111yescharacteristic, complemented
384C2×#537—612no—
385C2×#532—611no—
386C2×#529—612no—
387C2×#529—612no—
388C22×#125—611no—
389C2×#520—612no—
390C2×C4×#41—611no—
391C2×C61—48no—
392C2×C61—42no—
393C2×C61#351214yescomplemented
394C2×C61C23×#4111yescharacteristic
395C2×C61C2×#58512yes—
396D61—24no—
397D61—42no—
398C22×#41—612no—
399C22×#41—611no—
400#553—6164no—
401#553—6164no—
402#553—6164no—
403#552—6164no—
404#541—6116no—
405#541—6116no—
406#540—6116no—
407#540C2×D61116yescomplemented
408#537—6132no—
409#532—6116no—
410C2×C4⋊Q8—611no—
411C2×#127C2×D6111yescharacteristic
412#529—6132no—
413#529—6132no—
414C2×#126—614no—
415C2×#126—614no—
416C2×#126—614no—
417C2×#126—614no—
418C2×#125—6116no—
419C2×#125—614no—
420C2×#125—614no—
421C2×#125—612no—
422C2×#125—614no—
423C2×#125—611no—
424C2×#125C2×D6111yescharacteristic
425C2×#124—612no—
426C2×#123—614no—
427C2×#123—614no—
428C2×#123—614no—
429C2×#123C2×D6114yes—
430C2×C22⋊Q8—612no—
431C2×C22⋊Q8—612no—
432C2×C22⋊Q8—614no—
433C2×#121—612no—
434C2×#121—614no—
435C2×#121—614no—
436C2×#121—614no—
437C2×#121—614no—
438C2×#121—614no—
439C2×#121C2×D6112yes—
440C2×#121C2×D6114yes—
441#520—6132no—
442C4×#41—6116no—
443C2×C4×Q8—612no—
444C2×C4×Q8—612no—
445C2×C4×Q8—612no—
446C2×C4×D4—612no—
447C2×C4×D4—614no—
448C2×C4×D4—614no—
449C2×C4×D4—614no—
450C2×C4×D4—614no—
451C2×C4×D4—612no—
452C2×C4×D4—612no—
453C2×C4×D4—612no—
454C2×C4×D4—614no—
455C2×C4×D4C2×D6112yes—
456C2×#117—614no—
457C2×#117—614no—
458C2×#117—614no—
459C2×#117—611no—
460C2×#117—611no—
461C2×#117C2×D6111yescharacteristic
462C22×C4⋊C4—614no—
463C22×C4⋊C4—612no—
464C22×C4⋊C4—614no—
465C22×C42—611no—
466C22×C42—611no—
467C22×C42—611no—
468C61C2×#351211yescharacteristic, complemented, Sylow
469C2×#41—6116no—
470C2×#41—618no—
471C2×#41—1228no—
472C2×#41—12216no—
473C22×Q8—611no—
474C22×Q8—612no—
475C22×D4—611no—
476C22×D4—614no—
477C22×D4—611no—
478C22×D4—614no—
479C22×D4—611no—
480C22×D4C22×D6112yes—
481C22×D4C22×D6114yes—
482C22×D4C22×D6114yes—
483C23×C4—611no—
484C23×C4—614no—
485C23×C4—614no—
486C23×C4—612no—
487C23×C4—611no—
488C23×C4—614no—
489C23×C4—612no—
490C23×C4—612no—
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6114yes—
493C4⋊Q8—618no—
494#127C22×D6118yes—
495#126—6132no—
496#126—6132no—
497#126—6132no—
498#126—6132no—
499#125—6116no—
500#125—6132no—
501#125—6132no—
502#125—6132no—
503#125—618no—
504#125C22×D6118yes—
505#124—6116no—
506#123—6132no—
507#123—6132no—
508#123—6132no—
509#123C22×D61132yes—
510C22⋊Q8—6116no—
511C22⋊Q8—6116no—
512C22⋊Q8—6132no—
513#121—6116no—
514#121—6132no—
515#121—6132no—
516#121—6132no—
517#121—6132no—
518#121—6132no—
519#121C22×D61116yes—
520#121C22×D61132yes—
521C4×Q8—6116no—
522C4×Q8—6116no—
523C4×Q8—6116no—
524C4×D4—6116no—
525C4×D4—6132no—
526C4×D4—6132no—
527C4×D4—6132no—
528C4×D4—6132no—
529C4×D4—6116no—
530C4×D4—6116no—
531C4×D4—6116no—
532C4×D4—6132no—
533C4×D4C22×D61116yes—
534#117—6132no—
535#117—6132no—
536#117—6132no—
537#117—618no—
538#117—618no—
539#117C22×D6118yes—
540C2×C4⋊C4—612no—
541C2×C4⋊C4—614no—
542C2×C4⋊C4—614no—
543C2×C4⋊C4—614no—
544C2×C4⋊C4—612no—
545C2×C4⋊C4—614no—
546C2×C4⋊C4—614no—
547C2×C4⋊C4—6132no—
548C2×C4⋊C4—614no—
549C2×C4⋊C4—612no—
550C2×C4⋊C4—614no—
551C2×C4⋊C4—614no—
552C2×C4⋊C4—614no—
553C2×C4⋊C4—6116no—
554C2×C4⋊C4—6132no—
555C2×C4⋊C4C22×D6112yes—
556C2×C4⋊C4C22×D6114yes—
557C2×C4⋊C4C22×D6112yes—
558C2×C22⋊C4—614no—
559C2×C22⋊C4—614no—
560C2×C22⋊C4—614no—
561C2×C22⋊C4—614no—
562C2×C22⋊C4—614no—
563C2×C22⋊C4—612no—
564C2×C22⋊C4—612no—
565C2×C22⋊C4—614no—
566C2×C22⋊C4C22×D6114yes—
567C2×C22⋊C4C22×D6114yes—
568C2×C22⋊C4C22×D6112yes—
569C2×C42—611no—
570C2×C42—614no—
571C2×C42—614no—
572C2×C42—612no—
573C2×C42—612no—
574C2×C42—612no—
575C2×C42—618no—
576C2×C42—611no—
577C2×C42—618no—
578C2×C42—618no—
579C2×C42C22×D6111yescharacteristic
580C2×C42C22×D6111yescharacteristic
581C24—611no—
582C24—611no—
583C24C23×D6111yescharacteristic
584C24C23×D6114yes—
585#41—12232no—
586#41—12264no—
587C2×Q8—614no—
588C2×Q8—618no—
589C2×Q8—1224no—
590C2×Q8—1228no—
591C2×D4—28no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—614no—
595C2×D4—6116no—
596C2×D4—614no—
597C2×D4—6116no—
598C2×D4—614no—
599C2×D4—1224no—
600C2×D4—1224no—
601C2×D4—1224no—
602C2×D4—12216no—
603C2×D4—2448no—
604C2×D4C23×D6118yes—
605C2×D4C23×D61116yes—
606C2×D4C23×D61116yes—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—611no—
610C22×C4—618no—
611C22×C4—614no—
612C22×C4—6116no—
613C22×C4—612no—
614C22×C4—612no—
615C22×C4—614no—
616C22×C4—611no—
617C22×C4—614no—
618C22×C4—618no—
619C22×C4—6116no—
620C22×C4—614no—
621C22×C4—618no—
622C22×C4—618no—
623C22×C4—6116no—
624C22×C4—12216no—
625C22×C4—1224no—
626C22×C4—2444no—
627C22×C4—2448no—
628C22×C4—2444no—
629C22×C4—2444no—
630C22×C4—2448no—
631C22×C4C23×D6114yes—
632C22×C4C23×D6112yes—
633C22×C4C23×D6111yescharacteristic
634C22×C4C23×D6112yes—
635C22×C4C23×D6114yes—
636C22×C4C23×D61116yes—
637C22×C4C23×D6111yescharacteristic
638C4⋊C4—618no—
639C4⋊C4—6116no—
640C4⋊C4—6116no—
641C4⋊C4—6116no—
642C4⋊C4—6116no—
643C4⋊C4—6116no—
644C4⋊C4—6116no—
645C4⋊C4—618no—
646C4⋊C4—618no—
647C4⋊C4—6116no—
648C4⋊C4—6116no—
649C4⋊C4—6116no—
650C4⋊C4C23×D6118yes—
651C4⋊C4C23×D61116yes—
652C4⋊C4C23×D6118yes—
653C22⋊C4—6116no—
654C22⋊C4—6116no—
655C22⋊C4—6116no—
656C22⋊C4—6116no—
657C22⋊C4—6116no—
658C22⋊C4—618no—
659C22⋊C4—618no—
660C22⋊C4—6116no—
661C22⋊C4C23×D61116yes—
662C22⋊C4C23×D61116yes—
663C22⋊C4C23×D6118yes—
664C42—614no—
665C42—614no—
666C42—618no—
667C42—618no—
668C42—618no—
669C42—6116no—
670C42—6116no—
671C42C23×D6114yes—
672C42C23×D6114yes—
673C23—22no—
674C23—28no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—614no—
679C23—612no—
680C23—612no—
681C23—1224no—
682C23—1222no—
683C23—1224no—
684C23C24×D6112yes—
685C23C24×D6118yes—
686C23C24×D6111yescharacteristic
687Q8—1228no—
688Q8—12216no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—1228no—
693D4—1228no—
694D4—1228no—
695D4—12232no—
696D4—24416no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—614no—
704C2×C4—612no—
705C2×C4—6116no—
706C2×C4—614no—
707C2×C4—614no—
708C2×C4—618no—
709C2×C4—612no—
710C2×C4—618no—
711C2×C4—12232no—
712C2×C4—1222no—
713C2×C4—1228no—
714C2×C4—1224no—
715C2×C4—1224no—
716C2×C4—1228no—
717C2×C4—1228no—
718C2×C4—2448no—
719C2×C4—24416no—
720C2×C4—2448no—
721C2×C4—2448no—
722C2×C4—24416no—
723C2×C4#41×D6114yes—
724C2×C4C24×D6114yes—
725C2×C4C24×D6112yes—
726C2×C4C24×D6114yes—
727C2×C4C24×D6118yes—
728C2×C4C24×D6112yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—614no—
737C22—1228no—
738C22—1224no—
739C22—1222no—
740C22—1224no—
741C22—2444no—
742C22C2×#41×D6112yes—
743C22#1684059714yes—
744C22C25×D6111yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—614no—
750C4—1222no—
751C4—1228no—
752C4—1224no—
753C4—1224no—
754C4—1228no—
755C4C2×#41×D6114yes—
756C2—42no—
757C2—48no—
758C2—1224no—
759C2—2442no—
760C2#2145973814yesdirect product factor
761C2C22×#41×D6111yescharacteristic
762C2C2×#1684059712yes—
subgroupG/H
centerC23C24×D61
commutator, cosocleC22×C61C26
FrattiniC22C25×D61
FittingC2×C61×#540C2
socleC23×C61C25
hypercenterC2×#540D61
hypocenterC61C2×#3512
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #21459738C2direct (N × H)
2. C2×#16840459C2semidirect
3. C2×#16840457C2semidirect
4. C2×#16840455C2semidirect
5. C2×#16840449C2semidirect
6. C2×#16840375C2semidirect
7. C2×#16840374C2semidirect
8. C2×#16840366C2semidirect
9. C2×#16840341C2semidirect
10. C2×#16840310C2semidirect
11. C2×#16840294C2semidirect
12. C2×#16840293C2semidirect
13. C2×#125×D61C2semidirect
14. C2×#16840241C2semidirect
15. C2×#16840230C2semidirect
16. C2×C61×#540C2semidirect
19. #16840459C22semidirect
20. #16840457C22semidirect
21. #16840455C22semidirect
22. #16840449C22semidirect
23. #16840375C22semidirect
24. #16840374C22semidirect
25. #16840366C22semidirect
26. #16840341C22semidirect
27. #16840310C22semidirect
29. #16840294C22semidirect
30. #16840293C22semidirect
40. #125×D61C22semidirect
54. #16840241C22semidirect
55. #16840230C22semidirect
79. C61×#540C22semidirect
383. C2×#540D61semidirect
393. C2×C61#3512semidirect
407. #540C2×D61semidirect
468. C61C2×#3512semidirect
760. C2#21459738direct (N × H)

Maximal subgroups

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

subgroupindex
#214597382
C2×#168404592
C2×#168404572
C2×#168404552
C2×#168404492
C2×#168403752
C2×#168403742
C2×#168403662
C2×#168403412
C2×#168403102
C2×#168402942
C2×#168402932
C2×#125×D612
C2×#168402412
C2×#168402302
C2×C61×#5402
C2×#351261