Finite Group Databasebeta

← C2×#21456012 #30548254

Subgroups — C2×#21456012 #30548254

Order 15616.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840242C211yesmaximal, characteristic, complemented
2#21456012C2116yesmaximal, direct product factor
3C2×#16840078C211yesmaximal, characteristic, complemented
4C2×#16840073C211yesmaximal, characteristic, complemented
5C2×#16840066C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16839959C211yesmaximal, characteristic, complemented
8C2×#16839954C211yesmaximal, characteristic, complemented
9C2×#16839905C211yesmaximal, characteristic, complemented
10C2×#16839905C211yesmaximal, characteristic, complemented
11C2×#16839872C211yesmaximal, characteristic, complemented
12C2×#16839862C211yesmaximal, characteristic, complemented
13C2×C4×#11758200C211yesmaximal, characteristic, complemented
14C2×C4×#11758199C211yesmaximal, characteristic, complemented
15C2×#16839823C211yesmaximal, characteristic, complemented
16C2×C61×#540C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22#16840242—24no—
23#16840242C2218yescomplemented
24C2×C4×Dic122C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×C4×D244C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×#14519737—21no—
29C2×#14519737—21no—
30C2×#14519735—21no—
31C22×C4⋊Dic61C2211yescharacteristic
32C2×C4⋊C4×D61—21no—
33#16840078C2218yescomplemented
34#16840073C2218yescomplemented
35#16840066C2218yescomplemented
36#16840059C2218yescomplemented
37#16839959C2218yescomplemented
38#16839954C2218yescomplemented
39#16839905C2218yescomplemented
40#16839905C2218yescomplemented
41#16839872C2218yescomplemented
42#16839862C2218yescomplemented
43C4×#11758200C2218yescomplemented
44C4×#11758199C2218yescomplemented
45#16839823C2218yescomplemented
46C2×#14519710C2211yescharacteristic
47C2×#14519710C2211yescharacteristic
48C2×#14519708C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×#14519700C2211yescharacteristic
53C2×#14519700C2211yescharacteristic
54C2×#14519698C2211yescharacteristic
55C2×#14519698C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#540—24no—
65C61×#540C2218yescomplemented
66C2×#127×C61C2211yescharacteristic
67C2×#125×C61C2211yescharacteristic
68C2×#123×C61—21no—
69C2×#123×C61—21no—
70C2×#121×C61—21no—
71C2×#121×C61—21no—
72C2×#121×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C2×#117×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C2×#11758200—24no—
89C2×#11758200—24no—
90C2×#11758200C2314yes—
91C2×#11758200C2314yes—
92C2×#11758199—24no—
93C2×#11758199—24no—
94C2×#11758199C2314yes—
95C2×#11758199C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C4×Dic122—22no—
101C4×Dic122—22no—
102C4×Dic122C2314yes—
103C4×Dic122C2314yes—
104C4×D244—22no—
105C4×D244—22no—
106C4×D244C2314yes—
107C4×D244C2314yes—
108#14519737—28no—
109#14519737—28no—
110#14519735—28no—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61—22no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×C4⋊Dic61C2314yes—
116C2×#11758196—21no—
117C2×#11758196—21no—
118C4⋊C4×D61—28no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123#14519710C2314yes—
124#14519710C2314yes—
125#14519708C2314yes—
126#14519708C2314yes—
127C4⋊#92418C2314yes—
128C4⋊#92418C2314yes—
129#14519700C2314yes—
130#14519700C2314yes—
131#14519698C2314yes—
132#14519698C2314yes—
133#14519698C2314yes—
134#14519698C2314yes—
135#14519697C2314yes—
136#14519697C2314yes—
137C22⋊#92418C2314yes—
138C22⋊#92418C2314yes—
139#14519688C2314yes—
140C4×#92418C2314yes—
141C22×D4×C61—21no—
142C22×D4×C61—21no—
143C22×D4×C61—21no—
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C22×D4×C61C2311yescharacteristic
147C23×C4×C61—21no—
148C23×C4×C61—21no—
149C23×C4×C61C2311yescharacteristic
150#127×C61—22no—
151#127×C61C2314yes—
152#125×C61—22no—
153#125×C61C2314yes—
154#123×C61—28no—
155#123×C61—28no—
156#121×C61—22no—
157#121×C61—22no—
158#121×C61—28no—
159#121×C61—28no—
160#121×C61C2314yes—
161#121×C61C2314yes—
162C4×D4×C61—22no—
163C4×D4×C61—22no—
164C4×D4×C61C2314yes—
165C4×D4×C61C2314yes—
166#117×C61D414yes—
167#117×C61C2314yes—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61D411yescharacteristic
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C22⋊C4×C61D411yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2311yescharacteristic
182C24×C61—21no—
183C24×C61—21no—
184C24×C61C2×D411yescharacteristic
185C23×D61—21no—
186C2×D4×C61—24no—
187C2×D4×C61—24no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—82no—
197C2×D4×C61—82no—
198C2×D4×C61—82no—
199C2×D4×C61—82no—
200C2×D4×C61C2412yes—
201C2×D4×C61C2412yes—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—24no—
207C22×C4×C61—24no—
208C22×C4×C61—82no—
209C22×C4×C61—82no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C2×C22⋊D61—28no—
219C2×C22⋊D61—24no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—24no—
224C22×Dic61—82no—
225#11758222—216no—
226#11758222—28no—
227#11758222—28no—
228C2×D244—21no—
229C2×D244—22no—
230C2×D244#4114yes—
231C2×D244C2412yes—
232C2×C4×D61—28no—
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—82no—
237C2×C4×D61—82no—
238C2×Dic122—21no—
239C2×Dic122—22no—
240C2×Dic122#4114yes—
241C2×Dic122C2412yes—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61C2×D414yes—
247C4⋊C4×C61C2×D414yes—
248C4⋊C4×C61C2412yes—
249C4⋊C4×C61C2412yes—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—24no—
254C22⋊C4×C61C2×D414yes—
255C22⋊C4×C61C2×D414yes—
256C42×C61C2×D412yes—
257C42×C61C2×D412yes—
258C42×C61C2412yes—
259C42×C61C2412yes—
260#11758200—28no—
261#11758200—28no—
262#11758199—28no—
263#11758199—28no—
264#11758198—24no—
265#11758198—24no—
266C4⋊Dic61—24no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2412yes—
270C4⋊Dic61C2412yes—
271#11758196—24no—
272#11758196—24no—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418C2412yes—
280C2×#92418C2412yes—
281C2×#92418C2412yes—
282C2×#92418C2412yes—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61C22×D412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—24no—
297C22×D61—22no—
298C22×D61—42no—
299C22×D61—42no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—42no—
305D4×C61—42no—
306D4×C61—84no—
307D4×C61—84no—
308D4×C61—84no—
309D4×C61—84no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—84no—
323C2×C4×C61—84no—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D412yes—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C2×#4112yes—
331C2×C4×C61C2×#4112yes—
332C2×C4×C61C2511yescharacteristic
333C22⋊D61—216no—
334C2×Dic61—24no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—84no—
341D244—24no—
342D244—22no—
343D244C2×#4114yes—
344C4×D61—216no—
345C4×D61—84no—
346C4×D61—84no—
347Dic122—24no—
348Dic122—22no—
349Dic122C2×#4114yes—
350#92418—22no—
351#92418—22no—
352#92418—22no—
353#92418—22no—
354C2×#3119—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—44no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—84no—
366C22×C61—84no—
367C22×C61#52512yes—
368C22×C61#57612yes—
369C22×C61#57712yes—
370C22×C61C23×D411yescharacteristic
371C2×D61—24no—
372C2×D61—48no—
373C2×D61—42no—
374C2×D61—42no—
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61#52512yes—
383C4×C61C22×#4111yescharacteristic
384C4×C61C22×#4111yescharacteristic
385Dic61—24no—
386Dic61—42no—
387Dic61—42no—
388C2×#540D6111yescharacteristic, complemented
389C2×#520—611no—
390#3119—6116no—
391C2×#481—611no—
392C2×#480—611no—
393C2×#479—611no—
394C2×#478—611no—
395C2×#460—611no—
396C2×#459—611no—
397C2×#449—611no—
398C2×#449—611no—
399C2×#442—611no—
400C2×#440—611no—
401C2×C4×SD16—611no—
402C2×C4×D8—611no—
403C2×#433—611no—
404C2×C61—42no—
405C2×C61—82no—
406C2×C61—82no—
407C2×C61#311914yescomplemented
408C2×C61C2×#52511yescharacteristic
409C2×C61C2×#57611yescharacteristic
410C2×C61C2×#57711yescharacteristic
411D61—44no—
412C22×#41—611no—
413C22×SD16—611no—
414C22×SD16—611no—
415C22×D8—611no—
416C22×D8—611no—
417#540—24no—
418#540C2×D6118yescomplemented
419C2×#127C2×D6111yescharacteristic
420C2×#125C2×D6111yescharacteristic
421C2×#123—21no—
422C2×#123—21no—
423C2×#121—21no—
424C2×#121—21no—
425C2×#121C2×D6111yescharacteristic
426C2×#121C2×D6111yescharacteristic
427#520—618no—
428#520—1224no—
429C2×C4×Q8—611no—
430C2×C4×Q8—611no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433C2×C4×D4—1221no—
434C2×C4×D4—1221no—
435C2×C4×D4C2×D6111yescharacteristic
436C2×C4×D4C2×D6111yescharacteristic
437C2×#117—1221no—
438C2×#117C2×D6111yescharacteristic
439C22×C4⋊C4—611no—
440C22×C4⋊C4—1221no—
441#481—618no—
442#480—618no—
443#479—618no—
444#478—618no—
445#460—618no—
446#459—618no—
447#449—618no—
448#449—618no—
449#442—618no—
450#440—618no—
451C4×SD16—618no—
452C4×D8—618no—
453#433—618no—
454C2×#107—611no—
455C2×#107—611no—
456C2×#106—611no—
457C2×#106—611no—
458C2×C4⋊C8—611no—
459C2×C4⋊C8—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×#97—611no—
471C2×C4×C8—611no—
472C61C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—614no—
474C2×#41—1224no—
475C2×#41—1224no—
476C2×#41—1222no—
477C22×Q8—611no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—611no—
483C22×D4—1221no—
484C22×D4C22×D6111yescharacteristic
485C22×D4C22×D6111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4C22×D6111yescharacteristic
493C2×SD16—614no—
494C2×SD16—614no—
495C2×SD16—1224no—
496C2×SD16—1224no—
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1224no—
500C2×D8—1224no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505#127—22no—
506#127C22×D6114yes—
507#125—22no—
508#125C22×D6114yes—
509#123—28no—
510#123—28no—
511#121—22no—
512#121—22no—
513#121—28no—
514#121—28no—
515#121C22×D6114yes—
516#121C22×D6114yes—
517C4×Q8—614no—
518C4×Q8—614no—
519C4×Q8—1222no—
520C4×Q8—1222no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—614no—
524C4×D4—614no—
525C4×D4—1228no—
526C4×D4—1228no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4C22×D6114yes—
530C4×D4C22×D6114yes—
531#117—1228no—
532#117C22⋊D6114yes—
533#117C22×D6114yes—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—614no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1228no—
544C2×C4⋊C4C22⋊D6111yescharacteristic
545C2×C4⋊C4C22⋊D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4C22⋊D6111yescharacteristic
555C2×C22⋊C4C22⋊D6111yescharacteristic
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42C22×D6111yescharacteristic
559C2×C42C22×D6111yescharacteristic
560#107—614no—
561#107—614no—
562#106—614no—
563#106—614no—
564C4⋊C8—614no—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#102—614no—
569#102—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574C22⋊C8—614no—
575C22⋊C8—614no—
576#97—614no—
577C4×C8—614no—
578C24—21no—
579C24—21no—
580C24—1221no—
581C24C2×C22⋊D6111yescharacteristic
582#41—1228no—
583#41—1228no—
584#41—12216no—
585C2×Q8—614no—
586C2×Q8—612no—
587C2×Q8—1221no—
588C2×Q8—1222no—
589C2×D4—24no—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—24no—
594C2×D4—24no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—82no—
600C2×D4—82no—
601C2×D4—82no—
602C2×D4—82no—
603C2×D4—614no—
604C2×D4—612no—
605C2×D4—1228no—
606C2×D4—1224no—
607C2×D4—1221no—
608C2×D4—1222no—
609C2×D4C23×D6112yes—
610C2×D4C23×D6112yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—1228no—
620C22×C4—1221no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1224no—
626C22×C4—1224no—
627C22×C4—4882no—
628C22×C4—4882no—
629C22×C4—4882no—
630C22×C4C2×C22⋊D6112yes—
631C22×C4C2×C22⋊D6111yescharacteristic
632C22×C4C2×C22⋊D6111yescharacteristic
633C22×C4C2×C22⋊D6111yescharacteristic
634C22×C4C2×C22⋊D6111yescharacteristic
635C22×C4C2×C22⋊D6111yescharacteristic
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638SD16—1228no—
639SD16—1228no—
640D8—1228no—
641D8—1228no—
642C2×C8—612no—
643C2×C8—612no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—1222no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—1224no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4C2×C22⋊D6114yes—
662C4⋊C4C2×C22⋊D6114yes—
663C4⋊C4C23×D6112yes—
664C4⋊C4C23×D6112yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4C2×C22⋊D6114yes—
672C22⋊C4C2×C22⋊D6114yes—
673C42—1224no—
674C42—1224no—
675C42C2×C22⋊D6112yes—
676C42C2×C22⋊D6112yes—
677C42C23×D6112yes—
678C42C23×D6112yes—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—1224no—
691C23—1222no—
692C23—2442no—
693C23—2442no—
694C23C22×C22⋊D6112yes—
695C23C22×C22⋊D6111yescharacteristic
696Q8—614no—
697Q8—1224no—
698Q8—1222no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—614no—
710D4—12216no—
711D4—1224no—
712D4—1222no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—12216no—
728C2×C4—1224no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—4884no—
733C2×C4—4884no—
734C2×C4—4884no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4C22×C22⋊D6112yes—
738C2×C4C22×C22⋊D6112yes—
739C2×C4C22×C22⋊D6112yes—
740C2×C4C22×C22⋊D6112yes—
741C2×C4C22×C22⋊D6112yes—
742C2×C4C22×C22⋊D6111yescharacteristic
743C2×C4#41×D6112yes—
744C2×C4#41×D6112yes—
745C2×C4C24×D6111yescharacteristic
746C8—1222no—
747C8—1222no—
748C8—1222no—
749C8—1222no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—84no—
762C22—1224no—
763C22—2442no—
764C22—2442no—
765C22—2448no—
766C22#1684026912yes—
767C22#1684056512yes—
768C22#1684057312yes—
769C22C23×C22⋊D6111yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—42no—
776C4—42no—
777C4—1224no—
778C4—2442no—
779C4—2442no—
780C4#1684026912yes—
781C4C2×#41×D6111yescharacteristic
782C4C2×#41×D6111yescharacteristic
783C2—42no—
784C2—82no—
785C2—82no—
786C2—2444no—
787C2#2145601214yesdirect product factor
788C2C2×#1684026911yescharacteristic
789C2C2×#1684056511yescharacteristic
790C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#540C2
socleC23×C61C22×D4
hypercenterC2×#540D61
hypocenterC61C2×#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#16840242C2semidirect
2. #21456012C2direct (N × H)
3. C2×#16840078C2semidirect
4. C2×#16840073C2semidirect
5. C2×#16840066C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16839959C2semidirect
8. C2×#16839954C2semidirect
9. C2×#16839905C2semidirect
10. C2×#16839905C2semidirect
11. C2×#16839872C2semidirect
12. C2×#16839862C2semidirect
13. C2×C4×#11758200C2semidirect
14. C2×C4×#11758199C2semidirect
15. C2×#16839823C2semidirect
16. C2×C61×#540C2semidirect
23. #16840242C22semidirect
33. #16840078C22semidirect
34. #16840073C22semidirect
35. #16840066C22semidirect
36. #16840059C22semidirect
37. #16839959C22semidirect
38. #16839954C22semidirect
39. #16839905C22semidirect
40. #16839905C22semidirect
41. #16839872C22semidirect
42. #16839862C22semidirect
43. C4×#11758200C22semidirect
44. C4×#11758199C22semidirect
45. #16839823C22semidirect
65. C61×#540C22semidirect
388. C2×#540D61semidirect
407. C2×C61#3119semidirect
418. #540C2×D61semidirect
472. C61C2×#3119semidirect
787. C2#21456012direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402422
#214560122
C2×#168400782
C2×#168400732
C2×#168400662
C2×#168400592
C2×#168399592
C2×#168399542
C2×#168399052
C2×#168398722
C2×#168398622
C2×C4×#117582002
C2×C4×#117581992
C2×#168398232
C2×C61×#5402
C2×#311961