Finite Group Databasebeta

← #30616403

Subgroups — #30616403

Order 15616.

814 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462303C211yesmaximal, characteristic, complemented
2#21462302C211yesmaximal, characteristic
3#21461969C211yesmaximal, characteristic
4#21461964C211yesmaximal, characteristic
5#21461924C211yesmaximal, characteristic, complemented
6#21461923C211yesmaximal, characteristic, complemented
7#21461911C211yesmaximal, characteristic
8#21461910C211yesmaximal, characteristic, complemented
9#21461909C211yesmaximal, characteristic
10#21461908C211yesmaximal, characteristic, complemented
11#21461633C211yesmaximal, characteristic, complemented
12C4×#14519840C211yesmaximal, characteristic, complemented
13C4×#14519839C211yesmaximal, characteristic
14#21461477C211yesmaximal, characteristic, complemented
15#440×D61C211yesmaximal, characteristic
16C2×#14519846C2211yescharacteristic
17C2×#14519845C2211yescharacteristic
18C2×#14519840C2211yescharacteristic
19C2×#14519840C2211yescharacteristic
20C2×#14519839C2211yescharacteristic
21C2×#14519839C2211yescharacteristic
22C2×#14519831C2211yescharacteristic
23C2×#14519831C2211yescharacteristic
24C4×D61⋊C8C2211yescharacteristic
25C2×C8×#6923C2211yescharacteristic
26C2×C8×#6923C2211yescharacteristic
27(C2×#6923)⋊Q8C2211yescharacteristic
28(C2×#6923)⋊Q8C2211yescharacteristic
29#16840714C2211yescharacteristic
30#16840714C2211yescharacteristic
31#16840713C2211yescharacteristic
32#16840713C2211yescharacteristic
33#16840713C2211yescharacteristic
34#16840713C2211yescharacteristic
35#16840712—21no—
36#16840712—21no—
37#16840711—21no—
38#16840711—21no—
39#16840707—21no—
40#16840706—21no—
41#16840705—21no—
42#16840704—21no—
43C4×C4⋊#6923C2211yescharacteristic
44C4×C4⋊#6923C2211yescharacteristic
45#16840698C2211yescharacteristic
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839865C411yescharacteristic, complemented
56#16839864C411yescharacteristic, complemented
57#16839863C411yescharacteristic, complemented
58#16839862C411yescharacteristic, complemented
59#16839861C411yescharacteristic, complemented
60#16839860C411yescharacteristic, complemented
61#16839859C411yescharacteristic, complemented
62#107×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#440C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69C2×C4⋊#6923—21no—
70C2×C4⋊#6923—21no—
71C2×C4⋊#6923—21no—
72C2×C4⋊#6923—21no—
73C2×C4⋊#6923C2311yescharacteristic
74C2×C4⋊#6923C2311yescharacteristic
75C2×C4⋊#6923C2311yescharacteristic
76C2×C4⋊#6923C2311yescharacteristic
77C2×C22⋊#6923—21no—
78C2×C22⋊#6923—21no—
79C2×C22⋊#6923—21no—
80C2×C22⋊#6923—21no—
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923C2311yescharacteristic
84C2×C4×#6923C2311yescharacteristic
85#14519846—22no—
86#14519845—22no—
87#14519840—22no—
88#14519840—22no—
89#14519839—22no—
90#14519839—22no—
91#14519831—22no—
92#14519831—22no—
93C4×#92420—21no—
94C4×#92420—21no—
95C8×#6923—22no—
96C8×#6923—22no—
97(C2×#6923)⋊C4—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4D411yescharacteristic
108(C2×#6923)⋊C4D411yescharacteristic
109(C2×#6923)⋊C4D411yescharacteristic
110(C2×#6923)⋊C4D411yescharacteristic
111C2×Q8×D61C2311yescharacteristic
112C2×D4×D61C2311yescharacteristic
113C22×C4×D61—21no—
114C2×#11758190C2×C411yescharacteristic
115C2×#11758200C2×C411yescharacteristic
116C2×#11758201C2×C411yescharacteristic
117SD16×D61—22no—
118SD16×D61—22no—
119C2×C8×D61C2311yescharacteristic
120C2×C8×D61C2311yescharacteristic
121Q8×Dic61C2×C411yescharacteristic
122C4×Dic122—21no—
123C4×Dic122C2×C411yescharacteristic
124#14519742—21no—
125#14519742C2×C411yescharacteristic
126C4×D244C2×C411yescharacteristic
127D4×Dic61C2×C411yescharacteristic
128#14519739C2×C411yescharacteristic
129C4×C22⋊D61—21no—
130#14519737—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61C2311yescharacteristic
133C4⋊C4×D61C2311yescharacteristic
134C22⋊C4×D61—21no—
135C42×D61—21no—
136C42×D61C2311yescharacteristic
137#14519711C2×C411yescharacteristic
138#14519710C2×C411yescharacteristic
139#14519710C2×C411yescharacteristic
140#14519702C2×C411yescharacteristic
141#14519701C2×C411yescharacteristic
142#14519700C2×C411yescharacteristic
143#14519699C2×C411yescharacteristic
144#14519698C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519688C2×C411yescharacteristic
147#14519687C2×C411yescharacteristic
148#14519687C2×C411yescharacteristic
149C2×SD16×C61C2×C411yescharacteristic
150C4×Q8×C61C2×C411yescharacteristic
151C4×D4×C61C2×C411yescharacteristic
152#107×C61C2×C411yescharacteristic
153#103×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic
155#97×C61C2×C411yescharacteristic
156C23×D61—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923C2×D411yescharacteristic
162C22×#6923C2×D411yescharacteristic
163C22×#6923C2×D411yescharacteristic
164C22×#6923C2×D411yescharacteristic
165C2×Q8×C61C22×C411yescharacteristic
166C2×D4×C61C22×C411yescharacteristic
167C22×C4×C61—21no—
168C2×C22⋊D61—21no—
169C22×Dic61—21no—
170Q8×D61—21no—
171Q8×D61—21no—
172Q8×D61—21no—
173Q8×D61—21no—
174D4×D61—21no—
175D4×D61—21no—
176D4×D61—21no—
177D4×D61—21no—
178C2×D244C22×C411yescharacteristic
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—81no—
185C2×C4×D61—81no—
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2411yescharacteristic
189C2×Dic122—21no—
190C2×Dic122C22×C411yescharacteristic
191C22⋊#6923—81no—
192C22⋊#6923—81no—
193C22⋊#6923—81no—
194C22⋊#6923—81no—
195C2×#92420—21no—
196C2×#92420—21no—
197C4⋊#6923—21no—
198C4⋊#6923—21no—
199C4⋊#6923—21no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—81no—
206C4⋊#6923—81no—
207C4⋊#6923—81no—
208C4⋊#6923—81no—
209C4×#6923—21no—
210C4×#6923—21no—
211C4×#6923—21no—
212C4×#6923—21no—
213C4×#6923—81no—
214C4×#6923—81no—
215D61⋊C8—21no—
216D61⋊C8—21no—
217D61⋊C8#4112yes—
218D61⋊C8#4112yes—
219SD16×C61—22no—
220C2×C8×C61C22×C411yescharacteristic
221C2×C8×C61C22×C411yescharacteristic
222C4⋊C4×C61—21no—
223C4⋊C4×C61C22×C411yescharacteristic
224C4⋊C4×C61C22×C411yescharacteristic
225C22⋊C4×C61—21no—
226C42×C61—21no—
227C42×C61C22×C411yescharacteristic
228C22⋊Dic61—21no—
229#11758201—22no—
230#11758200—22no—
231#11758198—21no—
232#11758198—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61C22×C411yescharacteristic
235C4⋊Dic61C22×C411yescharacteristic
236#11758196—21no—
237#11758196—21no—
238#11758196—21no—
239#11758196—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61C22×C411yescharacteristic
244C4×Dic61#4111yescharacteristic
245C4×Dic61#4111yescharacteristic
246C2×#92418C22×C411yescharacteristic
247C2×#92418C22×C411yescharacteristic
248#11758190—22no—
249C8×D61—21no—
250C8×D61—21no—
251C8×D61#4112yes—
252C8×D61#4112yes—
253C23×C61—21no—
254C22×D61—21no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61C22×D411yescharacteristic
262C2×#6923—21no—
263C2×#6923—21no—
264C2×#6923—21no—
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—21no—
271C2×#6923—21no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—41no—
275C2×#6923—41no—
276C2×#6923—41no—
277C2×#6923—41no—
278C2×#6923—41no—
279C2×#6923—41no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—41no—
286Q8×C61—21no—
287Q8×C61—21no—
288D4×C61—21no—
289D4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—81no—
294C2×C4×C61C4×D411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C23×C411yescharacteristic
297C22⋊D61—41no—
298C22⋊D61—41no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—81no—
303C2×Dic61C4×D411yescharacteristic
304C2×Dic61C4×D411yescharacteristic
305C2×Dic61C2×#4111yescharacteristic
306D244—21no—
307D244—21no—
308C4×D61—21no—
309C4×D61—21no—
310C4×D61—21no—
311C4×D61—21no—
312C4×D61—41no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—81no—
319C4×D61—81no—
320C4×D61C2×#4111yescharacteristic
321C4×D61C2×#4111yescharacteristic
322C4×D61C2×#4111yescharacteristic
323C4×D61C2×#4111yescharacteristic
324Dic122—21no—
325Dic122—21no—
326Dic122—41no—
327Dic122—41no—
328#92420—22no—
329#92420—22no—
330C8×C61—21no—
331C8×C61#11712yes—
332#92418—21no—
333#92418#11712yes—
334#21291—611nomaximal, Sylow
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61C2×C4×D411yescharacteristic
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—81no—
343C2×D61—81no—
344C2×D61—81no—
345C2×D61—81no—
346C2×D61#53211yescharacteristic
347C2×D61#53211yescharacteristic
348C2×D61#57611yescharacteristic
349C2×D61#57711yescharacteristic
350C2×D61#57711yescharacteristic
351C2×D61#57811yescharacteristic
352#6923—41no—
353#6923—41no—
354#6923—41no—
355#6923—41no—
356#6923—81no—
357#6923—81no—
358#6923—81no—
359#6923—81no—
360C4×C61—21no—
361C4×C61—21no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61C2×#11711yescharacteristic
366C4×C61C4×#4111yescharacteristic
367Dic61—21no—
368Dic61—21no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61#52911yescharacteristic
373Dic61#52911yescharacteristic
374C2×#440—611no—
375#2320—611no—
376#2319—611no—
377#1973—611no—
378#1968—611no—
379#1943—611no—
380#1942—611no—
381#1936—611no—
382#1935—611no—
383#1934—611no—
384#1933—611no—
385#1776—611no—
386C4×#103—611no—
387C4×#102—611no—
388#1726—611no—
389C2×C61—81no—
390C2×C61#229311yescharacteristic
391C2×C61#294611yescharacteristic
392C2×C61#294711yescharacteristic
393D61—81no—
394D61#317411yescharacteristic
395D61#317511yescharacteristic
396D61#317811yescharacteristic
397D61#317911yescharacteristic
398C22×SD16—611no—
399C2×C4×Q8—611no—
400C2×C4×D4—611no—
401#440—611no—
402#440—611no—
403#440—611no—
404#440—611no—
405#440—611no—
406#440—611no—
407#440—611no—
408#440#692311yescharacteristic, complemented
409C2×#107—611no—
410C2×#107—611no—
411C2×#106—611no—
412C2×#103—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#102—611no—
416C2×#102—611no—
417C2×#102—611no—
418C2×#97—611no—
419C2×#97—611no—
420C2×#97—611no—
421C2×C4×C8—611no—
422C2×C4×C8—611no—
423C2×C4×C8—611no—
424#391—611no—
425#391—611no—
426#390—611no—
427#390—611no—
428#389—611no—
429#389—611no—
430#389—611no—
431#389—611no—
432#388—1221no—
433#388—1221no—
434#387—1221no—
435#387—1221no—
436#383—1221no—
437#382—1221no—
438#381—1221no—
439#380—1221no—
440C4×C4⋊C4—611no—
441C4×C4⋊C4—611no—
442#376—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449C61#2129111yescharacteristic, complemented, Sylow
450C22×Q8—611no—
451C22×D4—611no—
452C23×C4—1221no—
453C2×SD16—611no—
454C2×SD16—611no—
455C2×SD16—611no—
456C2×SD16—1222no—
457C2×SD16—1222no—
458C2×SD16C2×#692311yescharacteristic
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8—611no—
463C4×Q8—611no—
464C4×Q8—611no—
465C4×Q8—611no—
466C4×Q8—1221no—
467C4×Q8—1221no—
468C4×Q8C2×#692311yescharacteristic
469C4×D4—611no—
470C4×D4—611no—
471C4×D4—611no—
472C4×D4—1221no—
473C4×D4—1221no—
474C4×D4C2×#692311yescharacteristic
475C2×C4⋊C4—611no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—1221no—
495C2×C42—1221no—
496C2×C42—1221no—
497#107—611no—
498#107—611no—
499#107—611no—
500#107—1222no—
501#107C2×#692311yescharacteristic
502#106—1222no—
503#103—611no—
504#103—611no—
505#103—611no—
506#103—1222no—
507#103—1222no—
508#103C2×#692311yescharacteristic
509#102—611no—
510#102—611no—
511#102—611no—
512#102—1222no—
513#102—1222no—
514#102C2×#692311yescharacteristic
515#97—611no—
516#97—611no—
517#97—611no—
518#97—1222no—
519#97—1222no—
520#97C2×#692311yescharacteristic
521C4×C8—1221no—
522C4×C8—1221no—
523C4×C8—1222no—
524C4×C8—1222no—
525#95—611no—
526#95—611no—
527#95—611no—
528#95—611no—
529#95—1221no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—1221no—
540C2×Q8—611no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8C22×#692311yescharacteristic
547C2×D4—611no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—1221no—
553C2×D4C22×#692311yescharacteristic
554C22×C4—21no—
555C22×C4—611no—
556C22×C4—611no—
557C22×C4—611no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—4881no—
573C22×C4—4881no—
574SD16—22no—
575SD16—1222no—
576SD16—1222no—
577SD16—1222no—
578C2×C8—611no—
579C2×C8—612no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—612no—
583C2×C8—611no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8C22×#692311yescharacteristic
591C2×C8C22×#692311yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—611no—
594C4⋊C4—611no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—4881no—
609C4⋊C4—4881no—
610C4⋊C4—4881no—
611C4⋊C4—4881no—
612C4⋊C4C22×#692311yescharacteristic
613C4⋊C4C22×#692311yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—1221no—
616C22⋊C4—1221no—
617C22⋊C4—1221no—
618C22⋊C4—4881no—
619C22⋊C4—4881no—
620C22⋊C4—4881no—
621C22⋊C4—4881no—
622C42—21no—
623C42—611no—
624C42—611no—
625C42—611no—
626C42—1221no—
627C42—1221no—
628C42—1221no—
629C42—1221no—
630C42—1221no—
631C42—1221no—
632C42—1221no—
633C42—4881no—
634C42—4881no—
635C42C22×#692311yescharacteristic
636C23—21no—
637C23—611no—
638C23—1221no—
639C23—2441no—
640C23—2441no—
641C23—2441no—
642C23—2441no—
643C23—2441no—
644C23—2441no—
645Q8—21no—
646Q8—21no—
647Q8—1221no—
648Q8—1221no—
649Q8—2441no—
650Q8—2441no—
651D4—21no—
652D4—21no—
653D4—1221no—
654D4—1221no—
655D4—2441no—
656D4—2441no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—81no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—611no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—4881no—
688C2×C4—4881no—
689C2×C4—4881no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4D4×#692311yescharacteristic
709C2×C4D4×#692311yescharacteristic
710C2×C4C23×#692311yescharacteristic
711C8—21no—
712C8—612no—
713C8—1222no—
714C8—1222no—
715C8—1221no—
716C8#1451985612yes—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—611no—
721C22—611no—
722C22—611no—
723C22—611no—
724C22—611no—
725C22—611no—
726C22—4881no—
727C22—4881no—
728C22—4881no—
729C22—4881no—
730C22—2441no—
731C22—2441no—
732C22—2441no—
733C22C2×D4×#692311yescharacteristic
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—611no—
740C4—611no—
741C4—1221no—
742C4—1221no—
743C4—4881no—
744C4—4881no—
745C4—4881no—
746C4—4881no—
747C4—2441no—
748C4—2441no—
749C4—2441no—
750C4—2441no—
751C4—2441no—
752C4—2441no—
753C4—2441no—
754C4C2×#1451985611yescharacteristic
755C4#41×#692311yescharacteristic
756C2—81no—
757C2—611no—
758C2—611no—
759C2—611no—
760C2—611no—
761C2—4881no—
762C2#2146227611yescharacteristic
763C2#2146257611yescharacteristic
764C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#440C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#440#6923
hypocenterC61#21291
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #21462303C2semidirect
5. #21461924C2semidirect
6. #21461923C2semidirect
8. #21461910C2semidirect
10. #21461908C2semidirect
11. #21461633C2semidirect
12. C4×#14519840C2semidirect
14. #21461477C2semidirect
55. #16839865C4semidirect
56. #16839864C4semidirect
57. #16839863C4semidirect
58. #16839862C4semidirect
59. #16839861C4semidirect
60. #16839860C4semidirect
61. #16839859C4semidirect
66. C61×#440C4semidirect
408. #440#6923semidirect
449. C61#21291semidirect

Maximal subgroups

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

subgroupindex
#214623032
#214623022
#214619692
#214619642
#214619242
#214619232
#214619112
#214619102
#214619092
#214619082
#214616332
C4×#145198402
C4×#145198392
#214614772
#440×D612
#2129161