Finite Group Databasebeta

← #30622478

Subgroups — #30622478

Order 15616.

806 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#21462348C211yesmaximal, characteristic
2#21462339C211yesmaximal, characteristic
3#21461967C211yesmaximal, characteristic
4#21461965C211yesmaximal, characteristic
5#21461950C211yesmaximal, characteristic
6#21461932C211yesmaximal, characteristic
7#21461899C211yesmaximal, characteristic
8#21461898C211yesmaximal, characteristic
9#21461813C211yesmaximal, characteristic
10#21461813C211yesmaximal, characteristic
11#21461620C211yesmaximal, characteristic
12#21461592C211yesmaximal, characteristic
13#21461591C211yesmaximal, characteristic
14#103×#6923C211yesmaximal, characteristic
15#462×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519840C2211yescharacteristic
24C2×#14519840C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26#16840721C2211yescharacteristic
27C2×#14519831C2211yescharacteristic
28C2×C8×#6923C2211yescharacteristic
29(C2×#6923)⋊Q8C2211yescharacteristic
30(C2×#6923)⋊Q8C2211yescharacteristic
31(C2×#6923)⋊Q8C2211yescharacteristic
32(C2×#6923)⋊Q8C2211yescharacteristic
33#16840713—21no—
34#16840711—21no—
35#16840711—21no—
36#16840711—21no—
37#16840711—21no—
38#16840707—21no—
39#16840706C2211yescharacteristic
40C4⋊C4×#6923—21no—
41C4⋊C4×#6923C2211yescharacteristic
42C4⋊C4×#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44C4×C4⋊#6923C2211yescharacteristic
45#16840698—21no—
46#16840636C2211yescharacteristic
47#16840636C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×Q16×D61C2211yescharacteristic
53C2×Q16×D61C2211yescharacteristic
54C4⋊Q8×D61C2211yescharacteristic
55C4×Q8×D61C2211yescharacteristic
56#16839973C411yescharacteristic, complemented
57#16839972C411yescharacteristic, complemented
58#16839971C411yescharacteristic, complemented
59#16839971C411yescharacteristic, complemented
60#16839970C411yescharacteristic, complemented
61#16839970C411yescharacteristic, complemented
62#16839969C411yescharacteristic, complemented
63C4⋊C8×D61C2211yescharacteristic
64#103×D61C2211yescharacteristic
65#103×D61C2211yescharacteristic
66C61×#462C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69Q8×#6923—22no—
70Q8×#6923—22no—
71Q8×#6923—41no—
72Q8×#6923—41no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923D411yescharacteristic
76C2×C4⋊#6923D411yescharacteristic
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4×#6923—21no—
82C2×C4×#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923C2311yescharacteristic
87C2×C4×#6923C2311yescharacteristic
88#14519846—41no—
89#14519845—41no—
90#14519840—22no—
91#14519840—22no—
92#14519840—22no—
93#14519840—22no—
94#14519840—41no—
95#14519840—41no—
96#14519832—21no—
97#14519832—21no—
98#14519831—41no—
99C8×#6923—41no—
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)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4D411yescharacteristic
114(C2×#6923)⋊C4D411yescharacteristic
115C2×Q8×D61C2311yescharacteristic
116C2×Q8×D61C2311yescharacteristic
117C2×Q8×D61C2311yescharacteristic
118C2×Dic244C2×C411yescharacteristic
119C2×Dic244C2×C411yescharacteristic
120C2×#11758202C2×C411yescharacteristic
121C2×#11758202C2×C411yescharacteristic
122C2×#11758202C2×C411yescharacteristic
123C2×#11758202C2×C411yescharacteristic
124Q16×D61—41no—
125Q16×D61—41no—
126Q16×D61—41no—
127Q16×D61—41no—
128C2×C8×D61C2311yescharacteristic
129C2×C8×D61C2311yescharacteristic
130#14519777C2×C411yescharacteristic
131#14519776—21no—
132#14519776—21no—
133#14519775C2×C411yescharacteristic
134#14519775C2×C411yescharacteristic
135Q8×Dic61C2×C411yescharacteristic
136C4×Dic122—21no—
137C4×Dic122C2×C411yescharacteristic
138#14519742—21no—
139#14519742C2×C411yescharacteristic
140C4⋊C4×D61—21no—
141C4⋊C4×D61—21no—
142C4⋊C4×D61—21no—
143C4⋊C4×D61C2311yescharacteristic
144C42×D61—21no—
145C42×D61C2311yescharacteristic
146C4⋊#92418C2×C411yescharacteristic
147#14519706C2×C411yescharacteristic
148#14519706C2×C411yescharacteristic
149#14519702C2×C411yescharacteristic
150#14519702C2×C411yescharacteristic
151#14519701C2×C411yescharacteristic
152#14519701C2×C411yescharacteristic
153#14519700C2×C411yescharacteristic
154#14519700C2×C411yescharacteristic
155C2×Q16×C61C2×C411yescharacteristic
156C2×Q16×C61C2×C411yescharacteristic
157C4⋊Q8×C61C2×C411yescharacteristic
158C4×Q8×C61C2×C411yescharacteristic
159C4⋊C8×C61C2×C411yescharacteristic
160#103×C61C2×C411yescharacteristic
161#103×C61C2×C411yescharacteristic
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—21no—
165C22×#6923—21no—
166C22×#6923C2×D411yescharacteristic
167C22×#6923C2×D411yescharacteristic
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C2×Q8×C61C22×C411yescharacteristic
171C2×Q8×C61C22×C411yescharacteristic
172C2×Q8×C61C22×C411yescharacteristic
173Q8×D61—21no—
174Q8×D61—21no—
175Q8×D61—21no—
176Q8×D61—21no—
177Q8×D61—21no—
178Q8×D61—21no—
179Q8×D61—21no—
180Q8×D61—21no—
181Q8×D61—21no—
182Q8×D61—21no—
183Q8×D61—21no—
184Q8×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61C2×D411yescharacteristic
190C2×C4×D61C2×D411yescharacteristic
191C2×C4×D61C2411yescharacteristic
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122C22×C411yescharacteristic
196C2×Dic122C22×C411yescharacteristic
197C2×Dic122C22×C411yescharacteristic
198C2×#92420—21no—
199C2×#92420—21no—
200C4⋊#6923—22no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—21no—
207C4⋊#6923—21no—
208C4⋊#6923—41no—
209C4⋊#6923—42no—
210C4⋊#6923—42no—
211C4⋊#6923#4112yes—
212C4×#6923—21no—
213C4×#6923—21no—
214C4×#6923—21no—
215C4×#6923—21no—
216C4×#6923—42no—
217C4×#6923—42no—
218C4×#6923—42no—
219C4×#6923—42no—
220C4×#6923—42no—
221D61⋊C8—21no—
222D61⋊C8—21no—
223D61⋊C8—21no—
224D61⋊C8#4112yes—
225Q16×C61—41no—
226Q16×C61—41no—
227C2×C8×C61C22×C411yescharacteristic
228C2×C8×C61C22×C411yescharacteristic
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C22×C411yescharacteristic
233C42×C61—21no—
234C42×C61C22×C411yescharacteristic
235#11758202—41no—
236#11758202—41no—
237#11758202—41no—
238#11758202—41no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—21no—
242C4⋊Dic61C22×C411yescharacteristic
243#11758196—21no—
244#11758196—21no—
245#11758196—21no—
246#11758196—21no—
247#11758196—21no—
248#11758196—21no—
249#11758196—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61C22×C411yescharacteristic
254C4×Dic61#4111yescharacteristic
255C4×Dic61#4111yescharacteristic
256C2×#92418C22×C411yescharacteristic
257C2×#92418C22×C411yescharacteristic
258Dic244—41no—
259Dic244—41no—
260C8×D61—21no—
261C8×D61—21no—
262C8×D61—21no—
263C8×D61—21no—
264C22×D61C22×D411yescharacteristic
265C2×#6923—21no—
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—22no—
271C2×#6923—21no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—21no—
276C2×#6923—21no—
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—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923#13712yes—
289Q8×C61—21no—
290Q8×C61—21no—
291Q8×C61—21no—
292Q8×C61—21no—
293Q8×C61—21no—
294Q8×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C23×C411yescharacteristic
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61C4×D411yescharacteristic
307C2×Dic61C4×D411yescharacteristic
308C2×Dic61C2×#4111yescharacteristic
309C4×D61—21no—
310C4×D61—21no—
311C4×D61—21no—
312C4×D61—21no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61C2×#4111yescharacteristic
322C4×D61C2×#4111yescharacteristic
323C4×D61H(5,𝔽2)11yescharacteristic
324C4×D61H(5,𝔽2)11yescharacteristic
325Dic122—21no—
326Dic122—21no—
327Dic122—21no—
328Dic122—21no—
329Dic122—21no—
330Dic122—21no—
331Dic122—41no—
332Dic122—41no—
333Dic122—41no—
334Dic122—41no—
335Dic122—41no—
336Dic122—41no—
337#92420—22no—
338#92420—41no—
339C8×C61—21no—
340C8×C61—21no—
341#92418—21no—
342#92418—21no—
343#23110—611nomaximal, Sylow
344C22×C61C2×C4×D411yescharacteristic
345C2×D61#54611yescharacteristic
346C2×D61#55011yescharacteristic
347C2×D61C2×#13711yescharacteristic
348C2×D61#57511yescharacteristic
349C2×D61#57811yescharacteristic
350C2×D61#57811yescharacteristic
351#6923—22no—
352#6923—41no—
353#6923—41no—
354#6923—41no—
355#6923—42no—
356#6923—81no—
357#6923—81no—
358#6923—81no—
359C4×C61—21no—
360C4×C61—21no—
361C4×C61—41no—
362C4×C61—41no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61C4×#4111yescharacteristic
366C4×C61#51811yescharacteristic
367Dic61—21no—
368Dic61—21no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61—41no—
373Dic61#55311yescharacteristic
374Dic61#55511yescharacteristic
375C2×#462—611no—
376#2365—611no—
377#2356—611no—
378#1971—611no—
379#1969—611no—
380#1960—611no—
381#1949—611no—
382#1928—611no—
383#1927—611no—
384#1878—611no—
385#1878—611no—
386#1771—611no—
387#1763—611no—
388#1763—611no—
389C4×#103—611no—
390C2×C61#236311yescharacteristic
391C2×C61C4×#13711yescharacteristic
392C2×C61#295011yescharacteristic
393D61#331211yescharacteristic
394D61#331511yescharacteristic
395D61#339811yescharacteristic
396D61#340211yescharacteristic
397C22×Q16—611no—
398C22×Q16—611no—
399C2×C4⋊Q8—611no—
400C2×C4×Q8—611no—
401C2×C4×Q8—611no—
402C2×C4×Q8—611no—
403#462—611no—
404#462—611no—
405#462—611no—
406#462—611no—
407#462—611no—
408#462—611no—
409#462—611no—
410#462#692311yescharacteristic, complemented
411C2×#107—611no—
412C2×#106—611no—
413C2×C4⋊C8—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103—611no—
422C2×#97—611no—
423C2×#97—611no—
424C2×C4×C8—611no—
425#391—611no—
426#391—611no—
427#391—611no—
428#391—611no—
429#389—1221no—
430#387—1221no—
431#387—1221no—
432#387—1221no—
433#387—1221no—
434#383—1221no—
435#382—611no—
436C4×C4⋊C4—611no—
437C4×C4⋊C4—611no—
438C4×C4⋊C4—611no—
439C4×C4⋊C4—611no—
440C4×C4⋊C4—1221no—
441#376—1221no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#336—611no—
447#336—611no—
448C61#2311011yescharacteristic, complemented, Sylow
449C22×Q8—611no—
450C22×Q8—611no—
451C22×Q8—611no—
452C2×Q16—611no—
453C2×Q16—611no—
454C2×Q16—611no—
455C2×Q16—611no—
456C2×Q16—611no—
457C2×Q16—611no—
458C2×Q16—2441no—
459C2×Q16—2441no—
460C2×Q16—2441no—
461C2×Q16—2441no—
462C2×Q16C2×#692311yescharacteristic
463C2×Q16C2×#692311yescharacteristic
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C4⋊Q8—611no—
469C4⋊Q8—611no—
470C4⋊Q8—611no—
471C4⋊Q8—1221no—
472C4⋊Q8—1221no—
473C4⋊Q8C2×#692311yescharacteristic
474C4×Q8—611no—
475C4×Q8—611no—
476C4×Q8—611no—
477C4×Q8—1221no—
478C4×Q8—1221no—
479C4×Q8—1222no—
480C4×Q8—1222no—
481C4×Q8—2441no—
482C4×Q8—2441no—
483C4×Q8C2×#692311yescharacteristic
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—611no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505#107—2441no—
506#106—2441no—
507C4⋊C8—611no—
508C4⋊C8—611no—
509C4⋊C8—611no—
510C4⋊C8C2×#692311yescharacteristic
511#103—611no—
512#103—611no—
513#103—611no—
514#103—611no—
515#103—611no—
516#103—611no—
517#103—1222no—
518#103—1222no—
519#103—1222no—
520#103—1222no—
521#103—2441no—
522#103—2441no—
523#103C2×#692311yescharacteristic
524#103C2×#692311yescharacteristic
525#97—1221no—
526#97—1221no—
527#97—2441no—
528C4×C8—2441no—
529#95—611no—
530#95—611no—
531#95—1221no—
532#95—1221no—
533#95—1221no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543#95—1221no—
544C2×Q8—611no—
545C2×Q8—611no—
546C2×Q8—611no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8—1221no—
552C2×Q8—1221no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8—1221no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×Q8C22×#692311yescharacteristic
563C2×Q8C22×#692311yescharacteristic
564C2×Q8C22×#692311yescharacteristic
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580Q16—41no—
581Q16—41no—
582Q16—2441no—
583Q16—2441no—
584Q16—2441no—
585Q16—2441no—
586Q16—2441no—
587Q16—2441no—
588C2×C8—612no—
589C2×C8—611no—
590C2×C8—611no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8C22×#692311yescharacteristic
601C2×C8C22×#692311yescharacteristic
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—612no—
606C4⋊C4—611no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1222no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—2441no—
626C4⋊C4—2442no—
627C4⋊C4—2442no—
628C4⋊C4C22×#692311yescharacteristic
629C42—21no—
630C42—611no—
631C42—611no—
632C42—611no—
633C42—1221no—
634C42—1221no—
635C42—1221no—
636C42—1221no—
637C42—1221no—
638C42—1221no—
639C42—1221no—
640C42—2442no—
641C42—2442no—
642C42—2442no—
643C42—2442no—
644C42—2442no—
645C42C22×#692311yescharacteristic
646C23—611no—
647Q8—21no—
648Q8—21no—
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—1221no—
654Q8—1221no—
655Q8—1221no—
656Q8—1221no—
657Q8—1221no—
658Q8—1221no—
659Q8—2441no—
660Q8—2441no—
661Q8—2441no—
662Q8—2441no—
663Q8—2441no—
664Q8—2441no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—611no—
670C2×C4—611no—
671C2×C4—611no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—612no—
675C2×C4—611no—
676C2×C4—611no—
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—1222no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
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×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4D4×#692311yescharacteristic
717C2×C4D4×#692311yescharacteristic
718C2×C4C23×#692311yescharacteristic
719C8—21no—
720C8—21no—
721C8—1222no—
722C8—1221no—
723C8—1221no—
724C8—2441no—
725C22—611no—
726C22—611no—
727C22—611no—
728C22—611no—
729C22—611no—
730C22—611no—
731C22C2×D4×#692311yescharacteristic
732C4—21no—
733C4—21no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—611no—
739C4—611no—
740C4—1222no—
741C4—1221no—
742C4—1221no—
743C4—4881no—
744C4—4881no—
745C4—4881no—
746C4—2441no—
747C4—2441no—
748C4—2441no—
749C4—2442no—
750C4—2441no—
751C4—2441no—
752C4—2441no—
753C4—2441no—
754C4#41×#692311yescharacteristic
755C4#1684082911yescharacteristic
756C2—611no—
757C2—611no—
758C2—611no—
759C2—611no—
760C2#2146234611yescharacteristic
761C2#137×#692311yescharacteristic
762C2#2146258011yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#462C4
socleC22×C61C2×C4×D4
prime radicalC22×D61C22×D4
cosocleC2×C4×D61C24
hypercenter#462#6923
hypocenterC61#23110
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
56. #16839973C4semidirect
57. #16839972C4semidirect
58. #16839971C4semidirect
59. #16839971C4semidirect
60. #16839970C4semidirect
61. #16839970C4semidirect
62. #16839969C4semidirect
66. C61×#462C4semidirect
410. #462#6923semidirect
448. C61#23110semidirect

Maximal subgroups

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

subgroupindex
#214623482
#214623392
#214619672
#214619652
#214619502
#214619322
#214618992
#214618982
#214618132
#214616202
#214615922
#214615912
#103×#69232
#462×D612
#2311061