Finite Group Databasebeta

← #29748205

Subgroups — #29748205

Order 15616.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448855C211yesmaximal, characteristic
2#21447134C211yesmaximal, characteristic, complemented
3#21447001C211yesmaximal, characteristic
4#21446952C211yesmaximal, characteristic, complemented
5#21446820C211yesmaximal, characteristic
6#21446772C211yesmaximal, characteristic, complemented
7#21446498C211yesmaximal, characteristic, complemented
8#21446457C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446411C211yesmaximal, characteristic, complemented
11#21446156C211yesmaximal, characteristic, complemented
12#21446132C211yesmaximal, characteristic, complemented
13#21445911C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2492C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C4×#92418C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839662—21no—
33#16839660C2211yescharacteristic
34#16839651—21no—
35#16839638—21no—
36C4×C4⋊Dic61C2211yescharacteristic
37#16839609—21no—
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4⋊Q8×C61C2211yescharacteristic
49C2×C22⋊Q8×C61C2211yescharacteristic
50C61×#400—21no—
51C61×#393—21no—
52C61×#391—21no—
53C61×#391C2211yescharacteristic
54C61×#391C2211yescharacteristic
55C61×#388—21no—
56C61×#380C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C22×C4×D61—21no—
62C2×#11758201—22no—
63C2×#11758201—41no—
64C2×#11758201—41no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519751—22no—
70#14519751—22no—
71C4×D244—22no—
72C4×D244—41no—
73#14519736—22no—
74#14519736—41no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86#14519710—22no—
87C4⋊#92418—41no—
88#14519701—22no—
89#14519701—22no—
90#14519701—41no—
91#14519697—22no—
92#14519697—22no—
93#14519697—41no—
94C22⋊#92418—41no—
95C22⋊#92418—41no—
96C4×#92418—41no—
97#14519684—21no—
98#14519684—21no—
99C22×Q8×C61—21no—
100C22×Q8×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102C4⋊Q8×C61—22no—
103C4⋊Q8×C61—41no—
104C22⋊Q8×C61—22no—
105C22⋊Q8×C61—41no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61D411yescharacteristic
114C2×C22⋊C4×C61D411yescharacteristic
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118#95×C61—21no—
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C24×C61C2×D411yescharacteristic
127C23×D61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—42no—
135C2×Q8×C61—42no—
136C2×Q8×C61—81no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—24no—
154C2×C22⋊D61—81no—
155C2×C22⋊D61—81no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244#4112yes—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61—81no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—42no—
174C4⋊C4×C61—42no—
175C4⋊C4×C61#4112yes—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—42no—
179C22⋊C4×C61—81no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—81no—
185C22⋊Dic61—42no—
186#11758201—44no—
187#11758198—24no—
188#11758198—42no—
189#11758198—42no—
190#11758198—81no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61#4112yes—
196C4⋊Dic61#4112yes—
197#11758196—81no—
198C4×Dic61—42no—
199C4×Dic61—81no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61C22×D411yescharacteristic
220C22×D61—22no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—41no—
227Q8×C61—41no—
228Q8×C61—41no—
229Q8×C61—41no—
230Q8×C61—41no—
231Q8×C61—84no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—22no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61#13512yes—
262C2×C4×C61#13712yes—
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×C4×C61H(5,𝔽2)11yescharacteristic
269C22⋊D61—84no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279D244—22no—
280D244—22no—
281D244—41no—
282D244—41no—
283C4×D61—84no—
284#92418—41no—
285#92418—41no—
286#92418—41no—
287#92418—41no—
288#26731—611nomaximal, Sylow
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61#52511yescharacteristic
297C22×C61#54611yescharacteristic
298C22×C61#54611yescharacteristic
299C22×C61C2×#13511yescharacteristic
300C22×C61C2×#13711yescharacteristic
301C22×C61#57611yescharacteristic
302C22×C61#57711yescharacteristic
303C2×D61—42no—
304C2×D61—42no—
305C2×D61—42no—
306C2×D61—81no—
307C2×D61—81no—
308C2×D61—81no—
309C2×D61—81no—
310C4×C61—22no—
311C4×C61—22no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—42no—
315C4×C61—41no—
316C4×C61—81no—
317C4×C61—81no—
318C4×C61—81no—
319C4×C61#52911yescharacteristic
320C4×C61#53811yescharacteristic
321C4×C61#55511yescharacteristic
322C4×C61#55911yescharacteristic
323Dic61—42no—
324Dic61—42no—
325Dic61—81no—
326#2492D6111yescharacteristic, complemented
327#2363—611no—
328#2055—611no—
329#2033—611no—
330#2023—611no—
331#2000—611no—
332#1988—611no—
333#1933—611no—
334#1928—611no—
335#1923—611no—
336#1921—611no—
337#1877—611no—
338#1873—611no—
339#1825—611no—
340C4×#102—611no—
341C2×C61—81no—
342C2×C61#245911yescharacteristic
343C2×C61#310711yescharacteristic
344C2×C61#311811yescharacteristic
345C2×C61#329711yescharacteristic
346C2×C61#330411yescharacteristic
347C2×C61#331411yescharacteristic
348C2×C61#332911yescharacteristic
349D61—82no—
350C22×SD16—611no—
351C2×C4⋊Q8C2×D6111yescharacteristic
352C2×C22⋊Q8C2×D6111yescharacteristic
353C2×#121—611no—
354C2×C4×D4—611no—
355C2×#117—611no—
356C2×#107—611no—
357C2×C4⋊C8—611no—
358C2×#103—611no—
359C2×#103—611no—
360C2×#103—611no—
361C2×#102—611no—
362C2×#102—611no—
363C2×#102—611no—
364C2×C22⋊C8—611no—
365C2×C22⋊C8—611no—
366C2×C4×C8—611no—
367#400—21no—
368#393—21no—
369#391—21no—
370#391C2×D6111yescharacteristic
371#391C2×D6111yescharacteristic
372#390—611no—
373#390—1221no—
374#389—611no—
375#388—21no—
376#388—1221no—
377#386—1221no—
378#380C2×D6111yescharacteristic
379C4×C4⋊C4—611no—
380C4×C4⋊C4C2×D6111yescharacteristic
381C4×C22⋊C4—1221no—
382C4×C22⋊C4C2×D6111yescharacteristic
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340—611no—
389#340—611no—
390#340—611no—
391#336—611no—
392#336—611no—
393C61#2673111yescharacteristic, complemented, Sylow
394C22×Q8—21no—
395C22×Q8C22×D6111yescharacteristic
396C22×D4—611no—
397C22×D4—1221no—
398C23×C4—1221no—
399C23×C4C22×D6111yescharacteristic
400C2×SD16—1222no—
401C2×SD16—2441no—
402C2×SD16—2441no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—611no—
407C4⋊Q8—22no—
408C4⋊Q8—41no—
409C22⋊Q8—22no—
410C22⋊Q8—41no—
411#121—1222no—
412#121—1222no—
413C4×D4—1222no—
414C4×D4—2441no—
415#117—1222no—
416#117—2441no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4C22×D6111yescharacteristic
424C2×C4⋊C4C22×D6111yescharacteristic
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4C22⋊D6111yescharacteristic
434C2×C22⋊C4C22⋊D6111yescharacteristic
435C2×C42—21no—
436C2×C42—1221no—
437C2×C42—1221no—
438C2×C42C22×D6111yescharacteristic
439C2×C42C22×D6111yescharacteristic
440#107—1222no—
441C4⋊C8—2441no—
442#103—1222no—
443#103—1222no—
444#103—2441no—
445#102—1222no—
446#102—1222no—
447#102—2441no—
448C22⋊C8—2441no—
449C22⋊C8—2441no—
450C4×C8—2441no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—1221no—
458#95—1221no—
459#95C22⋊D6111yescharacteristic
460#95C22⋊D6111yescharacteristic
461C24—1221no—
462C24C2×C22⋊D6111yescharacteristic
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×D4—612no—
473C2×D4—1224no—
474C2×D4—1221no—
475C2×D4—1221no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—4881no—
480C2×D4—4881no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—4881no—
495C22×C4—2442no—
496C22×C4—2442no—
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C2×C22⋊D6111yescharacteristic
499C22×C4C2×C22⋊D6111yescharacteristic
500C22×C4C2×C22⋊D6111yescharacteristic
501C22×C4C2×C22⋊D6111yescharacteristic
502C22×C4C23×D6111yescharacteristic
503SD16—2444no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—612no—
524C4⋊C4—612no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—4881no—
530C4⋊C4#1175822412yes—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4—1224no—
536C22⋊C4—4881no—
537C22⋊C4—2442no—
538C22⋊C4—2442no—
539C22⋊C4—2442no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—81no—
545C42—4881no—
546C42—2442no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—1222no—
555C23—2441no—
556C23—2441no—
557C23—2441no—
558C23—2441no—
559C23—2441no—
560C23—2441no—
561C23C22×C22⋊D6111yescharacteristic
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—84no—
567D4—1222no—
568D4—1222no—
569D4—4884no—
570D4—2441no—
571D4—2441no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—4884no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4#1451979712yes—
612C2×C4#1451980812yes—
613C2×C4#41×D6111yescharacteristic
614C2×C4#41×D6111yescharacteristic
615C2×C4#41×D6111yescharacteristic
616C2×C4C2×#1175822411yescharacteristic
617C2×C4#1451982211yescharacteristic
618C2×C4#1451982311yescharacteristic
619C8—2441no—
620C8—2441no—
621C8—2441no—
622C8—2441no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—4881no—
631C22—4881no—
632C22—4881no—
633C22—4881no—
634C22—2442no—
635C22—2442no—
636C22—2442no—
637C22#1684026911yescharacteristic
638C22#1684040011yescharacteristic
639C22#1684040611yescharacteristic
640C22C2×#1451979711yescharacteristic
641C22C2×#1451980811yescharacteristic
642C22#1684056511yescharacteristic
643C22#1684057011yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—4881no—
654C4—2442no—
655C4—2442no—
656C4#1684029111yescharacteristic
657C4#1684034611yescharacteristic
658C4#1684047411yescharacteristic
659C4#1684049411yescharacteristic
660C2—81no—
661C2—4882no—
662C2#2144975211yescharacteristic
663C2#2145588411yescharacteristic
664C2#2145599711yescharacteristic
665C2#2145766911yescharacteristic
666C2#2145775211yescharacteristic
667C2#2145789411yescharacteristic
668C2#2145811311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2492C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2492D61
hypocenterC61#26731
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2492

Complements

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

NH ≅ G/Ntype
2. #21447134C2semidirect
4. #21446952C2semidirect
6. #21446772C2semidirect
7. #21446498C2semidirect
8. #21446457C2semidirect
9. #21446427C2semidirect
10. #21446411C2semidirect
11. #21446156C2semidirect
12. #21446132C2semidirect
13. #21445911C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2492C2semidirect
326. #2492D61semidirect
393. C61#26731semidirect

Maximal subgroups

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

subgroupindex
#214488552
#214471342
#214470012
#214469522
#214468202
#214467722
#214464982
#214464572
#214464272
#214464112
#214461562
#214461322
#214459112
C4×#145196972
C61×#24922
#2673161