Finite Group Databasebeta

← #29740635

Subgroups — #29740635

Order 15616.

794 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449242C211yesmaximal, characteristic
2#21448749C211yesmaximal, characteristic
3#21447390C211yesmaximal, characteristic, complemented
4#21447246C211yesmaximal, characteristic, complemented
5#21447241C211yesmaximal, characteristic, complemented
6#21447018C211yesmaximal, characteristic, complemented
7#21446458C211yesmaximal, characteristic, complemented
8#21446407C211yesmaximal, characteristic, complemented
9#21446242C211yesmaximal, characteristic, complemented
10#21446131C211yesmaximal, characteristic, complemented
11#21446125C211yesmaximal, characteristic, complemented
12#21446111C211yesmaximal, characteristic
13#21446018C211yesmaximal, characteristic, complemented
14#21445908C211yesmaximal, characteristic, complemented
15C61×#1735C211yesmaximal, characteristic, complemented
16C2×#14519757C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×C4⋊C4×D61C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519702C2211yescharacteristic
23C2×#14519702C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29#16839687—21no—
30#16839678—21no—
31#16839667C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839660—21no—
34#16839656—21no—
35#16839653—21no—
36#16839646—21no—
37#16839638—21no—
38#16839627C2211yescharacteristic
39#16839622C2211yescharacteristic
40#16839619C2211yescharacteristic
41#16839619C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758198—21no—
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C23×C8×C61C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C22×C22⋊D61D411yescharacteristic
61C22×C4×D61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519757—22no—
66#14519757—41no—
67#14519756—22no—
68#14519756—22no—
69C4×C22⋊D61—22no—
70C4×C22⋊D61—22no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196D411yescharacteristic
79C4⋊C4×D61—22no—
80C4⋊C4×D61—41no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61D411yescharacteristic
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198D411yescharacteristic
88C2×C4×Dic61—21no—
89C2×C4×Dic61C2311yescharacteristic
90#14519710—41no—
91#14519708—22no—
92#14519702—41no—
93#14519702—41no—
94#14519700—22no—
95#14519700—41no—
96C22⋊#92418—22no—
97#14519689—41no—
98#14519689—41no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108C23×C4×C61C2311yescharacteristic
109C22×C8×C61—22no—
110C22×C8×C61—41no—
111C22×C8×C61—41no—
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114#117×C61—22no—
115#117×C61—22no—
116#117×C61—41no—
117#117×C61—41no—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C42×C61—21no—
125C2×C42×C61—21no—
126C24×C61C2×D411yescharacteristic
127C23×D61C2×D411yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61#4112yes—
138C22×C4×C61#4112yes—
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—41no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61—81no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—44no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61#4112yes—
179C4⋊C4×C61#4112yes—
180C22⋊C4×C61—42no—
181C22⋊C4×C61—42no—
182C42×C61—42no—
183C42×C61—42no—
184C22⋊Dic61—22no—
185C22⋊Dic61—42no—
186C22⋊Dic61—81no—
187#11758198—22no—
188#11758198—42no—
189#11758198—42no—
190#11758198—42no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—42no—
198C4⋊Dic61—42no—
199#11758196—22no—
200#11758196—42no—
201#11758196—42no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—81no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61#12312yes—
218C23×C61C22×D411yescharacteristic
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61#13512yes—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61#12312yes—
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61H(5,𝔽2)11yescharacteristic
250C2×C4×C61H(5,𝔽2)11yescharacteristic
251C22⋊D61—44no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C4×D61—41no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—84no—
278Dic122—41no—
279Dic122—41no—
280Dic122—41no—
281Dic122—41no—
282C8×C61—41no—
283C8×C61—41no—
284#92418—41no—
285#92418—41no—
286#26201—611nomaximal, Sylow
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61C2×#12311yescharacteristic
295C22×C61#54611yescharacteristic
296C22×C61#54611yescharacteristic
297C22×C61C2×#13511yescharacteristic
298C22×C61#57511yescharacteristic
299C22×C61#57711yescharacteristic
300C22×C61#57811yescharacteristic
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C4×C61—22no—
309C4×C61—42no—
310C4×C61—42no—
311C4×C61—81no—
312C4×C61—81no—
313C4×C61#52911yescharacteristic
314C4×C61#53811yescharacteristic
315C4×C61#55311yescharacteristic
316C4×C61#55311yescharacteristic
317Dic61—41no—
318Dic61—41no—
319Dic61—41no—
320Dic61—81no—
321Dic61—81no—
322Dic61—81no—
323Dic61—81no—
324#2415—611no—
325#2352—611no—
326#2101—611no—
327#2075—611no—
328#2074—611no—
329#2035—611no—
330#1928—611no—
331#1920—611no—
332#1892—611no—
333#1873—611no—
334#1872—611no—
335#1869—611no—
336#1854—611no—
337#1824—611no—
338#1735D6111yescharacteristic, complemented
339C2×C61—42no—
340C2×C61#244411yescharacteristic
341C2×C61#309111yescharacteristic
342C2×C61#309711yescharacteristic
343C2×C61#330011yescharacteristic
344C2×C61#330111yescharacteristic
345C2×C61#331111yescharacteristic
346C2×C61#331511yescharacteristic
347D61—42no—
348C23×C8C2×D6111yescharacteristic
349C2×C22⋊Q8—611no—
350C2×C22⋊Q8—611no—
351C2×C4×D4—611no—
352C2×#117C2×D6111yescharacteristic
353C2×#117C2×D6111yescharacteristic
354C22×C4⋊C4—611no—
355C2×#107—611no—
356C2×#106—611no—
357C2×#103—611no—
358C2×#103—611no—
359C2×#103—611no—
360C2×#103—611no—
361C2×C22⋊C8—611no—
362C2×C22⋊C8—611no—
363C2×C22⋊C8—611no—
364#397—1221no—
365#394—1221no—
366#391—611no—
367#389—611no—
368#389—1221no—
369#388—1221no—
370#388—1221no—
371#387—1221no—
372#386—1221no—
373#382—611no—
374#380—611no—
375#380—611no—
376#380—611no—
377C4×C4⋊C4—611no—
378C4×C22⋊C4—1221no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340C2×D6111yescharacteristic
386#340C2×D6111yescharacteristic
387#340C2×D6111yescharacteristic
388#340C2×D6111yescharacteristic
389#336—611no—
390#336—611no—
391C61#2620111yescharacteristic, complemented, Sylow
392C22×Q8—611no—
393C22×D4—611no—
394C23×C4—611no—
395C23×C4—1221no—
396C23×C4C22×D6111yescharacteristic
397C22×C8—22no—
398C22×C8—41no—
399C22×C8—41no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8C22×D6111yescharacteristic
403C22×C8C22×D6111yescharacteristic
404C22⋊Q8—1222no—
405C22⋊Q8—1222no—
406C22⋊Q8—1222no—
407C22⋊Q8—2441no—
408C4×D4—1222no—
409C4×D4—1222no—
410#117—22no—
411#117—22no—
412#117—41no—
413#117—41no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—1222no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—2441no—
424C2×C4⋊C4C22×D6111yescharacteristic
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C4⋊C4C22×D6111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1221no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—611no—
440C2×C42—1221no—
441#107—2441no—
442#106—1222no—
443#103—1222no—
444#103—2441no—
445#103—2441no—
446#103—2441no—
447C22⋊C8—1222no—
448C22⋊C8—2441no—
449C22⋊C8—2441no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454#95—1221no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459C24—611no—
460C24D4×D6111yescharacteristic
461C2×Q8—1221no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—2441no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—4881no—
492C22×C4—2442no—
493C22×C4—2442no—
494C22×C4#1175822212yes—
495C22×C4D4×D6111yescharacteristic
496C22×C4#1175822612yes—
497C22×C4C23×D6111yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—44no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—1222no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—2442no—
525C4⋊C4—2442no—
526C4⋊C4—2442no—
527C4⋊C4—2442no—
528C4⋊C4#1175822212yes—
529C4⋊C4#1175822212yes—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—4881no—
535C22⋊C4—2442no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C22⋊C4—2442no—
539C42—42no—
540C42—42no—
541C42—1221no—
542C42—1221no—
543C42—4881no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—612no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23#1451976212yes—
558C23C2×D4×D6111yescharacteristic
559Q8—2441no—
560Q8—2441no—
561Q8—2441no—
562Q8—2441no—
563D4—2444no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—4884no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4#1451976212yes—
609C2×C4C2×#1175822211yescharacteristic
610C2×C4C2×#1175822211yescharacteristic
611C2×C4C2×#1175822211yescharacteristic
612C2×C4C2×#1175822611yescharacteristic
613C2×C4#1451982211yescharacteristic
614C2×C4#1451982211yescharacteristic
615C8—41no—
616C8—41no—
617C8—2441no—
618C8—2441no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—1222no—
627C22—1222no—
628C22—1222no—
629C22—2441no—
630C22—2441no—
631C22—2441no—
632C22—2441no—
633C22C2×#1451976211yescharacteristic
634C22#1684040211yescharacteristic
635C22#1684040211yescharacteristic
636C22#135×D6111yescharacteristic
637C22#1684055911yescharacteristic
638C22#1684056911yescharacteristic
639C22#1684057611yescharacteristic
640C4—22no—
641C4—42no—
642C4—42no—
643C4—81no—
644C4—81no—
645C4—4881no—
646C4—4881no—
647C4—4881no—
648C4—4881no—
649C4—2441no—
650C4—2441no—
651C4—2441no—
652C4#1684029611yescharacteristic
653C4#1684035011yescharacteristic
654C4#1684046011yescharacteristic
655C4#1684046011yescharacteristic
656C2—42no—
657C2—2442no—
658C2#2144956911yescharacteristic
659C2#2145573611yescharacteristic
660C2#2145579111yescharacteristic
661C2#2145770711yescharacteristic
662C2#2145772211yescharacteristic
663C2#2145785111yescharacteristic
664C2#2145791111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1735C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1735D61
hypocenterC61#26201
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
3. #21447390C2semidirect
4. #21447246C2semidirect
5. #21447241C2semidirect
6. #21447018C2semidirect
7. #21446458C2semidirect
8. #21446407C2semidirect
9. #21446242C2semidirect
10. #21446131C2semidirect
11. #21446125C2semidirect
13. #21446018C2semidirect
14. #21445908C2semidirect
15. C61×#1735C2semidirect
338. #1735D61semidirect
391. C61#26201semidirect

Maximal subgroups

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

subgroupindex
#214492422
#214487492
#214473902
#214472462
#214472412
#214470182
#214464582
#214464072
#214462422
#214461312
#214461252
#214461112
#214460182
#214459082
C61×#17352
#2620161