Finite Group Databasebeta

← #29740638

Subgroups — #29740638

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#21449251C211yesmaximal, characteristic
2#21448745C211yesmaximal, characteristic
3#21447386C211yesmaximal, characteristic, complemented
4#21447246C211yesmaximal, characteristic, complemented
5#21447014C211yesmaximal, characteristic, complemented
6#21446457C211yesmaximal, characteristic, complemented
7#21446405C211yesmaximal, characteristic, complemented
8#21446239C211yesmaximal, characteristic, complemented
9#21446128C211yesmaximal, characteristic, complemented
10#21446123C211yesmaximal, characteristic, complemented
11#21446110C211yesmaximal, characteristic
12#21446019C211yesmaximal, characteristic, complemented
13#21445908C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#2074C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×#14519753C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519735C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519709C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30#16839691—21no—
31#16839680—21no—
32#16839660C2211yescharacteristic
33#16839659—21no—
34#16839651—21no—
35#16839651—21no—
36#16839645—21no—
37#16839640—21no—
38#16839619C2211yescharacteristic
39#16839619C2211yescharacteristic
40#16839619C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42#16839609—21no—
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#103×C61C2211yescharacteristic
53C2×#103×C61C2211yescharacteristic
54C61×#391C2211yescharacteristic
55C61×#382C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244D411yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61C2311yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C2×C8×D61—22no—
66C2×C8×D61—41no—
67C2×C8×D61—41no—
68#14519753—22no—
69#14519753—22no—
70#14519753—22no—
71#14519753—41no—
72C4×D244—22no—
73C4×D244—22no—
74#14519735—22no—
75#14519735—22no—
76#14519735—41no—
77#14519735—41no—
78C2×C4⋊Dic61D411yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C4⋊C4×D61—22no—
88C4⋊C4×D61—41no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198D411yescharacteristic
97C2×#11758198D411yescharacteristic
98C2×C4×Dic61—21no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101#14519710—41no—
102#14519709—22no—
103#14519701—22no—
104#14519701—41no—
105#14519689—22no—
106#14519689—41no—
107#14519689—41no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C22×Q8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120#103×C61—41no—
121#103×C61—41no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C23×D61C2×D411yescharacteristic
127C23×D61C2×D411yescharacteristic
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2411yescharacteristic
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C2×D244—22no—
148C2×D244—22no—
149C2×D244—41no—
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—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—42no—
161C2×C4×D61—42no—
162C2×C4×D61—81no—
163C2×C4×D61#4112yes—
164C2×C4×D61#4112yes—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179#11758198—22no—
180#11758198—22no—
181#11758198—42no—
182#11758198—42no—
183#11758198—42no—
184#11758198—42no—
185#11758198—42no—
186#11758198—42no—
187#11758198—81no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—22no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61#4112yes—
196C4⋊Dic61#4112yes—
197#11758196—42no—
198#11758196—42no—
199#11758196—42no—
200#11758196—42no—
201C4×Dic61—42no—
202C4×Dic61—42no—
203C4×Dic61—81no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C8×D61—44no—
211C23×C61C22×D411yescharacteristic
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61#12312yes—
225C22×D61#13512yes—
226Q8×C61—41no—
227Q8×C61—41no—
228Q8×C61—41no—
229Q8×C61—41no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
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—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C2×C4×C61H(5,𝔽2)11yescharacteristic
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—22no—
258C2×Dic61—22no—
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#12312yes—
272D244—44no—
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—22no—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—84no—
282C8×C61—41no—
283C8×C61—41no—
284#92418—41no—
285#92418—41no—
286#26201—611nomaximal, Sylow
287C22×C61C2×#12311yescharacteristic
288C22×C61#54611yescharacteristic
289C22×C61#54611yescharacteristic
290C22×C61C2×#13511yescharacteristic
291C22×C61#57511yescharacteristic
292C22×C61#57711yescharacteristic
293C22×C61#57811yescharacteristic
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C2×D61—41no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—81no—
311C4×C61—81no—
312C4×C61—81no—
313C4×C61—81no—
314C4×C61#52911yescharacteristic
315C4×C61#53811yescharacteristic
316C4×C61#55311yescharacteristic
317C4×C61#55311yescharacteristic
318Dic61—22no—
319Dic61—41no—
320Dic61—42no—
321Dic61—42no—
322Dic61—81no—
323Dic61—81no—
324#2415—611no—
325#2352—611no—
326#2101—611no—
327#2075—611no—
328#2074D6111yescharacteristic, complemented
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#1735—611no—
339C2×C61#244411yescharacteristic
340C2×C61#309111yescharacteristic
341C2×C61#309711yescharacteristic
342C2×C61#330011yescharacteristic
343C2×C61#330111yescharacteristic
344C2×C61#331111yescharacteristic
345C2×C61#331511yescharacteristic
346D61—42no—
347D61—42no—
348C23×C8—611no—
349C2×C22⋊Q8—611no—
350C2×C22⋊Q8—611no—
351C2×C4×D4—611no—
352C2×#117—611no—
353C2×#117—611no—
354C22×C4⋊C4—611no—
355C2×#107—611no—
356C2×#106—611no—
357C2×#103—611no—
358C2×#103—611no—
359C2×#103C2×D6111yescharacteristic
360C2×#103C2×D6111yescharacteristic
361C2×C22⋊C8—611no—
362C2×C22⋊C8—611no—
363C2×C22⋊C8—611no—
364#397—1221no—
365#394—1221no—
366#391C2×D6111yescharacteristic
367#389—611no—
368#389—1221no—
369#388—1221no—
370#388—1221no—
371#387—1221no—
372#386—1221no—
373#382C2×D6111yescharacteristic
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#340—611no—
386#340—611no—
387#340C2×D6111yescharacteristic
388#340C2×D6111yescharacteristic
389#336—611no—
390#336C2×D6111yescharacteristic
391C61#2620111yescharacteristic, complemented, Sylow
392C22×Q8C22×D6111yescharacteristic
393C22×D4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—1221no—
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—1222no—
400C22×C8—2441no—
401C22×C8—2441no—
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—1222no—
411#117—1222no—
412#117—2441no—
413#117—2441no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—1222no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—2441no—
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C4⋊C4C22×D6111yescharacteristic
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—1221no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C22⋊C4—1221no—
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42C22×D6111yescharacteristic
441#107—2441no—
442#106—1222no—
443#103—41no—
444#103—41no—
445#103—1222no—
446#103—2441no—
447C22⋊C8—1222no—
448C22⋊C8—2441no—
449C22⋊C8—2441no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—1221no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459C24—611no—
460C24—611no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—2441no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—611no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—611no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
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—1221no—
492C22×C4—4881no—
493C22×C4—2442no—
494C22×C4—2442no—
495C22×C4D4×D6111yescharacteristic
496C22×C4D4×D6111yescharacteristic
497C22×C4C23×D6111yescharacteristic
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—2444no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—612no—
518C4⋊C4—612no—
519C4⋊C4—1222no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—2442no—
527C4⋊C4—2442no—
528C4⋊C4—2442no—
529C4⋊C4—2442no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—4881no—
533C22⋊C4—2442no—
534C22⋊C4—2442no—
535C22⋊C4—2442no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C22⋊C4—2442no—
539C42—21no—
540C42—21no—
541C42—4881no—
542C42—2442no—
543C42—2442no—
544C23—612no—
545C23—612no—
546C23—1221no—
547C23—1221no—
548C23—1221no—
549C23—1221no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23—1221no—
558C23C2×D4×D6111yescharacteristic
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—41no—
563D4—2444no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
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—612no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1221no—
590C2×C4—1222no—
591C2×C4—1221no—
592C2×C4—1222no—
593C2×C4—1221no—
594C2×C4—4884no—
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—2441no—
609C2×C4#41×D6111yescharacteristic
610C2×C4#41×D6111yescharacteristic
611C2×C4#41×D6111yescharacteristic
612C2×C4#41×D6111yescharacteristic
613C2×C4#1451982211yescharacteristic
614C2×C4#1451982311yescharacteristic
615C8—41no—
616C8—41no—
617C8—2441no—
618C8—2441no—
619C22—1222no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—1222no—
624C22—1222no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22—2441no—
630C22—2441no—
631C22—2441no—
632C22—2441no—
633C22#123×D6111yescharacteristic
634C22#1684040511yescharacteristic
635C22#1684040911yescharacteristic
636C22#135×D6111yescharacteristic
637C22#1684056111yescharacteristic
638C22#1684056911yescharacteristic
639C22#1684057811yescharacteristic
640C4—41no—
641C4—41no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4—81no—
646C4—1222no—
647C4—4881no—
648C4—4881no—
649C4—2441no—
650C4—2442no—
651C4—2442no—
652C4#1684029511yescharacteristic
653C4#1684034811yescharacteristic
654C4#1684045711yescharacteristic
655C4#1684046311yescharacteristic
656C2—2442no—
657C2—2442no—
658C2#2144957211yescharacteristic
659C2#2145573711yescharacteristic
660C2#2145578511yescharacteristic
661C2#2145771311yescharacteristic
662C2#2145772011yescharacteristic
663C2#2145786211yescharacteristic
664C2#2145791411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2074C2
socleC23×C61C22×D4
prime radicalC22×D244D4
hypercenter#2074D61
hypocenterC61#26201
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2074

Complements

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

NH ≅ G/Ntype
3. #21447386C2semidirect
4. #21447246C2semidirect
5. #21447014C2semidirect
6. #21446457C2semidirect
7. #21446405C2semidirect
8. #21446239C2semidirect
9. #21446128C2semidirect
10. #21446123C2semidirect
12. #21446019C2semidirect
13. #21445908C2semidirect
14. #21445534C2semidirect
15. C61×#2074C2semidirect
328. #2074D61semidirect
391. C61#26201semidirect

Maximal subgroups

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

subgroupindex
#214492512
#214487452
#214473862
#214472462
#214470142
#214464572
#214464052
#214462392
#214461282
#214461232
#214461102
#214460192
#214459082
#214455342
C61×#20742
#2620161