Finite Group Databasebeta

← #29740629

Subgroups — #29740629

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#21449248C211yesmaximal, characteristic
2#21447386C211yesmaximal, characteristic, complemented
3#21447245C211yesmaximal, characteristic, complemented
4#21447238C211yesmaximal, characteristic, complemented
5#21447015C211yesmaximal, characteristic, complemented
6#21446460C211yesmaximal, characteristic, complemented
7#21446404C211yesmaximal, characteristic, complemented
8#21446240C211yesmaximal, characteristic, complemented
9#21446131C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21446112C211yesmaximal, characteristic
12#21446016C211yesmaximal, characteristic, complemented
13#21445909C211yesmaximal, characteristic, complemented
14#21445535C211yesmaximal, characteristic, complemented
15C61×#2352C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×#14519756C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×#14519700C2211yescharacteristic
23C2×#14519700C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29#16839690—21no—
30#16839676—21no—
31#16839668C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839657—21no—
34#16839656—21no—
35#16839622C2211yescharacteristic
36#16839524C2211yescharacteristic
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4×D4×C61C2211yescharacteristic
49C2×#117×C61C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C61×#388—21no—
52C61×#387—21no—
53C61×#386—21no—
54C61×#382C2211yescharacteristic
55C61×#380C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61—21no—
59C22×Dic122C2311yescharacteristic
60C22×#92418—22no—
61C22×#92418—41no—
62C22×#92418—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519756—22no—
68#14519756—22no—
69#14519756—22no—
70#14519756—41no—
71#14519736—22no—
72#14519736—41no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C4×Dic61—21no—
84#14519710—41no—
85#14519708—22no—
86#14519700—22no—
87#14519700—41no—
88#14519700—41no—
89#14519700—41no—
90C22⋊#92418—22no—
91C22⋊#92418—41no—
92C22⋊#92418—41no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97C22×D4×C61D411yescharacteristic
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103#117×C61—22no—
104#117×C61—41no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—41no—
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61D411yescharacteristic
117C2×C22⋊C4×C61D411yescharacteristic
118C2×C42×C61—21no—
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C24×C61C2×D411yescharacteristic
127C24×C61C2×D411yescharacteristic
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C2×D4×C61—41no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
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—42no—
146C22×C4×C61—42no—
147C22×C4×C61—81no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61#4112yes—
153C22×C4×C61#4112yes—
154C22×C4×C61C2411yescharacteristic
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
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#4112yes—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—42no—
178C22⋊C4×C61—42no—
179C22⋊C4×C61—81no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—42no—
183C42×C61—81no—
184C22⋊Dic61—42no—
185C22⋊Dic61—42no—
186C22⋊Dic61—42no—
187C22⋊Dic61—42no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61#4112yes—
194#11758196—42no—
195#11758196—42no—
196#11758196—42no—
197C4×Dic61—42no—
198C2×#92418—21no—
199C2×#92418—21no—
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—44no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61#12312yes—
224C23×C61#13512yes—
225C23×C61C22×D411yescharacteristic
226D4×C61—44no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—22no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
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—84no—
259C2×C4×C61#12312yes—
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61H(5,𝔽2)11yescharacteristic
265C2×C4×C61H(5,𝔽2)11yescharacteristic
266C2×Dic61—22no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278Dic122—41no—
279Dic122—41no—
280Dic122—41no—
281Dic122—41no—
282#92418—41no—
283#92418—41no—
284#92418—41no—
285#92418—41no—
286#26201—611nomaximal, Sylow
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61C2×#12311yescharacteristic
302C22×C61#54611yescharacteristic
303C22×C61#54611yescharacteristic
304C22×C61C2×#13511yescharacteristic
305C22×C61#57511yescharacteristic
306C22×C61#57711yescharacteristic
307C22×C61#57811yescharacteristic
308C4×C61—22no—
309C4×C61—41no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—42no—
313C4×C61—81no—
314C4×C61—81no—
315C4×C61—81no—
316C4×C61#52911yescharacteristic
317C4×C61#53811yescharacteristic
318C4×C61#55311yescharacteristic
319C4×C61#55311yescharacteristic
320Dic61—42no—
321Dic61—81no—
322Dic61—81no—
323Dic61—81no—
324#2415—611no—
325#2352D6111yescharacteristic
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#1735—611no—
339C2×C61—42no—
340C2×C61—42no—
341C2×C61#244411yescharacteristic
342C2×C61#309111yescharacteristic
343C2×C61#309711yescharacteristic
344C2×C61#330011yescharacteristic
345C2×C61#330111yescharacteristic
346C2×C61#331111yescharacteristic
347C2×C61#331511yescharacteristic
348C23×C8—611no—
349C2×C22⋊Q8—611no—
350C2×C22⋊Q8—611no—
351C2×C4×D4C2×D6111yescharacteristic
352C2×#117—611no—
353C2×#117C2×D6111yescharacteristic
354C22×C4⋊C4C2×D6111yescharacteristic
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—21no—
370#388—1221no—
371#387—21no—
372#386—21no—
373#382C2×D6111yescharacteristic
374#380—611no—
375#380C2×D6111yescharacteristic
376#380C2×D6111yescharacteristic
377C4×C4⋊C4C2×D6111yescharacteristic
378C4×C22⋊C4—21no—
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#340—611no—
388#340—611no—
389#336—611no—
390#336—611no—
391C61#2620111yescharacteristic, complemented, Sylow
392C22×Q8—611no—
393C22×D4C22⋊D6111yescharacteristic
394C23×C4—21no—
395C23×C4C22×D6111yescharacteristic
396C23×C4C22×D6111yescharacteristic
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—1222no—
402C22×C8—2441no—
403C22×C8—2441no—
404C22⋊Q8—1222no—
405C22⋊Q8—1222no—
406C22⋊Q8—1222no—
407C22⋊Q8—2441no—
408C4×D4—22no—
409C4×D4—22no—
410#117—22no—
411#117—41no—
412#117—1222no—
413#117—2441no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4C22⋊D6111yescharacteristic
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—21no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4C22⋊D6111yescharacteristic
436C2×C22⋊C4C22⋊D6111yescharacteristic
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—1221no—
440C2×C42C22×D6111yescharacteristic
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—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459C24C2×C22⋊D6111yescharacteristic
460C24C2×C22⋊D6111yescharacteristic
461C2×Q8—1221no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—41no—
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—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4#1175822212yes—
492C22×C4#1175822212yes—
493C22×C4C2×C22⋊D6111yescharacteristic
494C22×C4C2×C22⋊D6111yescharacteristic
495C22×C4C2×C22⋊D6111yescharacteristic
496C22×C4C2×C22⋊D6111yescharacteristic
497C22×C4C23×D6111yescharacteristic
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
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—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—612no—
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#1175822412yes—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4—2442no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C22⋊C4—2442no—
539C42—21no—
540C42—21no—
541C42—42no—
542C42—81no—
543C42—2442no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23#1451976012yes—
557C23#1451979712yes—
558C23C22×C22⋊D6111yescharacteristic
559Q8—2441no—
560Q8—2441no—
561Q8—2441no—
562Q8—2441no—
563D4—44no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
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—84no—
596C2×C4—1222no—
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#1451976012yes—
609C2×C4#41×D6111yescharacteristic
610C2×C4C2×#1175822411yescharacteristic
611C2×C4C2×#1175822211yescharacteristic
612C2×C4C2×#1175822211yescharacteristic
613C2×C4#1451982211yescharacteristic
614C2×C4#1451982311yescharacteristic
615C8—2441no—
616C8—2441no—
617C8—2441no—
618C8—2441no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22C2×#1451976011yescharacteristic
634C22#1684040011yescharacteristic
635C22#1684040611yescharacteristic
636C22C2×#1451979711yescharacteristic
637C22#1684056011yescharacteristic
638C22#1684057311yescharacteristic
639C22#1684057711yescharacteristic
640C4—22no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—81no—
648C4—4881no—
649C4—4881no—
650C4—4881no—
651C4—2442no—
652C4#1684029211yescharacteristic
653C4#1684034511yescharacteristic
654C4#1684045811yescharacteristic
655C4#1684046111yescharacteristic
656C2—42no—
657C2—42no—
658C2#2144956311yescharacteristic
659C2#2145573211yescharacteristic
660C2#2145578811yescharacteristic
661C2#2145770611yescharacteristic
662C2#2145771511yescharacteristic
663C2#2145785511yescharacteristic
664C2#2145790911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2352C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#2352D61
hypocenterC61#26201
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #21447386C2semidirect
3. #21447245C2semidirect
4. #21447238C2semidirect
5. #21447015C2semidirect
6. #21446460C2semidirect
7. #21446404C2semidirect
8. #21446240C2semidirect
9. #21446131C2semidirect
10. #21446126C2semidirect
12. #21446016C2semidirect
13. #21445909C2semidirect
14. #21445535C2semidirect
391. C61#26201semidirect

Maximal subgroups

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

subgroupindex
#214492482
#214473862
#214472452
#214472382
#214470152
#214464602
#214464042
#214462402
#214461312
#214461262
#214461122
#214460162
#214459092
#214455352
C61×#23522
#2620161