Finite Group Databasebeta

← #29740632

Subgroups — #29740632

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#21449244C211yesmaximal, characteristic
2#21448744C211yesmaximal, characteristic
3#21447392C211yesmaximal, characteristic, complemented
4#21447242C211yesmaximal, characteristic, complemented
5#21447240C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21446462C211yesmaximal, characteristic, complemented
8#21446407C211yesmaximal, characteristic, complemented
9#21446239C211yesmaximal, characteristic, complemented
10#21446128C211yesmaximal, characteristic, complemented
11#21446108C211yesmaximal, characteristic
12#21446021C211yesmaximal, characteristic, complemented
13#21445909C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1872C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×#14519753C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C2×#14519711C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519701C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27#16839688—21no—
28#16839678—21no—
29#16839669C2211yescharacteristic
30#16839661C2211yescharacteristic
31#16839658—21no—
32#16839652—21no—
33#16839650—21no—
34#16839643—21no—
35#16839641—21no—
36#16839627C2211yescharacteristic
37#16839622C2211yescharacteristic
38#16839622C2211yescharacteristic
39#16839619C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C4×C22⋊Dic61—21no—
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×C22⋊D61D411yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C2×C8×D61—22no—
64C2×C8×D61—41no—
65C2×C8×D61—41no—
66#14519753—22no—
67#14519753—22no—
68C4×C22⋊D61—22no—
69C4×C22⋊D61—22no—
70#14519735—22no—
71#14519735—22no—
72#14519735—41no—
73#14519735—41no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196D411yescharacteristic
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61D411yescharacteristic
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198D411yescharacteristic
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61C2311yescharacteristic
93#14519711—41no—
94#14519708—22no—
95#14519701—41no—
96#14519701—41no—
97C22⋊#92418—41no—
98#14519689—22no—
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—
108C22×Q8×C61C2311yescharacteristic
109C23×C4×C61—21no—
110C23×C4×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—41no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—41no—
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61—21no—
123#103×C61—22no—
124#103×C61—41no—
125C22⋊C8×C61—41no—
126C24×C61C2×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×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—42no—
145C22×C4×C61—42no—
146C22×C4×C61—81no—
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2411yescharacteristic
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—41no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
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—42no—
176C4⋊C4×C61—42no—
177C4⋊C4×C61#4112yes—
178C4⋊C4×C61#4112yes—
179C22⋊C4×C61—42no—
180C22⋊Dic61—22no—
181C22⋊Dic61—42no—
182C22⋊Dic61—42no—
183#11758198—22no—
184#11758198—42no—
185#11758198—42no—
186#11758198—42no—
187#11758198—81no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—42no—
197#11758196—22no—
198#11758196—42no—
199C4×Dic61—21no—
200C4×Dic61—21no—
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×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61#13512yes—
218C23×C61C22×D411yescharacteristic
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61#12312yes—
226Q8×C61—41no—
227Q8×C61—41no—
228Q8×C61—41no—
229Q8×C61—41no—
230C2×C4×C61—21no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
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—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—84no—
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C2×C4×C61H(5,𝔽2)11yescharacteristic
256C22⋊D61—44no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—41no—
266C2×Dic61—41no—
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#12312yes—
278C4×D61—22no—
279C4×D61—22no—
280C4×D61—22no—
281C4×D61—22no—
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—41no—
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—22no—
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#1872D6111yescharacteristic, complemented
335#1869—611no—
336#1854—611no—
337#1824—611no—
338#1735—611no—
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×C8—611no—
349C2×C22⋊Q8—611no—
350C2×C22⋊Q8C2×D6111yescharacteristic
351C2×C4×D4—611no—
352C2×#117—611no—
353C2×#117—611no—
354C22×C4⋊C4C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
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#340—611no—
386#340—611no—
387#340C2×D6111yescharacteristic
388#340C2×D6111yescharacteristic
389#336—611no—
390#336—611no—
391C61#2620111yescharacteristic, complemented, Sylow
392C22×Q8C22×D6111yescharacteristic
393C22×D4—611no—
394C23×C4—21no—
395C23×C4—611no—
396C23×C4C22×D6111yescharacteristic
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—1222no—
400C22×C8—2441no—
401C22×C8—2441no—
402C22×C8C22×D6111yescharacteristic
403C22×C8C22×D6111yescharacteristic
404C22⋊Q8—22no—
405C22⋊Q8—41no—
406C22⋊Q8—1222no—
407C22⋊Q8—1222no—
408C4×D4—1222no—
409C4×D4—1222no—
410#117—1222no—
411#117—1222no—
412#117—2441no—
413#117—2441no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C4⋊C4C22×D6111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
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—611no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42—1221no—
441#107—2441no—
442#106—1222no—
443#103—22no—
444#103—41no—
445#103—2441no—
446#103—2441no—
447C22⋊C8—41no—
448C22⋊C8—1222no—
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—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—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—611no—
484C22×C4—612no—
485C22×C4—612no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
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—42no—
516C4⋊C4—42no—
517C4⋊C4—1222no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
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#1175822212yes—
529C4⋊C4#1175822412yes—
530C22⋊C4—42no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—4881no—
534C22⋊C4—2442no—
535C22⋊C4—2442no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C22⋊C4—2442no—
539C42—1221no—
540C42—1221no—
541C42—4881no—
542C42—2442no—
543C42—2442no—
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#1451980012yes—
558C23C2×D4×D6111yescharacteristic
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—41no—
563D4—2444no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—41no—
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—41no—
583C2×C4—84no—
584C2×C4—612no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—1222no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
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×C4C2×#1175822411yescharacteristic
612C2×C4C2×#1175822211yescharacteristic
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—
633C22#123×D6111yescharacteristic
634C22#1684039911yescharacteristic
635C22#1684040211yescharacteristic
636C22C2×#1451980011yescharacteristic
637C22#1684055811yescharacteristic
638C22#1684056811yescharacteristic
639C22#1684057811yescharacteristic
640C4—41no—
641C4—42no—
642C4—42no—
643C4—81no—
644C4—81no—
645C4—1222no—
646C4—4881no—
647C4—4881no—
648C4—4881no—
649C4—4881no—
650C4—2441no—
651C4—2441no—
652C4#1684029411yescharacteristic
653C4#1684034411yescharacteristic
654C4#1684045911yescharacteristic
655C4#1684046211yescharacteristic
656C2—42no—
657C2—2442no—
658C2#2144956611yescharacteristic
659C2#2145573511yescharacteristic
660C2#2145578111yescharacteristic
661C2#2145771011yescharacteristic
662C2#2145771711yescharacteristic
663C2#2145784811yescharacteristic
664C2#2145791611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1872D61
hypocenterC61#26201
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. #21447392C2semidirect
4. #21447242C2semidirect
5. #21447240C2semidirect
6. #21447012C2semidirect
7. #21446462C2semidirect
8. #21446407C2semidirect
9. #21446239C2semidirect
10. #21446128C2semidirect
12. #21446021C2semidirect
13. #21445909C2semidirect
14. #21445534C2semidirect
15. C61×#1872C2semidirect
334. #1872D61semidirect
391. C61#26201semidirect

Maximal subgroups

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

subgroupindex
#214492442
#214487442
#214473922
#214472422
#214472402
#214470122
#214464622
#214464072
#214462392
#214461282
#214461082
#214460212
#214459092
#214455342
C61×#18722
#2620161