Finite Group Databasebeta

← #29738102

Subgroups — #29738102

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450856C211yesmaximal, characteristic, complemented
2#21448767C211yesmaximal, characteristic
3#21447189C211yesmaximal, characteristic
4#21446965C211yesmaximal, characteristic
5#21446963C211yesmaximal, characteristic
6#21446774C211yesmaximal, characteristic, complemented
7#21446773C211yesmaximal, characteristic, complemented
8#21446579C211yesmaximal, characteristic, complemented
9#21446534C211yesmaximal, characteristic, complemented
10#21446399C211yesmaximal, characteristic, complemented
11#21446394C211yesmaximal, characteristic, complemented
12#21445945C211yesmaximal, characteristic, complemented
13#21445817C211yesmaximal, characteristic
14#102×Dic61C211yesmaximal, characteristic
15C61×#2065C211yesmaximal, characteristic
16C2×#14519769C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19C2×#14519733—21no—
20C2×#14519708C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×C8×Dic61C2211yescharacteristic
26#16839696—21no—
27#16839695—21no—
28#16839665C2211yescharacteristic
29#16839661C2211yescharacteristic
30#16839659—21no—
31#16839656—21no—
32#16839650—21no—
33#16839631—21no—
34#16839631C2211yescharacteristic
35#16839631C2211yescharacteristic
36#16839620—21no—
37C4⋊C4×Dic61C2211yescharacteristic
38C4⋊C4×Dic61C2211yescharacteristic
39C4×#11758196C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41#16839525C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#106×C61C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C23×Dic61—21no—
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62#14519769—22no—
63#14519769—41no—
64#14519768—22no—
65#14519768—41no—
66D4×Dic61—22no—
67D4×Dic61Q814yes—
68#14519733—44no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196D411yescharacteristic
83C2×#11758196D411yescharacteristic
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61C2311yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92#14519708—22no—
93#14519706—22no—
94#14519706—41no—
95#14519698—22no—
96#14519698—41no—
97C8×Dic61—22no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684D411yescharacteristic
103#14519684D411yescharacteristic
104C22×D4×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
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×C42×C61C2311yescharacteristic
114#106×C61—22no—
115C4⋊C8×C61—41no—
116#102×C61—22no—
117#102×C61—41no—
118#95×C61—21no—
119C24×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61C2×Q812yes—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2411yescharacteristic
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—24no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—42no—
138C22×Dic61—42no—
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—81no—
155C4⋊C4×C61#4112yes—
156C22⋊C4×C61—42no—
157C22⋊C4×C61—81no—
158C42×C61—21no—
159C42×C61—21no—
160C22⋊Dic61—24no—
161C22⋊Dic61—42no—
162C22⋊Dic61—81no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165C4⋊Dic61—21no—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—42no—
170C4⋊Dic61—81no—
171C4⋊Dic61C2×Q812yes—
172C4⋊Dic61#4112yes—
173#11758196—22no—
174#11758196—22no—
175#11758196—42no—
176#11758196—42no—
177#11758196—42no—
178#11758196—42no—
179#11758196—42no—
180#11758196—81no—
181#11758196—81no—
182C4×Dic61—21no—
183C4×Dic61—21no—
184C4×Dic61—42no—
185C4×Dic61—42no—
186C4×Dic61—42no—
187C4×Dic61C2×Q812yes—
188C4×Dic61#4112yes—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C23×C61—22no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61C22×D411yescharacteristic
203D4×C61—22no—
204D4×C61—22no—
205D4×C61—41no—
206D4×C61—41no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—22no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C22×Q811yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×C4×C61C2×#4111yescharacteristic
226C2×C4×C61H(5,𝔽2)11yescharacteristic
227C2×C4×C612−1+411yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—22no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—22no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—48no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61C22⋊Q812yes—
250C2×Dic61C22⋊Q812yes—
251C2×Dic61#13512yes—
252C2×Dic61AGL(1,ℤ/8)12yes—
253C8×C61—41no—
254C8×C61—41no—
255#92418—41no—
256#92418—41no—
257#26021—611nomaximal, Sylow
258C22×C61—42no—
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61—81no—
265C22×C61C2×C22⋊Q811yescharacteristic
266C22×C61#54611yescharacteristic
267C22×C61#54811yescharacteristic
268C22×C61C2×#13511yescharacteristic
269C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C61#57711yescharacteristic
271C22×C61#57711yescharacteristic
272C4×C61—41no—
273C4×C61—42no—
274C4×C61—41no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61#53311yescharacteristic
278C4×C61#54411yescharacteristic
279C4×C61#55511yescharacteristic
280C4×C61#55611yescharacteristic
281Dic61—22no—
282Dic61—42no—
283Dic61—41no—
284Dic61—41no—
285Dic61—42no—
286Dic61—81no—
287Dic61—81no—
288Dic61#47814yes—
289#2552—611no—
290#2354—611no—
291#2065—611no—
292#2065D6111yescharacteristic
293#2025—611no—
294#2025—611no—
295#1989—611no—
296#1989—611no—
297#1948—611no—
298#1939—611no—
299#1919—611no—
300#1919—611no—
301#1834—611no—
302#1802—611no—
303C4×#102—611no—
304C2×C61—82no—
305C2×C61#243911yescharacteristic
306C2×C61C2×#47811yescharacteristic
307C2×C61#308411yescharacteristic
308C2×C61#330311yescharacteristic
309C2×C61#333211yescharacteristic
310C2×C61#336011yescharacteristic
311C2×C61#336811yescharacteristic
312C2×#125—611no—
313C2×#125—611no—
314C2×C4×D4—611no—
315C2×#117—1221no—
316C2×#106—611no—
317C2×#106C2×D6111yescharacteristic
318C2×C4⋊C8—611no—
319C2×C4⋊C8—611no—
320C2×C4⋊C8C2×D6111yescharacteristic
321C2×#102—611no—
322C2×#102—611no—
323C2×#102C2×D6111yescharacteristic
324C2×#102C2×D6111yescharacteristic
325C2×C4×C8—611no—
326#398—1221no—
327#398—1221no—
328#390—611no—
329#390C2×D6111yescharacteristic
330#389—611no—
331#389—1221no—
332#389C2×D6111yescharacteristic
333#388—1221no—
334#388—1221no—
335#384—611no—
336#384—611no—
337#384—1221no—
338#380—1221no—
339C4×C4⋊C4—611no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4—611no—
342C4×C4⋊C4—611no—
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340C2×D6111yescharacteristic
353#336—611no—
354#336—611no—
355C61#2602111yescharacteristic, complemented, Sylow
356C22×D4C22×D6111yescharacteristic
357C23×C4—1221no—
358C22×C8—611no—
359C22×C8—611no—
360C22×C8C22×D6111yescharacteristic
361C22×C8C22×D6111yescharacteristic
362#125—1222no—
363#125—1222no—
364#125—2441no—
365#125—2441no—
366C4×D4—614no—
367C4×D4—1222no—
368#117—2444no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C4⋊C4C22×D6111yescharacteristic
387C2×C4⋊C4C22×D6111yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C42—611no—
394C2×C42—611no—
395C2×C42—1221no—
396C2×C42—1221no—
397C2×C42—1221no—
398C2×C42C22×D6111yescharacteristic
399#106—22no—
400#106—1222no—
401C4⋊C8—41no—
402C4⋊C8—1222no—
403C4⋊C8—2441no—
404#102—22no—
405#102—41no—
406#102—1222no—
407#102—2441no—
408C4×C8—1222no—
409#95—21no—
410#95—611no—
411#95—611no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416C24—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4Q8×D6112yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—1224no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—2442no—
436C22×C4—2442no—
437C22×C4D4×D6111yescharacteristic
438C22×C4D4×D6111yescharacteristic
439C22×C4C23×D6111yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—81no—
458C4⋊C4—612no—
459C4⋊C4—612no—
460C4⋊C4—1222no—
461C4⋊C4—1222no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—4881no—
469C4⋊C4—4881no—
470C4⋊C4—4881no—
471C4⋊C4—2442no—
472C4⋊C4—2442no—
473C4⋊C4—2442no—
474C4⋊C4—2442no—
475C4⋊C4—2442no—
476C4⋊C4—2442no—
477C4⋊C4#1175822412yes—
478C22⋊C4—42no—
479C22⋊C4—81no—
480C22⋊C4—1224no—
481C22⋊C4—4881no—
482C22⋊C4—2442no—
483C42—21no—
484C42—21no—
485C42—612no—
486C42—612no—
487C42—1221no—
488C42—1221no—
489C42—2442no—
490C42—2442no—
491C42—2442no—
492C23—22no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23C2×D4×D6111yescharacteristic
500D4—22no—
501D4—22no—
502D4—41no—
503D4—41no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—612no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1222no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1222no—
533C2×C4—2448no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4C2×Q8×D6111yescharacteristic
545C2×C4#41×D6111yescharacteristic
546C2×C4#41×D6111yescharacteristic
547C2×C4C2×#1175822411yescharacteristic
548C2×C4#1451982211yescharacteristic
549C2×C4#1451982411yescharacteristic
550C8—41no—
551C8—41no—
552C8—2441no—
553C8—2441no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22C22⋊Q8×D6111yescharacteristic
562C22#1684040111yescharacteristic
563C22#1684041811yescharacteristic
564C22#135×D6111yescharacteristic
565C22AGL(1,ℤ/8)×D6111yescharacteristic
566C22#1684056811yescharacteristic
567C22#1684057211yescharacteristic
568C4—42no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—614no—
574C4—1222no—
575C4—4881no—
576C4—4881no—
577C4—2441no—
578C4—2442no—
579C4—2442no—
580C4—2441no—
581C4#1684031411yescharacteristic
582C4#1684039111yescharacteristic
583C4#1684047611yescharacteristic
584C4#1684047911yescharacteristic
585C2—82no—
586C2#2144950511yescharacteristic
587C2#478×D6111yescharacteristic
588C2#2145567611yescharacteristic
589C2#2145774211yescharacteristic
590C2#2145814111yescharacteristic
591C2#2145846311yescharacteristic
592C2#2145854311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2065C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2065D61
hypocenterC61#26021
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. #21450856C2semidirect
6. #21446774C2semidirect
7. #21446773C2semidirect
8. #21446579C2semidirect
9. #21446534C2semidirect
10. #21446399C2semidirect
11. #21446394C2semidirect
12. #21445945C2semidirect
355. C61#26021semidirect

Maximal subgroups

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

subgroupindex
#214508562
#214487672
#214471892
#214469652
#214469632
#214467742
#214467732
#214465792
#214465342
#214463992
#214463942
#214459452
#214458172
#102×Dic612
C61×#20652
#2602161