Subgroups — #44529776

Order 31168.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29510214	C₂	1	3	yes	maximal
2	#29510207	C₂	1	3	yes	maximal
3	#29510206	C₂	1	3	yes	maximal
4	Q₈×Dic₄₈₇	C₂	1	1	yes	maximal, characteristic
5	Q₈×Dic₄₈₇	C₂	1	1	yes	maximal, characteristic
6	C₄×Dic₉₇₄	C₂	1	3	yes	maximal
7	C₄×Q₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₉₇₄	C₂²	1	3	yes	—
9	C₄⋊Dic₄₈₇	C₂²	1	3	yes	—
10	C₄⋊Dic₄₈₇	C₂²	1	3	yes	—
11	C₄⋊Dic₄₈₇	C₂²	1	3	yes	—
12	Dic₄₈₇⋊C₄	C₂²	1	1	yes	characteristic
13	Dic₄₈₇⋊C₄	C₂²	1	3	yes	—
14	Dic₄₈₇⋊C₄	C₂²	1	6	yes	—
15	C₄×Dic₄₈₇	C₂²	1	3	yes	—
16	C₄×Dic₄₈₇	C₂²	1	3	yes	—
17	C₂×Q₈×C₄₈₇	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₄₈₇	C₂²	1	3	yes	—
19	C₄²×C₄₈₇	C₂²	1	3	yes	—
20	Dic₉₇₄	—	2	6	no	—
21	C₂×Dic₄₈₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₈₇	C₂³	1	3	yes	—
23	C₂×Dic₄₈₇	C₂³	1	3	yes	—
24	C₂×Dic₄₈₇	C₂³	1	1	yes	characteristic
25	Q₈×C₄₈₇	Q₈	1	4	yes	complemented
26	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₄₈₇	C₂³	1	3	yes	—
28	C₂×C₄×C₄₈₇	C₂³	1	3	yes	—
29	C₂²×C₄₈₇	C₂⁴	1	1	yes	characteristic
30	C₄×C₄₈₇	—	2	3	no	—
31	C₄×C₄₈₇	—	2	1	no	—
32	C₄×C₄₈₇	C₂×Q₈	1	6	yes	—
33	Dic₄₈₇	—	2	3	no	—
34	Dic₄₈₇	—	2	1	no	—
35	Dic₄₈₇	—	2	3	no	—
36	Dic₄₈₇	#41	1	2	yes	—
37	C₂×C₄₈₇	C₂²×Q₈	1	1	yes	characteristic
38	C₂×C₄₈₇	C₂×#41	1	1	yes	characteristic
39	C₂×C₄₈₇	2₋¹⁺⁴	1	1	yes	characteristic
40	C₄₈₇	#557	1	1	yes	characteristic, complemented, Sylow
41	#557	—	487	1	no	maximal, Sylow
42	C₄⋊Q₈	—	487	3	no	—
43	#125	—	487	3	no	—
44	#125	—	487	3	no	—
45	C₄×Q₈	—	487	1	no	—
46	C₄×Q₈	—	487	1	no	—
47	C₄×Q₈	—	487	3	no	—
48	C₄×Q₈	D₄₈₇	1	1	yes	characteristic
49	C₂×Q₈	—	487	3	no	—
50	C₂×Q₈	C₂×D₄₈₇	1	1	yes	characteristic
51	C₄⋊C₄	—	487	1	no	—
52	C₄⋊C₄	—	487	3	no	—
53	C₄⋊C₄	—	487	3	no	—
54	C₄⋊C₄	—	487	3	no	—
55	C₄⋊C₄	—	487	3	no	—
56	C₄⋊C₄	—	487	6	no	—
57	C₄⋊C₄	C₂×D₄₈₇	1	3	yes	—
58	C₄²	—	487	3	no	—
59	C₄²	—	487	3	no	—
60	C₄²	C₂×D₄₈₇	1	3	yes	—
61	Q₈	—	974	6	no	—
62	Q₈	Dic₉₇₄	1	4	yes	complemented
63	C₂×C₄	—	487	1	no	—
64	C₂×C₄	—	487	3	no	—
65	C₂×C₄	—	487	3	no	—
66	C₂×C₄	—	487	1	no	—
67	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
68	C₂×C₄	C₂²×D₄₈₇	1	3	yes	—
69	C₂×C₄	C₂²×D₄₈₇	1	3	yes	—
70	C₂²	C₂³×D₄₈₇	1	1	yes	characteristic
71	C₄	—	2	3	no	—
72	C₄	—	2	1	no	—
73	C₄	—	974	3	no	—
74	C₄	—	974	1	no	—
75	C₄	—	974	3	no	—
76	C₄	—	487	2	no	—
77	C₄	C₂×Dic₉₇₄	1	6	yes	—
78	C₂	C₂²×Dic₉₇₄	1	1	yes	characteristic
79	C₂	#41×D₄₈₇	1	1	yes	characteristic
80	C₂	#29510263	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₈₇
commutator, socle, prime radical, cosocle	C₂²×C₄₈₇	C₂⁴
Fitting	C₄×Q₈×C₄₈₇	C₂
hypercenter	C₄×Q₈	D₄₈₇
hypocenter	C₄₈₇	#557
LCS	G ▷ C₂²×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
25. Q₈×C₄₈₇	Q₈	semidirect
40. C₄₈₇	#557	semidirect
62. Q₈	Dic₉₇₄	semidirect

Maximal subgroups

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

subgroup	index
#29510214	2
#29510207	2
#29510206	2
Q₈×Dic₄₈₇	2
C₄×Dic₉₇₄	2
C₄×Q₈×C₄₈₇	2
#557	487