Subgroups — #44529129

Order 31168.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21441244	C₂	1	2	yes	maximal, complemented
2	C₄×D₁₉₄₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₈₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₄₈₇)⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₉₄₈	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄₈₇	C₂²	1	2	yes	—
8	#21441244	—	2	4	no	—
9	C₂×C₄₈₇⋊C₈	C₂²	1	2	yes	—
10	C₄⋊Dic₄₈₇	C₄	1	1	yes	characteristic
11	(C₂×D₄₈₇)⋊C₄	C₄	1	2	yes	—
12	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
14	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
15	C₂²×D₄₈₇	C₂×C₄	1	2	yes	—
16	D₁₉₄₈	—	2	2	no	—
17	C₂×Dic₄₈₇	C₂×C₄	1	2	yes	—
18	C₄×D₄₈₇	—	2	2	no	—
19	C₄×D₄₈₇	—	2	2	no	—
20	C₄₈₇⋊C₈	—	2	2	no	—
21	C₂×C₄×C₄₈₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₈₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
24	C₈×C₄₈₇	—	2	1	no	—
25	C₈×C₄₈₇	D₄	1	2	yes	complemented
26	C₂²×C₄₈₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₄₈₇	—	2	2	no	—
28	C₂×D₄₈₇	—	2	2	no	—
29	C₂×D₄₈₇	—	2	2	no	—
30	C₄×C₄₈₇	—	2	1	no	—
31	C₄×C₄₈₇	M₁₆	1	2	yes	complemented
32	C₄×C₄₈₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₈₇	#41	1	1	yes	characteristic
34	Dic₄₈₇	—	2	2	no	—
35	C₂×C₄₈₇	C₄×D₄	1	1	yes	characteristic
36	C₂×C₄₈₇	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₄₈₇	#131	1	1	yes	characteristic
38	D₄₈₇	—	4	2	no	—
39	C₄₈₇	#436	1	1	yes	characteristic, complemented, Sylow
40	#436	—	487	1	no	maximal, Sylow
41	C₂×M₁₆	—	487	2	no	—
42	C₄×D₄	—	487	1	no	—
43	C₄⋊C₈	—	487	1	no	—
44	C₂²⋊C₈	—	487	2	no	—
45	C₄×C₈	D₄₈₇	1	1	yes	characteristic, complemented
46	C₂×D₄	—	487	1	no	—
47	C₂²×C₄	—	487	2	no	—
48	M₁₆	—	974	4	no	—
49	C₂×C₈	—	487	2	no	—
50	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
51	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
52	C₄⋊C₄	—	487	1	no	—
53	C₂²⋊C₄	—	487	2	no	—
54	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
55	C₂³	—	487	2	no	—
56	D₄	—	974	2	no	—
57	C₂×C₄	—	974	2	no	—
58	C₂×C₄	—	974	2	no	—
59	C₂×C₄	—	487	2	no	—
60	C₂×C₄	C₄×D₄₈₇	1	1	yes	characteristic
61	C₂×C₄	C₄×D₄₈₇	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	974	2	no	—
65	C₈	D₁₉₄₈	1	2	yes	complemented
66	C₂²	—	974	2	no	—
67	C₂²	—	974	2	no	—
68	C₂²	—	974	2	no	—
69	C₂²	C₂×C₄×D₄₈₇	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	974	2	no	—
72	C₄	#21441244	1	2	yes	complemented
73	C₄	C₂×D₁₉₄₈	1	1	yes	characteristic
74	C₄	#21441261	1	1	yes	characteristic
75	C₂	—	1948	2	no	—
76	C₂	C₄×D₁₉₄₈	1	1	yes	characteristic
77	C₂	C₂×#21441244	1	1	yes	characteristic
78	C₂	#29510221	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₈₇
commutator, socle	C₂²×C₄₈₇	C₂²×C₄
Fitting	C₄×C₈×C₄₈₇	C₂
prime radical	C₂×D₁₉₄₈	C₄
cosocle	C₂×C₄×C₄₈₇	C₂³
hypercenter	C₄×C₈	D₄₈₇
hypocenter	C₄₈₇	#436
LCS	G ▷ C₂²×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#21441244	C₂	semidirect
3. C₄⋊(C₄₈₇⋊C₈)	C₂	semidirect
4. (C₂×D₄₈₇)⋊C₈	C₂	semidirect
5. C₄×C₈×C₄₈₇	C₂	semidirect
25. C₈×C₄₈₇	D₄	semidirect
31. C₄×C₄₈₇	M₁₆	semidirect
39. C₄₈₇	#436	semidirect
45. C₄×C₈	D₄₈₇	semidirect
65. C₈	D₁₉₄₈	semidirect
72. C₄	#21441244	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21441244	2
C₄×D₁₉₄₈	2
C₄⋊(C₄₈₇⋊C₈)	2
(C₂×D₄₈₇)⋊C₈	2
C₄×C₈×C₄₈₇	2
#436	487