Subgroups — #15688848

Order 3008.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
5	C₂²×Dic₄₇	C₄	1	1	yes	characteristic
6	C₂²×Dic₄₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₇	—	2	1	no	—
8	Dic₄₇⋊C₄	—	2	1	no	—
9	Dic₄₇⋊C₄	—	2	1	no	—
10	C₂×C₄₇⋊C₈	—	2	1	no	—
11	C₂³×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₇	—	4	1	no	—
13	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
14	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
15	C₂×Dic₄₇	—	2	1	no	—
16	C₂×Dic₄₇	—	2	1	no	—
17	C₂×Dic₄₇	—	2	1	no	—
18	C₂×Dic₄₇	—	4	1	no	—
19	C₂×Dic₄₇	C₈	1	2	yes	complemented
20	C₈×C₄₇	—	4	1	no	—
21	C₄₇⋊C₈	—	4	1	no	—
22	C₂²×C₄₇	—	2	1	no	—
23	C₂²×C₄₇	—	2	1	no	—
24	C₂²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₄₇	M₁₆	1	1	yes	characteristic
27	C₄×C₄₇	—	2	1	no	—
28	C₄×C₄₇	—	2	1	no	—
29	Dic₄₇	—	2	2	no	—
30	Dic₄₇	—	4	1	no	—
31	C₂×C₄₇	—	2	1	no	—
32	C₂×C₄₇	—	2	1	no	—
33	C₂×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₄₇	#99	1	1	yes	characteristic
35	C₂×C₄₇	#101	1	1	yes	characteristic
36	#324	—	47	1	no	maximal, Sylow
37	C₄₇	#324	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₄⋊C₄	—	47	1	no	—
39	C₂²⋊C₈	—	47	1	no	—
40	C₂²⋊C₈	D₄₇	1	1	yes	characteristic
41	C₂²×C₄	—	47	1	no	—
42	C₂²×C₄	—	47	1	no	—
43	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	—	94	1	no	—
46	C₄⋊C₄	—	94	1	no	—
47	C₄⋊C₄	—	94	1	no	—
48	C₂³	C₄×D₄₇	1	1	yes	characteristic
49	C₂×C₄	—	4	1	no	—
50	C₂×C₄	—	47	2	no	—
51	C₂×C₄	—	94	1	no	—
52	C₂×C₄	—	94	1	no	—
53	C₂×C₄	—	94	1	no	—
54	C₂×C₄	—	188	1	no	—
55	C₂×C₄	D₁₈₈	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
57	C₈	—	4	1	no	—
58	C₈	—	188	1	no	—
59	C₂²	—	2	1	no	—
60	C₂²	—	2	1	no	—
61	C₂²	C₈×D₄₇	1	1	yes	characteristic
62	C₂²	#10625324	1	1	yes	characteristic
63	C₂²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	2	1	no	—
66	C₄	—	94	2	no	—
67	C₄	—	188	1	no	—
68	C₂	—	2	1	no	—
69	C₂	—	2	1	no	—
70	C₂	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
71	C₂	#13093938	1	1	yes	characteristic
72	C₂	#13093942	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₄₇)⋊C₄
commutator	C₂²×C₄₇	C₂×C₈
Frattini	C₂²×C₄	C₂×D₄₇
Fitting	C₂²⋊C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂²⋊C₄
prime radical	C₂³×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂²
hypercenter	C₂²⋊C₈	D₄₇
hypocenter	C₄₇	#324
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
19. C₂×Dic₄₇	C₈	semidirect
37. C₄₇	#324	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₄₇⋊C₄	2
C₂²⋊(C₄₇⋊C₈)	2
C₂²⋊C₈×C₄₇	2
#324	47