Subgroups — #15689566

Order 3008.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094046	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃₇₆	C₂	1	2	yes	maximal, complemented
4	#13093969	C₂	1	2	yes	maximal, complemented
5	M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10625350	—	2	1	no	—
7	C₂×Dic₉₄	—	2	1	no	—
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	Dic₁₈₈	—	2	1	no	—
10	Dic₁₈₈	C₂²	1	2	yes	—
11	Dic₁₈₈	C₂²	1	1	yes	characteristic
12	D₃₇₆	C₂²	1	1	yes	characteristic
13	#10625325	—	2	1	no	—
14	C₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₂²⋊D₄₇	—	4	1	no	—
17	C₂×Dic₄₇	—	4	1	no	—
18	D₁₈₈	—	2	1	no	—
19	C₄×D₄₇	—	4	1	no	—
20	Dic₉₄	—	2	1	no	—
21	Dic₉₄	—	2	2	no	—
22	Dic₉₄	—	4	1	no	—
23	C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₈×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×C₄₇	D₈	1	1	yes	characteristic
26	C₂×D₄₇	—	4	1	no	—
27	C₄×C₄₇	D₈	1	1	yes	characteristic
28	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
29	Dic₄₇	—	4	2	no	—
30	Dic₄₇	—	4	1	no	—
31	C₂×C₄₇	—	2	1	no	—
32	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
33	D₄₇	—	8	1	no	—
34	#510	—	47	1	no	maximal, Sylow
35	C₄₇	#510	1	1	yes	characteristic, complemented, Sylow
36	#135	—	47	1	no	—
37	C₂×Q₁₆	—	47	1	no	—
38	Q₃₂	—	47	2	no	—
39	SD₃₂	—	47	2	no	—
40	M₃₂	D₄₇	1	1	yes	characteristic, complemented
41	#41	—	94	1	no	—
42	C₂×Q₈	—	94	1	no	—
43	Q₁₆	—	47	2	no	—
44	Q₁₆	—	47	1	no	—
45	Q₁₆	—	94	1	no	—
46	SD₁₆	—	94	1	no	—
47	D₈	—	47	1	no	—
48	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
49	C₁₆	C₂×D₄₇	1	2	yes	—
50	Q₈	—	94	1	no	—
51	Q₈	—	94	2	no	—
52	Q₈	—	188	1	no	—
53	D₄	—	94	1	no	—
54	D₄	—	188	1	no	—
55	C₂×C₄	—	188	1	no	—
56	C₂×C₄	—	188	1	no	—
57	C₂×C₄	D₁₈₈	1	1	yes	characteristic
58	C₈	D₁₈₈	1	1	yes	characteristic
59	C₈	C₂²×D₄₇	1	1	yes	characteristic
60	C₂²	—	188	1	no	—
61	C₂²	D₃₇₆	1	1	yes	characteristic
62	C₄	—	188	1	no	—
63	C₄	—	188	2	no	—
64	C₄	D₃₇₆	1	1	yes	characteristic
65	C₄	C₂×D₁₈₈	1	1	yes	characteristic
66	C₂	—	2	1	no	—
67	C₂	—	376	1	no	—
68	C₂	C₂×D₃₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₃₇₆
commutator, cosocle	C₈×C₄₇	C₂³
Frattini	C₈	C₂²×D₄₇
Fitting	M₃₂×C₄₇	C₂
socle	C₂×C₄₇	C₂×D₈
prime radical	#13094046	C₂
hypercenter	M₃₂	D₄₇
hypocenter	C₄₇	#510
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₈₈	C₂	semidirect
3. Dic₃₇₆	C₂	semidirect
4. #13093969	C₂	semidirect
5. M₃₂×C₄₇	C₂	semidirect
35. C₄₇	#510	semidirect
40. M₃₂	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094046	2
C₂×Dic₁₈₈	2
Dic₃₇₆	2
#13093969	2
M₃₂×C₄₇	2
#510	47