Subgroups — #15688937

Order 3008.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₇₆	C₂	1	1	yes	maximal, characteristic
2	#13093960	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₈₈	—	2	1	no	—
5	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
6	#10625329	—	2	1	no	—
7	D₃₇₆	—	2	1	no	—
8	D₃₇₆	C₄	1	2	yes	—
9	C₁₆×C₄₇	—	2	1	no	—
10	C₂²×D₄₇	—	4	1	no	—
11	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
12	D₁₈₈	—	2	2	no	—
13	D₁₈₈	—	4	1	no	—
14	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₈×C₄₇	D₄	1	1	yes	characteristic
16	C₄₇⋊C₈	—	4	1	no	—
17	C₂²×C₄₇	SD₁₆	1	1	yes	characteristic
18	C₂×D₄₇	—	4	2	no	—
19	C₂×D₄₇	—	8	2	no	—
20	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₇	D₈	1	1	yes	characteristic
22	C₂×C₄₇	—	2	1	no	—
23	C₂×C₄₇	#102	1	1	yes	characteristic
24	D₄₇	—	8	2	no	—
25	#361	—	47	1	no	maximal, Sylow
26	C₄₇	#361	1	1	yes	characteristic, complemented, Sylow
27	C₂×D₈	—	47	1	no	—
28	M₃₂	D₄₇	1	1	yes	characteristic, complemented
29	#108	—	47	1	no	—
30	C₂×D₄	—	94	1	no	—
31	D₈	—	47	2	no	—
32	D₈	—	94	1	no	—
33	M₁₆	—	94	1	no	—
34	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	188	1	no	—
37	D₄	—	94	2	no	—
38	D₄	—	188	1	no	—
39	C₂×C₄	D₁₈₈	1	1	yes	characteristic
40	C₈	—	188	1	no	—
41	C₈	C₄×D₄₇	1	1	yes	characteristic
42	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
43	C₂²	—	376	2	no	—
44	C₂²	—	188	2	no	—
45	C₂²	#10625325	1	1	yes	characteristic
46	C₄	D₃₇₆	1	1	yes	characteristic
47	C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	376	2	no	—
50	C₂	#13093946	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093946
commutator	C₈×C₄₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₇
Fitting	M₃₂×C₄₇	C₂
socle	C₂×C₄₇	#102
prime radical	C₂×D₃₇₆	C₂
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	M₃₂	D₄₇
hypocenter	C₄₇	#361
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. #13093960	C₂	semidirect
3. M₃₂×C₄₇	C₂	semidirect
26. C₄₇	#361	semidirect
28. M₃₂	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₇₆	2
#13093960	2
M₃₂×C₄₇	2
#361	47