Subgroups — #15689394

Order 3008.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094052	C₂	1	2	yes	maximal, complemented
2	C₂×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#13094030	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093940	C₂	1	2	yes	maximal, complemented
5	#108×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#10625350	C₂²	1	1	yes	characteristic
7	C₂×D₁₈₈	C₂²	1	2	yes	—
8	M₁₆×C₄₇	C₂²	1	2	yes	—
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	#10625329	C₂²	1	1	yes	characteristic
11	D₃₇₆	—	2	2	no	—
12	D₃₇₆	—	2	1	no	—
13	D₃₇₆	—	2	1	no	—
14	#10625325	—	2	2	no	—
15	#10625324	—	2	1	no	—
16	C₈×D₄₇	—	2	1	no	—
17	C₂²×D₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂²⋊D₄₇	—	2	1	no	—
20	D₁₈₈	—	2	2	no	—
21	D₁₈₈	—	2	2	no	—
22	D₁₈₈	D₄	1	1	yes	characteristic
23	C₄×D₄₇	—	2	1	no	—
24	Dic₉₄	D₄	1	1	yes	characteristic
25	C₈×C₄₇	—	2	2	no	—
26	C₈×C₄₇	D₄	1	1	yes	characteristic
27	C₈×C₄₇	D₄	1	1	yes	characteristic
28	C₄₇⋊C₈	—	2	1	no	—
29	C₂²×C₄₇	#41	1	1	yes	characteristic
30	C₂×D₄₇	—	2	1	no	—
31	C₂×D₄₇	—	4	2	no	—
32	C₂×D₄₇	—	8	2	no	—
33	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	Dic₄₇	—	2	1	no	—
36	C₂×C₄₇	—	2	1	no	—
37	C₂×C₄₇	#121	1	1	yes	characteristic
38	D₄₇	—	4	1	no	—
39	D₄₇	—	8	2	no	—
40	#472	—	47	1	no	maximal, Sylow
41	C₄₇	#472	1	1	yes	characteristic, complemented, Sylow
42	AGL(1,ℤ/8)	—	47	2	no	—
43	C₂×D₈	—	47	1	no	—
44	#131	—	47	1	no	—
45	#108	D₄₇	1	1	yes	characteristic, complemented
46	#100	—	47	2	no	—
47	#41	—	47	1	no	—
48	C₂×D₄	—	47	2	no	—
49	SD₁₆	—	94	2	no	—
50	D₈	—	94	2	no	—
51	D₈	—	94	1	no	—
52	D₈	—	94	1	no	—
53	M₁₆	—	47	1	no	—
54	M₁₆	—	94	1	no	—
55	M₁₆	C₂×D₄₇	1	2	yes	—
56	C₂×C₈	—	94	1	no	—
57	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
58	C₂³	—	94	2	no	—
59	Q₈	—	47	1	no	—
60	D₄	—	47	1	no	—
61	D₄	—	94	1	no	—
62	D₄	—	94	2	no	—
63	D₄	—	94	2	no	—
64	C₂×C₄	—	94	1	no	—
65	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₈	—	94	1	no	—
68	C₈	D₁₈₈	1	1	yes	characteristic
69	C₈	D₁₈₈	1	1	yes	characteristic
70	C₂²	—	94	1	no	—
71	C₂²	—	376	2	no	—
72	C₂²	—	188	2	no	—
73	C₂²	#10625354	1	1	yes	characteristic
74	C₄	—	94	1	no	—
75	C₄	C₂×D₁₈₈	1	1	yes	characteristic
76	C₄	D₄×D₄₇	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	376	2	no	—
79	C₂	—	188	1	no	—
80	C₂	#13093999	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13093999
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#108×C₄₇	C₂
socle	C₂×C₄₇	#121
hypercenter	#108	D₄₇
hypocenter	C₄₇	#472
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
1. #13094052	C₂	semidirect
2. C₂×D₃₇₆	C₂	semidirect
3. #13094030	C₂	semidirect
4. #13093940	C₂	semidirect
5. #108×C₄₇	C₂	semidirect
41. C₄₇	#472	semidirect
45. #108	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094052	2
C₂×D₃₇₆	2
#13094030	2
#13093940	2
#108×C₄₇	2
#472	47