Subgroups — #15689562

Order 3008.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094043	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093970	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093968	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093963	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×D₄₇	—	2	1	no	—
9	#10625352	—	2	1	no	—
10	Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
11	D₈×C₄₇	C₂²	1	1	yes	characteristic
12	#10625337	—	2	1	no	—
13	#10625335	—	2	1	no	—
14	Dic₁₈₈	C₂²	1	1	yes	characteristic
15	Dic₁₈₈	C₂²	1	1	yes	characteristic
16	C₈×D₄₇	C₂²	1	1	yes	characteristic
17	C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
19	Q₈×C₄₇	—	2	1	no	—
20	D₄×C₄₇	—	2	1	no	—
21	C₂²⋊D₄₇	—	4	1	no	—
22	C₂×Dic₄₇	—	4	1	no	—
23	C₄×D₄₇	—	4	1	no	—
24	C₄×D₄₇	D₄	1	1	yes	characteristic
25	Dic₉₄	—	2	1	no	—
26	Dic₉₄	—	2	1	no	—
27	Dic₉₄	—	4	1	no	—
28	C₈×C₄₇	C₂³	1	1	yes	characteristic
29	C₄₇⋊C₈	D₄	1	1	yes	characteristic
30	C₂²×C₄₇	—	4	1	no	—
31	C₂×D₄₇	D₈	1	1	yes	characteristic
32	C₄×C₄₇	—	4	1	no	—
33	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	Dic₄₇	—	4	1	no	—
35	Dic₄₇	—	4	1	no	—
36	Dic₄₇	D₈	1	1	yes	characteristic
37	C₂×C₄₇	—	8	1	no	—
38	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
39	D₄₇	—	2	1	no	—
40	#510	—	47	1	no	maximal, Sylow
41	C₄₇	#510	1	1	yes	characteristic, complemented, Sylow
42	#135	—	47	1	no	—
43	C₂×Q₁₆	—	47	1	no	—
44	Q₃₂	—	47	1	no	—
45	Q₃₂	—	47	1	no	—
46	SD₃₂	—	47	1	no	—
47	SD₃₂	D₄₇	1	1	yes	characteristic, complemented
48	M₃₂	—	47	1	no	—
49	#41	—	94	1	no	—
50	C₂×Q₈	—	94	1	no	—
51	Q₁₆	—	47	1	no	—
52	Q₁₆	—	47	1	no	—
53	Q₁₆	—	94	1	no	—
54	Q₁₆	C₂×D₄₇	1	1	yes	characteristic
55	SD₁₆	—	94	1	no	—
56	D₈	C₂×D₄₇	1	1	yes	characteristic
57	C₂×C₈	—	47	1	no	—
58	C₁₆	—	47	1	no	—
59	C₁₆	C₂×D₄₇	1	1	yes	characteristic
60	Q₈	—	2	1	no	—
61	Q₈	—	94	1	no	—
62	Q₈	—	94	1	no	—
63	Q₈	—	188	1	no	—
64	D₄	—	2	1	no	—
65	D₄	—	188	1	no	—
66	C₂×C₄	—	47	1	no	—
67	C₂×C₄	—	188	1	no	—
68	C₂×C₄	—	188	1	no	—
69	C₈	—	47	1	no	—
70	C₈	C₂²×D₄₇	1	1	yes	characteristic
71	C₂²	—	4	1	no	—
72	C₂²	—	47	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	47	1	no	—
75	C₄	—	188	1	no	—
76	C₄	—	188	1	no	—
77	C₄	D₄×D₄₇	1	1	yes	characteristic
78	C₂	—	8	1	no	—
79	C₂	—	94	1	no	—
80	C₂	D₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₇
commutator, cosocle	C₈×C₄₇	C₂³
Frattini	C₈	C₂²×D₄₇
Fitting	SD₃₂×C₄₇	C₂
socle	C₂×C₄₇	C₂×D₈
prime radical	#13094043	C₂
hypercenter	SD₃₂	D₄₇
hypocenter	C₄₇	#510
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
2. Q₁₆×D₄₇	C₂	semidirect
3. Dic₃₇₆	C₂	semidirect
4. #13093970	C₂	semidirect
5. #13093968	C₂	semidirect
6. #13093963	C₂	semidirect
7. SD₃₂×C₄₇	C₂	semidirect
41. C₄₇	#510	semidirect
47. SD₃₂	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094043	2
Q₁₆×D₄₇	2
Dic₃₇₆	2
#13093970	2
#13093968	2
#13093963	2
SD₃₂×C₄₇	2
#510	47