Subgroups — #15689406

Order 3008.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094023	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093956	C₂	1	1	yes	maximal, characteristic
4	#13093955	C₂	1	1	yes	maximal, characteristic
5	Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#13093948	C₂	1	1	yes	maximal, characteristic
7	#103×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₉₄	—	2	1	no	—
10	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₇	—	2	1	no	—
13	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	Dic₄₇⋊C₄	—	2	1	no	—
16	C₄×Dic₄₇	—	2	1	no	—
17	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×C₄₇	—	2	1	no	—
20	Q₈×C₄₇	Q₈	1	2	yes	complemented
21	C₂×C₄×C₄₇	—	2	1	no	—
22	C₂×C₄×C₄₇	—	2	1	no	—
23	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₄₇	—	2	1	no	—
25	C₂×Dic₄₇	—	2	1	no	—
26	C₂×Dic₄₇	D₄	1	1	yes	characteristic
27	C₂×Dic₄₇	D₄	1	1	yes	characteristic
28	Dic₉₄	—	4	2	no	—
29	C₈×C₄₇	—	2	1	no	—
30	C₄₇⋊C₈	—	2	1	no	—
31	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
32	C₄×C₄₇	—	2	2	no	—
33	C₄×C₄₇	—	4	1	no	—
34	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₄₇	#41	1	1	yes	characteristic
36	Dic₄₇	—	2	1	no	—
37	Dic₄₇	—	4	1	no	—
38	Dic₄₇	—	4	1	no	—
39	Dic₄₇	SD₁₆	1	2	yes	—
40	C₂×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
41	C₂×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₄₇	#137	1	1	yes	characteristic
43	#475	—	47	1	no	maximal, Sylow
44	C₄₇	#475	1	1	yes	characteristic, complemented, Sylow
45	C₄⋊Q₈	—	47	1	no	—
46	C₄×Q₈	—	47	1	no	—
47	#106	—	47	1	no	—
48	#106	—	47	1	no	—
49	C₄⋊C₈	—	47	1	no	—
50	#103	—	47	1	no	—
51	#103	D₄₇	1	1	yes	characteristic
52	C₂×Q₈	—	94	1	no	—
53	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
54	C₂×C₈	—	47	1	no	—
55	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
56	C₄⋊C₄	—	47	1	no	—
57	C₄⋊C₄	—	47	1	no	—
58	C₄⋊C₄	—	94	1	no	—
59	C₄⋊C₄	—	94	1	no	—
60	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
61	C₄²	—	47	1	no	—
62	C₄²	—	94	1	no	—
63	Q₈	—	2	1	no	—
64	Q₈	—	188	2	no	—
65	Q₈	Dic₉₄	1	2	yes	complemented
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	47	1	no	—
69	C₂×C₄	—	47	1	no	—
70	C₂×C₄	—	94	1	no	—
71	C₂×C₄	—	94	1	no	—
72	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
73	C₈	—	2	1	no	—
74	C₈	—	94	1	no	—
75	C₂²	D₄×D₄₇	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	47	2	no	—
79	C₄	—	94	1	no	—
80	C₄	—	188	1	no	—
81	C₄	—	188	1	no	—
82	C₄	C₂×Dic₉₄	1	1	yes	characteristic
83	C₄	#10625352	1	1	yes	characteristic
84	C₂	#13094001	1	1	yes	characteristic
85	C₂	SD₁₆×D₄₇	1	1	yes	characteristic
86	C₂	#13094056	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#103×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
hypercenter	#103	D₄₇
hypocenter	C₄₇	#475
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
20. Q₈×C₄₇	Q₈	semidirect
44. C₄₇	#475	semidirect
65. Q₈	Dic₉₄	semidirect

Maximal subgroups

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

subgroup	index
#13094023	2
Q₈×Dic₄₇	2
#13093956	2
#13093955	2
Dic₄₇⋊C₈	2
#13093948	2
#103×C₄₇	2
#475	47