Subgroups — #15689412

Order 3008.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094023	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093986	C₂	1	1	yes	maximal, characteristic
3	#13093955	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093946	C₂	1	1	yes	maximal, characteristic
6	#13093944	C₂	1	1	yes	maximal, characteristic
7	#106×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄₇	—	2	1	no	—
10	C₂×Dic₉₄	—	2	1	no	—
11	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	(C₂×D₄₇)⋊C₄	—	2	1	no	—
15	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	Dic₄₇⋊C₄	—	2	1	no	—
17	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₄₇	—	2	1	no	—
20	C₂×C₄×C₄₇	—	2	1	no	—
21	C₂×C₄×C₄₇	—	2	1	no	—
22	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
23	C₂×Dic₄₇	—	2	1	no	—
24	C₂×Dic₄₇	D₄	1	1	yes	characteristic
25	C₂×Dic₄₇	D₄	1	1	yes	characteristic
26	D₁₈₈	—	2	1	no	—
27	D₁₈₈	Q₈	1	2	yes	complemented
28	C₄×D₄₇	—	4	2	no	—
29	Dic₉₄	—	4	2	no	—
30	C₈×C₄₇	—	2	1	no	—
31	C₄₇⋊C₈	—	2	1	no	—
32	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×D₄₇	—	2	2	no	—
34	C₂×D₄₇	—	4	1	no	—
35	C₂×D₄₇	—	4	1	no	—
36	C₄×C₄₇	—	4	1	no	—
37	C₄×C₄₇	—	4	1	no	—
38	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₄₇	#41	1	1	yes	characteristic
40	Dic₄₇	—	2	1	no	—
41	Dic₄₇	—	4	1	no	—
42	Dic₄₇	SD₁₆	1	2	yes	—
43	C₂×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
44	C₂×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
46	D₄₇	—	4	2	no	—
47	#476	—	47	1	no	maximal, Sylow
48	C₄₇	#476	1	1	yes	characteristic, complemented, Sylow
49	C₄⋊Q₈	—	47	1	no	—
50	C₄×D₄	—	47	1	no	—
51	#106	—	47	1	no	—
52	#106	D₄₇	1	1	yes	characteristic, complemented
53	C₄⋊C₈	—	47	1	no	—
54	#102	—	47	1	no	—
55	#102	—	47	1	no	—
56	C₂×Q₈	—	94	1	no	—
57	C₂×D₄	—	47	1	no	—
58	C₂²×C₄	—	94	1	no	—
59	C₂×C₈	—	47	1	no	—
60	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
61	C₄⋊C₄	—	47	1	no	—
62	C₄⋊C₄	—	94	1	no	—
63	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
64	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
65	C₂²⋊C₄	—	94	1	no	—
66	C₄²	—	47	1	no	—
67	C₂³	—	94	1	no	—
68	Q₈	—	188	2	no	—
69	D₄	—	47	2	no	—
70	D₄	—	94	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	47	1	no	—
74	C₂×C₄	—	47	1	no	—
75	C₂×C₄	—	94	1	no	—
76	C₂×C₄	—	188	2	no	—
77	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	94	1	no	—
80	C₂²	—	94	2	no	—
81	C₂²	—	188	1	no	—
82	C₂²	—	188	1	no	—
83	C₂²	D₄×D₄₇	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	47	2	no	—
87	C₄	—	94	1	no	—
88	C₄	—	188	1	no	—
89	C₄	#10625350	1	1	yes	characteristic
90	C₄	Q₈×D₄₇	1	1	yes	characteristic
91	C₂	—	188	2	no	—
92	C₂	#13094002	1	1	yes	characteristic
93	C₂	SD₁₆×D₄₇	1	1	yes	characteristic
94	C₂	#13094051	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#106×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂×D₁₈₈	C₂²
hypercenter	#106	D₄₇
hypocenter	C₄₇	#476
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. #13094023	C₂	semidirect
3. #13093955	C₂	semidirect
4. Dic₄₇⋊C₈	C₂	semidirect
7. #106×C₄₇	C₂	semidirect
27. D₁₈₈	Q₈	semidirect
48. C₄₇	#476	semidirect
52. #106	D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#13094023	2
#13093986	2
#13093955	2
Dic₄₇⋊C₈	2
#13093946	2
#13093944	2
#106×C₄₇	2
#476	47