Subgroups — #15689252

Order 3008.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic
2	Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#13093935	C₂	1	1	yes	maximal, characteristic
5	#13093934	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
7	C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₉₄	C₄	1	1	yes	characteristic
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
13	Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
14	Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
15	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₇	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₄₇	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₄₇	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₄₇	C₂×C₄	1	1	yes	characteristic
26	Dic₉₄	—	2	2	no	—
27	C₈×C₄₇	—	2	1	no	—
28	C₈×C₄₇	—	2	1	no	—
29	C₄₇⋊C₈	—	2	1	no	—
30	C₄₇⋊C₈	Q₈	1	2	yes	complemented
31	C₂²×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₄₇	—	2	1	no	—
33	C₄×C₄₇	—	2	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	—	2	1	no	—
38	Dic₄₇	—	2	1	no	—
39	Dic₄₇	M₁₆	1	2	yes	—
40	C₂×C₄₇	C₄×Q₈	1	1	yes	characteristic
41	C₂×C₄₇	C₂×M₁₆	1	1	yes	characteristic
42	C₂×C₄₇	#131	1	1	yes	characteristic
43	#446	—	47	1	no	maximal, Sylow
44	C₄₇	#446	1	1	yes	characteristic, complemented, Sylow
45	C₄×Q₈	—	47	1	no	—
46	C₄⋊C₈	—	47	1	no	—
47	C₄⋊C₈	—	47	1	no	—
48	C₄⋊C₈	D₄₇	1	1	yes	characteristic
49	#97	—	47	1	no	—
50	#97	—	47	1	no	—
51	C₄×C₈	—	47	1	no	—
52	C₂×Q₈	—	47	1	no	—
53	C₂×C₈	—	47	1	no	—
54	C₂×C₈	—	47	1	no	—
55	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
56	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
57	C₄⋊C₄	—	47	1	no	—
58	C₄⋊C₄	—	47	1	no	—
59	C₄⋊C₄	—	47	1	no	—
60	C₄²	—	47	1	no	—
61	C₄²	—	47	1	no	—
62	C₄²	C₂×D₄₇	1	1	yes	characteristic
63	Q₈	—	94	2	no	—
64	C₂×C₄	—	47	1	no	—
65	C₂×C₄	—	47	1	no	—
66	C₂×C₄	—	47	1	no	—
67	C₂×C₄	—	47	1	no	—
68	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
69	C₂×C₄	C₄×D₄₇	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	2	1	no	—
73	C₈	—	47	2	no	—
74	C₈	—	94	1	no	—
75	C₂²	C₂×C₄×D₄₇	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	1	no	—
78	C₄	—	47	2	no	—
79	C₄	—	94	1	no	—
80	C₄	—	94	1	no	—
81	C₄	—	94	1	no	—
82	C₄	#10625352	1	1	yes	characteristic
83	C₄	Q₈×D₄₇	1	1	yes	characteristic
84	C₂	#13093989	1	1	yes	characteristic
85	C₂	M₁₆×D₄₇	1	1	yes	characteristic
86	C₂	#13094030	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₇
commutator, socle, prime radical	C₂²×C₄₇	C₂²×C₄
Fitting	C₄⋊C₈×C₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₄⋊C₈	D₄₇
hypocenter	C₄₇	#446
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
30. C₄₇⋊C₈	Q₈	semidirect
44. C₄₇	#446	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₉₄	2
Dic₄₇⋊C₈	2
#13093935	2
#13093934	2
C₈×Dic₄₇	2
C₄⋊C₈×C₄₇	2
#446	47