Subgroups — #15689331

Order 3008.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625337	C₂	1	1	yes	maximal, characteristic
2	#13094022	C₂	1	1	yes	maximal, characteristic
3	Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
5	#13093949	C₂	1	1	yes	maximal, characteristic
6	#13093948	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₉₄	C₂²	1	1	yes	characteristic
11	Q₁₆×C₄₇	—	2	2	no	—
12	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	#10625337	—	2	2	no	—
14	C₄⋊Dic₄₇	—	2	1	no	—
15	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	Dic₄₇⋊C₄	—	2	1	no	—
17	Dic₄₇⋊C₄	—	2	1	no	—
18	C₄×Dic₄₇	—	2	1	no	—
19	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	Q₈×C₄₇	—	2	1	no	—
22	Q₈×C₄₇	—	2	1	no	—
23	Q₈×C₄₇	—	2	1	no	—
24	Q₈×C₄₇	D₄	1	2	yes	—
25	C₂×C₄×C₄₇	—	2	1	no	—
26	C₂×C₄×C₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₄₇	—	2	1	no	—
29	C₂×Dic₄₇	—	2	1	no	—
30	C₂×Dic₄₇	D₄	1	1	yes	characteristic
31	C₂×Dic₄₇	D₄	1	1	yes	characteristic
32	Dic₉₄	—	2	1	no	—
33	Dic₉₄	—	2	1	no	—
34	C₈×C₄₇	—	2	1	no	—
35	C₄₇⋊C₈	—	2	1	no	—
36	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₄×C₄₇	—	2	2	no	—
38	C₄×C₄₇	—	4	1	no	—
39	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
40	C₄×C₄₇	#41	1	1	yes	characteristic
41	Dic₄₇	—	2	1	no	—
42	Dic₄₇	—	4	1	no	—
43	Dic₄₇	—	4	1	no	—
44	Dic₄₇	Q₁₆	1	2	yes	complemented
45	C₂×C₄₇	#121	1	1	yes	characteristic
46	C₂×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₄₇	#137	1	1	yes	characteristic
48	#462	—	47	1	no	maximal, Sylow
49	C₄₇	#462	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	47	1	no	—
51	C₂×Q₁₆	D₄₇	1	1	yes	characteristic
52	C₄⋊Q₈	—	47	1	no	—
53	C₄×Q₈	—	47	1	no	—
54	C₄⋊C₈	—	47	1	no	—
55	#103	—	47	1	no	—
56	#103	—	47	1	no	—
57	C₂×Q₈	—	47	1	no	—
58	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
59	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
60	Q₁₆	—	2	2	no	—
61	Q₁₆	—	94	2	no	—
62	C₂×C₈	—	47	1	no	—
63	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
64	C₄⋊C₄	—	47	1	no	—
65	C₄⋊C₄	—	94	1	no	—
66	C₄⋊C₄	—	94	1	no	—
67	C₄⋊C₄	—	94	1	no	—
68	C₄²	—	47	1	no	—
69	C₄²	—	94	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	2	1	no	—
73	Q₈	—	94	1	no	—
74	Q₈	—	94	1	no	—
75	Q₈	C₂²⋊D₄₇	1	2	yes	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	47	1	no	—
79	C₂×C₄	—	47	1	no	—
80	C₂×C₄	—	94	1	no	—
81	C₂×C₄	—	94	1	no	—
82	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	94	1	no	—
85	C₂²	D₄×D₄₇	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	4	1	no	—
88	C₄	—	47	2	no	—
89	C₄	—	94	1	no	—
90	C₄	—	188	1	no	—
91	C₄	—	188	1	no	—
92	C₄	#10625352	1	1	yes	characteristic
93	C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
94	C₂	#13093996	1	1	yes	characteristic
95	C₂	Q₁₆×D₄₇	1	1	yes	characteristic
96	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	C₂×Q₁₆×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
hypercenter	C₂×Q₁₆	D₄₇
hypocenter	C₄₇	#462
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
44. Dic₄₇	Q₁₆	semidirect
49. C₄₇	#462	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625337	2
#13094022	2
Q₈×Dic₄₇	2
Dic₄₇⋊C₈	2
#13093949	2
#13093948	2
C₂×Q₁₆×C₄₇	2
#462	47