Subgroups — #20241434

Order 6016.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
2	#15688876	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#493	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	—	2	1	no	—
5	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
6	C₂×D₈×C₄₇	—	2	1	no	—
7	C₂×D₈×C₄₇	C₄	1	2	yes	—
8	#127×C₄₇	—	2	1	no	—
9	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×D₄×C₄₇	—	2	2	no	—
11	C₂×D₄×C₄₇	—	4	1	no	—
12	C₂×D₄×C₄₇	—	4	1	no	—
13	D₈×C₄₇	—	4	2	no	—
14	D₈×C₄₇	—	4	1	no	—
15	D₈×C₄₇	—	4	1	no	—
16	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₄²×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₄₇⋊C₈	—	4	1	no	—
20	C₄₇⋊C₁₆	—	4	1	no	—
21	C₂³×C₄₇	—	4	2	no	—
22	D₄×C₄₇	—	4	2	no	—
23	D₄×C₄₇	—	4	2	no	—
24	D₄×C₄₇	—	8	2	no	—
25	D₄×C₄₇	—	8	1	no	—
26	D₄×C₄₇	—	8	1	no	—
27	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₄₇	—	2	1	no	—
31	C₈×C₄₇	D₈	1	1	yes	characteristic
32	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
33	C₄₇⋊C₈	—	8	1	no	—
34	C₂²×C₄₇	—	8	2	no	—
35	C₂²×C₄₇	—	8	2	no	—
36	C₂²×C₄₇	—	8	2	no	—
37	C₂²×C₄₇	#102	1	1	yes	characteristic
38	C₄×C₄₇	—	2	1	no	—
39	C₄×C₄₇	#100	1	1	yes	characteristic
40	C₄×C₄₇	#102	1	1	yes	characteristic
41	C₄×C₄₇	D₁₆	1	1	yes	characteristic
42	C₄×C₄₇	SD₃₂	1	1	yes	characteristic
43	#1361	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	—	16	2	no	—
45	C₂×C₄₇	#331	1	1	yes	characteristic
46	C₂×C₄₇	#357	1	1	yes	characteristic
47	C₂×C₄₇	#361	1	1	yes	characteristic
48	#493	D₄₇	1	1	yes	characteristic
49	C₄⋊C₁₆	—	47	1	no	—
50	#335	—	47	1	no	—
51	C₄₇	#1361	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₈	—	2	1	no	—
53	C₂×D₈	Dic₄₇	1	2	yes	—
54	#127	—	2	1	no	—
55	C₂×C₁₆	—	94	1	no	—
56	C₄⋊C₈	—	94	1	no	—
57	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
58	C₂×D₄	—	2	2	no	—
59	C₂×D₄	—	4	1	no	—
60	C₂×D₄	—	4	1	no	—
61	D₈	—	4	2	no	—
62	D₈	—	4	1	no	—
63	D₈	—	4	1	no	—
64	C₂×C₈	—	188	1	no	—
65	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
67	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
68	C₁₆	—	188	1	no	—
69	C₂³	—	4	2	no	—
70	D₄	—	4	2	no	—
71	D₄	—	4	2	no	—
72	D₄	—	8	2	no	—
73	D₄	—	8	1	no	—
74	D₄	—	8	1	no	—
75	C₂×C₄	#10625334	1	1	yes	characteristic
76	C₂×C₄	#10625335	1	1	yes	characteristic
77	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	376	1	no	—
80	C₈	#10625334	1	1	yes	characteristic
81	C₈	#10625335	1	1	yes	characteristic
82	C₂²	—	8	2	no	—
83	C₂²	—	8	2	no	—
84	C₂²	—	8	2	no	—
85	C₂²	#13093945	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	#13093941	1	1	yes	characteristic
88	C₄	#13093945	1	1	yes	characteristic
89	C₄	#13093965	1	1	yes	characteristic
90	C₄	#13093968	1	1	yes	characteristic
91	C₂	—	16	2	no	—
92	C₂	#15688867	1	1	yes	characteristic
93	C₂	#15688924	1	1	yes	characteristic
94	C₂	#15688936	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13093945
commutator	C₂×C₈×C₄₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#493	C₂
socle	C₂²×C₄₇	#102
hypercenter	#493	D₄₇
hypocenter	C₄₇	#1361
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
1. C₄⋊(C₄₇⋊C₁₆)	C₂	semidirect
2. #15688876	C₂	semidirect
51. C₄₇	#1361	semidirect