Subgroups — #20241360

Order 6016.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689241	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#364	C₂	1	1	yes	maximal, characteristic, complemented
4	#13094046	C₄	1	1	yes	characteristic
5	#13094030	—	2	1	no	—
6	#13093960	C₄	1	1	yes	characteristic
7	#13093952	—	2	1	no	—
8	C₄×C₄₇⋊C₈	—	2	1	no	—
9	M₃₂×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	#10625350	—	2	1	no	—
12	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₄²×C₄₇	D₄	1	1	yes	characteristic
15	#10625329	—	2	1	no	—
16	C₂×C₄₇⋊C₈	—	2	2	no	—
17	Dic₁₈₈	C₈	1	1	yes	characteristic, complemented
18	D₃₇₆	C₈	1	1	yes	characteristic, complemented
19	#10625325	—	2	1	no	—
20	#10625324	—	4	1	no	—
21	C₈×D₄₇	—	4	1	no	—
22	C₁₆×C₄₇	—	4	1	no	—
23	C₂×C₄×C₄₇	—	2	1	no	—
24	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₄₇	—	4	1	no	—
26	D₁₈₈	—	2	1	no	—
27	C₄×D₄₇	—	4	1	no	—
28	Dic₉₄	—	2	1	no	—
29	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
30	C₈×C₄₇	M₁₆	1	1	yes	characteristic
31	C₈×C₄₇	D₈	1	1	yes	characteristic
32	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
33	C₄₇⋊C₈	—	2	4	no	—
34	C₄₇⋊C₈	—	4	1	no	—
35	C₂²×C₄₇	#104	1	1	yes	characteristic
36	C₂×D₄₇	—	4	1	no	—
37	C₄×C₄₇	—	2	2	no	—
38	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₄₇	#102	1	1	yes	characteristic
40	Dic₄₇	—	4	1	no	—
41	#1335	—	47	1	no	maximal, Sylow
42	C₂×C₄₇	—	2	1	no	—
43	C₂×C₄₇	D₄⋊C₈	1	1	yes	characteristic
44	D₄₇	—	8	1	no	—
45	#443	—	47	1	no	—
46	#364	D₄₇	1	1	yes	characteristic, complemented
47	C₈²	—	47	1	no	—
48	C₄₇	#1335	1	1	yes	characteristic, complemented, Sylow
49	#135	—	47	1	no	—
50	#131	—	94	1	no	—
51	M₃₂	—	2	1	no	—
52	#108	—	47	1	no	—
53	#104	—	94	1	no	—
54	C₄×C₈	—	94	1	no	—
55	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
56	#41	—	94	1	no	—
57	Q₁₆	—	47	1	no	—
58	SD₁₆	—	94	1	no	—
59	D₈	—	47	1	no	—
60	M₁₆	—	94	1	no	—
61	M₁₆	—	188	1	no	—
62	C₂×C₈	—	94	2	no	—
63	C₂×C₈	—	188	1	no	—
64	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
66	C₄²	D₁₈₈	1	1	yes	characteristic
67	C₁₆	—	4	1	no	—
68	Q₈	—	94	1	no	—
69	D₄	—	94	1	no	—
70	D₄	—	188	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	188	1	no	—
73	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
74	C₈	—	94	4	no	—
75	C₈	—	188	1	no	—
76	C₈	C₈×D₄₇	1	1	yes	characteristic
77	C₈	#10625324	1	1	yes	characteristic
78	C₈	#10625334	1	1	yes	characteristic
79	C₈	#10625336	1	1	yes	characteristic
80	C₂²	—	188	1	no	—
81	C₂²	#13093950	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	188	1	no	—
84	C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
85	C₄	#13093944	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	376	1	no	—
88	C₂	#15688850	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#10625334
commutator	C₈×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#364	C₂
socle	C₂×C₄₇	D₄⋊C₈
hypercenter	#364	D₄₇
hypocenter	C₄₇	#1335
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. C₈×C₄₇⋊C₈	C₂	semidirect
3. C₄₇×#364	C₂	semidirect
17. Dic₁₈₈	C₈	semidirect
18. D₃₇₆	C₈	semidirect
46. #364	D₄₇	semidirect
48. C₄₇	#1335	semidirect