Subgroups — #20241366

Order 6016.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₉₄	C₄	1	1	yes	characteristic
5	C₂×C₄₇⋊C₁₆	—	2	1	no	—
6	C₄⋊(C₄₇⋊C₈)	C₄	1	1	yes	characteristic
7	Dic₄₇⋊C₈	—	2	1	no	—
8	C₈×Dic₄₇	—	2	1	no	—
9	C₂×C₁₆×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₉₄	C₈	1	1	yes	characteristic
12	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
16	Dic₄₇⋊C₄	—	2	1	no	—
17	C₄×Dic₄₇	—	2	1	no	—
18	C₂×C₄₇⋊C₈	—	2	1	no	—
19	C₁₆×C₄₇	—	4	1	no	—
20	C₄₇⋊C₁₆	—	2	2	no	—
21	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
24	C₂×Dic₄₇	—	2	1	no	—
25	C₂×Dic₄₇	—	2	1	no	—
26	Dic₉₄	—	2	1	no	—
27	Dic₉₄	C₁₆	1	2	yes	complemented
28	C₈×C₄₇	—	2	1	no	—
29	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
30	C₈×C₄₇	Q₁₆	1	1	yes	characteristic
31	C₄₇⋊C₈	—	4	1	no	—
32	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₄₇	—	2	1	no	—
34	C₄×C₄₇	#103	1	1	yes	characteristic
35	C₄×C₄₇	#104	1	1	yes	characteristic
36	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₄₇	M₃₂	1	1	yes	characteristic
38	Dic₄₇	—	2	2	no	—
39	Dic₄₇	—	4	1	no	—
40	Q₈⋊C₁₆	—	47	1	no	maximal, Sylow
41	C₂×C₄₇	Q₈⋊C₈	1	1	yes	characteristic
42	C₂×C₄₇	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₂×C₄₇	#350	1	1	yes	characteristic
44	C₈×Q₈	—	47	1	no	—
45	C₄⋊C₁₆	D₄₇	1	1	yes	characteristic
46	C₄×C₁₆	—	47	1	no	—
47	C₄₇	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
48	C₄×Q₈	—	47	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	94	1	no	—
51	C₄⋊C₈	—	47	1	no	—
52	C₄⋊C₈	—	94	1	no	—
53	C₄×C₈	—	94	1	no	—
54	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
55	C₂×Q₈	—	47	1	no	—
56	C₂×C₈	—	94	1	no	—
57	C₂×C₈	D₁₈₈	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
59	C₄⋊C₄	—	47	1	no	—
60	C₄⋊C₄	—	94	1	no	—
61	C₄²	—	94	1	no	—
62	C₄²	C₄×D₄₇	1	1	yes	characteristic
63	C₁₆	—	4	1	no	—
64	C₁₆	—	94	2	no	—
65	Q₈	—	47	2	no	—
66	Q₈	—	94	1	no	—
67	C₂×C₄	—	94	1	no	—
68	C₂×C₄	—	94	1	no	—
69	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
70	C₂×C₄	#10625324	1	1	yes	characteristic
71	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	188	1	no	—
74	C₈	#10625335	1	1	yes	characteristic
75	C₈	#10625337	1	1	yes	characteristic
76	C₂²	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	94	2	no	—
79	C₄	—	188	1	no	—
80	C₄	#13093947	1	1	yes	characteristic
81	C₄	#13093950	1	1	yes	characteristic
82	C₄	C₁₆×D₄₇	1	1	yes	characteristic
83	C₄	#13093963	1	1	yes	characteristic
84	C₂	#15688853	1	1	yes	characteristic
85	C₂	(C₂×D₄₇)⋊C₁₆	1	1	yes	characteristic
86	C₂	#15688908	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×C₄⋊C₁₆	C₂
socle	C₂²×C₄₇	C₂²⋊C₈
hypercenter	C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	Q₈⋊C₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
27. Dic₉₄	C₁₆	semidirect
47. C₄₇	Q₈⋊C₁₆	semidirect