Subgroups — #20242995

Order 6016.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689500	C₂	1	1	yes	maximal, characteristic
2	#15689471	C₂	1	4	yes	maximal, complemented
3	C₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₇₆	—	2	2	no	—
6	#13094021	C₂²	1	2	yes	—
7	#13093944	—	2	8	no	—
8	C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₄₇	—	2	2	no	—
10	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
11	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₄₇	—	2	2	no	—
13	C₂×D₁₈₈	—	2	4	no	—
14	C₂×D₁₈₈	—	2	2	no	—
15	Q₁₆×C₄₇	—	4	4	no	—
16	C₂×C₈×C₄₇	D₄	1	2	yes	—
17	C₄⋊C₄×C₄₇	—	2	4	no	—
18	C₄²×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×C₄₇⋊C₈	D₄	1	4	yes	—
20	D₃₇₆	—	4	4	no	—
21	C₂²×D₄₇	—	4	2	no	—
22	Q₈×C₄₇	—	4	4	no	—
23	C₂×C₄×C₄₇	—	4	2	no	—
24	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
26	D₁₈₈	—	4	4	no	—
27	D₁₈₈	—	4	8	no	—
28	C₈×C₄₇	D₈	1	4	yes	—
29	C₄₇⋊C₈	—	2	4	no	—
30	C₂²×C₄₇	#127	1	1	yes	characteristic
31	C₂×D₄₇	—	8	2	no	—
32	C₂×D₄₇	—	8	4	no	—
33	C₄×C₄₇	—	8	2	no	—
34	C₄×C₄₇	C₂×D₈	1	2	yes	—
35	C₄×C₄₇	#135	1	4	yes	—
36	#1709	—	47	1	no	maximal, Sylow
37	C₂×C₄₇	#493	1	1	yes	characteristic
38	C₂×C₄₇	#495	1	2	yes	—
39	D₄₇	—	16	2	no	—
40	#494	D₄₇	1	1	yes	characteristic, complemented
41	#493	—	47	1	no	—
42	#486	—	47	4	no	—
43	C₈²	—	47	1	no	—
44	C₄₇	#1709	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	2	2	no	—
46	C₂×D₈	—	94	2	no	—
47	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
48	#127	—	47	2	no	—
49	#102	—	94	8	no	—
50	C₄×C₈	—	47	2	no	—
51	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
52	C₂×Q₈	—	2	2	no	—
53	C₂×D₄	—	94	4	no	—
54	C₂×D₄	—	94	2	no	—
55	Q₁₆	—	4	4	no	—
56	D₈	—	188	4	no	—
57	C₂×C₈	—	47	4	no	—
58	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
59	C₄⋊C₄	—	2	4	no	—
60	C₄²	C₂²×D₄₇	1	1	yes	characteristic
61	C₂³	—	188	2	no	—
62	Q₈	—	4	4	no	—
63	D₄	—	188	4	no	—
64	D₄	—	188	8	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	D₄×D₄₇	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
68	C₈	—	94	4	no	—
69	C₈	#10625334	1	4	yes	—
70	C₂²	—	376	2	no	—
71	C₂²	—	376	4	no	—
72	C₂²	#13094020	1	1	yes	characteristic
73	C₄	—	8	2	no	—
74	C₄	C₂×#10625334	1	2	yes	—
75	C₄	#13094047	1	4	yes	—
76	C₂	—	752	2	no	—
77	C₂	#15689499	1	1	yes	characteristic
78	C₂	#15689508	1	2	yes	—

	subgroup	G/H
center	C₂²	#13094020
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#494	C₂
socle	C₂²×C₄₇	#127
hypercenter	#494	D₄₇
hypocenter	C₄₇	#1709
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
2. #15689471	C₂	semidirect
3. C₈×C₄₇⋊C₈	C₂	semidirect
4. C₄₇×#494	C₂	semidirect
40. #494	D₄₇	semidirect
44. C₄₇	#1709	semidirect