Subgroups — #20242989

Order 6016.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689521	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689496	C₂	1	1	yes	maximal, characteristic
3	#15689474	C₂	1	2	yes	maximal, complemented
4	#15689470	C₂	1	2	yes	maximal
5	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625325	—	2	2	no	—
7	#13094024	C₂²	1	1	yes	characteristic
8	#13094024	C₂²	1	2	yes	—
9	#13094021	C₂²	1	1	yes	characteristic
10	#13093956	—	2	2	no	—
11	#13093949	—	2	4	no	—
12	#13093946	—	2	4	no	—
13	C₄×C₈×C₄₇	C₂²	1	2	yes	—
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×D₁₈₈	—	2	2	no	—
16	C₂×D₁₈₈	—	2	1	no	—
17	C₂×Dic₉₄	—	2	2	no	—
18	C₂×Dic₉₄	—	2	1	no	—
19	C₂×C₈×C₄₇	D₄	1	4	yes	—
20	C₂×C₈×C₄₇	D₄	1	2	yes	—
21	C₄²×C₄₇	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₄₇	—	2	2	no	—
23	C₄⋊Dic₄₇	—	2	2	no	—
24	C₄⋊Dic₄₇	—	2	2	no	—
25	#10625325	—	4	4	no	—
26	C₂²×D₄₇	—	4	1	no	—
27	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
29	C₂×Dic₄₇	—	4	1	no	—
30	C₂×Dic₄₇	—	4	2	no	—
31	D₁₈₈	—	4	2	no	—
32	D₁₈₈	—	4	4	no	—
33	Dic₉₄	—	4	2	no	—
34	Dic₉₄	—	4	4	no	—
35	C₈×C₄₇	—	2	4	no	—
36	C₈×C₄₇	SD₁₆	1	4	yes	—
37	C₂²×C₄₇	#127	1	1	yes	characteristic
38	C₂×D₄₇	—	8	1	no	—
39	C₂×D₄₇	—	8	2	no	—
40	C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
41	C₄×C₄₇	#135	1	4	yes	—
42	Dic₄₇	—	8	1	no	—
43	Dic₄₇	—	8	2	no	—
44	#1708	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	#492	1	1	yes	characteristic
46	C₂×C₄₇	#495	1	2	yes	—
47	D₄₇	—	16	1	no	—
48	#498	—	47	1	no	—
49	#492	—	47	1	no	—
50	#487	—	47	2	no	—
51	#486	—	47	2	no	—
52	C₈²	D₄₇	1	1	yes	characteristic, complemented
53	C₄₇	#1708	1	1	yes	characteristic, complemented, Sylow
54	C₂×SD₁₆	—	94	2	no	—
55	C₄⋊Q₈	—	47	2	no	—
56	C₄⋊Q₈	—	47	1	no	—
57	#127	—	47	1	no	—
58	#106	—	94	2	no	—
59	#103	—	94	4	no	—
60	#102	—	94	4	no	—
61	C₄×C₈	C₂×D₄₇	1	2	yes	—
62	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
63	C₂×Q₈	—	94	2	no	—
64	C₂×Q₈	—	94	1	no	—
65	C₂×D₄	—	94	2	no	—
66	C₂×D₄	—	94	1	no	—
67	SD₁₆	—	188	4	no	—
68	C₂×C₈	D₁₈₈	1	4	yes	—
69	C₂×C₈	D₁₈₈	1	2	yes	—
70	C₄⋊C₄	—	94	2	no	—
71	C₄⋊C₄	—	94	2	no	—
72	C₄⋊C₄	—	94	2	no	—
73	C₄²	C₂²×D₄₇	1	1	yes	characteristic
74	C₂³	—	188	1	no	—
75	Q₈	—	188	2	no	—
76	Q₈	—	188	4	no	—
77	D₄	—	188	2	no	—
78	D₄	—	188	4	no	—
79	C₂×C₄	—	188	1	no	—
80	C₂×C₄	—	188	2	no	—
81	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
82	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
83	C₈	—	2	4	no	—
84	C₈	#10625325	1	4	yes	—
85	C₂²	—	376	1	no	—
86	C₂²	—	376	2	no	—
87	C₂²	#13094021	1	1	yes	characteristic
88	C₄	—	376	1	no	—
89	C₄	—	376	2	no	—
90	C₄	C₂×#10625325	1	2	yes	—
91	C₄	#13094046	1	4	yes	—
92	C₂	—	752	1	no	—
93	C₂	#15689496	1	1	yes	characteristic
94	C₂	#15689507	1	2	yes	—

	subgroup	G/H
center	C₂²	#13094021
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₈²×C₄₇	C₂
socle	C₂²×C₄₇	#127
hypercenter	C₈²	D₄₇
hypocenter	C₄₇	#1708
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #15689521	C₂	semidirect
3. #15689474	C₂	semidirect
5. C₈²×C₄₇	C₂	semidirect
52. C₈²	D₄₇	semidirect
53. C₄₇	#1708	semidirect