Subgroups — #20241382

Order 6016.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688905	C₂	1	1	yes	maximal, characteristic
2	C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#470	C₂	1	1	yes	maximal, characteristic
4	C₂×#10625329	—	2	1	no	—
5	#13093964	—	2	1	no	—
6	C₂×Q₁₆×C₄₇	C₄	1	1	yes	characteristic
7	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²⋊Q₈×C₄₇	—	2	1	no	—
9	#106×C₄₇	C₄	1	1	yes	characteristic
10	#103×C₄₇	—	2	1	no	—
11	C₂×Q₈×C₄₇	—	2	1	no	—
12	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
13	Q₁₆×C₄₇	—	4	1	no	—
14	M₁₆×C₄₇	—	4	1	no	—
15	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₄₇	—	2	1	no	—
18	C₄⋊C₄×C₄₇	—	4	1	no	—
19	C₂²⋊C₄×C₄₇	—	4	1	no	—
20	#10625329	—	4	1	no	—
21	#10625329	—	4	1	no	—
22	C₂×C₄₇⋊C₈	—	2	2	no	—
23	C₄₇⋊C₁₆	—	4	1	no	—
24	C₂³×C₄₇	SD₁₆	1	1	yes	characteristic
25	Q₈×C₄₇	—	4	1	no	—
26	Q₈×C₄₇	—	4	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	—	2	1	no	—
29	C₂×C₄×C₄₇	—	4	1	no	—
30	C₂×C₄×C₄₇	—	4	1	no	—
31	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
33	C₈×C₄₇	—	2	1	no	—
34	C₈×C₄₇	—	2	1	no	—
35	C₄₇⋊C₈	—	4	2	no	—
36	C₂²×C₄₇	—	2	1	no	—
37	C₂²×C₄₇	—	4	1	no	—
38	C₂²×C₄₇	#102	1	1	yes	characteristic
39	C₄×C₄₇	—	2	1	no	—
40	C₄×C₄₇	—	8	1	no	—
41	C₄×C₄₇	—	8	1	no	—
42	C₄×C₄₇	#99	1	1	yes	characteristic
43	C₄×C₄₇	#104	1	1	yes	characteristic
44	#1342	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	—	2	1	no	—
46	C₂×C₄₇	—	4	1	no	—
47	C₂×C₄₇	#327	1	1	yes	characteristic
48	#470	D₄₇	1	1	yes	characteristic
49	#349	—	47	1	no	—
50	#338	—	47	1	no	—
51	C₄₇	#1342	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	Dic₄₇	1	1	yes	characteristic
53	C₂×M₁₆	—	94	1	no	—
54	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
55	C₂²⋊Q₈	—	2	1	no	—
56	M₃₂	—	94	1	no	—
57	#106	Dic₄₇	1	1	yes	characteristic
58	#103	—	2	1	no	—
59	C₂×Q₈	—	2	1	no	—
60	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
61	Q₁₆	—	4	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	188	1	no	—
64	M₁₆	—	188	1	no	—
65	C₂×C₈	—	94	2	no	—
66	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	4	1	no	—
71	C₁₆	—	188	1	no	—
72	C₂³	#10625335	1	1	yes	characteristic
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	#10625334	1	1	yes	characteristic
80	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	188	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#13093945	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	8	1	no	—
89	C₄	—	8	1	no	—
90	C₄	#13093939	1	1	yes	characteristic
91	C₄	#13093951	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#15688857	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688857
commutator	C₂×C₈×C₄₇	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₄₇
Fitting	C₄₇×#470	C₂
socle	C₂×C₄₇	#327
hypercenter	#470	D₄₇
hypocenter	C₄₇	#1342
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

Complements

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

N	H ≅ G/N	type
51. C₄₇	#1342	semidirect