Subgroups — #20245639

Order 6016.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₇₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093970	C₂	1	2	yes	maximal
3	#15689501	C₂	1	2	yes	maximal
4	C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₈₈	C₂²	1	2	yes	—
7	C₂×#10625337	—	2	2	no	—
8	#13094022	—	2	2	no	—
9	Dic₃₇₆	—	2	2	no	—
10	#13093970	—	2	4	no	—
11	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×Q₁₆×C₄₇	C₂²	1	2	yes	—
14	Q₃₂×C₄₇	—	2	2	no	—
15	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₄₇	—	2	2	no	—
17	C₂×Dic₉₄	—	2	2	no	—
18	Q₁₆×C₄₇	—	2	2	no	—
19	Q₁₆×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
21	#10625337	—	4	4	no	—
22	Dic₄₇⋊C₄	—	4	4	no	—
23	C₄×Dic₄₇	D₄	1	1	yes	characteristic
24	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
25	Dic₁₈₈	—	2	2	no	—
26	Dic₁₈₈	—	2	2	no	—
27	C₁₆×C₄₇	D₄	1	2	yes	—
28	C₄₇⋊C₁₆	D₄	1	2	yes	—
29	Q₈×C₄₇	—	4	2	no	—
30	Q₈×C₄₇	—	4	2	no	—
31	C₂×C₄×C₄₇	—	4	2	no	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₄₇	—	4	2	no	—
34	C₂×Dic₄₇	D₈	1	2	yes	—
35	Dic₉₄	—	4	2	no	—
36	Dic₉₄	—	4	2	no	—
37	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₄₇⋊C₈	D₈	1	2	yes	—
40	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
41	C₄×C₄₇	—	8	2	no	—
42	C₄×C₄₇	#127	1	1	yes	characteristic
43	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
44	Dic₄₇	—	8	2	no	—
45	Dic₄₇	Q₃₂	1	4	yes	complemented
46	#2247	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	#493	1	1	yes	characteristic
48	C₂×C₄₇	C₂×Q₃₂	1	2	yes	—
49	C₂×Q₃₂	—	47	2	no	—
50	C₂×Q₃₂	—	47	1	no	—
51	C₂×Q₃₂	D₄₇	1	1	yes	characteristic
52	#494	—	47	2	no	—
53	C₄×C₁₆	—	47	1	no	—
54	C₄₇	#2247	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	47	2	no	—
56	C₂×Q₁₆	—	94	2	no	—
57	C₂×Q₁₆	C₂×D₄₇	1	2	yes	—
58	C₄⋊Q₈	—	94	2	no	—
59	Q₃₂	—	2	2	no	—
60	Q₃₂	—	94	4	no	—
61	Q₃₂	—	94	2	no	—
62	C₂×C₁₆	—	47	1	no	—
63	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
64	C₄×C₈	—	47	1	no	—
65	C₂×Q₈	—	2	2	no	—
66	C₂×Q₈	—	94	2	no	—
67	Q₁₆	—	2	2	no	—
68	Q₁₆	—	2	2	no	—
69	Q₁₆	—	94	2	no	—
70	Q₁₆	—	94	2	no	—
71	Q₁₆	—	188	4	no	—
72	C₂×C₈	—	47	1	no	—
73	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
74	C₄⋊C₄	—	188	4	no	—
75	C₄²	—	47	1	no	—
76	C₁₆	—	47	2	no	—
77	C₁₆	C₂²⋊D₄₇	1	2	yes	—
78	Q₈	—	4	2	no	—
79	Q₈	—	4	2	no	—
80	Q₈	—	188	2	no	—
81	Q₈	—	188	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	47	2	no	—
84	C₂×C₄	—	188	2	no	—
85	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
86	C₈	—	47	2	no	—
87	C₈	D₄×D₄₇	1	1	yes	characteristic
88	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
89	C₂²	D₈×D₄₇	1	1	yes	characteristic
90	C₄	—	8	2	no	—
91	C₄	—	47	4	no	—
92	C₄	—	376	2	no	—
93	C₄	#13094020	1	1	yes	characteristic
94	C₄	D₈×D₄₇	1	1	yes	characteristic
95	C₂	#15689498	1	1	yes	characteristic
96	C₂	Q₃₂×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×Q₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂×Q₃₂	D₄₇
hypocenter	C₄₇	#2247
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
45. Dic₄₇	Q₃₂	semidirect
54. C₄₇	#2247	semidirect