Subgroups — #20243508

Order 6016.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal
2	#15688878	C₂	1	4	yes	maximal
3	C₄₇×#376	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₇⋊C₈	C₂²	1	4	yes	—
5	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
6	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
7	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
8	#95×C₄₇	C₄	1	4	yes	—
9	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
10	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
11	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
12	C₄²×C₄₇	—	2	4	no	—
13	C₄²×C₄₇	D₄	1	2	yes	—
14	C₄²×C₄₇	Q₈	1	2	yes	—
15	C₂×C₄₇⋊C₈	—	2	4	no	—
16	C₂×C₄₇⋊C₈	—	2	8	no	—
17	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₇	—	2	4	no	—
19	C₂×C₄×C₄₇	—	2	4	no	—
20	C₂×C₄×C₄₇	—	2	8	no	—
21	C₂×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₄₇	#41	1	4	yes	—
25	C₄₇⋊C₈	—	4	4	no	—
26	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₇	#117	1	2	yes	—
28	C₂²×C₄₇	#131	1	4	yes	—
29	C₄×C₄₇	—	2	4	no	—
30	C₄×C₄₇	—	4	4	no	—
31	C₄×C₄₇	#124	1	2	yes	—
32	C₄×C₄₇	#125	1	2	yes	—
33	#1832	—	47	1	no	maximal, Sylow
34	C₂×C₄₇	#382	1	1	yes	characteristic
35	C₂×C₄₇	#424	1	2	yes	—
36	C₂×C₄₇	#433	1	4	yes	—
37	C₂×C₄⋊C₈	—	47	2	no	—
38	#376	D₄₇	1	1	yes	characteristic
39	#336	—	47	4	no	—
40	C₄₇	#1832	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	—	47	4	no	—
42	C₂×C₄²	C₂×D₄₇	1	2	yes	—
43	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
44	C₄⋊C₈	—	94	4	no	—
45	#95	Dic₄₇	1	4	yes	—
46	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
47	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
48	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
49	C₂×C₈	—	94	4	no	—
50	C₂×C₈	—	94	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	Dic₉₄	1	2	yes	—
53	C₄²	D₁₈₈	1	2	yes	—
54	C₂³	C₂²×Dic₄₇	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	8	no	—
58	C₂×C₄	C₄⋊Dic₄₇	1	4	yes	—
59	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
60	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
61	C₂×C₄	#10625350	1	4	yes	—
62	C₈	—	188	4	no	—
63	C₂²	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
64	C₂²	#13093983	1	2	yes	—
65	C₂²	#13094031	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	4	4	no	—
68	C₄	#13094012	1	2	yes	—
69	C₄	#13094016	1	2	yes	—
70	C₂	#15688989	1	1	yes	characteristic
71	C₂	#15689150	1	2	yes	—
72	C₂	#15689184	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator, socle	C₂³×C₄₇	C₂²×C₄
Fitting	C₄₇×#376	C₂
hypercenter	#376	D₄₇
hypocenter	C₄₇	#1832
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
40. C₄₇	#1832	semidirect