Subgroups — #20243526

Order 6016.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689147	C₂	1	2	yes	maximal
2	#15688888	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10625329	C₂²	1	4	yes	—
5	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
6	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
7	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₄₇	C₄	1	2	yes	—
9	C₄×C₈×C₄₇	C₄	1	2	yes	—
10	C₂²×C₄×C₄₇	Q₈	1	2	yes	—
11	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
12	C₂×C₈×C₄₇	—	2	4	no	—
13	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
14	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₄²×C₄₇	D₄	1	2	yes	—
17	#10625329	—	2	8	no	—
18	C₂×C₄₇⋊C₈	—	2	4	no	—
19	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₄₇	—	2	4	no	—
21	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
22	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₄₇	#41	1	4	yes	—
26	C₈×C₄₇	—	2	4	no	—
27	C₄₇⋊C₈	—	4	4	no	—
28	C₂²×C₄₇	—	2	2	no	—
29	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄₇	#125	1	2	yes	—
31	C₄×C₄₇	—	2	2	no	—
32	C₄×C₄₇	#108	1	4	yes	—
33	C₄×C₄₇	#117	1	2	yes	—
34	C₄×C₄₇	#124	1	2	yes	—
35	#1837	—	47	1	no	maximal, Sylow
36	C₂×C₄₇	—	2	2	no	—
37	C₂×C₄₇	#382	1	1	yes	characteristic
38	C₂×C₄₇	C₂×#108	1	2	yes	—
39	#423	—	47	2	no	—
40	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
41	#341	—	47	4	no	—
42	C₄₇	#1837	1	1	yes	characteristic, complemented, Sylow
43	C₂×M₁₆	—	47	4	no	—
44	C₂²×C₈	C₂×D₄₇	1	2	yes	—
45	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
46	C₄⋊C₈	—	94	4	no	—
47	C₄×C₈	Dic₄₇	1	2	yes	—
48	C₄×C₈	Dic₄₇	1	2	yes	—
49	C₂²×C₄	Dic₉₄	1	2	yes	—
50	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
51	M₁₆	—	94	8	no	—
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	94	4	no	—
54	C₂×C₈	C₂×Dic₄₇	1	4	yes	—
55	C₄²	D₁₈₈	1	2	yes	—
56	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
57	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
58	C₂³	C₂×Dic₉₄	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
62	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
63	C₂×C₄	#10625350	1	4	yes	—
64	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₈	—	188	4	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
69	C₂²	#13094016	1	2	yes	—
70	C₄	—	2	2	no	—
71	C₄	#13093960	1	4	yes	—
72	C₄	#13093983	1	2	yes	—
73	C₄	#13094012	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	#15688989	1	1	yes	characteristic
76	C₂	C₂×#13093960	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄⋊C₄
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	#1837
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
42. C₄₇	#1837	semidirect