Subgroups — #20245641

Order 6016.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₇₆	C₂	1	4	yes	maximal
2	#15689503	C₂	1	2	yes	maximal
3	C₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₈₈	—	2	2	no	—
5	C₂×Dic₁₈₈	C₂²	1	4	yes	—
6	#13094024	—	2	2	no	—
7	Dic₃₇₆	—	2	8	no	—
8	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
9	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₉₄	—	2	4	no	—
11	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
12	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
13	C₄²×C₄₇	D₄	1	1	yes	characteristic
14	C₄⋊Dic₄₇	—	4	4	no	—
15	Dic₁₈₈	—	2	8	no	—
16	Dic₁₈₈	—	4	4	no	—
17	C₁₆×C₄₇	D₄	1	4	yes	—
18	C₂×C₄×C₄₇	D₈	1	2	yes	—
19	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
20	C₂×Dic₄₇	—	4	4	no	—
21	Dic₉₄	—	4	4	no	—
22	Dic₉₄	—	4	4	no	—
23	C₈×C₄₇	D₈	1	2	yes	—
24	C₈×C₄₇	C₂×D₄	1	2	yes	—
25	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
26	C₄×C₄₇	Q₃₂	1	4	yes	complemented
27	C₄×C₄₇	#127	1	1	yes	characteristic
28	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
29	Dic₄₇	—	8	4	no	—
30	#2247	—	47	1	no	maximal, Sylow
31	C₂×C₄₇	#493	1	1	yes	characteristic
32	C₂×C₄₇	C₂×Q₃₂	1	2	yes	—
33	C₂×Q₃₂	—	47	4	no	—
34	#494	—	47	2	no	—
35	C₄×C₁₆	D₄₇	1	1	yes	characteristic
36	C₄₇	#2247	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	47	4	no	—
38	C₂×Q₁₆	—	94	2	no	—
39	C₄⋊Q₈	—	94	2	no	—
40	Q₃₂	—	94	8	no	—
41	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
42	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
43	C₂×Q₈	—	94	4	no	—
44	Q₁₆	—	94	8	no	—
45	Q₁₆	—	188	4	no	—
46	C₂×C₈	D₁₈₈	1	1	yes	characteristic
47	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
48	C₄⋊C₄	—	188	4	no	—
49	C₄²	D₁₈₈	1	1	yes	characteristic
50	C₁₆	D₁₈₈	1	4	yes	—
51	Q₈	—	188	4	no	—
52	Q₈	—	188	4	no	—
53	C₂×C₄	—	188	4	no	—
54	C₂×C₄	D₃₇₆	1	2	yes	—
55	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
56	C₈	D₃₇₆	1	2	yes	—
57	C₈	C₂×D₁₈₈	1	2	yes	—
58	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
59	C₄	—	376	4	no	—
60	C₄	Dic₃₇₆	1	4	yes	complemented
61	C₄	#13094021	1	1	yes	characteristic
62	C₄	C₂×D₃₇₆	1	1	yes	characteristic
63	C₂	#15689500	1	1	yes	characteristic
64	C₂	C₂×Dic₃₇₆	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄×C₁₆	D₄₇
hypocenter	C₄₇	#2247
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
26. C₄×C₄₇	Q₃₂	semidirect
36. C₄₇	#2247	semidirect
60. C₄	Dic₃₇₆	semidirect