Subgroups — C₂²×Dic₃₇₆ #20256501

Order 6016.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₈₈	C₂	1	2	yes	maximal
2	C₂×Dic₃₇₆	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₉₄	—	2	2	no	—
5	C₂×Dic₁₈₈	—	2	6	no	—
6	C₂×Dic₁₈₈	C₂²	1	12	yes	—
7	Dic₃₇₆	C₂²	1	16	yes	direct product factor
8	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₄₇	C₂²	1	6	yes	—
10	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
11	C₂²×Dic₄₇	—	4	2	no	—
12	C₂×Dic₉₄	—	2	12	no	—
13	C₂×Dic₉₄	—	4	6	no	—
14	C₂×C₈×C₄₇	D₄	1	3	yes	—
15	C₂×C₈×C₄₇	C₂³	1	3	yes	—
16	Dic₁₈₈	—	2	12	no	—
17	Dic₁₈₈	C₂³	1	8	yes	—
18	C₁₆×C₄₇	C₂³	1	4	yes	—
19	C₂³×C₄₇	D₈	1	1	yes	characteristic
20	C₂×C₄×C₄₇	D₈	1	3	yes	—
21	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
22	C₂×Dic₄₇	—	4	12	no	—
23	Dic₉₄	—	2	8	no	—
24	Dic₉₄	—	4	12	no	—
25	C₈×C₄₇	C₂×D₄	1	3	yes	—
26	C₈×C₄₇	C₂⁴	1	1	yes	characteristic
27	C₂²×C₄₇	Q₃₂	1	4	yes	complemented
28	C₂²×C₄₇	C₂×D₈	1	3	yes	—
29	C₄×C₄₇	C₂×D₈	1	3	yes	—
30	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
31	Dic₄₇	—	4	8	no	—
32	C₂²×Q₃₂	—	47	1	no	maximal, Sylow
33	C₂×C₄₇	C₂×Q₃₂	1	6	yes	complemented
34	C₂×C₄₇	C₂²×D₈	1	1	yes	characteristic
35	C₂²×Q₁₆	—	47	2	no	—
36	C₂×Q₃₂	—	47	12	no	—
37	C₂²×C₁₆	D₄₇	1	1	yes	characteristic
38	C₄₇	C₂²×Q₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂²×Q₈	—	94	2	no	—
40	C₂×Q₁₆	—	47	12	no	—
41	C₂×Q₁₆	—	94	6	no	—
42	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
43	Q₃₂	—	47	16	no	—
44	C₂×C₁₆	C₂×D₄₇	1	6	yes	—
45	C₂×Q₈	—	94	12	no	—
46	C₂×Q₈	—	188	6	no	—
47	C₂²×C₄	—	188	2	no	—
48	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
49	Q₁₆	—	47	8	no	—
50	Q₁₆	—	94	12	no	—
51	C₂×C₈	D₁₈₈	1	3	yes	—
52	C₂×C₈	C₂²×D₄₇	1	3	yes	—
53	C₁₆	C₂²×D₄₇	1	4	yes	—
54	C₂³	D₃₇₆	1	1	yes	characteristic
55	Q₈	—	94	8	no	—
56	Q₈	—	188	12	no	—
57	C₂×C₄	—	188	12	no	—
58	C₂×C₄	D₃₇₆	1	3	yes	—
59	C₂×C₄	C₂×D₁₈₈	1	3	yes	—
60	C₈	C₂×D₁₈₈	1	3	yes	—
61	C₈	C₂³×D₄₇	1	1	yes	characteristic
62	C₂²	Dic₃₇₆	1	4	yes	direct product factor
63	C₂²	C₂×D₃₇₆	1	3	yes	—
64	C₄	—	188	8	no	—
65	C₄	C₂×D₃₇₆	1	3	yes	—
66	C₄	C₂²×D₁₈₈	1	1	yes	characteristic
67	C₂	C₂×Dic₃₇₆	1	6	yes	direct product factor
68	C₂	C₂²×D₃₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃₇₆
commutator	C₈×C₄₇	C₂⁴
Frattini	C₈	C₂³×D₄₇
Fitting	C₂²×C₁₆×C₄₇	C₂
socle	C₂³×C₄₇	D₈
hypercenter	C₂²×C₁₆	D₄₇
hypocenter	C₄₇	C₂²×Q₃₂
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₃₇₆	C₂	direct (N × H)
7. Dic₃₇₆	C₂²	direct (N × H)
27. C₂²×C₄₇	Q₃₂	semidirect
33. C₂×C₄₇	C₂×Q₃₂	semidirect
38. C₄₇	C₂²×Q₃₂	semidirect
62. C₂²	Dic₃₇₆	direct (N × H)
67. C₂	C₂×Dic₃₇₆	direct (N × H)

Subgroups — C22×Dic376 #20256501

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×Dic₃₇₆ #20256501