Subgroups — C₂²×D₅₉₂ #18007702

Order 4736.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₉₆	C₂	1	2	yes	maximal, complemented
2	C₂×D₅₉₂	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₄₈	—	2	2	no	—
5	C₂×D₂₉₆	—	2	6	no	—
6	C₂×D₂₉₆	C₂²	1	12	yes	complemented
7	D₅₉₂	C₂²	1	16	yes	direct product factor
8	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₃₇	C₂²	1	6	yes	complemented
10	C₂³×D₃₇	—	4	2	no	—
11	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
12	C₂×D₁₄₈	—	2	12	no	—
13	C₂×D₁₄₈	—	4	6	no	—
14	C₂×C₈×C₃₇	D₄	1	3	yes	—
15	C₂×C₈×C₃₇	C₂³	1	3	yes	—
16	D₂₉₆	—	2	12	no	—
17	D₂₉₆	C₂³	1	8	yes	complemented
18	C₁₆×C₃₇	C₂³	1	4	yes	complemented
19	C₂³×C₃₇	D₈	1	1	yes	characteristic
20	C₂²×D₃₇	—	4	12	no	—
21	C₂²×D₃₇	—	8	8	no	—
22	C₂×C₄×C₃₇	D₈	1	3	yes	—
23	C₂×C₄×C₃₇	C₂×D₄	1	3	yes	—
24	D₁₄₈	—	2	8	no	—
25	D₁₄₈	—	4	12	no	—
26	C₈×C₃₇	C₂×D₄	1	3	yes	—
27	C₈×C₃₇	C₂⁴	1	1	yes	characteristic
28	C₂²×C₃₇	D₁₆	1	4	yes	complemented
29	C₂²×C₃₇	C₂×D₈	1	3	yes	—
30	C₂×D₃₇	—	4	8	no	—
31	C₂×D₃₇	—	8	24	no	—
32	C₄×C₃₇	C₂×D₈	1	3	yes	—
33	C₄×C₃₇	C₂²×D₄	1	1	yes	characteristic
34	C₂²×D₁₆	—	37	1	no	maximal, Sylow
35	C₂×C₃₇	C₂×D₁₆	1	6	yes	complemented
36	C₂×C₃₇	C₂²×D₈	1	1	yes	characteristic
37	D₃₇	—	8	8	no	—
38	C₂²×D₈	—	37	2	no	—
39	C₂×D₁₆	—	37	12	no	—
40	C₂²×C₁₆	D₃₇	1	1	yes	characteristic, complemented
41	C₃₇	C₂²×D₁₆	1	1	yes	characteristic, complemented, Sylow
42	C₂²×D₄	—	74	2	no	—
43	C₂×D₈	—	37	12	no	—
44	C₂×D₈	—	74	6	no	—
45	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
46	D₁₆	—	37	16	no	—
47	C₂×C₁₆	C₂×D₃₇	1	6	yes	complemented
48	C₂⁴	—	148	2	no	—
49	C₂×D₄	—	74	12	no	—
50	C₂×D₄	—	148	6	no	—
51	C₂²×C₄	D₁₄₈	1	1	yes	characteristic
52	D₈	—	37	8	no	—
53	D₈	—	74	12	no	—
54	C₂×C₈	D₁₄₈	1	3	yes	—
55	C₂×C₈	C₂²×D₃₇	1	3	yes	—
56	C₁₆	C₂²×D₃₇	1	4	yes	complemented
57	C₂³	—	296	8	no	—
58	C₂³	—	148	12	no	—
59	C₂³	D₂₉₆	1	1	yes	characteristic
60	D₄	—	74	8	no	—
61	D₄	—	148	12	no	—
62	C₂×C₄	D₂₉₆	1	3	yes	—
63	C₂×C₄	C₂×D₁₄₈	1	3	yes	—
64	C₈	C₂×D₁₄₈	1	3	yes	—
65	C₈	C₂³×D₃₇	1	1	yes	characteristic
66	C₂²	—	296	24	no	—
67	C₂²	—	148	8	no	—
68	C₂²	D₅₉₂	1	4	yes	direct product factor
69	C₂²	C₂×D₂₉₆	1	3	yes	—
70	C₄	C₂×D₂₉₆	1	3	yes	—
71	C₄	C₂²×D₁₄₈	1	1	yes	characteristic
72	C₂	—	296	8	no	—
73	C₂	C₂×D₅₉₂	1	6	yes	direct product factor
74	C₂	C₂²×D₂₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₉₆
commutator, cosocle	C₈×C₃₇	C₂⁴
Frattini	C₈	C₂³×D₃₇
Fitting	C₂²×C₁₆×C₃₇	C₂
socle	C₂³×C₃₇	D₈
hypercenter	C₂²×C₁₆	D₃₇
hypocenter	C₃₇	C₂²×D₁₆
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
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
1. C₂²×D₂₉₆	C₂	semidirect
2. C₂×D₅₉₂	C₂	direct (N × H)
3. C₂²×C₁₆×C₃₇	C₂	semidirect
6. C₂×D₂₉₆	C₂²	semidirect
7. D₅₉₂	C₂²	direct (N × H)
9. C₂×C₁₆×C₃₇	C₂²	semidirect
17. D₂₉₆	C₂³	semidirect
18. C₁₆×C₃₇	C₂³	semidirect
28. C₂²×C₃₇	D₁₆	semidirect
35. C₂×C₃₇	C₂×D₁₆	semidirect
40. C₂²×C₁₆	D₃₇	semidirect
41. C₃₇	C₂²×D₁₆	semidirect
47. C₂×C₁₆	C₂×D₃₇	semidirect
56. C₁₆	C₂²×D₃₇	semidirect
68. C₂²	D₅₉₂	direct (N × H)
73. C₂	C₂×D₅₉₂	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×D₂₉₆	2
C₂×D₅₉₂	2
C₂²×C₁₆×C₃₇	2
C₂²×D₁₆	37

Subgroups — C22×D592 #18007702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₅₉₂ #18007702