Subgroups — C₂²×Dic₂₃₂ #16832605

Order 3712.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₁₆	C₂	1	2	yes	maximal
2	C₂×Dic₂₃₂	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₅₈	—	2	2	no	—
5	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×Dic₁₁₆	—	2	6	no	—
7	C₂×Dic₁₁₆	C₂²	1	12	yes	—
8	C₂×C₁₆×C₂₉	C₂²	1	6	yes	—
9	Dic₂₃₂	C₂²	1	16	yes	direct product factor
10	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
11	C₂²×Dic₂₉	—	4	2	no	—
12	C₂×Dic₅₈	—	2	12	no	—
13	C₂×Dic₅₈	—	4	6	no	—
14	C₂×C₈×C₂₉	D₄	1	3	yes	—
15	C₂×C₈×C₂₉	C₂³	1	3	yes	—
16	Dic₁₁₆	—	2	12	no	—
17	Dic₁₁₆	C₂³	1	8	yes	—
18	C₁₆×C₂₉	C₂³	1	4	yes	—
19	C₂³×C₂₉	D₈	1	1	yes	characteristic
20	C₂×C₄×C₂₉	D₈	1	3	yes	—
21	C₂×C₄×C₂₉	C₂×D₄	1	3	yes	—
22	C₂×Dic₂₉	—	4	12	no	—
23	Dic₅₈	—	2	8	no	—
24	Dic₅₈	—	4	12	no	—
25	C₈×C₂₉	C₂×D₄	1	3	yes	—
26	C₈×C₂₉	C₂⁴	1	1	yes	characteristic
27	C₂²×Q₃₂	—	29	1	no	maximal, Sylow
28	C₂²×C₂₉	Q₃₂	1	4	yes	complemented
29	C₂²×C₂₉	C₂×D₈	1	3	yes	—
30	C₄×C₂₉	C₂×D₈	1	3	yes	—
31	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
32	Dic₂₉	—	4	8	no	—
33	C₂²×Q₁₆	—	29	2	no	—
34	C₂×Q₃₂	—	29	12	no	—
35	C₂²×C₁₆	D₂₉	1	1	yes	characteristic
36	C₂×C₂₉	C₂×Q₃₂	1	6	yes	complemented
37	C₂×C₂₉	C₂²×D₈	1	1	yes	characteristic
38	C₂²×Q₈	—	58	2	no	—
39	C₂×Q₁₆	—	29	12	no	—
40	C₂×Q₁₆	—	58	6	no	—
41	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic
42	Q₃₂	—	29	16	no	—
43	C₂×C₁₆	C₂×D₂₉	1	6	yes	—
44	C₂₉	C₂²×Q₃₂	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	58	12	no	—
46	C₂×Q₈	—	116	6	no	—
47	C₂²×C₄	—	116	2	no	—
48	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
49	Q₁₆	—	29	8	no	—
50	Q₁₆	—	58	12	no	—
51	C₂×C₈	D₁₁₆	1	3	yes	—
52	C₂×C₈	C₂²×D₂₉	1	3	yes	—
53	C₁₆	C₂²×D₂₉	1	4	yes	—
54	C₂³	D₂₃₂	1	1	yes	characteristic
55	Q₈	—	58	8	no	—
56	Q₈	—	116	12	no	—
57	C₂×C₄	—	116	12	no	—
58	C₂×C₄	D₂₃₂	1	3	yes	—
59	C₂×C₄	C₂×D₁₁₆	1	3	yes	—
60	C₈	C₂×D₁₁₆	1	3	yes	—
61	C₈	C₂³×D₂₉	1	1	yes	characteristic
62	C₂²	Dic₂₃₂	1	4	yes	direct product factor
63	C₂²	C₂×D₂₃₂	1	3	yes	—
64	C₄	—	116	8	no	—
65	C₄	C₂×D₂₃₂	1	3	yes	—
66	C₄	C₂²×D₁₁₆	1	1	yes	characteristic
67	C₂	C₂×Dic₂₃₂	1	6	yes	direct product factor
68	C₂	C₂²×D₂₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₃₂
commutator, cosocle	C₈×C₂₉	C₂⁴
Frattini	C₈	C₂³×D₂₉
Fitting	C₂²×C₁₆×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	D₈
hypercenter	C₂²×C₁₆	D₂₉
hypocenter	C₂₉	C₂²×Q₃₂
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
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×Dic₂₃₂	C₂	direct (N × H)
9. Dic₂₃₂	C₂²	direct (N × H)
28. C₂²×C₂₉	Q₃₂	semidirect
36. C₂×C₂₉	C₂×Q₃₂	semidirect
44. C₂₉	C₂²×Q₃₂	semidirect
62. C₂²	Dic₂₃₂	direct (N × H)
67. C₂	C₂×Dic₂₃₂	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×Dic₁₁₆	2
C₂×Dic₂₃₂	2
C₂²×C₁₆×C₂₉	2
C₂²×Q₃₂	29

Subgroups — C22×Dic232 #16832605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₂₃₂ #16832605