Subgroups — C₄×Dic₂₃₂ #16821352

Order 3712.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₁₆	C₂	1	2	yes	maximal
3	#14270989	C₂	1	1	yes	maximal, characteristic
4	#14270968	C₂	1	2	yes	maximal
5	C₄×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₁₆	C₂²	1	2	yes	—
7	C₄×Dic₅₈	—	2	2	no	—
8	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	#11745166	C₂²	1	2	yes	—
12	#11745164	—	2	2	no	—
13	Dic₂₃₂	C₄	1	4	yes	direct product factor
14	C₂×Dic₅₈	—	2	2	no	—
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
17	C₄²×C₂₉	D₄	1	1	yes	characteristic
18	C₄⋊Dic₂₉	—	2	2	no	—
19	#90779	—	4	2	no	—
20	C₄×Dic₂₉	—	4	2	no	—
21	Dic₁₁₆	—	2	2	no	—
22	Dic₁₁₆	C₂×C₄	1	4	yes	—
23	C₁₆×C₂₉	—	2	1	no	—
24	C₁₆×C₂₉	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
26	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₂₉	—	4	2	no	—
29	C₂×Dic₂₉	—	4	2	no	—
30	Dic₅₈	—	2	4	no	—
31	Dic₅₈	—	4	2	no	—
32	C₈×C₂₉	—	2	1	no	—
33	C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₂₉	#41	1	1	yes	characteristic
35	C₄×Q₃₂	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂×D₈	1	1	yes	characteristic
37	C₄×C₂₉	—	2	1	no	—
38	C₄×C₂₉	Q₃₂	1	2	yes	complemented
39	C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
40	C₄×C₂₉	#135	1	1	yes	characteristic
41	Dic₂₉	—	4	4	no	—
42	Dic₂₉	—	8	2	no	—
43	C₂×Q₃₂	—	29	1	no	—
44	C₄×Q₁₆	—	29	2	no	—
45	#366	—	29	1	no	—
46	#358	—	29	2	no	—
47	C₄×C₁₆	D₂₉	1	1	yes	characteristic
48	C₂×C₂₉	C₄×D₈	1	1	yes	characteristic
49	C₂×C₂₉	C₂×Q₃₂	1	1	yes	characteristic
50	C₂×C₂₉	#508	1	1	yes	characteristic
51	C₂×Q₁₆	—	29	2	no	—
52	C₄×Q₈	—	58	2	no	—
53	Q₃₂	—	29	4	no	—
54	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
55	C₂×C₁₆	C₂×D₂₉	1	1	yes	characteristic
56	#107	—	29	2	no	—
57	#103	—	58	2	no	—
58	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
59	C₂₉	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	58	2	no	—
61	Q₁₆	—	29	4	no	—
62	Q₁₆	—	58	2	no	—
63	C₂×C₈	D₁₁₆	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
65	C₄⋊C₄	—	58	2	no	—
66	C₄⋊C₄	—	116	2	no	—
67	C₄²	—	116	2	no	—
68	C₄²	D₁₁₆	1	1	yes	characteristic
69	C₁₆	—	2	1	no	—
70	C₁₆	C₄×D₂₉	1	2	yes	—
71	Q₈	—	58	4	no	—
72	Q₈	—	116	2	no	—
73	C₂×C₄	—	116	2	no	—
74	C₂×C₄	—	116	2	no	—
75	C₂×C₄	D₂₃₂	1	1	yes	characteristic
76	C₂×C₄	D₂₃₂	1	1	yes	characteristic
77	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	C₂×C₄×D₂₉	1	1	yes	characteristic
80	C₈	#90805	1	1	yes	characteristic
81	C₂²	C₂×D₂₃₂	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	116	4	no	—
84	C₄	—	232	2	no	—
85	C₄	Dic₂₃₂	1	2	yes	direct product factor
86	C₄	C₄×D₁₁₆	1	1	yes	characteristic
87	C₄	#11745266	1	1	yes	characteristic
88	C₂	C₄×D₂₃₂	1	1	yes	characteristic
89	C₂	C₂×Dic₂₃₂	1	1	yes	characteristic
90	C₂	#14271595	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₃₂
commutator	C₈×C₂₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₉
Fitting	C₄×C₁₆×C₂₉	C₂
socle, prime radical	C₂²×C₂₉	C₂×D₈
cosocle	C₂×C₈×C₂₉	C₂³
hypercenter	C₄×C₁₆	D₂₉
hypocenter	C₂₉	C₄×Q₃₂
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
13. Dic₂₃₂	C₄	direct (N × H)
38. C₄×C₂₉	Q₃₂	semidirect
59. C₂₉	C₄×Q₃₂	semidirect
85. C₄	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
C₂×Dic₂₃₂	2
C₄×Dic₁₁₆	2
#14270989	2
#14270968	2
C₄×C₁₆×C₂₉	2
C₄×Q₃₂	29

Subgroups — C4×Dic232 #16821352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₂₃₂ #16821352