Subgroups — C₂×#63765 #10593761

Order 576.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#3708	C₂	1	2	yes	maximal, complemented
3	#63765	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₃⋊D₃	C₄	1	1	yes	characteristic
5	C₂×C₃²×C₈	C₄	1	1	yes	characteristic
6	C₂×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
7	C₈×C₃⋊D₃	C₄	1	2	yes	—
8	C₈×C₃⋊D₃	C₂²	1	2	yes	—
9	#3708	C₂²	1	4	yes	complemented
10	C₂×D₃×C₈	—	6	2	no	—
11	C₂²×C₃⋊D₃	C₈	1	1	yes	characteristic
12	C₂×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃⋊Dic₃	C₈	1	1	yes	characteristic
14	C₄×C₃⋊D₃	C₈	1	2	yes	—
15	C₄×C₃⋊D₃	C₂×C₄	1	2	yes	—
16	C₃²×C₈	C₂×C₄	1	2	yes	—
17	C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
18	C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
19	C₂×M₃₂	—	9	1	no	maximal, Sylow
20	C₂×C₄×D₃	—	6	2	no	—
21	C₂×C₃×C₈	—	2	2	no	—
22	C₂×C₃⋊C₈	—	6	2	no	—
23	D₃×C₈	—	6	4	no	—
24	D₃×C₈	—	6	4	no	—
25	C₂²×C₃²	C₂×C₈	1	1	yes	characteristic
26	C₂×C₃⋊D₃	—	2	2	no	—
27	C₂×C₃⋊D₃	C₂×C₈	1	2	yes	—
28	C₃²×C₄	C₂×C₈	1	1	yes	characteristic
29	C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
30	C₃⋊Dic₃	C₂×C₈	1	2	yes	—
31	C₂²×C₈	—	9	1	no	—
32	M₃₂	—	9	4	no	—
33	C₂×C₁₆	—	9	2	no	—
34	C₂²×D₃	—	6	2	no	—
35	C₂×C₃×C₄	—	2	2	no	—
36	C₂×Dic₃	—	6	2	no	—
37	C₄×D₃	—	6	4	no	—
38	C₄×D₃	—	6	4	no	—
39	C₃×C₈	—	2	4	no	—
40	C₃⋊C₈	—	6	2	no	—
41	C₃⋊C₈	—	6	2	no	—
42	C₂×C₃²	M₃₂	1	2	yes	complemented
43	C₂×C₃²	C₂²×C₈	1	1	yes	characteristic
44	C₃⋊D₃	—	2	2	no	—
45	C₂²×C₄	—	9	1	no	—
46	C₂×C₈	—	9	1	no	—
47	C₂×C₈	—	9	2	no	—
48	C₂×C₈	—	9	2	no	—
49	C₂×C₈	#157	1	1	yes	characteristic
50	C₁₆	—	9	4	no	—
51	C₂²×C₃	—	2	2	no	—
52	C₂×D₃	—	6	4	no	—
53	C₂×D₃	—	6	8	no	—
54	C₃×C₄	—	2	2	no	—
55	C₃×C₄	—	2	2	no	—
56	Dic₃	—	6	4	no	—
57	C₃²	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	9	1	no	—
59	C₂×C₄	—	9	1	no	—
60	C₂×C₄	—	9	2	no	—
61	C₂×C₄	—	9	2	no	—
62	C₂×C₄	C₂×#157	1	1	yes	characteristic
63	C₈	—	9	1	no	—
64	C₈	—	9	1	no	—
65	C₈	C₂×#157	1	2	yes	—
66	C₂×C₃	—	2	4	no	—
67	C₂×C₃	—	2	2	no	—
68	D₃	—	6	8	no	—
69	C₂²	—	9	2	no	—
70	C₂²	—	18	2	no	—
71	C₂²	#3787	1	1	yes	characteristic
72	C₄	—	9	2	no	—
73	C₄	#3787	1	1	yes	characteristic
74	C₄	C₂²×#157	1	1	yes	characteristic
75	C₃	—	2	2	no	—
76	C₂	—	18	2	no	—
77	C₂	#63765	1	2	yes	direct product factor
78	C₂	C₂×#3787	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#157
commutator	C₂×C₃²	C₂²×C₈
Frattini	C₄	C₂²×#157
Fitting	C₂×C₃²×C₈	C₄
socle	C₂²×C₃²	C₂×C₈
prime radical	C₂²×C₃⋊D₃	C₈
cosocle	C₃⋊(C₃⋊C₈)	C₂³
hypercenter	C₂×C₈	#157
hypocenter	C₃²	C₂×M₃₂
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#3708	C₂	semidirect
3. #63765	C₂	direct (N × H)
9. #3708	C₂²	semidirect
42. C₂×C₃²	M₃₂	semidirect
57. C₃²	C₂×M₃₂	semidirect
77. C₂	#63765	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×C₈×C₃⋊D₃	2
C₂×#3708	2
#63765	2
C₂×M₃₂	9

Subgroups — C2×#63765 #10593761

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63765 #10593761