Subgroups — C₂×#64289 #10596643

Order 576.

430 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3832	C₂	1	1	yes	maximal, characteristic
2	#64289	C₂	1	8	yes	maximal, direct product factor
3	C₂×#3788	C₂	1	3	yes	maximal, complemented
4	C₂×#3787	C₂	1	3	yes	maximal, complemented
5	C₂×C₃²×Q₈	C₄	1	1	yes	characteristic
6	#3832	C₄	1	4	yes	—
7	#3832	C₂²	1	4	yes	—
8	C₂×C₄⋊(C₃⋊D₃)	C₄	1	3	yes	—
9	C₂×C₄×C₃⋊D₃	C₂²	1	3	yes	—
10	C₂×#622	C₂²	1	1	yes	characteristic
11	C₂×#622	C₂²	1	3	yes	—
12	#3788	C₂²	1	12	yes	complemented
13	#3787	C₂²	1	12	yes	complemented
14	C₂×#239	—	6	2	no	—
15	C₂²×C₃⋊D₃	C₂×C₄	1	3	yes	—
16	C₃²×Q₈	C₂×C₄	1	4	yes	—
17	C₂×C₃²×C₄	C₂×C₄	1	3	yes	—
18	C₂×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
19	C₄⋊(C₃⋊D₃)	C₂×C₄	1	12	yes	—
20	C₄×C₃⋊D₃	C₂×C₄	1	6	yes	—
21	C₄×C₃⋊D₃	C₂³	1	6	yes	—
22	#622	C₂³	1	2	yes	—
23	#622	C₂³	1	6	yes	—
24	C₂×#131	—	9	1	no	maximal, Sylow
25	C₂×C₃×Q₈	—	2	2	no	—
26	#239	—	6	8	no	—
27	#239	—	6	8	no	—
28	C₂×D₁₂	—	6	6	no	—
29	C₂×C₄×D₃	—	6	6	no	—
30	C₂²×C₃²	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₃⋊D₃	—	2	6	no	—
32	C₂×C₃⋊D₃	C₂²×C₄	1	6	yes	—
33	C₃²×C₄	C₂²×C₄	1	6	yes	—
34	C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
35	C₃⋊Dic₃	C₂⁴	1	1	yes	characteristic
36	C₂×#41	—	9	1	no	—
37	#131	—	9	8	no	—
38	C₂×M₁₆	—	9	3	no	—
39	C₂²×C₈	—	9	3	no	—
40	C₂²×D₃	—	6	6	no	—
41	C₃×Q₈	—	2	8	no	—
42	C₂×C₃×C₄	—	2	6	no	—
43	C₂×Dic₃	—	6	2	no	—
44	D₁₂	—	6	24	no	—
45	C₄×D₃	—	6	12	no	—
46	C₄×D₃	—	6	12	no	—
47	C₂×C₃²	#131	1	2	yes	complemented
48	C₂×C₃²	C₂³×C₄	1	1	yes	characteristic
49	C₃⋊D₃	—	2	6	no	—
50	#41	—	9	4	no	—
51	#41	—	9	4	no	—
52	C₂×Q₈	#157	1	1	yes	characteristic
53	C₂×D₄	—	9	3	no	—
54	C₂²×C₄	—	9	3	no	—
55	M₁₆	—	9	12	no	—
56	C₂×C₈	—	9	1	no	—
57	C₂×C₈	—	9	3	no	—
58	C₂×C₈	—	9	12	no	—
59	C₂²×C₃	—	2	2	no	—
60	C₂×D₃	—	6	12	no	—
61	C₂×D₃	—	12	12	no	—
62	C₃×C₄	—	2	12	no	—
63	Dic₃	—	6	2	no	—
64	Dic₃	—	6	2	no	—
65	C₃²	C₂×#131	1	1	yes	characteristic, complemented, Sylow
66	C₂³	—	9	3	no	—
67	Q₈	C₂×#157	1	4	yes	—
68	D₄	—	9	12	no	—
69	C₂×C₄	—	9	1	no	—
70	C₂×C₄	—	9	6	no	—
71	C₂×C₄	—	9	6	no	—
72	C₂×C₄	C₂×#157	1	3	yes	—
73	C₈	—	9	2	no	—
74	C₈	—	9	6	no	—
75	C₂×C₃	—	2	4	no	—
76	C₂×C₃	—	2	2	no	—
77	D₃	—	12	12	no	—
78	C₂²	—	9	6	no	—
79	C₂²	—	18	6	no	—
80	C₂²	C₂²×#157	1	1	yes	characteristic
81	C₄	—	9	1	no	—
82	C₄	—	9	1	no	—
83	C₄	C₂²×#157	1	6	yes	—
84	C₃	—	2	2	no	—
85	C₂	—	18	6	no	—
86	C₂	#64289	1	2	yes	direct product factor
87	C₂	C₂³×#157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#157
commutator	C₂×C₃²	C₂³×C₄
Frattini	C₂	C₂³×#157
Fitting	C₂×C₃²×Q₈	C₄
socle	C₂²×C₃²	C₂²×C₄
prime radical	C₂×#3832	C₂
cosocle	C₃⋊Dic₃	C₂⁴
hypercenter	C₂×Q₈	#157
hypocenter	C₃²	C₂×#131
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #64289	C₂	direct (N × H)
3. C₂×#3788	C₂	semidirect
4. C₂×#3787	C₂	semidirect
12. #3788	C₂²	semidirect
13. #3787	C₂²	semidirect
47. C₂×C₃²	#131	semidirect
65. C₃²	C₂×#131	semidirect
86. C₂	#64289	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×#3832	2
#64289	2
C₂×#3788	2
C₂×#3787	2
C₂×#131	9

Subgroups — C2×#64289 #10596643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#64289 #10596643