Subgroups — C₂×#235 #1001

Order 96.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#67	C₂	1	2	yes	maximal, complemented
3	#235	C₂	1	8	yes	maximal, direct product factor
4	C₂×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×D₃	C₂	1	2	yes	maximal, complemented
6	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#41	—	3	1	no	maximal, Sylow
8	C₂³×C₃	C₂²	1	1	yes	characteristic
9	C₂²×D₃	C₂²	1	2	yes	—
10	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄	C₂²	1	4	yes	complemented
13	#67	C₂²	1	8	yes	complemented
14	C₂×Dic₃	C₂²	1	2	yes	—
15	D₁₂	C₂²	1	4	yes	complemented
16	C₄×D₃	C₂²	1	8	yes	complemented
17	Dic₆	C₂²	1	4	yes	complemented
18	#41	—	3	8	no	—
19	C₂×Q₈	—	3	1	no	—
20	C₂×D₄	—	3	2	no	—
21	C₂×D₄	—	3	1	no	—
22	C₂²×C₄	—	3	2	no	—
23	C₂²×C₄	D₃	1	1	yes	characteristic, complemented
24	C₂²×C₃	—	2	2	no	—
25	C₂²×C₃	C₂³	1	2	yes	—
26	C₂²×C₃	C₂³	1	1	yes	characteristic
27	C₂×D₃	—	2	4	no	—
28	C₂×D₃	C₂³	1	4	yes	—
29	C₃×C₄	C₂³	1	2	yes	—
30	C₃×C₄	C₂³	1	2	yes	—
31	Dic₃	C₂³	1	4	yes	—
32	C₂³	—	3	2	no	—
33	C₂³	C₂×D₃	1	1	yes	characteristic
34	Q₈	—	3	4	no	—
35	D₄	—	3	8	no	—
36	D₄	—	3	4	no	—
37	C₂×C₄	—	3	2	no	—
38	C₂×C₄	—	3	8	no	—
39	C₂×C₄	C₂×D₃	1	1	yes	characteristic
40	C₂×C₄	C₂×D₃	1	1	yes	characteristic
41	C₂×C₄	C₂×D₃	1	4	yes	complemented
42	C₂×C₃	—	2	2	no	—
43	C₂×C₃	#41	1	2	yes	complemented
44	C₂×C₃	C₂⁴	1	1	yes	characteristic
45	D₃	—	2	4	no	—
46	C₂²	—	2	2	no	—
47	C₂²	—	3	4	no	—
48	C₂²	—	6	4	no	—
49	C₂²	C₂²×D₃	1	2	yes	—
50	C₂²	C₂²×D₃	1	1	yes	characteristic
51	C₄	—	3	4	no	—
52	C₄	C₂²×D₃	1	2	yes	—
53	C₄	C₂²×D₃	1	2	yes	—
54	C₃	C₂×#41	1	1	yes	characteristic, complemented, Sylow
55	C₂	—	2	2	no	—
56	C₂	—	6	4	no	—
57	C₂	#235	1	2	yes	direct product factor
58	C₂	C₂³×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃
commutator, cosocle	C₂×C₃	C₂⁴
Frattini	C₂	C₂³×D₃
Fitting	C₂²×C₃×C₄	C₂
socle	C₂²×C₃	C₂³
hypercenter	C₂²×C₄	D₃
hypocenter	C₃	C₂×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₄	C₂	semidirect
2. C₂×#67	C₂	semidirect
3. #235	C₂	direct (N × H)
4. C₂×D₁₂	C₂	semidirect
5. C₂×C₄×D₃	C₂	semidirect
6. C₂×Dic₆	C₂	semidirect
12. C₂×C₃×C₄	C₂²	semidirect
13. #67	C₂²	semidirect
15. D₁₂	C₂²	semidirect
16. C₄×D₃	C₂²	semidirect
17. Dic₆	C₂²	semidirect
23. C₂²×C₄	D₃	semidirect
41. C₂×C₄	C₂×D₃	semidirect
43. C₂×C₃	#41	semidirect
54. C₃	C₂×#41	semidirect
57. C₂	#235	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×C₃×C₄	2
C₂×#67	2
#235	2
C₂×D₁₂	2
C₂×C₄×D₃	2
C₂×Dic₆	2
C₂×#41	3

Subgroups — C2×#235 #1001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#235 #1001