Subgroups — C₂×#237 #1003

Order 96.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#67	C₂	1	2	yes	maximal, complemented
3	C₂²×Dic₃	C₂	1	2	yes	maximal, complemented
4	#237	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#41	—	3	1	no	maximal, Sylow
8	C₂³×C₃	C₂²	1	2	yes	—
9	C₂²×D₃	C₂²	1	1	yes	characteristic
10	C₃×D₄	C₂²	1	4	yes	complemented
11	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
12	#67	C₂²	1	8	yes	complemented
13	C₂×Dic₃	C₂²	1	2	yes	—
14	C₂×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₃	C₂²	1	8	yes	complemented
16	C₄×D₃	C₂²	1	4	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	D₃	1	1	yes	characteristic, complemented
22	C₂²×C₄	—	3	2	no	—
23	C₂²×C₄	—	3	1	no	—
24	C₂²×C₃	—	2	4	no	—
25	C₂²×C₃	C₂³	1	4	yes	—
26	C₂²×C₃	C₂³	1	1	yes	characteristic
27	C₂×D₃	—	2	2	no	—
28	C₂×D₃	C₂³	1	2	yes	—
29	C₃×C₄	C₂³	1	2	yes	—
30	Dic₃	C₂³	1	4	yes	—
31	Dic₃	C₂³	1	2	yes	—
32	C₂³	—	3	1	no	—
33	C₂³	C₂×D₃	1	2	yes	—
34	Q₈	—	3	4	no	—
35	D₄	—	3	8	no	—
36	D₄	C₂×D₃	1	4	yes	complemented
37	C₂×C₄	—	3	8	no	—
38	C₂×C₄	—	3	1	no	—
39	C₂×C₄	—	3	2	no	—
40	C₂×C₄	—	3	4	no	—
41	C₂×C₄	C₂×D₃	1	1	yes	characteristic
42	C₂×C₃	—	2	4	no	—
43	C₂×C₃	#41	1	2	yes	complemented
44	C₂×C₃	C₂⁴	1	1	yes	characteristic
45	D₃	—	2	2	no	—
46	C₂²	—	2	4	no	—
47	C₂²	—	3	2	no	—
48	C₂²	—	6	2	no	—
49	C₂²	C₂²×D₃	1	4	yes	—
50	C₂²	C₂²×D₃	1	1	yes	characteristic
51	C₄	—	3	2	no	—
52	C₄	—	3	4	no	—
53	C₄	C₂²×D₃	1	2	yes	—
54	C₃	C₂×#41	1	1	yes	characteristic, complemented, Sylow
55	C₂	—	2	4	no	—
56	C₂	—	6	2	no	—
57	C₂	#237	1	2	yes	direct product factor
58	C₂	C₂³×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂⁴
Frattini	C₂	C₂³×D₃
Fitting	C₂×C₃×D₄	C₂
socle	C₂²×C₃	C₂³
hypercenter	C₂×D₄	D₃
hypocenter	C₃	C₂×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄	C₂	semidirect
2. C₂×#67	C₂	semidirect
3. C₂²×Dic₃	C₂	semidirect
4. #237	C₂	direct (N × H)
5. C₂×C₄×D₃	C₂	semidirect
6. C₂×Dic₆	C₂	semidirect
10. C₃×D₄	C₂²	semidirect
12. #67	C₂²	semidirect
15. C₂×Dic₃	C₂²	semidirect
16. C₄×D₃	C₂²	semidirect
17. Dic₆	C₂²	semidirect
21. C₂×D₄	D₃	semidirect
36. D₄	C₂×D₃	semidirect
43. C₂×C₃	#41	semidirect
54. C₃	C₂×#41	semidirect
57. C₂	#237	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×C₃×D₄	2
C₂×#67	2
C₂²×Dic₃	2
#237	2
C₂×C₄×D₃	2
C₂×Dic₆	2
C₂×#41	3

Subgroups — C2×#237 #1003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#237 #1003