Subgroups — C₄×#67 #928

Order 96.

94 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	1	yes	maximal, characteristic
3	C₂×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#217	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₄	—	3	1	no	maximal, Sylow
9	C₂³×C₃	C₂²	1	1	yes	characteristic
10	C₂²×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄	—	2	2	no	—
12	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
14	#67	C₄	1	4	yes	direct product factor
15	C₂×Dic₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₃	C₂²	1	1	yes	characteristic
18	C₄×D₃	—	2	2	no	—
19	C₂×D₄	—	3	1	no	—
20	C₂²×C₄	—	3	1	no	—
21	C₂²×C₄	D₃	1	1	yes	characteristic, complemented
22	C₄⋊C₄	—	3	1	no	—
23	C₂²⋊C₄	—	3	1	no	—
24	C₂²⋊C₄	—	3	1	no	—
25	C₄²	—	3	1	no	—
26	C₂²×C₃	—	2	1	no	—
27	C₂²×C₃	—	2	1	no	—
28	C₂²×C₃	C₂×C₄	1	2	yes	complemented
29	C₂²×C₃	C₂³	1	1	yes	characteristic
30	C₂×D₃	—	2	1	no	—
31	C₂×D₃	—	2	1	no	—
32	C₂×D₃	C₂×C₄	1	2	yes	complemented
33	C₃×C₄	—	2	1	no	—
34	C₃×C₄	D₄	1	2	yes	complemented
35	Dic₃	—	2	1	no	—
36	Dic₃	—	2	1	no	—
37	Dic₃	C₂×C₄	1	2	yes	complemented
38	C₂³	—	3	1	no	—
39	C₂³	C₂×D₃	1	1	yes	characteristic
40	D₄	—	3	4	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	3	1	no	—
43	C₂×C₄	—	3	1	no	—
44	C₂×C₄	—	3	1	no	—
45	C₂×C₄	—	6	2	no	—
46	C₂×C₄	C₂×D₃	1	1	yes	characteristic
47	C₂×C₄	C₂×D₃	1	1	yes	characteristic
48	C₂×C₃	—	2	2	no	—
49	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₃	#41	1	1	yes	characteristic
52	D₃	—	2	2	no	—
53	C₂²	—	2	1	no	—
54	C₂²	—	2	1	no	—
55	C₂²	—	3	2	no	—
56	C₂²	—	6	1	no	—
57	C₂²	—	6	1	no	—
58	C₂²	C₄×D₃	1	2	yes	complemented
59	C₂²	C₂²×D₃	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	3	2	no	—
62	C₄	—	6	1	no	—
63	C₄	—	6	1	no	—
64	C₄	#67	1	2	yes	direct product factor
65	C₃	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
66	C₂	—	2	2	no	—
67	C₂	—	6	2	no	—
68	C₂	C₂×C₄×D₃	1	1	yes	characteristic
69	C₂	#235	1	1	yes	characteristic
70	C₂	C₂×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃
commutator	C₂×C₃	C₂²×C₄
Frattini	C₂²	C₂²×D₃
Fitting	C₂²×C₃×C₄	C₂
socle, cosocle	C₂²×C₃	C₂³
prime radical	C₂×#67	C₂
hypercenter	C₂²×C₄	D₃
hypocenter	C₃	C₄×D₄
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
3. C₂×C₄×D₃	C₂	semidirect
4. #217	C₂	semidirect
5. (C₂×D₃)⋊C₄	C₂	semidirect
6. Dic₃⋊C₄	C₂	semidirect
7. C₄×Dic₃	C₂	semidirect
14. #67	C₄	direct (N × H)
21. C₂²×C₄	D₃	semidirect
28. C₂²×C₃	C₂×C₄	semidirect
32. C₂×D₃	C₂×C₄	semidirect
34. C₃×C₄	D₄	semidirect
37. Dic₃	C₂×C₄	semidirect
58. C₂²	C₄×D₃	semidirect
64. C₄	#67	direct (N × H)
65. C₃	C₄×D₄	semidirect

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
C₂×C₄×D₃	2
#217	2
(C₂×D₃)⋊C₄	2
Dic₃⋊C₄	2
C₄×Dic₃	2
C₄×D₄	3

Subgroups — C4×#67 #928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#67 #928