Subgroups — #950

Order 96.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	#235	C₂	1	1	yes	maximal, characteristic, complemented
3	#216	C₂	1	1	yes	maximal, characteristic, complemented
4	#215	C₂	1	1	yes	maximal, characteristic, complemented
5	#214	C₂	1	1	yes	maximal, characteristic, complemented
6	#213	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#135	—	3	1	no	maximal, Sylow
9	C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₃×D₄	—	2	1	no	—
11	C₃×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄	—	2	1	no	—
13	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
14	#67	—	2	1	no	—
15	D₁₂	C₂²	1	1	yes	characteristic
16	C₄×D₃	—	2	1	no	—
17	Dic₆	C₂²	1	1	yes	characteristic
18	C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₃⋊C₈	C₂²	1	1	yes	characteristic
20	#41	—	3	1	no	—
21	#41	D₃	1	1	yes	characteristic, complemented
22	Q₁₆	—	3	1	no	—
23	SD₁₆	—	3	1	no	—
24	SD₁₆	—	3	1	no	—
25	D₈	—	3	1	no	—
26	C₂×C₈	—	3	1	no	—
27	C₂²×C₃	—	2	1	no	—
28	C₂²×C₃	D₄	1	1	yes	characteristic
29	C₂×D₃	—	2	1	no	—
30	C₃×C₄	—	2	1	no	—
31	C₃×C₄	D₄	1	1	yes	characteristic
32	C₃×C₄	C₂³	1	1	yes	characteristic
33	Dic₃	—	2	1	no	—
34	Q₈	—	3	1	no	—
35	Q₈	C₂×D₃	1	1	yes	characteristic
36	D₄	—	2	1	no	—
37	D₄	—	3	1	no	—
38	D₄	—	6	1	no	—
39	D₄	C₂×D₃	1	1	yes	characteristic
40	C₂×C₄	—	2	1	no	—
41	C₂×C₄	—	6	1	no	—
42	C₂×C₄	C₂×D₃	1	1	yes	characteristic
43	C₈	—	3	1	no	—
44	C₈	—	3	1	no	—
45	C₂×C₃	—	2	1	no	—
46	C₂×C₃	—	4	1	no	—
47	C₂×C₃	C₂×D₄	1	1	yes	characteristic
48	D₃	—	4	1	no	—
49	C₂²	—	2	1	no	—
50	C₂²	—	6	1	no	—
51	C₂²	#67	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	6	1	no	—
54	C₄	#67	1	1	yes	characteristic
55	C₄	C₂²×D₃	1	1	yes	characteristic
56	C₃	#135	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	2	1	no	—
58	C₂	—	4	1	no	—
59	C₂	—	12	1	no	—
60	C₂	C₂×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#67
commutator, cosocle	C₃×C₄	C₂³
Frattini	C₄	C₂²×D₃
Fitting	C₃×#41	C₂
socle	C₂×C₃	C₂×D₄
hypercenter	#41	D₃
hypocenter	C₃	#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. C₃×#41	C₂	semidirect
2. #235	C₂	semidirect
3. #216	C₂	semidirect
4. #215	C₂	semidirect
5. #214	C₂	semidirect
6. #213	C₂	semidirect
7. C₂×C₃⋊C₈	C₂	semidirect
21. #41	D₃	semidirect
56. C₃	#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#41	2
#235	2
#216	2
#215	2
#214	2
#213	2
C₂×C₃⋊C₈	2
#135	3