Subgroups — #4477

Order 192.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#947	C₂	1	1	yes	maximal, characteristic
2	C₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
3	#836	C₂	1	1	yes	maximal, characteristic, complemented
4	#355	—	3	1	no	maximal, Sylow
5	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
6	C₂×D₁₂	C₄	1	1	yes	characteristic
7	C₃×M₁₆	—	2	1	no	—
8	(C₂×D₃)⋊C₄	—	2	1	no	—
9	(C₂×D₃)⋊C₄	—	2	1	no	—
10	C₄×Dic₃	C₄	1	1	yes	characteristic
11	#208	—	2	1	no	—
12	#124	—	3	1	no	—
13	#101	—	3	1	no	—
14	#101	D₃	1	1	yes	characteristic, complemented
15	C₂²×D₃	—	2	1	no	—
16	C₃×Q₈	—	4	1	no	—
17	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	D₄	1	1	yes	characteristic
19	C₂×C₃×C₄	D₄	1	1	yes	characteristic
20	C₂×Dic₃	—	2	1	no	—
21	D₁₂	—	4	1	no	—
22	C₃×C₈	—	4	1	no	—
23	C₃⋊C₈	—	4	1	no	—
24	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
25	C₂×D₄	—	3	1	no	—
26	M₁₆	—	2	1	no	—
27	M₁₆	—	6	1	no	—
28	C₂²⋊C₄	—	6	1	no	—
29	C₂²⋊C₄	—	6	1	no	—
30	C₄²	—	3	1	no	—
31	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×D₃	—	4	2	no	—
33	C₂×D₃	—	4	1	no	—
34	C₃×C₄	—	2	1	no	—
35	C₃×C₄	—	2	1	no	—
36	C₃×C₄	—	2	1	no	—
37	Dic₃	—	4	1	no	—
38	C₂³	—	6	1	no	—
39	Q₈	—	4	1	no	—
40	D₄	—	12	1	no	—
41	C₂×C₄	—	6	1	no	—
42	C₂×C₄	C₄×D₃	1	1	yes	characteristic
43	C₂×C₄	D₁₂	1	1	yes	characteristic
44	C₂×C₄	#67	1	1	yes	characteristic
45	C₈	—	4	1	no	—
46	C₈	—	12	1	no	—
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	#99	1	1	yes	characteristic
49	D₃	—	8	1	no	—
50	C₂²	—	12	2	no	—
51	C₂²	—	12	1	no	—
52	C₂²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	2	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	12	1	no	—
57	C₃	#355	1	1	yes	characteristic, complemented, Sylow
58	C₂	—	2	1	no	—
59	C₂	—	24	1	no	—
60	C₂	#806	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#806
commutator	C₂×C₃×C₄	C₂×C₄
Frattini	C₂×Q₈	C₂×D₃
Fitting	C₃×#101	C₂
socle	C₂×C₃	#99
prime radical	C₂×D₁₂	C₄
cosocle	C₂×C₃×Q₈	C₂²
hypercenter	#101	D₃
hypocenter	C₃	#355
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
2. C₃×#101	C₂	semidirect
3. #836	C₂	semidirect
14. #101	D₃	semidirect
57. C₃	#355	semidirect

Maximal subgroups

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

subgroup	index
#947	2
C₃×#101	2
#836	2
#355	3