Subgroups — #4478

Order 192.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#944	C₂	1	1	yes	maximal, characteristic
2	C₃×#101	C₂	1	1	yes	maximal, characteristic
3	#836	C₂	1	1	yes	maximal, characteristic
4	#356	—	3	1	no	maximal, Sylow
5	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
6	C₂×Dic₆	C₄	1	1	yes	characteristic
7	C₃×M₁₆	—	2	1	no	—
8	Dic₃⋊C₄	—	2	1	no	—
9	Dic₃⋊C₄	—	2	1	no	—
10	C₄×Dic₃	C₄	1	1	yes	characteristic
11	#208	—	2	1	no	—
12	C₄⋊Q₈	—	3	1	no	—
13	#101	—	3	1	no	—
14	#101	D₃	1	1	yes	characteristic
15	C₃×Q₈	—	4	1	no	—
16	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₄	D₄	1	1	yes	characteristic
18	C₂×C₃×C₄	D₄	1	1	yes	characteristic
19	C₂×Dic₃	—	2	1	no	—
20	C₂×Dic₃	—	2	1	no	—
21	Dic₆	—	4	1	no	—
22	C₃×C₈	—	4	1	no	—
23	C₃⋊C₈	—	4	1	no	—
24	C₂×Q₈	—	3	1	no	—
25	C₂×Q₈	C₂×D₃	1	1	yes	characteristic
26	M₁₆	—	2	1	no	—
27	M₁₆	—	6	1	no	—
28	C₄⋊C₄	—	6	1	no	—
29	C₄⋊C₄	—	6	1	no	—
30	C₄²	—	3	1	no	—
31	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₃×C₄	—	2	1	no	—
33	C₃×C₄	—	2	1	no	—
34	C₃×C₄	—	2	1	no	—
35	Dic₃	—	2	2	no	—
36	Dic₃	—	4	1	no	—
37	Q₈	—	4	1	no	—
38	Q₈	—	12	1	no	—
39	C₂×C₄	—	6	1	no	—
40	C₂×C₄	—	6	1	no	—
41	C₂×C₄	C₄×D₃	1	1	yes	characteristic
42	C₂×C₄	D₁₂	1	1	yes	characteristic
43	C₂×C₄	#67	1	1	yes	characteristic
44	C₈	—	4	1	no	—
45	C₈	—	12	1	no	—
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	#99	1	1	yes	characteristic
48	C₂²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
49	C₄	—	2	1	no	—
50	C₄	—	2	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	6	2	no	—
53	C₄	—	12	1	no	—
54	C₃	#356	1	1	yes	characteristic, complemented, Sylow
55	C₂	—	2	1	no	—
56	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	C₂²×C₃	C₂²⋊C₄
cosocle	C₂×C₃×Q₈	C₂²
hypercenter	#101	D₃
hypocenter	C₃	#356
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
54. C₃	#356	semidirect

Maximal subgroups

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

subgroup	index
#944	2
C₃×#101	2
#836	2
#356	3