Subgroups — #4465

Order 192.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#870	C₂	1	1	yes	maximal, characteristic
2	C₃×#97	C₂	1	1	yes	maximal, characteristic
3	#803	C₂	1	1	yes	maximal, characteristic
4	#330	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₈	—	2	1	no	—
6	C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₃	C₄	1	1	yes	characteristic
8	C₄⋊Dic₃	C₄	1	1	yes	characteristic
9	Dic₃⋊C₄	—	2	1	no	—
10	Dic₃⋊C₄	—	2	1	no	—
11	C₂×C₃⋊C₈	—	2	1	no	—
12	#125	—	3	1	no	—
13	#97	—	3	1	no	—
14	#97	D₃	1	1	yes	characteristic
15	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₄	D₄	1	1	yes	characteristic
17	C₂×C₃×C₄	D₄	1	1	yes	characteristic
18	C₂×Dic₃	—	2	1	no	—
19	C₂×Dic₃	—	2	1	no	—
20	C₃×C₈	—	2	2	no	—
21	C₃⋊C₈	—	2	2	no	—
22	C₂×C₈	—	2	1	no	—
23	C₂×C₈	—	6	1	no	—
24	C₄⋊C₄	—	3	1	no	—
25	C₄⋊C₄	—	3	1	no	—
26	C₄⋊C₄	—	6	1	no	—
27	C₄⋊C₄	—	6	1	no	—
28	C₄²	C₂×D₃	1	1	yes	characteristic
29	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₃×C₄	—	2	1	no	—
31	C₃×C₄	—	2	1	no	—
32	C₃×C₄	—	2	1	no	—
33	Dic₃	—	4	1	no	—
34	Dic₃	—	4	1	no	—
35	C₂×C₄	—	6	1	no	—
36	C₂×C₄	—	6	1	no	—
37	C₂×C₄	C₄×D₃	1	1	yes	characteristic
38	C₂×C₄	D₁₂	1	1	yes	characteristic
39	C₂×C₄	#67	1	1	yes	characteristic
40	C₈	—	2	2	no	—
41	C₈	—	6	2	no	—
42	C₂×C₃	#101	1	1	yes	characteristic
43	C₂×C₃	#104	1	1	yes	characteristic
44	C₂×C₃	#104	1	1	yes	characteristic
45	C₂²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	2	1	no	—
48	C₄	—	2	1	no	—
49	C₄	—	12	1	no	—
50	C₄	—	12	1	no	—
51	C₃	#330	1	1	yes	characteristic, complemented, Sylow
52	C₂	#805	1	1	yes	characteristic
53	C₂	#824	1	1	yes	characteristic
54	C₂	#825	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂×C₄
Frattini	C₄²	C₂×D₃
Fitting	C₃×#97	C₂
socle, prime radical	C₂²×C₃	C₂²⋊C₄
cosocle	C₃×C₄²	C₂²
hypercenter	#97	D₃
hypocenter	C₃	#330
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
51. C₃	#330	semidirect

Maximal subgroups

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

subgroup	index
#870	2
C₃×#97	2
#803	2
#330	3