Subgroups — #4901

Order 192.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#901	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#812	C₂	1	1	yes	maximal, characteristic, complemented
4	#798	C₂	1	2	yes	maximal, complemented
5	D₃×C₁₆	C₂	1	2	yes	maximal, complemented
6	#504	—	3	1	no	maximal, Sylow
7	#235	C₄	1	1	yes	characteristic
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	#208	C₄	1	1	yes	characteristic
10	ΓL(1,𝔽₂₅)	C₄	1	2	yes	—
11	D₃×C₈	C₂²	1	2	yes	—
12	C₃×C₁₆	C₂²	1	1	yes	characteristic
13	C₃×C₁₆	C₂²	1	1	yes	characteristic
14	C₃⋊C₁₆	C₂²	1	2	yes	—
15	#131	—	3	1	no	—
16	M₃₂	—	3	1	no	—
17	M₃₂	—	3	2	no	—
18	C₂×C₁₆	—	3	2	no	—
19	C₂×C₁₆	D₃	1	1	yes	characteristic, complemented
20	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
21	#67	C₈	1	2	yes	—
22	D₁₂	C₈	1	1	yes	characteristic
23	C₄×D₃	C₂×C₄	1	2	yes	—
24	Dic₆	C₈	1	1	yes	characteristic
25	C₃×C₈	C₂×C₄	1	1	yes	characteristic
26	C₃×C₈	C₂³	1	1	yes	characteristic
27	C₃⋊C₈	C₂×C₄	1	2	yes	—
28	#41	—	3	1	no	—
29	M₁₆	—	3	1	no	—
30	M₁₆	—	3	2	no	—
31	C₂×C₈	—	3	2	no	—
32	C₂×C₈	C₂×D₃	1	1	yes	characteristic
33	C₁₆	—	3	2	no	—
34	C₁₆	C₂×D₃	1	1	yes	characteristic
35	C₁₆	C₂×D₃	1	1	yes	characteristic
36	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
37	C₂×D₃	C₂×C₈	1	2	yes	—
38	C₃×C₄	C₂×C₈	1	1	yes	characteristic
39	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
40	Dic₃	C₂×C₈	1	2	yes	—
41	Q₈	—	3	1	no	—
42	D₄	—	3	2	no	—
43	D₄	—	3	1	no	—
44	C₂×C₄	—	3	2	no	—
45	C₂×C₄	C₄×D₃	1	1	yes	characteristic
46	C₈	—	3	2	no	—
47	C₈	C₄×D₃	1	1	yes	characteristic
48	C₈	C₂²×D₃	1	1	yes	characteristic
49	C₂×C₃	—	2	1	no	—
50	C₂×C₃	C₂²×C₈	1	1	yes	characteristic
51	D₃	—	2	2	no	—
52	C₂²	—	3	2	no	—
53	C₂²	D₃×C₈	1	1	yes	characteristic
54	C₄	—	3	2	no	—
55	C₄	D₃×C₈	1	1	yes	characteristic
56	C₄	C₂×C₄×D₃	1	1	yes	characteristic
57	C₃	#504	1	1	yes	characteristic, complemented, Sylow
58	C₂	—	2	1	no	—
59	C₂	—	6	2	no	—
60	C₂	C₂×D₃×C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×D₃
commutator, socle	C₂×C₃	C₂²×C₈
Frattini	C₈	C₂²×D₃
Fitting	C₂×C₃×C₁₆	C₂
prime radical	#235	C₄
cosocle	C₃×C₈	C₂³
hypercenter	C₂×C₁₆	D₃
hypocenter	C₃	#504
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₁₆	C₂	semidirect
3. #812	C₂	semidirect
4. #798	C₂	semidirect
5. D₃×C₁₆	C₂	semidirect
19. C₂×C₁₆	D₃	semidirect
57. C₃	#504	semidirect

Maximal subgroups

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

subgroup	index
#901	2
C₂×C₃×C₁₆	2
#812	2
#798	2
D₃×C₁₆	2
#504	3