Subgroups — #4893

Order 192.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
3	C₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	#822	C₂	1	2	yes	maximal, complemented
5	#819	C₂	1	1	yes	maximal, characteristic, complemented
6	#430	—	3	1	no	maximal, Sylow
7	C₂×C₄×D₃	C₂²	1	1	yes	characteristic
8	C₃×M₁₆	C₂²	1	2	yes	—
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	#208	C₂²	1	2	yes	—
11	C₂×C₃⋊C₈	C₂²	1	1	yes	characteristic
12	ΓL(1,𝔽₂₅)	—	2	2	no	—
13	ΓL(1,𝔽₂₅)	C₄	1	4	yes	—
14	D₃×C₈	—	2	2	no	—
15	C₂×M₁₆	—	3	1	no	—
16	C₂×M₁₆	—	3	2	no	—
17	#108	—	3	2	no	—
18	#108	—	3	1	no	—
19	#108	D₃	1	1	yes	characteristic, complemented
20	C₂²×D₃	Q₈	1	1	yes	characteristic
21	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
22	C₂×Dic₃	Q₈	1	1	yes	characteristic
23	C₄×D₃	C₂×C₄	1	2	yes	—
24	C₄×D₃	D₄	1	2	yes	—
25	C₃×C₈	—	2	2	no	—
26	C₃×C₈	C₂×C₄	1	2	yes	—
27	C₃⋊C₈	—	2	2	no	—
28	C₃⋊C₈	C₂×C₄	1	2	yes	—
29	C₂²×C₄	—	3	1	no	—
30	M₁₆	—	3	4	no	—
31	M₁₆	—	3	2	no	—
32	M₁₆	—	6	2	no	—
33	M₁₆	C₂×D₃	1	2	yes	—
34	C₂×C₈	—	3	1	no	—
35	C₂×C₈	—	6	2	no	—
36	C₂×C₈	C₂×D₃	1	1	yes	characteristic
37	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×D₃	—	4	1	no	—
39	C₂×D₃	C₄⋊C₄	1	2	yes	—
40	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
41	C₃×C₄	C₂×D₄	1	1	yes	characteristic
42	Dic₃	C₄⋊C₄	1	2	yes	—
43	C₂³	—	3	1	no	—
44	C₂×C₄	—	3	1	no	—
45	C₂×C₄	—	3	2	no	—
46	C₂×C₄	—	3	2	no	—
47	C₂×C₄	C₂²×D₃	1	1	yes	characteristic
48	C₈	—	2	2	no	—
49	C₈	—	3	2	no	—
50	C₈	—	6	2	no	—
51	C₈	C₄×D₃	1	2	yes	—
52	C₂×C₃	—	2	1	no	—
53	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	D₃	—	2	2	no	—
55	C₂²	—	3	2	no	—
56	C₂²	—	12	1	no	—
57	C₂²	D₃×Q₈	1	1	yes	characteristic
58	C₄	—	3	2	no	—
59	C₄	C₂×C₄×D₃	1	1	yes	characteristic
60	C₄	D₃×D₄	1	1	yes	characteristic
61	C₃	#430	1	1	yes	characteristic, complemented, Sylow
62	C₂	—	2	1	no	—
63	C₂	—	6	2	no	—
64	C₂	D₃×C₄⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃×D₄
commutator	C₃×C₄	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃
Fitting	C₃×#108	C₂
socle	C₂×C₃	C₂×C₄⋊C₄
prime radical	C₂²×D₃	Q₈
cosocle	C₂×C₃×C₄	C₂³
hypercenter	#108	D₃
hypocenter	C₃	#430
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. C₃×#108	C₂	semidirect
4. #822	C₂	semidirect
5. #819	C₂	semidirect
19. #108	D₃	semidirect
61. C₃	#430	semidirect

Maximal subgroups

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

subgroup	index
D₃×M₁₆	2
C₂×ΓL(1,𝔽₂₅)	2
C₃×#108	2
#822	2
#819	2
#430	3