Subgroups — #4911

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#912	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#827	C₂	1	1	yes	maximal, characteristic, complemented
5	#826	C₂	1	1	yes	maximal, characteristic, complemented
6	#800	C₂	1	1	yes	maximal, characteristic, complemented
7	#798	C₂	1	1	yes	maximal, characteristic, complemented
8	#509	—	3	1	no	maximal, Sylow
9	#237	—	2	1	no	—
10	D₃×D₄	—	2	1	no	—
11	C₃×D₈	C₂²	1	1	yes	characteristic
12	C₃×D₈	C₂²	1	1	yes	characteristic, complemented
13	#214	—	2	1	no	—
14	#213	—	2	1	no	—
15	Dic₁₂	C₂²	1	1	yes	characteristic, complemented
16	D₂₄	C₂²	1	1	yes	characteristic
17	D₃×C₈	C₂²	1	1	yes	characteristic
18	C₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
20	#135	—	3	1	no	—
21	C₂×D₈	—	3	1	no	—
22	SD₃₂	—	3	1	no	—
23	SD₃₂	—	3	1	no	—
24	D₁₆	—	3	1	no	—
25	D₁₆	D₃	1	1	yes	characteristic, complemented
26	M₃₂	—	3	1	no	—
27	C₂²×D₃	—	4	1	no	—
28	C₃×D₄	—	2	1	no	—
29	C₃×D₄	—	2	1	no	—
30	#67	—	4	1	no	—
31	#67	—	4	1	no	—
32	C₂×Dic₃	—	4	1	no	—
33	D₁₂	—	2	1	no	—
34	C₄×D₃	D₄	1	1	yes	characteristic
35	Dic₆	—	2	1	no	—
36	C₃×C₈	C₂³	1	1	yes	characteristic
37	C₃⋊C₈	D₄	1	1	yes	characteristic
38	#41	—	6	1	no	—
39	C₂×D₄	—	6	1	no	—
40	Q₁₆	—	3	1	no	—
41	SD₁₆	—	6	1	no	—
42	D₈	—	3	1	no	—
43	D₈	—	6	1	no	—
44	D₈	C₂×D₃	1	1	yes	characteristic
45	D₈	C₂×D₃	1	1	yes	characteristic, complemented
46	C₂×C₈	—	3	1	no	—
47	C₁₆	—	3	1	no	—
48	C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
49	C₂²×C₃	—	4	1	no	—
50	C₂²×C₃	—	4	1	no	—
51	C₂×D₃	—	4	1	no	—
52	C₂×D₃	—	8	2	no	—
53	C₂×D₃	D₈	1	1	yes	characteristic
54	C₃×C₄	C₂×D₄	1	1	yes	characteristic
55	Dic₃	—	4	1	no	—
56	Dic₃	D₈	1	1	yes	characteristic
57	C₂³	—	12	1	no	—
58	Q₈	—	6	1	no	—
59	D₄	—	2	1	no	—
60	D₄	—	2	1	no	—
61	D₄	—	6	1	no	—
62	D₄	—	12	1	no	—
63	D₄	—	12	1	no	—
64	C₂×C₄	—	3	1	no	—
65	C₂×C₄	—	12	1	no	—
66	C₈	—	3	1	no	—
67	C₈	C₂²×D₃	1	1	yes	characteristic
68	C₂×C₃	—	8	1	no	—
69	C₂×C₃	—	8	1	no	—
70	C₂×C₃	C₂×D₈	1	1	yes	characteristic
71	D₃	—	2	1	no	—
72	D₃	—	8	1	no	—
73	C₂²	—	3	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	—	4	1	no	—
76	C₂²	—	12	1	no	—
77	C₂²	—	24	2	no	—
78	C₄	—	3	1	no	—
79	C₄	—	12	1	no	—
80	C₄	D₃×D₄	1	1	yes	characteristic
81	C₃	#509	1	1	yes	characteristic, complemented, Sylow
82	C₂	—	6	1	no	—
83	C₂	—	8	1	no	—
84	C₂	—	8	1	no	—
85	C₂	—	24	1	no	—
86	C₂	D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃×D₈
commutator, cosocle	C₃×C₈	C₂³
Frattini	C₈	C₂²×D₃
Fitting	C₃×D₁₆	C₂
socle	C₂×C₃	C₂×D₈
hypercenter	D₁₆	D₃
hypocenter	C₃	#509
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #912	C₂	semidirect
2. D₃×D₈	C₂	semidirect
3. C₃×D₁₆	C₂	semidirect
4. #827	C₂	semidirect
5. #826	C₂	semidirect
6. #800	C₂	semidirect
7. #798	C₂	semidirect
12. C₃×D₈	C₂²	semidirect
15. Dic₁₂	C₂²	semidirect
18. C₃×C₁₆	C₂²	semidirect
19. C₃⋊C₁₆	C₂²	semidirect
25. D₁₆	D₃	semidirect
45. D₈	C₂×D₃	semidirect
48. C₁₆	C₂×D₃	semidirect
81. C₃	#509	semidirect

Maximal subgroups

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

subgroup	index
#912	2
D₃×D₈	2
C₃×D₁₆	2
#827	2
#826	2
#800	2
#798	2
#509	3