Subgroups — #4914

Order 192.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#919	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#828	C₂	1	1	yes	maximal, characteristic, complemented
5	#826	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#798	C₂	1	1	yes	maximal, characteristic, complemented
8	#509	—	3	1	no	maximal, Sylow
9	#239	—	2	1	no	—
10	D₃×D₄	—	2	1	no	—
11	C₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
12	C₃×D₈	C₂²	1	1	yes	characteristic
13	#215	—	2	1	no	—
14	#213	—	2	1	no	—
15	D₂₄	C₂²	1	1	yes	characteristic
16	D₂₄	C₂²	1	1	yes	characteristic, complemented
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	D₃	1	1	yes	characteristic, complemented
24	D₁₆	—	3	1	no	—
25	D₁₆	—	3	1	no	—
26	M₃₂	—	3	1	no	—
27	C₂²×D₃	—	4	1	no	—
28	C₃×Q₈	—	2	1	no	—
29	C₃×D₄	—	2	1	no	—
30	#67	—	4	1	no	—
31	D₁₂	—	2	1	no	—
32	D₁₂	—	2	1	no	—
33	D₁₂	—	4	1	no	—
34	C₄×D₃	—	4	1	no	—
35	C₄×D₃	D₄	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic, complemented
41	SD₁₆	—	6	1	no	—
42	D₈	—	3	1	no	—
43	D₈	—	3	1	no	—
44	D₈	—	6	1	no	—
45	D₈	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	—	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	—	4	1	no	—
55	C₃×C₄	C₂×D₄	1	1	yes	characteristic
56	Dic₃	D₈	1	1	yes	characteristic
57	C₂³	—	12	1	no	—
58	Q₈	—	2	1	no	—
59	D₄	—	2	1	no	—
60	D₄	—	6	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	C₂×D₈	1	1	yes	characteristic
70	D₃	—	2	1	no	—
71	D₃	—	8	1	no	—
72	D₃	—	8	1	no	—
73	C₂²	—	3	1	no	—
74	C₂²	—	4	1	no	—
75	C₂²	—	12	1	no	—
76	C₂²	—	12	1	no	—
77	C₂²	—	24	2	no	—
78	C₄	—	3	1	no	—
79	C₄	—	4	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	—	24	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×SD₃₂	C₂
socle	C₂×C₃	C₂×D₈
hypercenter	SD₃₂	D₃
hypocenter	C₃	#509
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. #919	C₂	semidirect
2. D₃×D₈	C₂	semidirect
3. C₃×SD₃₂	C₂	semidirect
4. #828	C₂	semidirect
5. #826	C₂	semidirect
6. D₄₈	C₂	semidirect
7. #798	C₂	semidirect
11. C₃×Q₁₆	C₂²	semidirect
16. D₂₄	C₂²	semidirect
18. C₃×C₁₆	C₂²	semidirect
19. C₃⋊C₁₆	C₂²	semidirect
23. SD₃₂	D₃	semidirect
40. Q₁₆	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
#919	2
D₃×D₈	2
C₃×SD₃₂	2
#828	2
#826	2
D₄₈	2
#798	2
#509	3