Subgroups — C₃×#451 #5325

Order 192.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Q₁₆	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#103	C₂	1	2	yes	maximal, complemented
5	C₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#451	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	—	2	4	no	—
8	C₂×C₃×Q₈	—	2	1	no	—
9	C₂×C₃×Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×Q₈	C₂²	1	2	yes	—
11	C₂²×C₃×C₄	—	2	1	no	—
12	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₃×Q₁₆	—	2	4	no	—
14	C₂×C₃×C₈	C₂²	1	2	yes	—
15	C₃×C₄⋊C₄	—	2	1	no	—
16	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₂²⋊C₄	—	2	1	no	—
18	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic
19	C₂×Q₁₆	C₂×C₃	1	2	yes	complemented
20	C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
21	#103	C₂×C₃	1	2	yes	complemented
22	C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
23	C₂³×C₃	D₄	1	1	yes	characteristic
24	C₃×Q₈	—	2	4	no	—
25	C₃×Q₈	—	2	2	no	—
26	C₃×Q₈	—	2	2	no	—
27	C₃×Q₈	D₄	1	4	yes	—
28	C₂×C₃×C₄	—	2	4	no	—
29	C₂×C₃×C₄	—	2	2	no	—
30	C₂×C₃×C₄	—	2	2	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	2	1	no	—
33	C₂×C₃×C₄	D₄	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
35	C₃×C₈	—	2	2	no	—
36	C₂×Q₈	—	2	4	no	—
37	C₂×Q₈	—	2	1	no	—
38	C₂×Q₈	C₂²×C₃	1	1	yes	characteristic
39	C₂×Q₈	C₂²×C₃	1	2	yes	—
40	C₂²×C₄	—	2	1	no	—
41	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
42	Q₁₆	—	2	4	no	—
43	C₂×C₈	C₂²×C₃	1	2	yes	—
44	C₄⋊C₄	—	2	1	no	—
45	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
46	C₂²⋊C₄	—	2	1	no	—
47	C₂²×C₃	—	2	1	no	—
48	C₂²×C₃	—	2	1	no	—
49	C₂²×C₃	Q₁₆	1	2	yes	complemented
50	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
51	C₃×C₄	—	2	4	no	—
52	C₃×C₄	—	2	1	no	—
53	C₃×C₄	—	4	1	no	—
54	C₃×C₄	—	4	1	no	—
55	C₃×C₄	C₂×D₄	1	2	yes	—
56	C₂³	C₃×D₄	1	1	yes	characteristic
57	Q₈	—	2	4	no	—
58	Q₈	—	2	2	no	—
59	Q₈	—	2	2	no	—
60	Q₈	C₃×D₄	1	4	yes	—
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	C₃×D₄	1	1	yes	characteristic
67	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₂×C₃	—	2	2	no	—
70	C₂×C₃	#120	1	1	yes	characteristic
71	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
72	C₂×C₃	#137	1	1	yes	characteristic
73	C₂²	—	2	1	no	—
74	C₂²	—	2	1	no	—
75	C₂²	C₃×Q₁₆	1	2	yes	complemented
76	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
77	C₄	—	2	4	no	—
78	C₄	—	2	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	4	1	no	—
81	C₄	C₂×C₃×D₄	1	2	yes	—
82	C₃	#451	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	2	2	no	—
84	C₂	C₃×#120	1	1	yes	characteristic
85	C₂	C₂×C₃×Q₁₆	1	1	yes	characteristic
86	C₂	C₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂³×C₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Q₁₆	C₂	semidirect
4. C₃×#103	C₂	semidirect
6. #451	C₃	direct (N × H)
19. C₂×Q₁₆	C₂×C₃	semidirect
21. #103	C₂×C₃	semidirect
49. C₂²×C₃	Q₁₆	semidirect
75. C₂²	C₃×Q₁₆	semidirect
82. C₃	#451	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Q₈	2
C₂×C₃×Q₁₆	2
C₃×C₂²⋊Q₈	2
C₃×#103	2
C₃×C₂²⋊C₈	2
#451	3

Subgroups — C3×#451 #5325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#451 #5325