Subgroups — C₃×#392 #5266

Order 192.

322 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄	C₂	1	3	yes	maximal, complemented
2	C₂×C₃×C₂²⋊C₄	C₂	1	3	yes	maximal, complemented
3	C₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	#392	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂⁴×C₃	C₂²	1	3	yes	—
6	C₂×C₃×D₄	—	2	12	no	—
7	C₂×C₃×D₄	—	2	6	no	—
8	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄	C₂²	1	3	yes	—
10	C₃×C₂²⋊C₄	—	2	6	no	—
11	C₂²×D₄	C₂×C₃	1	3	yes	complemented
12	C₂×C₂²⋊C₄	C₂×C₃	1	3	yes	complemented
13	#95	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂³×C₃	—	2	3	no	—
15	C₂³×C₃	—	2	6	no	—
16	C₂³×C₃	—	2	6	no	—
17	C₂³×C₃	—	2	3	no	—
18	C₂³×C₃	D₄	1	6	yes	complemented
19	C₂³×C₃	C₂³	1	1	yes	characteristic
20	C₃×D₄	—	2	24	no	—
21	C₂×C₃×C₄	—	2	6	no	—
22	C₂×C₃×C₄	—	2	3	no	—
23	C₂×C₃×C₄	D₄	1	6	yes	complemented
24	C₂⁴	C₂²×C₃	1	3	yes	—
25	C₂×D₄	—	2	12	no	—
26	C₂×D₄	—	2	6	no	—
27	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
28	C₂²×C₄	C₂²×C₃	1	3	yes	—
29	C₂²⋊C₄	—	2	6	no	—
30	C₂²×C₃	—	2	12	no	—
31	C₂²×C₃	—	2	6	no	—
32	C₂²×C₃	—	4	3	no	—
33	C₂²×C₃	—	4	6	no	—
34	C₂²×C₃	—	4	3	no	—
35	C₂²×C₃	C₂×D₄	1	3	yes	—
36	C₂²×C₃	C₂×D₄	1	3	yes	—
37	C₂²×C₃	#41	1	1	yes	characteristic
38	C₃×C₄	—	2	6	no	—
39	C₃×C₄	—	4	1	no	—
40	C₂³	—	2	3	no	—
41	C₂³	—	2	6	no	—
42	C₂³	—	2	6	no	—
43	C₂³	—	2	3	no	—
44	C₂³	C₃×D₄	1	6	yes	complemented
45	C₂³	C₂³×C₃	1	1	yes	characteristic
46	D₄	—	2	24	no	—
47	C₂×C₄	—	2	6	no	—
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	C₃×D₄	1	6	yes	complemented
50	C₂×C₃	—	4	6	no	—
51	C₂×C₃	#120	1	3	yes	—
52	C₂×C₃	#121	1	3	yes	—
53	C₂×C₃	#127	1	1	yes	characteristic
54	C₂²	—	2	12	no	—
55	C₂²	—	2	6	no	—
56	C₂²	—	4	3	no	—
57	C₂²	—	4	6	no	—
58	C₂²	—	4	3	no	—
59	C₂²	C₂×C₃×D₄	1	3	yes	—
60	C₂²	C₂×C₃×D₄	1	3	yes	—
61	C₂²	C₃×#41	1	1	yes	characteristic
62	C₄	—	2	6	no	—
63	C₄	—	4	1	no	—
64	C₃	#392	1	1	yes	characteristic, direct product factor, Sylow
65	C₂	—	4	6	no	—
66	C₂	C₃×#120	1	3	yes	—
67	C₂	C₃×#121	1	3	yes	—
68	C₂	C₃×#127	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄	C₂	semidirect
2. C₂×C₃×C₂²⋊C₄	C₂	semidirect
3. C₃×#95	C₂	semidirect
4. #392	C₃	direct (N × H)
11. C₂²×D₄	C₂×C₃	semidirect
12. C₂×C₂²⋊C₄	C₂×C₃	semidirect
13. #95	C₂×C₃	semidirect
18. C₂³×C₃	D₄	semidirect
23. C₂×C₃×C₄	D₄	semidirect
44. C₂³	C₃×D₄	semidirect
49. C₂×C₄	C₃×D₄	semidirect
64. C₃	#392	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×D₄	2
C₂×C₃×C₂²⋊C₄	2
C₃×#95	2
#392	3

Subgroups — C3×#392 #5266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#392 #5266