Subgroups — C₃×#461 #5335

Order 192.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×SD₁₆	C₂	1	2	yes	maximal
2	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#103	C₂	1	2	yes	maximal, complemented
6	#461	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	2	yes	—
8	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄	—	2	1	no	—
10	C₃×SD₁₆	—	2	4	no	—
11	C₂×C₃×C₈	C₂²	1	2	yes	—
12	C₃×C₄⋊C₄	—	2	1	no	—
13	C₃×C₄⋊C₄	—	2	1	no	—
14	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₃×C₂²⋊C₄	—	2	1	no	—
16	C₃×C₄²	C₂²	1	1	yes	characteristic
17	C₂×SD₁₆	C₂×C₃	1	2	yes	—
18	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
19	C₄×D₄	C₂×C₃	1	1	yes	characteristic
20	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
21	#103	C₂×C₃	1	2	yes	complemented
22	C₂³×C₃	—	2	1	no	—
23	C₃×Q₈	—	2	2	no	—
24	C₃×Q₈	—	2	2	no	—
25	C₃×D₄	—	2	1	no	—
26	C₃×D₄	D₄	1	2	yes	—
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	—	2	2	no	—
29	C₂×C₃×C₄	—	4	2	no	—
30	C₂×C₃×C₄	D₄	1	1	yes	characteristic
31	C₂×C₃×C₄	D₄	1	1	yes	characteristic
32	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
33	C₃×C₈	—	2	2	no	—
34	C₂×Q₈	C₂²×C₃	1	2	yes	—
35	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
36	C₂²×C₄	—	2	1	no	—
37	SD₁₆	—	2	4	no	—
38	C₂×C₈	C₂²×C₃	1	2	yes	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	2	1	no	—
41	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
42	C₂²⋊C₄	—	2	1	no	—
43	C₄²	C₂²×C₃	1	1	yes	characteristic
44	C₂²×C₃	—	2	2	no	—
45	C₂²×C₃	—	4	1	no	—
46	C₂²×C₃	—	4	1	no	—
47	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
48	C₃×C₄	—	2	1	no	—
49	C₃×C₄	—	4	2	no	—
50	C₃×C₄	—	4	1	no	—
51	C₃×C₄	SD₁₆	1	2	yes	complemented
52	C₃×C₄	C₂×D₄	1	1	yes	characteristic
53	C₃×C₄	#41	1	1	yes	characteristic
54	C₂³	—	2	1	no	—
55	Q₈	—	2	2	no	—
56	Q₈	—	2	2	no	—
57	D₄	—	2	1	no	—
58	D₄	C₃×D₄	1	2	yes	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	4	2	no	—
62	C₂×C₄	C₃×D₄	1	1	yes	characteristic
63	C₂×C₄	C₃×D₄	1	1	yes	characteristic
64	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂×C₃	—	4	2	no	—
67	C₂×C₃	#121	1	1	yes	characteristic
68	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
69	C₂×C₃	#137	1	1	yes	characteristic
70	C₂²	—	2	2	no	—
71	C₂²	—	4	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	4	2	no	—
76	C₄	—	4	1	no	—
77	C₄	C₃×SD₁₆	1	2	yes	complemented
78	C₄	C₂×C₃×D₄	1	1	yes	characteristic
79	C₄	C₃×#41	1	1	yes	characteristic
80	C₃	#461	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	—	4	2	no	—
82	C₂	C₃×#121	1	1	yes	characteristic
83	C₂	C₂×C₃×SD₁₆	1	1	yes	characteristic
84	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	C₂×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄⋊Q₈	C₂	semidirect
4. C₃×C₄⋊C₈	C₂	semidirect
5. C₃×#103	C₂	semidirect
6. #461	C₃	direct (N × H)
18. C₄⋊Q₈	C₂×C₃	semidirect
20. C₄⋊C₈	C₂×C₃	semidirect
21. #103	C₂×C₃	semidirect
51. C₃×C₄	SD₁₆	semidirect
77. C₄	C₃×SD₁₆	semidirect
80. C₃	#461	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×SD₁₆	2
C₃×C₄⋊Q₈	2
C₃×C₄×D₄	2
C₃×C₄⋊C₈	2
C₃×#103	2
#461	3

Subgroups — C3×#461 #5335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#461 #5335