Subgroups — C₃×#419 #5293

Order 192.

150 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×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×#103	C₂	1	4	yes	maximal, complemented
5	#419	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₈	—	2	2	no	—
7	C₂×C₃×Q₈	—	2	1	no	—
8	C₂×C₃×Q₈	C₄	1	4	yes	complemented
9	C₂×C₃×Q₈	C₂²	1	2	yes	—
10	C₂²×C₃×C₄	—	2	1	no	—
11	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₃×M₁₆	—	2	2	no	—
13	C₂×C₃×C₈	C₂²	1	2	yes	—
14	C₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₃×C₂²⋊C₄	—	2	1	no	—
16	C₃×C₄²	—	2	1	no	—
17	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic
18	C₂×M₁₆	C₂×C₃	1	1	yes	characteristic
19	#117	C₂×C₃	1	1	yes	characteristic
20	#103	C₂×C₃	1	4	yes	complemented
21	C₂³×C₃	D₄	1	1	yes	characteristic
22	C₃×Q₈	—	2	4	no	—
23	C₃×Q₈	—	2	2	no	—
24	C₃×Q₈	C₂×C₄	1	4	yes	—
25	C₂×C₃×C₄	—	2	4	no	—
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	—	2	2	no	—
28	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
29	C₂×C₃×C₄	D₄	1	1	yes	characteristic
30	C₂×C₃×C₄	D₄	1	2	yes	—
31	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
32	C₃×C₈	—	2	2	no	—
33	C₂×Q₈	—	2	2	no	—
34	C₂×Q₈	—	2	1	no	—
35	C₂×Q₈	C₃×C₄	1	4	yes	complemented
36	C₂×Q₈	C₂²×C₃	1	2	yes	—
37	C₂²×C₄	—	2	1	no	—
38	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
39	M₁₆	—	2	2	no	—
40	C₂×C₈	C₂²×C₃	1	2	yes	—
41	C₄⋊C₄	C₂²×C₃	1	2	yes	—
42	C₂²⋊C₄	—	2	1	no	—
43	C₄²	—	2	1	no	—
44	C₂²×C₃	—	2	2	no	—
45	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
47	C₃×C₄	—	2	4	no	—
48	C₃×C₄	—	4	2	no	—
49	C₃×C₄	C₂²⋊C₄	1	2	yes	—
50	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
51	C₃×C₄	C₂×D₄	1	1	yes	characteristic
52	C₂³	C₃×D₄	1	1	yes	characteristic
53	Q₈	—	2	4	no	—
54	Q₈	—	2	2	no	—
55	Q₈	C₂×C₃×C₄	1	4	yes	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
60	C₂×C₄	C₃×D₄	1	1	yes	characteristic
61	C₂×C₄	C₃×D₄	1	2	yes	—
62	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₂×C₃	—	2	2	no	—
65	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₃	#137	1	2	yes	—
67	C₂²	—	2	2	no	—
68	C₂²	C₃×C₂²⋊C₄	1	2	yes	—
69	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
70	C₄	—	2	4	no	—
71	C₄	—	4	2	no	—
72	C₄	C₃×C₂²⋊C₄	1	2	yes	—
73	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
74	C₄	C₂×C₃×D₄	1	1	yes	characteristic
75	C₃	#419	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	2	2	no	—
77	C₂	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
78	C₂	C₃×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂³×C₃	D₄
LCS	G ▷ 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
4. C₃×#103	C₂	semidirect
5. #419	C₃	direct (N × H)
8. C₂×C₃×Q₈	C₄	semidirect
20. #103	C₂×C₃	semidirect
35. C₂×Q₈	C₃×C₄	semidirect
75. C₃	#419	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×M₁₆	2
C₃×#117	2
C₃×#103	2
#419	3

Subgroups — C3×#419 #5293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#419 #5293