Subgroups — C₃×#391 #5265

Order 192.

186 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×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
4	C₃×#95	C₂	1	4	yes	maximal
5	#391	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂×C₃×Q₈	—	2	2	no	—
7	C₂×C₃×Q₈	—	2	2	no	—
8	C₂×C₃×Q₈	C₄	1	4	yes	complemented
9	C₂²×C₃×C₄	C₂²	1	2	yes	—
10	C₂²×C₃×C₄	C₂²	1	2	yes	—
11	C₂²×C₃×C₄	C₂²	1	2	yes	—
12	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₃×C₄⋊C₄	—	2	2	no	—
14	C₃×C₄²	—	2	2	no	—
15	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic
16	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
17	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
18	#95	C₂×C₃	1	4	yes	—
19	C₂³×C₃	C₂³	1	1	yes	characteristic
20	C₃×Q₈	—	2	8	no	—
21	C₂×C₃×C₄	—	2	2	no	—
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	—	2	2	no	—
25	C₂×C₃×C₄	—	2	2	no	—
26	C₂×C₃×C₄	—	2	4	no	—
27	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
28	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
29	C₂×C₃×C₄	D₄	1	2	yes	—
30	C₂×C₃×C₄	D₄	1	2	yes	—
31	C₂×C₃×C₄	Q₈	1	4	yes	complemented
32	C₂×Q₈	—	2	2	no	—
33	C₂×Q₈	—	2	2	no	—
34	C₂×Q₈	C₃×C₄	1	4	yes	complemented
35	C₂²×C₄	C₂²×C₃	1	2	yes	—
36	C₂²×C₄	C₂²×C₃	1	2	yes	—
37	C₂²×C₄	C₂²×C₃	1	2	yes	—
38	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
39	C₄⋊C₄	—	2	2	no	—
40	C₄²	—	2	2	no	—
41	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₃	C₂×Q₈	1	2	yes	—
45	C₂²×C₃	#41	1	2	yes	—
46	C₃×C₄	—	2	4	no	—
47	C₃×C₄	—	2	4	no	—
48	C₃×C₄	—	4	2	no	—
49	C₃×C₄	C₂²⋊C₄	1	4	yes	—
50	C₂³	C₂³×C₃	1	1	yes	characteristic
51	Q₈	—	2	8	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	4	no	—
58	C₂×C₄	C₂×C₃×C₄	1	4	yes	—
59	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
60	C₂×C₄	C₃×D₄	1	2	yes	—
61	C₂×C₄	C₃×D₄	1	2	yes	—
62	C₂×C₄	C₃×Q₈	1	4	yes	complemented
63	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₃	C₄×Q₈	1	2	yes	—
65	C₂×C₃	C₂²⋊Q₈	1	2	yes	—
66	C₂×C₃	#124	1	1	yes	characteristic
67	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
68	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
69	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
70	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
71	C₂²	C₂×C₃×Q₈	1	2	yes	—
72	C₂²	C₃×#41	1	2	yes	—
73	C₄	—	2	4	no	—
74	C₄	—	2	4	no	—
75	C₄	—	4	2	no	—
76	C₄	C₃×C₂²⋊C₄	1	4	yes	—
77	C₃	#391	1	1	yes	characteristic, direct product factor, Sylow
78	C₂	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
79	C₂	C₃×C₄×Q₈	1	2	yes	—
80	C₂	C₃×C₂²⋊Q₈	1	2	yes	—
81	C₂	C₃×#124	1	1	yes	characteristic
82	C₂	C₃×C₄⋊Q₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. #391	C₃	direct (N × H)
8. C₂×C₃×Q₈	C₄	semidirect
31. C₂×C₃×C₄	Q₈	semidirect
34. C₂×Q₈	C₃×C₄	semidirect
62. C₂×C₄	C₃×Q₈	semidirect
77. C₃	#391	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×C₄⋊C₄	2
C₂×C₃×C₄²	2
C₃×#95	2
#391	3

Subgroups — C3×#391 #5265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#391 #5265