Subgroups — C₃×#342 #4589

Order 192.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₂²⋊C₄	C₂	1	2	yes	maximal
3	#342	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁴×C₃	C₂²	1	1	yes	characteristic
5	C₂²×C₃×C₄	—	2	2	no	—
6	C₂²×C₃×C₄	C₄	1	2	yes	complemented
7	C₃×C₂²⋊C₄	—	2	2	no	—
8	C₃×C₂²⋊C₄	—	2	2	no	—
9	C₃×C₂²⋊C₄	C₄	1	4	yes	complemented
10	C₂×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
11	C₂×C₂²⋊C₄	C₂×C₃	1	2	yes	—
12	C₂³×C₃	—	4	2	no	—
13	C₂³×C₃	C₂×C₄	1	1	yes	characteristic
14	C₂³×C₃	C₂×C₄	1	2	yes	—
15	C₂³×C₃	D₄	1	2	yes	—
16	C₂³×C₃	D₄	1	1	yes	characteristic
17	C₂³×C₃	Q₈	1	1	yes	characteristic
18	C₂×C₃×C₄	—	2	4	no	—
19	C₂×C₃×C₄	—	2	2	no	—
20	C₂×C₃×C₄	—	4	4	no	—
21	C₂×C₃×C₄	—	4	2	no	—
22	C₂⁴	C₂²×C₃	1	1	yes	characteristic
23	C₂²×C₄	—	2	2	no	—
24	C₂²×C₄	C₃×C₄	1	2	yes	complemented
25	C₂²⋊C₄	—	2	2	no	—
26	C₂²⋊C₄	—	2	2	no	—
27	C₂²⋊C₄	C₃×C₄	1	4	yes	complemented
28	C₂²×C₃	—	2	2	no	—
29	C₂²×C₃	—	2	4	no	—
30	C₂²×C₃	—	4	2	no	—
31	C₂²×C₃	—	4	1	no	—
32	C₂²×C₃	—	4	1	no	—
33	C₂²×C₃	C₄²	1	1	yes	characteristic
34	C₂²×C₃	C₂²⋊C₄	1	2	yes	—
35	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₃	C₄⋊C₄	1	2	yes	—
38	C₃×C₄	—	4	4	no	—
39	C₃×C₄	—	4	2	no	—
40	C₂³	—	4	2	no	—
41	C₂³	C₂×C₃×C₄	1	1	yes	characteristic
42	C₂³	C₂×C₃×C₄	1	2	yes	—
43	C₂³	C₃×D₄	1	2	yes	—
44	C₂³	C₃×D₄	1	1	yes	characteristic
45	C₂³	C₃×Q₈	1	1	yes	characteristic
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	2	4	no	—
48	C₂×C₄	—	4	4	no	—
49	C₂×C₄	—	4	2	no	—
50	C₂×C₃	—	2	2	no	—
51	C₂×C₃	—	2	1	no	—
52	C₂×C₃	—	2	1	no	—
53	C₂×C₃	—	2	2	no	—
54	C₂×C₃	#95	1	1	yes	characteristic
55	C₂×C₃	#99	1	2	yes	—
56	C₂²	—	2	2	no	—
57	C₂²	—	2	4	no	—
58	C₂²	—	4	2	no	—
59	C₂²	—	4	1	no	—
60	C₂²	—	4	1	no	—
61	C₂²	C₃×C₄²	1	1	yes	characteristic
62	C₂²	C₃×C₂²⋊C₄	1	2	yes	—
63	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
64	C₂²	C₃×C₄⋊C₄	1	1	yes	characteristic
65	C₂²	C₃×C₄⋊C₄	1	2	yes	—
66	C₄	—	4	4	no	—
67	C₄	—	4	2	no	—
68	C₃	#342	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	—	2	2	no	—
70	C₂	—	2	1	no	—
71	C₂	—	2	1	no	—
72	C₂	—	2	2	no	—
73	C₂	C₃×#95	1	1	yes	characteristic
74	C₂	C₃×#99	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃	C₂²⋊C₄
commutator	C₂²	C₃×C₄²
Frattini, cosocle	C₂⁴	C₂²×C₃
prime radical	C₂⁴×C₃	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂⁴×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. #342	C₃	direct (N × H)
6. C₂²×C₃×C₄	C₄	semidirect
9. C₃×C₂²⋊C₄	C₄	semidirect
24. C₂²×C₄	C₃×C₄	semidirect
27. C₂²⋊C₄	C₃×C₄	semidirect
68. C₃	#342	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×C₂²⋊C₄	2
#342	3

Subgroups — C3×#342 #4589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#342 #4589