Subgroups — C₃×#381 #5255

Order 192.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₃×#95	C₂	1	4	yes	maximal, complemented
4	#381	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂⁴×C₃	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄	—	2	4	no	—
7	C₂²×C₃×C₄	C₄	1	4	yes	complemented
8	C₂²×C₃×C₄	C₂²	1	4	yes	—
9	C₂²×C₃×C₄	C₂²	1	2	yes	—
10	C₃×C₂²⋊C₄	—	2	4	no	—
11	C₂³×C₄	C₂×C₃	1	1	yes	characteristic
12	C₂×C₂²⋊C₄	C₂×C₃	1	2	yes	—
13	#95	C₂×C₃	1	4	yes	complemented
14	C₂³×C₃	—	2	4	no	—
15	C₂³×C₃	C₂×C₄	1	2	yes	—
16	C₂³×C₃	D₄	1	4	yes	—
17	C₂³×C₃	C₂³	1	1	yes	characteristic
18	C₂×C₃×C₄	—	2	8	no	—
19	C₂×C₃×C₄	—	2	4	no	—
20	C₂×C₃×C₄	—	2	4	no	—
21	C₂×C₃×C₄	—	2	8	no	—
22	C₂×C₃×C₄	C₂×C₄	1	4	yes	—
23	C₂⁴	C₂²×C₃	1	1	yes	characteristic
24	C₂²×C₄	—	2	4	no	—
25	C₂²×C₄	C₃×C₄	1	4	yes	complemented
26	C₂²×C₄	C₂²×C₃	1	4	yes	—
27	C₂²×C₄	C₂²×C₃	1	2	yes	—
28	C₂²⋊C₄	—	2	4	no	—
29	C₂²×C₃	—	2	4	no	—
30	C₂²×C₃	—	2	8	no	—
31	C₂²×C₃	C₂²⋊C₄	1	4	yes	—
32	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₃	C₂×D₄	1	2	yes	—
34	C₂²×C₃	#41	1	4	yes	—
35	C₃×C₄	—	2	4	no	—
36	C₃×C₄	—	4	4	no	—
37	C₂³	—	2	4	no	—
38	C₂³	C₂×C₃×C₄	1	2	yes	—
39	C₂³	C₃×D₄	1	4	yes	—
40	C₂³	C₂³×C₃	1	1	yes	characteristic
41	C₂×C₄	—	2	8	no	—
42	C₂×C₄	—	2	4	no	—
43	C₂×C₄	—	2	4	no	—
44	C₂×C₄	—	2	8	no	—
45	C₂×C₄	C₂×C₃×C₄	1	4	yes	—
46	C₂×C₃	—	2	4	no	—
47	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₃	#117	1	2	yes	—
49	C₂×C₃	#123	1	4	yes	—
50	C₂²	—	2	4	no	—
51	C₂²	—	2	8	no	—
52	C₂²	C₃×C₂²⋊C₄	1	4	yes	—
53	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
54	C₂²	C₂×C₃×D₄	1	2	yes	—
55	C₂²	C₃×#41	1	4	yes	—
56	C₄	—	2	4	no	—
57	C₄	—	4	4	no	—
58	C₃	#381	1	1	yes	characteristic, direct product factor, Sylow
59	C₂	—	2	4	no	—
60	C₂	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
61	C₂	C₃×#117	1	2	yes	—
62	C₂	C₃×#123	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂³
commutator	C₂²	C₂²×C₃×C₄
Frattini, cosocle	C₂³	C₂³×C₃
prime radical	C₂⁴×C₃	C₂²
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
3. C₃×#95	C₂	semidirect
4. #381	C₃	direct (N × H)
7. C₂²×C₃×C₄	C₄	semidirect
13. #95	C₂×C₃	semidirect
25. C₂²×C₄	C₃×C₄	semidirect
58. C₃	#381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄	2
C₂×C₃×C₂²⋊C₄	2
C₃×#95	2
#381	3

Subgroups — C3×#381 #5255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#381 #5255