Subgroups — C₃×#395 #5269

Order 192.

182 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	3	yes	maximal
3	C₃×#95	C₂	1	3	yes	maximal
4	#395	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₈	—	2	6	no	—
6	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₄	C₂²	1	3	yes	—
8	C₂²×C₃×C₄	C₂²	1	3	yes	—
9	C₃×C₄⋊C₄	—	2	6	no	—
10	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic
11	C₂×C₄⋊C₄	C₂×C₃	1	3	yes	—
12	#95	C₂×C₃	1	3	yes	—
13	C₂³×C₃	C₂³	1	1	yes	characteristic
14	C₃×Q₈	—	2	8	no	—
15	C₂×C₃×C₄	—	2	3	no	—
16	C₂×C₃×C₄	—	2	6	no	—
17	C₂×C₃×C₄	—	2	3	no	—
18	C₂×C₃×C₄	—	2	3	no	—
19	C₂×C₃×C₄	D₄	1	6	yes	—
20	C₂×C₃×C₄	Q₈	1	6	yes	complemented
21	C₂×Q₈	—	2	6	no	—
22	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
23	C₂²×C₄	C₂²×C₃	1	3	yes	—
24	C₂²×C₄	C₂²×C₃	1	3	yes	—
25	C₄⋊C₄	—	2	6	no	—
26	C₂²×C₃	C₂×D₄	1	3	yes	—
27	C₂²×C₃	C₂×Q₈	1	3	yes	—
28	C₂²×C₃	#41	1	1	yes	characteristic
29	C₃×C₄	—	2	6	no	—
30	C₃×C₄	—	2	6	no	—
31	C₃×C₄	—	4	1	no	—
32	C₂³	C₂³×C₃	1	1	yes	characteristic
33	Q₈	—	2	8	no	—
34	C₂×C₄	—	2	3	no	—
35	C₂×C₄	—	2	6	no	—
36	C₂×C₄	—	2	3	no	—
37	C₂×C₄	—	2	3	no	—
38	C₂×C₄	C₃×D₄	1	6	yes	—
39	C₂×C₄	C₃×Q₈	1	6	yes	complemented
40	C₂×C₃	#120	1	1	yes	characteristic
41	C₂×C₃	C₂²⋊Q₈	1	3	yes	—
42	C₂×C₃	C₄⋊Q₈	1	3	yes	—
43	C₂²	C₂×C₃×D₄	1	3	yes	—
44	C₂²	C₂×C₃×Q₈	1	3	yes	—
45	C₂²	C₃×#41	1	1	yes	characteristic
46	C₄	—	2	6	no	—
47	C₄	—	2	6	no	—
48	C₄	—	4	1	no	—
49	C₃	#395	1	1	yes	characteristic, direct product factor, Sylow
50	C₂	C₃×#120	1	1	yes	characteristic
51	C₂	C₃×C₂²⋊Q₈	1	3	yes	—
52	C₂	C₃×C₄⋊Q₈	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
4. #395	C₃	direct (N × H)
20. C₂×C₃×C₄	Q₈	semidirect
39. C₂×C₄	C₃×Q₈	semidirect
49. C₃	#395	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
C₃×#95	2
#395	3

Subgroups — C3×#395 #5269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#395 #5269