Subgroups — C₂×C₃×#95 #5249

Order 192.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	3	yes	maximal
2	C₃×#95	C₂	1	4	yes	maximal, direct product factor
3	C₂×#95	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁴×C₃	C₂²	1	1	yes	characteristic
5	C₂²×C₃×C₄	—	2	12	no	—
6	C₂²×C₃×C₄	C₄	1	12	yes	complemented
7	C₂²×C₃×C₄	C₂²	1	6	yes	—
8	C₂³×C₄	C₂×C₃	1	3	yes	—
9	#95	C₂×C₃	1	4	yes	direct product factor
10	C₂³×C₃	C₂×C₄	1	6	yes	—
11	C₂³×C₃	D₄	1	6	yes	—
12	C₂³×C₃	Q₈	1	2	yes	—
13	C₂³×C₃	C₂³	1	1	yes	characteristic
14	C₂×C₃×C₄	—	2	24	no	—
15	C₂×C₃×C₄	—	2	12	no	—
16	C₂×C₃×C₄	C₂×C₄	1	12	yes	complemented
17	C₂⁴	C₂²×C₃	1	1	yes	characteristic
18	C₂²×C₄	—	2	12	no	—
19	C₂²×C₄	C₃×C₄	1	12	yes	complemented
20	C₂²×C₄	C₂²×C₃	1	6	yes	—
21	C₂²×C₃	C₄²	1	4	yes	—
22	C₂²×C₃	C₂²⋊C₄	1	12	yes	—
23	C₂²×C₃	C₄⋊C₄	1	12	yes	—
24	C₂²×C₃	C₂²×C₄	1	3	yes	—
25	C₂²×C₃	C₂×D₄	1	3	yes	—
26	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
27	C₃×C₄	—	2	12	no	—
28	C₂³	C₂×C₃×C₄	1	6	yes	—
29	C₂³	C₃×D₄	1	6	yes	—
30	C₂³	C₃×Q₈	1	2	yes	—
31	C₂³	C₂³×C₃	1	1	yes	characteristic
32	C₂×C₄	—	2	24	no	—
33	C₂×C₄	—	2	12	no	—
34	C₂×C₄	C₂×C₃×C₄	1	12	yes	complemented
35	C₂×C₃	#95	1	8	yes	direct product factor
36	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
37	C₂×C₃	C₂×C₂²⋊C₄	1	3	yes	—
38	C₂×C₃	C₂×C₄⋊C₄	1	3	yes	—
39	C₂²	C₃×C₄²	1	4	yes	—
40	C₂²	C₃×C₂²⋊C₄	1	12	yes	—
41	C₂²	C₃×C₄⋊C₄	1	12	yes	—
42	C₂²	C₂²×C₃×C₄	1	3	yes	—
43	C₂²	C₂×C₃×D₄	1	3	yes	—
44	C₂²	C₂×C₃×Q₈	1	1	yes	characteristic
45	C₄	—	2	12	no	—
46	C₃	C₂×#95	1	1	yes	characteristic, direct product factor, Sylow
47	C₂	C₃×#95	1	8	yes	direct product factor
48	C₂	C₂×C₃×C₄²	1	1	yes	characteristic
49	C₂	C₂×C₃×C₂²⋊C₄	1	3	yes	—
50	C₂	C₂×C₃×C₄⋊C₄	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃	C₂²
commutator	C₂	C₂×C₃×C₄²
Frattini, cosocle	C₂³	C₂³×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#95	C₂	direct (N × H)
3. C₂×#95	C₃	direct (N × H)
6. C₂²×C₃×C₄	C₄	semidirect
9. #95	C₂×C₃	direct (N × H)
16. C₂×C₃×C₄	C₂×C₄	semidirect
19. C₂²×C₄	C₃×C₄	semidirect
34. C₂×C₄	C₂×C₃×C₄	semidirect
35. C₂×C₃	#95	direct (N × H)
46. C₃	C₂×#95	direct (N × H)
47. C₂	C₃×#95	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
C₃×#95	2
C₂×#95	3

Subgroups — C2×C3×#95 #5249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#95 #5249