Subgroups — C₂×C₃×C₂²⋊C₄ #955

Order 96.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂³×C₃	C₂²
commutator	C₂	C₂²×C₃×C₄
Frattini, cosocle	C₂²	C₂³×C₃
prime radical	C₂⁴×C₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄	C₂	semidirect
3. C₃×C₂²⋊C₄	C₂	direct (N × H)
4. C₂×C₂²⋊C₄	C₃	direct (N × H)
6. C₂³×C₃	C₄	semidirect
10. C₂×C₃×C₄	C₂²	semidirect
12. C₂²×C₄	C₂×C₃	semidirect
13. C₂²⋊C₄	C₂×C₃	direct (N × H)
17. C₂²×C₃	C₂×C₄	semidirect
22. C₂³	C₃×C₄	semidirect
26. C₂×C₄	C₂²×C₃	semidirect
28. C₂×C₃	C₂²⋊C₄	direct (N × H)
34. C₂²	C₂×C₃×C₄	semidirect
38. C₃	C₂×C₂²⋊C₄	direct (N × H)
40. C₂	C₃×C₂²⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃	2
C₂²×C₃×C₄	2
C₃×C₂²⋊C₄	2
C₂×C₂²⋊C₄	3

Subgroups — C2×C3×C22⋊C4 #955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂²⋊C₄ #955