Subgroups — C₃×C₂²⋊Q₈ #962

Order 96.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈	C₂	semidirect
3. C₃×C₄⋊C₄	C₂	semidirect
4. C₃×C₄⋊C₄	C₂	semidirect
6. C₂²⋊Q₈	C₃	direct (N × H)
14. C₂×Q₈	C₂×C₃	semidirect
16. C₄⋊C₄	C₂×C₃	semidirect
17. C₄⋊C₄	C₂×C₃	semidirect
21. C₂²×C₃	Q₈	semidirect
40. C₂²	C₃×Q₈	semidirect
46. C₃	C₂²⋊Q₈	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×Q₈	2
C₂²×C₃×C₄	2
C₃×C₄⋊C₄	2
C₃×C₂²⋊C₄	2
C₂²⋊Q₈	3

Subgroups — C3×C22⋊Q8 #962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊Q₈ #962