Subgroups — C₂×C₂²⋊Q₈ #523

Order 64.

161 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₈	C₂	semidirect
3. C₂²⋊Q₈	C₂	direct (N × H)
4. C₂×C₄⋊C₄	C₂	semidirect
5. C₂×C₄⋊C₄	C₂	semidirect
9. C₂×Q₈	C₂²	semidirect
16. C₄⋊C₄	C₂²	semidirect
17. C₄⋊C₄	C₂²	semidirect
21. C₂³	Q₈	semidirect
39. C₂²	C₂×Q₈	semidirect
47. C₂	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
C₂²×Q₈	2
C₂³×C₄	2
C₂²⋊Q₈	2
C₂×C₄⋊C₄	2
C₂×C₂²⋊C₄	2

Subgroups — C2×C22⋊Q8 #523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊Q₈ #523