Subgroups — #541

Order 64.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#126	C₂	1	4	yes	maximal
3	#125	C₂	1	1	yes	maximal, characteristic, complemented
4	#125	C₂	1	4	yes	maximal, complemented
5	C₂²⋊Q₈	C₂	1	2	yes	maximal
6	C₄×Q₈	C₂	1	2	yes	maximal, complemented
7	#117	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈	C₂²	1	2	yes	—
9	C₂²×C₄	C₂²	1	1	yes	characteristic
10	C₄⋊C₄	C₂²	1	2	yes	—
11	C₄⋊C₄	C₂²	1	2	yes	—
12	C₄⋊C₄	C₂²	1	4	yes	—
13	C₄⋊C₄	C₂²	1	4	yes	—
14	C₄⋊C₄	C₂²	1	4	yes	—
15	C₄⋊C₄	C₂²	1	4	yes	—
16	C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂²⋊C₄	C₂²	1	4	yes	—
18	C₄²	C₂²	1	1	yes	characteristic
19	C₄²	C₂²	1	1	yes	characteristic
20	C₄²	C₂²	1	4	yes	—
21	C₂³	C₂³	1	1	yes	characteristic
22	Q₈	—	2	4	no	—
23	C₂×C₄	—	2	2	no	—
24	C₂×C₄	C₂³	1	2	yes	—
25	C₂×C₄	C₂³	1	2	yes	—
26	C₂×C₄	C₂³	1	4	yes	—
27	C₂×C₄	C₂³	1	4	yes	—
28	C₂×C₄	C₂³	1	1	yes	characteristic
29	C₂×C₄	C₂³	1	1	yes	characteristic
30	C₂²	—	2	1	no	—
31	C₂²	—	2	2	no	—
32	C₂²	C₂⁴	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	2	4	no	—
35	C₄	—	2	2	no	—
36	C₄	—	2	2	no	—
37	C₄	—	2	4	no	—
38	C₄	#41	1	2	yes	—
39	C₂	—	4	1	no	—
40	C₂	C₂×#41	1	1	yes	characteristic
41	C₂	2₋¹⁺⁴	1	2	yes	—

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

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

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