Subgroups — #398

Order 64.

75 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄	C₂	1	2	yes	maximal
4	#95	C₂	1	2	yes	maximal
5	#95	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₄	C₂²	1	2	yes	—
8	C₂²×C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₄	C₂²	1	2	yes	—
11	C₄⋊C₄	—	2	2	no	—
12	C₄⋊C₄	—	2	4	no	—
13	C₄⋊C₄	—	2	2	no	—
14	C₂³	C₂³	1	1	yes	characteristic
15	C₂×C₄	—	2	1	no	—
16	C₂×C₄	—	2	2	no	—
17	C₂×C₄	—	2	1	no	—
18	C₂×C₄	—	2	2	no	—
19	C₂×C₄	—	2	2	no	—
20	C₂×C₄	—	2	2	no	—
21	C₂×C₄	—	2	2	no	—
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	—	2	2	no	—
24	C₂×C₄	—	2	2	no	—
25	C₂×C₄	D₄	1	2	yes	—
26	C₂×C₄	D₄	1	2	yes	—
27	C₂×C₄	Q₈	1	4	yes	—
28	C₂²	C₂×D₄	1	1	yes	characteristic
29	C₂²	C₂×D₄	1	1	yes	characteristic
30	C₂²	C₂×Q₈	1	2	yes	—
31	C₂²	#41	1	1	yes	characteristic
32	C₂²	#41	1	2	yes	—
33	C₄	—	2	2	no	—
34	C₄	—	2	4	no	—
35	C₄	—	2	2	no	—
36	C₄	—	4	2	no	—
37	C₄	—	4	1	no	—
38	C₂	#121	1	1	yes	characteristic
39	C₂	C₂²⋊Q₈	1	2	yes	—
40	C₂	#123	1	1	yes	characteristic
41	C₂	#125	1	2	yes	—
42	C₂	C₄⋊Q₈	1	1	yes	characteristic

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

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

subgroup	index
C₂×C₄⋊C₄	2
#95	2