Subgroups — #328

Order 64.

40 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
2	C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#95	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈	C₄	1	1	yes	characteristic, complemented
5	C₂²×C₄	—	2	1	no	—
6	C₂²×C₄	C₂²	1	1	yes	characteristic
7	C₂×C₈	—	2	1	no	—
8	C₄⋊C₄	—	2	1	no	—
9	C₄⋊C₄	C₄	1	1	yes	characteristic, complemented
10	C₂²⋊C₄	—	2	1	no	—
11	C₂³	D₄	1	1	yes	characteristic
12	Q₈	—	4	1	no	—
13	C₂×C₄	—	2	2	no	—
14	C₂×C₄	—	2	1	no	—
15	C₂×C₄	—	2	1	no	—
16	C₂×C₄	—	4	1	no	—
17	C₂×C₄	—	4	1	no	—
18	C₂×C₄	—	4	1	no	—
19	C₂×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄	D₄	1	1	yes	characteristic
21	C₈	—	4	1	no	—
22	C₂²	—	2	1	no	—
23	C₂²	—	2	1	no	—
24	C₂²	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²	SD₁₆	1	1	yes	characteristic
26	C₂²	Q₁₆	1	1	yes	characteristic
27	C₄	—	2	1	no	—
28	C₄	—	2	1	no	—
29	C₄	—	4	2	no	—
30	C₄	—	4	1	no	—
31	C₄	—	4	1	no	—
32	C₂	—	2	1	no	—
33	C₂	—	2	1	no	—
34	C₂	#99	1	1	yes	characteristic
35	C₂	#103	1	1	yes	characteristic
36	C₂	#104	1	1	yes	characteristic

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

N	H ≅ G/N	type
4. C₂×Q₈	C₄	semidirect
9. C₄⋊C₄	C₄	semidirect

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