Subgroups — #441

Order 64.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈	C₂	1	2	yes	maximal
3	#106	C₂	1	1	yes	maximal, characteristic
4	#103	C₂	1	2	yes	maximal
5	#97	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈	C₂²	1	2	yes	—
7	Q₁₆	C₄	1	4	yes	complemented
8	C₂×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₈	C₂²	1	1	yes	characteristic
10	C₄⋊C₄	—	2	2	no	—
11	C₄⋊C₄	C₂²	1	2	yes	—
12	C₄²	—	2	2	no	—
13	C₄²	C₂²	1	1	yes	characteristic
14	Q₈	—	2	2	no	—
15	Q₈	C₂×C₄	1	4	yes	—
16	C₂×C₄	—	2	2	no	—
17	C₂×C₄	—	2	2	no	—
18	C₂×C₄	D₄	1	2	yes	—
19	C₂×C₄	C₂³	1	1	yes	characteristic
20	C₈	—	2	1	no	—
21	C₈	C₂×C₄	1	2	yes	—
22	C₂²	C₂×D₄	1	1	yes	characteristic
23	C₄	—	2	4	no	—
24	C₄	—	2	2	no	—
25	C₄	—	4	2	no	—
26	C₄	C₂²×C₄	1	1	yes	characteristic
27	C₄	#41	1	1	yes	characteristic
28	C₂	C₄×D₄	1	1	yes	characteristic
29	C₂	#137	1	2	yes	—

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

N	H ≅ G/N	type
7. Q₁₆	C₄	semidirect

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