Subgroups — C₂×#108 #429

Order 64.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆	C₂	1	2	yes	maximal
2	C₂²×C₈	C₂	1	1	yes	maximal, characteristic
3	#108	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄	C₂²	1	1	yes	characteristic
5	M₁₆	—	2	2	no	—
6	M₁₆	C₂²	1	4	yes	—
7	C₂×C₈	—	2	2	no	—
8	C₂×C₈	C₄	1	2	yes	—
9	C₂×C₈	C₄	1	2	yes	—
10	C₂×C₈	C₂²	1	2	yes	—
11	C₂³	Q₈	1	1	yes	characteristic
12	C₂×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄	D₄	1	1	yes	characteristic
15	C₂×C₄	D₄	1	1	yes	characteristic
16	C₂×C₄	Q₈	1	1	yes	characteristic
17	C₂×C₄	C₂³	1	1	yes	characteristic
18	C₈	—	2	4	no	—
19	C₈	C₂×C₄	1	4	yes	—
20	C₂²	—	2	2	no	—
21	C₂²	C₄⋊C₄	1	1	yes	characteristic
22	C₂²	C₄⋊C₄	1	1	yes	characteristic
23	C₂²	C₂×Q₈	1	1	yes	characteristic
24	C₄	C₄⋊C₄	1	1	yes	characteristic
25	C₄	C₄⋊C₄	1	1	yes	characteristic
26	C₄	C₂²×C₄	1	1	yes	characteristic
27	C₄	C₂×D₄	1	1	yes	characteristic
28	C₂	—	2	1	no	—
29	C₂	—	2	1	no	—
30	C₂	#108	1	2	yes	direct product factor
31	C₂	C₂×C₄⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #108	C₂	direct (N × H)
30. C₂	#108	direct (N × H)

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