Subgroups — #1384

Order 128.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	1	yes	maximal, characteristic
2	#427	C₂	1	2	yes	maximal
3	C₂²×C₈	C₂²	1	1	yes	characteristic
4	#117	—	2	2	no	—
5	M₃₂	—	2	2	no	—
6	C₂×C₁₆	C₄	1	2	yes	complemented
7	#107	—	2	2	no	—
8	#106	C₄	1	4	yes	complemented
9	C₂²×C₄	D₄	1	1	yes	characteristic
10	C₂×C₈	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈	C₂×C₄	1	2	yes	—
12	C₂×C₈	D₄	1	2	yes	—
13	C₂×C₈	Q₈	1	1	yes	characteristic
14	C₄⋊C₄	—	2	4	no	—
15	C₂²⋊C₄	—	4	2	no	—
16	C₄²	—	4	2	no	—
17	C₁₆	—	2	2	no	—
18	C₂³	D₈	1	1	yes	characteristic
19	C₂×C₄	—	4	4	no	—
20	C₂×C₄	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄	SD₁₆	1	2	yes	—
23	C₂×C₄	Q₁₆	1	1	yes	characteristic
24	C₈	C₄²	1	1	yes	characteristic
25	C₈	C₂²⋊C₄	1	1	yes	characteristic
26	C₈	C₄⋊C₄	1	2	yes	—
27	C₂²	—	4	1	no	—
28	C₂²	#102	1	2	yes	—
29	C₂²	#107	1	1	yes	characteristic
30	C₄	—	8	4	no	—
31	C₄	#95	1	1	yes	characteristic
32	C₄	#103	1	2	yes	—
33	C₄	#106	1	1	yes	characteristic
34	C₂	—	2	2	no	—
35	C₂	—	2	1	no	—
36	C₂	#340	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. C₂×C₁₆	C₄	semidirect
8. #106	C₄	semidirect

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

subgroup	index
C₂×M₃₂	2
#427	2