Subgroups — #1355

Order 128.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#490	C₂	1	1	yes	maximal, characteristic
2	#347	C₂	1	2	yes	maximal, complemented
3	#127	C₄	1	1	yes	characteristic
4	#125	C₄	1	1	yes	characteristic
5	M₃₂	—	2	2	no	—
6	#102	—	2	2	no	—
7	#97	C₂²	1	1	yes	characteristic
8	C₂×D₄	—	2	1	no	—
9	C₂×D₄	—	4	1	no	—
10	C₂×C₈	D₄	1	2	yes	—
11	C₄⋊C₄	—	2	1	no	—
12	C₄⋊C₄	—	4	1	no	—
13	C₄²	C₂×C₄	1	1	yes	characteristic
14	C₁₆	—	2	4	no	—
15	C₂³	—	4	1	no	—
16	D₄	—	4	2	no	—
17	D₄	—	8	2	no	—
18	C₂×C₄	—	2	1	no	—
19	C₂×C₄	—	4	1	no	—
20	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
21	C₈	—	2	2	no	—
22	C₂²	—	8	2	no	—
23	C₂²	—	8	1	no	—
24	C₂²	#100	1	1	yes	characteristic
25	C₄	—	4	1	no	—
26	C₄	—	8	1	no	—
27	C₄	#104	1	2	yes	—
28	C₂	—	2	1	no	—
29	C₂	—	16	1	no	—
30	C₂	#329	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #347	C₂	semidirect

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

subgroup	index
#490	2
#347	2