Subgroups — #1295

Order 128.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#97	C₂	1	2	yes	maximal
2	#382	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈	—	2	2	no	—
4	C₂×C₄⋊C₄	C₄	1	2	yes	—
5	C₂×C₄²	C₂²	1	1	yes	characteristic
6	#97	—	2	2	no	—
7	#97	C₄	1	4	yes	complemented
8	#95	—	2	2	no	—
9	C₂²×C₄	—	2	2	no	—
10	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄	D₄	1	2	yes	—
12	C₂×C₈	—	2	8	no	—
13	C₂×C₈	—	2	4	no	—
14	C₄⋊C₄	—	4	2	no	—
15	C₄²	C₂×C₄	1	2	yes	—
16	C₄²	D₄	1	1	yes	characteristic
17	C₄²	Q₈	1	1	yes	characteristic
18	C₂³	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	—	2	1	no	—
21	C₂×C₄	—	2	4	no	—
22	C₂×C₄	—	4	2	no	—
23	C₂×C₄	—	4	4	no	—
24	C₂×C₄	C₄²	1	1	yes	characteristic
25	C₂×C₄	C₂²⋊C₄	1	2	yes	—
26	C₂×C₄	C₄⋊C₄	1	2	yes	—
27	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
28	C₈	—	2	8	no	—
29	C₂²	#95	1	1	yes	characteristic
30	C₂²	#100	1	1	yes	characteristic
31	C₂²	#101	1	1	yes	characteristic
32	C₂²	#104	1	4	yes	—
33	C₄	—	2	2	no	—
34	C₄	—	2	2	no	—
35	C₄	—	2	1	no	—
36	C₄	—	2	1	no	—
37	C₄	—	8	2	no	—
38	C₂	#329	1	2	yes	—
39	C₂	#330	1	2	yes	—
40	C₂	#339	1	2	yes	—
41	C₂	#343	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. #97	C₄	semidirect

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

subgroup	index
C₂×#97	2
#382	2