Subgroups — #1324

Order 128.

59 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#382	C₂	1	1	yes	maximal, characteristic
2	#324	C₂	1	2	yes	maximal
3	C₂×C₄⋊C₄	C₄	1	1	yes	characteristic
4	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
5	C₂×C₄²	C₄	1	1	yes	characteristic
6	C₂²⋊C₈	—	2	2	no	—
7	#95	—	2	2	no	—
8	C₂²×C₄	—	2	1	no	—
9	C₂²×C₄	—	2	1	no	—
10	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄	D₄	1	2	yes	—
12	C₂×C₈	—	4	2	no	—
13	C₄⋊C₄	—	4	1	no	—
14	C₄⋊C₄	—	4	1	no	—
15	C₄²	—	2	1	no	—
16	C₄²	C₈	1	2	yes	complemented
17	C₂³	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₄	—	2	1	no	—
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	—	2	2	no	—
21	C₂×C₄	—	2	2	no	—
22	C₂×C₄	—	4	1	no	—
23	C₂×C₄	—	4	1	no	—
24	C₂×C₄	—	4	2	no	—
25	C₂×C₄	—	4	2	no	—
26	C₂×C₄	—	4	1	no	—
27	C₂×C₄	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄	M₁₆	1	1	yes	characteristic
29	C₈	—	8	2	no	—
30	C₂²	—	2	1	no	—
31	C₂²	—	2	1	no	—
32	C₂²	C₂²⋊C₈	1	1	yes	characteristic
33	C₂²	#99	1	1	yes	characteristic
34	C₂²	#101	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	—	2	1	no	—
37	C₄	—	4	2	no	—
38	C₄	—	4	2	no	—
39	C₄	—	8	1	no	—
40	C₂	—	2	1	no	—
41	C₂	—	2	1	no	—
42	C₂	#324	1	1	yes	characteristic
43	C₂	#354	1	1	yes	characteristic
44	C₂	#355	1	1	yes	characteristic

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

N	H ≅ G/N	type
16. C₄²	C₈	semidirect

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

subgroup	index
#382	2
#324	2