Subgroups — #1322

Order 128.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊C₁₆	C₂	1	2	yes	maximal
3	C₂²×C₈	C₄	1	1	yes	characteristic
4	C₂²×C₈	C₂²	1	1	yes	characteristic
5	C₂×C₄²	C₄	1	1	yes	characteristic
6	C₂×C₁₆	—	2	2	no	—
7	C₄⋊C₈	—	2	2	no	—
8	C₂²×C₄	C₈	1	1	yes	characteristic
9	C₂²×C₄	C₈	1	1	yes	characteristic
10	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈	—	2	1	no	—
12	C₂×C₈	—	4	1	no	—
13	C₂×C₈	—	4	1	no	—
14	C₂×C₈	D₄	1	2	yes	—
15	C₄²	—	2	1	no	—
16	C₄²	—	2	1	no	—
17	C₁₆	—	4	2	no	—
18	C₂³	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	—	2	1	no	—
21	C₂×C₄	—	2	1	no	—
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	—	2	1	no	—
24	C₂×C₄	—	4	1	no	—
25	C₂×C₄	C₁₆	1	2	yes	complemented
26	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄	M₁₆	1	1	yes	characteristic
28	C₈	—	2	2	no	—
29	C₈	—	4	1	no	—
30	C₂²	—	2	1	no	—
31	C₂²	—	2	1	no	—
32	C₂²	C₂²⋊C₈	1	1	yes	characteristic
33	C₂²	C₂×C₁₆	1	1	yes	characteristic
34	C₂²	M₃₂	1	1	yes	characteristic
35	C₄	—	2	1	no	—
36	C₄	—	2	2	no	—
37	C₄	—	4	1	no	—
38	C₄	#99	1	1	yes	characteristic
39	C₄	#101	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	2	1	no	—
42	C₂	#324	1	1	yes	characteristic
43	C₂	C₂²⋊C₁₆	1	1	yes	characteristic
44	C₂	#349	1	1	yes	characteristic

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

N	H ≅ G/N	type
25. C₂×C₄	C₁₆	semidirect

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

subgroup	index
C₂×C₄⋊C₈	2
C₂²⋊C₁₆	2