Subgroups — #2151

Order 128.

80 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	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#405	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₁₆	C₂	1	4	yes	maximal, complemented
5	C₂×M₁₆	C₄	1	1	yes	characteristic
6	C₂²×C₈	C₂²	1	1	yes	characteristic
7	#117	C₄	1	1	yes	characteristic
8	M₃₂	—	2	2	no	—
9	C₂×C₁₆	—	2	2	no	—
10	C₂×C₁₆	C₂²	1	2	yes	—
11	C₂×C₁₆	C₂²	1	2	yes	—
12	#97	C₄	1	2	yes	—
13	C₄×C₈	C₂²	1	2	yes	—
14	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
15	M₁₆	—	2	2	no	—
16	C₂×C₈	C₂×C₄	1	2	yes	—
17	C₂×C₈	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈	D₄	1	2	yes	—
19	C₂×C₈	Q₈	1	2	yes	—
20	C₂×C₈	C₂³	1	1	yes	characteristic
21	C₄⋊C₄	C₈	1	2	yes	—
22	C₂²⋊C₄	C₈	1	2	yes	—
23	C₄²	C₂×C₄	1	2	yes	—
24	C₁₆	—	2	2	no	—
25	C₁₆	—	2	2	no	—
26	C₂³	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄	C₄⋊C₄	1	2	yes	—
28	C₂×C₄	C₂×C₈	1	4	yes	—
29	C₂×C₄	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄	M₁₆	1	2	yes	—
31	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
32	C₈	—	2	2	no	—
33	C₈	C₄⋊C₄	1	2	yes	—
34	C₈	C₂×D₄	1	1	yes	characteristic
35	C₈	C₂×Q₈	1	1	yes	characteristic
36	C₂²	—	2	2	no	—
37	C₂²	C₄⋊C₈	1	2	yes	—
38	C₂²	C₂²×C₈	1	1	yes	characteristic
39	C₄	—	2	4	no	—
40	C₄	C₄⋊C₈	1	2	yes	—
41	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄	C₂×M₁₆	1	1	yes	characteristic
43	C₂	—	2	2	no	—
44	C₂	C₂×C₄⋊C₈	1	1	yes	characteristic
45	C₂	#504	1	2	yes	—

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

N	H ≅ G/N	type
4. C₄⋊C₁₆	C₂	semidirect

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