Subgroups — #1375

Order 128.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	2	yes	maximal
2	C₂×#97	C₂	1	1	yes	maximal, characteristic
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	M₃₂	—	2	2	no	—
7	M₃₂	—	2	2	no	—
8	C₂×C₁₆	C₄	1	4	yes	complemented
9	#97	—	2	2	no	—
10	C₂²×C₄	—	2	1	no	—
11	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈	—	2	1	no	—
13	C₂×C₈	—	2	1	no	—
14	C₂×C₈	C₈	1	2	yes	—
15	C₂×C₈	C₂×C₄	1	2	yes	—
16	C₂×C₈	D₄	1	1	yes	characteristic
17	C₂×C₈	D₄	1	2	yes	—
18	C₂×C₈	Q₈	1	1	yes	characteristic
19	C₄²	—	2	1	no	—
20	C₄²	C₈	1	2	yes	—
21	C₁₆	—	2	4	no	—
22	C₂³	M₁₆	1	1	yes	characteristic
23	C₂×C₄	—	2	2	no	—
24	C₂×C₄	—	4	2	no	—
25	C₂×C₄	C₄²	1	1	yes	characteristic
26	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄	M₁₆	1	1	yes	characteristic
31	C₈	—	2	2	no	—
32	C₈	C₂²⋊C₄	1	2	yes	—
33	C₈	C₄⋊C₄	1	2	yes	—
34	C₂²	—	2	2	no	—
35	C₂²	#97	1	1	yes	characteristic
36	C₂²	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²	C₄⋊C₈	1	1	yes	characteristic
38	C₄	—	4	2	no	—
39	C₄	#95	1	1	yes	characteristic
40	C₄	C₄×C₈	1	1	yes	characteristic
41	C₄	C₂²⋊C₈	1	1	yes	characteristic
42	C₄	C₄⋊C₈	1	1	yes	characteristic
43	C₂	—	2	1	no	—
44	C₂	—	2	1	no	—
45	C₂	#336	1	1	yes	characteristic
46	C₂	#347	1	2	yes	—

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

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

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

subgroup	index
C₂×M₃₂	2
C₂×#97	2