Subgroups — #1287

Order 128.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#432	C₂	1	1	yes	maximal, characteristic
2	#432	C₂	1	1	yes	maximal, characteristic
3	#431	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²	C₂²	1	1	yes	characteristic
5	C₄⋊C₈	—	2	1	no	—
6	C₄⋊C₈	—	2	1	no	—
7	C₄⋊C₈	—	2	1	no	—
8	C₂²⋊C₈	—	2	1	no	—
9	C₂²⋊C₈	—	2	1	no	—
10	C₂²⋊C₈	C₄	1	2	yes	—
11	#97	—	2	1	no	—
12	#97	C₄	1	2	yes	—
13	C₄×C₈	C₄	1	2	yes	—
14	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄	D₄	1	1	yes	characteristic
16	C₂²×C₄	Q₈	1	1	yes	characteristic
17	C₂×C₈	—	2	2	no	—
18	C₂×C₈	—	2	2	no	—
19	C₂×C₈	—	2	2	no	—
20	C₄²	C₂×C₄	1	1	yes	characteristic
21	C₄²	C₂×C₄	1	1	yes	characteristic
22	C₄²	D₄	1	1	yes	characteristic
23	C₄²	D₄	1	1	yes	characteristic
24	C₂³	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄	—	2	2	no	—
26	C₂×C₄	—	4	1	no	—
27	C₂×C₄	—	4	1	no	—
28	C₂×C₄	C₄²	1	1	yes	characteristic
29	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
34	C₈	—	4	2	no	—
35	C₈	—	4	2	no	—
36	C₈	—	4	2	no	—
37	C₂²	—	2	1	no	—
38	C₂²	—	2	1	no	—
39	C₂²	—	2	1	no	—
40	C₂²	#95	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	—	2	1	no	—
43	C₄	—	2	1	no	—
44	C₄	—	2	1	no	—
45	C₄	—	2	1	no	—
46	C₄	#108	1	2	yes	—
47	C₂	—	4	1	no	—
48	C₂	H(3,ℤ/4)	1	1	yes	characteristic
49	C₂	#341	1	1	yes	characteristic
50	C₂	#344	1	1	yes	characteristic

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

subgroup	index
#432	2
#431	2