Subgroups — #1291

Order 128.

69 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	C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆	—	2	1	no	—
5	C₂×C₄²	C₂²	1	1	yes	characteristic
6	C₄⋊C₈	—	2	1	no	—
7	C₄⋊C₈	C₄	1	2	yes	—
8	C₂²⋊C₈	—	2	1	no	—
9	C₂²⋊C₈	C₄	1	2	yes	—
10	#97	—	2	1	no	—
11	#97	—	2	1	no	—
12	#97	—	2	1	no	—
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	M₁₆	—	2	4	no	—
18	C₂×C₈	—	2	2	no	—
19	C₂×C₈	—	2	2	no	—
20	C₂×C₈	—	2	2	no	—
21	C₄²	C₂×C₄	1	1	yes	characteristic
22	C₄²	C₂×C₄	1	1	yes	characteristic
23	C₄²	D₄	1	1	yes	characteristic
24	C₄²	D₄	1	1	yes	characteristic
25	C₂³	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	—	4	1	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
35	C₈	—	2	4	no	—
36	C₈	—	4	2	no	—
37	C₈	—	4	2	no	—
38	C₂²	—	2	1	no	—
39	C₂²	—	2	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	#95	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	2	1	no	—
44	C₄	—	2	1	no	—
45	C₄	—	2	1	no	—
46	C₄	—	2	1	no	—
47	C₄	#104	1	2	yes	—
48	C₂	—	4	1	no	—
49	C₂	#338	1	1	yes	characteristic
50	C₂	#339	1	1	yes	characteristic
51	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
C₄×M₁₆	2