Subgroups — #1307

Order 128.

65 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#432	C₂	1	2	yes	maximal
2	#423	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆	C₄	1	2	yes	—
4	C₂×C₄²	C₂²	1	1	yes	characteristic
5	C₄⋊C₈	—	2	2	no	—
6	C₄⋊C₈	—	2	2	no	—
7	C₂²⋊C₈	C₄	1	4	yes	—
8	#97	—	2	2	no	—
9	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄	C₂×C₄	1	2	yes	—
11	M₁₆	—	4	2	no	—
12	C₂×C₈	—	2	4	no	—
13	C₂×C₈	—	2	2	no	—
14	C₄²	D₄	1	1	yes	characteristic
15	C₄²	D₄	1	2	yes	—
16	C₄²	Q₈	1	1	yes	characteristic
17	C₂³	C₄²	1	1	yes	characteristic
18	C₂×C₄	—	2	1	no	—
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	—	4	2	no	—
21	C₂×C₄	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄	C₄⋊C₄	1	2	yes	—
25	C₈	—	4	4	no	—
26	C₈	—	4	2	no	—
27	C₂²	—	2	1	no	—
28	C₂²	—	2	2	no	—
29	C₂²	#95	1	1	yes	characteristic
30	C₄	—	2	1	no	—
31	C₄	—	2	2	no	—
32	C₄	—	2	2	no	—
33	C₄	#100	1	1	yes	characteristic
34	C₄	#101	1	1	yes	characteristic
35	C₂	—	4	1	no	—
36	C₂	#343	1	1	yes	characteristic
37	C₂	#344	1	2	yes	—

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

subgroup	index
#432	2
#423	2