Subgroups — #1323

Order 128.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#424	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊C₁₆	C₂	1	2	yes	maximal
3	C₂×M₁₆	C₄	1	1	yes	characteristic
4	C₂²×C₈	C₂²	1	1	yes	characteristic
5	#117	C₄	1	1	yes	characteristic
6	C₂×C₁₆	—	2	2	no	—
7	C₄⋊C₈	—	2	2	no	—
8	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
9	M₁₆	—	4	1	no	—
10	C₂×C₈	—	2	1	no	—
11	C₂×C₈	—	4	1	no	—
12	C₂×C₈	D₄	1	2	yes	—
13	C₄⋊C₄	C₈	1	2	yes	—
14	C₂²⋊C₄	—	2	1	no	—
15	C₄²	—	2	1	no	—
16	C₁₆	—	4	2	no	—
17	C₂³	M₁₆	1	1	yes	characteristic
18	C₂×C₄	—	2	1	no	—
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	—	2	2	no	—
21	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄	C₂×C₈	1	1	yes	characteristic
23	C₈	—	2	2	no	—
24	C₈	—	4	1	no	—
25	C₂²	—	2	1	no	—
26	C₂²	—	2	2	no	—
27	C₂²	C₂²⋊C₈	1	1	yes	characteristic
28	C₄	—	2	1	no	—
29	C₄	—	4	2	no	—
30	C₄	#99	1	1	yes	characteristic
31	C₄	#101	1	1	yes	characteristic
32	C₂	—	4	1	no	—
33	C₂	#324	1	1	yes	characteristic
34	C₂	#350	1	2	yes	—

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

subgroup	index
#424	2
C₂²⋊C₁₆	2