Subgroups — #1290

Order 128.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#432	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈	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	—	2	2	no	—
8	#97	C₄	1	4	yes	—
9	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄	D₄	1	1	yes	characteristic
11	C₂²×C₄	Q₈	1	1	yes	characteristic
12	C₂×C₈	—	2	4	no	—
13	C₂×C₈	—	2	2	no	—
14	C₂×C₈	—	4	2	no	—
15	C₄²	C₂×C₄	1	2	yes	—
16	C₄²	D₄	1	2	yes	—
17	C₂³	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄	—	2	2	no	—
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	—	2	1	no	—
21	C₂×C₄	—	4	1	no	—
22	C₂×C₄	C₄²	1	1	yes	characteristic
23	C₂×C₄	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄	C₄⋊C₄	1	2	yes	—
26	C₈	—	4	4	no	—
27	C₈	—	4	2	no	—
28	C₂²	—	2	1	no	—
29	C₂²	—	2	1	no	—
30	C₂²	#95	1	1	yes	characteristic
31	C₂²	#108	1	2	yes	—
32	C₄	—	2	2	no	—
33	C₄	—	2	2	no	—
34	C₄	—	2	1	no	—
35	C₄	#100	1	1	yes	characteristic
36	C₄	#101	1	1	yes	characteristic
37	C₂	—	2	2	no	—
38	C₂	H(3,ℤ/4)	1	1	yes	characteristic
39	C₂	#341	1	1	yes	characteristic
40	C₂	#343	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
C₂×C₄⋊C₈	2