Subgroups — #1327

Order 128.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#423	C₂	1	1	yes	maximal, characteristic
2	#349	C₂	1	2	yes	maximal
3	C₂×M₁₆	C₄	1	1	yes	characteristic
4	C₂×M₁₆	C₂²	1	1	yes	characteristic
5	C₂×C₄²	C₄	1	1	yes	characteristic
6	M₃₂	—	2	2	no	—
7	C₄⋊C₈	—	2	2	no	—
8	C₂²×C₄	—	2	1	no	—
9	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
10	M₁₆	—	4	1	no	—
11	M₁₆	—	4	1	no	—
12	C₂×C₈	—	2	1	no	—
13	C₂×C₈	D₄	1	2	yes	—
14	C₄²	—	2	1	no	—
15	C₄²	C₈	1	1	yes	characteristic
16	C₄²	C₈	1	1	yes	characteristic
17	C₁₆	—	4	2	no	—
18	C₂³	M₁₆	1	1	yes	characteristic
19	C₂×C₄	—	2	1	no	—
20	C₂×C₄	—	2	1	no	—
21	C₂×C₄	—	2	1	no	—
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	—	4	2	no	—
24	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄	C₂×C₈	1	1	yes	characteristic
26	C₈	—	2	2	no	—
27	C₈	—	4	1	no	—
28	C₂²	—	2	1	no	—
29	C₂²	—	4	1	no	—
30	C₂²	C₂²⋊C₈	1	1	yes	characteristic
31	C₄	—	2	2	no	—
32	C₄	—	2	1	no	—
33	C₄	—	4	1	no	—
34	C₄	#99	1	1	yes	characteristic
35	C₄	#101	1	1	yes	characteristic
36	C₂	—	2	1	no	—
37	C₂	—	4	1	no	—
38	C₂	#324	1	1	yes	characteristic

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

subgroup	index
#423	2
#349	2