Subgroups — #1385

Order 128.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#108	C₂	1	2	yes	maximal
3	C₂×M₁₆	—	2	2	no	—
4	C₂²×C₈	C₂²	1	1	yes	characteristic
5	M₃₂	—	2	2	no	—
6	C₂×C₁₆	C₄	1	2	yes	—
7	#108	—	2	2	no	—
8	#108	C₄	1	4	yes	—
9	C₂²×C₄	D₄	1	1	yes	characteristic
10	M₁₆	—	2	4	no	—
11	M₁₆	—	4	2	no	—
12	C₂×C₈	—	4	2	no	—
13	C₂×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈	C₂×C₄	1	2	yes	—
15	C₂×C₈	D₄	1	2	yes	—
16	C₂×C₈	Q₈	1	1	yes	characteristic
17	C₁₆	—	2	2	no	—
18	C₂³	Q₁₆	1	1	yes	characteristic
19	C₂×C₄	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄	D₈	1	1	yes	characteristic
22	C₂×C₄	SD₁₆	1	2	yes	—
23	C₈	—	4	4	no	—
24	C₈	C₄²	1	1	yes	characteristic
25	C₈	C₂²⋊C₄	1	1	yes	characteristic
26	C₈	C₄⋊C₄	1	2	yes	—
27	C₂²	—	4	1	no	—
28	C₂²	#103	1	2	yes	—
29	C₂²	#107	1	1	yes	characteristic
30	C₄	#95	1	1	yes	characteristic
31	C₄	#102	1	2	yes	—
32	C₄	#106	1	1	yes	characteristic
33	C₂	—	2	2	no	—
34	C₂	—	2	1	no	—
35	C₂	#340	1	1	yes	characteristic

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

subgroup	index
C₂×M₃₂	2
C₂×#108	2