Subgroups — #2161

Order 128.

70 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	#368	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆	—	2	2	no	—
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	M₃₂	C₄	1	4	yes	—
7	C₂×C₁₆	C₂²	1	2	yes	—
8	#108	—	2	2	no	—
9	#108	C₂²	1	4	yes	—
10	C₂²×C₄	D₄	1	1	yes	characteristic
11	M₁₆	—	2	4	no	—
12	M₁₆	—	4	2	no	—
13	C₂×C₈	—	4	2	no	—
14	C₂×C₈	C₂×C₄	1	2	yes	—
15	C₂×C₈	D₄	1	1	yes	characteristic
16	C₂×C₈	Q₈	1	2	yes	—
17	C₂×C₈	C₂³	1	1	yes	characteristic
18	C₁₆	C₂×C₄	1	4	yes	—
19	C₂³	Q₁₆	1	1	yes	characteristic
20	C₂×C₄	C₄⋊C₄	1	2	yes	—
21	C₂×C₄	D₈	1	2	yes	—
22	C₂×C₄	Q₁₆	1	1	yes	characteristic
23	C₂×C₄	C₂×D₄	1	1	yes	characteristic
24	C₈	—	4	4	no	—
25	C₈	C₄⋊C₄	1	2	yes	—
26	C₈	C₂²×C₄	1	1	yes	characteristic
27	C₈	C₂×Q₈	1	1	yes	characteristic
28	C₂²	—	4	1	no	—
29	C₂²	#107	1	2	yes	—
30	C₂²	C₂×Q₁₆	1	1	yes	characteristic
31	C₄	#107	1	2	yes	—
32	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₄	C₂×D₈	1	1	yes	characteristic
34	C₂	—	2	2	no	—
35	C₂	—	2	1	no	—
36	C₂	C₂×#107	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #368	C₂	semidirect

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