Subgroups — #2158

Order 128.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic
2	#427	C₂	1	2	yes	maximal
3	#367	C₂	1	2	yes	maximal, complemented
4	#366	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	#117	—	2	2	no	—
7	C₂×C₁₆	C₄	1	4	yes	complemented
8	C₂×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₆	C₂²	1	1	yes	characteristic
10	#107	C₂²	1	4	yes	—
11	#106	—	2	2	no	—
12	C₂²×C₄	D₄	1	1	yes	characteristic
13	C₂×C₈	C₂×C₄	1	2	yes	—
14	C₂×C₈	D₄	1	1	yes	characteristic
15	C₂×C₈	Q₈	1	2	yes	—
16	C₂×C₈	C₂³	1	1	yes	characteristic
17	C₄⋊C₄	—	2	4	no	—
18	C₂²⋊C₄	—	4	2	no	—
19	C₄²	—	4	2	no	—
20	C₁₆	C₂×C₄	1	2	yes	—
21	C₁₆	C₂×C₄	1	2	yes	—
22	C₂³	D₈	1	1	yes	characteristic
23	C₂×C₄	—	4	4	no	—
24	C₂×C₄	C₄⋊C₄	1	2	yes	—
25	C₂×C₄	D₈	1	1	yes	characteristic
26	C₂×C₄	Q₁₆	1	2	yes	—
27	C₂×C₄	C₂×D₄	1	1	yes	characteristic
28	C₈	C₄⋊C₄	1	2	yes	—
29	C₈	C₂²×C₄	1	1	yes	characteristic
30	C₈	C₂×Q₈	1	1	yes	characteristic
31	C₂²	—	2	2	no	—
32	C₂²	#107	1	2	yes	—
33	C₂²	C₂×D₈	1	1	yes	characteristic
34	C₄	—	8	4	no	—
35	C₄	#107	1	2	yes	—
36	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₄	C₂×Q₁₆	1	1	yes	characteristic
38	C₂	—	2	2	no	—
39	C₂	C₂×#107	1	1	yes	characteristic
40	C₂	#508	1	2	yes	—

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

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