Subgroups — #1277

Order 128.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈	—	2	2	no	—
4	C₂²×C₈	C₄	1	2	yes	—
5	C₂×C₄²	C₂²	1	1	yes	characteristic
6	C₄⋊C₈	—	2	2	no	—
7	C₄⋊C₈	C₄	1	4	yes	—
8	C₄×C₈	—	2	2	no	—
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	2	no	—
13	C₂×C₈	—	2	2	no	—
14	C₂×C₈	—	2	4	no	—
15	C₂×C₈	—	4	2	no	—
16	C₂×C₈	—	4	2	no	—
17	C₂×C₈	C₈	1	4	yes	complemented
18	C₄²	C₂×C₄	1	2	yes	—
19	C₄²	D₄	1	2	yes	—
20	C₂³	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄	—	2	2	no	—
22	C₂×C₄	C₄²	1	1	yes	characteristic
23	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄	C₂²⋊C₄	1	2	yes	—
25	C₂×C₄	C₄⋊C₄	1	2	yes	—
26	C₂×C₄	C₂×C₈	1	2	yes	—
27	C₂×C₄	M₁₆	1	2	yes	—
28	C₂×C₄	D₈	1	1	yes	characteristic
29	C₂×C₄	SD₁₆	1	2	yes	—
30	C₂×C₄	Q₁₆	1	1	yes	characteristic
31	C₈	—	2	4	no	—
32	C₈	—	4	4	no	—
33	C₂²	#95	1	1	yes	characteristic
34	C₂²	C₄⋊C₈	1	2	yes	—
35	C₂²	#106	1	1	yes	characteristic
36	C₂²	#107	1	1	yes	characteristic
37	C₂²	#108	1	2	yes	—
38	C₄	—	2	2	no	—
39	C₄	C₄×C₈	1	1	yes	characteristic
40	C₄	#97	1	1	yes	characteristic
41	C₄	C₂²⋊C₈	1	2	yes	—
42	C₄	#102	1	2	yes	—
43	C₄	#103	1	2	yes	—
44	C₂	#334	1	2	yes	—
45	C₂	#335	1	2	yes	—
46	C₂	#336	1	1	yes	characteristic
47	C₂	#340	1	1	yes	characteristic
48	C₂	#341	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. C₂×C₈	C₈	semidirect

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

subgroup	index
C₂×C₄⋊C₈	2
C₂×C₄×C₈	2