Subgroups — #1331

Order 128.

55 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#335	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈	C₄	1	1	yes	characteristic
5	C₄×D₄	—	2	1	no	—
6	C₂×C₁₆	—	2	1	no	—
7	#107	C₄	1	1	yes	characteristic
8	C₄⋊C₈	—	2	1	no	—
9	#102	—	2	1	no	—
10	C₄×C₈	C₂²	1	1	yes	characteristic
11	C₂×D₄	—	2	1	no	—
12	C₂²×C₄	—	4	1	no	—
13	D₈	—	2	1	no	—
14	D₈	C₈	1	2	yes	complemented
15	C₂×C₈	—	4	1	no	—
16	C₂×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈	D₄	1	1	yes	characteristic
18	C₄⋊C₄	—	2	1	no	—
19	C₂²⋊C₄	—	4	1	no	—
20	C₄²	D₄	1	1	yes	characteristic
21	C₁₆	—	2	2	no	—
22	C₂³	—	4	1	no	—
23	D₄	—	2	2	no	—
24	D₄	—	4	1	no	—
25	C₂×C₄	—	4	1	no	—
26	C₂×C₄	—	8	1	no	—
27	C₂×C₄	—	8	1	no	—
28	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄	D₈	1	1	yes	characteristic
30	C₂×C₄	SD₁₆	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₈	—	8	1	no	—
33	C₈	C₂×C₈	1	1	yes	characteristic
34	C₈	M₁₆	1	1	yes	characteristic
35	C₂²	—	4	2	no	—
36	C₂²	—	8	1	no	—
37	C₂²	—	8	1	no	—
38	C₂²	#102	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	8	1	no	—
41	C₄	C₂²⋊C₈	1	1	yes	characteristic
42	C₄	#104	1	1	yes	characteristic
43	C₄	D₁₆	1	1	yes	characteristic
44	C₄	SD₃₂	1	1	yes	characteristic
45	C₂	—	8	2	no	—
46	C₂	D₄⋊C₈	1	1	yes	characteristic
47	C₂	#357	1	1	yes	characteristic
48	C₂	#359	1	1	yes	characteristic

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.