Subgroups — #2179

Order 128.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508	C₂	1	1	yes	maximal, characteristic
2	#443	C₂	1	2	yes	maximal, complemented
3	#368	C₂	1	1	yes	maximal, characteristic, complemented
4	#359	C₂	1	2	yes	maximal, complemented
5	#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#135	C₂²	1	2	yes	—
7	#131	—	2	2	no	—
8	Q₃₂	C₄	1	1	yes	characteristic, complemented
9	SD₃₂	C₄	1	2	yes	complemented
10	D₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₆	C₂²	1	1	yes	characteristic
13	#108	C₂²	1	2	yes	—
14	#104	—	2	2	no	—
15	C₄×C₈	C₂²	1	1	yes	characteristic
16	#41	—	2	2	no	—
17	Q₁₆	C₂×C₄	1	2	yes	—
18	SD₁₆	—	2	2	no	—
19	D₈	C₂×C₄	1	2	yes	—
20	M₁₆	—	2	2	no	—
21	M₁₆	—	4	2	no	—
22	C₂×C₈	—	4	2	no	—
23	C₂×C₈	D₄	1	1	yes	characteristic
24	C₂×C₈	C₂³	1	1	yes	characteristic
25	C₄²	D₄	1	1	yes	characteristic
26	C₁₆	—	2	1	no	—
27	C₁₆	C₂×C₄	1	1	yes	characteristic
28	C₁₆	C₂×C₄	1	1	yes	characteristic
29	Q₈	—	2	2	no	—
30	D₄	—	2	2	no	—
31	D₄	—	4	2	no	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	4	2	no	—
34	C₂×C₄	C₂×D₄	1	1	yes	characteristic
35	C₈	—	4	2	no	—
36	C₈	D₈	1	2	yes	—
37	C₈	C₂²×C₄	1	1	yes	characteristic
38	C₈	#41	1	1	yes	characteristic
39	C₂²	—	4	2	no	—
40	C₂²	#135	1	1	yes	characteristic
41	C₄	—	4	1	no	—
42	C₄	—	4	2	no	—
43	C₄	C₄×D₄	1	1	yes	characteristic
44	C₄	C₂×D₈	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	—	8	2	no	—
47	C₂	C₄×D₈	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.