Subgroups — #2171

Order 128.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#504	C₂	1	2	yes	maximal, complemented
2	#443	C₂	1	1	yes	maximal, characteristic
3	#364	C₂	1	1	yes	maximal, characteristic, complemented
4	#350	C₂	1	2	yes	maximal, complemented
5	#346	C₂	1	1	yes	maximal, characteristic, complemented
6	#135	C₄	1	1	yes	characteristic
7	#131	C₂²	1	2	yes	—
8	M₃₂	—	2	2	no	—
9	M₃₂	C₂²	1	2	yes	—
10	C₂×C₁₆	—	2	2	no	—
11	C₂×C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₆	C₂²	1	1	yes	characteristic
13	#108	C₄	1	1	yes	characteristic
14	#104	C₄	1	2	yes	—
15	C₄×C₈	C₂²	1	1	yes	characteristic
16	#41	C₂×C₄	1	2	yes	—
17	Q₁₆	C₈	1	1	yes	characteristic
18	SD₁₆	C₈	1	2	yes	—
19	D₈	C₈	1	1	yes	characteristic
20	M₁₆	—	2	2	no	—
21	M₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₈	—	2	2	no	—
23	C₂×C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈	C₂³	1	1	yes	characteristic
25	C₄²	C₂×C₄	1	1	yes	characteristic
26	C₁₆	—	2	2	no	—
27	C₁₆	—	2	1	no	—
28	C₁₆	D₄	1	2	yes	—
29	Q₈	C₂×C₈	1	2	yes	—
30	D₄	—	2	2	no	—
31	D₄	C₂×C₈	1	2	yes	—
32	C₂×C₄	—	2	2	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
35	C₈	—	2	2	no	—
36	C₈	C₂×C₈	1	1	yes	characteristic
37	C₈	C₂×C₈	1	1	yes	characteristic
38	C₈	C₂×D₄	1	1	yes	characteristic
39	C₈	#41	1	1	yes	characteristic
40	C₂²	—	2	2	no	—
41	C₂²	#131	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	4	1	no	—
44	C₄	C₄×D₄	1	1	yes	characteristic
45	C₄	C₂²×C₈	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	2	no	—
48	C₂	C₈×D₄	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.