Subgroups — #1453

Order 128.

95 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431	C₂	1	2	yes	maximal
2	C₄×M₁₆	C₂	1	1	yes	maximal, characteristic
3	#322	C₂	1	1	yes	maximal, characteristic, complemented
4	#322	C₂	1	2	yes	maximal, complemented
5	C₈²	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×M₁₆	C₄	1	2	yes	—
7	C₂×C₄²	C₂²	1	1	yes	characteristic
8	C₄⋊C₈	C₄	1	4	yes	—
9	C₂²⋊C₈	C₄	1	4	yes	—
10	#97	C₄	1	2	yes	—
11	C₄×C₈	C₂²	1	1	yes	characteristic
12	C₄×C₈	C₂²	1	2	yes	—
13	C₄×C₈	C₂²	1	1	yes	characteristic
14	C₄×C₈	C₂²	1	2	yes	—
15	C₂²×C₄	C₂×C₄	1	2	yes	—
16	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
17	M₁₆	—	2	4	no	—
18	C₂×C₈	C₂×C₄	1	2	yes	—
19	C₂×C₈	C₂×C₄	1	4	yes	—
20	C₂×C₈	C₂×C₄	1	4	yes	—
21	C₂×C₈	C₂×C₄	1	2	yes	—
22	C₄²	C₂×C₄	1	1	yes	characteristic
23	C₄²	C₂×C₄	1	2	yes	—
24	C₄²	C₂³	1	1	yes	characteristic
25	C₂³	C₄²	1	1	yes	characteristic
26	C₂×C₄	—	2	2	no	—
27	C₂×C₄	—	2	4	no	—
28	C₂×C₄	C₄²	1	1	yes	characteristic
29	C₂×C₄	C₄²	1	2	yes	—
30	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄	C₂²×C₄	1	2	yes	—
32	C₈	—	2	2	no	—
33	C₈	—	2	4	no	—
34	C₈	—	2	4	no	—
35	C₈	M₁₆	1	4	yes	—
36	C₂²	—	2	1	no	—
37	C₂²	—	2	2	no	—
38	C₂²	C₂×C₄²	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	2	2	no	—
41	C₄	C₂×M₁₆	1	2	yes	—
42	C₄	#131	1	4	yes	—
43	C₂	—	4	1	no	—
44	C₂	C₄×M₁₆	1	1	yes	characteristic
45	C₂	#405	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.