Subgroups — #27179527

Order 12928.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692252	C₂	1	14	yes	maximal, complemented
2	C₄³×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₄₀₄	C₂²	1	28	yes	—
4	#15692252	—	2	56	no	—
5	C₂×C₄²×C₁₀₁	C₂²	1	7	yes	—
6	C₂³×D₁₀₁	C₂³	1	8	yes	—
7	C₂×D₄₀₄	—	2	168	no	—
8	C₂²×C₄×C₁₀₁	C₂³	1	7	yes	—
9	C₄²×C₁₀₁	D₄	1	28	yes	complemented
10	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
11	C₂²×D₁₀₁	—	2	56	no	—
12	C₂×C₄×C₁₀₁	C₂×D₄	1	42	yes	—
13	D₄₀₄	—	4	112	no	—
14	C₂²×C₁₀₁	C₂²×D₄	1	7	yes	—
15	C₂×D₁₀₁	—	4	56	no	—
16	C₄×C₁₀₁	#127	1	28	yes	complemented
17	C₂×C₁₀₁	C₂×#127	1	7	yes	—
18	D₁₀₁	—	8	8	no	—
19	#2867	—	101	1	no	maximal, Sylow
20	C₁₀₁	#2867	1	1	yes	characteristic, complemented, Sylow
21	C₂×#127	—	101	14	no	—
22	C₄³	D₁₀₁	1	1	yes	characteristic, complemented
23	C₂²×D₄	—	101	28	no	—
24	#127	—	202	56	no	—
25	C₂×C₄²	C₂×D₁₀₁	1	7	yes	—
26	C₂⁴	—	101	8	no	—
27	C₂×D₄	—	202	168	no	—
28	C₂²×C₄	C₂²×D₁₀₁	1	7	yes	—
29	C₄²	D₄₀₄	1	28	yes	complemented
30	C₂³	—	202	56	no	—
31	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
32	D₄	—	404	112	no	—
33	C₂×C₄	C₂×D₄₀₄	1	42	yes	—
34	C₂²	—	404	56	no	—
35	C₂²	C₂²×D₄₀₄	1	7	yes	—
36	C₄	#15692252	1	28	yes	complemented
37	C₂	—	808	8	no	—
38	C₂	C₂×#15692252	1	7	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.