Subgroups — #30647125

Order 16256.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861206	C₂	1	14	yes	maximal, complemented
2	C₄³×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₅₀₈	C₂²	1	28	yes	—
4	#16861206	—	2	56	no	—
5	C₂×C₄²×C₁₂₇	C₂²	1	7	yes	—
6	C₂³×D₁₂₇	C₂³	1	8	yes	—
7	C₂×D₅₀₈	—	2	168	no	—
8	C₂²×C₄×C₁₂₇	C₂³	1	7	yes	—
9	C₄²×C₁₂₇	D₄	1	28	yes	complemented
10	C₂²×D₁₂₇	—	2	56	no	—
11	D₅₀₈	—	4	112	no	—
12	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
13	C₂×C₄×C₁₂₇	C₂×D₄	1	42	yes	—
14	C₂²×C₁₂₇	C₂²×D₄	1	7	yes	—
15	C₂×D₁₂₇	—	4	56	no	—
16	C₄×C₁₂₇	#127	1	28	yes	complemented
17	C₂×C₁₂₇	C₂×#127	1	7	yes	—
18	D₁₂₇	—	8	8	no	—
19	#2867	—	127	1	no	maximal, Sylow
20	C₁₂₇	#2867	1	1	yes	characteristic, complemented, Sylow
21	C₂×#127	—	127	14	no	—
22	C₄³	D₁₂₇	1	1	yes	characteristic, complemented
23	C₂²×D₄	—	127	28	no	—
24	#127	—	254	56	no	—
25	C₂×C₄²	C₂×D₁₂₇	1	7	yes	—
26	C₂⁴	—	127	8	no	—
27	C₂×D₄	—	254	168	no	—
28	C₂²×C₄	C₂²×D₁₂₇	1	7	yes	—
29	C₄²	D₅₀₈	1	28	yes	complemented
30	C₂³	—	254	56	no	—
31	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
32	D₄	—	508	112	no	—
33	C₂×C₄	C₂×D₅₀₈	1	42	yes	—
34	C₂²	—	508	56	no	—
35	C₂²	C₂²×D₅₀₈	1	7	yes	—
36	C₄	#16861206	1	28	yes	complemented
37	C₂	—	1016	8	no	—
38	C₂	C₂×#16861206	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.