Subgroups — C₂⁴×Dic₁₂₇ #22550695

Order 8128.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₁₂₇	C₂	1	30	yes	maximal, direct product factor
2	C₂⁵×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₁₂₇	C₂²	1	140	yes	direct product factor
4	C₂⁴×C₁₂₇	C₄	1	16	yes	complemented
5	C₂⁴×C₁₂₇	C₂²	1	15	yes	—
6	C₂×Dic₁₂₇	C₂³	1	120	yes	direct product factor
7	C₂³×C₁₂₇	C₂×C₄	1	120	yes	complemented
8	C₂³×C₁₂₇	C₂³	1	35	yes	—
9	C₂²×C₁₂₇	C₂²×C₄	1	140	yes	complemented
10	C₂²×C₁₂₇	C₂⁴	1	15	yes	—
11	Dic₁₂₇	C₂⁴	1	16	yes	direct product factor
12	C₂×C₁₂₇	C₂³×C₄	1	30	yes	complemented
13	C₂×C₁₂₇	C₂⁵	1	1	yes	characteristic
14	C₁₂₇	C₂⁴×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂⁴×C₄	—	127	1	no	maximal, Sylow
16	C₂⁵	D₁₂₇	1	1	yes	characteristic
17	C₂³×C₄	—	127	30	no	—
18	C₂⁴	Dic₁₂₇	1	16	yes	direct product factor
19	C₂⁴	C₂×D₁₂₇	1	15	yes	—
20	C₂²×C₄	—	127	140	no	—
21	C₂³	C₂×Dic₁₂₇	1	120	yes	direct product factor
22	C₂³	C₂²×D₁₂₇	1	35	yes	—
23	C₂×C₄	—	127	120	no	—
24	C₂²	C₂²×Dic₁₂₇	1	140	yes	direct product factor
25	C₂²	C₂³×D₁₂₇	1	15	yes	—
26	C₄	—	127	16	no	—
27	C₂	C₂³×Dic₁₂₇	1	30	yes	direct product factor
28	C₂	C₂⁴×D₁₂₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.