Subgroups — #401×D₁₂₇ #30642025

Order 16256.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₇⋊#401	C₂	1	7	yes	maximal, complemented
2	#95×D₁₂₇	C₂	1	7	yes	maximal
3	#401×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₁₂₇	C₂²	1	7	yes	—
5	C₁₂₇⋊#95	C₂²	1	21	yes	—
6	#95×C₁₂₇	C₂²	1	7	yes	—
7	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
8	C₂²×Dic₁₂₇	C₂³	1	7	yes	—
9	C₂×C₄×D₁₂₇	—	2	42	no	—
10	C₂²×C₄×C₁₂₇	C₂³	1	7	yes	—
11	C₂²×D₁₂₇	#41	1	14	yes	—
12	C₂×Dic₁₂₇	—	2	21	no	—
13	C₄×D₁₂₇	—	4	28	no	—
14	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
15	C₂×C₄×C₁₂₇	—	2	21	no	—
16	C₂²×C₁₂₇	C₂×#41	1	7	yes	—
17	C₂×D₁₂₇	#126	1	28	yes	—
18	C₄×C₁₂₇	—	4	7	no	—
19	Dic₁₂₇	—	4	7	no	—
20	C₂×C₁₂₇	C₂×#126	1	7	yes	—
21	D₁₂₇	#401	1	8	yes	direct product factor
22	C₂×#401	—	127	1	no	maximal, Sylow
23	C₁₂₇	C₂×#401	1	1	yes	characteristic, complemented, Sylow
24	#401	—	127	7	no	—
25	#401	D₁₂₇	1	1	yes	characteristic, direct product factor
26	C₂×#95	—	127	7	no	—
27	C₂³×C₄	—	127	7	no	—
28	#95	—	127	21	no	—
29	#95	C₂×D₁₂₇	1	7	yes	—
30	C₂⁴	—	127	1	no	—
31	C₂²×C₄	—	127	7	no	—
32	C₂²×C₄	—	254	42	no	—
33	C₂²×C₄	C₂²×D₁₂₇	1	7	yes	—
34	C₂³	—	127	14	no	—
35	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
36	C₂×C₄	—	2	21	no	—
37	C₂×C₄	—	508	28	no	—
38	C₂×C₄	—	254	21	no	—
39	C₂²	—	127	28	no	—
40	C₂²	#41×D₁₂₇	1	7	yes	—
41	C₄	—	4	7	no	—
42	C₄	—	508	7	no	—
43	C₂	—	127	8	no	—
44	C₂	#126×D₁₂₇	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.