Subgroups — #401×D₁₃₇ #31784084

Order 17536.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃₇⋊#401	C₂	1	7	yes	maximal, complemented
2	#95×D₁₃₇	C₂	1	7	yes	maximal
3	#401×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₁₃₇	C₂²	1	7	yes	—
5	#17983995	C₂²	1	21	yes	—
6	#95×C₁₃₇	C₂²	1	7	yes	—
7	C₂³×D₁₃₇	C₂³	1	1	yes	characteristic
8	C₂²×Dic₁₃₇	C₂³	1	7	yes	—
9	C₂×C₄×D₁₃₇	—	2	42	no	—
10	C₂²×C₄×C₁₃₇	C₂³	1	7	yes	—
11	C₂²×D₁₃₇	#41	1	14	yes	—
12	C₂×Dic₁₃₇	—	2	21	no	—
13	C₄×D₁₃₇	—	4	28	no	—
14	C₂³×C₁₃₇	C₂⁴	1	1	yes	characteristic
15	C₂×C₄×C₁₃₇	—	2	21	no	—
16	C₂²×C₁₃₇	C₂×#41	1	7	yes	—
17	C₂×D₁₃₇	#126	1	28	yes	—
18	C₄×C₁₃₇	—	4	7	no	—
19	Dic₁₃₇	—	4	7	no	—
20	C₂×C₁₃₇	C₂×#126	1	7	yes	—
21	D₁₃₇	#401	1	8	yes	direct product factor
22	C₁₃₇	C₂×#401	1	1	yes	characteristic, complemented, Sylow
23	C₂×#401	—	137	1	no	maximal, Sylow
24	#401	—	137	7	no	—
25	#401	D₁₃₇	1	1	yes	characteristic, direct product factor
26	C₂×#95	—	137	7	no	—
27	C₂³×C₄	—	137	7	no	—
28	#95	—	137	21	no	—
29	#95	C₂×D₁₃₇	1	7	yes	—
30	C₂⁴	—	137	1	no	—
31	C₂²×C₄	—	274	42	no	—
32	C₂²×C₄	—	137	7	no	—
33	C₂²×C₄	C₂²×D₁₃₇	1	7	yes	—
34	C₂³	—	137	14	no	—
35	C₂³	C₂³×D₁₃₇	1	1	yes	characteristic
36	C₂×C₄	—	2	21	no	—
37	C₂×C₄	—	274	21	no	—
38	C₂×C₄	—	548	28	no	—
39	C₂²	—	137	28	no	—
40	C₂²	#41×D₁₃₇	1	7	yes	—
41	C₄	—	4	7	no	—
42	C₄	—	548	7	no	—
43	C₂	—	137	8	no	—
44	C₂	#126×D₁₃₇	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.