Subgroups — #31797893

Order 17536.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22578485	C₂	1	2	yes	maximal, complemented
2	C₂×#17984138	C₂	1	1	yes	maximal, characteristic
3	#17984138	C₄	1	1	yes	characteristic
4	#17984138	C₂²	1	1	yes	characteristic
5	C₂×#14555485	C₄	1	1	yes	characteristic
6	#14555485	C₈	1	1	yes	characteristic
7	#14555485	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₁₃₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₃₇	C₁₆	1	1	yes	characteristic
10	C₈×C₁₃₇	C₁₆	1	1	yes	characteristic
11	C₈×C₁₃₇	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₁₃₇	C₃₂	1	1	yes	characteristic
13	C₄×C₁₃₇	C₃₂	1	1	yes	characteristic
14	C₄×C₁₃₇	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₃₇	—	2	1	no	—
16	C₂×C₁₃₇	C₂×C₃₂	1	1	yes	characteristic
17	C₁₃₇	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
18	M₁₂₈	—	137	1	no	maximal, Sylow
19	C₂×C₃₂	—	137	1	no	—
20	C₆₄	—	137	2	no	—
21	C₂×C₁₆	—	137	1	no	—
22	C₃₂	—	137	1	no	—
23	C₃₂	—	137	1	no	—
24	C₂×C₈	#11764049	1	1	yes	characteristic
25	C₁₆	—	137	1	no	—
26	C₁₆	—	137	1	no	—
27	C₂×C₄	#14555522	1	1	yes	characteristic
28	C₈	#14555522	1	1	yes	characteristic
29	C₈	C₂×#11764049	1	1	yes	characteristic
30	C₂²	#17984178	1	1	yes	characteristic
31	C₄	#17984178	1	1	yes	characteristic
32	C₄	C₂×#14555522	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#17984178	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #22578485	C₂	semidirect
17. C₁₃₇	M₁₂₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.