Subgroups — #31795950

Order 17536.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22578329	C₂	1	2	yes	maximal
2	C₃₂×D₁₃₇	C₂	1	1	yes	maximal, characteristic
3	#17984157	—	2	2	no	—
4	C₁₆×D₁₃₇	C₂²	1	1	yes	characteristic
5	#17983994	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₁₃₇	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#10587739	—	4	2	no	—
8	C₈×D₁₃₇	D₄	1	1	yes	characteristic
9	#14555485	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₃₇	C₂×C₄	1	1	yes	characteristic
11	C₂×#10587739	—	8	2	no	—
12	C₄×D₁₃₇	D₈	1	1	yes	characteristic
13	#11764040	Q₁₆	1	1	yes	characteristic
14	C₈×C₁₃₇	C₄⋊C₄	1	1	yes	characteristic
15	C₂×D₁₃₇	D₁₆	1	1	yes	characteristic
16	#10587739	—	16	2	no	—
17	C₄×C₁₃₇	#107	1	1	yes	characteristic
18	Dic₁₃₇	Q₃₂	1	1	yes	characteristic
19	C₂×C₁₃₇	#366	1	1	yes	characteristic
20	D₁₃₇	D₃₂	1	1	yes	characteristic
21	D₁₃₇	Q₆₄	1	1	yes	characteristic
22	C₁₃₇	#1423	1	1	yes	characteristic, complemented, Sylow
23	#1423	—	137	1	no	maximal, Sylow
24	C₂×C₃₂	—	137	1	no	—
25	#366	—	137	2	no	—
26	C₂×C₁₆	—	137	1	no	—
27	#107	—	274	2	no	—
28	C₃₂	—	137	1	no	—
29	C₃₂	#10587739	1	1	yes	characteristic, complemented
30	C₂×C₈	—	137	1	no	—
31	C₄⋊C₄	—	548	2	no	—
32	C₁₆	—	137	1	no	—
33	C₁₆	C₂×#10587739	1	1	yes	characteristic
34	C₂×C₄	—	1096	2	no	—
35	C₂×C₄	—	137	1	no	—
36	C₈	—	137	1	no	—
37	C₈	C₄⋊#10587739	1	1	yes	characteristic
38	C₂²	—	137	1	no	—
39	C₄	—	137	1	no	—
40	C₄	—	2192	2	no	—
41	C₄	#17984157	1	1	yes	characteristic
42	C₂	—	137	1	no	—
43	C₂	—	137	1	no	—
44	C₂	#22578329	1	1	yes	characteristic

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.