Subgroups — #34115297

Order 20096.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758199	C₂	1	2	yes	maximal
2	C₃₂×D₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#19097840	—	2	2	no	—
4	C₁₆×D₁₅₇	C₂²	1	1	yes	characteristic
5	#19097677	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₁₅₇	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#10597845	—	4	2	no	—
8	C₈×D₁₅₇	D₄	1	1	yes	characteristic
9	#14578929	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₅₇	C₂×C₄	1	1	yes	characteristic
11	C₂×#10597845	—	8	2	no	—
12	C₄×D₁₅₇	D₈	1	1	yes	characteristic
13	#11929434	Q₁₆	1	1	yes	characteristic
14	C₈×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
15	C₂×D₁₅₇	D₁₆	1	1	yes	characteristic
16	#10597845	—	16	2	no	—
17	C₄×C₁₅₇	#107	1	1	yes	characteristic
18	Dic₁₅₇	Q₃₂	1	1	yes	characteristic
19	C₂×C₁₅₇	#366	1	1	yes	characteristic
20	D₁₅₇	D₃₂	1	1	yes	characteristic
21	D₁₅₇	Q₆₄	1	1	yes	characteristic
22	C₁₅₇	#1423	1	1	yes	characteristic, complemented, Sylow
23	#1423	—	157	1	no	maximal, Sylow
24	C₂×C₃₂	—	157	1	no	—
25	#366	—	157	2	no	—
26	C₂×C₁₆	—	157	1	no	—
27	#107	—	314	2	no	—
28	C₃₂	—	157	1	no	—
29	C₃₂	#10597845	1	1	yes	characteristic, complemented
30	C₂×C₈	—	157	1	no	—
31	C₄⋊C₄	—	628	2	no	—
32	C₁₆	—	157	1	no	—
33	C₁₆	C₂×#10597845	1	1	yes	characteristic
34	C₂×C₄	—	157	1	no	—
35	C₂×C₄	—	1256	2	no	—
36	C₈	—	157	1	no	—
37	C₈	C₄⋊#10597845	1	1	yes	characteristic
38	C₂²	—	157	1	no	—
39	C₄	—	157	1	no	—
40	C₄	—	2512	2	no	—
41	C₄	#19097840	1	1	yes	characteristic
42	C₂	—	157	1	no	—
43	C₂	—	157	1	no	—
44	C₂	#23758199	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.