Subgroups — #34115299

Order 20096.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758201	C₂	1	2	yes	maximal
2	C₃₂×D₁₅₇	C₂	1	1	yes	maximal, characteristic
3	#19097842	—	2	2	no	—
4	C₁₆×D₁₅₇	C₂²	1	1	yes	characteristic
5	#19097677	C₄	1	1	yes	characteristic
6	C₃₂×C₁₅₇	C₄	1	1	yes	characteristic
7	#14578964	—	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	#11929441	—	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	Q₃₂	1	1	yes	characteristic
16	C₄×C₁₅₇	#107	1	1	yes	characteristic
17	Dic₁₅₇	D₁₆	1	1	yes	characteristic
18	C₂×C₁₅₇	#366	1	1	yes	characteristic
19	D₁₅₇	—	2	1	no	—
20	C₁₅₇	#1425	1	1	yes	characteristic, complemented, Sylow
21	#1425	—	157	1	no	maximal, Sylow
22	C₂×C₃₂	—	157	1	no	—
23	#368	—	157	2	no	—
24	C₂×C₁₆	—	157	1	no	—
25	#108	—	314	2	no	—
26	C₃₂	—	157	1	no	—
27	C₃₂	#10597845	1	1	yes	characteristic
28	M₁₆	—	628	2	no	—
29	C₂×C₈	—	157	1	no	—
30	C₁₆	—	157	1	no	—
31	C₁₆	C₂×#10597845	1	1	yes	characteristic
32	C₂×C₄	—	157	1	no	—
33	C₈	—	157	1	no	—
34	C₈	—	1256	2	no	—
35	C₈	C₄⋊#10597845	1	1	yes	characteristic
36	C₂²	—	157	1	no	—
37	C₄	—	157	1	no	—
38	C₄	#19097840	1	1	yes	characteristic
39	C₂	—	314	1	no	—
40	C₂	#23758199	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₁₅₇	#1425	semidirect

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