Subgroups — #17992513

Order 4736.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10596925	C₂	1	2	yes	maximal
2	C₈²×C₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596925	C₄	1	4	yes	—
4	C₄×C₈×C₃₇	C₄	1	2	yes	—
5	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₇	C₈	1	4	yes	—
7	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
8	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
9	#10596925	C₈	1	8	yes	complemented
10	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
11	C₂×C₄×C₃₇	C₂×C₈	1	2	yes	—
12	C₈×C₃₇	—	2	4	no	—
13	C₈×C₃₇	C₂×C₈	1	4	yes	—
14	C₂²×C₃₇	C₄×C₈	1	1	yes	characteristic
15	C₄×C₃₇	C₄×C₈	1	2	yes	—
16	C₄×C₃₇	M₃₂	1	4	yes	—
17	#1311	—	37	1	no	maximal, Sylow
18	C₂×C₃₇	C₈²	1	1	yes	characteristic
19	C₂×C₃₇	#346	1	2	yes	—
20	C₄×C₁₆	—	37	2	no	—
21	C₈²	D₃₇	1	1	yes	characteristic
22	C₃₇	#1311	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	37	4	no	—
24	C₄×C₈	Dic₃₇	1	2	yes	—
25	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
26	C₂×C₈	#64436	1	4	yes	—
27	C₂×C₈	C₄×D₃₇	1	2	yes	—
28	C₄²	C₂×Dic₃₇	1	1	yes	characteristic
29	C₁₆	—	37	8	no	—
30	C₂×C₄	C₂×#64436	1	2	yes	—
31	C₂×C₄	C₄×Dic₃₇	1	1	yes	characteristic
32	C₈	—	2	4	no	—
33	C₈	C₈×D₃₇	1	4	yes	—
34	C₂²	C₄×#64436	1	1	yes	characteristic
35	C₄	C₈×Dic₃₇	1	2	yes	—
36	C₄	#11924476	1	4	yes	—
37	C₂	C₈×#64436	1	1	yes	characteristic
38	C₂	#14557309	1	2	yes	—

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

N	H ≅ G/N	type
9. #10596925	C₈	semidirect
22. C₃₇	#1311	semidirect

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