Subgroups — #18009757

Order 4736.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558459	C₂	1	2	yes	maximal
2	C₃₂×D₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924605	—	2	2	no	—
4	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
5	#11924442	C₄	1	1	yes	characteristic, complemented
6	C₃₂×C₃₇	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#3866	—	4	2	no	—
8	C₈×D₃₇	D₄	1	1	yes	characteristic
9	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
10	#10596925	Q₈	1	1	yes	characteristic
11	C₂×#3866	—	8	2	no	—
12	C₄×D₃₇	D₈	1	1	yes	characteristic
13	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
14	#64436	Q₁₆	1	1	yes	characteristic
15	C₂×D₃₇	D₁₆	1	1	yes	characteristic
16	#3866	—	16	2	no	—
17	C₄×C₃₇	#107	1	1	yes	characteristic
18	Dic₃₇	Q₃₂	1	1	yes	characteristic
19	#1423	—	37	1	no	maximal, Sylow
20	C₂×C₃₇	#366	1	1	yes	characteristic
21	D₃₇	D₃₂	1	1	yes	characteristic
22	D₃₇	Q₆₄	1	1	yes	characteristic
23	C₂×C₃₂	—	37	1	no	—
24	#366	—	37	2	no	—
25	C₃₇	#1423	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₆	—	37	1	no	—
27	#107	—	74	2	no	—
28	C₃₂	—	37	1	no	—
29	C₃₂	#3866	1	1	yes	characteristic, complemented
30	C₂×C₈	—	37	1	no	—
31	C₄⋊C₄	—	148	2	no	—
32	C₁₆	—	37	1	no	—
33	C₁₆	C₂×#3866	1	1	yes	characteristic
34	C₂×C₄	—	37	1	no	—
35	C₂×C₄	—	296	2	no	—
36	C₈	—	37	1	no	—
37	C₈	C₄⋊#3866	1	1	yes	characteristic
38	C₂²	—	37	1	no	—
39	C₄	—	37	1	no	—
40	C₄	—	592	2	no	—
41	C₄	#11924605	1	1	yes	characteristic
42	C₂	—	37	1	no	—
43	C₂	—	37	1	no	—
44	C₂	#14558459	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.