Subgroups — #14558423

Order 2368.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924611	C₂	1	1	yes	maximal, characteristic
2	#11924590	C₂	1	1	yes	maximal, characteristic
3	#11924475	C₂	1	1	yes	maximal, characteristic
4	C₄×#3866	C₄	1	1	yes	characteristic
5	D₃₇⋊C₈	C₄	1	1	yes	characteristic
6	C₈×D₃₇	C₂²	1	1	yes	characteristic
7	#10596927	C₄	1	2	yes	complemented
8	C₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
9	#10596925	C₄	1	1	yes	characteristic, complemented
10	C₂×#3866	—	2	1	no	—
11	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
12	#64438	—	2	1	no	—
13	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
14	#64436	C₂×C₄	1	1	yes	characteristic
15	C₂×D₃₇	M₁₆	1	1	yes	characteristic
16	#3866	—	4	1	no	—
17	C₄×C₃₇	C₄²	1	1	yes	characteristic
18	Dic₃₇	M₁₆	1	1	yes	characteristic
19	C₂×C₃₇	#97	1	1	yes	characteristic
20	D₃₇	—	2	1	no	—
21	#347	—	37	1	no	maximal, Sylow
22	C₃₇	#347	1	1	yes	characteristic, complemented, Sylow
23	M₃₂	—	37	1	no	—
24	M₃₂	—	37	1	no	—
25	#97	—	37	1	no	—
26	C₂×C₈	—	37	1	no	—
27	C₂×C₈	—	37	1	no	—
28	C₄²	—	37	1	no	—
29	C₁₆	—	37	2	no	—
30	C₁₆	—	37	1	no	—
31	C₁₆	#3866	1	1	yes	characteristic, complemented
32	C₂×C₄	—	37	1	no	—
33	C₂×C₄	—	74	1	no	—
34	C₈	—	37	1	no	—
35	C₈	—	74	1	no	—
36	C₈	C₂×#3866	1	1	yes	characteristic
37	C₂²	—	37	1	no	—
38	C₄	—	37	1	no	—
39	C₄	—	148	1	no	—
40	C₄	C₄×#3866	1	1	yes	characteristic
41	C₂	—	74	1	no	—
42	C₂	#11924590	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.