Subgroups — C₄²×#3866 #14558467

Order 2368.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#3866	C₂	1	6	yes	maximal
2	C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3866	C₂²	1	4	yes	—
4	C₂×C₄×D₃₇	C₂²	1	3	yes	—
5	C₄×#3866	C₄	1	24	yes	direct product factor
6	C₄²×C₃₇	C₄	1	1	yes	characteristic, complemented
7	C₄×Dic₃₇	C₄	1	3	yes	complemented
8	C₂²×D₃₇	C₂³	1	1	yes	characteristic
9	C₂×#3866	C₂×C₄	1	24	yes	—
10	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
11	C₂×Dic₃₇	C₂×C₄	1	3	yes	—
12	C₄×D₃₇	C₂×C₄	1	12	yes	—
13	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
14	C₂×D₃₇	C₂²×C₄	1	6	yes	—
15	#3866	C₄²	1	16	yes	direct product factor
16	C₄×C₃₇	C₄²	1	6	yes	complemented
17	Dic₃₇	C₄²	1	6	yes	complemented
18	C₂×C₃₇	C₂×C₄²	1	3	yes	—
19	D₃₇	C₂×C₄²	1	4	yes	—
20	C₄³	—	37	1	no	maximal, Sylow
21	C₃₇	C₄³	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₄²	—	37	6	no	—
23	C₂×C₄²	—	37	1	no	—
24	C₂²×C₄	—	37	4	no	—
25	C₂²×C₄	—	37	3	no	—
26	C₄²	—	37	24	no	—
27	C₄²	—	37	3	no	—
28	C₄²	#3866	1	1	yes	characteristic, direct product factor
29	C₂³	—	37	1	no	—
30	C₂×C₄	—	37	24	no	—
31	C₂×C₄	—	37	3	no	—
32	C₂×C₄	—	37	12	no	—
33	C₂×C₄	C₂×#3866	1	3	yes	—
34	C₂²	—	37	6	no	—
35	C₂²	C₂²×#3866	1	1	yes	characteristic
36	C₄	—	37	16	no	—
37	C₄	—	37	6	no	—
38	C₄	C₄×#3866	1	6	yes	direct product factor
39	C₂	—	37	4	no	—
40	C₂	C₂×C₄×#3866	1	3	yes	—

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.