Subgroups — #11924599

Order 1184.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₃₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3866	C₂	1	1	yes	maximal, characteristic
3	D₃₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#3866	—	2	1	no	—
5	Q₈×C₃₇	C₄	1	1	yes	characteristic, complemented
6	C₄×D₃₇	—	2	1	no	—
7	C₄×D₃₇	C₂²	1	1	yes	characteristic
8	Dic₇₄	—	2	1	no	—
9	Dic₇₄	C₄	1	1	yes	characteristic, complemented
10	#64438	—	2	1	no	—
11	C₂×D₃₇	D₄	1	1	yes	characteristic
12	#3866	—	4	1	no	—
13	C₄×C₃₇	—	2	1	no	—
14	C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
15	Dic₃₇	—	2	1	no	—
16	Dic₃₇	D₄	1	1	yes	characteristic
17	C₂×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
18	D₃₇	SD₁₆	1	1	yes	characteristic
19	D₃₇	Q₁₆	1	1	yes	characteristic
20	C₃₇	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	37	1	no	maximal, Sylow
22	C₂×Q₈	—	37	1	no	—
23	C₂×C₈	—	37	1	no	—
24	C₄⋊C₄	—	37	1	no	—
25	Q₈	—	37	1	no	—
26	Q₈	—	74	1	no	—
27	Q₈	#3866	1	1	yes	characteristic, complemented
28	C₂×C₄	—	37	1	no	—
29	C₂×C₄	—	74	1	no	—
30	C₂×C₄	—	74	1	no	—
31	C₈	—	74	1	no	—
32	C₂²	—	37	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	37	1	no	—
35	C₄	—	74	1	no	—
36	C₄	—	148	1	no	—
37	C₄	C₂×#3866	1	1	yes	characteristic
38	C₂	—	37	1	no	—
39	C₂	—	37	1	no	—
40	C₂	C₂²⋊#3866	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.