Subgroups — #37612919

Order 24736.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20260070	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₇₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₇₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₇₃	C₄	1	1	yes	characteristic
5	C₂×Dic₇₇₃	C₄	1	1	yes	characteristic
6	#20260070	—	2	1	no	—
7	C₂×C₄×C₇₇₃	C₂²	1	1	yes	characteristic
8	C₈×C₇₇₃	—	2	1	no	—
9	C₂²×C₇₇₃	C₂×C₄	1	1	yes	characteristic
10	C₄×C₇₇₃	D₄	1	1	yes	characteristic
11	C₄×C₇₇₃	Q₈	1	1	yes	characteristic
12	Dic₇₇₃	—	2	1	no	—
13	Dic₇₇₃	C₈	1	2	yes	complemented
14	C₂×C₇₇₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₇₇₃	C₂×C₈	1	1	yes	characteristic
16	C₂×C₇₇₃	M₁₆	1	1	yes	characteristic
17	C₇₇₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
18	C₄⋊C₈	—	773	1	no	maximal, Sylow
19	C₂×C₈	—	773	1	no	—
20	C₂×C₈	D₇₇₃	1	1	yes	characteristic
21	C₄²	—	773	1	no	—
22	C₂×C₄	—	773	1	no	—
23	C₂×C₄	—	773	1	no	—
24	C₂×C₄	C₂×D₇₇₃	1	1	yes	characteristic
25	C₈	—	2	1	no	—
26	C₈	—	1546	1	no	—
27	C₂²	C₄×D₇₇₃	1	1	yes	characteristic
28	C₄	—	773	2	no	—
29	C₄	—	1546	1	no	—
30	C₄	C₂²⋊D₇₇₃	1	1	yes	characteristic
31	C₄	Dic₁₅₄₆	1	1	yes	characteristic
32	C₂	#27136458	1	1	yes	characteristic
33	C₂	C₈×D₇₇₃	1	1	yes	characteristic
34	C₂	#27136462	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. Dic₇₇₃	C₈	semidirect
17. C₇₇₃	C₄⋊C₈	semidirect

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