Subgroups — #31799822

Order 17728.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22579820	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₂₇₇	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#14555660	C₄	1	1	yes	characteristic
5	C₄×Dic₂₇₇	C₄	1	1	yes	characteristic
6	#17984538	—	2	1	no	—
7	C₂×C₈×C₂₇₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₂₇₇	—	2	1	no	—
9	C₂×Dic₂₇₇	—	2	1	no	—
10	#14555660	C₈	1	2	yes	—
11	C₂×C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₇₇	D₄	1	1	yes	characteristic
13	C₈×C₂₇₇	Q₈	1	1	yes	characteristic
14	C₂²×C₂₇₇	M₁₆	1	1	yes	characteristic
15	C₄×C₂₇₇	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₂₇₇	C₂×C₈	1	1	yes	characteristic
17	Dic₂₇₇	—	2	2	no	—
18	C₂×C₂₇₇	—	2	1	no	—
19	C₂×C₂₇₇	C₄⋊C₈	1	1	yes	characteristic
20	C₂₇₇	#364	1	1	yes	characteristic, complemented, Sylow
21	#364	—	277	1	no	maximal, Sylow
22	M₃₂	—	277	1	no	—
23	M₃₂	D₂₇₇	1	1	yes	characteristic
24	C₄×C₈	—	277	1	no	—
25	C₂×C₈	—	277	1	no	—
26	C₂×C₈	C₂×D₂₇₇	1	1	yes	characteristic
27	C₄²	—	277	1	no	—
28	C₁₆	—	2	1	no	—
29	C₁₆	—	554	1	no	—
30	C₂×C₄	—	554	1	no	—
31	C₂×C₄	C₄×D₂₇₇	1	1	yes	characteristic
32	C₈	—	277	2	no	—
33	C₈	C₂²⋊D₂₇₇	1	1	yes	characteristic
34	C₈	Dic₅₅₄	1	1	yes	characteristic
35	C₂²	#17984546	1	1	yes	characteristic
36	C₄	—	554	2	no	—
37	C₄	#17984542	1	1	yes	characteristic
38	C₄	C₈×D₂₇₇	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	#22579809	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₂₇₇	#364	semidirect

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