Subgroups — #22579967

Order 8864.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984573	C₂	1	1	yes	maximal, characteristic, complemented
2	#17984572	C₂	1	2	yes	maximal, complemented
3	D₂₇₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14555667	C₂	1	2	yes	maximal, complemented
5	#17984562	C₂	1	1	yes	maximal, characteristic
6	#14555667	C₂²	1	1	yes	characteristic
7	#14555667	C₂²	1	2	yes	—
8	#14555667	C₂²	1	1	yes	characteristic
9	Dic₅₅₄	C₄	1	1	yes	characteristic
10	C₂²⋊D₂₇₇	C₄	1	2	yes	—
11	C₂×Dic₂₇₇	C₂²	1	2	yes	—
12	C₄×D₂₇₇	C₂²	1	1	yes	characteristic
13	D₄×C₂₇₇	C₄	1	1	yes	characteristic
14	C₂²×C₂₇₇	C₂×C₄	1	2	yes	—
15	C₂×D₂₇₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
17	Dic₂₇₇	C₂×C₄	1	2	yes	—
18	Dic₂₇₇	C₂³	1	1	yes	characteristic
19	C₂×C₂₇₇	—	2	2	no	—
20	C₂×C₂₇₇	C₂²×C₄	1	1	yes	characteristic
21	D₂₇₇	—	2	1	no	—
22	C₂₇₇	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	277	1	no	maximal, Sylow
24	#41	—	277	1	no	—
25	M₁₆	—	277	2	no	—
26	M₁₆	—	277	1	no	—
27	C₂×C₈	—	277	2	no	—
28	C₂×C₈	—	277	1	no	—
29	Q₈	—	277	1	no	—
30	D₄	—	277	2	no	—
31	D₄	#11764308	1	1	yes	characteristic
32	C₂×C₄	—	277	2	no	—
33	C₂×C₄	—	277	1	no	—
34	C₈	—	277	1	no	—
35	C₈	—	277	2	no	—
36	C₈	—	277	1	no	—
37	C₂²	—	277	1	no	—
38	C₂²	C₂×#11764308	1	2	yes	—
39	C₄	—	277	1	no	—
40	C₄	—	277	2	no	—
41	C₄	C₂×#11764308	1	1	yes	characteristic
42	C₂	—	2	2	no	—
43	C₂	—	554	1	no	—
44	C₂	C₂²×#11764308	1	1	yes	characteristic

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