Subgroups — #31800843

Order 17728.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14555667	C₂	1	2	yes	maximal
2	C₈×Dic₂₇₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#14555667	C₄	1	4	yes	—
4	C₂×#14555660	C₄	1	1	yes	characteristic
5	C₄×Dic₂₇₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₂₇₇	C₄	1	1	yes	characteristic
7	#14555667	—	2	4	no	—
8	C₂×Dic₂₇₇	C₂×C₄	1	2	yes	—
9	#14555660	C₈	1	2	yes	complemented
10	C₂×C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
11	C₈×C₂₇₇	C₈	1	2	yes	complemented
12	C₂²×C₂₇₇	C₄²	1	1	yes	characteristic
13	C₄×C₂₇₇	C₂×C₈	1	1	yes	characteristic
14	C₄×C₂₇₇	C₂×C₈	1	1	yes	characteristic
15	Dic₂₇₇	M₁₆	1	4	yes	—
16	C₂×C₂₇₇	C₄×C₈	1	1	yes	characteristic
17	C₂×C₂₇₇	#97	1	2	yes	—
18	C₂₇₇	#322	1	1	yes	characteristic, complemented, Sylow
19	#322	—	277	1	no	maximal, Sylow
20	C₄×C₈	—	277	2	no	—
21	C₄×C₈	—	277	1	no	—
22	C₂×C₈	—	277	1	no	—
23	C₂×C₈	—	277	4	no	—
24	C₂×C₈	#11764308	1	1	yes	characteristic
25	C₄²	—	277	1	no	—
26	C₂×C₄	—	277	2	no	—
27	C₂×C₄	C₂×#11764308	1	1	yes	characteristic
28	C₈	—	277	2	no	—
29	C₈	—	554	4	no	—
30	C₈	#14555667	1	2	yes	complemented
31	C₂²	C₄×#11764308	1	1	yes	characteristic
32	C₄	—	277	4	no	—
33	C₄	C₂×#14555667	1	1	yes	characteristic
34	C₄	D₂₇₇⋊C₈	1	1	yes	characteristic
35	C₂	C₄×#14555667	1	1	yes	characteristic
36	C₂	#22579934	1	2	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.