Subgroups — #31800858

Order 17728.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22579935	C₂	1	2	yes	maximal, complemented
2	#22579869	C₂	1	1	yes	maximal, characteristic
3	C₂×#14555667	—	2	2	no	—
4	C₂×D₁₁₀₈	C₄	1	1	yes	characteristic
5	#17984540	—	2	2	no	—
6	C₄×Dic₂₇₇	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₂₇₇	C₄	1	1	yes	characteristic
8	#14555667	—	2	4	no	—
9	C₂²×D₂₇₇	—	2	1	no	—
10	D₁₁₀₈	—	4	1	no	—
11	C₂×Dic₂₇₇	D₄	1	2	yes	—
12	Q₈×C₂₇₇	—	4	1	no	—
13	C₂×C₄×C₂₇₇	—	2	1	no	—
14	C₂×C₄×C₂₇₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₂₇₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₂₇₇	—	4	1	no	—
17	C₂×D₂₇₇	—	4	2	no	—
18	C₄×C₂₇₇	—	2	1	no	—
19	C₄×C₂₇₇	—	4	1	no	—
20	Dic₂₇₇	—	2	2	no	—
21	C₂×C₂₇₇	#100	1	1	yes	characteristic
22	C₂×C₂₇₇	#104	1	2	yes	—
23	D₂₇₇	—	8	1	no	—
24	C₂₇₇	#329	1	1	yes	characteristic, complemented, Sylow
25	#329	—	277	1	no	maximal, Sylow
26	#124	—	277	1	no	—
27	#97	—	277	2	no	—
28	C₂×Q₈	#11764308	1	1	yes	characteristic
29	C₂×D₄	—	277	1	no	—
30	C₂×C₈	—	554	2	no	—
31	C₂²⋊C₄	—	554	2	no	—
32	C₄²	—	277	1	no	—
33	C₂³	—	554	1	no	—
34	Q₈	—	4	1	no	—
35	D₄	—	1108	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	277	2	no	—
38	C₂×C₄	C₂×#11764308	1	1	yes	characteristic
39	C₈	—	554	4	no	—
40	C₂²	—	1108	1	no	—
41	C₂²	—	1108	2	no	—
42	C₂²	C₂²⋊#11764308	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	554	2	no	—
46	C₂	—	2216	1	no	—
47	C₂	#22579940	1	1	yes	characteristic
48	C₂	#22579945	1	2	yes	—

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

N	H ≅ G/N	type
1. #22579935	C₂	semidirect
24. C₂₇₇	#329	semidirect

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