Subgroups — #47982923

Order 35456.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31799960	C₂	1	3	yes	maximal
2	#31799759	C₂	1	3	yes	maximal
3	#338×C₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14555660	C₂²	1	1	yes	characteristic
5	#22579839	C₂²	1	3	yes	—
6	#22579790	C₄	1	6	yes	complemented
7	C₈×Dic₂₇₇	C₄	1	6	yes	complemented
8	C₂×M₁₆×C₂₇₇	C₂²	1	3	yes	—
9	C₂×#14555660	C₂×C₄	1	3	yes	—
10	C₂×#14555660	C₂×C₄	1	3	yes	—
11	C₄⋊Dic₂₇₇	—	2	3	no	—
12	C₂²⋊Dic₂₇₇	—	2	3	no	—
13	C₄×Dic₂₇₇	C₂×C₄	1	6	yes	—
14	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
15	M₁₆×C₂₇₇	—	2	6	no	—
16	C₂×C₈×C₂₇₇	C₂×C₄	1	6	yes	—
17	C₂×Dic₂₇₇	—	2	6	no	—
18	#14555660	C₄²	1	1	yes	characteristic
19	#14555660	C₄²	1	3	yes	—
20	C₂³×C₂₇₇	#41	1	1	yes	characteristic
21	C₂×C₄×C₂₇₇	C₂²×C₄	1	3	yes	—
22	C₂×C₄×C₂₇₇	#41	1	3	yes	—
23	C₈×C₂₇₇	—	2	6	no	—
24	C₂²×C₂₇₇	—	4	1	no	—
25	C₂²×C₂₇₇	#117	1	3	yes	—
26	C₄×C₂₇₇	C₂×C₄²	1	1	yes	characteristic
27	C₄×C₂₇₇	#117	1	3	yes	—
28	Dic₂₇₇	—	4	6	no	—
29	C₂×C₂₇₇	—	2	3	no	—
30	C₂×C₂₇₇	#376	1	1	yes	characteristic
31	C₂₇₇	#1747	1	1	yes	characteristic, complemented, Sylow
32	#1747	—	277	1	no	maximal, Sylow
33	#405	—	277	3	no	—
34	#338	D₂₇₇	1	1	yes	characteristic
35	H(3,ℤ/4)	—	277	3	no	—
36	C₂×M₁₆	C₂×D₂₇₇	1	3	yes	—
37	C₂²×C₈	—	277	1	no	—
38	#117	—	277	3	no	—
39	#97	—	277	6	no	—
40	C₄×C₈	—	277	6	no	—
41	C₂²×C₄	C₂²×D₂₇₇	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	277	3	no	—
44	C₂×C₈	—	277	3	no	—
45	C₂×C₈	C₄×D₂₇₇	1	6	yes	—
46	C₄⋊C₄	—	554	3	no	—
47	C₂²⋊C₄	—	554	3	no	—
48	C₄²	—	277	6	no	—
49	C₂³	#17984564	1	1	yes	characteristic
50	C₂×C₄	—	554	6	no	—
51	C₂×C₄	C₂×C₄×D₂₇₇	1	3	yes	—
52	C₂×C₄	#17984562	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	277	1	no	—
55	C₈	—	277	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#22579838	1	3	yes	—
58	C₄	—	1108	6	no	—
59	C₄	C₄²×D₂₇₇	1	1	yes	characteristic
60	C₄	#22579836	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#31799847	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₂₇₇
commutator	C₄×C₂₇₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₂₇₇
Fitting	#338×C₂₇₇	C₂
socle	C₂×C₂₇₇	#376
prime radical	C₂³×C₂₇₇	#41
cosocle	C₂²×C₄×C₂₇₇	C₂³
hypercenter	#338	D₂₇₇
hypocenter	C₂₇₇	#1747
LCS	G ▷ C₄×C₂₇₇ ▷ C₂₇₇
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #22579790	C₄	semidirect
7. C₈×Dic₂₇₇	C₄	semidirect
31. C₂₇₇	#1747	semidirect

Maximal subgroups

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

subgroup	index
#31799960	2
#31799759	2
#338×C₂₇₇	2
#1747	277