Subgroups — #20290644

Order 6784.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811489	C₂	1	6	yes	maximal
2	#16810468	C₂	1	1	yes	maximal, characteristic
3	C₂²×#88324	C₂²	1	4	yes	—
4	C₂×C₄×Dic₅₃	C₂²	1	3	yes	—
5	#13133124	C₄	1	3	yes	—
6	#95×C₅₃	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₅₃	C₂×C₄	1	3	yes	—
8	C₂²×Dic₅₃	C₂×C₄	1	3	yes	—
9	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
10	C₂×#88324	—	2	12	no	—
11	C₄×Dic₅₃	—	2	6	no	—
12	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅₃	—	2	3	no	—
14	C₂×C₄×C₅₃	—	2	6	no	—
15	C₂×Dic₅₃	—	2	3	no	—
16	C₂×Dic₅₃	—	2	3	no	—
17	C₂×Dic₅₃	—	2	3	no	—
18	C₂×Dic₅₃	#41	1	6	yes	—
19	#88324	—	4	4	no	—
20	C₂²×C₅₃	#117	1	3	yes	—
21	C₂²×C₅₃	#131	1	3	yes	—
22	C₂²×C₅₃	#131	1	1	yes	characteristic
23	C₄×C₅₃	—	4	3	no	—
24	Dic₅₃	—	4	3	no	—
25	Dic₅₃	#126	1	4	yes	—
26	#1840	—	53	1	no	maximal, Sylow
27	C₂×C₅₃	#383	1	1	yes	characteristic
28	C₂×C₅₃	#433	1	3	yes	—
29	C₂×C₅₃	#433	1	3	yes	—
30	#376	—	53	1	no	—
31	#336	—	53	6	no	—
32	C₅₃	#1840	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₈	—	53	4	no	—
34	C₂×C₄²	—	53	3	no	—
35	#95	—	53	3	no	—
36	#95	#6157	1	1	yes	characteristic
37	C₂²×C₄	—	53	1	no	—
38	C₂²×C₄	—	53	3	no	—
39	C₂²×C₄	C₂×#6157	1	3	yes	—
40	C₂×C₈	—	106	12	no	—
41	C₄²	—	106	6	no	—
42	C₂³	C₂²×#6157	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	53	6	no	—
46	C₂×C₄	—	106	3	no	—
47	C₂×C₄	—	106	3	no	—
48	C₂×C₄	—	106	3	no	—
49	C₈	—	212	4	no	—
50	C₂²	#13133296	1	3	yes	—
51	C₂²	#13133304	1	3	yes	—
52	C₂²	#13133305	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	53	4	no	—
55	C₄	—	212	3	no	—
56	C₂	#16811568	1	1	yes	characteristic
57	C₂	#16811647	1	3	yes	—
58	C₂	#16811648	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#6157
commutator, socle	C₂³×C₅₃	C₂²×C₄
Fitting	#95×C₅₃	C₄
hypercenter	#95	#6157
hypocenter	C₅₃	#1840
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
32. C₅₃	#1840	semidirect