Subgroups — C₂²×#22603722 #49143040

Order 36544.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₁₄₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₂₂₈₄	C₂	1	1	yes	maximal, characteristic
3	C₂×#22603722	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₈×C₅₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₅₇₁	—	2	1	no	—
6	C₂×Dic₁₁₄₂	—	2	3	no	—
7	C₂×Dic₁₁₄₂	C₂²	1	6	yes	complemented
8	C₂×D₂₂₈₄	—	2	3	no	—
9	C₂×D₂₂₈₄	C₂²	1	6	yes	—
10	C₂²×Dic₅₇₁	—	2	1	no	—
11	#22603722	C₂²	1	16	yes	direct product factor
12	C₂²×C₄×C₅₇₁	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₅₇₁	C₂²	1	6	yes	complemented
14	C₂²×D₅₇₁	—	2	6	no	—
15	C₂²×D₅₇₁	—	4	4	no	—
16	Dic₁₁₄₂	—	2	6	no	—
17	Dic₁₁₄₂	C₂³	1	4	yes	complemented
18	D₂₂₈₄	—	2	6	no	—
19	D₂₂₈₄	C₂³	1	4	yes	—
20	C₂×Dic₅₇₁	—	2	6	no	—
21	C₂³×C₅₇₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₅₇₁	D₄	1	3	yes	—
23	C₂×C₄×C₅₇₁	C₂³	1	3	yes	—
24	C₈×C₅₇₁	C₂³	1	4	yes	complemented
25	C₂²×C₅₇₁	SD₁₆	1	4	yes	complemented
26	C₂²×C₅₇₁	C₂×D₄	1	3	yes	—
27	C₂×D₅₇₁	—	2	4	no	—
28	C₂×D₅₇₁	—	4	12	no	—
29	C₄×C₅₇₁	C₂×D₄	1	3	yes	—
30	C₄×C₅₇₁	C₂⁴	1	1	yes	characteristic
31	Dic₅₇₁	—	2	4	no	—
32	C₂×C₅₇₁	C₂×SD₁₆	1	6	yes	complemented
33	C₂×C₅₇₁	C₂²×D₄	1	1	yes	characteristic
34	D₅₇₁	—	4	4	no	—
35	C₅₇₁	C₂²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₂²×SD₁₆	—	571	1	no	maximal, Sylow
37	C₂²×Q₈	—	571	1	no	—
38	C₂²×D₄	—	571	1	no	—
39	C₂×SD₁₆	—	571	12	no	—
40	C₂²×C₈	D₅₇₁	1	1	yes	characteristic, complemented
41	C₂⁴	—	1142	1	no	—
42	C₂×Q₈	—	571	6	no	—
43	C₂×Q₈	—	1142	3	no	—
44	C₂×D₄	—	571	6	no	—
45	C₂×D₄	—	1142	3	no	—
46	C₂²×C₄	—	1142	1	no	—
47	C₂²×C₄	C₂×D₅₇₁	1	1	yes	characteristic
48	SD₁₆	—	571	16	no	—
49	C₂×C₈	C₂×D₅₇₁	1	6	yes	complemented
50	C₂³	—	1142	6	no	—
51	C₂³	—	2284	4	no	—
52	C₂³	D₂₂₈₄	1	1	yes	characteristic
53	Q₈	—	571	4	no	—
54	Q₈	—	1142	6	no	—
55	D₄	—	571	4	no	—
56	D₄	—	1142	6	no	—
57	C₂×C₄	—	1142	6	no	—
58	C₂×C₄	D₂₂₈₄	1	3	yes	—
59	C₂×C₄	C₂²×D₅₇₁	1	3	yes	—
60	C₈	C₂²×D₅₇₁	1	4	yes	complemented
61	C₂²	—	1142	4	no	—
62	C₂²	—	2284	12	no	—
63	C₂²	#22603722	1	4	yes	direct product factor
64	C₂²	C₂×D₂₂₈₄	1	3	yes	—
65	C₄	—	1142	4	no	—
66	C₄	C₂×D₂₂₈₄	1	3	yes	—
67	C₄	C₂³×D₅₇₁	1	1	yes	characteristic
68	C₂	—	2284	4	no	—
69	C₂	C₂×#22603722	1	6	yes	direct product factor
70	C₂	C₂²×D₂₂₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₂₈₄
commutator, cosocle	C₄×C₅₇₁	C₂⁴
Frattini	C₄	C₂³×D₅₇₁
Fitting	C₂²×C₈×C₅₇₁	C₂
socle	C₂³×C₅₇₁	D₄
prime radical	C₂²×D₂₂₈₄	C₂
hypercenter	C₂²×C₈	D₅₇₁
hypocenter	C₅₇₁	C₂²×SD₁₆
LCS	G ▷ C₄×C₅₇₁ ▷ C₂×C₅₇₁ ▷ C₅₇₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₁₁₄₂	C₂	semidirect
3. C₂×#22603722	C₂	direct (N × H)
4. C₂²×C₈×C₅₇₁	C₂	semidirect
7. C₂×Dic₁₁₄₂	C₂²	semidirect
11. #22603722	C₂²	direct (N × H)
13. C₂×C₈×C₅₇₁	C₂²	semidirect
17. Dic₁₁₄₂	C₂³	semidirect
24. C₈×C₅₇₁	C₂³	semidirect
25. C₂²×C₅₇₁	SD₁₆	semidirect
32. C₂×C₅₇₁	C₂×SD₁₆	semidirect
35. C₅₇₁	C₂²×SD₁₆	semidirect
40. C₂²×C₈	D₅₇₁	semidirect
49. C₂×C₈	C₂×D₅₇₁	semidirect
60. C₈	C₂²×D₅₇₁	semidirect
63. C₂²	#22603722	direct (N × H)
69. C₂	C₂×#22603722	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₁₄₂	2
C₂²×D₂₂₈₄	2
C₂×#22603722	2
C₂²×C₈×C₅₇₁	2
C₂²×SD₁₆	571

Subgroups — C22×#22603722 #49143040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#22603722 #49143040