Subgroups — C₂²×Dic₄₅₂ #20299375

Order 7232.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₂₆	C₂	1	2	yes	maximal
2	C₂×Dic₄₅₂	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₂₆	—	2	6	no	—
5	C₂×Dic₂₂₆	C₂²	1	12	yes	—
6	C₂²×Dic₁₁₃	—	2	2	no	—
7	Dic₄₅₂	C₂²	1	16	yes	direct product factor
8	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₁₁₃	C₂²	1	6	yes	—
10	C₂³×C₁₁₃	D₄	1	1	yes	characteristic
11	C₂×C₄×C₁₁₃	D₄	1	3	yes	—
12	C₂×C₄×C₁₁₃	C₂³	1	3	yes	—
13	C₂×Dic₁₁₃	—	2	12	no	—
14	Dic₂₂₆	—	2	12	no	—
15	Dic₂₂₆	C₂³	1	8	yes	—
16	C₈×C₁₁₃	C₂³	1	4	yes	—
17	C₂²×C₁₁₃	Q₁₆	1	4	yes	complemented
18	C₂²×C₁₁₃	C₂×D₄	1	3	yes	—
19	C₄×C₁₁₃	C₂×D₄	1	3	yes	—
20	C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
21	Dic₁₁₃	—	2	8	no	—
22	C₂×C₁₁₃	C₂×Q₁₆	1	6	yes	complemented
23	C₂×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
24	C₁₁₃	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂²×Q₁₆	—	113	1	no	maximal, Sylow
26	C₂²×Q₈	—	113	2	no	—
27	C₂×Q₁₆	—	113	12	no	—
28	C₂²×C₈	D₁₁₃	1	1	yes	characteristic
29	C₂×Q₈	—	113	12	no	—
30	C₂×Q₈	—	226	6	no	—
31	C₂²×C₄	—	226	2	no	—
32	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
33	Q₁₆	—	113	16	no	—
34	C₂×C₈	C₂×D₁₁₃	1	6	yes	—
35	C₂³	D₄₅₂	1	1	yes	characteristic
36	Q₈	—	113	8	no	—
37	Q₈	—	226	12	no	—
38	C₂×C₄	—	226	12	no	—
39	C₂×C₄	D₄₅₂	1	3	yes	—
40	C₂×C₄	C₂²×D₁₁₃	1	3	yes	—
41	C₈	C₂²×D₁₁₃	1	4	yes	—
42	C₂²	Dic₄₅₂	1	4	yes	direct product factor
43	C₂²	C₂×D₄₅₂	1	3	yes	—
44	C₄	—	226	8	no	—
45	C₄	C₂×D₄₅₂	1	3	yes	—
46	C₄	C₂³×D₁₁₃	1	1	yes	characteristic
47	C₂	C₂×Dic₄₅₂	1	6	yes	direct product factor
48	C₂	C₂²×D₄₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄₅₂
commutator	C₄×C₁₁₃	C₂⁴
Frattini	C₄	C₂³×D₁₁₃
Fitting	C₂²×C₈×C₁₁₃	C₂
socle	C₂³×C₁₁₃	D₄
hypercenter	C₂²×C₈	D₁₁₃
hypocenter	C₁₁₃	C₂²×Q₁₆
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₄₅₂	C₂	direct (N × H)
7. Dic₄₅₂	C₂²	direct (N × H)
17. C₂²×C₁₁₃	Q₁₆	semidirect
22. C₂×C₁₁₃	C₂×Q₁₆	semidirect
24. C₁₁₃	C₂²×Q₁₆	semidirect
42. C₂²	Dic₄₅₂	direct (N × H)
47. C₂	C₂×Dic₄₅₂	direct (N × H)

Subgroups — C22×Dic452 #20299375

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×Dic₄₅₂ #20299375