Subgroups — C₂²×#13182018 #20295800

Order 6976.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₁₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄₃₆	C₂	1	1	yes	maximal, characteristic
3	C₂×#13182018	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₀₉	—	2	1	no	—
6	C₂×Dic₂₁₈	—	2	3	no	—
7	C₂×Dic₂₁₈	C₂²	1	6	yes	complemented
8	C₂×D₄₃₆	—	2	3	no	—
9	C₂×D₄₃₆	C₂²	1	6	yes	—
10	C₂²×Dic₁₀₉	—	2	1	no	—
11	#13182018	C₂²	1	16	yes	direct product factor
12	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₂×C₈×C₁₀₉	C₂²	1	6	yes	complemented
14	C₂³×C₁₀₉	D₄	1	1	yes	characteristic
15	C₂²×D₁₀₉	—	2	6	no	—
16	C₂²×D₁₀₉	—	4	4	no	—
17	C₂×C₄×C₁₀₉	D₄	1	3	yes	—
18	C₂×C₄×C₁₀₉	C₂³	1	3	yes	—
19	C₂×Dic₁₀₉	—	2	6	no	—
20	D₄₃₆	—	2	6	no	—
21	D₄₃₆	C₂³	1	4	yes	—
22	Dic₂₁₈	—	2	6	no	—
23	Dic₂₁₈	C₂³	1	4	yes	complemented
24	C₈×C₁₀₉	C₂³	1	4	yes	complemented
25	C₂²×C₁₀₉	SD₁₆	1	4	yes	complemented
26	C₂²×C₁₀₉	C₂×D₄	1	3	yes	—
27	C₂×D₁₀₉	—	2	4	no	—
28	C₂×D₁₀₉	—	4	12	no	—
29	C₄×C₁₀₉	C₂×D₄	1	3	yes	—
30	C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
31	Dic₁₀₉	—	2	4	no	—
32	C₂×C₁₀₉	C₂×SD₁₆	1	6	yes	complemented
33	C₂×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
34	D₁₀₉	—	4	4	no	—
35	C₁₀₉	C₂²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₂²×SD₁₆	—	109	1	no	maximal, Sylow
37	C₂²×Q₈	—	109	1	no	—
38	C₂²×D₄	—	109	1	no	—
39	C₂×SD₁₆	—	109	12	no	—
40	C₂²×C₈	D₁₀₉	1	1	yes	characteristic, complemented
41	C₂⁴	—	218	1	no	—
42	C₂×Q₈	—	109	6	no	—
43	C₂×Q₈	—	218	3	no	—
44	C₂×D₄	—	109	6	no	—
45	C₂×D₄	—	218	3	no	—
46	C₂²×C₄	—	218	1	no	—
47	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
48	SD₁₆	—	109	16	no	—
49	C₂×C₈	C₂×D₁₀₉	1	6	yes	complemented
50	C₂³	—	436	4	no	—
51	C₂³	—	218	6	no	—
52	C₂³	D₄₃₆	1	1	yes	characteristic
53	Q₈	—	109	4	no	—
54	Q₈	—	218	6	no	—
55	D₄	—	109	4	no	—
56	D₄	—	218	6	no	—
57	C₂×C₄	—	218	6	no	—
58	C₂×C₄	D₄₃₆	1	3	yes	—
59	C₂×C₄	C₂²×D₁₀₉	1	3	yes	—
60	C₈	C₂²×D₁₀₉	1	4	yes	complemented
61	C₂²	—	436	12	no	—
62	C₂²	—	218	4	no	—
63	C₂²	#13182018	1	4	yes	direct product factor
64	C₂²	C₂×D₄₃₆	1	3	yes	—
65	C₄	—	218	4	no	—
66	C₄	C₂×D₄₃₆	1	3	yes	—
67	C₄	C₂³×D₁₀₉	1	1	yes	characteristic
68	C₂	—	436	4	no	—
69	C₂	C₂×#13182018	1	6	yes	direct product factor
70	C₂	C₂²×D₄₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄₃₆
commutator	C₄×C₁₀₉	C₂⁴
Frattini	C₄	C₂³×D₁₀₉
Fitting	C₂²×C₈×C₁₀₉	C₂
socle	C₂³×C₁₀₉	D₄
hypercenter	C₂²×C₈	D₁₀₉
hypocenter	C₁₀₉	C₂²×SD₁₆
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
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×Dic₂₁₈	C₂	semidirect
3. C₂×#13182018	C₂	direct (N × H)
4. C₂²×C₈×C₁₀₉	C₂	semidirect
7. C₂×Dic₂₁₈	C₂²	semidirect
11. #13182018	C₂²	direct (N × H)
13. C₂×C₈×C₁₀₉	C₂²	semidirect
23. Dic₂₁₈	C₂³	semidirect
24. C₈×C₁₀₉	C₂³	semidirect
25. C₂²×C₁₀₉	SD₁₆	semidirect
32. C₂×C₁₀₉	C₂×SD₁₆	semidirect
35. C₁₀₉	C₂²×SD₁₆	semidirect
40. C₂²×C₈	D₁₀₉	semidirect
49. C₂×C₈	C₂×D₁₀₉	semidirect
60. C₈	C₂²×D₁₀₉	semidirect
63. C₂²	#13182018	direct (N × H)
69. C₂	C₂×#13182018	direct (N × H)

Subgroups — C22×#13182018 #20295800

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13182018 #20295800