Subgroups — C₂²×#13182008 #20295476

Order 6976.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#13182008	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀₉	—	2	4	no	—
6	C₂²×Dic₁₀₉	C₄	1	8	yes	complemented
7	C₂²×Dic₁₀₉	C₂²	1	6	yes	—
8	C₂²×Dic₁₀₉	C₂²	1	6	yes	—
9	#13182008	C₂²	1	16	yes	direct product factor
10	C₂⁴×C₁₀₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₁₀₉	—	2	4	no	—
12	C₂²×C₄×C₁₀₉	C₂²	1	6	yes	—
13	C₂³×C₁₀₉	C₂×C₄	1	4	yes	—
14	C₂³×C₁₀₉	D₄	1	4	yes	—
15	C₂³×C₁₀₉	Q₈	1	4	yes	—
16	C₂³×C₁₀₉	C₂³	1	3	yes	—
17	C₂×C₄×C₁₀₉	—	2	12	no	—
18	C₂×C₄×C₁₀₉	C₂³	1	4	yes	—
19	C₂×Dic₁₀₉	—	2	12	no	—
20	C₂×Dic₁₀₉	C₂×C₄	1	24	yes	complemented
21	C₂×Dic₁₀₉	C₂³	1	4	yes	—
22	C₂×Dic₁₀₉	C₂³	1	4	yes	—
23	C₂²×C₁₀₉	C₄⋊C₄	1	16	yes	complemented
24	C₂²×C₁₀₉	C₂²×C₄	1	6	yes	—
25	C₂²×C₁₀₉	C₂×D₄	1	6	yes	—
26	C₂²×C₁₀₉	C₂×Q₈	1	6	yes	—
27	C₂²×C₁₀₉	C₂⁴	1	1	yes	characteristic
28	C₄×C₁₀₉	—	2	4	no	—
29	Dic₁₀₉	—	2	4	no	—
30	Dic₁₀₉	C₂²×C₄	1	8	yes	complemented
31	C₂×C₁₀₉	C₂×C₄⋊C₄	1	12	yes	complemented
32	C₂×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
33	C₂×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
34	C₂×C₁₀₉	C₂²×Q₈	1	1	yes	characteristic
35	C₁₀₉	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₄⋊C₄	—	109	1	no	maximal, Sylow
37	C₂³×C₄	—	109	1	no	—
38	C₂³×C₄	—	109	1	no	—
39	C₂³×C₄	D₁₀₉	1	1	yes	characteristic
40	C₂×C₄⋊C₄	—	109	12	no	—
41	C₂⁴	C₂×D₁₀₉	1	1	yes	characteristic
42	C₂²×C₄	—	2	4	no	—
43	C₂²×C₄	—	109	8	no	—
44	C₂²×C₄	—	109	6	no	—
45	C₂²×C₄	—	109	6	no	—
46	C₂²×C₄	—	218	4	no	—
47	C₂²×C₄	C₂×D₁₀₉	1	6	yes	—
48	C₄⋊C₄	—	109	16	no	—
49	C₂³	Dic₂₁₈	1	4	yes	—
50	C₂³	C₄×D₁₀₉	1	4	yes	—
51	C₂³	C₂²⋊D₁₀₉	1	4	yes	—
52	C₂³	C₂²×D₁₀₉	1	3	yes	—
53	C₂×C₄	—	2	12	no	—
54	C₂×C₄	—	109	24	no	—
55	C₂×C₄	—	109	4	no	—
56	C₂×C₄	—	109	4	no	—
57	C₂×C₄	—	218	12	no	—
58	C₂×C₄	C₂²×D₁₀₉	1	4	yes	—
59	C₂²	#13182008	1	16	yes	direct product factor
60	C₂²	C₂×C₄×D₁₀₉	1	6	yes	—
61	C₂²	C₂×C₂²⋊D₁₀₉	1	6	yes	—
62	C₂²	C₂×Dic₂₁₈	1	6	yes	—
63	C₂²	C₂³×D₁₀₉	1	1	yes	characteristic
64	C₄	—	2	4	no	—
65	C₄	—	109	8	no	—
66	C₄	—	218	4	no	—
67	C₂	C₂×#13182008	1	12	yes	direct product factor
68	C₂	C₂²×C₄×D₁₀₉	1	1	yes	characteristic
69	C₂	C₂²×C₂²⋊D₁₀₉	1	1	yes	characteristic
70	C₂	C₂²×Dic₂₁₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₂³×C₄
Frattini	C₂²	C₂³×D₁₀₉
Fitting	C₂³×C₄×C₁₀₉	C₂
socle	C₂⁴×C₁₀₉	C₂²
hypercenter	C₂³×C₄	D₁₀₉
hypocenter	C₁₀₉	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×#13182008	C₂	direct (N × H)
6. C₂²×Dic₁₀₉	C₄	semidirect
9. #13182008	C₂²	direct (N × H)
20. C₂×Dic₁₀₉	C₂×C₄	semidirect
23. C₂²×C₁₀₉	C₄⋊C₄	semidirect
30. Dic₁₀₉	C₂²×C₄	semidirect
31. C₂×C₁₀₉	C₂×C₄⋊C₄	semidirect
35. C₁₀₉	C₂²×C₄⋊C₄	semidirect
59. C₂²	#13182008	direct (N × H)
67. C₂	C₂×#13182008	direct (N × H)

Subgroups — C22×#13182008 #20295476

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13182008 #20295476