Subgroups — C₂²×#13182019 #20295802

Order 6976.

258 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
2	C₂×#13182019	C₂	1	12	yes	maximal, direct product factor
3	C₂²×#11724784	C₂	1	1	yes	maximal, characteristic
4	C₂²×Q₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₁₈	—	2	3	no	—
6	C₂×Dic₂₁₈	C₂²	1	6	yes	—
7	C₂²×Dic₁₀₉	—	2	1	no	—
8	#13182019	C₂²	1	16	yes	direct product factor
9	C₂×#11724784	C₂²	1	6	yes	—
10	C₂×Q₈×C₁₀₉	—	2	3	no	—
11	C₂×Q₈×C₁₀₉	C₂²	1	6	yes	—
12	C₂²×C₄×C₁₀₉	—	2	1	no	—
13	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂³×C₁₀₉	D₄	1	1	yes	characteristic
15	Q₈×C₁₀₉	—	2	6	no	—
16	Q₈×C₁₀₉	C₂³	1	4	yes	—
17	C₂×C₄×C₁₀₉	—	2	6	no	—
18	C₂×C₄×C₁₀₉	D₄	1	3	yes	—
19	C₂×C₄×C₁₀₉	C₂³	1	3	yes	—
20	C₂×Dic₁₀₉	—	2	6	no	—
21	Dic₂₁₈	—	2	6	no	—
22	Dic₂₁₈	C₂³	1	4	yes	—
23	#11724784	C₂³	1	4	yes	—
24	C₂²×C₁₀₉	Q₁₆	1	4	yes	complemented
25	C₂²×C₁₀₉	C₂×D₄	1	3	yes	—
26	C₄×C₁₀₉	—	2	4	no	—
27	C₄×C₁₀₉	C₂×D₄	1	3	yes	—
28	C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
29	Dic₁₀₉	—	2	4	no	—
30	C₂×C₁₀₉	C₂×Q₁₆	1	6	yes	complemented
31	C₂×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
32	C₁₀₉	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
33	C₂²×Q₁₆	—	109	1	no	maximal, Sylow
34	C₂²×Q₈	—	109	1	no	—
35	C₂²×Q₈	D₁₀₉	1	1	yes	characteristic
36	C₂×Q₁₆	—	109	12	no	—
37	C₂²×C₈	—	109	1	no	—
38	C₂×Q₈	—	2	3	no	—
39	C₂×Q₈	—	109	6	no	—
40	C₂×Q₈	—	218	3	no	—
41	C₂×Q₈	C₂×D₁₀₉	1	6	yes	—
42	C₂²×C₄	—	2	1	no	—
43	C₂²×C₄	—	218	1	no	—
44	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
45	Q₁₆	—	109	16	no	—
46	C₂×C₈	—	109	6	no	—
47	C₂³	C₂²⋊D₁₀₉	1	1	yes	characteristic
48	Q₈	—	2	6	no	—
49	Q₈	—	109	4	no	—
50	Q₈	—	218	6	no	—
51	Q₈	C₂²×D₁₀₉	1	4	yes	—
52	C₂×C₄	—	2	6	no	—
53	C₂×C₄	—	218	6	no	—
54	C₂×C₄	C₂²⋊D₁₀₉	1	3	yes	—
55	C₂×C₄	C₂²×D₁₀₉	1	3	yes	—
56	C₈	—	109	4	no	—
57	C₂²	#13182019	1	4	yes	direct product factor
58	C₂²	C₂×C₂²⋊D₁₀₉	1	3	yes	—
59	C₄	—	2	4	no	—
60	C₄	—	218	4	no	—
61	C₄	C₂×C₂²⋊D₁₀₉	1	3	yes	—
62	C₄	C₂³×D₁₀₉	1	1	yes	characteristic
63	C₂	C₂×#13182019	1	6	yes	direct product factor
64	C₂	C₂²×C₂²⋊D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₁₀₉
commutator	C₄×C₁₀₉	C₂⁴
Frattini	C₄	C₂³×D₁₀₉
Fitting	C₂²×Q₈×C₁₀₉	C₂
socle	C₂³×C₁₀₉	D₄
hypercenter	C₂²×Q₈	D₁₀₉
hypocenter	C₁₀₉	C₂²×Q₁₆
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×#13182019	C₂	direct (N × H)
8. #13182019	C₂²	direct (N × H)
24. C₂²×C₁₀₉	Q₁₆	semidirect
30. C₂×C₁₀₉	C₂×Q₁₆	semidirect
32. C₁₀₉	C₂²×Q₁₆	semidirect
57. C₂²	#13182019	direct (N × H)
63. C₂	C₂×#13182019	direct (N × H)

Subgroups — C22×#13182019 #20295802

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13182019 #20295802