Subgroups — C₂×#16812656 #20295480

Order 6976.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic
2	#16812656	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13182008	C₂	1	2	yes	maximal, complemented
4	C₂×#13182006	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₁₀₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₁₀₉	C₂²	1	2	yes	—
9	C₂²×Dic₁₀₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₁₀₉	C₄	1	8	yes	complemented
11	C₂×C₄×D₁₀₉	C₂²	1	4	yes	—
12	#13182008	C₂²	1	8	yes	complemented
13	#13182006	C₂²	1	8	yes	—
14	C₄×Dic₁₀₉	C₂²	1	4	yes	complemented
15	C₂²×C₄×C₁₀₉	C₂²	1	2	yes	—
16	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₄²×C₁₀₉	C₂²	1	4	yes	complemented
18	C₂³×C₁₀₉	C₂³	1	1	yes	characteristic
19	C₂²×D₁₀₉	—	2	4	no	—
20	C₂²×D₁₀₉	C₂×C₄	1	4	yes	—
21	C₂²×D₁₀₉	C₂³	1	2	yes	—
22	C₂×C₄×C₁₀₉	—	2	4	no	—
23	C₂×C₄×C₁₀₉	C₂×C₄	1	4	yes	—
24	C₂×C₄×C₁₀₉	C₂³	1	4	yes	—
25	C₂×C₄×C₁₀₉	C₂³	1	2	yes	—
26	C₂×Dic₁₀₉	—	2	4	no	—
27	C₂×Dic₁₀₉	C₂×C₄	1	4	yes	—
28	C₂×Dic₁₀₉	C₂³	1	4	yes	—
29	C₂×Dic₁₀₉	C₂³	1	2	yes	—
30	C₄×D₁₀₉	C₂×C₄	1	16	yes	complemented
31	C₂²×C₁₀₉	C₂²×C₄	1	2	yes	—
32	C₂²×C₁₀₉	#41	1	4	yes	—
33	C₂²×C₁₀₉	C₂⁴	1	1	yes	characteristic
34	C₂×D₁₀₉	—	2	8	no	—
35	C₂×D₁₀₉	—	2	4	no	—
36	C₂×D₁₀₉	C₂²×C₄	1	4	yes	—
37	C₄×C₁₀₉	—	2	4	no	—
38	C₄×C₁₀₉	C₂²×C₄	1	4	yes	—
39	Dic₁₀₉	—	2	4	no	—
40	Dic₁₀₉	C₂²×C₄	1	4	yes	—
41	C₂×C₁₀₉	#117	1	4	yes	complemented
42	C₂×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
43	C₂×C₁₀₉	C₂×#41	1	2	yes	—
44	D₁₀₉	—	2	4	no	—
45	C₁₀₉	C₂×#117	1	1	yes	characteristic, complemented, Sylow
46	C₂×#117	—	109	1	no	maximal, Sylow
47	C₂³×C₄	—	109	1	no	—
48	#117	—	109	8	no	—
49	C₂×C₄⋊C₄	—	109	2	no	—
50	C₂×C₂²⋊C₄	—	109	2	no	—
51	C₂×C₄²	—	109	1	no	—
52	C₂×C₄²	D₁₀₉	1	1	yes	characteristic, complemented
53	C₂⁴	—	109	1	no	—
54	C₂²×C₄	—	109	1	no	—
55	C₂²×C₄	—	109	8	no	—
56	C₂²×C₄	—	109	4	no	—
57	C₂²×C₄	—	109	2	no	—
58	C₂²×C₄	C₂×D₁₀₉	1	2	yes	—
59	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
60	C₄⋊C₄	—	109	8	no	—
61	C₂²⋊C₄	—	109	8	no	—
62	C₄²	—	109	4	no	—
63	C₄²	C₂×D₁₀₉	1	4	yes	complemented
64	C₂³	—	109	4	no	—
65	C₂³	—	109	2	no	—
66	C₂³	—	218	4	no	—
67	C₂³	C₂²×D₁₀₉	1	1	yes	characteristic
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	109	4	no	—
70	C₂×C₄	—	109	2	no	—
71	C₂×C₄	—	109	16	no	—
72	C₂×C₄	—	109	4	no	—
73	C₂×C₄	—	218	4	no	—
74	C₂×C₄	C₄×D₁₀₉	1	4	yes	—
75	C₂×C₄	C₂²×D₁₀₉	1	4	yes	—
76	C₂×C₄	C₂²×D₁₀₉	1	2	yes	—
77	C₂²	—	109	4	no	—
78	C₂²	—	218	8	no	—
79	C₂²	—	218	4	no	—
80	C₂²	C₂×C₄×D₁₀₉	1	2	yes	—
81	C₂²	#13182029	1	4	yes	—
82	C₂²	C₂³×D₁₀₉	1	1	yes	characteristic
83	C₄	—	2	4	no	—
84	C₄	—	109	4	no	—
85	C₄	—	218	4	no	—
86	C₄	C₂×C₄×D₁₀₉	1	4	yes	—
87	C₂	—	218	4	no	—
88	C₂	#16812656	1	4	yes	direct product factor
89	C₂	C₂²×C₄×D₁₀₉	1	1	yes	characteristic
90	C₂	C₂×#13182029	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₂³×C₄
Frattini	C₂²	C₂³×D₁₀₉
Fitting	C₂×C₄²×C₁₀₉	C₂
socle	C₂³×C₁₀₉	C₂³
hypercenter	C₂×C₄²	D₁₀₉
hypocenter	C₁₀₉	C₂×#117
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #16812656	C₂	direct (N × H)
3. C₂×#13182008	C₂	semidirect
5. C₂×C₄×Dic₁₀₉	C₂	semidirect
6. C₂×C₄²×C₁₀₉	C₂	semidirect
10. C₂×C₄×D₁₀₉	C₄	semidirect
12. #13182008	C₂²	semidirect
14. C₄×Dic₁₀₉	C₂²	semidirect
17. C₄²×C₁₀₉	C₂²	semidirect
30. C₄×D₁₀₉	C₂×C₄	semidirect
41. C₂×C₁₀₉	#117	semidirect
45. C₁₀₉	C₂×#117	semidirect
52. C₂×C₄²	D₁₀₉	semidirect
63. C₄²	C₂×D₁₀₉	semidirect
88. C₂	#16812656	direct (N × H)

Subgroups — C2×#16812656 #20295480

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16812656 #20295480