Subgroups — #106×D₁₀₉ #20295055

Order 6976.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₁₀₉	C₂	1	2	yes	maximal
3	#16812631	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812630	C₂	1	2	yes	maximal, complemented
5	#106×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₀₉	—	2	2	no	—
7	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
8	C₂×#11724784	C₂²	1	1	yes	characteristic
9	C₈×D₁₀₉	C₄	1	4	yes	complemented
10	C₄⋊Dic₁₀₉	C₂²	1	2	yes	—
11	#13182008	—	2	2	no	—
12	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	—
14	C₂²×D₁₀₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₉	—	2	2	no	—
16	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₀₉	—	2	2	no	—
18	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
19	C₄×D₁₀₉	—	4	4	no	—
20	C₄×D₁₀₉	C₂×C₄	1	2	yes	—
21	C₄×D₁₀₉	Q₈	1	2	yes	—
22	C₈×C₁₀₉	C₂×C₄	1	2	yes	complemented
23	#11724784	C₂×C₄	1	2	yes	complemented
24	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
25	C₂×D₁₀₉	C₄⋊C₄	1	2	yes	—
26	C₂×D₁₀₉	SD₁₆	1	4	yes	—
27	C₄×C₁₀₉	—	4	2	no	—
28	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
30	Dic₁₀₉	—	4	2	no	—
31	Dic₁₀₉	C₄⋊C₄	1	2	yes	—
32	C₂×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₁₀₉	C₂×SD₁₆	1	2	yes	—
34	D₁₀₉	#106	1	4	yes	direct product factor
35	C₁₀₉	C₂×#106	1	1	yes	characteristic, complemented, Sylow
36	C₂×#106	—	109	1	no	maximal, Sylow
37	C₂²×C₈	—	109	1	no	—
38	C₂×C₄⋊C₄	—	109	2	no	—
39	#106	—	109	1	no	—
40	#106	—	109	2	no	—
41	#106	D₁₀₉	1	1	yes	characteristic, direct product factor
42	C₂²×C₄	—	109	1	no	—
43	C₂²×C₄	—	218	2	no	—
44	C₂×C₈	—	109	1	no	—
45	C₂×C₈	—	109	4	no	—
46	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
47	C₄⋊C₄	—	109	2	no	—
48	C₄⋊C₄	—	218	2	no	—
49	C₄⋊C₄	C₂×D₁₀₉	1	2	yes	—
50	C₂³	—	109	1	no	—
51	C₂×C₄	—	2	2	no	—
52	C₂×C₄	—	109	1	no	—
53	C₂×C₄	—	109	2	no	—
54	C₂×C₄	—	109	2	no	—
55	C₂×C₄	—	436	4	no	—
56	C₂×C₄	—	218	2	no	—
57	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
58	C₈	—	109	2	no	—
59	C₈	C₄×D₁₀₉	1	2	yes	complemented
60	C₂²	—	109	2	no	—
61	C₂²	—	109	4	no	—
62	C₂²	D₄×D₁₀₉	1	1	yes	characteristic
63	C₄	—	4	2	no	—
64	C₄	—	109	2	no	—
65	C₄	—	436	2	no	—
66	C₄	C₂×C₄×D₁₀₉	1	1	yes	characteristic
67	C₄	Q₈×D₁₀₉	1	1	yes	characteristic
68	C₂	—	109	4	no	—
69	C₂	C₄⋊C₄×D₁₀₉	1	1	yes	characteristic
70	C₂	SD₁₆×D₁₀₉	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₀₉
commutator	C₄×C₁₀₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	#106×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	#106	D₁₀₉
hypocenter	C₁₀₉	C₂×#106
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. #16812631	C₂	semidirect
4. #16812630	C₂	semidirect
5. #106×C₁₀₉	C₂	semidirect
9. C₈×D₁₀₉	C₄	semidirect
22. C₈×C₁₀₉	C₂×C₄	semidirect
23. #11724784	C₂×C₄	semidirect
34. D₁₀₉	#106	direct (N × H)
35. C₁₀₉	C₂×#106	semidirect
41. #106	D₁₀₉	direct (N × H)
59. C₈	C₄×D₁₀₉	semidirect

Subgroups — #106×D109 #20295055

Conjugacy classes of subgroups

Complements

Subgroups — #106×D₁₀₉ #20295055