Subgroups — #20294791

Order 6976.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182013	C₂	1	2	yes	maximal
2	C₂²×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#13182013	—	2	2	no	—
4	#13182013	C₄	1	4	yes	—
5	C₂×#11724784	—	2	2	no	—
6	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₀₉	—	2	2	no	—
8	C₂×C₈×C₁₀₉	C₄	1	2	yes	—
9	C₂³×C₁₀₉	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
14	C₈×C₁₀₉	—	2	2	no	—
15	#11724784	—	2	4	no	—
16	C₂²×C₁₀₉	—	2	2	no	—
17	C₂²×C₁₀₉	C₄⋊C₄	1	2	yes	—
18	C₂²×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₉	C₄²	1	1	yes	characteristic
20	C₄×C₁₀₉	C₂²⋊C₄	1	2	yes	—
21	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₁₀₉	—	2	2	no	—
23	C₂×C₁₀₉	#95	1	1	yes	characteristic
24	C₂×C₁₀₉	#108	1	2	yes	—
25	C₁₀₉	#341	1	1	yes	characteristic, complemented, Sylow
26	#341	—	109	1	no	maximal, Sylow
27	C₂×M₁₆	—	109	2	no	—
28	C₂²×C₈	D₁₀₉	1	1	yes	characteristic
29	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
30	M₁₆	—	109	4	no	—
31	M₁₆	—	218	2	no	—
32	C₂×C₈	—	2	2	no	—
33	C₂×C₈	—	218	2	no	—
34	C₂×C₈	Dic₁₀₉	1	2	yes	—
35	C₂³	Dic₂₁₈	1	1	yes	characteristic
36	C₂×C₄	C₄×D₁₀₉	1	2	yes	—
37	C₂×C₄	D₄₃₆	1	1	yes	characteristic
38	C₂×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
39	C₂×C₄	C₂²⋊D₁₀₉	1	2	yes	—
40	C₈	—	2	2	no	—
41	C₈	—	218	4	no	—
42	C₂²	—	2	2	no	—
43	C₂²	#13182008	1	2	yes	—
44	C₂²	C₄⋊Dic₁₀₉	1	1	yes	characteristic
45	C₄	C₄×Dic₁₀₉	1	1	yes	characteristic
46	C₄	#13182006	1	2	yes	—
47	C₄	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
48	C₂	—	2	2	no	—
49	C₂	#16812606	1	1	yes	characteristic
50	C₂	#16812635	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄₃₆
commutator	C₄×C₁₀₉	C₄²
Frattini	C₂²×C₄	C₂×D₁₀₉
Fitting	C₂²×C₈×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₄⋊C₄
hypercenter	C₂²×C₈	D₁₀₉
hypocenter	C₁₀₉	#341
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
25. C₁₀₉	#341	semidirect