Subgroups — #20294830

Order 6976.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182004	C₂	1	1	yes	maximal, characteristic
2	#16812633	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₀₉	—	2	1	no	—
5	#13182004	—	2	1	no	—
6	C₂×Q₈×C₁₀₉	—	2	1	no	—
7	Q₁₆×C₁₀₉	—	2	1	no	—
8	Q₁₆×C₁₀₉	C₄	1	2	yes	complemented
9	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
10	Q₈×C₁₀₉	—	2	2	no	—
11	Q₈×C₁₀₉	—	4	1	no	—
12	C₂×C₄×C₁₀₉	—	4	1	no	—
13	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
14	C₂×Dic₁₀₉	—	4	1	no	—
15	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₀₉	D₄	1	1	yes	characteristic
17	C₂²×C₁₀₉	D₈	1	1	yes	characteristic
18	C₄×C₁₀₉	—	4	2	no	—
19	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₀₉	SD₁₆	1	1	yes	characteristic
21	Dic₁₀₉	—	8	1	no	—
22	C₂×C₁₀₉	#102	1	1	yes	characteristic
23	C₂×C₁₀₉	SD₃₂	1	1	yes	characteristic
24	C₂×C₁₀₉	Q₃₂	1	1	yes	characteristic
25	C₁₀₉	#358	1	1	yes	characteristic, complemented, Sylow
26	#358	—	109	1	no	maximal, Sylow
27	C₂×Q₁₆	D₁₀₉	1	1	yes	characteristic
28	C₂×C₁₆	—	109	1	no	—
29	#107	—	109	1	no	—
30	C₂×Q₈	—	2	1	no	—
31	Q₁₆	—	2	1	no	—
32	Q₁₆	Dic₁₀₉	1	2	yes	complemented
33	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
34	C₄⋊C₄	—	218	1	no	—
35	C₁₆	—	218	1	no	—
36	Q₈	—	2	2	no	—
37	Q₈	—	4	1	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	436	1	no	—
40	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
41	C₈	C₂×Dic₁₀₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
43	C₂²	#13182014	1	1	yes	characteristic
44	C₄	—	4	2	no	—
45	C₄	—	872	1	no	—
46	C₄	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
47	C₄	#13182017	1	1	yes	characteristic
48	C₂	#16812620	1	1	yes	characteristic
49	C₂	#16812642	1	1	yes	characteristic
50	C₂	#16812645	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13182014
commutator	C₈×C₁₀₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₉
Fitting	C₂×Q₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	D₈
hypercenter	C₂×Q₁₆	D₁₀₉
hypocenter	C₁₀₉	#358
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
8. Q₁₆×C₁₀₉	C₄	semidirect
25. C₁₀₉	#358	semidirect
32. Q₁₆	Dic₁₀₉	semidirect