Subgroups — #20294844

Order 6976.

50 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	C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11724784	C₄	1	1	yes	characteristic
5	C₄×Dic₁₀₉	C₄	1	1	yes	characteristic
6	#13182004	—	2	1	no	—
7	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₀₉	—	2	1	no	—
9	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₀₉	C₈	1	1	yes	characteristic
11	C₂×Dic₁₀₉	C₈	1	1	yes	characteristic
12	C₈×C₁₀₉	D₄	1	1	yes	characteristic
13	C₈×C₁₀₉	Q₈	1	1	yes	characteristic
14	#11724784	—	2	1	no	—
15	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
18	Dic₁₀₉	—	2	1	no	—
19	Dic₁₀₉	C₁₆	1	2	yes	complemented
20	C₂×C₁₀₉	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₁₀₉	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₀₉	M₃₂	1	1	yes	characteristic
23	C₁₀₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	109	1	no	maximal, Sylow
25	C₂×C₁₆	—	109	1	no	—
26	C₂×C₁₆	D₁₀₉	1	1	yes	characteristic
27	C₄×C₈	—	109	1	no	—
28	C₂×C₈	—	109	1	no	—
29	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
30	C₄²	—	109	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	218	1	no	—
33	C₂×C₄	—	109	1	no	—
34	C₂×C₄	—	109	1	no	—
35	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
36	C₈	—	218	1	no	—
37	C₈	Dic₂₁₈	1	1	yes	characteristic
38	C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
39	C₂²	C₈×D₁₀₉	1	1	yes	characteristic
40	C₄	—	109	2	no	—
41	C₄	—	218	1	no	—
42	C₄	#13182008	1	1	yes	characteristic
43	C₄	#13182012	1	1	yes	characteristic
44	C₂	#16812628	1	1	yes	characteristic
45	C₂	C₁₆×D₁₀₉	1	1	yes	characteristic
46	C₂	#16812638	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₂×C₁₆
Fitting	C₂×C₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×C₈
hypercenter	C₂×C₁₆	D₁₀₉
hypocenter	C₁₀₉	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₁₀₉	C₁₆	semidirect
23. C₁₀₉	C₄⋊C₁₆	semidirect