Subgroups — #20295889

Order 6976.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11724786	C₂	1	2	yes	maximal
2	C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11724786	—	2	2	no	—
4	C₂×#11724784	C₄	1	1	yes	characteristic
5	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
9	C₂×Dic₁₀₉	Q₈	1	1	yes	characteristic
10	#11724786	—	4	2	no	—
11	C₈×C₁₀₉	C₈	1	2	yes	complemented
12	#11724784	—	2	1	no	—
13	C₂²×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
16	Dic₁₀₉	—	2	1	no	—
17	Dic₁₀₉	D₈	1	1	yes	characteristic
18	Dic₁₀₉	Q₁₆	1	1	yes	characteristic
19	C₂×C₁₀₉	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₁₀₉	#107	1	1	yes	characteristic
21	C₂×C₁₀₉	#108	1	1	yes	characteristic
22	C₁₀₉	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	109	1	no	maximal, Sylow
24	C₄⋊C₈	—	109	2	no	—
25	C₄×C₈	—	109	1	no	—
26	C₂×C₈	—	109	1	no	—
27	C₂×C₈	—	218	2	no	—
28	C₂×C₈	#89137	1	1	yes	characteristic
29	C₄²	—	109	1	no	—
30	C₂×C₄	—	109	1	no	—
31	C₂×C₄	—	109	1	no	—
32	C₂×C₄	C₂×#89137	1	1	yes	characteristic
33	C₈	—	436	2	no	—
34	C₈	—	218	1	no	—
35	C₈	#11724786	1	2	yes	complemented
36	C₂²	C₄⋊#89137	1	1	yes	characteristic
37	C₄	—	109	1	no	—
38	C₄	—	109	1	no	—
39	C₄	—	218	1	no	—
40	C₄	C₂×#11724786	1	1	yes	characteristic
41	C₄	#13182039	1	1	yes	characteristic
42	C₂	C₄⋊#11724786	1	1	yes	characteristic
43	C₂	#16812768	1	1	yes	characteristic
44	C₂	#16812770	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#89137
commutator	C₄×C₁₀₉	C₂×C₈
Frattini	C₂×C₄	C₂×#89137
Fitting	C₂×C₈×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₄⋊C₄
hypercenter	C₂×C₈	#89137
hypocenter	C₁₀₉	#335
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
11. C₈×C₁₀₉	C₈	semidirect
22. C₁₀₉	#335	semidirect
35. C₈	#11724786	semidirect