Subgroups — #20294842

Order 6976.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812639	C₂	1	1	yes	maximal, characteristic
2	#16812635	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	#13182013	—	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	—
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	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₈×C₁₀₉	D₄	1	1	yes	characteristic
16	#11724784	—	4	1	no	—
17	C₂²×C₁₀₉	SD₁₆	1	1	yes	characteristic
18	C₄×C₁₀₉	—	4	2	no	—
19	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₀₉	D₈	1	1	yes	characteristic
21	C₂×C₁₀₉	—	2	1	no	—
22	C₂×C₁₀₉	#102	1	1	yes	characteristic
23	C₁₀₉	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	109	1	no	maximal, Sylow
25	C₂×Q₁₆	D₁₀₉	1	1	yes	characteristic
26	M₃₂	—	109	1	no	—
27	#108	—	109	1	no	—
28	C₂×Q₈	—	2	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	Dic₁₀₉	1	2	yes	—
31	M₁₆	—	218	1	no	—
32	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
33	C₁₆	—	218	1	no	—
34	Q₈	—	2	2	no	—
35	Q₈	—	4	1	no	—
36	C₂×C₄	—	4	1	no	—
37	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
38	C₈	—	436	1	no	—
39	C₈	C₂×Dic₁₀₉	1	1	yes	characteristic
40	C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
41	C₂²	#13182017	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
44	C₄	#13182014	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#16812620	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812620
commutator	C₈×C₁₀₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₉
Fitting	C₂×Q₁₆×C₁₀₉	C₂
socle	C₂×C₁₀₉	#102
hypercenter	C₂×Q₁₆	D₁₀₉
hypocenter	C₁₀₉	#362
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
23. C₁₀₉	#362	semidirect