Subgroups — #20295444

Order 6976.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812705	C₂	1	1	yes	maximal, characteristic
2	#16812638	C₂	1	2	yes	maximal, complemented
3	C₂×#13182004	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₁₀₉	C₂	1	2	yes	maximal, complemented
5	M₃₂×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#13182029	C₄	1	1	yes	characteristic
7	#13182013	C₄	1	1	yes	characteristic
8	#13182012	C₄	1	2	yes	—
9	C₈×D₁₀₉	C₂²	1	2	yes	—
10	#13182004	C₂²	1	1	yes	characteristic
11	#13182004	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₁₆×C₁₀₉	C₂²	1	2	yes	—
14	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊D₁₀₉	C₈	1	2	yes	—
16	D₄₃₆	C₈	1	1	yes	characteristic
17	C₄×D₁₀₉	C₂×C₄	1	2	yes	—
18	Dic₂₁₈	C₈	1	1	yes	characteristic
19	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
20	C₈×C₁₀₉	C₂³	1	1	yes	characteristic
21	#11724784	C₂×C₄	1	2	yes	—
22	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
23	C₂×D₁₀₉	C₂×C₈	1	2	yes	—
24	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
25	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
26	Dic₁₀₉	C₂×C₈	1	2	yes	—
27	C₂×C₁₀₉	—	2	1	no	—
28	C₂×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
29	D₁₀₉	—	2	2	no	—
30	C₁₀₉	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	109	1	no	maximal, Sylow
32	#131	—	109	1	no	—
33	M₃₂	—	109	2	no	—
34	M₃₂	D₁₀₉	1	1	yes	characteristic, complemented
35	C₂×C₁₆	—	109	1	no	—
36	C₂×C₁₆	—	109	2	no	—
37	#41	—	109	1	no	—
38	M₁₆	—	109	1	no	—
39	M₁₆	—	109	2	no	—
40	C₂×C₈	—	109	2	no	—
41	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
42	C₁₆	—	109	1	no	—
43	C₁₆	—	109	1	no	—
44	C₁₆	C₂×D₁₀₉	1	2	yes	—
45	Q₈	—	109	1	no	—
46	D₄	—	109	2	no	—
47	D₄	—	109	1	no	—
48	C₂×C₄	—	109	2	no	—
49	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
50	C₈	—	109	2	no	—
51	C₈	C₄×D₁₀₉	1	1	yes	characteristic
52	C₈	C₂²×D₁₀₉	1	1	yes	characteristic
53	C₂²	—	109	2	no	—
54	C₂²	C₈×D₁₀₉	1	1	yes	characteristic
55	C₄	—	109	2	no	—
56	C₄	C₈×D₁₀₉	1	1	yes	characteristic
57	C₄	C₂×C₄×D₁₀₉	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	218	2	no	—
60	C₂	C₂×C₈×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₁₀₉
commutator, socle	C₂×C₁₀₉	C₂²×C₈
Fitting	M₃₂×C₁₀₉	C₂
hypercenter	M₃₂	D₁₀₉
hypocenter	C₁₀₉	#504
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #16812638	C₂	semidirect
3. C₂×#13182004	C₂	semidirect
4. C₁₆×D₁₀₉	C₂	semidirect
5. M₃₂×C₁₀₉	C₂	semidirect
30. C₁₀₉	#504	semidirect
34. M₃₂	D₁₀₉	semidirect