Subgroups — #20294765

Order 6976.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812687	C₂	1	1	yes	maximal, characteristic
2	#16812610	C₂	1	1	yes	maximal, characteristic, complemented
3	#97×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₂₁₈	C₄	1	1	yes	characteristic
5	C₂×D₄₃₆	C₄	1	1	yes	characteristic
6	C₂×#11724784	—	2	1	no	—
7	#13182006	—	2	1	no	—
8	#13182006	—	2	1	no	—
9	C₂×C₈×C₁₀₉	—	2	1	no	—
10	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
11	C₂²×D₁₀₉	—	2	1	no	—
12	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
15	C₂×Dic₁₀₉	—	2	1	no	—
16	D₄₃₆	—	4	1	no	—
17	Dic₂₁₈	—	4	1	no	—
18	C₈×C₁₀₉	—	2	2	no	—
19	#11724784	—	2	2	no	—
20	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×D₁₀₉	—	4	1	no	—
22	C₂×D₁₀₉	—	4	1	no	—
23	C₂×D₁₀₉	—	4	1	no	—
24	C₄×C₁₀₉	—	2	1	no	—
25	C₄×C₁₀₉	—	2	1	no	—
26	C₄×C₁₀₉	—	2	1	no	—
27	Dic₁₀₉	—	4	1	no	—
28	C₂×C₁₀₉	#100	1	1	yes	characteristic
29	C₂×C₁₀₉	#104	1	1	yes	characteristic
30	C₂×C₁₀₉	#104	1	1	yes	characteristic
31	D₁₀₉	—	8	1	no	—
32	C₁₀₉	#329	1	1	yes	characteristic, complemented, Sylow
33	#329	—	109	1	no	maximal, Sylow
34	#124	—	109	1	no	—
35	#97	—	109	1	no	—
36	#97	D₁₀₉	1	1	yes	characteristic, complemented
37	C₂×Q₈	—	109	1	no	—
38	C₂×D₄	—	109	1	no	—
39	C₂×C₈	—	2	1	no	—
40	C₂×C₈	—	218	1	no	—
41	C₂²⋊C₄	—	218	1	no	—
42	C₂²⋊C₄	—	218	1	no	—
43	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
44	C₂³	—	218	1	no	—
45	Q₈	—	436	1	no	—
46	D₄	—	436	1	no	—
47	C₂×C₄	—	218	1	no	—
48	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
49	C₂×C₄	D₄₃₆	1	1	yes	characteristic
50	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	218	2	no	—
53	C₂²	—	436	1	no	—
54	C₂²	—	436	1	no	—
55	C₂²	—	436	1	no	—
56	C₂²	#13182006	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	436	1	no	—
61	C₂	—	872	1	no	—
62	C₂	#16812615	1	1	yes	characteristic
63	C₂	#16812625	1	1	yes	characteristic
64	C₂	#16812627	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13182006
commutator	C₂×C₄×C₁₀₉	C₂×C₄
Frattini	C₄²	C₂×D₁₀₉
Fitting	#97×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²⋊C₄
hypercenter	#97	D₁₀₉
hypocenter	C₁₀₉	#329
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #16812610	C₂	semidirect
3. #97×C₁₀₉	C₂	semidirect
32. C₁₀₉	#329	semidirect
36. #97	D₁₀₉	semidirect