Subgroups — #20295404

Order 6976.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#13182019	C₂	1	2	yes	maximal
3	#16812697	C₂	1	2	yes	maximal
4	C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₁₈	C₂²	1	2	yes	—
7	Dic₄₃₆	—	2	2	no	—
8	#13182019	—	2	4	no	—
9	C₂×#11724784	C₂²	1	1	yes	characteristic
10	#13182008	—	2	4	no	—
11	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₁₀₉	C₂²	1	2	yes	—
13	Q₁₆×C₁₀₉	—	2	2	no	—
14	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
15	Q₈×C₁₀₉	—	2	2	no	—
16	Q₈×C₁₀₉	—	2	2	no	—
17	C₂×C₄×C₁₀₉	—	2	2	no	—
18	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₉	—	2	2	no	—
20	C₂×Dic₁₀₉	D₄	1	2	yes	—
21	Dic₂₁₈	—	2	2	no	—
22	Dic₂₁₈	—	2	2	no	—
23	C₈×C₁₀₉	D₄	1	2	yes	—
24	#11724784	D₄	1	2	yes	—
25	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
26	C₄×C₁₀₉	—	4	2	no	—
27	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
29	Dic₁₀₉	—	4	2	no	—
30	Dic₁₀₉	Q₁₆	1	4	yes	complemented
31	C₂×C₁₀₉	#127	1	1	yes	characteristic
32	C₂×C₁₀₉	C₂×Q₁₆	1	2	yes	—
33	C₁₀₉	#494	1	1	yes	characteristic, complemented, Sylow
34	#494	—	109	1	no	maximal, Sylow
35	C₂×Q₁₆	—	109	2	no	—
36	C₂×Q₁₆	—	109	1	no	—
37	C₂×Q₁₆	D₁₀₉	1	1	yes	characteristic
38	C₄⋊Q₈	—	109	2	no	—
39	C₄×C₈	—	109	1	no	—
40	C₂×Q₈	—	109	2	no	—
41	C₂×Q₈	C₂×D₁₀₉	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	218	4	no	—
44	Q₁₆	—	218	2	no	—
45	C₂×C₈	—	109	1	no	—
46	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
47	C₄⋊C₄	—	218	4	no	—
48	C₄²	—	109	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	218	2	no	—
52	Q₈	—	218	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	109	2	no	—
55	C₂×C₄	—	218	2	no	—
56	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
57	C₈	—	109	2	no	—
58	C₈	C₂²⋊D₁₀₉	1	2	yes	—
59	C₂²	D₄×D₁₀₉	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	109	4	no	—
62	C₄	—	436	2	no	—
63	C₄	D₄×D₁₀₉	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
65	C₂	#16812695	1	1	yes	characteristic
66	C₂	Q₁₆×D₁₀₉	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₀₉
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₂×Q₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	C₂×Q₁₆	D₁₀₉
hypocenter	C₁₀₉	#494
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
30. Dic₁₀₉	Q₁₆	semidirect
33. C₁₀₉	#494	semidirect