Subgroups — #20295883

Order 6976.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812754	C₂	1	1	yes	maximal, characteristic
2	#16812754	C₂	1	1	yes	maximal, characteristic
3	#16812690	C₂	1	1	yes	maximal, characteristic
4	C₂×#11724786	—	2	1	no	—
5	C₂×#11724786	—	2	1	no	—
6	C₄⋊Dic₁₀₉	—	2	1	no	—
7	C₄⋊Dic₁₀₉	C₄	1	1	yes	characteristic
8	#13182008	—	2	1	no	—
9	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₀₉	C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₀₉	—	2	1	no	—
12	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₁₀₉	—	2	1	no	—
14	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
15	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
16	#11724786	—	2	2	no	—
17	#11724786	—	2	2	no	—
18	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₉	—	2	1	no	—
20	C₄×C₁₀₉	—	4	1	no	—
21	Dic₁₀₉	—	2	1	no	—
22	Dic₁₀₉	—	2	1	no	—
23	Dic₁₀₉	—	4	1	no	—
24	C₂×C₁₀₉	#101	1	1	yes	characteristic
25	C₂×C₁₀₉	#104	1	1	yes	characteristic
26	C₂×C₁₀₉	#104	1	1	yes	characteristic
27	C₁₀₉	#330	1	1	yes	characteristic, complemented, Sylow
28	#330	—	109	1	no	maximal, Sylow
29	#125	—	109	1	no	—
30	#97	—	109	1	no	—
31	#97	—	109	1	no	—
32	C₂×C₈	—	218	1	no	—
33	C₂×C₈	—	218	1	no	—
34	C₄⋊C₄	—	109	1	no	—
35	C₄⋊C₄	—	218	1	no	—
36	C₄⋊C₄	—	218	1	no	—
37	C₄⋊C₄	#89137	1	1	yes	characteristic
38	C₄²	—	109	1	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	—	109	1	no	—
41	C₂×C₄	—	109	1	no	—
42	C₂×C₄	—	218	1	no	—
43	C₂×C₄	C₂×#89137	1	1	yes	characteristic
44	C₈	—	218	2	no	—
45	C₈	—	218	2	no	—
46	C₂²	C₂²⋊#89137	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	4	1	no	—
49	C₄	—	436	1	no	—
50	C₄	—	218	1	no	—
51	C₄	—	218	1	no	—
52	C₂	#16812760	1	1	yes	characteristic
53	C₂	#16812763	1	1	yes	characteristic
54	C₂	#16812764	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#89137
commutator	C₂×C₄×C₁₀₉	C₂×C₄
Frattini	C₂×C₄	C₂×#89137
Fitting	C₄⋊C₄×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²⋊C₄
hypercenter	C₄⋊C₄	#89137
hypocenter	C₁₀₉	#330
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
27. C₁₀₉	#330	semidirect