Subgroups — #20295906

Order 6976.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182038	C₂	1	2	yes	maximal
2	C₂×#13182008	C₂	1	1	yes	maximal, characteristic
3	#13182038	—	2	2	no	—
4	#13182038	C₄	1	4	yes	complemented
5	C₂×#11724786	—	2	2	no	—
6	C₂²×Dic₁₀₉	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₀₉	C₂²	1	1	yes	characteristic
8	#13182008	—	2	2	no	—
9	C₂²×C₄×C₁₀₉	C₄	1	1	yes	characteristic
10	C₂³×C₁₀₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₀₉	—	2	1	no	—
12	C₂×C₄×C₁₀₉	—	4	1	no	—
13	C₂×Dic₁₀₉	—	2	1	no	—
14	C₂×Dic₁₀₉	—	4	1	no	—
15	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
16	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
17	C₂×Dic₁₀₉	D₄	1	2	yes	—
18	C₂×Dic₁₀₉	Q₈	1	1	yes	characteristic
19	#11724786	—	2	4	no	—
20	C₂²×C₁₀₉	—	2	1	no	—
21	C₂²×C₁₀₉	—	2	1	no	—
22	C₂²×C₁₀₉	C₄²	1	1	yes	characteristic
23	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂²×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
25	C₄×C₁₀₉	—	4	1	no	—
26	Dic₁₀₉	—	4	1	no	—
27	Dic₁₀₉	C₂²⋊C₄	1	2	yes	—
28	Dic₁₀₉	C₄⋊C₄	1	2	yes	—
29	C₂×C₁₀₉	—	2	1	no	—
30	C₂×C₁₀₉	—	2	1	no	—
31	C₂×C₁₀₉	#95	1	1	yes	characteristic
32	C₂×C₁₀₉	#100	1	1	yes	characteristic
33	C₂×C₁₀₉	#101	1	1	yes	characteristic
34	C₁₀₉	#343	1	1	yes	characteristic, complemented, Sylow
35	#343	—	109	1	no	maximal, Sylow
36	C₂×M₁₆	—	109	2	no	—
37	C₂×C₄⋊C₄	—	109	1	no	—
38	C₂²×C₄	—	109	1	no	—
39	C₂²×C₄	—	109	1	no	—
40	C₂²×C₄	#89137	1	1	yes	characteristic
41	M₁₆	—	109	4	no	—
42	M₁₆	—	218	2	no	—
43	C₂×C₈	—	218	2	no	—
44	C₄⋊C₄	—	218	2	no	—
45	C₂³	C₂×#89137	1	1	yes	characteristic
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	109	2	no	—
49	C₂×C₄	—	109	2	no	—
50	C₂×C₄	—	109	1	no	—
51	C₂×C₄	—	109	1	no	—
52	C₂×C₄	—	436	1	no	—
53	C₂×C₄	—	218	1	no	—
54	C₈	—	218	4	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	2	1	no	—
57	C₂²	C₄×#89137	1	1	yes	characteristic
58	C₂²	C₂²⋊#89137	1	1	yes	characteristic
59	C₂²	C₄⋊#89137	1	1	yes	characteristic
60	C₄	—	4	1	no	—
61	C₄	—	109	2	no	—
62	C₄	—	109	2	no	—
63	C₄	—	436	1	no	—
64	C₂	—	2	1	no	—
65	C₂	—	2	1	no	—
66	C₂	(C₂×#89137)⋊C₄	1	1	yes	characteristic
67	C₂	#16812759	1	1	yes	characteristic
68	C₂	#16812760	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#89137
commutator	C₂²×C₁₀₉	C₄²
Frattini	C₂³	C₂×#89137
Fitting	C₂²×C₄×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²⋊C₄
hypercenter	C₂²×C₄	#89137
hypocenter	C₁₀₉	#343
LCS	G ▷ C₂²×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
4. #13182038	C₄	semidirect
34. C₁₀₉	#343	semidirect