Subgroups — #28378961

Order 13952.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295892	C₂	1	6	yes	maximal
2	#20294871	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11724786	C₂²	1	4	yes	—
4	C₂×C₄×Dic₁₀₉	C₂²	1	3	yes	—
5	#16812606	C₄	1	3	yes	—
6	#95×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂×#11724786	—	2	12	no	—
8	C₂²×Dic₁₀₉	C₂×C₄	1	3	yes	—
9	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
10	C₄×Dic₁₀₉	—	2	6	no	—
11	C₂²×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
12	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₀₉	—	2	3	no	—
14	C₂×C₄×C₁₀₉	—	2	6	no	—
15	C₂×Dic₁₀₉	—	2	3	no	—
16	C₂×Dic₁₀₉	—	2	3	no	—
17	C₂×Dic₁₀₉	—	2	3	no	—
18	C₂×Dic₁₀₉	#41	1	6	yes	—
19	#11724786	—	4	4	no	—
20	C₂²×C₁₀₉	#117	1	3	yes	—
21	C₂²×C₁₀₉	#131	1	3	yes	—
22	C₂²×C₁₀₉	#131	1	1	yes	characteristic
23	C₄×C₁₀₉	—	4	3	no	—
24	Dic₁₀₉	—	4	3	no	—
25	Dic₁₀₉	#126	1	4	yes	—
26	C₂×C₁₀₉	#383	1	1	yes	characteristic
27	C₂×C₁₀₉	#433	1	3	yes	—
28	C₂×C₁₀₉	#433	1	3	yes	—
29	#1840	—	109	1	no	maximal, Sylow
30	C₁₀₉	#1840	1	1	yes	characteristic, complemented, Sylow
31	#376	—	109	1	no	—
32	#336	—	109	6	no	—
33	C₂²×C₈	—	109	4	no	—
34	C₂×C₄²	—	109	3	no	—
35	#95	—	109	3	no	—
36	#95	#89137	1	1	yes	characteristic
37	C₂²×C₄	—	109	1	no	—
38	C₂²×C₄	—	109	3	no	—
39	C₂²×C₄	C₂×#89137	1	3	yes	—
40	C₂×C₈	—	218	12	no	—
41	C₄²	—	218	6	no	—
42	C₂³	C₂²×#89137	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	109	6	no	—
46	C₂×C₄	—	218	3	no	—
47	C₂×C₄	—	218	3	no	—
48	C₂×C₄	—	218	3	no	—
49	C₈	—	436	4	no	—
50	C₂²	#16812778	1	3	yes	—
51	C₂²	#16812786	1	3	yes	—
52	C₂²	#16812787	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	109	4	no	—
55	C₄	—	436	3	no	—
56	C₂	#20295971	1	1	yes	characteristic
57	C₂	#20296050	1	3	yes	—
58	C₂	#20296051	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#89137
commutator, socle, prime radical	C₂³×C₁₀₉	C₂²×C₄
Fitting	#95×C₁₀₉	C₄
cosocle	C₂²×Dic₁₀₉	C₂³
hypercenter	#95	#89137
hypocenter	C₁₀₉	#1840
LCS	G ▷ C₂³×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
30. C₁₀₉	#1840	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20295892	2
#20294871	2
#1840	109