Subgroups — #41013543

Order 27008.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27212901	C₂	1	6	yes	maximal
2	#376×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₁₁⋊C₈	C₂²	1	4	yes	—
4	C₂×C₄²×C₂₁₁	C₂²	1	3	yes	—
5	#95×C₂₁₁	C₄	1	4	yes	—
6	C₂×C₂₁₁⋊C₈	—	2	12	no	—
7	C₂²×C₄×C₂₁₁	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
9	C₄²×C₂₁₁	—	2	6	no	—
10	C₂₁₁⋊C₈	—	4	4	no	—
11	C₂³×C₂₁₁	C₂²×C₄	1	1	yes	characteristic
12	C₂×C₄×C₂₁₁	—	2	6	no	—
13	C₂×C₄×C₂₁₁	—	2	12	no	—
14	C₂×C₄×C₂₁₁	#41	1	6	yes	—
15	C₂²×C₂₁₁	#117	1	3	yes	—
16	C₂²×C₂₁₁	#131	1	4	yes	—
17	C₄×C₂₁₁	—	4	6	no	—
18	C₄×C₂₁₁	#126	1	4	yes	—
19	C₂×C₂₁₁	#383	1	1	yes	characteristic
20	C₂×C₂₁₁	#433	1	6	yes	—
21	C₂₁₁	#1840	1	1	yes	characteristic, complemented, Sylow
22	#1840	—	211	1	no	maximal, Sylow
23	#376	D₂₁₁	1	1	yes	characteristic
24	#336	—	211	6	no	—
25	C₂²×C₈	—	211	4	no	—
26	C₂×C₄²	C₂×D₂₁₁	1	3	yes	—
27	#95	Dic₂₁₁	1	4	yes	—
28	C₂²×C₄	C₂×Dic₂₁₁	1	6	yes	—
29	C₂²×C₄	C₂²×D₂₁₁	1	1	yes	characteristic
30	C₂×C₈	—	422	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×Dic₂₁₁	1	1	yes	characteristic
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	#16809962	1	6	yes	—
36	C₈	—	844	4	no	—
37	C₂²	#20269936	1	3	yes	—
38	C₂²	#20269984	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#20269971	1	4	yes	—
41	C₂	#27213014	1	1	yes	characteristic
42	C₂	#27213207	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₂₁₁
commutator, socle, prime radical	C₂³×C₂₁₁	C₂²×C₄
Fitting	#376×C₂₁₁	C₂
cosocle	C₂²×C₄×C₂₁₁	C₂³
hypercenter	#376	D₂₁₁
hypocenter	C₂₁₁	#1840
LCS	G ▷ C₂³×C₂₁₁ ▷ C₂₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ #376

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

N	H ≅ G/N	type
21. C₂₁₁	#1840	semidirect

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