Subgroups — #1839×C₂₁₁ #41009459

Order 27008.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	#336×C₂₁₁	C₂	1	6	yes	maximal
3	C₂²×C₈×C₂₁₁	C₂²	1	4	yes	—
4	C₂×C₄²×C₂₁₁	C₄	1	3	yes	—
5	C₂×C₄²×C₂₁₁	C₄	1	1	yes	characteristic
6	C₂×C₄²×C₂₁₁	C₂²	1	3	yes	—
7	C₂²×C₄×C₂₁₁	C₂×C₄	1	3	yes	—
8	C₂²×C₄×C₂₁₁	C₂×C₄	1	3	yes	—
9	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
10	C₂×C₈×C₂₁₁	—	2	12	no	—
11	C₄²×C₂₁₁	—	2	6	no	—
12	C₄²×C₂₁₁	—	2	6	no	—
13	C₄²×C₂₁₁	C₈	1	4	yes	complemented
14	C₂³×C₂₁₁	C₂²×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₁₁	—	2	3	no	—
16	C₂×C₄×C₂₁₁	—	2	3	no	—
17	C₂×C₄×C₂₁₁	—	2	3	no	—
18	C₂×C₄×C₂₁₁	—	2	3	no	—
19	C₂×C₄×C₂₁₁	C₂×C₈	1	6	yes	—
20	C₂×C₄×C₂₁₁	M₁₆	1	6	yes	—
21	C₂×C₄×C₂₁₁	#41	1	6	yes	—
22	C₈×C₂₁₁	—	4	4	no	—
23	C₂²×C₂₁₁	#117	1	3	yes	—
24	C₂²×C₂₁₁	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₂₁₁	C₂×M₁₆	1	3	yes	—
26	C₄×C₂₁₁	—	2	6	no	—
27	C₄×C₂₁₁	—	2	6	no	—
28	C₄×C₂₁₁	#126	1	4	yes	—
29	C₂×C₂₁₁	#383	1	1	yes	characteristic
30	C₂×C₂₁₁	#431	1	3	yes	—
31	C₂×C₂₁₁	#432	1	3	yes	—
32	C₂₁₁	#1839	1	1	yes	characteristic, direct product factor, Sylow
33	#1839	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₄³	C₂×C₂₁₁	1	1	yes	characteristic
35	#336	C₂×C₂₁₁	1	6	yes	—
36	C₂²×C₈	C₂²×C₂₁₁	1	4	yes	—
37	C₂×C₄²	C₄×C₂₁₁	1	3	yes	—
38	C₂×C₄²	C₄×C₂₁₁	1	1	yes	characteristic
39	C₂×C₄²	C₂²×C₂₁₁	1	3	yes	—
40	C₂²×C₄	C₂×C₄×C₂₁₁	1	3	yes	—
41	C₂²×C₄	C₂×C₄×C₂₁₁	1	3	yes	—
42	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
43	C₂×C₈	—	2	12	no	—
44	C₄²	—	2	6	no	—
45	C₄²	—	2	6	no	—
46	C₄²	C₈×C₂₁₁	1	4	yes	complemented
47	C₂³	C₂²×C₄×C₂₁₁	1	1	yes	characteristic
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	—	2	3	no	—
50	C₂×C₄	—	2	3	no	—
51	C₂×C₄	—	2	3	no	—
52	C₂×C₄	C₂×C₈×C₂₁₁	1	6	yes	—
53	C₂×C₄	M₁₆×C₂₁₁	1	6	yes	—
54	C₂×C₄	#41×C₂₁₁	1	6	yes	—
55	C₈	—	4	4	no	—
56	C₂²	#117×C₂₁₁	1	3	yes	—
57	C₂²	C₂²×C₈×C₂₁₁	1	1	yes	characteristic
58	C₂²	C₂×M₁₆×C₂₁₁	1	3	yes	—
59	C₄	—	2	6	no	—
60	C₄	—	2	6	no	—
61	C₄	#126×C₂₁₁	1	4	yes	—
62	C₂	#383×C₂₁₁	1	1	yes	characteristic
63	C₂	#431×C₂₁₁	1	3	yes	—
64	C₂	#432×C₂₁₁	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₁₁	C₂³
commutator	C₂²	C₂²×C₈×C₂₁₁
Frattini, cosocle	C₂²×C₄	C₂³×C₂₁₁
socle, prime radical	C₂³×C₂₁₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₄²×C₂₁₁	C₈	semidirect
32. C₂₁₁	#1839	direct (N × H)
33. #1839	C₂₁₁	direct (N × H)
46. C₄²	C₈×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₄³×C₂₁₁	2
#336×C₂₁₁	2
#1839	211

Subgroups — #1839×C211 #41009459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1839×C₂₁₁ #41009459