Subgroups — #1420×C₂₁₁ #41009040

Order 27008.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	M₆₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	#368×C₂₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₁₁	—	2	1	no	—
5	Q₃₂×C₂₁₁	—	2	1	no	—
6	Q₃₂×C₂₁₁	C₄	1	2	yes	—
7	C₂×C₁₆×C₂₁₁	C₂²	1	1	yes	characteristic
8	#108×C₂₁₁	—	2	1	no	—
9	C₃₂×C₂₁₁	—	2	1	no	—
10	C₂×Q₈×C₂₁₁	—	4	1	no	—
11	Q₁₆×C₂₁₁	—	2	2	no	—
12	Q₁₆×C₂₁₁	—	4	1	no	—
13	M₁₆×C₂₁₁	—	4	1	no	—
14	C₂×C₈×C₂₁₁	D₄	1	1	yes	characteristic
15	C₁₆×C₂₁₁	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₁₁	D₄	1	1	yes	characteristic
17	Q₈×C₂₁₁	—	4	2	no	—
18	Q₈×C₂₁₁	—	8	1	no	—
19	C₂×C₄×C₂₁₁	—	8	1	no	—
20	C₂×C₄×C₂₁₁	D₈	1	1	yes	characteristic
21	C₈×C₂₁₁	—	8	1	no	—
22	C₈×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₂₁₁	SD₁₆	1	1	yes	characteristic
24	C₂²×C₂₁₁	SD₃₂	1	1	yes	characteristic
25	C₄×C₂₁₁	—	8	2	no	—
26	C₄×C₂₁₁	#102	1	1	yes	characteristic
27	C₄×C₂₁₁	D₁₆	1	1	yes	characteristic
28	C₂×C₂₁₁	—	2	1	no	—
29	C₂×C₂₁₁	#357	1	1	yes	characteristic
30	C₂₁₁	#1420	1	1	yes	characteristic, direct product factor, Sylow
31	#1420	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂×Q₃₂	C₂×C₂₁₁	1	1	yes	characteristic
33	M₆₄	C₂×C₂₁₁	1	1	yes	characteristic
34	#368	C₂×C₂₁₁	1	1	yes	characteristic
35	C₂×Q₁₆	—	2	1	no	—
36	Q₃₂	—	2	1	no	—
37	Q₃₂	C₄×C₂₁₁	1	2	yes	—
38	C₂×C₁₆	C₂²×C₂₁₁	1	1	yes	characteristic
39	#108	—	2	1	no	—
40	C₃₂	—	2	1	no	—
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	4	1	no	—
45	C₂×C₈	D₄×C₂₁₁	1	1	yes	characteristic
46	C₁₆	C₂×C₄×C₂₁₁	1	1	yes	characteristic
47	C₁₆	D₄×C₂₁₁	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	D₈×C₂₁₁	1	1	yes	characteristic
52	C₈	—	8	1	no	—
53	C₈	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
54	C₈	SD₁₆×C₂₁₁	1	1	yes	characteristic
55	C₂²	SD₃₂×C₂₁₁	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#102×C₂₁₁	1	1	yes	characteristic
58	C₄	D₁₆×C₂₁₁	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#357×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₁₁	#357
commutator	C₁₆	C₂×C₄×C₂₁₁
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₁₁
prime radical	C₂²×C₂₁₁	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₁₁ ◁ C₂×C₄×C₂₁₁ ◁ C₂×C₈×C₂₁₁ ◁ C₂×C₁₆×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
30. C₂₁₁	#1420	direct (N × H)
31. #1420	C₂₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×C₂₁₁	2
M₆₄×C₂₁₁	2
#368×C₂₁₁	2
#1420	211

Subgroups — #1420×C211 #41009040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1420×C₂₁₁ #41009040