Subgroups — #1380×C₂₁₁ #41009000

Order 27008.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#107×C₂₁₁	C₂	1	2	yes	maximal
3	C₂²×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
4	C₂×C₄⋊C₄×C₂₁₁	—	2	2	no	—
5	C₂×C₁₆×C₂₁₁	—	2	2	no	—
6	C₂×C₁₆×C₂₁₁	C₄	1	2	yes	complemented
7	#107×C₂₁₁	—	2	2	no	—
8	#107×C₂₁₁	C₄	1	4	yes	complemented
9	C₂²×C₄×C₂₁₁	—	4	2	no	—
10	C₂²×C₄×C₂₁₁	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₁₁	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₂₁₁	D₄	1	2	yes	—
14	C₂×C₈×C₂₁₁	Q₈	1	1	yes	characteristic
15	C₄⋊C₄×C₂₁₁	—	2	4	no	—
16	C₄⋊C₄×C₂₁₁	—	4	2	no	—
17	C₁₆×C₂₁₁	—	2	2	no	—
18	C₂³×C₂₁₁	D₈	1	1	yes	characteristic
19	C₂×C₄×C₂₁₁	—	4	4	no	—
20	C₂×C₄×C₂₁₁	—	8	2	no	—
21	C₂×C₄×C₂₁₁	—	8	2	no	—
22	C₂×C₄×C₂₁₁	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₂₁₁	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₁₁	SD₁₆	1	2	yes	—
25	C₂×C₄×C₂₁₁	Q₁₆	1	1	yes	characteristic
26	C₈×C₂₁₁	C₄²	1	1	yes	characteristic
27	C₈×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₂₁₁	C₄⋊C₄	1	2	yes	—
29	C₂²×C₂₁₁	#102	1	2	yes	—
30	C₂²×C₂₁₁	#107	1	1	yes	characteristic
31	C₂²×C₂₁₁	D₁₆	1	1	yes	characteristic
32	C₂²×C₂₁₁	SD₃₂	1	2	yes	—
33	C₂²×C₂₁₁	Q₃₂	1	1	yes	characteristic
34	C₄×C₂₁₁	—	8	4	no	—
35	C₄×C₂₁₁	#95	1	1	yes	characteristic
36	C₄×C₂₁₁	#103	1	2	yes	—
37	C₄×C₂₁₁	#106	1	1	yes	characteristic
38	C₂×C₂₁₁	#340	1	1	yes	characteristic
39	C₂×C₂₁₁	#357	1	2	yes	—
40	C₂×C₂₁₁	#358	1	2	yes	—
41	C₂×C₂₁₁	#366	1	1	yes	characteristic
42	C₂×C₂₁₁	#367	1	1	yes	characteristic
43	C₂₁₁	#1380	1	1	yes	characteristic, direct product factor, Sylow
44	#1380	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₁₆	C₂×C₂₁₁	1	1	yes	characteristic
46	C₂×#107	C₂×C₂₁₁	1	2	yes	—
47	C₂²×C₈	C₂²×C₂₁₁	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	C₄×C₂₁₁	1	2	yes	complemented
51	#107	—	2	2	no	—
52	#107	C₄×C₂₁₁	1	4	yes	complemented
53	C₂²×C₄	—	4	2	no	—
54	C₂²×C₄	D₄×C₂₁₁	1	1	yes	characteristic
55	C₂×C₈	C₂×C₄×C₂₁₁	1	1	yes	characteristic
56	C₂×C₈	C₂×C₄×C₂₁₁	1	2	yes	—
57	C₂×C₈	D₄×C₂₁₁	1	2	yes	—
58	C₂×C₈	Q₈×C₂₁₁	1	1	yes	characteristic
59	C₄⋊C₄	—	2	4	no	—
60	C₄⋊C₄	—	4	2	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₈×C₂₁₁	1	1	yes	characteristic
63	C₂×C₄	—	4	4	no	—
64	C₂×C₄	—	8	2	no	—
65	C₂×C₄	—	8	2	no	—
66	C₂×C₄	C₂²⋊C₄×C₂₁₁	1	2	yes	—
67	C₂×C₄	C₄⋊C₄×C₂₁₁	1	1	yes	characteristic
68	C₂×C₄	SD₁₆×C₂₁₁	1	2	yes	—
69	C₂×C₄	Q₁₆×C₂₁₁	1	1	yes	characteristic
70	C₈	C₄²×C₂₁₁	1	1	yes	characteristic
71	C₈	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
72	C₈	C₄⋊C₄×C₂₁₁	1	2	yes	—
73	C₂²	#102×C₂₁₁	1	2	yes	—
74	C₂²	#107×C₂₁₁	1	1	yes	characteristic
75	C₂²	D₁₆×C₂₁₁	1	1	yes	characteristic
76	C₂²	SD₃₂×C₂₁₁	1	2	yes	—
77	C₂²	Q₃₂×C₂₁₁	1	1	yes	characteristic
78	C₄	—	8	4	no	—
79	C₄	#95×C₂₁₁	1	1	yes	characteristic
80	C₄	#103×C₂₁₁	1	2	yes	—
81	C₄	#106×C₂₁₁	1	1	yes	characteristic
82	C₂	#340×C₂₁₁	1	1	yes	characteristic
83	C₂	#357×C₂₁₁	1	2	yes	—
84	C₂	#358×C₂₁₁	1	2	yes	—
85	C₂	#366×C₂₁₁	1	1	yes	characteristic
86	C₂	#367×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₁₁	D₈
commutator	C₈	C₄²×C₂₁₁
Frattini, cosocle	C₂²×C₈	C₂²×C₂₁₁
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₁₁ ◁ C₂²×C₄×C₂₁₁ ◁ C₂²×C₈×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₆×C₂₁₁	C₄	semidirect
8. #107×C₂₁₁	C₄	semidirect
43. C₂₁₁	#1380	direct (N × H)
44. #1380	C₂₁₁	direct (N × H)
50. C₂×C₁₆	C₄×C₂₁₁	semidirect
52. #107	C₄×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×C₂₁₁	2
C₂×#107×C₂₁₁	2
#1380	211

Subgroups — #1380×C211 #41009000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1380×C₂₁₁ #41009000