Subgroups — C₃×C₁₁²×Dic₂₁ #44479042

Order 30492.

392 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₁²	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×Dic₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₁²×Dic₇	—	3	1	no	maximal
4	C₃²×C₇×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₁₁²	—	2	1	no	—
6	C₂×C₃×C₇×C₁₁²	D₃	1	1	yes	characteristic
7	C₂×C₃×C₇×C₁₁²	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₁²×Dic₃	—	7	1	no	maximal, Hall
9	C₁₁²×Dic₇	—	3	1	no	Hall
10	C₃×C₁₁×Dic₂₁	C₁₁	1	12	yes	maximal, direct product factor
11	C₃×C₇×C₁₁²	—	2	1	no	—
12	C₃×C₇×C₁₁²	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₇×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented
14	C₂×C₃²×C₁₁²	D₇	1	1	yes	characteristic
15	C₂×C₇×C₁₁²	C₃×D₃	1	1	yes	characteristic
16	C₃×C₄×C₁₁²	—	21	1	no	—
17	C₁₁²×Dic₃	—	7	1	no	—
18	C₂×C₃²×C₇×C₁₁	C₂×C₁₁	1	12	yes	—
19	C₃²×C₁₁²	Dic₇	1	1	yes	characteristic, complemented, Hall
20	C₁₁×Dic₂₁	C₃×C₁₁	1	12	yes	direct product factor
21	C₃×C₁₁×Dic₇	—	3	12	no	—
22	C₇×C₁₁²	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₁₁²	—	2	1	no	—
24	C₂×C₃×C₁₁²	C₃×D₇	1	1	yes	characteristic
25	C₂×C₃×C₁₁²	D₂₁	1	1	yes	characteristic
26	C₃²×C₇×C₁₁	C₄×C₁₁	1	12	yes	complemented
27	C₄×C₁₁²	—	21	1	no	Hall
28	C₂×C₃×C₇×C₁₁	—	2	12	no	—
29	C₂×C₃×C₇×C₁₁	D₃×C₁₁	1	12	yes	—
30	C₂×C₃×C₇×C₁₁	C₂×C₃×C₁₁	1	12	yes	—
31	C₃×C₁₁×Dic₃	—	7	12	no	—
32	C₃×C₁₁²	—	2	1	no	—
33	C₃×C₁₁²	C₃×Dic₇	1	1	yes	characteristic, complemented
34	C₃×C₁₁²	Dic₂₁	1	1	yes	characteristic, direct product factor
35	C₁₁×Dic₇	—	3	12	no	—
36	C₃×Dic₂₁	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₁₁²	C₃×D₂₁	1	1	yes	characteristic
38	C₃×C₇×C₁₁	—	2	12	no	—
39	C₃×C₇×C₁₁	C₁₁×Dic₃	1	12	yes	complemented
40	C₃×C₇×C₁₁	C₃×C₄×C₁₁	1	12	yes	complemented
41	C₂×C₃²×C₁₁	C₁₁×D₇	1	12	yes	—
42	C₂×C₇×C₁₁	C₃×D₃×C₁₁	1	12	yes	—
43	C₃×C₄×C₁₁	—	21	12	no	—
44	C₁₁×Dic₃	—	7	12	no	—
45	C₂×C₃²×C₇	C₂×C₁₁²	1	1	yes	characteristic
46	C₁₁²	C₃×Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
47	C₃²×C₁₁	C₁₁×Dic₇	1	12	yes	complemented
48	Dic₂₁	C₃×C₁₁²	1	1	yes	characteristic, direct product factor
49	C₃×Dic₇	—	3	1	no	—
50	C₇×C₁₁	C₃×C₁₁×Dic₃	1	12	yes	complemented
51	C₂×C₃×C₁₁	—	2	12	no	—
52	C₂×C₃×C₁₁	C₃×C₁₁×D₇	1	12	yes	—
53	C₂×C₃×C₁₁	C₁₁×D₂₁	1	12	yes	—
54	C₃²×C₇	C₄×C₁₁²	1	1	yes	characteristic, complemented, Hall
55	C₄×C₁₁	—	21	12	no	—
56	C₂×C₃×C₇	—	2	1	no	—
57	C₂×C₃×C₇	D₃×C₁₁²	1	1	yes	characteristic
58	C₂×C₃×C₇	C₂×C₃×C₁₁²	1	1	yes	characteristic
59	C₃×Dic₃	—	7	1	no	Hall
60	C₃×C₁₁	—	2	12	no	—
61	C₃×C₁₁	C₃×C₁₁×Dic₇	1	12	yes	complemented
62	C₃×C₁₁	C₁₁×Dic₂₁	1	12	yes	direct product factor
63	Dic₇	—	3	1	no	Hall
64	C₂×C₁₁	C₃×C₁₁×D₂₁	1	12	yes	—
65	C₃×C₇	—	2	1	no	—
66	C₃×C₇	C₁₁²×Dic₃	1	1	yes	characteristic, complemented
67	C₃×C₇	C₃×C₄×C₁₁²	1	1	yes	characteristic, complemented
68	C₂×C₃²	C₁₁²×D₇	1	1	yes	characteristic
69	C₂×C₇	C₃×D₃×C₁₁²	1	1	yes	characteristic
70	C₃×C₄	—	21	1	no	—
71	Dic₃	—	7	1	no	—
72	C₁₁	C₃×C₁₁×Dic₂₁	1	12	yes	direct product factor
73	C₃²	C₁₁²×Dic₇	1	1	yes	characteristic, complemented, Sylow
74	C₇	C₃×C₁₁²×Dic₃	1	1	yes	characteristic, complemented, Sylow
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	C₃×C₁₁²×D₇	1	1	yes	characteristic
77	C₂×C₃	C₁₁²×D₂₁	1	1	yes	characteristic
78	C₄	—	21	1	no	Sylow
79	C₃	—	2	1	no	—
80	C₃	C₃×C₁₁²×Dic₇	1	1	yes	characteristic, complemented
81	C₃	C₁₁²×Dic₂₁	1	1	yes	characteristic, direct product factor
82	C₂	C₃×C₁₁²×D₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁²	D₂₁
commutator, hypocenter	C₃×C₇	C₃×C₄×C₁₁²
Frattini	C₂	C₃×C₁₁²×D₂₁
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₁²	C₂
cosocle	C₂×C₃×C₇	C₂×C₃×C₁₁²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃×C₁₁²

Complements

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

N	H ≅ G/N	type
2. C₁₁²×Dic₂₁	C₃	direct (N × H)
4. C₃²×C₇×C₁₁²	C₄	semidirect
10. C₃×C₁₁×Dic₂₁	C₁₁	direct (N × H)
12. C₃×C₇×C₁₁²	Dic₃	semidirect
13. C₃×C₇×C₁₁²	C₃×C₄	semidirect
19. C₃²×C₁₁²	Dic₇	semidirect
20. C₁₁×Dic₂₁	C₃×C₁₁	direct (N × H)
22. C₇×C₁₁²	C₃×Dic₃	semidirect
26. C₃²×C₇×C₁₁	C₄×C₁₁	semidirect
33. C₃×C₁₁²	C₃×Dic₇	semidirect
34. C₃×C₁₁²	Dic₂₁	direct (N × H)
36. C₃×Dic₂₁	C₁₁²	direct (N × H)
39. C₃×C₇×C₁₁	C₁₁×Dic₃	semidirect
40. C₃×C₇×C₁₁	C₃×C₄×C₁₁	semidirect
46. C₁₁²	C₃×Dic₂₁	direct (N × H)
47. C₃²×C₁₁	C₁₁×Dic₇	semidirect
48. Dic₂₁	C₃×C₁₁²	direct (N × H)
50. C₇×C₁₁	C₃×C₁₁×Dic₃	semidirect
54. C₃²×C₇	C₄×C₁₁²	semidirect
61. C₃×C₁₁	C₃×C₁₁×Dic₇	semidirect
62. C₃×C₁₁	C₁₁×Dic₂₁	direct (N × H)
66. C₃×C₇	C₁₁²×Dic₃	semidirect
67. C₃×C₇	C₃×C₄×C₁₁²	semidirect
72. C₁₁	C₃×C₁₁×Dic₂₁	direct (N × H)
73. C₃²	C₁₁²×Dic₇	semidirect
74. C₇	C₃×C₁₁²×Dic₃	semidirect
80. C₃	C₃×C₁₁²×Dic₇	semidirect
81. C₃	C₁₁²×Dic₂₁	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×C₃²×C₇×C₁₁²	2
C₁₁²×Dic₂₁	3
C₃×C₁₁²×Dic₇	3
C₃×C₁₁²×Dic₃	7
C₃×C₁₁×Dic₂₁	11

Subgroups — C3×C112×Dic21 #44479042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁²×Dic₂₁ #44479042