Subgroups — #13097049

Order 1584.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₃)⋊Dic₁₁	—	3	4	no	maximal
5	C₂²×C₃²×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₁₁×C₃⋊D₃	—	2	1	no	—
7	C₂×C₁₁×C₃⋊D₃	—	2	1	no	—
8	C₂×C₁₁×C₃⋊D₃	C₄	1	2	yes	complemented
9	C₃⋊Dic₃₃	—	2	1	no	—
10	C₃²×Dic₁₁	—	2	1	no	—
11	C₂²×D₃×C₁₁	—	3	4	no	—
12	C₂×Dic₃₃	—	3	4	no	—
13	C₂×C₃×Dic₁₁	D₃	1	4	yes	complemented
14	C₂×C₃²×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
16	C₂×C₃²×C₁₁	D₄	1	1	yes	characteristic
17	C₁₁×C₃⋊D₃	—	2	2	no	—
18	C₂²⋊Dic₁₁	—	9	1	no	Hall
19	#3752	—	11	1	no	maximal, Hall
20	C₂²×C₃×C₁₁	C₂×D₃	1	4	yes	—
21	C₂×D₃×C₁₁	—	3	8	no	—
22	C₂×D₃×C₁₁	—	6	4	no	—
23	C₂×D₃×C₁₁	—	6	4	no	—
24	Dic₃₃	—	6	4	no	—
25	C₃×Dic₁₁	—	2	4	no	—
26	C₃²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
27	C₂³×C₁₁	—	9	1	no	—
28	C₂×Dic₁₁	—	9	1	no	—
29	C₂×Dic₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented
30	C₂²×C₃⋊D₃	D₁₁	1	1	yes	characteristic
31	C₂×C₃²×C₄	—	11	1	no	—
32	C₂×C₃⋊Dic₃	—	11	1	no	—
33	C₂×C₃×C₁₁	C₄×D₃	1	4	yes	—
34	C₂×C₃×C₁₁	D₁₂	1	4	yes	—
35	C₂×C₃×C₁₁	#67	1	4	yes	—
36	D₃×C₁₁	—	6	8	no	—
37	(C₂×D₃)⋊C₄	—	33	4	no	—
38	C₂²×C₁₁	—	9	2	no	—
39	C₂²×C₁₁	—	18	1	no	—
40	C₂²×C₁₁	—	18	1	no	—
41	C₂²×C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic
42	Dic₁₁	—	2	1	no	—
43	Dic₁₁	—	18	1	no	—
44	C₂²×C₃²	C₂×D₁₁	1	1	yes	characteristic
45	C₂×C₃⋊D₃	—	2	1	no	—
46	C₂×C₃⋊D₃	—	2	1	no	—
47	C₂×C₃⋊D₃	Dic₁₁	1	2	yes	complemented
48	C₃²×C₄	—	22	1	no	—
49	C₃⋊Dic₃	—	22	1	no	—
50	C₃×C₁₁	(C₂×D₃)⋊C₄	1	4	yes	complemented
51	C₂²×D₃	—	3	4	no	—
52	C₂×C₃×C₄	—	11	4	no	—
53	C₂×Dic₃	—	33	4	no	—
54	C₂×C₁₁	—	18	2	no	—
55	C₂×C₁₁	C₄×C₃⋊D₃	1	1	yes	characteristic
56	C₂×C₁₁	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
57	C₂×C₁₁	#638	1	1	yes	characteristic
58	C₂×C₃²	C₂×Dic₁₁	1	1	yes	characteristic
59	C₂×C₃²	C₂²⋊D₁₁	1	1	yes	characteristic
60	C₂×C₃²	C₂²⋊D₁₁	1	1	yes	characteristic
61	C₃⋊D₃	—	2	2	no	—
62	C₂²⋊C₄	—	99	1	no	Sylow
63	C₂²×C₃	D₃×D₁₁	1	4	yes	—
64	C₂×D₃	—	3	8	no	—
65	C₂×D₃	—	6	4	no	—
66	C₂×D₃	—	6	4	no	—
67	C₃×C₄	—	22	4	no	—
68	Dic₃	—	66	4	no	—
69	C₁₁	#3752	1	1	yes	characteristic, complemented, Sylow
70	C₃²	C₂²⋊Dic₁₁	1	1	yes	characteristic, complemented, Sylow
71	C₂³	—	9	1	no	—
72	C₂×C₄	—	11	1	no	—
73	C₂×C₄	—	99	1	no	—
74	C₂×C₃	D₃×Dic₁₁	1	4	yes	—
75	C₂×C₃	#63140	1	4	yes	—
76	C₂×C₃	#63142	1	4	yes	—
77	D₃	—	6	8	no	—
78	C₂²	—	9	2	no	—
79	C₂²	—	18	1	no	—
80	C₂²	—	18	1	no	—
81	C₂²	C₃⋊D₃×D₁₁	1	1	yes	characteristic
82	C₄	—	22	1	no	—
83	C₄	—	198	1	no	—
84	C₃	(C₂×D₃)⋊Dic₁₁	1	4	yes	complemented
85	C₂	—	18	2	no	—
86	C₂	C₃⋊D₃×Dic₁₁	1	1	yes	characteristic
87	C₂	#11716228	1	1	yes	characteristic
88	C₂	#11716230	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	C₃⋊D₃×D₁₁
commutator	C₂×C₃²×C₁₁	C₂×C₄
Fitting, socle, cosocle	C₂²×C₃²×C₁₁	C₂²
prime radical	C₂²×C₁₁×C₃⋊D₃	C₂
hypocenter	C₃²×C₁₁	C₂²⋊C₄
LCS	G ▷ C₂×C₃²×C₁₁ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊Dic₃₃	C₂	semidirect
3. C₂×C₃²×Dic₁₁	C₂	semidirect
8. C₂×C₁₁×C₃⋊D₃	C₄	semidirect
13. C₂×C₃×Dic₁₁	D₃	semidirect
26. C₃²×C₁₁	C₂²⋊C₄	semidirect
29. C₂×Dic₁₁	C₃⋊D₃	semidirect
47. C₂×C₃⋊D₃	Dic₁₁	semidirect
50. C₃×C₁₁	(C₂×D₃)⋊C₄	semidirect
69. C₁₁	#3752	semidirect
70. C₃²	C₂²⋊Dic₁₁	semidirect
84. C₃	(C₂×D₃)⋊Dic₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×C₃⋊D₃	2
C₂×C₃⋊Dic₃₃	2
C₂×C₃²×Dic₁₁	2
(C₂×D₃)⋊Dic₁₁	3
#3752	11