Subgroups — #14644201

Order 2816.

446 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068361	C₂	1	2	yes	maximal
2	C₄×C₈×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁⋊#1273	C₂	1	2	yes	maximal
4	C₁₁⋊#1273	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂×C₈×Dic₁₁	C₄	1	2	yes	—
9	C₂×C₈×Dic₁₁	C₄	1	2	yes	—
10	C₄²×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
13	#10622188	C₄	1	4	yes	—
14	#10622188	C₄	1	4	yes	—
15	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
16	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
20	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
23	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
24	C₄×C₈×C₁₁	—	2	2	no	—
25	C₄×C₈×C₁₁	—	2	2	no	—
26	C₄×C₈×C₁₁	—	2	2	no	—
27	C₈×Dic₁₁	—	2	4	no	—
28	C₈×Dic₁₁	C₈	1	8	yes	complemented
29	C₄×C₁₁⋊C₈	—	2	1	no	—
30	C₄×C₁₁⋊C₈	—	2	2	no	—
31	C₄×C₁₁⋊C₈	—	2	1	no	—
32	C₄×C₁₁⋊C₈	—	2	2	no	—
33	#8133	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
36	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
37	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
38	C₂²×Dic₁₁	C₄²	1	2	yes	—
39	C₂×C₈×C₁₁	—	2	2	no	—
40	C₂×C₈×C₁₁	—	2	4	no	—
41	C₂×C₈×C₁₁	—	2	2	no	—
42	C₂×C₈×C₁₁	—	2	4	no	—
43	C₂×C₈×C₁₁	—	2	4	no	—
44	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
45	C₄²×C₁₁	#41	1	2	yes	—
46	C₄²×C₁₁	#41	1	1	yes	characteristic
47	C₄²×C₁₁	#41	1	1	yes	characteristic
48	C₄×Dic₁₁	—	2	4	no	—
49	C₄×Dic₁₁	—	2	4	no	—
50	C₄×Dic₁₁	C₂×C₈	1	4	yes	—
51	C₄×Dic₁₁	M₁₆	1	4	yes	—
52	C₂×C₁₁⋊C₈	—	2	2	no	—
53	C₂×C₁₁⋊C₈	—	2	4	no	—
54	C₂×C₁₁⋊C₈	—	2	2	no	—
55	C₂×C₁₁⋊C₈	—	2	4	no	—
56	C₂×C₁₁⋊C₈	—	2	4	no	—
57	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
58	#1744	—	11	2	no	—
59	C₄²×C₈	—	11	1	no	—
60	#1273	—	11	2	no	—
61	#1273	—	11	1	no	—
62	#1273	D₁₁	1	1	yes	characteristic
63	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
64	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
65	C₂×C₄×C₁₁	#117	1	2	yes	—
66	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
67	C₂×C₄×C₁₁	#117	1	2	yes	—
68	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
69	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
70	C₂×C₄×C₁₁	#131	1	4	yes	—
71	C₂×C₄×C₁₁	#131	1	4	yes	—
72	C₂×Dic₁₁	—	2	2	no	—
73	C₂×Dic₁₁	—	2	2	no	—
74	C₂×Dic₁₁	—	2	2	no	—
75	C₂×Dic₁₁	—	2	2	no	—
76	C₂×Dic₁₁	C₄×C₈	1	2	yes	—
77	C₂×Dic₁₁	C₄×C₈	1	2	yes	—
78	C₂×Dic₁₁	#97	1	4	yes	—
79	C₈×C₁₁	—	2	4	no	—
80	C₈×C₁₁	—	4	4	no	—
81	C₁₁⋊C₈	—	2	4	no	—
82	C₁₁⋊C₈	—	4	4	no	—
83	C₂×C₄×C₈	—	11	2	no	—
84	C₂×C₄×C₈	—	11	2	no	—
85	C₂×C₄×C₈	—	11	1	no	—
86	C₂×C₄×C₈	—	11	2	no	—
87	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
88	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
89	C₄³	—	11	1	no	—
90	#336	—	11	4	no	—
91	#336	—	11	4	no	—
92	C₂²×C₁₁	#376	1	1	yes	characteristic
93	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
94	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
95	C₂²×C₁₁	#405	1	2	yes	—
96	C₂²×C₁₁	#405	1	2	yes	—
97	C₄×C₁₁	#431	1	2	yes	—
98	C₄×C₁₁	#431	1	2	yes	—
99	C₄×C₁₁	#433	1	4	yes	—
100	C₄×C₁₁	#433	1	4	yes	—
101	Dic₁₁	—	2	2	no	—
102	Dic₁₁	—	2	2	no	—
103	Dic₁₁	—	2	4	no	—
104	C₂²×C₈	—	11	2	no	—
105	C₂²×C₈	—	11	4	no	—
106	C₂²×C₈	C₄×D₁₁	1	4	yes	—
107	C₂²×C₈	C₄×D₁₁	1	2	yes	—
108	C₂×C₄²	—	11	1	no	—
109	C₂×C₄²	—	11	1	no	—
110	C₂×C₄²	—	11	2	no	—
111	C₂×C₄²	—	11	2	no	—
112	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
113	C₄×C₈	—	2	2	no	—
114	C₄×C₈	—	2	2	no	—
115	C₄×C₈	—	2	2	no	—
116	C₄×C₈	—	11	8	no	—
117	C₄×C₈	—	22	4	no	—
118	C₄×C₈	—	22	1	no	—
119	C₄×C₈	—	22	2	no	—
120	C₄×C₈	—	22	1	no	—
121	C₄×C₈	—	22	2	no	—
122	C₂×C₁₁	#1450	1	1	yes	characteristic
123	C₂×C₁₁	#1450	1	1	yes	characteristic
124	C₂×C₁₁	#1452	1	2	yes	—
125	C₂×C₁₁	#1744	1	1	yes	characteristic
126	C₂×C₁₁	#1746	1	2	yes	—
127	C₂²×C₄	—	11	1	no	—
128	C₂²×C₄	—	11	1	no	—
129	C₂²×C₄	—	11	2	no	—
130	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
131	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	2	4	no	—
135	C₂×C₈	—	2	4	no	—
136	C₂×C₈	—	2	4	no	—
137	C₂×C₈	—	11	4	no	—
138	C₂×C₈	—	22	2	no	—
139	C₂×C₈	—	22	2	no	—
140	C₂×C₈	—	22	4	no	—
141	C₂×C₈	—	22	4	no	—
142	C₂×C₈	—	22	4	no	—
143	C₂×C₈	C₈×D₁₁	1	4	yes	—
144	C₄²	—	11	4	no	—
145	C₄²	—	11	4	no	—
146	C₄²	—	22	4	no	—
147	C₄²	—	22	4	no	—
148	C₄²	#4341	1	2	yes	—
149	C₄²	#4341	1	1	yes	characteristic
150	C₄²	#4343	1	1	yes	characteristic
151	C₁₁	#8133	1	1	yes	characteristic, complemented, Sylow
152	C₂³	C₄²×D₁₁	1	1	yes	characteristic
153	C₂×C₄	—	11	2	no	—
154	C₂×C₄	—	11	2	no	—
155	C₂×C₄	—	11	4	no	—
156	C₂×C₄	—	22	2	no	—
157	C₂×C₄	—	22	2	no	—
158	C₂×C₄	—	22	2	no	—
159	C₂×C₄	—	22	2	no	—
160	C₂×C₄	#66930	1	1	yes	characteristic
161	C₂×C₄	#66930	1	2	yes	—
162	C₂×C₄	#66945	1	1	yes	characteristic
163	C₂×C₄	#66945	1	2	yes	—
164	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
165	C₂×C₄	#66954	1	4	yes	—
166	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
167	C₂×C₄	#66960	1	4	yes	—
168	C₈	—	2	4	no	—
169	C₈	—	4	4	no	—
170	C₈	—	22	4	no	—
171	C₈	—	44	4	no	—
172	C₂²	#10622261	1	1	yes	characteristic
173	C₂²	C₄×C₈×D₁₁	1	1	yes	characteristic
174	C₂²	#10622302	1	2	yes	—
175	C₂²	D₁₁×#97	1	1	yes	characteristic
176	C₂²	#10622321	1	2	yes	—
177	C₄	—	22	2	no	—
178	C₄	—	22	2	no	—
179	C₄	—	22	4	no	—
180	C₄	#10622331	1	2	yes	—
181	C₄	#10622333	1	4	yes	—
182	C₄	#10622446	1	2	yes	—
183	C₄	#10622453	1	4	yes	—
184	C₂	#13066898	1	1	yes	characteristic
185	C₂	#13066901	1	1	yes	characteristic
186	C₂	#13066907	1	2	yes	—
187	C₂	#13068360	1	1	yes	characteristic
188	C₂	#13068366	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator	C₂²×C₁₁	C₂×C₄×C₈
Fitting	C₁₁×#1273	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1273	D₁₁
hypocenter	C₁₁	#8133
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ #1273

Complements

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

N	H ≅ G/N	type
28. C₈×Dic₁₁	C₈	semidirect
151. C₁₁	#8133	semidirect

Maximal subgroups

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

subgroup	index
#13068361	2
C₄×C₈×Dic₁₁	2
C₁₁⋊#1273	2
C₁₁×#1273	2
#8133	11