Subgroups — #14658484

Order 2816.

366 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13069552	C₂	1	1	yes	maximal, characteristic
2	#13068618	C₂	1	2	yes	maximal
3	#13066499	C₂	1	2	yes	maximal
4	#13066451	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1845	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₂₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×#107	—	2	1	no	—
8	C₂×C₁₁×#107	—	2	1	no	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×#384	C₂²	1	2	yes	—
11	C₂×#66874	—	2	2	no	—
12	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
14	#10622188	—	2	1	no	—
15	#10622188	—	2	1	no	—
16	#10622167	—	2	2	no	—
17	C₂²×Dic₂₂	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
21	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
22	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
23	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₁	D₄	1	1	yes	characteristic
25	C₂×Dic₁₁⋊C₄	—	2	1	no	—
26	C₂×C₄×Dic₁₁	—	2	1	no	—
27	C₂²×C₁₁⋊C₈	—	2	2	no	—
28	C₂²×C₁₁⋊C₈	—	2	1	no	—
29	C₄×Dic₂₂	—	2	2	no	—
30	C₄×Dic₂₂	—	2	2	no	—
31	C₁₁×#107	—	4	2	no	—
32	C₁₁×#107	—	4	2	no	—
33	C₄×C₈×C₁₁	—	2	2	no	—
34	#66874	—	4	4	no	—
35	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
36	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
37	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
38	#10617	—	11	1	no	maximal, Sylow
39	C₂²×C₄×C₁₁	—	4	2	no	—
40	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
43	C₂²×Dic₁₁	—	2	1	no	—
44	C₂²×Dic₁₁	—	2	1	no	—
45	C₂×Dic₂₂	—	2	2	no	—
46	C₂×Dic₂₂	—	2	1	no	—
47	C₂×Dic₂₂	—	2	2	no	—
48	C₂×Dic₂₂	D₈	1	2	yes	—
49	C₂×C₈×C₁₁	—	2	1	no	—
50	C₂×C₈×C₁₁	—	2	1	no	—
51	C₂×C₈×C₁₁	—	2	1	no	—
52	C₂×C₈×C₁₁	—	2	1	no	—
53	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
54	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
55	C₁₁×C₄⋊C₄	—	4	2	no	—
56	C₁₁×C₄⋊C₄	—	4	2	no	—
57	C₁₁×C₄⋊C₄	—	4	2	no	—
58	C₁₁×C₄⋊C₄	—	4	2	no	—
59	C₁₁×C₄⋊C₄	—	8	2	no	—
60	C₄²×C₁₁	#41	1	2	yes	—
61	C₄²×C₁₁	#41	1	2	yes	—
62	C₄⋊Dic₁₁	—	2	2	no	—
63	Dic₁₁⋊C₄	—	4	2	no	—
64	C₄×Dic₁₁	—	4	1	no	—
65	C₄×Dic₁₁	—	4	1	no	—
66	C₂×C₁₁⋊C₈	—	4	2	no	—
67	C₂×C₁₁⋊C₈	—	4	1	no	—
68	C₂×C₁₁⋊C₈	—	4	2	no	—
69	C₂×C₁₁⋊C₈	—	4	1	no	—
70	C₂×C₁₁⋊C₈	—	4	2	no	—
71	C₂×C₁₁⋊C₈	—	4	1	no	—
72	#1984	—	11	1	no	—
73	#1845	D₁₁	1	1	yes	characteristic
74	#1803	—	11	2	no	—
75	#1296	—	11	2	no	—
76	#1277	—	11	1	no	—
77	C₂³×C₁₁	#121	1	1	yes	characteristic
78	C₂×C₄×C₁₁	—	2	1	no	—
79	C₂×C₄×C₁₁	—	2	1	no	—
80	C₂×C₄×C₁₁	—	8	2	no	—
81	C₂×C₄×C₁₁	—	8	2	no	—
82	C₂×C₄×C₁₁	—	8	2	no	—
83	C₂×C₄×C₁₁	#123	1	2	yes	—
84	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
85	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
86	C₂×C₄×C₁₁	#126	1	2	yes	—
87	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
91	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
92	C₂×C₄×C₁₁	#137	1	2	yes	—
93	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
94	C₂×Dic₁₁	—	2	2	no	—
95	C₂×Dic₁₁	—	4	1	no	—
96	C₂×Dic₁₁	—	4	1	no	—
97	C₂×Dic₁₁	—	4	1	no	—
98	C₂×Dic₁₁	—	4	1	no	—
99	C₂×Dic₁₁	—	4	1	no	—
100	Dic₂₂	—	2	4	no	—
101	Dic₂₂	—	4	2	no	—
102	C₈×C₁₁	—	2	2	no	—
103	C₈×C₁₁	—	2	2	no	—
104	C₁₁⋊C₈	—	8	2	no	—
105	C₁₁⋊C₈	—	8	1	no	—
106	C₂×C₄×Q₈	—	11	1	no	—
107	C₂×#107	—	2	1	no	—
108	C₂×#107	—	2	1	no	—
109	C₂×C₄⋊C₈	—	11	2	no	—
110	C₂×C₄⋊C₈	—	11	1	no	—
111	C₂×#103	—	22	2	no	—
112	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
113	#384	C₂×D₁₁	1	2	yes	—
114	#340	—	22	2	no	—
115	#336	—	22	1	no	—
116	#336	—	22	1	no	—
117	C₂²×C₁₁	#397	1	1	yes	characteristic
118	C₂²×C₁₁	#460	1	1	yes	characteristic
119	C₂²×C₁₁	#462	1	1	yes	characteristic
120	C₂²×C₁₁	#466	1	1	yes	characteristic
121	C₂²×C₁₁	#470	1	1	yes	characteristic
122	C₂²×C₁₁	#472	1	1	yes	characteristic
123	C₂²×C₁₁	#473	1	1	yes	characteristic
124	C₄×C₁₁	—	2	2	no	—
125	C₄×C₁₁	—	16	2	no	—
126	C₄×C₁₁	#480	1	2	yes	—
127	C₄×C₁₁	#483	1	1	yes	characteristic
128	C₄×C₁₁	#484	1	1	yes	characteristic
129	C₄×C₁₁	#485	1	2	yes	—
130	C₄×C₁₁	#487	1	1	yes	characteristic
131	C₄×C₁₁	#489	1	1	yes	characteristic
132	Dic₁₁	—	4	2	no	—
133	Dic₁₁	—	8	1	no	—
134	C₂²×Q₈	—	11	1	no	—
135	C₂²×C₈	—	22	2	no	—
136	C₂²×C₈	—	22	1	no	—
137	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
138	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
139	C₄×Q₈	—	22	2	no	—
140	C₄×Q₈	—	22	2	no	—
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	2	no	—
144	C₂×C₄⋊C₄	—	11	1	no	—
145	C₂×C₄⋊C₄	—	22	1	no	—
146	C₂×C₄²	—	22	1	no	—
147	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
148	#107	—	4	2	no	—
149	#107	—	4	2	no	—
150	C₄⋊C₈	—	22	2	no	—
151	C₄⋊C₈	—	22	2	no	—
152	C₄⋊C₈	—	22	2	no	—
153	#103	—	44	4	no	—
154	C₄×C₈	—	2	2	no	—
155	C₂×C₁₁	#1668	1	1	yes	characteristic
156	C₂×C₁₁	#1674	1	1	yes	characteristic
157	C₂×C₁₁	#1690	1	1	yes	characteristic
158	C₂×C₁₁	#1696	1	1	yes	characteristic
159	C₂×C₁₁	#2072	1	1	yes	characteristic
160	C₂×C₁₁	#2075	1	1	yes	characteristic
161	C₂×C₁₁	#2078	1	1	yes	characteristic
162	C₂×Q₈	—	11	2	no	—
163	C₂×Q₈	—	22	1	no	—
164	C₂×Q₈	—	22	2	no	—
165	C₂×Q₈	—	22	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	—	22	1	no	—
168	C₂²×C₄	—	22	1	no	—
169	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
170	C₂²×C₄	#4341	1	1	yes	characteristic
171	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	1	no	—
174	C₂×C₈	—	2	1	no	—
175	C₂×C₈	—	2	1	no	—
176	C₂×C₈	—	44	2	no	—
177	C₂×C₈	—	44	2	no	—
178	C₂×C₈	—	44	2	no	—
179	C₂×C₈	—	44	1	no	—
180	C₂×C₈	—	44	1	no	—
181	C₂×C₈	—	44	1	no	—
182	C₂×C₈	#4324	1	2	yes	—
183	C₂×C₈	#4326	1	2	yes	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	8	2	no	—
189	C₄⋊C₄	—	22	2	no	—
190	C₄⋊C₄	—	44	2	no	—
191	C₄²	—	44	1	no	—
192	C₄²	—	44	1	no	—
193	C₄²	#4339	1	2	yes	—
194	C₄²	#4343	1	2	yes	—
195	C₁₁	#10617	1	1	yes	characteristic, complemented, Sylow
196	C₂³	#66991	1	1	yes	characteristic
197	Q₈	—	22	4	no	—
198	Q₈	—	44	2	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	8	2	no	—
202	C₂×C₄	—	8	2	no	—
203	C₂×C₄	—	8	2	no	—
204	C₂×C₄	—	22	2	no	—
205	C₂×C₄	—	44	1	no	—
206	C₂×C₄	—	44	1	no	—
207	C₂×C₄	—	44	1	no	—
208	C₂×C₄	—	44	1	no	—
209	C₂×C₄	—	44	1	no	—
210	C₂×C₄	#66947	1	2	yes	—
211	C₂×C₄	#66951	1	2	yes	—
212	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
213	C₂×C₄	#66965	1	1	yes	characteristic
214	C₂×C₄	#66971	1	2	yes	—
215	C₂×C₄	#66982	1	1	yes	characteristic
216	C₂×C₄	#66985	1	1	yes	characteristic
217	C₂×C₄	C₂×#4324	1	1	yes	characteristic
218	C₂×C₄	#66995	1	1	yes	characteristic
219	C₂×C₄	C₂×#4326	1	1	yes	characteristic
220	C₂×C₄	#67000	1	1	yes	characteristic
221	C₈	—	2	2	no	—
222	C₈	—	2	2	no	—
223	C₈	—	88	2	no	—
224	C₈	—	88	1	no	—
225	C₂²	#10622606	1	1	yes	characteristic
226	C₂²	#10622688	1	1	yes	characteristic
227	C₂²	#10622703	1	1	yes	characteristic
228	C₂²	#10622770	1	1	yes	characteristic
229	C₂²	#10622773	1	1	yes	characteristic
230	C₂²	#10622802	1	1	yes	characteristic
231	C₂²	#10622805	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	16	2	no	—
234	C₄	—	44	2	no	—
235	C₄	—	88	1	no	—
236	C₄	#10622495	1	2	yes	—
237	C₄	#10622501	1	2	yes	—
238	C₄	#10622583	1	1	yes	characteristic
239	C₄	#10622584	1	1	yes	characteristic
240	C₄	#10622702	1	1	yes	characteristic
241	C₄	#10622706	1	1	yes	characteristic
242	C₂	#13067973	1	1	yes	characteristic
243	C₂	#13068007	1	1	yes	characteristic
244	C₂	#13068107	1	1	yes	characteristic
245	C₂	#13068141	1	1	yes	characteristic
246	C₂	#13070025	1	1	yes	characteristic
247	C₂	#13070040	1	1	yes	characteristic
248	C₂	#13070057	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66991
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1845	C₂
socle, prime radical	C₂³×C₁₁	#121
hypercenter	#1845	D₁₁
hypocenter	C₁₁	#10617
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

Complements

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

N	H ≅ G/N	type
195. C₁₁	#10617	semidirect

Maximal subgroups

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

subgroup	index
#13069552	2
#13068618	2
#13066499	2
#13066451	2
C₁₁×#1845	2
#10617	11