Subgroups — #14653934

Order 2816.

438 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068768	C₂	1	1	yes	maximal, characteristic
2	#13068469	C₂	1	1	yes	maximal, characteristic
3	#13066499	C₂	1	2	yes	maximal
4	#13066499	C₂	1	2	yes	maximal
5	C₁₁×#2859	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#125	C₄	1	2	yes	—
7	C₁₁×#389	—	2	1	no	—
8	C₁₁×#389	—	2	1	no	—
9	C₁₁×#389	—	2	1	no	—
10	C₁₁×#389	—	2	1	no	—
11	C₁₁×#384	C₂²	1	1	yes	characteristic
12	C₁₁×#384	C₂²	1	1	yes	characteristic
13	C₁₁×#382	C₄	1	2	yes	—
14	C₄³×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
16	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
17	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
19	C₂×#66867	—	2	1	no	—
20	#10622162	—	2	1	no	—
21	C₁₁×#125	—	4	4	no	—
22	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
24	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
25	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
29	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	C₂²×C₁₁⋊C₈	—	2	2	no	—
38	C₂²×C₁₁⋊C₈	—	2	2	no	—
39	C₁₁×#95	—	2	2	no	—
40	C₁₁×#95	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
43	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
44	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
45	C₄⋊(C₁₁⋊C₈)	Q₈	1	4	yes	—
46	#66867	—	4	2	no	—
47	#9906	—	11	1	no	maximal, Sylow
48	C₂²×C₄×C₁₁	—	2	2	no	—
49	C₂²×C₄×C₁₁	—	2	2	no	—
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₁₁×C₄⋊C₄	—	4	4	no	—
58	C₁₁×C₄⋊C₄	—	4	2	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₄⋊C₄	—	4	4	no	—
61	C₁₁×C₄⋊C₄	—	4	2	no	—
62	C₁₁×C₄⋊C₄	—	4	1	no	—
63	C₁₁×C₄⋊C₄	—	4	1	no	—
64	C₁₁×C₄⋊C₄	—	4	1	no	—
65	C₁₁×C₄⋊C₄	—	4	1	no	—
66	C₁₁×C₄⋊C₄	—	4	1	no	—
67	C₁₁×C₄⋊C₄	—	4	1	no	—
68	C₄²×C₁₁	—	2	2	no	—
69	C₄²×C₁₁	—	2	2	no	—
70	C₄²×C₁₁	—	2	2	no	—
71	C₄²×C₁₁	—	2	1	no	—
72	C₄²×C₁₁	—	2	1	no	—
73	C₄²×C₁₁	—	2	1	no	—
74	C₄²×C₁₁	—	2	1	no	—
75	C₄²×C₁₁	—	2	1	no	—
76	C₄²×C₁₁	—	2	1	no	—
77	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
78	C₄²×C₁₁	#41	1	2	yes	—
79	C₂×C₁₁⋊C₈	—	2	4	no	—
80	C₂×C₁₁⋊C₈	—	4	2	no	—
81	C₂×C₁₁⋊C₈	—	4	2	no	—
82	C₂×C₁₁⋊C₈	—	4	2	no	—
83	C₂×C₁₁⋊C₈	—	4	2	no	—
84	C₂×C₁₁⋊C₈	—	4	2	no	—
85	#2859	D₁₁	1	1	yes	characteristic
86	#1842	—	11	1	no	—
87	#1767	—	11	1	no	—
88	#1296	—	11	2	no	—
89	#1296	—	11	2	no	—
90	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₁	—	2	1	no	—
92	C₂×C₄×C₁₁	—	2	1	no	—
93	C₂×C₄×C₁₁	—	2	1	no	—
94	C₂×C₄×C₁₁	—	2	1	no	—
95	C₂×C₄×C₁₁	—	2	1	no	—
96	C₂×C₄×C₁₁	—	2	1	no	—
97	C₂×C₄×C₁₁	—	2	1	no	—
98	C₂×C₄×C₁₁	—	2	1	no	—
99	C₂×C₄×C₁₁	—	2	1	no	—
100	C₂×C₄×C₁₁	—	2	1	no	—
101	C₂×C₄×C₁₁	—	2	1	no	—
102	C₂×C₄×C₁₁	—	2	1	no	—
103	C₂×C₄×C₁₁	—	4	2	no	—
104	C₂×C₄×C₁₁	—	4	2	no	—
105	C₂×C₄×C₁₁	—	4	2	no	—
106	C₂×C₄×C₁₁	—	4	2	no	—
107	C₂×C₄×C₁₁	—	4	2	no	—
108	C₂×C₄×C₁₁	—	4	2	no	—
109	C₂×C₄×C₁₁	#100	1	2	yes	—
110	C₂×C₄×C₁₁	#101	1	2	yes	—
111	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
112	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
113	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
114	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
115	C₂×C₄×C₁₁	#135	1	2	yes	—
116	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
117	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
118	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
119	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
120	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
121	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
122	C₁₁⋊C₈	—	4	4	no	—
123	C₁₁⋊C₈	—	8	2	no	—
124	C₂×#125	Dic₁₁	1	2	yes	—
125	C₂×C₄⋊C₈	—	11	2	no	—
126	C₂×C₄⋊C₈	—	11	2	no	—
127	C₂×C₄⋊C₈	—	22	1	no	—
128	C₂×C₄⋊C₈	—	22	1	no	—
129	C₂×#97	—	22	1	no	—
130	#389	—	2	1	no	—
131	#389	—	2	1	no	—
132	#389	—	2	1	no	—
133	#389	—	2	1	no	—
134	#384	C₂×D₁₁	1	1	yes	characteristic
135	#384	C₂×D₁₁	1	1	yes	characteristic
136	#382	Dic₁₁	1	2	yes	—
137	C₄³	C₂×D₁₁	1	1	yes	characteristic
138	#336	—	22	1	no	—
139	C₂²×C₁₁	#391	1	1	yes	characteristic
140	C₂²×C₁₁	C₂×#100	1	1	yes	characteristic
141	C₂²×C₁₁	C₂×#101	1	1	yes	characteristic
142	C₂²×C₁₁	#416	1	1	yes	characteristic
143	C₂²×C₁₁	#417	1	1	yes	characteristic
144	C₂²×C₁₁	#417	1	1	yes	characteristic
145	C₂²×C₁₁	#417	1	1	yes	characteristic
146	C₄×C₁₁	—	2	2	no	—
147	C₄×C₁₁	—	2	2	no	—
148	C₄×C₁₁	—	2	2	no	—
149	C₄×C₁₁	—	4	1	no	—
150	C₄×C₁₁	—	4	1	no	—
151	C₄×C₁₁	—	8	2	no	—
152	C₄×C₁₁	—	8	2	no	—
153	C₄×C₁₁	#478	1	2	yes	—
154	C₄×C₁₁	#479	1	2	yes	—
155	C₄×C₁₁	#490	1	1	yes	characteristic
156	C₄×C₁₁	#491	1	1	yes	characteristic
157	C₄×C₁₁	#501	1	1	yes	characteristic
158	C₄×C₁₁	#501	1	1	yes	characteristic
159	C₂²×C₈	—	22	2	no	—
160	C₂²×C₈	—	22	2	no	—
161	#125	—	4	4	no	—
162	C₂×C₄⋊C₄	—	2	2	no	—
163	C₂×C₄⋊C₄	—	2	2	no	—
164	C₂×C₄⋊C₄	—	2	1	no	—
165	C₂×C₄⋊C₄	—	2	1	no	—
166	C₂×C₄⋊C₄	—	2	1	no	—
167	C₂×C₄⋊C₄	—	2	1	no	—
168	C₂×C₄⋊C₄	C₂×Dic₁₁	1	2	yes	—
169	C₂×C₄⋊C₄	C₂×Dic₁₁	1	2	yes	—
170	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
171	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
172	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
173	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
174	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
175	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
176	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
177	C₄⋊C₈	—	11	4	no	—
178	C₄⋊C₈	—	22	2	no	—
179	C₄⋊C₈	—	22	4	no	—
180	C₄⋊C₈	—	44	2	no	—
181	C₄⋊C₈	—	44	2	no	—
182	#97	—	44	2	no	—
183	#95	—	2	2	no	—
184	#95	—	2	2	no	—
185	C₂×C₁₁	#1551	1	1	yes	characteristic
186	C₂×C₁₁	#1552	1	1	yes	characteristic
187	C₂×C₁₁	#1560	1	1	yes	characteristic
188	C₂×C₁₁	#1561	1	1	yes	characteristic
189	C₂×C₁₁	#1989	1	1	yes	characteristic
190	C₂×C₁₁	#1992	1	1	yes	characteristic
191	C₂×C₁₁	#1997	1	1	yes	characteristic
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	2	2	no	—
194	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
195	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
196	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
197	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
198	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
200	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
201	C₂×C₈	—	22	4	no	—
202	C₂×C₈	—	44	2	no	—
203	C₂×C₈	—	44	2	no	—
204	C₂×C₈	—	44	2	no	—
205	C₂×C₈	—	44	2	no	—
206	C₂×C₈	—	44	2	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₄⋊C₄	—	4	2	no	—
209	C₄⋊C₄	—	4	4	no	—
210	C₄⋊C₄	—	4	4	no	—
211	C₄⋊C₄	—	4	1	no	—
212	C₄⋊C₄	—	4	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₄⋊C₄	—	4	2	no	—
215	C₄⋊C₄	—	4	1	no	—
216	C₄⋊C₄	—	4	1	no	—
217	C₄⋊C₄	—	4	1	no	—
218	C₄²	—	2	2	no	—
219	C₄²	—	2	2	no	—
220	C₄²	—	2	1	no	—
221	C₄²	—	2	1	no	—
222	C₄²	—	2	1	no	—
223	C₄²	—	2	2	no	—
224	C₄²	—	2	1	no	—
225	C₄²	—	2	1	no	—
226	C₄²	—	2	1	no	—
227	C₄²	Q₈×D₁₁	1	2	yes	—
228	C₄²	#4343	1	2	yes	—
229	C₁₁	#9906	1	1	yes	characteristic, complemented, Sylow
230	C₂³	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	4	2	no	—
244	C₂×C₄	—	4	2	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	4	2	no	—
248	C₂×C₄	—	4	2	no	—
249	C₂×C₄	#66897	1	2	yes	—
250	C₂×C₄	#66900	1	2	yes	—
251	C₂×C₄	#66997	1	1	yes	characteristic
252	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
253	C₂×C₄	#66999	1	2	yes	—
254	C₂×C₄	#67000	1	1	yes	characteristic
255	C₂×C₄	#67002	1	1	yes	characteristic
256	C₂×C₄	#67002	1	1	yes	characteristic
257	C₂×C₄	#67002	1	1	yes	characteristic
258	C₂×C₄	#67003	1	2	yes	—
259	C₂×C₄	#67004	1	1	yes	characteristic
260	C₂×C₄	#67004	1	1	yes	characteristic
261	C₂×C₄	#67004	1	1	yes	characteristic
262	C₈	—	44	4	no	—
263	C₈	—	88	2	no	—
264	C₂²	C₂×#66897	1	1	yes	characteristic
265	C₂²	C₂×#66900	1	1	yes	characteristic
266	C₂²	#10622843	1	1	yes	characteristic
267	C₂²	#10622845	1	1	yes	characteristic
268	C₂²	#10622845	1	1	yes	characteristic
269	C₂²	#10622845	1	1	yes	characteristic
270	C₂²	#10622846	1	1	yes	characteristic
271	C₄	—	2	2	no	—
272	C₄	—	2	2	no	—
273	C₄	—	2	2	no	—
274	C₄	—	4	1	no	—
275	C₄	—	4	1	no	—
276	C₄	—	8	2	no	—
277	C₄	—	8	2	no	—
278	C₄	#10622676	1	2	yes	—
279	C₄	#10622678	1	1	yes	characteristic
280	C₄	#10622678	1	1	yes	characteristic
281	C₄	#10622679	1	2	yes	—
282	C₄	#10622680	1	1	yes	characteristic
283	C₄	#10622682	1	1	yes	characteristic
284	C₂	#13067311	1	1	yes	characteristic
285	C₂	#13067316	1	1	yes	characteristic
286	C₂	#13067351	1	1	yes	characteristic
287	C₂	#13067354	1	1	yes	characteristic
288	C₂	#13069574	1	1	yes	characteristic
289	C₂	#13069586	1	1	yes	characteristic
290	C₂	#13069606	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₁
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2859	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2859	D₁₁
hypocenter	C₁₁	#9906
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

Complements

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

N	H ≅ G/N	type
229. C₁₁	#9906	semidirect

Maximal subgroups

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

subgroup	index
#13068768	2
#13068469	2
#13066499	2
C₁₁×#2859	2
#9906	11