Subgroups — #14722992

Order 2816.

572 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077735	C₂	1	2	yes	maximal
2	#13077258	C₂	1	1	yes	maximal, characteristic
3	#13067403	C₂	1	2	yes	maximal, complemented
4	#13067398	C₂	1	2	yes	maximal, complemented
5	#13067395	C₂	1	2	yes	maximal, complemented
6	#13067389	C₂	1	2	yes	maximal, complemented
7	#13067384	C₂	1	2	yes	maximal, complemented
8	#13067375	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#4339	C₂²	1	1	yes	characteristic
11	C₁₁×#432	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#10622723	C₄	1	2	yes	—
14	#10622715	C₄	1	2	yes	—
15	#10622537	C₂²	1	2	yes	—
16	C₄×#4318	C₂²	1	1	yes	characteristic
17	#10622450	C₂²	1	2	yes	—
18	#10622448	C₂²	1	2	yes	—
19	#10622446	C₂²	1	2	yes	—
20	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
21	#10622342	—	2	2	no	—
22	#10622341	—	2	2	no	—
23	#10622319	—	2	2	no	—
24	#10622314	—	2	2	no	—
25	#10622303	C₄	1	4	yes	—
26	#10622298	C₂²	1	2	yes	—
27	#10622298	C₂²	1	2	yes	—
28	C₁₁×#335	C₂²	1	1	yes	characteristic
29	C₁₁×#335	C₂²	1	1	yes	characteristic
30	C₁₁×#334	C₂²	1	2	yes	—
31	#10622118	C₂²	1	2	yes	—
32	#10622118	C₂²	1	2	yes	—
33	#10622117	C₂²	1	2	yes	—
34	#10622117	C₂²	1	2	yes	—
35	#10622096	C₂²	1	2	yes	—
36	#10622096	C₂²	1	1	yes	characteristic
37	#10622096	C₂²	1	1	yes	characteristic
38	C₂×#4339	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
41	C₄×C₂²⋊D₁₁	D₄	1	2	yes	—
42	C₄×C₂²⋊D₁₁	Q₈	1	2	yes	—
43	#66979	C₂×C₄	1	1	yes	characteristic
44	C₂×#4318	—	2	2	no	—
45	C₂×#4318	C₂×C₄	1	2	yes	—
46	C₂×#4313	—	2	2	no	—
47	C₂×C₈×D₁₁	—	2	2	no	—
48	C₄×D₄₄	D₄	1	1	yes	characteristic
49	C₄×D₄₄	Q₈	1	1	yes	characteristic
50	#66925	C₂×C₄	1	2	yes	—
51	C₄²×D₁₁	C₂³	1	2	yes	—
52	C₄×Dic₂₂	D₄	1	1	yes	characteristic
53	C₄×Dic₂₂	Q₈	1	1	yes	characteristic
54	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
55	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
56	C₁₁×C₂²⋊C₈	—	2	2	no	—
57	C₁₁×#97	—	2	2	no	—
58	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
59	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	(C₂×D₁₁)⋊C₈	—	2	2	no	—
62	(C₂×D₁₁)⋊C₈	—	2	2	no	—
63	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
64	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
65	#66879	—	2	2	no	—
66	Dic₁₁⋊C₈	—	2	2	no	—
67	Dic₁₁⋊C₈	—	2	2	no	—
68	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
69	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
70	C₈×Dic₁₁	—	2	2	no	—
71	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
72	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
73	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
74	#66867	C₂×C₄	1	2	yes	—
75	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
76	#17825	—	11	1	no	maximal, Sylow
77	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
80	C₂×C₂²⋊D₁₁	C₄⋊C₄	1	2	yes	—
81	#4339	—	4	2	no	—
82	C₂×D₄₄	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
84	C₂×C₄×D₁₁	C₂×D₄	1	2	yes	—
85	C₂×C₄×D₁₁	C₂×Q₈	1	2	yes	—
86	C₂×Dic₂₂	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	—	2	2	no	—
89	C₂×C₈×C₁₁	—	4	2	no	—
90	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
92	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
95	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
96	C₂²⋊Dic₁₁	C₄⋊C₄	1	2	yes	—
97	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	2	yes	—
98	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	2	yes	—
99	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
101	Dic₁₁⋊C₄	C₄⋊C₄	1	2	yes	—
102	Dic₁₁⋊C₄	C₄⋊C₄	1	2	yes	—
103	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
104	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
105	C₄×Dic₁₁	C₂×Q₈	1	2	yes	—
106	#4318	—	4	2	no	—
107	#4318	—	8	2	no	—
108	C₂×C₁₁⋊C₈	—	2	2	no	—
109	C₂×C₁₁⋊C₈	—	2	2	no	—
110	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
111	#4313	—	8	2	no	—
112	C₈×D₁₁	—	8	2	no	—
113	#2989	—	11	2	no	—
114	#2922	—	11	1	no	—
115	#1574	—	11	2	no	—
116	#1573	—	11	2	no	—
117	#1572	—	11	2	no	—
118	#1571	—	11	2	no	—
119	#1569	—	11	2	no	—
120	#1568	D₁₁	1	1	yes	characteristic, complemented
121	#1567	—	11	1	no	—
122	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂²×D₁₁	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	1	no	—
126	C₂×C₄×C₁₁	—	2	1	no	—
127	C₂×C₄×C₁₁	—	4	1	no	—
128	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
133	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
134	C₂²⋊D₁₁	—	4	2	no	—
135	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
138	D₄₄	—	4	1	no	—
139	C₄×D₁₁	—	2	4	no	—
140	C₄×D₁₁	—	2	2	no	—
141	C₄×D₁₁	—	2	2	no	—
142	C₄×D₁₁	—	4	2	no	—
143	Dic₂₂	—	4	1	no	—
144	C₈×C₁₁	—	2	2	no	—
145	C₈×C₁₁	—	2	2	no	—
146	C₈×C₁₁	—	4	2	no	—
147	C₈×C₁₁	—	4	2	no	—
148	C₁₁⋊C₈	—	2	4	no	—
149	C₁₁⋊C₈	—	4	2	no	—
150	C₁₁⋊C₈	—	4	2	no	—
151	C₄×#41	—	11	1	no	—
152	#446	—	22	2	no	—
153	#436	—	22	2	no	—
154	#435	—	22	2	no	—
155	#435	—	22	2	no	—
156	#433	—	11	4	no	—
157	#432	—	11	2	no	—
158	#432	C₂×D₁₁	1	2	yes	—
159	#431	—	11	2	no	—
160	#431	—	11	2	no	—
161	#431	—	11	2	no	—
162	#424	—	11	2	no	—
163	#423	—	11	2	no	—
164	#423	—	11	2	no	—
165	C₂×C₄⋊C₈	—	11	2	no	—
166	#408	—	11	2	no	—
167	C₄×M₁₆	—	11	1	no	—
168	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
169	#335	—	11	2	no	—
170	#335	—	11	2	no	—
171	#335	—	11	2	no	—
172	#335	—	11	1	no	—
173	#335	—	11	1	no	—
174	#335	C₂×D₁₁	1	1	yes	characteristic
175	#335	C₂×D₁₁	1	1	yes	characteristic
176	#334	—	11	2	no	—
177	#334	—	11	2	no	—
178	#334	C₂×D₁₁	1	2	yes	—
179	C₂²×C₁₁	—	2	1	no	—
180	C₂²×C₁₁	—	2	1	no	—
181	C₂²×C₁₁	—	2	1	no	—
182	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂×D₁₁	—	2	2	no	—
184	C₂×D₁₁	—	2	2	no	—
185	C₂×D₁₁	—	2	2	no	—
186	C₄×C₁₁	—	2	1	no	—
187	C₄×C₁₁	—	2	1	no	—
188	C₄×C₁₁	—	2	1	no	—
189	C₄×C₁₁	—	2	1	no	—
190	C₄×C₁₁	#568	1	2	yes	—
191	C₄×C₁₁	#576	1	1	yes	characteristic
192	C₄×C₁₁	#578	1	1	yes	characteristic
193	Dic₁₁	—	2	2	no	—
194	Dic₁₁	—	2	2	no	—
195	Dic₁₁	—	2	2	no	—
196	C₂×#41	—	11	1	no	—
197	C₂×M₁₆	—	11	2	no	—
198	C₂×M₁₆	—	22	2	no	—
199	C₂×M₁₆	—	22	2	no	—
200	C₂²×C₈	—	22	2	no	—
201	C₂²×C₈	C₄×D₁₁	1	2	yes	—
202	C₄×Q₈	—	11	1	no	—
203	C₄×Q₈	—	11	1	no	—
204	C₄×D₄	—	11	2	no	—
205	C₄×D₄	—	11	2	no	—
206	C₄×D₄	—	11	1	no	—
207	C₄×D₄	—	11	1	no	—
208	#117	—	11	1	no	—
209	#117	—	11	2	no	—
210	C₂×C₄²	—	11	2	no	—
211	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
212	C₄⋊C₈	—	11	4	no	—
213	C₄⋊C₈	—	11	4	no	—
214	C₄⋊C₈	—	11	2	no	—
215	C₄⋊C₈	—	11	2	no	—
216	C₄⋊C₈	—	22	2	no	—
217	C₄⋊C₈	—	22	2	no	—
218	C₄⋊C₈	—	22	2	no	—
219	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
220	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
221	C₂²⋊C₈	—	2	2	no	—
222	C₂²⋊C₈	—	11	4	no	—
223	C₂²⋊C₈	—	11	4	no	—
224	C₂²⋊C₈	—	22	2	no	—
225	C₂²⋊C₈	—	22	2	no	—
226	#97	—	2	2	no	—
227	#97	—	11	2	no	—
228	#97	—	22	2	no	—
229	C₄×C₈	—	11	2	no	—
230	C₄×C₈	—	22	2	no	—
231	C₄×C₈	C₄×D₁₁	1	2	yes	—
232	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
233	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
234	C₂×C₁₁	—	4	1	no	—
235	C₂×C₁₁	#2905	1	1	yes	characteristic
236	C₂×C₁₁	#2913	1	1	yes	characteristic
237	C₂×C₁₁	#2916	1	1	yes	characteristic
238	D₁₁	—	4	2	no	—
239	#41	—	44	2	no	—
240	C₂×Q₈	—	11	1	no	—
241	C₂×D₄	—	11	2	no	—
242	C₂×D₄	—	11	1	no	—
243	C₂²×C₄	—	11	2	no	—
244	C₂²×C₄	—	11	2	no	—
245	C₂²×C₄	—	11	2	no	—
246	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
247	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
248	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
249	M₁₆	—	44	2	no	—
250	M₁₆	—	88	2	no	—
251	M₁₆	—	88	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	4	2	no	—
255	C₂×C₈	—	11	4	no	—
256	C₂×C₈	—	22	2	no	—
257	C₂×C₈	—	22	2	no	—
258	C₂×C₈	—	88	2	no	—
259	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
260	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
261	C₄⋊C₄	—	11	2	no	—
262	C₄⋊C₄	—	11	2	no	—
263	C₄⋊C₄	—	11	1	no	—
264	C₄⋊C₄	—	11	1	no	—
265	C₂²⋊C₄	—	11	2	no	—
266	C₂²⋊C₄	—	11	2	no	—
267	C₂²⋊C₄	—	11	2	no	—
268	C₄²	—	11	2	no	—
269	C₄²	—	11	2	no	—
270	C₄²	—	11	2	no	—
271	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
272	C₄²	D₄×D₁₁	1	1	yes	characteristic
273	C₄²	Q₈×D₁₁	1	1	yes	characteristic
274	C₄²	C₂³×D₁₁	1	1	yes	characteristic
275	C₁₁	#17825	1	1	yes	characteristic, complemented, Sylow
276	C₂³	—	11	2	no	—
277	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
278	Q₈	—	44	1	no	—
279	D₄	—	44	1	no	—
280	D₄	—	44	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	4	1	no	—
285	C₂×C₄	—	11	2	no	—
286	C₂×C₄	—	11	2	no	—
287	C₂×C₄	—	11	2	no	—
288	C₂×C₄	—	22	4	no	—
289	C₂×C₄	—	22	2	no	—
290	C₂×C₄	—	22	2	no	—
291	C₂×C₄	—	44	2	no	—
292	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
293	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
294	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
295	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
296	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
297	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
298	C₈	—	2	2	no	—
299	C₈	—	2	2	no	—
300	C₈	—	4	2	no	—
301	C₈	—	4	2	no	—
302	C₈	—	22	4	no	—
303	C₈	—	44	2	no	—
304	C₈	—	44	2	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	1	no	—
307	C₂²	—	2	1	no	—
308	C₂²	—	22	2	no	—
309	C₂²	—	22	2	no	—
310	C₂²	—	22	2	no	—
311	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	2	1	no	—
315	C₄	—	2	1	no	—
316	C₄	—	22	2	no	—
317	C₄	—	22	2	no	—
318	C₄	—	22	2	no	—
319	C₄	#10623276	1	2	yes	—
320	C₄	#10623300	1	1	yes	characteristic
321	C₄	#10623302	1	1	yes	characteristic
322	C₂	—	4	1	no	—
323	C₂	—	44	2	no	—
324	C₂	#13077178	1	1	yes	characteristic
325	C₂	#13077213	1	1	yes	characteristic
326	C₂	#13077224	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1568	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×#4339	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1568	D₁₁
hypocenter	C₁₁	#17825
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #13067403	C₂	semidirect
4. #13067398	C₂	semidirect
5. #13067395	C₂	semidirect
6. #13067389	C₂	semidirect
7. #13067384	C₂	semidirect
8. #13067375	C₂	semidirect
9. C₁₁×#1568	C₂	semidirect
120. #1568	D₁₁	semidirect
275. C₁₁	#17825	semidirect

Maximal subgroups

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

subgroup	index
#13077735	2
#13077258	2
#13067403	2
#13067398	2
#13067395	2
#13067389	2
#13067384	2
#13067375	2
C₁₁×#1568	2
#17825	11