Subgroups — #14784652

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077520	C₂	1	1	yes	maximal, characteristic
2	#13070196	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070191	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070067	C₂	1	2	yes	maximal, complemented
5	#13069922	C₂	1	1	yes	maximal, characteristic
6	#13069903	C₂	1	1	yes	maximal, characteristic
7	#13069785	C₂	1	2	yes	maximal, complemented
8	#13068453	C₂	1	2	yes	maximal, complemented
9	#13068417	C₂	1	2	yes	maximal, complemented
10	#13068371	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#533	C₂²	1	1	yes	characteristic
13	#10623279	C₂²	1	1	yes	characteristic
14	C₂×#66954	C₂²	1	2	yes	—
15	C₁₁×#446	—	2	2	no	—
16	C₈×Q₈×C₁₁	—	2	2	no	—
17	C₁₁×#424	C₂²	1	1	yes	characteristic
18	C₁₁×#424	C₂²	1	1	yes	characteristic
19	C₁₁×#423	C₂²	1	1	yes	characteristic
20	C₁₁×#405	C₂²	1	1	yes	characteristic
21	C₁₁×#405	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	#10622745	C₂²	1	2	yes	—
24	#10622738	C₂²	1	1	yes	characteristic
25	#10622726	C₂²	1	2	yes	—
26	#10622714	C₂²	1	2	yes	—
27	#10622619	C₂²	1	2	yes	—
28	#10622618	C₂²	1	2	yes	—
29	C₂×#66869	C₂²	1	2	yes	—
30	#10622330	—	2	2	no	—
31	#10622313	—	2	2	no	—
32	C₁₁⋊#338	C₂²	1	1	yes	characteristic
33	#10622197	C₂²	1	2	yes	—
34	#10622195	C₂²	1	1	yes	characteristic
35	#10622190	C₂²	1	2	yes	—
36	#10622171	C₂²	1	2	yes	—
37	#10622169	C₂²	1	2	yes	—
38	#10622161	C₂²	1	2	yes	—
39	C₂×#4339	C₂³	1	2	yes	—
40	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
41	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×C₄⋊Q₈	—	2	1	no	—
45	C₁₁×#125	—	2	1	no	—
46	C₁₁×C₂²⋊Q₈	—	2	2	no	—
47	C₄×Q₈×C₁₁	—	2	2	no	—
48	C₁₁×#117	C₂³	1	1	yes	characteristic
49	C₁₁×#117	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	#66979	C₂³	1	2	yes	—
52	C₂×#4318	C₂³	1	2	yes	—
53	C₂×#4318	C₂³	1	2	yes	—
54	#66962	—	2	2	no	—
55	#66961	—	2	2	no	—
56	#66957	—	2	2	no	—
57	#66954	—	2	2	no	—
58	#66954	—	2	2	no	—
59	#66954	—	2	2	no	—
60	#66954	—	2	2	no	—
61	C₂×#4313	—	2	2	no	—
62	C₂×C₈×D₁₁	—	2	2	no	—
63	C₁₁×C₄⋊C₈	—	2	2	no	—
64	C₁₁×C₄⋊C₈	—	2	2	no	—
65	C₁₁×C₄⋊C₈	—	2	2	no	—
66	C₁₁×#97	—	2	1	no	—
67	C₁₁×#97	D₄	1	2	yes	—
68	C₄×C₈×C₁₁	—	2	1	no	—
69	C₄×C₈×C₁₁	—	2	1	no	—
70	C₄×C₈×C₁₁	—	2	1	no	—
71	C₄×C₈×C₁₁	D₄	1	2	yes	—
72	#66888	—	2	2	no	—
73	#66887	—	2	2	no	—
74	#66885	—	2	2	no	—
75	#66883	—	2	2	no	—
76	#66880	—	2	2	no	—
77	#66879	—	2	2	no	—
78	C₈×Dic₁₁	—	2	2	no	—
79	#66870	—	2	4	no	—
80	#66869	—	2	4	no	—
81	#66869	—	2	2	no	—
82	#66869	—	2	2	no	—
83	#23833	—	11	1	no	maximal, Sylow
84	C₂×Q₈×C₁₁	—	2	2	no	—
85	C₂²×C₄×C₁₁	—	2	1	no	—
86	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
87	C₂×C₂²⋊D₁₁	—	2	2	no	—
88	#4339	—	2	2	no	—
89	#4339	—	2	2	no	—
90	#4339	—	2	2	no	—
91	#4339	—	2	2	no	—
92	C₂×D₄₄	#41	1	2	yes	—
93	C₂×C₄×D₁₁	—	2	2	no	—
94	C₂×Dic₂₂	#41	1	2	yes	—
95	C₁₁×M₁₆	—	2	2	no	—
96	C₁₁×M₁₆	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	1	no	—
98	C₂×C₈×C₁₁	—	2	1	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₂×C₈×C₁₁	#41	1	2	yes	—
104	C₂×C₈×C₁₁	#41	1	2	yes	—
105	C₁₁×C₄⋊C₄	—	2	4	no	—
106	C₁₁×C₄⋊C₄	—	2	2	no	—
107	C₁₁×C₄⋊C₄	—	2	1	no	—
108	C₁₁×C₄⋊C₄	—	2	1	no	—
109	C₁₁×C₂²⋊C₄	—	2	1	no	—
110	C₁₁×C₂²⋊C₄	#41	1	2	yes	—
111	C₄²×C₁₁	—	2	1	no	—
112	C₄²×C₁₁	—	2	1	no	—
113	C₄²×C₁₁	C₂×D₄	1	2	yes	—
114	C₄²×C₁₁	#41	1	1	yes	characteristic
115	C₄²×C₁₁	#41	1	1	yes	characteristic
116	C₂²⋊Dic₁₁	—	2	2	no	—
117	C₄⋊Dic₁₁	—	2	2	no	—
118	C₄×Dic₁₁	—	2	2	no	—
119	#4318	—	2	2	no	—
120	#4318	—	2	2	no	—
121	#4318	—	2	2	no	—
122	#4318	—	2	2	no	—
123	C₂×C₁₁⋊C₈	—	2	2	no	—
124	C₂×C₁₁⋊C₈	—	2	2	no	—
125	Dic₄₄	—	2	2	no	—
126	D₈₈	—	2	2	no	—
127	#4314	—	2	4	no	—
128	#4313	—	4	2	no	—
129	#4313	—	4	2	no	—
130	C₈×D₁₁	—	4	2	no	—
131	C₈×D₁₁	—	4	2	no	—
132	#2960	D₁₁	1	1	yes	characteristic, complemented
133	#2955	—	11	1	no	—
134	#2103	—	11	1	no	—
135	#2102	—	11	1	no	—
136	#2080	—	11	2	no	—
137	#2053	—	11	1	no	—
138	#2050	—	11	1	no	—
139	#2031	—	11	2	no	—
140	#1764	—	11	2	no	—
141	#1757	—	11	2	no	—
142	#1747	—	11	1	no	—
143	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
144	C₂²×D₁₁	—	2	2	no	—
145	Q₈×C₁₁	—	4	4	no	—
146	C₂×C₄×C₁₁	—	2	1	no	—
147	C₂×C₄×C₁₁	—	2	1	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	4	2	no	—
151	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
154	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
155	C₂²⋊D₁₁	—	4	2	no	—
156	C₂²⋊D₁₁	—	4	2	no	—
157	C₂×Dic₁₁	—	2	2	no	—
158	C₂×Dic₁₁	—	4	2	no	—
159	D₄₄	—	2	2	no	—
160	D₄₄	—	2	2	no	—
161	C₄×D₁₁	—	4	2	no	—
162	C₄×D₁₁	—	4	2	no	—
163	Dic₂₂	—	2	2	no	—
164	Dic₂₂	—	2	2	no	—
165	C₈×C₁₁	—	2	2	no	—
166	C₈×C₁₁	—	4	1	no	—
167	C₈×C₁₁	—	4	1	no	—
168	C₈×C₁₁	#124	1	2	yes	—
169	C₈×C₁₁	#124	1	1	yes	characteristic
170	C₈×C₁₁	#124	1	1	yes	characteristic
171	C₁₁⋊C₈	—	4	2	no	—
172	C₁₁⋊C₈	—	4	2	no	—
173	#575	—	11	1	no	—
174	C₂×#131	—	11	2	no	—
175	#533	C₂×D₁₁	1	1	yes	characteristic
176	#446	—	2	2	no	—
177	C₈×Q₈	—	2	2	no	—
178	#444	—	22	2	no	—
179	#443	—	22	2	no	—
180	#430	—	11	1	no	—
181	#424	C₂×D₁₁	1	1	yes	characteristic
182	#424	C₂×D₁₁	1	1	yes	characteristic
183	#423	C₂×D₁₁	1	1	yes	characteristic
184	#421	—	11	2	no	—
185	C₂×#104	—	11	2	no	—
186	#416	—	11	2	no	—
187	#413	—	11	2	no	—
188	#410	—	11	2	no	—
189	#405	—	11	2	no	—
190	#405	C₂×D₁₁	1	1	yes	characteristic
191	#405	C₂×D₁₁	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
193	#344	—	11	2	no	—
194	#344	—	11	2	no	—
195	#341	—	11	2	no	—
196	#339	—	11	2	no	—
197	#338	—	11	1	no	—
198	H(3,ℤ/4)	—	11	1	no	—
199	H(3,ℤ/4)	—	11	2	no	—
200	C₂²×C₁₁	—	4	1	no	—
201	C₂²×C₁₁	#525	1	1	yes	characteristic
202	C₂²×C₁₁	#529	1	2	yes	—
203	C₂×D₁₁	—	4	2	no	—
204	C₂×D₁₁	—	8	2	no	—
205	C₄×C₁₁	—	2	2	no	—
206	C₄×C₁₁	—	4	1	no	—
207	C₄×C₁₁	—	4	2	no	—
208	C₄×C₁₁	—	4	2	no	—
209	C₄×C₁₁	#525	1	1	yes	characteristic
210	C₄×C₁₁	C₂×#124	1	1	yes	characteristic
211	C₄×C₁₁	#529	1	2	yes	—
212	Dic₁₁	—	4	2	no	—
213	Dic₁₁	—	8	2	no	—
214	C₂×#41	—	11	2	no	—
215	#137	—	22	2	no	—
216	AGL(1,ℤ/8)	—	22	2	no	—
217	#135	—	22	2	no	—
218	#131	—	22	2	no	—
219	#131	—	22	2	no	—
220	#131	—	22	2	no	—
221	#131	—	22	2	no	—
222	C₂×M₁₆	—	11	2	no	—
223	C₂×M₁₆	—	11	2	no	—
224	C₂×M₁₆	—	22	2	no	—
225	C₂×M₁₆	C₂²×D₁₁	1	1	yes	characteristic
226	C₂×M₁₆	C₂²×D₁₁	1	1	yes	characteristic
227	C₂²×C₈	—	22	2	no	—
228	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
229	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
230	C₄⋊Q₈	—	2	1	no	—
231	#125	—	2	1	no	—
232	C₂²⋊Q₈	—	2	2	no	—
233	C₄×Q₈	—	2	2	no	—
234	#117	—	11	2	no	—
235	#117	C₂²×D₁₁	1	1	yes	characteristic
236	#117	C₂²×D₁₁	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
238	#108	—	22	2	no	—
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	#104	—	22	2	no	—
243	#104	—	22	2	no	—
244	#104	—	22	4	no	—
245	#103	—	22	2	no	—
246	#102	—	22	2	no	—
247	#101	—	22	2	no	—
248	#100	—	22	2	no	—
249	#99	—	22	4	no	—
250	#97	—	2	1	no	—
251	#97	—	22	2	no	—
252	#97	C₂²⋊D₁₁	1	2	yes	—
253	C₄×C₈	—	2	1	no	—
254	C₄×C₈	—	2	1	no	—
255	C₄×C₈	—	2	1	no	—
256	C₄×C₈	—	22	2	no	—
257	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
258	C₂×C₁₁	—	2	2	no	—
259	C₂×C₁₁	—	2	1	no	—
260	C₂×C₁₁	#2398	1	1	yes	characteristic
261	D₁₁	—	8	2	no	—
262	#41	—	22	2	no	—
263	#41	—	22	2	no	—
264	#41	—	22	2	no	—
265	#41	—	22	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	11	2	no	—
268	C₂×D₄	—	11	2	no	—
269	C₂×D₄	—	22	2	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	22	2	no	—
272	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
273	Q₁₆	—	22	2	no	—
274	SD₁₆	—	22	4	no	—
275	D₈	—	22	2	no	—
276	M₁₆	—	2	2	no	—
277	M₁₆	—	2	2	no	—
278	M₁₆	—	22	2	no	—
279	M₁₆	—	22	2	no	—
280	M₁₆	—	22	2	no	—
281	M₁₆	—	22	2	no	—
282	M₁₆	—	44	2	no	—
283	M₁₆	—	44	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	22	2	no	—
288	C₂×C₈	—	22	2	no	—
289	C₂×C₈	—	44	2	no	—
290	C₂×C₈	—	44	2	no	—
291	C₂×C₈	#4343	1	2	yes	—
292	C₂×C₈	#4343	1	2	yes	—
293	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
294	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
295	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	22	2	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	22	2	no	—
303	C₂²⋊C₄	#4339	1	2	yes	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	22	2	no	—
307	C₄²	#4339	1	1	yes	characteristic
308	C₄²	#4339	1	1	yes	characteristic
309	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
310	C₁₁	#23833	1	1	yes	characteristic, complemented, Sylow
311	C₂³	—	22	2	no	—
312	C₂³	C₂×#4339	1	1	yes	characteristic
313	Q₈	—	4	4	no	—
314	Q₈	—	22	2	no	—
315	Q₈	—	22	2	no	—
316	D₄	—	22	2	no	—
317	D₄	—	22	2	no	—
318	D₄	—	44	2	no	—
319	D₄	—	44	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	22	2	no	—
326	C₂×C₄	—	44	2	no	—
327	C₂×C₄	—	44	2	no	—
328	C₂×C₄	—	44	2	no	—
329	C₂×C₄	C₂×#4339	1	1	yes	characteristic
330	C₂×C₄	C₂×#4343	1	2	yes	—
331	C₂×C₄	#41×D₁₁	1	2	yes	—
332	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
333	C₈	—	2	2	no	—
334	C₈	—	4	1	no	—
335	C₈	—	4	1	no	—
336	C₈	—	44	2	no	—
337	C₈	—	44	2	no	—
338	C₈	#67000	1	2	yes	—
339	C₈	#67000	1	1	yes	characteristic
340	C₈	#67000	1	1	yes	characteristic
341	C₂²	—	4	1	no	—
342	C₂²	—	44	2	no	—
343	C₂²	—	88	2	no	—
344	C₂²	#10623111	1	2	yes	—
345	C₂²	#10623322	1	1	yes	characteristic
346	C₄	—	2	2	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	2	no	—
349	C₄	—	4	2	no	—
350	C₄	—	44	2	no	—
351	C₄	—	88	2	no	—
352	C₄	#10623111	1	2	yes	—
353	C₄	C₂×#67000	1	1	yes	characteristic
354	C₄	#10623359	1	1	yes	characteristic
355	C₂	—	2	1	no	—
356	C₂	—	2	2	no	—
357	C₂	—	88	2	no	—
358	C₂	#13071899	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#67000
commutator, cosocle	C₂²×C₄×C₁₁	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₁₁×#2960	C₂
socle	C₂×C₁₁	#2398
prime radical	#10623279	C₂²
hypercenter	#2960	D₁₁
hypocenter	C₁₁	#23833
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
2. #13070196	C₂	semidirect
3. #13070191	C₂	semidirect
4. #13070067	C₂	semidirect
7. #13069785	C₂	semidirect
8. #13068453	C₂	semidirect
9. #13068417	C₂	semidirect
10. #13068371	C₂	semidirect
11. C₁₁×#2960	C₂	semidirect
132. #2960	D₁₁	semidirect
310. C₁₁	#23833	semidirect

Maximal subgroups

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

subgroup	index
#13077520	2
#13070196	2
#13070191	2
#13070067	2
#13069922	2
#13069903	2
#13069785	2
#13068453	2
#13068417	2
#13068371	2
C₁₁×#2960	2
#23833	11