Subgroups — #14909373

Order 2816.

532 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079266	C₂	1	1	yes	maximal, characteristic, complemented
2	#13070892	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070865	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070859	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070857	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070717	C₂	1	2	yes	maximal, complemented
7	#13070700	C₂	1	2	yes	maximal, complemented
8	#13070490	C₂	1	2	yes	maximal, complemented
9	C₄×#66890	C₂	1	2	yes	maximal, complemented
10	#13070213	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#3176	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#540	—	2	1	no	—
13	#10623066	—	2	1	no	—
14	C₁₁×#499	C₂²	1	1	yes	characteristic
15	C₁₁×#493	C₂²	1	1	yes	characteristic
16	C₁₁×#490	—	2	1	no	—
17	C₁₁×#469	—	2	1	no	—
18	C₁₁×#466	C₂²	1	2	yes	—
19	C₁₁×#442	—	2	1	no	—
20	C₄×C₁₁×D₈	C₂²	1	2	yes	—
21	C₁₁×#405	C₂²	1	1	yes	characteristic
22	C₂×#66890	C₂²	1	2	yes	—
23	C₂×#66890	C₂²	1	2	yes	—
24	#10622748	—	2	1	no	—
25	#10622728	C₂²	1	2	yes	—
26	C₂×#66876	C₂²	1	1	yes	characteristic
27	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
28	#10622326	—	2	1	no	—
29	#10622324	—	2	1	no	—
30	#10622308	C₂²	1	1	yes	characteristic
31	C₄×D₈₈	C₂²	1	2	yes	—
32	#10622296	C₂²	1	1	yes	characteristic
33	#10622200	C₂²	1	2	yes	—
34	#10622200	C₂²	1	2	yes	—
35	#10622129	C₂²	1	2	yes	—
36	#10622129	C₂²	1	2	yes	—
37	#10622128	C₂²	1	2	yes	—
38	#10622127	C₂²	1	2	yes	—
39	#10622099	C₂²	1	1	yes	characteristic
40	#10622099	C₂²	1	1	yes	characteristic
41	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₂×C₁₁×D₈	—	2	1	no	—
44	C₂×C₁₁×D₈	C₂³	1	2	yes	—
45	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₁₁×#127	—	2	1	no	—
48	C₁₁×#125	—	2	1	no	—
49	C₁₁×#123	—	4	2	no	—
50	C₁₁×#121	—	2	2	no	—
51	C₁₁×#121	—	4	2	no	—
52	C₄×D₄×C₁₁	—	2	2	no	—
53	C₁₁×#117	D₄	1	1	yes	characteristic
54	#66983	—	2	2	no	—
55	C₂×D₈₈	—	2	1	no	—
56	C₂×D₈₈	C₂³	1	2	yes	—
57	#66947	—	4	2	no	—
58	#66937	—	4	2	no	—
59	#66927	—	2	1	no	—
60	C₄×D₄₄	—	2	2	no	—
61	#66923	—	2	1	no	—
62	C₁₁×#107	C₂³	1	2	yes	—
63	C₁₁×#106	—	2	1	no	—
64	C₁₁×#102	—	2	2	no	—
65	C₁₁×#102	—	2	2	no	—
66	C₁₁×#97	D₄	1	1	yes	characteristic
67	C₁₁×#97	D₄	1	1	yes	characteristic
68	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	#66890	—	2	4	no	—
71	#66890	—	2	4	no	—
72	#66885	—	2	2	no	—
73	#66885	—	2	2	no	—
74	#66882	C₂³	1	2	yes	—
75	#66881	—	2	1	no	—
76	#66876	—	2	2	no	—
77	C₂×C₁₁⋊C₁₆	—	2	2	no	—
78	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
82	#33740	—	11	1	no	maximal, Sylow
83	C₂×D₄×C₁₁	—	2	2	no	—
84	C₂×D₄×C₁₁	—	4	2	no	—
85	C₂×D₄×C₁₁	—	4	2	no	—
86	C₂²×C₄×C₁₁	—	4	2	no	—
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂×C₂²⋊D₁₁	—	4	2	no	—
89	C₂×D₄₄	—	2	2	no	—
90	C₂×D₄₄	—	4	2	no	—
91	C₂×C₄×D₁₁	—	4	2	no	—
92	C₁₁×D₈	—	2	2	no	—
93	C₁₁×D₈	—	2	2	no	—
94	C₁₁×D₈	—	4	2	no	—
95	C₁₁×M₁₆	—	2	2	no	—
96	C₂×C₈×C₁₁	—	2	1	no	—
97	C₂×C₈×C₁₁	—	2	1	no	—
98	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	—	4	2	no	—
104	C₁₁×C₄⋊C₄	D₈	1	2	yes	—
105	C₁₁×C₂²⋊C₄	—	4	2	no	—
106	C₁₁×C₂²⋊C₄	—	4	2	no	—
107	C₁₁×C₂²⋊C₄	D₈	1	2	yes	—
108	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
110	(C₂×D₁₁)⋊C₄	—	4	2	no	—
111	(C₂×D₁₁)⋊C₄	—	4	2	no	—
112	C₄⋊Dic₁₁	—	2	2	no	—
113	Dic₁₁⋊C₄	—	4	2	no	—
114	D₈₈	—	2	2	no	—
115	D₈₈	—	2	2	no	—
116	D₈₈	—	4	2	no	—
117	C₁₁⋊C₁₆	—	2	1	no	—
118	C₁₁⋊C₁₆	—	2	1	no	—
119	C₁₁⋊C₁₆	#41	1	2	yes	—
120	C₁₁⋊C₁₆	#41	1	2	yes	—
121	#3176	—	11	1	no	—
122	#3176	D₁₁	1	1	yes	characteristic, complemented
123	#2253	—	11	1	no	—
124	#2246	—	11	1	no	—
125	#2244	—	11	1	no	—
126	#2244	—	11	1	no	—
127	#2218	—	11	2	no	—
128	#2215	—	11	2	no	—
129	#2177	—	11	2	no	—
130	C₄×D₁₆	—	11	2	no	—
131	#2108	—	11	1	no	—
132	C₂³×C₁₁	—	4	2	no	—
133	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
134	C₂²×D₁₁	—	4	2	no	—
135	D₄×C₁₁	—	4	2	no	—
136	D₄×C₁₁	—	4	2	no	—
137	D₄×C₁₁	—	16	2	no	—
138	D₄×C₁₁	—	16	2	no	—
139	C₂×C₄×C₁₁	—	2	1	no	—
140	C₂×C₄×C₁₁	—	2	1	no	—
141	C₂×C₄×C₁₁	—	4	2	no	—
142	C₂×C₄×C₁₁	—	16	2	no	—
143	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
144	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
146	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
147	C₂²⋊D₁₁	—	16	2	no	—
148	C₂×Dic₁₁	—	4	2	no	—
149	D₄₄	—	4	2	no	—
150	D₄₄	—	4	2	no	—
151	D₄₄	—	16	2	no	—
152	C₄×D₁₁	—	16	2	no	—
153	C₈×C₁₁	—	2	1	no	—
154	C₈×C₁₁	—	2	1	no	—
155	C₈×C₁₁	#135	1	2	yes	—
156	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
157	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
158	#540	—	2	1	no	—
159	#540	—	22	1	no	—
160	C₂×D₁₆	—	11	2	no	—
161	C₂×D₁₆	—	11	2	no	—
162	C₂×M₃₂	—	11	1	no	—
163	C₂²×C₁₆	—	11	1	no	—
164	#499	—	11	1	no	—
165	#499	C₂×D₁₁	1	1	yes	characteristic
166	#493	—	11	1	no	—
167	#493	C₂×D₁₁	1	1	yes	characteristic
168	#490	—	2	1	no	—
169	#490	—	22	1	no	—
170	#469	—	2	1	no	—
171	#469	—	22	1	no	—
172	#466	—	11	2	no	—
173	#466	C₂×D₁₁	1	2	yes	—
174	#442	—	2	1	no	—
175	#442	—	22	1	no	—
176	C₄×D₈	—	11	2	no	—
177	C₄×D₈	C₂×D₁₁	1	2	yes	—
178	#405	C₂×D₁₁	1	1	yes	characteristic
179	#367	—	11	2	no	—
180	#366	—	11	2	no	—
181	#357	—	11	2	no	—
182	#357	—	11	2	no	—
183	#357	—	11	2	no	—
184	#357	—	11	2	no	—
185	#346	—	11	1	no	—
186	#346	—	11	1	no	—
187	C₄×C₁₆	—	11	1	no	—
188	C₄×C₁₆	—	11	1	no	—
189	C₂²×C₁₁	—	2	2	no	—
190	C₂²×C₁₁	—	2	1	no	—
191	C₂²×C₁₁	—	8	2	no	—
192	C₂²×C₁₁	—	8	2	no	—
193	C₂²×C₁₁	—	8	2	no	—
194	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
195	C₂×D₁₁	—	8	2	no	—
196	C₂×D₁₁	—	8	2	no	—
197	C₂×D₁₁	—	8	2	no	—
198	C₄×C₁₁	—	2	2	no	—
199	C₄×C₁₁	—	2	2	no	—
200	C₄×C₁₁	—	2	1	no	—
201	C₄×C₁₁	—	8	2	no	—
202	C₄×C₁₁	#532	1	1	yes	characteristic
203	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
204	Dic₁₁	—	8	2	no	—
205	C₂×D₈	—	2	1	no	—
206	C₂×D₈	—	11	2	no	—
207	C₂×D₈	—	22	1	no	—
208	C₂×D₈	C₂²×D₁₁	1	2	yes	—
209	C₂×M₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
210	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
211	#127	—	2	1	no	—
212	#127	—	22	1	no	—
213	#125	—	2	1	no	—
214	#125	—	22	1	no	—
215	#123	—	4	2	no	—
216	#123	—	44	2	no	—
217	#121	—	2	2	no	—
218	#121	—	4	2	no	—
219	#121	—	22	2	no	—
220	#121	—	44	2	no	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	—	22	2	no	—
223	#117	C₂²⋊D₁₁	1	1	yes	characteristic
224	D₁₆	—	22	4	no	—
225	D₁₆	—	22	4	no	—
226	M₃₂	—	22	2	no	—
227	C₂×C₁₆	—	11	1	no	—
228	C₂×C₁₆	—	11	1	no	—
229	C₂×C₁₆	—	11	1	no	—
230	C₂×C₁₆	—	11	1	no	—
231	C₂×C₁₆	—	22	2	no	—
232	#107	—	11	2	no	—
233	#107	C₂²×D₁₁	1	2	yes	—
234	#106	—	2	1	no	—
235	#106	—	22	1	no	—
236	#102	—	2	2	no	—
237	#102	—	2	2	no	—
238	#102	—	22	2	no	—
239	#102	—	22	2	no	—
240	#97	C₂²⋊D₁₁	1	1	yes	characteristic
241	#97	C₂²⋊D₁₁	1	1	yes	characteristic
242	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
243	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
244	C₂×C₁₁	—	4	1	no	—
245	C₂×C₁₁	—	16	2	no	—
246	C₂×C₁₁	#3169	1	1	yes	characteristic
247	C₂×C₁₁	#3415	1	2	yes	—
248	D₁₁	—	16	2	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	4	2	no	—
251	C₂×D₄	—	4	2	no	—
252	C₂×D₄	—	22	2	no	—
253	C₂×D₄	—	44	2	no	—
254	C₂×D₄	—	44	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	—	44	2	no	—
257	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
258	D₈	—	2	2	no	—
259	D₈	—	2	2	no	—
260	D₈	—	4	2	no	—
261	D₈	—	22	2	no	—
262	D₈	—	22	2	no	—
263	D₈	—	44	2	no	—
264	M₁₆	—	2	2	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	1	no	—
267	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
268	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
269	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
270	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	4	2	no	—
273	C₄⋊C₄	—	22	2	no	—
274	C₄⋊C₄	—	44	2	no	—
275	C₄⋊C₄	#4323	1	2	yes	—
276	C₂²⋊C₄	—	4	2	no	—
277	C₂²⋊C₄	—	4	2	no	—
278	C₂²⋊C₄	—	44	2	no	—
279	C₂²⋊C₄	—	44	2	no	—
280	C₂²⋊C₄	#4323	1	2	yes	—
281	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
282	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
283	C₁₆	—	11	2	no	—
284	C₁₆	—	11	2	no	—
285	C₁₆	—	22	1	no	—
286	C₁₆	—	22	1	no	—
287	C₁₁	#33740	1	1	yes	characteristic, complemented, Sylow
288	C₂³	—	4	2	no	—
289	C₂³	—	44	2	no	—
290	C₂³	C₂×#4323	1	1	yes	characteristic
291	D₄	—	4	2	no	—
292	D₄	—	4	2	no	—
293	D₄	—	16	2	no	—
294	D₄	—	16	2	no	—
295	D₄	—	44	2	no	—
296	D₄	—	44	2	no	—
297	D₄	—	176	2	no	—
298	D₄	—	176	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	16	2	no	—
303	C₂×C₄	—	44	2	no	—
304	C₂×C₄	—	176	2	no	—
305	C₂×C₄	C₂×#4323	1	2	yes	—
306	C₂×C₄	C₂×#4323	1	2	yes	—
307	C₂×C₄	C₂×#4323	1	1	yes	characteristic
308	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
309	C₈	—	2	1	no	—
310	C₈	—	2	1	no	—
311	C₈	#67003	1	2	yes	—
312	C₈	#41×D₁₁	1	1	yes	characteristic
313	C₈	#41×D₁₁	1	1	yes	characteristic
314	C₂²	—	2	1	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	8	2	no	—
317	C₂²	—	8	2	no	—
318	C₂²	—	8	2	no	—
319	C₂²	—	88	2	no	—
320	C₂²	—	88	2	no	—
321	C₂²	—	88	2	no	—
322	C₂²	C₂²×#4323	1	1	yes	characteristic
323	C₄	—	2	1	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	—	8	2	no	—
327	C₄	—	88	2	no	—
328	C₄	C₂×#67003	1	1	yes	characteristic
329	C₄	#10623363	1	1	yes	characteristic
330	C₂	—	4	1	no	—
331	C₂	—	16	2	no	—
332	C₂	—	176	2	no	—
333	C₂	#13079191	1	1	yes	characteristic
334	C₂	#13081755	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×#4323
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#3176	C₂
socle	C₂²×C₁₁	C₂²×D₈
hypercenter	#3176	D₁₁
hypocenter	C₁₁	#33740
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405 ◁ #3176

Complements

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

N	H ≅ G/N	type
1. #13079266	C₂	semidirect
2. #13070892	C₂	semidirect
3. #13070865	C₂	semidirect
4. #13070859	C₂	semidirect
5. #13070857	C₂	semidirect
6. #13070717	C₂	semidirect
7. #13070700	C₂	semidirect
8. #13070490	C₂	semidirect
9. C₄×#66890	C₂	semidirect
10. #13070213	C₂	semidirect
11. C₁₁×#3176	C₂	semidirect
122. #3176	D₁₁	semidirect
287. C₁₁	#33740	semidirect

Maximal subgroups

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

subgroup	index
#13079266	2
#13070892	2
#13070865	2
#13070859	2
#13070857	2
#13070717	2
#13070700	2
#13070490	2
C₄×#66890	2
#13070213	2
C₁₁×#3176	2
#33740	11