Subgroups — #13082541

Order 1408.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623337	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623337	C₂	1	1	yes	maximal, characteristic, complemented
4	#10623337	C₂	1	2	yes	maximal, complemented
5	#10623329	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#66988	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623250	C₂	1	1	yes	maximal, characteristic, complemented
9	#10623244	C₂	1	1	yes	maximal, characteristic, complemented
10	#10623145	C₂	1	1	yes	maximal, characteristic, complemented
11	#10623142	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623134	C₂	1	1	yes	maximal, characteristic, complemented
13	#10623133	C₂	1	2	yes	maximal, complemented
14	#10623132	C₂	1	2	yes	maximal, complemented
15	#10623131	C₂	1	1	yes	maximal, characteristic, complemented
16	#10623124	C₂	1	2	yes	maximal, complemented
17	#10623118	C₂	1	2	yes	maximal, complemented
18	#10623118	C₂	1	2	yes	maximal, complemented
19	#10623117	C₂	1	2	yes	maximal, complemented
20	#10623077	C₂	1	1	yes	maximal, characteristic, complemented
21	#10623072	C₂	1	1	yes	maximal, characteristic, complemented
22	#10623070	C₂	1	1	yes	maximal, characteristic, complemented
23	#10623069	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
25	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
26	C₂²×D₄×C₁₁	C₂²	1	2	yes	—
27	C₂³×Dic₁₁	C₂²	1	2	yes	complemented
28	C₂×#4341	C₂²	1	1	yes	characteristic
29	C₂×#4341	C₂²	1	2	yes	complemented
30	C₁₁×#127	C₂²	1	1	yes	characteristic
31	C₁₁×#121	C₂²	1	1	yes	characteristic
32	C₁₁×#121	C₂²	1	2	yes	—
33	C₁₁×#121	C₂²	1	1	yes	characteristic
34	C₁₁×#120	C₂²	1	2	yes	—
35	C₁₁×#120	C₂²	1	2	yes	—
36	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
38	#67006	C₂²	1	2	yes	complemented
39	#67006	C₂²	1	2	yes	complemented
40	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	complemented
41	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	complemented
43	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	complemented
44	C₂×C₂²⋊Dic₁₁	C₂²	1	2	yes	complemented
45	#66992	C₂²	1	1	yes	characteristic
46	#66992	C₂²	1	2	yes	complemented
47	#66992	C₂²	1	2	yes	complemented
48	#66992	C₂²	1	2	yes	complemented
49	#66992	C₂²	1	2	yes	complemented
50	#66991	C₂²	1	1	yes	characteristic, complemented
51	#66991	C₂²	1	1	yes	characteristic, complemented
52	#66991	C₂²	1	2	yes	complemented
53	#66989	C₂²	1	1	yes	characteristic, complemented
54	#66989	C₂²	1	1	yes	characteristic, complemented
55	#66989	C₂²	1	2	yes	complemented
56	#66989	C₂²	1	2	yes	complemented
57	#66988	C₂²	1	1	yes	characteristic
58	#66988	C₂²	1	2	yes	—
59	#66988	C₂²	1	2	yes	complemented
60	#66988	C₂²	1	2	yes	complemented
61	#66988	C₂²	1	2	yes	complemented
62	#66988	C₂²	1	2	yes	complemented
63	#66988	C₂²	1	2	yes	complemented
64	#66988	C₂²	1	2	yes	complemented
65	#66988	C₂²	1	2	yes	complemented
66	#66988	C₂²	1	2	yes	complemented
67	#66988	C₂²	1	2	yes	complemented
68	#66988	C₂²	1	2	yes	complemented
69	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
70	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
71	D₄×Dic₁₁	C₂²	1	1	yes	characteristic
72	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
73	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₁₁	C₂²	1	2	yes	complemented
75	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
76	D₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
77	D₄×Dic₁₁	C₂²	1	2	yes	complemented
78	D₄×Dic₁₁	C₂²	1	2	yes	complemented
79	D₄×Dic₁₁	C₂²	1	2	yes	complemented
80	D₄×Dic₁₁	C₂²	1	2	yes	complemented
81	D₄×Dic₁₁	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₁₁	C₂²	1	2	yes	complemented
85	#66979	C₂²	1	1	yes	characteristic, complemented
86	#66979	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic, complemented
88	#66977	C₂²	1	2	yes	complemented
89	#66977	C₂²	1	1	yes	characteristic, complemented
90	#66977	C₂²	1	1	yes	characteristic, complemented
91	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
92	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	complemented
93	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic, complemented
94	#66951	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₁₁	C₂²	1	1	yes	characteristic, complemented
96	#66943	C₂²	1	1	yes	characteristic, complemented
97	#66942	C₂²	1	1	yes	characteristic, complemented
98	#66942	C₂²	1	2	yes	complemented
99	#66941	C₂²	1	1	yes	characteristic, complemented
100	#66940	C₂²	1	1	yes	characteristic, complemented
101	#66939	C₂²	1	1	yes	characteristic, complemented
102	#66938	C₂²	1	1	yes	characteristic, complemented
103	#66936	C₂²	1	2	yes	complemented
104	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
105	(C₂²⋊D₁₁)⋊C₄	C₂²	1	2	yes	complemented
106	#66932	C₂²	1	1	yes	characteristic, complemented
107	#66932	C₂²	1	2	yes	complemented
108	#66932	C₂²	1	2	yes	complemented
109	#66932	C₂²	1	2	yes	complemented
110	#66932	C₂²	1	2	yes	complemented
111	#66931	C₂²	1	1	yes	characteristic, complemented
112	#66931	C₂²	1	2	yes	complemented
113	#66931	C₂²	1	2	yes	complemented
114	#66931	C₂²	1	2	yes	complemented
115	#66931	C₂²	1	2	yes	complemented
116	#66930	C₂²	1	2	yes	complemented
117	#66930	C₂²	1	2	yes	complemented
118	#66930	C₂²	1	2	yes	complemented
119	#66925	C₂²	1	1	yes	characteristic, complemented
120	#66923	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₂	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₁	C₂³	1	2	yes	—
124	C₂⁴×C₁₁	C₂³	1	2	yes	—
125	C₂×D₄×C₁₁	—	2	4	no	—
126	C₂×D₄×C₁₁	—	2	4	no	—
127	C₂×D₄×C₁₁	—	4	4	no	—
128	C₂×D₄×C₁₁	C₂³	1	2	yes	—
129	C₂×D₄×C₁₁	C₂³	1	2	yes	—
130	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₁	C₂³	1	2	yes	—
133	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₁	C₂³	1	2	yes	—
135	C₂×D₄×C₁₁	C₂³	1	2	yes	—
136	C₂×D₄×C₁₁	C₂³	1	2	yes	—
137	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₁	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₁	—	4	4	no	—
147	C₂²×Dic₁₁	C₂³	1	2	yes	—
148	C₂²×Dic₁₁	C₂³	1	2	yes	—
149	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
150	C₂²×Dic₁₁	C₂³	1	2	yes	—
151	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
152	C₂²×Dic₁₁	C₂³	1	2	yes	—
153	C₂²×Dic₁₁	C₂³	1	2	yes	—
154	C₂²×Dic₁₁	C₂³	1	2	yes	—
155	C₂²×Dic₁₁	C₂³	1	2	yes	—
156	C₂²×Dic₁₁	C₂³	1	2	yes	—
157	C₂²×Dic₁₁	C₂³	1	2	yes	—
158	#4341	—	2	4	no	—
159	#4341	—	4	4	no	—
160	C₂×C₄×D₁₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₁	C₂³	1	2	yes	—
162	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₂	C₂³	1	1	yes	characteristic
164	C₂×Dic₂₂	C₂³	1	2	yes	—
165	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₁×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₄²×C₁₁	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
191	C₂²⋊Dic₁₁	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₁	C₂³	1	1	yes	characteristic
193	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₁)⋊C₄	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₁	C₂³	1	2	yes	—
203	C₄⋊Dic₁₁	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₁	C₂³	1	2	yes	—
205	Dic₁₁⋊C₄	C₂³	1	2	yes	—
206	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₁₁⋊C₄	C₂³	1	2	yes	—
209	Dic₁₁⋊C₄	C₂³	1	2	yes	—
210	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₁₁⋊C₄	C₂³	1	2	yes	—
213	Dic₁₁⋊C₄	C₂³	1	2	yes	—
214	Dic₁₁⋊C₄	C₂³	1	2	yes	—
215	Dic₁₁⋊C₄	C₂³	1	2	yes	—
216	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₁₁⋊C₄	C₂³	1	1	yes	characteristic
218	Dic₁₁⋊C₄	C₂³	1	2	yes	—
219	Dic₁₁⋊C₄	C₂³	1	2	yes	—
220	C₄×Dic₁₁	C₂³	1	2	yes	—
221	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₁	C₂³	1	2	yes	—
225	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₁	C₂³	1	2	yes	—
227	C₄×Dic₁₁	C₂³	1	1	yes	characteristic
228	#3513	—	11	1	no	maximal, Sylow
229	C₂³×C₁₁	—	2	4	no	—
230	C₂³×C₁₁	—	2	4	no	—
231	C₂³×C₁₁	—	2	4	no	—
232	C₂³×C₁₁	—	4	2	no	—
233	C₂³×C₁₁	—	4	2	no	—
234	C₂³×C₁₁	—	4	2	no	—
235	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₁	C₂⁴	1	2	yes	—
237	C₂³×C₁₁	C₂⁴	1	2	yes	—
238	C₂³×C₁₁	C₂⁴	1	2	yes	—
239	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₁	C₂⁴	1	1	yes	characteristic
241	D₄×C₁₁	—	2	4	no	—
242	D₄×C₁₁	—	2	4	no	—
243	D₄×C₁₁	—	2	4	no	—
244	D₄×C₁₁	—	2	2	no	—
245	D₄×C₁₁	—	2	2	no	—
246	D₄×C₁₁	—	2	2	no	—
247	D₄×C₁₁	—	4	2	no	—
248	D₄×C₁₁	—	4	2	no	—
249	D₄×C₁₁	—	4	2	no	—
250	D₄×C₁₁	#41	1	4	yes	complemented
251	C₂×C₄×C₁₁	—	2	2	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	4	2	no	—
254	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₁₁	—	2	4	no	—
261	C₂²⋊D₁₁	—	2	2	no	—
262	C₂²⋊D₁₁	—	4	2	no	—
263	C₂²⋊D₁₁	—	4	1	no	—
264	C₂²⋊D₁₁	—	4	2	no	—
265	C₂×Dic₁₁	—	2	4	no	—
266	C₂×Dic₁₁	—	2	4	no	—
267	C₂×Dic₁₁	—	2	2	no	—
268	C₂×Dic₁₁	—	4	2	no	—
269	C₂×Dic₁₁	—	4	2	no	—
270	C₂×Dic₁₁	—	4	2	no	—
271	C₂×Dic₁₁	—	4	2	no	—
272	C₂×Dic₁₁	—	4	2	no	—
273	C₂×Dic₁₁	—	4	2	no	—
274	C₂×Dic₁₁	—	4	1	no	—
275	C₂×Dic₁₁	—	4	2	no	—
276	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₁	C₂⁴	1	2	yes	—
278	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₁	C₂⁴	1	2	yes	—
282	C₂×Dic₁₁	C₂⁴	1	2	yes	—
283	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₁₁	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₁₁	C₂⁴	1	2	yes	—
287	C₄×D₁₁	—	2	2	no	—
288	C₄×D₁₁	—	4	2	no	—
289	Dic₂₂	—	2	2	no	—
290	Dic₂₂	—	4	1	no	—
291	Dic₂₂	—	4	2	no	—
292	#559	—	11	1	no	—
293	#554	—	11	1	no	—
294	#553	—	11	2	no	—
295	#553	—	11	1	no	—
296	#552	—	11	1	no	—
297	#551	—	11	2	no	—
298	#551	—	11	2	no	—
299	#547	—	11	1	no	—
300	#546	—	11	2	no	—
301	#546	—	11	1	no	—
302	#546	—	11	1	no	—
303	D₄²	D₁₁	1	1	yes	characteristic, complemented
304	#542	—	11	1	no	—
305	#540	—	11	1	no	—
306	#539	—	11	2	no	—
307	#538	—	11	2	no	—
308	#529	—	11	1	no	—
309	#529	—	11	1	no	—
310	#525	—	11	2	no	—
311	C₂×#123	—	11	2	no	—
312	#520	—	11	1	no	—
313	#518	—	11	1	no	—
314	C₂×C₄×D₄	—	11	1	no	—
315	C₂²×C₁₁	—	2	1	no	—
316	C₂²×C₁₁	—	2	2	no	—
317	C₂²×C₁₁	—	2	1	no	—
318	C₂²×C₁₁	—	2	2	no	—
319	C₂²×C₁₁	—	2	1	no	—
320	C₂²×C₁₁	—	2	2	no	—
321	C₂²×C₁₁	—	2	2	no	—
322	C₂²×C₁₁	—	2	1	no	—
323	C₂²×C₁₁	—	2	2	no	—
324	C₂²×C₁₁	—	2	2	no	—
325	C₂²×C₁₁	—	2	2	no	—
326	C₂²×C₁₁	—	2	2	no	—
327	C₂²×C₁₁	—	2	1	no	—
328	C₂²×C₁₁	—	4	8	no	—
329	C₂²×C₁₁	—	8	4	no	—
330	C₂²×C₁₁	C₂×#41	1	4	yes	—
331	C₂²×C₁₁	H(5,𝔽₂)	1	2	yes	—
332	C₂²×C₁₁	C₂⁵	1	1	yes	characteristic
333	C₂×D₁₁	—	2	1	no	—
334	C₂×D₁₁	—	2	1	no	—
335	C₂×D₁₁	—	2	1	no	—
336	C₄×C₁₁	—	2	1	no	—
337	C₄×C₁₁	—	2	1	no	—
338	C₄×C₁₁	—	2	1	no	—
339	C₄×C₁₁	—	2	2	no	—
340	C₄×C₁₁	—	2	1	no	—
341	C₄×C₁₁	C₂×#41	1	2	yes	—
342	Dic₁₁	—	2	2	no	—
343	Dic₁₁	—	2	1	no	—
344	Dic₁₁	—	2	1	no	—
345	Dic₁₁	—	2	2	no	—
346	Dic₁₁	—	2	2	no	—
347	Dic₁₁	—	2	1	no	—
348	Dic₁₁	—	2	1	no	—
349	Dic₁₁	—	2	1	no	—
350	Dic₁₁	—	2	1	no	—
351	Dic₁₁	—	2	1	no	—
352	Dic₁₁	—	2	2	no	—
353	C₂×#41	—	11	1	no	—
354	C₂×#41	—	11	2	no	—
355	C₂²×D₄	C₂×D₁₁	1	1	yes	characteristic
356	C₂²×D₄	C₂×D₁₁	1	1	yes	characteristic
357	C₂²×D₄	C₂×D₁₁	1	2	yes	—
358	C₂³×C₄	—	11	2	no	—
359	C₄⋊Q₈	—	11	1	no	—
360	#127	C₂×D₁₁	1	1	yes	characteristic
361	#126	—	11	1	no	—
362	#126	—	11	2	no	—
363	#126	—	11	1	no	—
364	#126	—	11	2	no	—
365	#126	—	11	2	no	—
366	#126	—	11	2	no	—
367	#125	—	11	1	no	—
368	#125	—	11	1	no	—
369	#125	—	11	2	no	—
370	#125	—	11	1	no	—
371	#124	—	11	1	no	—
372	#124	—	11	2	no	—
373	#124	—	11	2	no	—
374	#124	—	11	1	no	—
375	#124	—	11	1	no	—
376	#123	—	11	1	no	—
377	#123	—	11	2	no	—
378	#123	—	11	2	no	—
379	#123	—	11	2	no	—
380	#123	—	11	2	no	—
381	#123	—	11	2	no	—
382	#123	—	11	2	no	—
383	#123	—	11	2	no	—
384	#123	—	11	2	no	—
385	#123	—	11	2	no	—
386	#123	—	11	2	no	—
387	#123	—	11	2	no	—
388	#123	—	11	1	no	—
389	#123	—	11	2	no	—
390	C₂²⋊Q₈	—	11	1	no	—
391	C₂²⋊Q₈	—	11	2	no	—
392	C₂²⋊Q₈	—	11	1	no	—
393	C₂²⋊Q₈	—	11	2	no	—
394	C₂²⋊Q₈	—	11	2	no	—
395	C₂²⋊Q₈	—	11	1	no	—
396	C₂²⋊Q₈	—	11	2	no	—
397	C₂²⋊Q₈	—	11	2	no	—
398	#121	—	11	2	no	—
399	#121	—	11	2	no	—
400	#121	—	11	1	no	—
401	#121	—	11	2	no	—
402	#121	—	11	2	no	—
403	#121	—	11	1	no	—
404	#121	—	11	1	no	—
405	#121	—	11	2	no	—
406	#121	C₂×D₁₁	1	1	yes	characteristic
407	#121	C₂×D₁₁	1	2	yes	—
408	#121	C₂×D₁₁	1	1	yes	characteristic
409	#120	—	11	2	no	—
410	#120	—	11	2	no	—
411	#120	C₂×D₁₁	1	2	yes	—
412	#120	C₂×D₁₁	1	2	yes	—
413	C₄×Q₈	—	11	1	no	—
414	C₄×Q₈	—	11	1	no	—
415	C₄×Q₈	—	11	1	no	—
416	C₄×D₄	—	11	1	no	—
417	C₄×D₄	—	11	2	no	—
418	C₄×D₄	—	11	1	no	—
419	C₄×D₄	—	11	1	no	—
420	C₄×D₄	—	11	2	no	—
421	C₄×D₄	—	11	1	no	—
422	C₄×D₄	—	11	2	no	—
423	C₄×D₄	—	11	1	no	—
424	C₄×D₄	—	11	1	no	—
425	C₄×D₄	—	11	1	no	—
426	C₄×D₄	—	11	2	no	—
427	C₄×D₄	—	11	2	no	—
428	C₄×D₄	—	11	2	no	—
429	C₄×D₄	—	11	2	no	—
430	C₄×D₄	—	11	1	no	—
431	C₄×D₄	—	11	1	no	—
432	C₄×D₄	—	11	2	no	—
433	C₄×D₄	—	11	2	no	—
434	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
435	C₄×D₄	C₂×D₁₁	1	1	yes	characteristic
436	#117	—	11	1	no	—
437	#117	—	11	1	no	—
438	#117	—	11	2	no	—
439	#117	—	11	2	no	—
440	#117	—	11	2	no	—
441	#117	—	11	1	no	—
442	C₂×C₄⋊C₄	—	11	1	no	—
443	C₂×C₄⋊C₄	—	11	2	no	—
444	C₂×C₄⋊C₄	—	11	2	no	—
445	C₂×C₄⋊C₄	—	11	1	no	—
446	C₂×C₂²⋊C₄	—	11	2	no	—
447	C₂×C₂²⋊C₄	—	11	2	no	—
448	C₂×C₂²⋊C₄	—	11	2	no	—
449	C₂×C₂²⋊C₄	—	11	2	no	—
450	C₂×C₂²⋊C₄	—	11	2	no	—
451	C₂×C₄²	—	11	1	no	—
452	C₂×C₁₁	—	2	2	no	—
453	C₂×C₁₁	—	2	4	no	—
454	C₂×C₁₁	—	4	2	no	—
455	C₂×C₁₁	—	4	2	no	—
456	C₂×C₁₁	—	4	1	no	—
457	C₂×C₁₁	C₂²×#41	1	1	yes	characteristic
458	C₂×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₁₁	#585	1	1	yes	characteristic
460	D₁₁	—	4	1	no	—
461	C₂⁴	C₂²×D₁₁	1	2	yes	—
462	C₂⁴	C₂²×D₁₁	1	2	yes	—
463	#41	—	22	4	no	—
464	#41	—	44	4	no	—
465	C₂×Q₈	—	11	1	no	—
466	C₂×Q₈	—	11	1	no	—
467	C₂×Q₈	—	11	2	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	4	4	no	—
471	C₂×D₄	—	11	2	no	—
472	C₂×D₄	—	11	1	no	—
473	C₂×D₄	—	11	1	no	—
474	C₂×D₄	—	11	2	no	—
475	C₂×D₄	—	11	2	no	—
476	C₂×D₄	C₂²×D₁₁	1	2	yes	—
477	C₂×D₄	C₂²×D₁₁	1	2	yes	—
478	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
480	C₂×D₄	C₂²×D₁₁	1	2	yes	—
481	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₁	1	2	yes	—
483	C₂×D₄	C₂²×D₁₁	1	2	yes	—
484	C₂×D₄	C₂²×D₁₁	1	2	yes	—
485	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
486	C₂²×C₄	—	11	1	no	—
487	C₂²×C₄	—	11	2	no	—
488	C₂²×C₄	—	11	2	no	—
489	C₂²×C₄	—	11	1	no	—
490	C₂²×C₄	—	11	2	no	—
491	C₂²×C₄	—	11	2	no	—
492	C₂²×C₄	—	11	2	no	—
493	C₂²×C₄	—	11	2	no	—
494	C₂²×C₄	—	11	2	no	—
495	C₂²×C₄	—	11	2	no	—
496	C₂²×C₄	—	11	2	no	—
497	C₂²×C₄	—	11	1	no	—
498	C₂²×C₄	—	11	2	no	—
499	C₂²×C₄	—	44	4	no	—
500	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
502	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
503	C₄⋊C₄	—	11	1	no	—
504	C₄⋊C₄	—	11	2	no	—
505	C₄⋊C₄	—	11	1	no	—
506	C₄⋊C₄	—	11	1	no	—
507	C₄⋊C₄	—	11	2	no	—
508	C₄⋊C₄	—	11	1	no	—
509	C₄⋊C₄	—	11	2	no	—
510	C₄⋊C₄	—	11	2	no	—
511	C₄⋊C₄	—	11	2	no	—
512	C₄⋊C₄	—	11	2	no	—
513	C₄⋊C₄	—	11	2	no	—
514	C₄⋊C₄	—	11	1	no	—
515	C₄⋊C₄	—	11	1	no	—
516	C₄⋊C₄	—	11	1	no	—
517	C₄⋊C₄	—	11	1	no	—
518	C₄⋊C₄	—	11	2	no	—
519	C₄⋊C₄	—	11	2	no	—
520	C₄⋊C₄	—	11	2	no	—
521	C₄⋊C₄	—	11	1	no	—
522	C₄⋊C₄	—	11	2	no	—
523	C₄⋊C₄	—	11	1	no	—
524	C₄⋊C₄	—	11	1	no	—
525	C₄⋊C₄	—	11	1	no	—
526	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
528	C₂²⋊C₄	—	11	2	no	—
529	C₂²⋊C₄	—	11	2	no	—
530	C₂²⋊C₄	—	11	1	no	—
531	C₂²⋊C₄	—	11	1	no	—
532	C₂²⋊C₄	—	11	1	no	—
533	C₂²⋊C₄	—	11	1	no	—
534	C₂²⋊C₄	—	11	2	no	—
535	C₂²⋊C₄	—	11	2	no	—
536	C₂²⋊C₄	—	11	2	no	—
537	C₂²⋊C₄	—	11	2	no	—
538	C₂²⋊C₄	—	11	2	no	—
539	C₂²⋊C₄	—	11	2	no	—
540	C₂²⋊C₄	—	11	2	no	—
541	C₂²⋊C₄	—	11	2	no	—
542	C₂²⋊C₄	—	11	2	no	—
543	C₂²⋊C₄	—	11	2	no	—
544	C₂²⋊C₄	—	11	2	no	—
545	C₂²⋊C₄	—	11	2	no	—
546	C₂²⋊C₄	—	11	2	no	—
547	C₂²⋊C₄	—	11	2	no	—
548	C₂²⋊C₄	—	11	1	no	—
549	C₂²⋊C₄	—	11	1	no	—
550	C₂²⋊C₄	—	11	1	no	—
551	C₂²⋊C₄	—	11	1	no	—
552	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₁	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
557	C₄²	—	11	1	no	—
558	C₄²	—	11	1	no	—
559	C₄²	—	11	1	no	—
560	C₄²	—	11	1	no	—
561	C₄²	—	11	2	no	—
562	C₄²	—	11	2	no	—
563	C₄²	—	11	2	no	—
564	C₄²	—	11	1	no	—
565	C₄²	C₂²×D₁₁	1	1	yes	characteristic
566	C₁₁	#3513	1	1	yes	characteristic, complemented, Sylow
567	C₂³	—	2	4	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	11	1	no	—
574	C₂³	C₂³×D₁₁	1	1	yes	characteristic
575	C₂³	C₂³×D₁₁	1	2	yes	—
576	C₂³	C₂³×D₁₁	1	2	yes	—
577	C₂³	C₂³×D₁₁	1	2	yes	—
578	C₂³	C₂³×D₁₁	1	1	yes	characteristic
579	Q₈	—	22	2	no	—
580	Q₈	—	44	2	no	—
581	Q₈	—	44	1	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	4	no	—
586	D₄	—	2	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	22	4	no	—
592	D₄	—	22	2	no	—
593	D₄	—	44	2	no	—
594	D₄	—	44	2	no	—
595	D₄	—	44	1	no	—
596	D₄	#4341	1	4	yes	complemented
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	11	1	no	—
601	C₂×C₄	—	11	2	no	—
602	C₂×C₄	—	11	1	no	—
603	C₂×C₄	—	11	1	no	—
604	C₂×C₄	—	11	1	no	—
605	C₂×C₄	—	11	2	no	—
606	C₂×C₄	—	11	1	no	—
607	C₂×C₄	—	11	2	no	—
608	C₂×C₄	—	11	1	no	—
609	C₂×C₄	—	11	1	no	—
610	C₂×C₄	—	11	2	no	—
611	C₂×C₄	—	22	4	no	—
612	C₂×C₄	—	22	2	no	—
613	C₂×C₄	—	22	4	no	—
614	C₂×C₄	—	22	2	no	—
615	C₂×C₄	—	44	2	no	—
616	C₂×C₄	—	44	2	no	—
617	C₂×C₄	—	44	2	no	—
618	C₂×C₄	—	44	2	no	—
619	C₂×C₄	—	44	2	no	—
620	C₂×C₄	—	44	2	no	—
621	C₂×C₄	—	44	2	no	—
622	C₂×C₄	—	44	1	no	—
623	C₂×C₄	—	44	2	no	—
624	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₁₁	1	2	yes	—
628	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	4	8	no	—
644	C₂²	—	8	4	no	—
645	C₂²	—	22	1	no	—
646	C₂²	—	22	1	no	—
647	C₂²	—	22	1	no	—
648	C₂²	C₂×#4341	1	4	yes	—
649	C₂²	#67037	1	2	yes	—
650	C₂²	C₂⁴×D₁₁	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	22	1	no	—
657	C₄	—	22	2	no	—
658	C₄	—	22	1	no	—
659	C₄	—	22	1	no	—
660	C₄	—	22	2	no	—
661	C₄	—	22	2	no	—
662	C₄	—	22	1	no	—
663	C₄	—	22	1	no	—
664	C₄	—	22	2	no	—
665	C₄	—	22	1	no	—
666	C₄	—	22	1	no	—
667	C₄	C₂×#4341	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	44	1	no	—
674	C₂	C₂²×#4341	1	1	yes	characteristic
675	C₂	C₂×#67037	1	1	yes	characteristic
676	C₂	#10623455	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁
commutator, socle, cosocle	C₂²×C₁₁	C₂⁵
Fitting	D₄²×C₁₁	C₂
hypercenter	D₄²	D₁₁
hypocenter	C₁₁	#3513
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. D₄²×C₁₁	C₂	semidirect
2. #10623337	C₂	semidirect
3. #10623337	C₂	semidirect
4. #10623337	C₂	semidirect
5. #10623329	C₂	semidirect
6. C₂×#66988	C₂	semidirect
7. C₂×D₄×Dic₁₁	C₂	semidirect
8. #10623250	C₂	semidirect
9. #10623244	C₂	semidirect
10. #10623145	C₂	semidirect
11. #10623142	C₂	semidirect
12. #10623134	C₂	semidirect
13. #10623133	C₂	semidirect
14. #10623132	C₂	semidirect
15. #10623131	C₂	semidirect
16. #10623124	C₂	semidirect
17. #10623118	C₂	semidirect
18. #10623118	C₂	semidirect
19. #10623117	C₂	semidirect
20. #10623077	C₂	semidirect
21. #10623072	C₂	semidirect
22. #10623070	C₂	semidirect
23. #10623069	C₂	semidirect
27. C₂³×Dic₁₁	C₂²	semidirect
29. C₂×#4341	C₂²	semidirect
38. #67006	C₂²	semidirect
39. #67006	C₂²	semidirect
40. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
41. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
43. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
44. C₂×C₂²⋊Dic₁₁	C₂²	semidirect
46. #66992	C₂²	semidirect
47. #66992	C₂²	semidirect
48. #66992	C₂²	semidirect
49. #66992	C₂²	semidirect
50. #66991	C₂²	semidirect
51. #66991	C₂²	semidirect
52. #66991	C₂²	semidirect
53. #66989	C₂²	semidirect
54. #66989	C₂²	semidirect
55. #66989	C₂²	semidirect
56. #66989	C₂²	semidirect
59. #66988	C₂²	semidirect
60. #66988	C₂²	semidirect
61. #66988	C₂²	semidirect
62. #66988	C₂²	semidirect
63. #66988	C₂²	semidirect
64. #66988	C₂²	semidirect
65. #66988	C₂²	semidirect
66. #66988	C₂²	semidirect
67. #66988	C₂²	semidirect
68. #66988	C₂²	semidirect
72. D₄×Dic₁₁	C₂²	semidirect
73. D₄×Dic₁₁	C₂²	semidirect
74. D₄×Dic₁₁	C₂²	semidirect
75. D₄×Dic₁₁	C₂²	semidirect
76. D₄×Dic₁₁	C₂²	semidirect
77. D₄×Dic₁₁	C₂²	semidirect
78. D₄×Dic₁₁	C₂²	semidirect
79. D₄×Dic₁₁	C₂²	semidirect
80. D₄×Dic₁₁	C₂²	semidirect
81. D₄×Dic₁₁	C₂²	semidirect
82. C₄×C₂²⋊D₁₁	C₂²	semidirect
83. C₄×C₂²⋊D₁₁	C₂²	semidirect
84. C₄×C₂²⋊D₁₁	C₂²	semidirect
85. #66979	C₂²	semidirect
86. #66979	C₂²	semidirect
87. C₂×C₄⋊Dic₁₁	C₂²	semidirect
88. #66977	C₂²	semidirect
89. #66977	C₂²	semidirect
90. #66977	C₂²	semidirect
91. C₂×Dic₁₁⋊C₄	C₂²	semidirect
92. C₂×Dic₁₁⋊C₄	C₂²	semidirect
93. C₂×C₄×Dic₁₁	C₂²	semidirect
94. #66951	C₂²	semidirect
95. C₄⋊C₄×D₁₁	C₂²	semidirect
96. #66943	C₂²	semidirect
97. #66942	C₂²	semidirect
98. #66942	C₂²	semidirect
99. #66941	C₂²	semidirect
100. #66940	C₂²	semidirect
101. #66939	C₂²	semidirect
102. #66938	C₂²	semidirect
103. #66936	C₂²	semidirect
104. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
105. (C₂²⋊D₁₁)⋊C₄	C₂²	semidirect
106. #66932	C₂²	semidirect
107. #66932	C₂²	semidirect
108. #66932	C₂²	semidirect
109. #66932	C₂²	semidirect
110. #66932	C₂²	semidirect
111. #66931	C₂²	semidirect
112. #66931	C₂²	semidirect
113. #66931	C₂²	semidirect
114. #66931	C₂²	semidirect
115. #66931	C₂²	semidirect
116. #66930	C₂²	semidirect
117. #66930	C₂²	semidirect
118. #66930	C₂²	semidirect
119. #66925	C₂²	semidirect
120. #66923	C₂²	semidirect
121. C₄×Dic₂₂	C₂²	semidirect
122. C₄×Dic₂₂	C₂²	semidirect
250. D₄×C₁₁	#41	semidirect
303. D₄²	D₁₁	semidirect
566. C₁₁	#3513	semidirect
596. D₄	#4341	semidirect

Maximal subgroups

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

subgroup	index
D₄²×C₁₁	2
#10623337	2
#10623329	2
C₂×#66988	2
C₂×D₄×Dic₁₁	2
#10623250	2
#10623244	2
#10623145	2
#10623142	2
#10623134	2
#10623133	2
#10623132	2
#10623131	2
#10623124	2
#10623118	2
#10623117	2
#10623077	2
#10623072	2
#10623070	2
#10623069	2
#3513	11