Subgroups — #14722784

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077249	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13067377	C₂	1	4	yes	maximal, complemented
4	#13067374	C₂	1	2	yes	maximal, complemented
5	#13067371	C₂	1	2	yes	maximal, complemented
6	#13067362	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2920	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂³×C₁₁⋊C₈	C₄	1	2	yes	—
10	C₁₁×#432	—	2	1	no	—
11	C₁₁×#432	C₂²	1	2	yes	—
12	C₁₁×#431	—	2	1	no	—
13	C₁₁×#431	C₂²	1	2	yes	—
14	C₁₁×#423	C₂²	1	2	yes	—
15	C₁₁×#407	—	2	1	no	—
16	C₄×C₁₁×M₁₆	—	2	1	no	—
17	#10622820	—	2	1	no	—
18	#10622539	—	2	1	no	—
19	#10622539	C₂²	1	2	yes	—
20	#10622538	—	2	1	no	—
21	#10622538	C₂²	1	2	yes	—
22	#10622537	C₂²	1	2	yes	—
23	C₄×#4318	—	2	1	no	—
24	C₂×C₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₁⋊C₈	C₄	1	2	yes	—
28	C₂×C₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
30	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
33	#10622118	C₂²	1	8	yes	complemented
34	#10622117	C₂²	1	8	yes	complemented
35	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
38	C₂×C₁₁×M₁₆	—	2	2	no	—
39	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₂×#4318	—	2	2	no	—
52	C₂²×C₁₁⋊C₈	—	2	8	no	—
53	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
54	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
55	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
56	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
57	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
58	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
59	C₁₁×C₄⋊C₈	—	2	2	no	—
60	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
61	C₁₁×C₂²⋊C₈	—	2	2	no	—
62	C₁₁×C₂²⋊C₈	—	2	2	no	—
63	C₁₁×#97	—	2	2	no	—
64	C₄×C₈×C₁₁	—	2	2	no	—
65	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
67	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
68	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
69	#66867	—	2	2	no	—
70	C₄×C₁₁⋊C₈	—	2	2	no	—
71	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
74	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
75	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
76	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
79	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
80	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
81	#17793	—	11	1	no	maximal, Sylow
82	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	—	2	4	no	—
84	C₂²×C₄×C₁₁	—	2	4	no	—
85	C₂²×C₄×C₁₁	—	2	4	no	—
86	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
104	C₁₁×M₁₆	—	4	4	no	—
105	C₂×C₈×C₁₁	—	2	4	no	—
106	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
120	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
121	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
122	#4318	—	4	4	no	—
123	C₂×C₁₁⋊C₈	—	2	4	no	—
124	C₂×C₁₁⋊C₈	—	2	4	no	—
125	C₂×C₁₁⋊C₈	—	2	4	no	—
126	C₂×C₁₁⋊C₈	—	2	4	no	—
127	C₂×C₁₁⋊C₈	—	2	4	no	—
128	C₂×C₁₁⋊C₈	—	2	4	no	—
129	C₂×C₁₁⋊C₈	M₁₆	1	8	yes	complemented
130	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
134	#2920	—	11	1	no	—
135	#2920	D₁₁	1	1	yes	characteristic
136	C₂²×C₄×C₈	—	11	1	no	—
137	#1568	—	11	4	no	—
138	#1567	—	11	2	no	—
139	#1566	—	11	2	no	—
140	#1564	—	11	4	no	—
141	C₂³×C₁₁	—	2	2	no	—
142	C₂³×C₁₁	—	2	2	no	—
143	C₂³×C₁₁	—	2	2	no	—
144	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	2	2	no	—
152	C₂×C₄×C₁₁	—	2	2	no	—
153	C₂×C₄×C₁₁	—	2	2	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	2	2	no	—
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	—	2	2	no	—
159	C₂×C₄×C₁₁	—	2	2	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	#108	1	4	yes	—
163	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
173	C₂×C₄×C₁₁	#135	1	4	yes	—
174	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
177	C₈×C₁₁	—	4	4	no	—
178	C₁₁⋊C₈	—	2	2	no	—
179	C₁₁⋊C₈	—	2	2	no	—
180	C₁₁⋊C₈	—	4	4	no	—
181	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	—
182	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	—
183	C₂³×C₈	—	11	2	no	—
184	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
185	#432	—	2	1	no	—
186	#432	—	11	2	no	—
187	#432	—	22	1	no	—
188	#432	C₂×D₁₁	1	2	yes	—
189	#431	—	2	1	no	—
190	#431	—	11	2	no	—
191	#431	—	22	1	no	—
192	#431	C₂×D₁₁	1	2	yes	—
193	#423	—	11	2	no	—
194	#423	C₂×D₁₁	1	2	yes	—
195	#407	—	2	1	no	—
196	#407	—	22	1	no	—
197	C₄×M₁₆	—	2	1	no	—
198	C₄×M₁₆	—	22	1	no	—
199	C₂×C₄×C₈	—	11	2	no	—
200	C₂×C₄×C₈	—	11	1	no	—
201	C₂×C₄×C₈	—	11	1	no	—
202	C₂×C₄×C₈	—	11	2	no	—
203	C₂×C₄×C₈	—	11	1	no	—
204	C₂×C₄×C₈	—	11	1	no	—
205	C₂×C₄×C₈	—	11	1	no	—
206	C₂×C₄×C₈	—	11	2	no	—
207	C₂×C₄×C₈	—	11	1	no	—
208	#335	—	11	8	no	—
209	#334	—	11	8	no	—
210	C₂²×C₁₁	—	2	8	no	—
211	C₂²×C₁₁	—	2	1	no	—
212	C₂²×C₁₁	—	2	1	no	—
213	C₂²×C₁₁	—	2	1	no	—
214	C₂²×C₁₁	—	2	1	no	—
215	C₂²×C₁₁	—	2	1	no	—
216	C₂²×C₁₁	—	2	1	no	—
217	C₂²×C₁₁	#423	1	2	yes	—
218	C₂²×C₁₁	#427	1	2	yes	—
219	C₂²×C₁₁	C₂×#108	1	2	yes	—
220	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
221	C₄×C₁₁	—	2	1	no	—
222	C₄×C₁₁	—	2	1	no	—
223	C₄×C₁₁	—	2	1	no	—
224	C₄×C₁₁	—	2	1	no	—
225	C₄×C₁₁	—	2	1	no	—
226	C₄×C₁₁	—	2	1	no	—
227	C₄×C₁₁	#423	1	2	yes	—
228	C₄×C₁₁	#427	1	2	yes	—
229	C₄×C₁₁	C₂×#108	1	2	yes	—
230	C₄×C₁₁	C₂×#108	1	2	yes	—
231	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
232	C₄×C₁₁	C₂×#135	1	2	yes	—
233	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
234	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
235	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	22	2	no	—
238	C₂²×C₈	—	11	2	no	—
239	C₂²×C₈	—	11	2	no	—
240	C₂²×C₈	—	11	2	no	—
241	C₂²×C₈	—	11	2	no	—
242	C₂²×C₈	—	11	2	no	—
243	C₂²×C₈	—	11	2	no	—
244	C₂²×C₈	—	22	8	no	—
245	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
246	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
247	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
248	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
249	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
250	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
254	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	11	4	no	—
259	C₄⋊C₈	—	22	2	no	—
260	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	—	2	2	no	—
263	C₂²⋊C₈	—	22	2	no	—
264	C₂²⋊C₈	—	22	2	no	—
265	#97	—	2	2	no	—
266	#97	—	22	2	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	—	11	1	no	—
269	C₄×C₈	—	11	1	no	—
270	C₄×C₈	—	11	2	no	—
271	C₄×C₈	—	11	2	no	—
272	C₄×C₈	—	11	2	no	—
273	C₄×C₈	—	11	1	no	—
274	C₄×C₈	—	11	1	no	—
275	C₄×C₈	—	11	2	no	—
276	C₄×C₈	—	11	2	no	—
277	C₄×C₈	—	11	2	no	—
278	C₄×C₈	—	22	2	no	—
279	C₂×C₁₁	—	2	2	no	—
280	C₂×C₁₁	—	2	2	no	—
281	C₂×C₁₁	—	2	2	no	—
282	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
283	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
284	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
285	C₂⁴	Dic₁₁⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
294	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
295	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
299	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
300	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
307	M₁₆	—	4	4	no	—
308	M₁₆	—	44	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	11	8	no	—
311	C₂×C₈	—	11	2	no	—
312	C₂×C₈	—	11	2	no	—
313	C₂×C₈	—	11	2	no	—
314	C₂×C₈	—	11	2	no	—
315	C₂×C₈	—	22	4	no	—
316	C₂×C₈	—	22	4	no	—
317	C₂×C₈	—	22	4	no	—
318	C₂×C₈	—	22	4	no	—
319	C₂×C₈	—	22	4	no	—
320	C₂×C₈	—	22	4	no	—
321	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
322	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
323	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
324	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
325	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
326	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
327	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
328	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
329	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
330	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
332	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
333	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
335	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
336	C₄²	C₂³×D₁₁	1	1	yes	characteristic
337	C₁₁	#17793	1	1	yes	characteristic, complemented, Sylow
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
342	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
343	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	#66886	1	4	yes	—
360	C₂×C₄	M₁₆×D₁₁	1	4	yes	—
361	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
367	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
368	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
369	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
370	C₂×C₄	#67003	1	4	yes	—
371	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
374	C₈	—	4	4	no	—
375	C₈	—	11	4	no	—
376	C₈	—	11	4	no	—
377	C₈	—	22	2	no	—
378	C₈	—	22	2	no	—
379	C₈	—	44	4	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	#10622611	1	2	yes	—
388	C₂²	#10622731	1	2	yes	—
389	C₂²	C₂×#66886	1	2	yes	—
390	C₂²	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	#10622611	1	2	yes	—
398	C₄	#10622731	1	2	yes	—
399	C₄	C₂×#66886	1	2	yes	—
400	C₄	C₂×#66886	1	2	yes	—
401	C₄	C₂×M₁₆×D₁₁	1	2	yes	—
402	C₄	C₂×#67003	1	2	yes	—
403	C₂	—	2	2	no	—
404	C₂	—	2	2	no	—
405	C₂	—	2	2	no	—
406	C₂	C₂×#10622731	1	1	yes	characteristic
407	C₂	C₂×#10622611	1	1	yes	characteristic
408	C₂	C₂²×#66886	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#2920	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2920	D₁₁
hypocenter	C₁₁	#17793
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #13067377	C₂	semidirect
4. #13067374	C₂	semidirect
5. #13067371	C₂	semidirect
6. #13067362	C₂	semidirect
33. #10622118	C₂²	semidirect
34. #10622117	C₂²	semidirect
129. C₂×C₁₁⋊C₈	M₁₆	semidirect
337. C₁₁	#17793	semidirect

Maximal subgroups

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

subgroup	index
#13077249	2
C₂²×C₄×C₁₁⋊C₈	2
#13067377	2
#13067374	2
#13067371	2
#13067362	2
C₁₁×#2920	2
#17793	11