Subgroups — #14723014

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#13077282	C₂	1	1	yes	maximal, characteristic
3	#13067397	C₂	1	2	yes	maximal, complemented
4	#13067394	C₂	1	2	yes	maximal, complemented
5	#13067388	C₂	1	1	yes	maximal, characteristic, complemented
6	#13067386	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067377	C₂	1	2	yes	maximal, complemented
8	#13067374	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067362	C₂	1	2	yes	maximal, complemented
10	C₂×#10622117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2925	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₁₁×#433	—	2	2	no	—
14	C₁₁×#432	C₂²	1	2	yes	—
15	C₁₁×#431	C₂²	1	2	yes	—
16	C₁₁×#423	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₁₁×#408	—	2	1	no	—
19	C₁₁×#405	—	2	1	no	—
20	#10622847	—	2	1	no	—
21	Q₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
22	Q₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
23	D₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
24	D₄×C₁₁⋊C₈	C₄	1	2	yes	—
25	D₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
26	D₄×C₁₁⋊C₈	C₄	1	2	yes	—
27	#10622613	—	2	2	no	—
28	#10622610	—	2	1	no	—
29	#10622539	C₂²	1	2	yes	—
30	#10622538	C₂²	1	2	yes	—
31	#10622538	C₂²	1	1	yes	characteristic
32	#10622538	C₂²	1	2	yes	—
33	#10622537	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
37	#10622118	C₂²	1	2	yes	—
38	#10622118	C₂²	1	2	yes	—
39	#10622118	C₂²	1	2	yes	—
40	#10622118	C₂²	1	2	yes	—
41	#10622117	C₂²	1	1	yes	characteristic
42	#10622117	C₂²	1	1	yes	characteristic
43	#10622117	C₂²	1	1	yes	characteristic
44	#10622117	C₂²	1	1	yes	characteristic
45	#10622117	C₂²	1	2	yes	—
46	#10622117	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	D₄	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₁	Q₈	1	1	yes	characteristic
52	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₄×D₄×C₁₁	Q₈	1	2	yes	—
55	C₄×D₄×C₁₁	Q₈	1	1	yes	characteristic
56	C₁₁×#117	D₄	1	1	yes	characteristic
57	C₁₁×#117	D₄	1	2	yes	—
58	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
60	C₂×#4318	—	2	1	no	—
61	C₂²×C₁₁⋊C₈	—	2	1	no	—
62	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
64	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
66	C₁₁×C₄⋊C₈	—	2	1	no	—
67	C₁₁×C₄⋊C₈	—	2	1	no	—
68	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
69	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
70	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₁×C₂²⋊C₈	—	2	2	no	—
72	C₁₁×C₂²⋊C₈	—	2	2	no	—
73	C₁₁×#97	—	2	2	no	—
74	C₄×C₈×C₁₁	—	2	2	no	—
75	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
78	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
79	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
80	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
81	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
82	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
83	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
84	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
85	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
86	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
87	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
88	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
89	#66867	—	2	2	no	—
90	C₄×C₁₁⋊C₈	—	2	2	no	—
91	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
93	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
95	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
96	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
97	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
98	#17829	—	11	1	no	maximal, Sylow
99	C₁₁×#41	—	2	2	no	—
100	C₁₁×#41	—	2	2	no	—
101	C₂×Q₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₂×D₄×C₁₁	C₄⋊C₄	1	2	yes	—
103	C₂×D₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
110	C₁₁×M₁₆	—	4	2	no	—
111	C₂×C₈×C₁₁	—	2	1	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	4	2	no	—
115	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
116	C₁₁×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
117	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
118	C₁₁×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
119	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
121	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
122	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
123	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₁	C₂×D₄	1	2	yes	—
125	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
127	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
129	#4318	—	4	2	no	—
130	C₂×C₁₁⋊C₈	—	2	2	no	—
131	C₂×C₁₁⋊C₈	—	2	4	no	—
132	C₂×C₁₁⋊C₈	—	2	1	no	—
133	C₂×C₁₁⋊C₈	—	2	2	no	—
134	C₂×C₁₁⋊C₈	—	2	1	no	—
135	C₂×C₁₁⋊C₈	—	4	1	no	—
136	C₂×C₁₁⋊C₈	—	4	2	no	—
137	C₂×C₁₁⋊C₈	—	4	2	no	—
138	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₈×#41	—	11	1	no	—
145	#2925	—	11	1	no	—
146	#2925	D₁₁	1	1	yes	characteristic
147	#1572	—	11	2	no	—
148	#1572	—	11	2	no	—
149	#1570	—	11	1	no	—
150	#1570	—	11	1	no	—
151	#1568	—	11	2	no	—
152	#1567	—	11	1	no	—
153	#1564	—	11	2	no	—
154	C₂×#335	—	11	1	no	—
155	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
156	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
157	Q₈×C₁₁	—	2	2	no	—
158	D₄×C₁₁	—	2	4	no	—
159	D₄×C₁₁	—	2	2	no	—
160	C₂×C₄×C₁₁	—	2	1	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	4	1	no	—
167	C₂×C₄×C₁₁	—	4	2	no	—
168	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁	#135	1	2	yes	—
175	C₂×C₄×C₁₁	#135	1	2	yes	—
176	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
179	C₈×C₁₁	—	4	1	no	—
180	C₈×C₁₁	—	4	1	no	—
181	C₈×C₁₁	—	4	2	no	—
182	C₁₁⋊C₈	—	2	1	no	—
183	C₁₁⋊C₈	—	2	2	no	—
184	C₁₁⋊C₈	—	2	1	no	—
185	C₁₁⋊C₈	—	2	1	no	—
186	C₁₁⋊C₈	—	2	2	no	—
187	C₁₁⋊C₈	—	4	1	no	—
188	C₁₁⋊C₈	—	4	1	no	—
189	C₁₁⋊C₈	—	4	2	no	—
190	C₁₁⋊C₈	#131	1	2	yes	—
191	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
192	C₈×Q₈	—	11	1	no	—
193	C₈×Q₈	—	11	1	no	—
194	C₈×D₄	—	11	1	no	—
195	C₈×D₄	—	11	2	no	—
196	C₈×D₄	—	11	1	no	—
197	C₈×D₄	—	11	2	no	—
198	#433	—	2	2	no	—
199	#433	—	22	2	no	—
200	#432	—	11	2	no	—
201	#432	C₂×D₁₁	1	2	yes	—
202	#431	—	11	1	no	—
203	#431	—	11	2	no	—
204	#431	—	11	2	no	—
205	#431	C₂×D₁₁	1	2	yes	—
206	#423	—	11	1	no	—
207	#423	C₂×D₁₁	1	1	yes	characteristic
208	C₂×C₄⋊C₈	—	11	1	no	—
209	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
210	#408	—	2	1	no	—
211	#408	—	22	1	no	—
212	#405	—	2	1	no	—
213	#405	—	22	1	no	—
214	C₂×C₄×C₈	—	11	1	no	—
215	C₂×C₄×C₈	—	11	2	no	—
216	#335	—	11	1	no	—
217	#335	—	11	1	no	—
218	#335	—	11	1	no	—
219	#335	—	11	1	no	—
220	#335	—	11	2	no	—
221	#335	—	11	2	no	—
222	#334	—	11	2	no	—
223	#334	—	11	2	no	—
224	#334	—	11	2	no	—
225	#334	—	11	2	no	—
226	C₂²×C₁₁	—	2	1	no	—
227	C₂²×C₁₁	—	2	1	no	—
228	C₂²×C₁₁	—	2	2	no	—
229	C₂²×C₁₁	—	2	2	no	—
230	C₂²×C₁₁	—	2	2	no	—
231	C₂²×C₁₁	#427	1	2	yes	—
232	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
233	C₄×C₁₁	—	2	1	no	—
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	—	2	2	no	—
236	C₄×C₁₁	—	2	1	no	—
237	C₄×C₁₁	—	2	1	no	—
238	C₄×C₁₁	—	2	2	no	—
239	C₄×C₁₁	#427	1	2	yes	—
240	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
241	C₄×C₁₁	#568	1	1	yes	characteristic
242	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
243	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
244	C₂×#41	C₂²⋊D₁₁	1	1	yes	characteristic
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	22	1	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	11	1	no	—
249	C₂²×C₈	—	11	2	no	—
250	C₂²×C₈	—	11	1	no	—
251	C₂²×C₈	—	11	2	no	—
252	C₂²×C₈	—	22	1	no	—
253	C₄×Q₈	Dic₂₂	1	1	yes	characteristic
254	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
255	C₄×D₄	Dic₂₂	1	2	yes	—
256	C₄×D₄	Dic₂₂	1	1	yes	characteristic
257	C₄×D₄	C₄×D₁₁	1	2	yes	—
258	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
259	#117	C₂²⋊D₁₁	1	1	yes	characteristic
260	#117	C₂²⋊D₁₁	1	2	yes	—
261	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	11	1	no	—
266	C₄⋊C₈	—	11	1	no	—
267	C₄⋊C₈	—	11	2	no	—
268	C₄⋊C₈	—	11	2	no	—
269	C₄⋊C₈	—	11	1	no	—
270	C₄⋊C₈	—	11	1	no	—
271	C₄⋊C₈	—	11	2	no	—
272	C₄⋊C₈	—	22	1	no	—
273	C₄⋊C₈	—	22	1	no	—
274	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
275	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
276	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	2	2	no	—
279	C₂²⋊C₈	—	11	2	no	—
280	C₂²⋊C₈	—	11	2	no	—
281	C₂²⋊C₈	—	11	2	no	—
282	C₂²⋊C₈	—	22	2	no	—
283	C₂²⋊C₈	—	22	2	no	—
284	#97	—	2	2	no	—
285	#97	—	22	2	no	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	11	1	no	—
288	C₄×C₈	—	11	2	no	—
289	C₄×C₈	—	11	1	no	—
290	C₄×C₈	—	11	2	no	—
291	C₄×C₈	—	11	2	no	—
292	C₄×C₈	—	11	1	no	—
293	C₄×C₈	—	11	1	no	—
294	C₄×C₈	—	22	2	no	—
295	C₂×C₁₁	—	2	2	no	—
296	C₂×C₁₁	—	4	2	no	—
297	C₂×C₁₁	#2906	1	1	yes	characteristic
298	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
299	C₂×C₁₁	#2916	1	1	yes	characteristic
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	C₂×Q₈	Dic₁₁⋊C₄	1	1	yes	characteristic
303	C₂×D₄	Dic₁₁⋊C₄	1	2	yes	—
304	C₂×D₄	Dic₁₁⋊C₄	1	1	yes	characteristic
305	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
306	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
308	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₁₁	1	2	yes	—
310	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
311	M₁₆	—	4	2	no	—
312	M₁₆	—	44	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	11	1	no	—
318	C₂×C₈	—	11	1	no	—
319	C₂×C₈	—	11	2	no	—
320	C₂×C₈	—	11	1	no	—
321	C₂×C₈	—	11	2	no	—
322	C₂×C₈	—	11	1	no	—
323	C₂×C₈	—	22	2	no	—
324	C₂×C₈	—	22	4	no	—
325	C₂×C₈	—	22	1	no	—
326	C₂×C₈	—	22	2	no	—
327	C₂×C₈	—	22	1	no	—
328	C₂×C₈	—	44	1	no	—
329	C₂×C₈	—	44	2	no	—
330	C₂×C₈	—	44	2	no	—
331	C₄⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
332	C₄⋊C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
333	C₄⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
334	C₄⋊C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
335	C₂²⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
336	C₂²⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
337	C₂²⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
338	C₄²	C₂×Dic₂₂	1	2	yes	—
339	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₁₁	1	2	yes	—
341	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
342	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
343	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
344	C₄²	C₂³×D₁₁	1	1	yes	characteristic
345	C₁₁	#17829	1	1	yes	characteristic, complemented, Sylow
346	C₂³	C₂×Dic₁₁⋊C₄	1	2	yes	—
347	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
348	Q₈	—	2	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×Dic₁₁⋊C₄	1	2	yes	—
360	C₂×C₄	C₂×Dic₁₁⋊C₄	1	2	yes	—
361	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₁₁⋊C₄	1	2	yes	—
363	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
365	C₂×C₄	#67003	1	2	yes	—
366	C₂×C₄	#67003	1	2	yes	—
367	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
370	C₈	—	4	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	11	2	no	—
374	C₈	—	22	2	no	—
375	C₈	—	22	1	no	—
376	C₈	—	22	1	no	—
377	C₈	—	22	2	no	—
378	C₈	—	22	1	no	—
379	C₈	—	44	1	no	—
380	C₈	—	44	1	no	—
381	C₈	—	44	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	#10622611	1	2	yes	—
388	C₂²	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	#10622611	1	2	yes	—
396	C₄	D₁₁×#131	1	1	yes	characteristic
397	C₄	#10623281	1	1	yes	characteristic
398	C₄	C₂×#67003	1	1	yes	characteristic
399	C₄	C₂×#67003	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	#13077182	1	1	yes	characteristic
403	C₂	C₂×#10622611	1	1	yes	characteristic
404	C₂	#13077225	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#2925	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×C₁₁×#41	D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2925	D₁₁
hypocenter	C₁₁	#17829
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2925

Complements

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

N	H ≅ G/N	type
3. #13067397	C₂	semidirect
4. #13067394	C₂	semidirect
5. #13067388	C₂	semidirect
6. #13067386	C₂	semidirect
7. #13067377	C₂	semidirect
8. #13067374	C₂	semidirect
9. #13067362	C₂	semidirect
10. C₂×#10622117	C₂	semidirect
345. C₁₁	#17829	semidirect

Maximal subgroups

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

subgroup	index
#41×C₁₁⋊C₈	2
#13077282	2
#13067397	2
#13067394	2
#13067388	2
#13067386	2
#13067377	2
#13067374	2
#13067362	2
C₂×#10622117	2
C₁₁×#2925	2
#17829	11