Subgroups — #14723075

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077741	C₂	1	1	yes	maximal, characteristic
2	#41×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13067407	C₂	1	1	yes	maximal, characteristic, complemented
4	#13067404	C₂	1	1	yes	maximal, characteristic, complemented
5	#13067402	C₂	1	2	yes	maximal, complemented
6	#13067399	C₂	1	2	yes	maximal, complemented
7	#13067377	C₂	1	2	yes	maximal, complemented
8	#13067374	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067362	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10622117	C₂	1	2	yes	maximal, complemented
11	C₁₁×#2990	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₁₁×#446	—	2	1	no	—
14	C₁₁×#435	—	2	2	no	—
15	C₈×D₄×C₁₁	—	2	1	no	—
16	C₁₁×#432	C₂²	1	2	yes	—
17	C₁₁×#431	C₂²	1	1	yes	characteristic
18	C₁₁×#423	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
20	#10622637	—	2	1	no	—
21	Q₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
22	Q₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
23	#10622624	—	2	2	no	—
24	D₄×C₁₁⋊C₈	—	2	1	no	—
25	D₄×C₁₁⋊C₈	C₄	1	2	yes	—
26	D₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
27	D₄×C₁₁⋊C₈	C₄	1	2	yes	—
28	D₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
29	#10622539	C₂²	1	2	yes	—
30	#10622538	C₂²	1	1	yes	characteristic
31	#10622538	C₂²	1	2	yes	—
32	#10622538	C₂²	1	1	yes	characteristic
33	#10622537	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
35	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
36	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
37	#10622118	C₂²	1	1	yes	characteristic
38	#10622118	C₂²	1	1	yes	characteristic
39	#10622118	C₂²	1	2	yes	—
40	#10622118	C₂²	1	2	yes	—
41	#10622117	C₂²	1	1	yes	characteristic
42	#10622117	C₂²	1	2	yes	—
43	#10622117	C₂²	1	2	yes	—
44	#10622117	C₂²	1	2	yes	—
45	#10622117	C₂²	1	1	yes	characteristic
46	#10622117	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	Q₈	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	2	no	—
50	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₁	D₄	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	D₄	1	1	yes	characteristic
55	C₄×D₄×C₁₁	D₄	1	2	yes	—
56	C₁₁×#117	Q₈	1	1	yes	characteristic
57	C₁₁×#117	Q₈	1	2	yes	—
58	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×#4318	—	2	1	no	—
61	C₂²×C₁₁⋊C₈	—	2	2	no	—
62	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
63	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
65	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₁₁×C₄⋊C₈	—	2	2	no	—
67	C₁₁×C₄⋊C₈	—	2	1	no	—
68	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
69	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
70	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
71	C₁₁×C₂²⋊C₈	—	2	1	no	—
72	C₁₁×C₂²⋊C₈	—	2	2	no	—
73	C₁₁×#97	—	2	2	no	—
74	C₄×C₈×C₁₁	—	2	1	no	—
75	C₂²⋊(C₁₁⋊C₈)	—	2	1	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	2	no	—
81	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
82	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
83	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
84	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
85	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
86	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
87	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
88	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
89	#66867	—	2	2	no	—
90	C₄×C₁₁⋊C₈	—	2	1	no	—
91	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
92	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
94	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
96	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
97	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
98	#17836	—	11	1	no	maximal, Sylow
99	C₁₁×#41	—	2	4	no	—
100	C₂×Q₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₄×C₁₁	C₄⋊C₄	1	2	yes	—
102	C₂×D₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
109	C₁₁×M₁₆	—	8	1	no	—
110	C₂×C₈×C₁₁	—	2	1	no	—
111	C₂×C₈×C₁₁	—	2	1	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	8	2	no	—
114	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
115	C₁₁×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
116	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
117	C₁₁×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
118	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
119	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
121	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
122	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₁	C₂×D₄	1	2	yes	—
125	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
126	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
128	#4318	—	8	1	no	—
129	C₂×C₁₁⋊C₈	—	2	4	no	—
130	C₂×C₁₁⋊C₈	—	2	2	no	—
131	C₂×C₁₁⋊C₈	—	2	1	no	—
132	C₂×C₁₁⋊C₈	—	2	1	no	—
133	C₂×C₁₁⋊C₈	—	2	2	no	—
134	C₂×C₁₁⋊C₈	—	4	2	no	—
135	C₂×C₁₁⋊C₈	—	4	1	no	—
136	C₂×C₁₁⋊C₈	—	8	2	no	—
137	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
143	#2990	—	11	1	no	—
144	#2990	D₁₁	1	1	yes	characteristic
145	C₈×#41	—	11	1	no	—
146	#1574	—	11	1	no	—
147	#1574	—	11	1	no	—
148	#1573	—	11	2	no	—
149	#1573	—	11	2	no	—
150	#1568	—	11	2	no	—
151	#1567	—	11	1	no	—
152	#1564	—	11	1	no	—
153	C₂×#335	—	11	2	no	—
154	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
156	Q₈×C₁₁	—	2	2	no	—
157	D₄×C₁₁	—	2	4	no	—
158	D₄×C₁₁	#108	1	4	yes	—
159	C₂×C₄×C₁₁	—	2	4	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	2	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
178	C₈×C₁₁	—	4	1	no	—
179	C₈×C₁₁	—	4	2	no	—
180	C₈×C₁₁	—	4	1	no	—
181	C₁₁⋊C₈	—	2	2	no	—
182	C₁₁⋊C₈	—	2	1	no	—
183	C₁₁⋊C₈	—	2	1	no	—
184	C₁₁⋊C₈	—	2	2	no	—
185	C₁₁⋊C₈	—	2	1	no	—
186	C₁₁⋊C₈	—	4	1	no	—
187	C₁₁⋊C₈	—	4	2	no	—
188	C₁₁⋊C₈	—	4	1	no	—
189	C₁₁⋊C₈	#131	1	2	yes	—
190	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
191	#446	—	2	1	no	—
192	#446	—	22	1	no	—
193	C₈×Q₈	—	11	1	no	—
194	C₈×Q₈	—	11	1	no	—
195	#435	—	2	2	no	—
196	#435	—	22	2	no	—
197	C₈×D₄	—	2	1	no	—
198	C₈×D₄	—	11	2	no	—
199	C₈×D₄	—	11	1	no	—
200	C₈×D₄	—	11	2	no	—
201	C₈×D₄	—	11	1	no	—
202	C₈×D₄	—	22	1	no	—
203	#432	—	11	2	no	—
204	#432	C₂×D₁₁	1	2	yes	—
205	#431	—	11	2	no	—
206	#431	—	11	1	no	—
207	#431	—	11	1	no	—
208	#431	C₂×D₁₁	1	1	yes	characteristic
209	#423	—	11	1	no	—
210	#423	C₂×D₁₁	1	1	yes	characteristic
211	C₂×C₄⋊C₈	—	11	2	no	—
212	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
213	C₂×C₄×C₈	—	11	2	no	—
214	C₂×C₄×C₈	—	11	1	no	—
215	#335	—	11	1	no	—
216	#335	—	11	2	no	—
217	#335	—	11	2	no	—
218	#335	—	11	2	no	—
219	#335	—	11	1	no	—
220	#335	—	11	2	no	—
221	#334	—	11	1	no	—
222	#334	—	11	1	no	—
223	#334	—	11	2	no	—
224	#334	—	11	2	no	—
225	C₂²×C₁₁	—	2	2	no	—
226	C₂²×C₁₁	—	2	2	no	—
227	C₂²×C₁₁	—	2	1	no	—
228	C₂²×C₁₁	—	2	1	no	—
229	C₂²×C₁₁	—	2	1	no	—
230	C₂²×C₁₁	C₂×#108	1	4	yes	—
231	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
232	C₄×C₁₁	—	2	2	no	—
233	C₄×C₁₁	—	2	1	no	—
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	—	2	1	no	—
236	C₄×C₁₁	—	2	1	no	—
237	C₄×C₁₁	—	2	2	no	—
238	C₄×C₁₁	C₂×#108	1	2	yes	—
239	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
240	C₄×C₁₁	#568	1	1	yes	characteristic
241	C₄×C₁₁	#576	1	1	yes	characteristic
242	C₄×C₁₁	#578	1	1	yes	characteristic
243	C₂×#41	Dic₂₂	1	1	yes	characteristic
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	22	1	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	11	2	no	—
248	C₂²×C₈	—	11	1	no	—
249	C₂²×C₈	—	11	2	no	—
250	C₂²×C₈	—	11	1	no	—
251	C₂²×C₈	—	22	2	no	—
252	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
253	C₄×Q₈	C₂²⋊D₁₁	1	1	yes	characteristic
254	C₄×D₄	C₄×D₁₁	1	2	yes	—
255	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
256	C₄×D₄	C₂²⋊D₁₁	1	1	yes	characteristic
257	C₄×D₄	C₂²⋊D₁₁	1	2	yes	—
258	#117	Dic₂₂	1	1	yes	characteristic
259	#117	Dic₂₂	1	2	yes	—
260	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
261	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	11	2	no	—
265	C₄⋊C₈	—	11	2	no	—
266	C₄⋊C₈	—	11	1	no	—
267	C₄⋊C₈	—	11	1	no	—
268	C₄⋊C₈	—	11	1	no	—
269	C₄⋊C₈	—	11	1	no	—
270	C₄⋊C₈	—	11	2	no	—
271	C₄⋊C₈	—	22	2	no	—
272	C₄⋊C₈	—	22	1	no	—
273	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
274	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
275	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	11	2	no	—
279	C₂²⋊C₈	—	11	2	no	—
280	C₂²⋊C₈	—	11	2	no	—
281	C₂²⋊C₈	—	22	1	no	—
282	C₂²⋊C₈	—	22	2	no	—
283	#97	—	2	2	no	—
284	#97	—	22	2	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	11	2	no	—
287	C₄×C₈	—	11	1	no	—
288	C₄×C₈	—	11	2	no	—
289	C₄×C₈	—	11	1	no	—
290	C₄×C₈	—	11	1	no	—
291	C₄×C₈	—	11	2	no	—
292	C₄×C₈	—	11	1	no	—
293	C₄×C₈	—	22	1	no	—
294	C₂×C₁₁	—	2	4	no	—
295	C₂×C₁₁	—	4	1	no	—
296	C₂×C₁₁	#2906	1	1	yes	characteristic
297	C₂×C₁₁	#2913	1	1	yes	characteristic
298	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
299	#41	—	2	4	no	—
300	C₂×Q₈	Dic₁₁⋊C₄	1	1	yes	characteristic
301	C₂×D₄	Dic₁₁⋊C₄	1	2	yes	—
302	C₂×D₄	Dic₁₁⋊C₄	1	1	yes	characteristic
303	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
304	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
307	C₂²×C₄	C₂×C₂²⋊D₁₁	1	2	yes	—
308	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
309	M₁₆	—	8	1	no	—
310	M₁₆	—	88	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	8	2	no	—
315	C₂×C₈	—	11	1	no	—
316	C₂×C₈	—	11	1	no	—
317	C₂×C₈	—	11	2	no	—
318	C₂×C₈	—	11	1	no	—
319	C₂×C₈	—	11	2	no	—
320	C₂×C₈	—	11	1	no	—
321	C₂×C₈	—	22	4	no	—
322	C₂×C₈	—	22	2	no	—
323	C₂×C₈	—	22	1	no	—
324	C₂×C₈	—	22	1	no	—
325	C₂×C₈	—	22	2	no	—
326	C₂×C₈	—	44	2	no	—
327	C₂×C₈	—	44	1	no	—
328	C₂×C₈	—	88	2	no	—
329	C₄⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
330	C₄⋊C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
331	C₄⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
332	C₄⋊C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
333	C₂²⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
334	C₂²⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
335	C₂²⋊C₄	Dic₁₁⋊C₄	1	2	yes	—
336	C₄²	C₂×Dic₂₂	1	2	yes	—
337	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₁₁	1	2	yes	—
339	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
341	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
342	C₄²	C₂³×D₁₁	1	1	yes	characteristic
343	C₁₁	#17836	1	1	yes	characteristic, complemented, Sylow
344	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
345	C₂³	C₂×Dic₁₁⋊C₄	1	2	yes	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	4	no	—
348	D₄	#66886	1	4	yes	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	C₂×Dic₁₁⋊C₄	1	2	yes	—
360	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
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	2	yes	—
364	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
368	C₈	—	4	1	no	—
369	C₈	—	4	2	no	—
370	C₈	—	4	1	no	—
371	C₈	—	11	2	no	—
372	C₈	—	22	2	no	—
373	C₈	—	22	1	no	—
374	C₈	—	22	1	no	—
375	C₈	—	22	2	no	—
376	C₈	—	22	1	no	—
377	C₈	—	44	1	no	—
378	C₈	—	44	2	no	—
379	C₈	—	44	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	C₂×#66886	1	4	yes	—
386	C₂²	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	C₂×#66886	1	2	yes	—
394	C₄	D₁₁×#131	1	1	yes	characteristic
395	C₄	#10623281	1	1	yes	characteristic
396	C₄	#10623366	1	1	yes	characteristic
397	C₄	#10623369	1	1	yes	characteristic
398	C₂	—	2	4	no	—
399	C₂	—	4	1	no	—
400	C₂	#13077182	1	1	yes	characteristic
401	C₂	#13077214	1	1	yes	characteristic
402	C₂	C₂²×#66886	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×#2990	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×C₁₁×#41	Q₈
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2990	D₁₁
hypocenter	C₁₁	#17836
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
3. #13067407	C₂	semidirect
4. #13067404	C₂	semidirect
5. #13067402	C₂	semidirect
6. #13067399	C₂	semidirect
7. #13067377	C₂	semidirect
8. #13067374	C₂	semidirect
9. #13067362	C₂	semidirect
10. C₂×#10622117	C₂	semidirect
343. C₁₁	#17836	semidirect

Maximal subgroups

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

subgroup	index
#13077741	2
#41×C₁₁⋊C₈	2
#13067407	2
#13067404	2
#13067402	2
#13067399	2
#13067377	2
#13067374	2
#13067362	2
C₂×#10622117	2
C₁₁×#2990	2
#17836	11