Subgroups — #14907342

Order 2816.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#4339	C₂	1	1	yes	maximal, characteristic
2	#13070523	C₂	1	2	yes	maximal, complemented
3	#13070440	C₂	1	2	yes	maximal, complemented
4	#13070438	C₂	1	2	yes	maximal, complemented
5	(C₂²⋊D₁₁)⋊C₁₆	C₂	1	2	yes	maximal, complemented
6	#13070417	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070417	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070209	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10622099	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4339	C₄	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
15	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
16	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
17	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
18	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
19	#10622538	C₄	1	1	yes	characteristic
20	C₂×#66862	C₂²	1	2	yes	—
21	C₂×C₁₆×D₁₁	C₂²	1	2	yes	—
22	C₈×D₄₄	C₄	1	1	yes	characteristic
23	C₈×D₄₄	C₂²	1	1	yes	characteristic
24	#10622298	C₄	1	1	yes	characteristic
25	#10622298	C₄	1	1	yes	characteristic
26	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
28	C₈×Dic₂₂	C₄	1	1	yes	characteristic
29	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
30	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
31	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
32	C₁₁×#346	C₂²	1	1	yes	characteristic
33	C₁₁×#346	C₂²	1	1	yes	characteristic
34	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	—
35	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	—
36	#10622140	C₂²	1	2	yes	—
37	Dic₁₁⋊C₁₆	C₂²	1	2	yes	—
38	Dic₁₁⋊C₁₆	C₂²	1	2	yes	—
39	C₁₆×Dic₁₁	C₂²	1	2	yes	—
40	#10622099	C₂²	1	1	yes	characteristic
41	#10622099	C₂²	1	2	yes	—
42	#10622099	C₂²	1	1	yes	characteristic
43	C₂×#4339	C₈	1	1	yes	characteristic
44	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
49	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
51	#66979	C₈	1	1	yes	characteristic
52	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
56	C₄×D₄₄	C₈	1	1	yes	characteristic
57	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
58	#66925	C₈	1	1	yes	characteristic
59	#66925	C₈	1	1	yes	characteristic
60	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₂₂	C₈	1	1	yes	characteristic
63	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
65	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
66	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
67	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
71	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
72	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
73	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
74	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
75	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
76	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
77	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
78	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
79	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
83	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
84	C₂×C₁₁⋊C₁₆	—	2	4	no	—
85	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
86	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
87	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
88	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
89	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
91	#66862	—	2	4	no	—
92	C₁₆×D₁₁	—	2	4	no	—
93	#33484	—	11	1	no	maximal, Sylow
94	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
99	#4339	—	2	4	no	—
100	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
114	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
115	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
116	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
119	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
120	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
121	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
122	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
123	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
124	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
125	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
126	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
127	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
128	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
129	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₈×D₁₁	—	2	2	no	—
141	C₈×D₁₁	—	2	2	no	—
142	C₈×D₁₁	—	2	2	no	—
143	C₈×D₁₁	—	2	2	no	—
144	C₁₁×C₁₆	—	2	2	no	—
145	C₁₁×C₁₆	—	2	2	no	—
146	C₁₁⋊C₁₆	—	2	2	no	—
147	C₁₁⋊C₁₆	#41	1	4	yes	complemented
148	C₈×#41	—	11	1	no	—
149	#2183	—	11	2	no	—
150	#2168	—	11	2	no	—
151	#2168	—	11	2	no	—
152	D₄×C₁₆	—	11	2	no	—
153	#2163	—	11	1	no	—
154	#2163	—	11	1	no	—
155	#2163	D₁₁	1	1	yes	characteristic, complemented
156	C₄×M₃₂	—	11	1	no	—
157	C₂×#346	—	11	1	no	—
158	C₂×#346	—	11	1	no	—
159	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₁₁	—	2	2	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	1	no	—
165	C₂×C₄×C₁₁	—	4	1	no	—
166	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
172	C₂²⋊D₁₁	—	2	2	no	—
173	C₂²⋊D₁₁	M₃₂	1	4	yes	complemented
174	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
180	D₄₄	—	2	2	no	—
181	C₄×D₁₁	—	2	2	no	—
182	C₄×D₁₁	—	2	1	no	—
183	C₄×D₁₁	—	2	1	no	—
184	C₄×D₁₁	—	2	1	no	—
185	C₄×D₁₁	—	2	1	no	—
186	C₄×D₁₁	—	2	2	no	—
187	C₄×D₁₁	—	4	1	no	—
188	C₄×D₁₁	—	4	1	no	—
189	Dic₂₂	—	2	2	no	—
190	C₈×C₁₁	—	2	1	no	—
191	C₈×C₁₁	—	2	1	no	—
192	C₈×C₁₁	#131	1	2	yes	—
193	C₈×C₁₁	C₂×#41	1	2	yes	—
194	C₁₁⋊C₈	—	2	1	no	—
195	C₁₁⋊C₈	—	2	1	no	—
196	C₁₁⋊C₈	—	2	1	no	—
197	C₁₁⋊C₈	—	2	1	no	—
198	C₄×#41	—	11	1	no	—
199	C₂×M₃₂	—	11	2	no	—
200	C₂²×C₁₆	—	11	2	no	—
201	C₂²×C₁₆	—	11	2	no	—
202	C₈×Q₈	—	11	1	no	—
203	C₈×Q₈	—	11	1	no	—
204	C₈×D₄	—	11	1	no	—
205	C₈×D₄	—	11	1	no	—
206	C₈×D₄	—	11	1	no	—
207	C₈×D₄	—	11	1	no	—
208	C₈×D₄	—	11	1	no	—
209	C₈×D₄	—	11	1	no	—
210	#431	—	11	1	no	—
211	#431	—	11	1	no	—
212	#431	—	11	1	no	—
213	C₂×C₄×C₈	—	11	1	no	—
214	C₂×C₄×C₈	—	11	1	no	—
215	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
216	C₄⋊C₁₆	—	11	2	no	—
217	C₄⋊C₁₆	—	11	2	no	—
218	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
219	C₂²⋊C₁₆	—	11	2	no	—
220	C₂²⋊C₁₆	—	11	2	no	—
221	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	—
222	#346	—	11	2	no	—
223	#346	—	11	1	no	—
224	#346	—	11	1	no	—
225	#346	—	11	2	no	—
226	#346	C₂×D₁₁	1	1	yes	characteristic
227	#346	C₂×D₁₁	1	1	yes	characteristic
228	C₄×C₁₆	—	11	2	no	—
229	C₂²×C₁₁	—	2	1	no	—
230	C₂²×C₁₁	—	2	1	no	—
231	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
232	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
233	C₂×D₁₁	—	2	1	no	—
234	C₂×D₁₁	—	2	1	no	—
235	C₂×D₁₁	—	2	1	no	—
236	C₂×D₁₁	—	2	1	no	—
237	C₂×D₁₁	—	2	1	no	—
238	C₂×D₁₁	C₂×M₃₂	1	2	yes	—
239	C₄×C₁₁	—	2	1	no	—
240	C₄×C₁₁	—	2	1	no	—
241	C₄×C₁₁	—	2	1	no	—
242	C₄×C₁₁	—	2	1	no	—
243	C₄×C₁₁	—	2	1	no	—
244	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
245	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
246	Dic₁₁	—	2	1	no	—
247	Dic₁₁	—	2	1	no	—
248	Dic₁₁	—	2	1	no	—
249	Dic₁₁	—	2	1	no	—
250	Dic₁₁	—	2	1	no	—
251	Dic₁₁	C₂×M₃₂	1	2	yes	—
252	C₂×#41	—	11	1	no	—
253	C₂²×C₈	—	11	1	no	—
254	C₂²×C₈	—	11	1	no	—
255	C₂²×C₈	—	11	1	no	—
256	C₂²×C₈	—	11	1	no	—
257	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
259	C₄×Q₈	—	11	1	no	—
260	C₄×Q₈	—	11	1	no	—
261	C₄×D₄	—	11	1	no	—
262	C₄×D₄	—	11	1	no	—
263	C₄×D₄	—	11	1	no	—
264	C₄×D₄	—	11	1	no	—
265	C₄×D₄	—	11	1	no	—
266	C₄×D₄	—	11	1	no	—
267	#117	—	11	1	no	—
268	#117	—	11	1	no	—
269	#117	—	11	1	no	—
270	C₂×C₄²	—	11	1	no	—
271	C₂×C₄²	—	11	1	no	—
272	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
273	M₃₂	—	22	4	no	—
274	C₂×C₁₆	—	11	2	no	—
275	C₂×C₁₆	—	11	2	no	—
276	C₂×C₁₆	—	22	4	no	—
277	C₂×C₁₆	—	22	4	no	—
278	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
279	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
280	C₄⋊C₈	—	11	1	no	—
281	C₄⋊C₈	—	11	1	no	—
282	C₄⋊C₈	—	11	1	no	—
283	C₄⋊C₈	—	11	1	no	—
284	C₄⋊C₈	—	11	1	no	—
285	C₄⋊C₈	—	11	1	no	—
286	C₂²⋊C₈	—	11	1	no	—
287	C₂²⋊C₈	—	11	1	no	—
288	C₂²⋊C₈	—	11	1	no	—
289	C₂²⋊C₈	—	11	1	no	—
290	C₂²⋊C₈	—	11	1	no	—
291	C₂²⋊C₈	—	11	1	no	—
292	C₄×C₈	—	11	1	no	—
293	C₄×C₈	—	11	1	no	—
294	C₄×C₈	—	11	1	no	—
295	C₄×C₈	—	11	1	no	—
296	C₄×C₈	—	11	1	no	—
297	C₄×C₈	—	11	1	no	—
298	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
299	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
300	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
302	C₂×C₁₁	—	2	2	no	—
303	C₂×C₁₁	C₈×#41	1	1	yes	characteristic
304	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
305	C₂×C₁₁	#3407	1	1	yes	characteristic
306	D₁₁	—	2	2	no	—
307	D₁₁	—	4	1	no	—
308	#41	—	22	4	no	—
309	C₂×Q₈	—	11	1	no	—
310	C₂×D₄	—	11	1	no	—
311	C₂×D₄	—	11	1	no	—
312	C₂×D₄	—	11	1	no	—
313	C₂²×C₄	—	11	1	no	—
314	C₂²×C₄	—	11	1	no	—
315	C₂²×C₄	—	11	1	no	—
316	C₂²×C₄	—	11	1	no	—
317	C₂²×C₄	—	11	1	no	—
318	C₂²×C₄	—	11	1	no	—
319	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
320	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	11	1	no	—
325	C₂×C₈	—	11	1	no	—
326	C₂×C₈	—	11	1	no	—
327	C₂×C₈	—	11	1	no	—
328	C₂×C₈	—	22	2	no	—
329	C₂×C₈	—	22	2	no	—
330	C₂×C₈	—	22	2	no	—
331	C₂×C₈	—	22	2	no	—
332	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
335	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
336	C₄⋊C₄	—	11	1	no	—
337	C₄⋊C₄	—	11	1	no	—
338	C₄⋊C₄	—	11	1	no	—
339	C₄⋊C₄	—	11	1	no	—
340	C₄⋊C₄	—	11	1	no	—
341	C₄⋊C₄	—	11	1	no	—
342	C₂²⋊C₄	—	11	1	no	—
343	C₂²⋊C₄	—	11	1	no	—
344	C₂²⋊C₄	—	11	1	no	—
345	C₂²⋊C₄	—	11	1	no	—
346	C₂²⋊C₄	—	11	1	no	—
347	C₂²⋊C₄	—	11	1	no	—
348	C₄²	—	11	1	no	—
349	C₄²	—	11	1	no	—
350	C₄²	—	11	1	no	—
351	C₄²	—	11	1	no	—
352	C₄²	—	11	1	no	—
353	C₄²	—	11	1	no	—
354	C₄²	C₈×D₁₁	1	1	yes	characteristic
355	C₄²	C₈×D₁₁	1	1	yes	characteristic
356	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
358	C₁₆	—	2	2	no	—
359	C₁₆	—	2	2	no	—
360	C₁₆	—	11	4	no	—
361	C₁₆	—	22	2	no	—
362	C₁₁	#33484	1	1	yes	characteristic, complemented, Sylow
363	C₂³	—	11	1	no	—
364	C₂³	—	11	1	no	—
365	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
366	Q₈	—	22	2	no	—
367	D₄	—	11	4	no	—
368	D₄	—	22	2	no	—
369	D₄	—	22	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	11	1	no	—
375	C₂×C₄	—	11	1	no	—
376	C₂×C₄	—	11	1	no	—
377	C₂×C₄	—	11	1	no	—
378	C₂×C₄	—	11	1	no	—
379	C₂×C₄	—	11	1	no	—
380	C₂×C₄	—	22	2	no	—
381	C₂×C₄	—	22	2	no	—
382	C₂×C₄	—	22	1	no	—
383	C₂×C₄	—	22	1	no	—
384	C₂×C₄	—	22	1	no	—
385	C₂×C₄	—	22	1	no	—
386	C₂×C₄	—	44	1	no	—
387	C₂×C₄	—	44	1	no	—
388	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
389	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
390	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
391	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
392	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	22	1	no	—
397	C₈	—	22	1	no	—
398	C₈	—	22	1	no	—
399	C₈	—	22	1	no	—
400	C₈	#66960	1	2	yes	—
401	C₈	#41×D₁₁	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	11	2	no	—
405	C₂²	—	22	1	no	—
406	C₂²	—	22	1	no	—
407	C₂²	—	22	1	no	—
408	C₂²	—	22	1	no	—
409	C₂²	—	22	1	no	—
410	C₂²	D₁₁×M₃₂	1	2	yes	—
411	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	11	2	no	—
418	C₄	—	22	1	no	—
419	C₄	—	22	1	no	—
420	C₄	—	22	1	no	—
421	C₄	—	22	1	no	—
422	C₄	—	22	1	no	—
423	C₄	#10623053	1	1	yes	characteristic
424	C₄	C₂×#66960	1	1	yes	characteristic
425	C₂	—	2	2	no	—
426	C₂	—	22	2	no	—
427	C₂	—	44	1	no	—
428	C₂	#13077572	1	1	yes	characteristic
429	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
430	C₂	#13081718	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2163	C₂
prime radical	C₂×#4339	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2163	D₁₁
hypocenter	C₁₁	#33484
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #13070523	C₂	semidirect
3. #13070440	C₂	semidirect
4. #13070438	C₂	semidirect
5. (C₂²⋊D₁₁)⋊C₁₆	C₂	semidirect
6. #13070417	C₂	semidirect
7. #13070417	C₂	semidirect
8. #13070209	C₂	semidirect
9. C₂×#10622099	C₂	semidirect
10. D₁₁×#346	C₂	semidirect
11. C₁₁×#2163	C₂	semidirect
147. C₁₁⋊C₁₆	#41	semidirect
155. #2163	D₁₁	semidirect
173. C₂²⋊D₁₁	M₃₂	semidirect
362. C₁₁	#33484	semidirect

Maximal subgroups

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

subgroup	index
C₈×#4339	2
#13070523	2
#13070440	2
#13070438	2
(C₂²⋊D₁₁)⋊C₁₆	2
#13070417	2
#13070209	2
C₂×#10622099	2
D₁₁×#346	2
C₁₁×#2163	2
#33484	11