Subgroups — #14906971

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#66876	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077310	C₂	1	1	yes	maximal, characteristic
4	#13070445	C₂	1	2	yes	maximal, complemented
5	#13070444	C₂	1	2	yes	maximal, complemented
6	#13070438	C₂	1	2	yes	maximal, complemented
7	(C₂²⋊D₁₁)⋊C₁₆	C₂	1	2	yes	maximal, complemented
8	#13070374	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070229	C₂	1	1	yes	maximal, characteristic, complemented
10	#13070212	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	#10623322	C₄	1	1	yes	characteristic
14	C₂×#66954	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
17	#10622820	C₄	1	1	yes	characteristic
18	#10622724	C₄	1	2	yes	—
19	#10622724	C₄	1	2	yes	—
20	#10622723	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₁₁	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₁₁	C₂²	1	2	yes	—
23	#10622715	C₄	1	1	yes	characteristic
24	#10622714	C₂²	1	1	yes	characteristic
25	C₂×#66876	—	2	4	no	—
26	C₂×#66876	C₂²	1	1	yes	characteristic
27	C₂×#66876	C₂²	1	2	yes	—
28	C₂×#66876	C₂²	1	1	yes	characteristic
29	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
30	#10622514	—	2	4	no	—
31	C₂×#66862	C₂²	1	2	yes	complemented
32	C₂×C₁₆×D₁₁	C₂²	1	2	yes	complemented
33	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
37	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
38	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	complemented
39	#10622140	C₂²	1	2	yes	complemented
40	Dic₁₁⋊C₁₆	C₂²	1	2	yes	complemented
41	Dic₁₁⋊C₁₆	C₂²	1	2	yes	complemented
42	C₁₆×Dic₁₁	C₂²	1	2	yes	complemented
43	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂×#4339	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	—	2	2	no	—
46	C₂²×C₈×C₁₁	—	2	2	no	—
47	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	#67006	C₈	1	2	yes	—
54	#66983	C₈	1	1	yes	characteristic
55	#66983	C₈	1	1	yes	characteristic
56	#66982	C₈	1	2	yes	—
57	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
58	C₄×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
59	#66979	C₂×C₄	1	1	yes	characteristic
60	#66977	C₈	1	1	yes	characteristic
61	#66977	C₈	1	1	yes	characteristic
62	C₂×#4318	C₂×C₄	1	1	yes	characteristic
63	C₂×#4318	C₂×C₄	1	1	yes	characteristic
64	#66954	—	2	2	no	—
65	#66954	—	2	2	no	—
66	C₂×#4313	C₂×C₄	1	2	yes	—
67	C₂×C₈×D₁₁	C₂³	1	2	yes	—
68	C₂×C₁₁×C₁₆	—	2	2	no	—
69	C₂×C₁₁×C₁₆	—	2	2	no	—
70	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
74	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
76	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
78	#66879	C₂×C₄	1	2	yes	—
79	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
80	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
81	C₈×Dic₁₁	C₂³	1	2	yes	—
82	#66876	—	2	2	no	—
83	#66876	—	2	4	no	—
84	#66876	D₄	1	4	yes	complemented
85	C₂×C₁₁⋊C₁₆	—	2	4	no	—
86	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
87	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
88	#66862	—	2	4	no	—
89	C₁₆×D₁₁	—	2	4	no	—
90	#33436	—	11	1	no	maximal, Sylow
91	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₁	—	2	2	no	—
93	C₂²×C₄×C₁₁	—	2	2	no	—
94	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
101	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
102	C₂×C₂²⋊D₁₁	C₂×C₈	1	2	yes	—
103	#4339	—	2	2	no	—
104	#4339	—	2	2	no	—
105	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
111	C₂×C₈×C₁₁	—	2	1	no	—
112	C₂×C₈×C₁₁	—	2	1	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₁	#41	1	2	yes	—
120	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
121	C₂²⋊Dic₁₁	C₂×C₈	1	2	yes	—
122	C₂²⋊Dic₁₁	C₂×C₈	1	2	yes	—
123	C₂²⋊Dic₁₁	C₂×C₈	1	2	yes	—
124	(C₂×D₁₁)⋊C₄	C₂×C₈	1	2	yes	—
125	(C₂×D₁₁)⋊C₄	C₂×C₈	1	2	yes	—
126	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
127	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
128	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
129	Dic₁₁⋊C₄	C₂×C₈	1	2	yes	—
130	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
131	#4318	—	2	2	no	—
132	#4318	—	2	2	no	—
133	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
135	#4313	—	2	4	no	—
136	C₈×D₁₁	—	2	2	no	—
137	C₈×D₁₁	—	2	2	no	—
138	C₁₁×C₁₆	—	2	1	no	—
139	C₁₁×C₁₆	—	2	1	no	—
140	C₁₁×C₁₆	—	2	1	no	—
141	C₁₁×C₁₆	—	2	1	no	—
142	C₁₁⋊C₁₆	—	2	2	no	—
143	C₁₁⋊C₁₆	C₂×D₄	1	4	yes	—
144	C₂×#504	—	11	1	no	—
145	C₂²×M₃₂	—	11	1	no	—
146	#2929	—	11	1	no	—
147	#2169	—	11	2	no	—
148	#2168	—	11	2	no	—
149	#2168	—	11	2	no	—
150	D₄×C₁₆	—	11	2	no	—
151	#2151	—	11	1	no	—
152	#2113	—	11	1	no	—
153	C₂×C₂²⋊C₁₆	D₁₁	1	1	yes	characteristic, complemented
154	#2108	—	11	1	no	—
155	C₂³×C₁₁	—	2	2	no	—
156	C₂³×C₁₁	—	2	2	no	—
157	C₂³×C₁₁	—	4	1	no	—
158	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
159	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
160	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₁₁	C₂²×C₈	1	2	yes	—
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	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₁₁	#131	1	2	yes	—
174	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
175	C₂²⋊D₁₁	—	2	4	no	—
176	C₂²⋊D₁₁	—	2	4	no	—
177	C₂²⋊D₁₁	—	4	2	no	—
178	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
179	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
180	C₂×Dic₁₁	C₂²×C₈	1	2	yes	—
181	D₄₄	—	2	2	no	—
182	C₄×D₁₁	—	2	2	no	—
183	C₄×D₁₁	—	2	2	no	—
184	Dic₂₂	—	2	2	no	—
185	C₈×C₁₁	—	2	1	no	—
186	C₈×C₁₁	—	2	1	no	—
187	C₈×C₁₁	C₄×D₄	1	2	yes	—
188	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
190	C₁₁⋊C₈	—	2	2	no	—
191	C₁₁⋊C₈	—	2	2	no	—
192	C₂×#131	—	11	1	no	—
193	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
194	#525	—	11	1	no	—
195	#504	—	22	4	no	—
196	C₂×M₃₂	—	11	1	no	—
197	C₂×M₃₂	—	11	1	no	—
198	C₂×M₃₂	—	11	2	no	—
199	C₂×M₃₂	—	11	2	no	—
200	C₂×M₃₂	—	22	4	no	—
201	C₂²×C₁₆	—	11	2	no	—
202	C₂²×C₁₆	—	11	2	no	—
203	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
204	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
205	#435	—	11	2	no	—
206	#435	—	11	2	no	—
207	C₈×D₄	—	11	2	no	—
208	C₈×D₄	—	11	2	no	—
209	#424	—	11	1	no	—
210	#408	—	11	1	no	—
211	#407	—	11	1	no	—
212	#405	—	11	1	no	—
213	C₄⋊C₁₆	—	11	2	no	—
214	C₄⋊C₁₆	—	11	2	no	—
215	C₂²⋊C₁₆	—	11	2	no	—
216	C₂²⋊C₁₆	—	11	2	no	—
217	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
218	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
219	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
220	C₂²⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
221	#346	—	11	2	no	—
222	C₄×C₁₆	—	11	2	no	—
223	C₂²×C₁₁	—	2	1	no	—
224	C₂²×C₁₁	—	2	1	no	—
225	C₂²×C₁₁	—	2	1	no	—
226	C₂²×C₁₁	—	2	1	no	—
227	C₂²×C₁₁	—	2	1	no	—
228	C₂²×C₁₁	—	2	1	no	—
229	C₂²×C₁₁	—	2	1	no	—
230	C₂²×C₁₁	—	4	4	no	—
231	C₂²×C₁₁	C₈×D₄	1	2	yes	—
232	C₂²×C₁₁	#504	1	2	yes	complemented
233	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
234	C₂×D₁₁	—	2	2	no	—
235	C₂×D₁₁	—	2	2	no	—
236	C₂×D₁₁	—	2	2	no	—
237	C₄×C₁₁	—	2	1	no	—
238	C₄×C₁₁	—	2	1	no	—
239	C₄×C₁₁	C₈×D₄	1	2	yes	—
240	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
242	Dic₁₁	—	2	2	no	—
243	Dic₁₁	—	2	2	no	—
244	Dic₁₁	—	2	2	no	—
245	C₂×#41	—	11	1	no	—
246	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
247	#131	—	22	2	no	—
248	#131	—	22	2	no	—
249	C₂×M₁₆	—	11	1	no	—
250	C₂×M₁₆	—	11	1	no	—
251	C₂×M₁₆	—	11	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	11	2	no	—
255	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
256	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
257	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
259	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
261	#123	—	11	2	no	—
262	C₂²⋊Q₈	—	11	1	no	—
263	C₂²⋊Q₈	—	11	1	no	—
264	#121	—	11	1	no	—
265	#121	—	11	1	no	—
266	#120	—	11	2	no	—
267	C₄×D₄	—	11	2	no	—
268	C₄×D₄	—	11	2	no	—
269	#117	—	11	1	no	—
270	M₃₂	—	11	4	no	—
271	M₃₂	—	22	4	no	—
272	M₃₂	—	22	4	no	—
273	M₃₂	—	22	2	no	—
274	C₂×C₁₆	—	2	2	no	—
275	C₂×C₁₆	—	2	2	no	—
276	C₂×C₁₆	—	11	2	no	—
277	C₂×C₁₆	—	11	2	no	—
278	C₂×C₁₆	—	22	4	no	—
279	C₂×C₁₆	—	22	4	no	—
280	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
281	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
282	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
283	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
284	C₄⋊C₈	—	11	2	no	—
285	C₄⋊C₈	—	11	2	no	—
286	C₂²⋊C₈	—	11	2	no	—
287	C₂²⋊C₈	—	11	2	no	—
288	C₂²⋊C₈	—	11	2	no	—
289	C₂²⋊C₈	—	11	2	no	—
290	#97	—	11	2	no	—
291	C₄×C₈	—	11	2	no	—
292	C₂×C₁₁	—	2	2	no	—
293	C₂×C₁₁	—	2	2	no	—
294	C₂×C₁₁	—	4	1	no	—
295	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
296	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
297	C₂×C₁₁	#3407	1	1	yes	characteristic
298	D₁₁	—	4	2	no	—
299	C₂⁴	C₈×D₁₁	1	1	yes	characteristic
300	#41	—	22	2	no	—
301	#41	—	22	2	no	—
302	C₂×Q₈	—	11	1	no	—
303	C₂×D₄	—	11	2	no	—
304	C₂×D₄	—	11	2	no	—
305	C₂×D₄	—	11	2	no	—
306	C₂×D₄	—	11	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	11	2	no	—
310	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
311	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
312	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
316	M₁₆	—	22	2	no	—
317	M₁₆	—	22	2	no	—
318	M₁₆	—	22	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	11	2	no	—
327	C₂×C₈	—	11	2	no	—
328	C₂×C₈	—	22	2	no	—
329	C₂×C₈	—	22	2	no	—
330	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
331	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
333	C₂×C₈	D₄×D₁₁	1	2	yes	—
334	C₂×C₈	#4341	1	2	yes	—
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	2	no	—
339	C₄⋊C₄	—	11	2	no	—
340	C₂²⋊C₄	—	11	2	no	—
341	C₂²⋊C₄	—	11	2	no	—
342	C₂²⋊C₄	—	11	2	no	—
343	C₂²⋊C₄	—	11	2	no	—
344	C₂²⋊C₄	—	11	2	no	—
345	C₄²	—	11	2	no	—
346	C₁₆	—	2	1	no	—
347	C₁₆	—	2	1	no	—
348	C₁₆	—	2	1	no	—
349	C₁₆	—	2	1	no	—
350	C₁₆	—	11	4	no	—
351	C₁₆	—	22	2	no	—
352	C₁₁	#33436	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	11	2	no	—
357	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
358	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
359	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
360	Q₈	—	22	2	no	—
361	D₄	—	22	4	no	—
362	D₄	—	22	4	no	—
363	D₄	—	22	2	no	—
364	D₄	—	44	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	11	2	no	—
373	C₂×C₄	—	11	2	no	—
374	C₂×C₄	—	11	2	no	—
375	C₂×C₄	—	22	2	no	—
376	C₂×C₄	—	22	2	no	—
377	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
378	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
379	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
380	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
381	C₂×C₄	#66960	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	22	2	no	—
386	C₈	—	22	2	no	—
387	C₈	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
388	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
389	C₈	C₂×#4341	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	22	2	no	—
399	C₂²	—	22	2	no	—
400	C₂²	—	22	2	no	—
401	C₂²	(C₂²⋊D₁₁)⋊C₈	1	2	yes	—
402	C₂²	#10622514	1	2	yes	complemented
403	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	22	2	no	—
407	C₄	—	22	2	no	—
408	C₄	—	22	2	no	—
409	C₄	(C₂²⋊D₁₁)⋊C₈	1	2	yes	—
410	C₄	C₂×(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
411	C₄	C₂×#66960	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	44	2	no	—
416	C₂	C₂×(C₂²⋊D₁₁)⋊C₈	1	1	yes	characteristic
417	C₂	C₂×#10622514	1	1	yes	characteristic
418	C₂	#13081718	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₂×C₁₁×C₂²⋊C₁₆	C₂
prime radical	#10623322	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×C₂²⋊C₁₆	D₁₁
hypocenter	C₁₁	#33436
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#10622514	C₂	semidirect
2. C₂²×#66876	C₂	semidirect
4. #13070445	C₂	semidirect
5. #13070444	C₂	semidirect
6. #13070438	C₂	semidirect
7. (C₂²⋊D₁₁)⋊C₁₆	C₂	semidirect
8. #13070374	C₂	semidirect
9. #13070229	C₂	semidirect
10. #13070212	C₂	semidirect
11. C₂×C₁₁×C₂²⋊C₁₆	C₂	semidirect
31. C₂×#66862	C₂²	semidirect
32. C₂×C₁₆×D₁₁	C₂²	semidirect
37. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
38. (C₂×D₁₁)⋊C₁₆	C₂²	semidirect
39. #10622140	C₂²	semidirect
40. Dic₁₁⋊C₁₆	C₂²	semidirect
41. Dic₁₁⋊C₁₆	C₂²	semidirect
42. C₁₆×Dic₁₁	C₂²	semidirect
84. #66876	D₄	semidirect
153. C₂×C₂²⋊C₁₆	D₁₁	semidirect
232. C₂²×C₁₁	#504	semidirect
352. C₁₁	#33436	semidirect
402. C₂²	#10622514	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622514	2
C₂²×#66876	2
#13077310	2
#13070445	2
#13070444	2
#13070438	2
(C₂²⋊D₁₁)⋊C₁₆	2
#13070374	2
#13070229	2
#13070212	2
C₂×C₁₁×C₂²⋊C₁₆	2
#33436	11