Subgroups — #14758720

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077253	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622453	C₂	1	1	yes	maximal, characteristic
3	#13077033	C₂	1	1	yes	maximal, characteristic
4	#13069392	C₂	1	1	yes	maximal, characteristic, complemented
5	#13069391	C₂	1	1	yes	maximal, characteristic, complemented
6	#13069389	C₂	1	1	yes	maximal, characteristic, complemented
7	#13068822	C₂	1	1	yes	maximal, characteristic
8	#13068822	C₂	1	1	yes	maximal, characteristic
9	#13068819	C₂	1	1	yes	maximal, characteristic
10	#13068819	C₂	1	1	yes	maximal, characteristic
11	#13068524	C₂	1	1	yes	maximal, characteristic, complemented
12	#13068521	C₂	1	1	yes	maximal, characteristic, complemented
13	#108×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#13068517	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×M₁₆×D₁₁	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₁₁	C₂²	1	1	yes	characteristic
18	C₂×#66925	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
21	C₁₁×#423	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
24	#10622739	C₂²	1	1	yes	characteristic
25	#10622739	C₂²	1	1	yes	characteristic
26	C₂×#66886	C₂²	1	1	yes	characteristic
27	C₂×#66886	C₂²	1	1	yes	characteristic
28	C₂×#66886	C₂²	1	1	yes	characteristic
29	C₂×#66886	C₂²	1	1	yes	characteristic
30	M₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
31	M₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
32	M₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
33	M₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
34	C₂×(C₂×D₁₁)⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×(C₂×D₁₁)⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×#66883	C₂²	1	1	yes	characteristic
37	C₂×#66883	C₂²	1	1	yes	characteristic
38	C₂×#66879	C₂²	1	1	yes	characteristic
39	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
40	#10622537	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
42	C₄×#4318	C₂²	1	1	yes	characteristic
43	#10622453	—	2	1	no	—
44	#10622453	—	2	1	no	—
45	#10622453	—	2	1	no	—
46	#10622453	—	2	1	no	—
47	#10622453	C₄	1	2	yes	—
48	#10622453	C₄	1	2	yes	—
49	#10622453	C₄	1	2	yes	—
50	#10622453	C₄	1	2	yes	—
51	#10622321	—	2	1	no	—
52	#10622321	—	2	1	no	—
53	#10622302	—	2	1	no	—
54	#10622302	—	2	1	no	—
55	C₁₁×#341	C₂²	1	1	yes	characteristic
56	C₁₁×#341	C₂²	1	1	yes	characteristic
57	#10622196	C₂²	1	1	yes	characteristic
58	#10622196	C₂²	1	1	yes	characteristic
59	#10622196	C₂²	1	1	yes	characteristic
60	#10622196	C₂²	1	1	yes	characteristic
61	#10622190	C₂²	1	1	yes	characteristic
62	#10622190	C₂²	1	1	yes	characteristic
63	C₂²×C₄×D₁₁	C₂³	1	1	yes	characteristic
64	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
71	C₂×(C₂×D₁₁)⋊C₄	Q₈	1	1	yes	characteristic
72	C₂×(C₂×D₁₁)⋊C₄	Q₈	1	1	yes	characteristic
73	C₂×Dic₁₁⋊C₄	Q₈	1	1	yes	characteristic
74	C₂×Dic₁₁⋊C₄	Q₈	1	1	yes	characteristic
75	C₂×C₄×Dic₁₁	C₂³	1	1	yes	characteristic
76	C₂×#4318	C₂³	1	1	yes	characteristic
77	C₂×#4318	C₂³	1	1	yes	characteristic
78	C₂×#4318	C₂³	1	1	yes	characteristic
79	C₂×#4318	C₂³	1	1	yes	characteristic
80	C₂²×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
82	M₁₆×D₁₁	—	2	2	no	—
83	M₁₆×D₁₁	—	2	2	no	—
84	M₁₆×D₁₁	—	2	2	no	—
85	M₁₆×D₁₁	—	2	2	no	—
86	C₂×#4313	—	2	1	no	—
87	C₂×#4313	—	2	1	no	—
88	C₂×C₈×D₁₁	—	2	1	no	—
89	C₂×C₈×D₁₁	—	2	1	no	—
90	#66925	C₂×C₄	1	1	yes	characteristic
91	#66925	C₂×C₄	1	1	yes	characteristic
92	#66925	C₂×C₄	1	1	yes	characteristic
93	#66925	C₂×C₄	1	1	yes	characteristic
94	#66925	D₄	1	1	yes	characteristic
95	#66925	D₄	1	1	yes	characteristic
96	#66925	D₄	1	1	yes	characteristic
97	#66925	D₄	1	1	yes	characteristic
98	C₁₁×#108	—	2	2	no	—
99	C₁₁×#108	—	2	2	no	—
100	C₁₁×C₄⋊C₈	—	2	1	no	—
101	C₁₁×C₄⋊C₈	—	2	1	no	—
102	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
103	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
104	C₁₁×#97	—	2	1	no	—
105	C₄×C₈×C₁₁	—	2	1	no	—
106	#66886	—	2	2	no	—
107	#66886	—	2	2	no	—
108	#66886	—	2	2	no	—
109	#66886	—	2	2	no	—
110	(C₂×D₁₁)⋊C₈	—	2	1	no	—
111	(C₂×D₁₁)⋊C₈	—	2	1	no	—
112	(C₂×D₁₁)⋊C₈	—	2	1	no	—
113	(C₂×D₁₁)⋊C₈	—	2	1	no	—
114	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
115	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
116	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
117	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
118	#66883	—	2	2	no	—
119	#66883	—	2	2	no	—
120	#66879	—	2	1	no	—
121	#66879	—	2	1	no	—
122	#66879	—	2	1	no	—
123	#66879	—	2	1	no	—
124	#66879	C₂×C₄	1	2	yes	—
125	#66879	C₂×C₄	1	2	yes	—
126	C₈×Dic₁₁	—	2	1	no	—
127	C₈×Dic₁₁	—	2	1	no	—
128	C₈×Dic₁₁	—	2	1	no	—
129	C₈×Dic₁₁	—	2	1	no	—
130	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
131	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
132	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
133	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
134	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
135	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
136	#66867	—	2	1	no	—
137	C₄×C₁₁⋊C₈	—	2	1	no	—
138	#21372	—	11	1	no	maximal, Sylow
139	C₂³×D₁₁	C₂×Q₈	1	1	yes	characteristic
140	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
141	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
142	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
143	C₂²×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
144	C₂²×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
145	C₂²×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
146	C₂×C₄×D₁₁	—	2	1	no	—
147	C₂×C₄×D₁₁	—	2	1	no	—
148	C₂×C₄×D₁₁	—	2	1	no	—
149	C₂×C₄×D₁₁	—	2	1	no	—
150	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
154	C₁₁×M₁₆	—	2	1	no	—
155	C₁₁×M₁₆	—	2	1	no	—
156	C₁₁×M₁₆	—	2	1	no	—
157	C₁₁×M₁₆	—	2	1	no	—
158	C₁₁×M₁₆	—	2	1	no	—
159	C₁₁×M₁₆	—	2	1	no	—
160	C₁₁×M₁₆	#41	1	2	yes	—
161	C₁₁×M₁₆	#41	1	2	yes	—
162	C₂×C₈×C₁₁	—	2	1	no	—
163	C₂×C₈×C₁₁	—	2	1	no	—
164	C₂×C₈×C₁₁	—	2	1	no	—
165	C₂×C₈×C₁₁	—	2	1	no	—
166	C₂×C₈×C₁₁	—	2	1	no	—
167	C₂×C₈×C₁₁	—	2	1	no	—
168	C₂×C₈×C₁₁	—	2	1	no	—
169	C₂×C₈×C₁₁	—	2	1	no	—
170	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
171	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
172	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
176	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
177	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
178	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
179	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
180	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
181	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
182	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
183	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
184	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
185	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
186	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
187	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
188	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
189	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
190	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
191	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
192	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
196	#4318	—	2	1	no	—
197	#4318	—	2	1	no	—
198	#4318	—	2	1	no	—
199	#4318	—	2	1	no	—
200	#4318	—	2	1	no	—
201	#4318	—	2	1	no	—
202	#4318	#41	1	2	yes	—
203	#4318	#41	1	2	yes	—
204	C₂×C₁₁⋊C₈	—	2	1	no	—
205	C₂×C₁₁⋊C₈	—	2	1	no	—
206	C₂×C₁₁⋊C₈	—	2	1	no	—
207	C₂×C₁₁⋊C₈	—	2	1	no	—
208	C₂×C₁₁⋊C₈	—	2	1	no	—
209	C₂×C₁₁⋊C₈	—	2	1	no	—
210	C₂×C₁₁⋊C₈	—	2	1	no	—
211	C₂×C₁₁⋊C₈	—	2	1	no	—
212	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
213	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
214	#4313	—	2	4	no	—
215	#4313	—	2	4	no	—
216	C₈×D₁₁	—	2	4	no	—
217	C₈×D₁₁	—	2	4	no	—
218	#2921	—	11	1	no	—
219	C₂×#433	—	11	1	no	—
220	#2873	—	11	1	no	—
221	#1950	—	11	1	no	—
222	#1950	—	11	1	no	—
223	#1950	—	11	1	no	—
224	#1950	D₁₁	1	1	yes	characteristic, complemented
225	#1855	—	11	1	no	—
226	#1855	—	11	1	no	—
227	#1855	—	11	1	no	—
228	#1855	—	11	1	no	—
229	#1778	—	11	1	no	—
230	#1778	—	11	1	no	—
231	C₄×#108	—	11	1	no	—
232	C₄×#108	—	11	1	no	—
233	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
234	C₂²×D₁₁	—	2	1	no	—
235	C₂²×D₁₁	—	2	1	no	—
236	C₂²×D₁₁	—	4	1	no	—
237	C₂²×D₁₁	—	4	1	no	—
238	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₁	—	4	1	no	—
241	C₂×C₄×C₁₁	—	4	1	no	—
242	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
252	C₂×Dic₁₁	—	2	1	no	—
253	C₂×Dic₁₁	—	2	1	no	—
254	C₂×Dic₁₁	—	4	1	no	—
255	C₂×Dic₁₁	—	4	1	no	—
256	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
258	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
259	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
260	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
261	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
262	C₄×D₁₁	—	2	1	no	—
263	C₄×D₁₁	—	2	1	no	—
264	C₄×D₁₁	—	2	1	no	—
265	C₄×D₁₁	—	2	1	no	—
266	C₄×D₁₁	—	2	1	no	—
267	C₄×D₁₁	—	2	1	no	—
268	C₄×D₁₁	—	2	1	no	—
269	C₄×D₁₁	—	2	1	no	—
270	C₈×C₁₁	—	2	2	no	—
271	C₈×C₁₁	—	2	2	no	—
272	C₈×C₁₁	—	2	2	no	—
273	C₈×C₁₁	—	2	2	no	—
274	C₈×C₁₁	—	4	1	no	—
275	C₈×C₁₁	—	4	1	no	—
276	C₁₁⋊C₈	—	2	2	no	—
277	C₁₁⋊C₈	—	2	2	no	—
278	C₁₁⋊C₈	—	2	2	no	—
279	C₁₁⋊C₈	—	2	2	no	—
280	C₁₁⋊C₈	—	4	1	no	—
281	C₁₁⋊C₈	—	4	1	no	—
282	C₂²×M₁₆	—	11	1	no	—
283	C₂²×M₁₆	—	11	1	no	—
284	C₂×#117	—	11	1	no	—
285	#433	—	11	2	no	—
286	#433	—	11	2	no	—
287	#433	—	11	2	no	—
288	#433	—	11	2	no	—
289	#433	—	22	1	no	—
290	#433	—	22	1	no	—
291	#433	—	22	1	no	—
292	#433	—	22	1	no	—
293	C₂×#108	—	11	1	no	—
294	C₂×#108	—	11	1	no	—
295	C₂×#108	—	11	1	no	—
296	C₂×#108	—	11	1	no	—
297	C₂×#108	—	11	1	no	—
298	C₂×#108	—	11	1	no	—
299	C₂×#108	C₂×D₁₁	1	1	yes	characteristic
300	C₂×#108	C₂×D₁₁	1	1	yes	characteristic
301	#423	—	11	1	no	—
302	#423	C₂×D₁₁	1	1	yes	characteristic
303	C₂×C₄⋊C₈	—	11	1	no	—
304	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
305	#407	—	11	1	no	—
306	#407	—	11	1	no	—
307	C₂×C₂²⋊C₈	—	11	1	no	—
308	C₂×C₂²⋊C₈	—	11	1	no	—
309	#405	—	22	1	no	—
310	#405	—	22	1	no	—
311	#405	—	22	1	no	—
312	#405	—	22	1	no	—
313	C₄×M₁₆	—	11	1	no	—
314	C₄×M₁₆	—	11	1	no	—
315	C₄×M₁₆	—	11	1	no	—
316	C₄×M₁₆	—	11	1	no	—
317	C₄×M₁₆	—	11	1	no	—
318	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
319	C₂×#97	—	11	1	no	—
320	C₂×C₄×C₈	—	11	1	no	—
321	#341	—	11	1	no	—
322	#341	—	11	1	no	—
323	#341	—	11	1	no	—
324	#341	—	11	1	no	—
325	#341	—	11	1	no	—
326	#341	—	11	1	no	—
327	#341	C₂×D₁₁	1	1	yes	characteristic
328	#341	C₂×D₁₁	1	1	yes	characteristic
329	C₂²×C₁₁	—	2	1	no	—
330	C₂²×C₁₁	—	2	1	no	—
331	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
332	C₂²×C₁₁	#533	1	1	yes	characteristic
333	C₂²×C₁₁	#533	1	1	yes	characteristic
334	C₂×D₁₁	—	2	1	no	—
335	C₂×D₁₁	—	2	1	no	—
336	C₂×D₁₁	—	2	1	no	—
337	C₂×D₁₁	—	2	1	no	—
338	C₂×D₁₁	—	2	1	no	—
339	C₂×D₁₁	—	2	1	no	—
340	C₂×D₁₁	—	8	1	no	—
341	C₂×D₁₁	—	8	1	no	—
342	C₄×C₁₁	—	2	1	no	—
343	C₄×C₁₁	—	2	1	no	—
344	C₄×C₁₁	—	2	1	no	—
345	C₄×C₁₁	—	2	1	no	—
346	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
347	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
348	C₄×C₁₁	#525	1	1	yes	characteristic
349	C₄×C₁₁	#525	1	1	yes	characteristic
350	Dic₁₁	—	2	1	no	—
351	Dic₁₁	—	2	1	no	—
352	Dic₁₁	—	2	1	no	—
353	Dic₁₁	—	2	1	no	—
354	Dic₁₁	—	2	1	no	—
355	Dic₁₁	—	2	1	no	—
356	C₂³×C₄	—	11	1	no	—
357	C₂×M₁₆	—	11	1	no	—
358	C₂×M₁₆	—	11	1	no	—
359	C₂×M₁₆	—	11	1	no	—
360	C₂×M₁₆	—	11	1	no	—
361	C₂×M₁₆	—	22	1	no	—
362	C₂×M₁₆	—	22	1	no	—
363	C₂×M₁₆	—	22	2	no	—
364	C₂×M₁₆	—	22	2	no	—
365	C₂×M₁₆	—	22	2	no	—
366	C₂×M₁₆	—	22	2	no	—
367	C₂×M₁₆	C₂²×D₁₁	1	1	yes	characteristic
368	C₂×M₁₆	C₂²×D₁₁	1	1	yes	characteristic
369	C₂×M₁₆	C₂²×D₁₁	1	1	yes	characteristic
370	C₂×M₁₆	C₂²×D₁₁	1	1	yes	characteristic
371	C₂²×C₈	—	11	1	no	—
372	C₂²×C₈	—	11	1	no	—
373	C₂²×C₈	—	22	1	no	—
374	C₂²×C₈	—	22	1	no	—
375	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
376	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
377	#117	—	11	1	no	—
378	#117	—	11	1	no	—
379	#117	—	11	1	no	—
380	#117	—	11	1	no	—
381	#117	—	11	1	no	—
382	#117	—	11	1	no	—
383	#117	—	11	1	no	—
384	#117	—	11	1	no	—
385	C₂×C₄⋊C₄	—	11	1	no	—
386	C₂×C₄⋊C₄	—	11	1	no	—
387	C₂×C₂²⋊C₄	—	11	1	no	—
388	C₂×C₂²⋊C₄	—	11	1	no	—
389	C₂×C₄²	—	11	1	no	—
390	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
391	#108	—	2	2	no	—
392	#108	—	2	2	no	—
393	#108	—	22	2	no	—
394	#108	—	22	2	no	—
395	#108	—	22	2	no	—
396	#108	—	22	2	no	—
397	#108	—	22	2	no	—
398	#108	—	22	2	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	—	11	2	no	—
402	C₄⋊C₈	—	11	2	no	—
403	C₄⋊C₈	—	22	1	no	—
404	C₄⋊C₈	—	22	1	no	—
405	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
406	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
407	C₂²⋊C₈	—	11	2	no	—
408	C₂²⋊C₈	—	11	2	no	—
409	C₂²⋊C₈	—	11	2	no	—
410	C₂²⋊C₈	—	11	2	no	—
411	C₂²⋊C₈	—	22	1	no	—
412	C₂²⋊C₈	—	22	1	no	—
413	C₂²⋊C₈	—	22	1	no	—
414	C₂²⋊C₈	—	22	1	no	—
415	#97	—	2	1	no	—
416	#97	—	11	2	no	—
417	#97	—	11	2	no	—
418	#97	—	22	1	no	—
419	#97	—	22	1	no	—
420	#97	—	22	1	no	—
421	#97	—	22	1	no	—
422	#97	—	22	1	no	—
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	—	11	2	no	—
425	C₄×C₈	—	11	2	no	—
426	C₄×C₈	—	22	1	no	—
427	C₄×C₈	—	22	1	no	—
428	C₄×C₈	—	22	1	no	—
429	C₄×C₈	—	22	1	no	—
430	C₄×C₈	—	22	1	no	—
431	C₂×C₁₁	—	2	1	no	—
432	C₂×C₁₁	—	2	1	no	—
433	C₂×C₁₁	#2296	1	1	yes	characteristic
434	C₂×C₁₁	#2916	1	1	yes	characteristic
435	C₂×C₁₁	#2916	1	1	yes	characteristic
436	D₁₁	—	4	1	no	—
437	D₁₁	—	4	1	no	—
438	C₂⁴	—	11	1	no	—
439	C₂²×C₄	—	11	1	no	—
440	C₂²×C₄	—	11	1	no	—
441	C₂²×C₄	—	11	1	no	—
442	C₂²×C₄	—	11	1	no	—
443	C₂²×C₄	—	11	1	no	—
444	C₂²×C₄	—	11	1	no	—
445	C₂²×C₄	—	11	1	no	—
446	C₂²×C₄	—	22	1	no	—
447	C₂²×C₄	—	22	1	no	—
448	C₂²×C₄	—	22	1	no	—
449	C₂²×C₄	—	22	1	no	—
450	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
451	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
452	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
453	M₁₆	—	2	1	no	—
454	M₁₆	—	2	1	no	—
455	M₁₆	—	2	1	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	2	1	no	—
458	M₁₆	—	2	1	no	—
459	M₁₆	—	11	2	no	—
460	M₁₆	—	11	2	no	—
461	M₁₆	—	22	4	no	—
462	M₁₆	—	22	4	no	—
463	M₁₆	—	22	1	no	—
464	M₁₆	—	22	1	no	—
465	M₁₆	—	22	1	no	—
466	M₁₆	—	22	1	no	—
467	M₁₆	—	22	1	no	—
468	M₁₆	—	22	1	no	—
469	M₁₆	#4341	1	2	yes	—
470	M₁₆	#4343	1	2	yes	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	11	2	no	—
480	C₂×C₈	—	11	2	no	—
481	C₂×C₈	—	22	4	no	—
482	C₂×C₈	—	22	4	no	—
483	C₂×C₈	—	22	1	no	—
484	C₂×C₈	—	22	1	no	—
485	C₂×C₈	—	22	1	no	—
486	C₂×C₈	—	22	1	no	—
487	C₂×C₈	—	22	1	no	—
488	C₂×C₈	—	22	1	no	—
489	C₂×C₈	—	22	1	no	—
490	C₂×C₈	—	22	1	no	—
491	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
492	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
493	C₄⋊C₄	—	11	1	no	—
494	C₄⋊C₄	—	11	1	no	—
495	C₄⋊C₄	—	11	1	no	—
496	C₄⋊C₄	—	11	1	no	—
497	C₄⋊C₄	—	11	1	no	—
498	C₄⋊C₄	—	11	1	no	—
499	C₄⋊C₄	—	11	1	no	—
500	C₄⋊C₄	—	11	1	no	—
501	C₂²⋊C₄	—	11	1	no	—
502	C₂²⋊C₄	—	11	1	no	—
503	C₂²⋊C₄	—	11	1	no	—
504	C₂²⋊C₄	—	11	1	no	—
505	C₂²⋊C₄	—	11	1	no	—
506	C₂²⋊C₄	—	11	1	no	—
507	C₂²⋊C₄	—	11	1	no	—
508	C₂²⋊C₄	—	11	1	no	—
509	C₄²	—	11	1	no	—
510	C₄²	—	11	1	no	—
511	C₄²	—	11	1	no	—
512	C₄²	—	11	1	no	—
513	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
514	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
515	C₄²	D₄×D₁₁	1	1	yes	characteristic
516	C₄²	D₄×D₁₁	1	1	yes	characteristic
517	C₁₁	#21372	1	1	yes	characteristic, complemented, Sylow
518	C₂³	—	11	1	no	—
519	C₂³	—	11	1	no	—
520	C₂³	—	22	1	no	—
521	C₂³	—	22	1	no	—
522	C₂³	—	44	1	no	—
523	C₂³	—	44	1	no	—
524	C₂³	C₂×Q₈×D₁₁	1	1	yes	characteristic
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	11	1	no	—
528	C₂×C₄	—	11	1	no	—
529	C₂×C₄	—	11	1	no	—
530	C₂×C₄	—	11	1	no	—
531	C₂×C₄	—	11	1	no	—
532	C₂×C₄	—	11	1	no	—
533	C₂×C₄	—	22	1	no	—
534	C₂×C₄	—	22	1	no	—
535	C₂×C₄	—	22	1	no	—
536	C₂×C₄	—	22	1	no	—
537	C₂×C₄	—	22	1	no	—
538	C₂×C₄	—	22	1	no	—
539	C₂×C₄	—	22	1	no	—
540	C₂×C₄	—	22	1	no	—
541	C₂×C₄	—	22	1	no	—
542	C₂×C₄	—	22	1	no	—
543	C₂×C₄	—	44	1	no	—
544	C₂×C₄	—	44	1	no	—
545	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
546	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
547	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
548	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
550	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
551	C₂×C₄	C₂×#4341	1	1	yes	characteristic
552	C₂×C₄	C₂×#4343	1	1	yes	characteristic
553	C₂×C₄	#41×D₁₁	1	1	yes	characteristic
554	C₂×C₄	#41×D₁₁	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	2	2	no	—
558	C₈	—	2	2	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	22	2	no	—
562	C₈	—	22	2	no	—
563	C₈	—	22	2	no	—
564	C₈	—	22	2	no	—
565	C₈	—	44	1	no	—
566	C₈	—	44	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	22	1	no	—
570	C₂²	—	22	1	no	—
571	C₂²	—	22	1	no	—
572	C₂²	—	22	1	no	—
573	C₂²	—	22	1	no	—
574	C₂²	—	22	1	no	—
575	C₂²	—	88	1	no	—
576	C₂²	—	88	1	no	—
577	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
578	C₂²	#10623219	1	1	yes	characteristic
579	C₂²	#10623259	1	1	yes	characteristic
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	22	1	no	—
585	C₄	—	22	1	no	—
586	C₄	—	22	1	no	—
587	C₄	—	22	1	no	—
588	C₄	—	22	1	no	—
589	C₄	—	22	1	no	—
590	C₄	C₄×#4341	1	1	yes	characteristic
591	C₄	C₄×#4343	1	1	yes	characteristic
592	C₄	#10623137	1	1	yes	characteristic
593	C₄	#10623158	1	1	yes	characteristic
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	44	1	no	—
597	C₂	—	44	1	no	—
598	C₂	#13071097	1	1	yes	characteristic
599	C₂	#13077224	1	1	yes	characteristic
600	C₂	#13077226	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₁₁×#1950	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	#1950	D₁₁
hypocenter	C₁₁	#21372
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. #13069392	C₂	semidirect
5. #13069391	C₂	semidirect
6. #13069389	C₂	semidirect
11. #13068524	C₂	semidirect
12. #13068521	C₂	semidirect
13. #108×Dic₁₁	C₂	semidirect
14. #13068517	C₂	semidirect
15. C₁₁×#1950	C₂	semidirect
224. #1950	D₁₁	semidirect
517. C₁₁	#21372	semidirect

Maximal subgroups

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

subgroup	index
#13077253	2
C₂×#10622453	2
#13077033	2
#13069392	2
#13069391	2
#13069389	2
#13068822	2
#13068819	2
#13068524	2
#13068521	2
#108×Dic₁₁	2
#13068517	2
C₁₁×#1950	2
#21372	11