Subgroups — #14756999

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077260	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#67001	C₂	1	1	yes	maximal, characteristic, complemented
3	#13069266	C₂	1	2	yes	maximal, complemented
4	#13069217	C₂	1	2	yes	maximal, complemented
5	#13068945	C₂	1	2	yes	maximal
6	#13068893	C₂	1	2	yes	maximal, complemented
7	C₄×#66883	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#66901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#66901	C₂	1	1	yes	maximal, characteristic, complemented
10	#13068361	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
15	C₂×#67001	C₂²	1	2	yes	—
16	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic, complemented
18	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic, complemented
19	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic, complemented
20	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic, complemented
21	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic, complemented
22	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic, complemented
23	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic, complemented
24	C₁₁×#427	C₂²	1	1	yes	characteristic
25	C₁₁×#416	C₂²	1	1	yes	characteristic
26	C₁₁×#416	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₂×#66901	C₂²	1	2	yes	—
29	C₂×#66901	C₂²	1	2	yes	—
30	#10622847	C₂²	1	2	yes	—
31	C₂×#66883	C₂²	1	2	yes	—
32	#10622613	—	2	2	no	—
33	#10622612	C₂²	1	2	yes	—
34	#10622610	—	2	2	no	—
35	#10622610	C₂²	1	2	yes	—
36	C₄²×Dic₁₁	C₂²	1	1	yes	characteristic
37	#10622538	—	2	1	no	—
38	#10622538	—	2	1	no	—
39	C₄×#4318	—	2	1	no	—
40	C₄×#4318	C₂²	1	1	yes	characteristic
41	C₄×#4318	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
43	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
44	#10622190	C₂²	1	2	yes	—
45	#10622188	C₂²	1	2	yes	—
46	#10622188	C₂²	1	2	yes	—
47	#10622170	C₂²	1	2	yes	—
48	#10622170	C₂²	1	2	yes	—
49	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
50	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
51	C₁₁×#135	—	2	4	no	—
52	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₄×D₄×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	—	2	1	no	—
65	C₄×D₄×C₁₁	—	2	1	no	—
66	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₁₁×#117	—	2	1	no	—
71	C₁₁×#117	—	2	1	no	—
72	C₁₁×#117	C₂³	1	1	yes	characteristic
73	C₁₁×#117	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₁	—	2	1	no	—
75	C₂×C₄²×C₁₁	—	2	1	no	—
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	#67001	—	2	4	no	—
78	#67001	—	2	4	no	—
79	C₂×C₄×Dic₁₁	—	2	1	no	—
80	C₂×C₄×Dic₁₁	—	2	1	no	—
81	C₂×C₄×Dic₁₁	C₂³	1	2	yes	—
82	C₂×#4318	—	2	2	no	—
83	C₂×#4318	C₂³	1	2	yes	—
84	C₂×#4318	C₂³	1	2	yes	—
85	C₂²×C₁₁⋊C₈	—	2	2	no	—
86	C₂²×C₁₁⋊C₈	C₂³	1	2	yes	—
87	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
89	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
91	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
92	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
93	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
94	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
95	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
96	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
97	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
98	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
101	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
103	#66901	—	2	4	no	—
104	#66901	—	2	4	no	—
105	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
106	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
107	#66883	—	2	4	no	—
108	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
109	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
110	#66867	—	2	1	no	—
111	#66867	—	2	1	no	—
112	#66867	—	2	2	no	—
113	C₄×C₁₁⋊C₈	—	2	1	no	—
114	C₄×C₁₁⋊C₈	—	2	1	no	—
115	C₄×C₁₁⋊C₈	—	2	2	no	—
116	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
117	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
118	C₄×C₁₁⋊C₈	D₄	1	2	yes	—
119	#21137	—	11	1	no	maximal, Sylow
120	C₁₁×#41	—	2	2	no	—
121	C₁₁×#41	—	2	2	no	—
122	C₁₁×#41	—	2	2	no	—
123	C₁₁×#41	#41	1	4	yes	—
124	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₂×D₄×C₁₁	—	2	1	no	—
127	C₂×D₄×C₁₁	—	2	1	no	—
128	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	—	2	1	no	—
131	C₂²×C₄×C₁₁	—	2	1	no	—
132	C₂²×C₄×C₁₁	—	2	1	no	—
133	C₂²×C₄×C₁₁	—	2	1	no	—
134	C₂²×C₄×C₁₁	—	2	1	no	—
135	C₂²×C₄×C₁₁	—	2	1	no	—
136	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
139	C₂²×Dic₁₁	—	2	2	no	—
140	C₁₁×Q₁₆	—	2	2	no	—
141	C₁₁×SD₁₆	—	2	2	no	—
142	C₁₁×SD₁₆	—	2	2	no	—
143	C₁₁×D₈	—	2	2	no	—
144	C₂×C₈×C₁₁	—	2	2	no	—
145	C₂×C₈×C₁₁	—	2	2	no	—
146	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₁₁×C₄⋊C₄	—	2	1	no	—
151	C₁₁×C₄⋊C₄	—	2	1	no	—
152	C₁₁×C₄⋊C₄	—	2	1	no	—
153	C₁₁×C₄⋊C₄	—	2	1	no	—
154	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
155	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
156	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₁₁×C₂²⋊C₄	—	2	1	no	—
159	C₁₁×C₂²⋊C₄	—	2	1	no	—
160	C₁₁×C₂²⋊C₄	—	2	1	no	—
161	C₁₁×C₂²⋊C₄	—	2	1	no	—
162	C₁₁×C₂²⋊C₄	—	2	1	no	—
163	C₁₁×C₂²⋊C₄	—	2	1	no	—
164	C₄²×C₁₁	—	2	1	no	—
165	C₄²×C₁₁	—	2	1	no	—
166	C₄²×C₁₁	—	2	1	no	—
167	C₄²×C₁₁	—	2	1	no	—
168	C₄²×C₁₁	—	2	1	no	—
169	C₄²×C₁₁	—	2	1	no	—
170	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
174	C₄×Dic₁₁	—	2	4	no	—
175	C₄×Dic₁₁	—	2	2	no	—
176	C₄×Dic₁₁	—	2	2	no	—
177	C₄×Dic₁₁	—	4	2	no	—
178	#4318	—	2	8	no	—
179	#4318	—	2	2	no	—
180	#4318	—	2	2	no	—
181	#4318	—	2	2	no	—
182	#4318	#41	1	4	yes	—
183	C₂×C₁₁⋊C₈	—	2	8	no	—
184	C₂×C₁₁⋊C₈	—	2	2	no	—
185	C₂×C₁₁⋊C₈	—	2	2	no	—
186	C₂×C₁₁⋊C₈	—	2	2	no	—
187	C₂×C₁₁⋊C₈	—	2	2	no	—
188	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
189	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
190	C₄×#135	D₁₁	1	1	yes	characteristic
191	#2922	—	11	1	no	—
192	C₄×#131	—	11	1	no	—
193	#1929	—	11	2	no	—
194	#1922	—	11	2	no	—
195	#1876	—	11	2	no	—
196	#1866	—	11	2	no	—
197	C₄×#108	—	11	1	no	—
198	C₄×#104	—	11	1	no	—
199	C₄×#104	—	11	1	no	—
200	#1744	—	11	1	no	—
201	C₂³×C₁₁	—	2	1	no	—
202	C₂³×C₁₁	—	2	1	no	—
203	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
204	Q₈×C₁₁	—	2	1	no	—
205	Q₈×C₁₁	—	2	1	no	—
206	Q₈×C₁₁	—	2	1	no	—
207	Q₈×C₁₁	#117	1	2	yes	—
208	D₄×C₁₁	—	2	4	no	—
209	D₄×C₁₁	—	2	1	no	—
210	D₄×C₁₁	—	2	1	no	—
211	D₄×C₁₁	—	2	1	no	—
212	D₄×C₁₁	—	4	2	no	—
213	D₄×C₁₁	#117	1	2	yes	—
214	C₂×C₄×C₁₁	—	2	1	no	—
215	C₂×C₄×C₁₁	—	2	4	no	—
216	C₂×C₄×C₁₁	—	2	2	no	—
217	C₂×C₄×C₁₁	—	2	2	no	—
218	C₂×C₄×C₁₁	—	2	1	no	—
219	C₂×C₄×C₁₁	—	2	1	no	—
220	C₂×C₄×C₁₁	—	2	1	no	—
221	C₂×C₄×C₁₁	—	2	1	no	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	4	2	no	—
224	C₂×C₄×C₁₁	—	4	2	no	—
225	C₂×C₄×C₁₁	—	4	2	no	—
226	C₂×C₄×C₁₁	—	4	2	no	—
227	C₂×C₄×C₁₁	—	4	2	no	—
228	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
236	C₂×Dic₁₁	—	2	4	no	—
237	C₂×Dic₁₁	—	4	2	no	—
238	C₂×Dic₁₁	—	4	2	no	—
239	C₈×C₁₁	—	2	1	no	—
240	C₈×C₁₁	—	2	1	no	—
241	C₈×C₁₁	—	2	1	no	—
242	C₈×C₁₁	—	2	1	no	—
243	C₁₁⋊C₈	—	2	2	no	—
244	C₁₁⋊C₈	—	2	4	no	—
245	C₁₁⋊C₈	—	2	2	no	—
246	C₁₁⋊C₈	—	4	2	no	—
247	C₂×#135	C₂×D₁₁	1	1	yes	characteristic
248	C₂×#131	—	11	2	no	—
249	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
250	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
251	C₄×Q₁₆	Dic₁₁	1	1	yes	characteristic, complemented
252	C₄×Q₁₆	Dic₁₁	1	1	yes	characteristic, complemented
253	C₄×SD₁₆	Dic₁₁	1	1	yes	characteristic, complemented
254	C₄×SD₁₆	Dic₁₁	1	1	yes	characteristic, complemented
255	C₄×SD₁₆	Dic₁₁	1	1	yes	characteristic, complemented
256	C₄×SD₁₆	Dic₁₁	1	1	yes	characteristic, complemented
257	C₄×D₈	Dic₁₁	1	1	yes	characteristic, complemented
258	C₄×D₈	Dic₁₁	1	1	yes	characteristic, complemented
259	#433	—	22	2	no	—
260	#431	—	22	1	no	—
261	#431	—	22	1	no	—
262	C₂×#108	—	11	2	no	—
263	#427	C₂×D₁₁	1	1	yes	characteristic
264	#424	—	11	2	no	—
265	C₂×#104	—	11	2	no	—
266	C₂×#104	—	11	2	no	—
267	#416	C₂×D₁₁	1	1	yes	characteristic
268	#416	C₂×D₁₁	1	1	yes	characteristic
269	#408	—	11	2	no	—
270	#405	—	11	2	no	—
271	#405	—	22	2	no	—
272	C₄×M₁₆	—	11	1	no	—
273	C₄×M₁₆	—	11	1	no	—
274	C₄×M₁₆	—	22	1	no	—
275	C₂×C₄×C₈	—	11	1	no	—
276	C₂×C₄×C₈	—	22	1	no	—
277	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
278	C₄³	—	11	1	no	—
279	#341	—	11	2	no	—
280	#339	—	11	2	no	—
281	#339	—	11	2	no	—
282	#336	—	11	2	no	—
283	#336	—	11	2	no	—
284	C₂²×C₁₁	—	2	1	no	—
285	C₂²×C₁₁	—	2	1	no	—
286	C₂²×C₁₁	—	2	2	no	—
287	C₂²×C₁₁	—	4	1	no	—
288	C₂²×C₁₁	—	4	1	no	—
289	C₂²×C₁₁	—	4	1	no	—
290	C₂²×C₁₁	—	4	1	no	—
291	C₂²×C₁₁	—	4	1	no	—
292	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×C₁₁	#529	1	2	yes	—
294	C₄×C₁₁	—	2	1	no	—
295	C₄×C₁₁	—	2	1	no	—
296	C₄×C₁₁	—	2	2	no	—
297	C₄×C₁₁	—	4	1	no	—
298	C₄×C₁₁	—	4	1	no	—
299	C₄×C₁₁	—	4	1	no	—
300	C₄×C₁₁	—	4	1	no	—
301	C₄×C₁₁	—	4	1	no	—
302	C₄×C₁₁	#443	1	2	yes	—
303	C₄×C₁₁	#444	1	2	yes	—
304	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
305	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
306	C₄×C₁₁	#525	1	2	yes	—
307	Dic₁₁	—	4	4	no	—
308	C₂×#41	C₂²×D₁₁	1	1	yes	characteristic
309	C₂×#41	C₂²×D₁₁	1	1	yes	characteristic
310	#135	—	2	4	no	—
311	C₂×Q₁₆	C₂×Dic₁₁	1	1	yes	characteristic
312	C₂×SD₁₆	C₂×Dic₁₁	1	1	yes	characteristic
313	C₂×SD₁₆	C₂×Dic₁₁	1	1	yes	characteristic
314	C₂×D₈	C₂×Dic₁₁	1	1	yes	characteristic
315	#131	—	22	4	no	—
316	#131	—	22	4	no	—
317	C₂×M₁₆	—	11	2	no	—
318	C₂×M₁₆	—	11	2	no	—
319	C₂×M₁₆	—	22	2	no	—
320	C₂²×C₈	—	11	2	no	—
321	C₂²×C₈	—	22	2	no	—
322	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
323	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
324	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
325	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
326	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
327	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
333	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
334	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
335	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	C₂²×D₁₁	1	1	yes	characteristic
339	#117	C₂²×D₁₁	1	1	yes	characteristic
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	11	2	no	—
343	C₂×C₄²	—	22	1	no	—
344	C₂×C₄²	—	22	1	no	—
345	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
346	#108	—	22	4	no	—
347	#107	C₂×Dic₁₁	1	1	yes	characteristic
348	#107	C₂×Dic₁₁	1	1	yes	characteristic
349	#106	C₂×Dic₁₁	1	1	yes	characteristic
350	#106	C₂×Dic₁₁	1	1	yes	characteristic
351	C₄⋊C₈	—	22	2	no	—
352	C₄⋊C₈	—	22	2	no	—
353	#104	—	22	4	no	—
354	#104	—	22	4	no	—
355	#103	C₂×Dic₁₁	1	1	yes	characteristic
356	#103	C₂×Dic₁₁	1	1	yes	characteristic
357	#103	C₂×Dic₁₁	1	1	yes	characteristic
358	#103	C₂×Dic₁₁	1	1	yes	characteristic
359	#102	C₂×Dic₁₁	1	1	yes	characteristic
360	#102	C₂×Dic₁₁	1	1	yes	characteristic
361	#102	C₂×Dic₁₁	1	1	yes	characteristic
362	#102	C₂×Dic₁₁	1	1	yes	characteristic
363	C₂²⋊C₈	—	22	2	no	—
364	C₂²⋊C₈	—	22	2	no	—
365	#97	—	22	2	no	—
366	#97	—	22	1	no	—
367	#97	—	22	1	no	—
368	C₄×C₈	—	11	2	no	—
369	C₄×C₈	—	11	1	no	—
370	C₄×C₈	—	11	1	no	—
371	C₄×C₈	—	22	2	no	—
372	C₄×C₈	—	22	1	no	—
373	C₄×C₈	—	22	1	no	—
374	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
375	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
376	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
377	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
378	C₂×C₁₁	—	2	2	no	—
379	C₂×C₁₁	—	4	2	no	—
380	C₂×C₁₁	—	8	1	no	—
381	C₂×C₁₁	#2290	1	1	yes	characteristic
382	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
383	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	#4339	1	4	yes	—
388	C₂×Q₈	C₂²×Dic₁₁	1	1	yes	characteristic
389	C₂×Q₈	C₂²×Dic₁₁	1	1	yes	characteristic
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂²×Dic₁₁	1	1	yes	characteristic
393	C₂×D₄	C₂²×Dic₁₁	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	22	2	no	—
401	C₂²×C₄	#4341	1	1	yes	characteristic
402	C₂²×C₄	#4341	1	1	yes	characteristic
403	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
404	Q₁₆	—	2	2	no	—
405	SD₁₆	—	2	2	no	—
406	SD₁₆	—	2	2	no	—
407	D₈	—	2	2	no	—
408	M₁₆	—	11	4	no	—
409	M₁₆	—	22	8	no	—
410	M₁₆	—	22	2	no	—
411	M₁₆	—	22	2	no	—
412	M₁₆	—	22	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	11	2	no	—
416	C₂×C₈	—	11	2	no	—
417	C₂×C₈	—	22	8	no	—
418	C₂×C₈	—	22	2	no	—
419	C₂×C₈	—	22	2	no	—
420	C₂×C₈	—	22	2	no	—
421	C₂×C₈	—	22	2	no	—
422	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
423	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
424	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
425	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
432	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
433	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	22	4	no	—
447	C₄²	—	22	2	no	—
448	C₄²	—	22	2	no	—
449	C₄²	—	44	2	no	—
450	C₄²	D₄×D₁₁	1	1	yes	characteristic
451	C₄²	D₄×D₁₁	1	1	yes	characteristic
452	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
453	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
454	C₁₁	#21137	1	1	yes	characteristic, complemented, Sylow
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	C₂×#4341	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	#66979	1	2	yes	—
462	D₄	—	2	4	no	—
463	D₄	—	2	1	no	—
464	D₄	—	2	1	no	—
465	D₄	—	2	1	no	—
466	D₄	—	4	2	no	—
467	D₄	#66979	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	22	4	no	—
483	C₂×C₄	—	44	2	no	—
484	C₂×C₄	—	44	2	no	—
485	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
486	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
487	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
488	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
489	C₂×C₄	C₂×#4339	1	2	yes	—
490	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
491	C₂×C₄	#41×D₁₁	1	2	yes	—
492	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	1	no	—
496	C₈	—	2	1	no	—
497	C₈	—	22	2	no	—
498	C₈	—	22	2	no	—
499	C₈	—	22	4	no	—
500	C₈	—	44	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	#10623069	1	2	yes	—
510	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	2	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	1	no	—
519	C₄	—	44	4	no	—
520	C₄	#10622809	1	2	yes	—
521	C₄	#10622810	1	2	yes	—
522	C₄	#10623078	1	2	yes	—
523	C₄	C₂×#66979	1	1	yes	characteristic
524	C₄	#41×Dic₁₁	1	1	yes	characteristic
525	C₂	—	2	2	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	1	no	—
528	C₂	#13071061	1	1	yes	characteristic
529	C₂	C₂×#10622809	1	1	yes	characteristic
530	C₂	C₂×#10622810	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₄×C₁₁×#135	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₂²
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	C₄×#135	D₁₁
hypocenter	C₁₁	#21137
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13077260	C₂	semidirect
2. C₄×#67001	C₂	semidirect
3. #13069266	C₂	semidirect
4. #13069217	C₂	semidirect
6. #13068893	C₂	semidirect
7. C₄×#66883	C₂	semidirect
8. C₄×#66901	C₂	semidirect
9. C₄×#66901	C₂	semidirect
10. #13068361	C₂	semidirect
16. C₄×C₁₁×Q₁₆	C₄	semidirect
17. C₄×C₁₁×Q₁₆	C₄	semidirect
18. C₄×C₁₁×SD₁₆	C₄	semidirect
19. C₄×C₁₁×SD₁₆	C₄	semidirect
20. C₄×C₁₁×SD₁₆	C₄	semidirect
21. C₄×C₁₁×SD₁₆	C₄	semidirect
22. C₄×C₁₁×D₈	C₄	semidirect
23. C₄×C₁₁×D₈	C₄	semidirect
251. C₄×Q₁₆	Dic₁₁	semidirect
252. C₄×Q₁₆	Dic₁₁	semidirect
253. C₄×SD₁₆	Dic₁₁	semidirect
254. C₄×SD₁₆	Dic₁₁	semidirect
255. C₄×SD₁₆	Dic₁₁	semidirect
256. C₄×SD₁₆	Dic₁₁	semidirect
257. C₄×D₈	Dic₁₁	semidirect
258. C₄×D₈	Dic₁₁	semidirect
454. C₁₁	#21137	semidirect

Maximal subgroups

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

subgroup	index
#13077260	2
C₄×#67001	2
#13069266	2
#13069217	2
#13068945	2
#13068893	2
C₄×#66883	2
C₄×#66901	2
#13068361	2
C₄×C₁₁×#135	2
#21137	11