Subgroups — #14723348

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077583	C₂	1	1	yes	maximal, characteristic, complemented
2	#41×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#13067495	C₂	1	2	yes	maximal, complemented
4	#13067488	C₂	1	2	yes	maximal, complemented
5	#13067481	C₂	1	2	yes	maximal, complemented
6	#13067474	C₂	1	2	yes	maximal, complemented
7	#13067364	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066998	C₂	1	1	yes	maximal, characteristic, complemented
9	#13066998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10622092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
15	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
16	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
18	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
19	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
21	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
22	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
23	C₁₁×#427	C₄	1	1	yes	characteristic
24	C₁₁×#416	C₄	1	1	yes	characteristic
25	C₁₁×#416	C₄	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	#10622637	C₂²	1	2	yes	—
28	Q₈×C₁₁⋊C₈	C₂²	1	2	yes	—
29	#10622625	C₂²	1	2	yes	—
30	#10622624	—	2	2	no	—
31	D₄×C₁₁⋊C₈	—	2	2	no	—
32	D₄×C₁₁⋊C₈	C₂²	1	2	yes	—
33	#10622538	—	2	1	no	—
34	#10622538	—	2	1	no	—
35	#10622538	C₂²	1	1	yes	characteristic
36	#10622538	C₂²	1	1	yes	characteristic
37	C₄×#4318	—	2	1	no	—
38	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
39	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
42	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
43	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
44	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
45	#10622096	C₂²	1	2	yes	—
46	#10622095	C₂²	1	2	yes	—
47	#10622092	C₂²	1	2	yes	—
48	#10622092	C₂²	1	2	yes	—
49	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×#41	C₂×C₄	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	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂×C₄	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	C₂³	1	1	yes	characteristic
61	C₄×Q₈×C₁₁	C₂³	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	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×#117	—	2	1	no	—
71	C₁₁×#117	—	2	1	no	—
72	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
73	C₁₁×#117	C₂×C₄	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	C₂×#4318	—	2	2	no	—
78	C₂²×C₁₁⋊C₈	—	2	1	no	—
79	C₂²×C₁₁⋊C₈	—	2	2	no	—
80	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
81	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
82	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
83	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
84	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
85	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
86	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
87	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
89	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
91	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
92	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
97	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
98	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
99	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
100	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
101	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
102	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
103	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
104	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
105	#66867	—	2	2	no	—
106	C₄×C₁₁⋊C₈	—	2	1	no	—
107	C₄×C₁₁⋊C₈	—	2	1	no	—
108	C₄×C₁₁⋊C₈	—	2	1	no	—
109	C₄×C₁₁⋊C₈	—	2	2	no	—
110	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
111	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
112	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
113	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
114	#17868	—	11	1	no	maximal, Sylow
115	C₁₁×#41	—	2	2	no	—
116	C₁₁×#41	—	2	2	no	—
117	C₁₁×#41	—	2	2	no	—
118	C₁₁×#41	M₁₆	1	4	yes	complemented
119	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₁	—	2	1	no	—
122	C₂×D₄×C₁₁	—	2	1	no	—
123	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	—	2	1	no	—
126	C₂²×C₄×C₁₁	—	2	1	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	2	1	no	—
129	C₂²×C₄×C₁₁	—	2	1	no	—
130	C₂²×C₄×C₁₁	—	2	1	no	—
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
134	C₁₁×Q₁₆	—	2	2	no	—
135	C₁₁×SD₁₆	—	2	2	no	—
136	C₁₁×SD₁₆	—	2	2	no	—
137	C₁₁×D₈	—	2	2	no	—
138	C₂×C₈×C₁₁	—	2	2	no	—
139	C₂×C₈×C₁₁	—	2	2	no	—
140	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
144	C₁₁×C₄⋊C₄	—	2	1	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	—	2	1	no	—
147	C₁₁×C₄⋊C₄	—	2	1	no	—
148	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₁×C₂²⋊C₄	—	2	1	no	—
153	C₁₁×C₂²⋊C₄	—	2	1	no	—
154	C₁₁×C₂²⋊C₄	—	2	1	no	—
155	C₁₁×C₂²⋊C₄	—	2	1	no	—
156	C₁₁×C₂²⋊C₄	—	2	1	no	—
157	C₁₁×C₂²⋊C₄	—	2	1	no	—
158	C₄²×C₁₁	—	2	1	no	—
159	C₄²×C₁₁	—	2	1	no	—
160	C₄²×C₁₁	—	2	1	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	2	1	no	—
164	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₁	#41	1	1	yes	characteristic
167	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
168	#4318	—	4	4	no	—
169	C₂×C₁₁⋊C₈	—	2	4	no	—
170	C₂×C₁₁⋊C₈	—	2	2	no	—
171	C₂×C₁₁⋊C₈	—	2	2	no	—
172	C₂×C₁₁⋊C₈	—	2	2	no	—
173	C₂×C₁₁⋊C₈	—	4	2	no	—
174	C₂×C₁₁⋊C₈	—	4	4	no	—
175	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
176	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
177	#2965	—	11	1	no	—
178	C₈×#41	—	11	1	no	—
179	C₄×#135	D₁₁	1	1	yes	characteristic
180	#1588	—	11	2	no	—
181	#1587	—	11	2	no	—
182	#1586	—	11	2	no	—
183	#1585	—	11	2	no	—
184	#1564	—	11	1	no	—
185	#1476	—	11	1	no	—
186	#1476	—	11	1	no	—
187	C₂×#322	—	11	1	no	—
188	C₂³×C₁₁	—	2	1	no	—
189	C₂³×C₁₁	—	2	1	no	—
190	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
191	Q₈×C₁₁	—	2	1	no	—
192	Q₈×C₁₁	—	2	1	no	—
193	Q₈×C₁₁	—	2	1	no	—
194	Q₈×C₁₁	C₂×M₁₆	1	2	yes	—
195	D₄×C₁₁	—	2	4	no	—
196	D₄×C₁₁	—	2	1	no	—
197	D₄×C₁₁	—	2	1	no	—
198	D₄×C₁₁	—	2	1	no	—
199	D₄×C₁₁	—	4	2	no	—
200	D₄×C₁₁	C₂×M₁₆	1	2	yes	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	2	4	no	—
204	C₂×C₄×C₁₁	—	2	2	no	—
205	C₂×C₄×C₁₁	—	2	1	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	1	no	—
208	C₂×C₄×C₁₁	—	2	1	no	—
209	C₂×C₄×C₁₁	—	2	1	no	—
210	C₂×C₄×C₁₁	—	4	2	no	—
211	C₂×C₄×C₁₁	—	4	2	no	—
212	C₂×C₄×C₁₁	—	4	2	no	—
213	C₂×C₄×C₁₁	—	4	2	no	—
214	C₂×C₄×C₁₁	—	4	2	no	—
215	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
219	C₂×C₄×C₁₁	#131	1	2	yes	—
220	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
223	C₈×C₁₁	—	2	1	no	—
224	C₈×C₁₁	—	2	1	no	—
225	C₈×C₁₁	—	2	1	no	—
226	C₈×C₁₁	—	2	1	no	—
227	C₁₁⋊C₈	—	2	4	no	—
228	C₁₁⋊C₈	—	2	2	no	—
229	C₁₁⋊C₈	—	2	2	no	—
230	C₁₁⋊C₈	—	4	2	no	—
231	C₁₁⋊C₈	—	4	2	no	—
232	C₂×#135	Dic₁₁	1	1	yes	characteristic
233	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
234	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
235	#446	—	11	2	no	—
236	C₈×Q₈	—	11	2	no	—
237	C₄×Q₁₆	Dic₁₁	1	1	yes	characteristic
238	C₄×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
239	C₄×SD₁₆	Dic₁₁	1	1	yes	characteristic
240	C₄×SD₁₆	Dic₁₁	1	1	yes	characteristic
241	C₄×SD₁₆	C₂×D₁₁	1	1	yes	characteristic
242	C₄×SD₁₆	C₂×D₁₁	1	1	yes	characteristic
243	C₄×D₈	Dic₁₁	1	1	yes	characteristic
244	C₄×D₈	C₂×D₁₁	1	1	yes	characteristic
245	#436	—	11	2	no	—
246	#435	—	22	2	no	—
247	C₈×D₄	—	11	2	no	—
248	C₈×D₄	—	22	2	no	—
249	#431	—	11	1	no	—
250	#431	—	11	1	no	—
251	#431	—	22	1	no	—
252	#431	—	22	1	no	—
253	#427	Dic₁₁	1	1	yes	characteristic
254	#416	Dic₁₁	1	1	yes	characteristic
255	#416	Dic₁₁	1	1	yes	characteristic
256	C₄×M₁₆	—	22	1	no	—
257	C₂×C₄×C₈	—	11	1	no	—
258	C₂×C₄×C₈	—	11	1	no	—
259	C₂×C₄×C₈	—	22	1	no	—
260	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
261	#335	—	11	2	no	—
262	#334	—	11	2	no	—
263	Q₈⋊C₈	—	11	2	no	—
264	Q₈⋊C₈	—	11	2	no	—
265	D₄⋊C₈	—	11	2	no	—
266	D₄⋊C₈	—	11	2	no	—
267	#322	—	11	2	no	—
268	#322	—	11	2	no	—
269	C₂²×C₁₁	—	2	1	no	—
270	C₂²×C₁₁	—	2	1	no	—
271	C₂²×C₁₁	—	2	2	no	—
272	C₂²×C₁₁	—	4	1	no	—
273	C₂²×C₁₁	—	4	1	no	—
274	C₂²×C₁₁	—	4	1	no	—
275	C₂²×C₁₁	—	4	1	no	—
276	C₂²×C₁₁	—	4	1	no	—
277	C₂²×C₁₁	#435	1	2	yes	—
278	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
279	C₄×C₁₁	—	2	2	no	—
280	C₄×C₁₁	—	2	1	no	—
281	C₄×C₁₁	—	2	1	no	—
282	C₄×C₁₁	—	4	1	no	—
283	C₄×C₁₁	—	4	1	no	—
284	C₄×C₁₁	—	4	1	no	—
285	C₄×C₁₁	—	4	1	no	—
286	C₄×C₁₁	—	4	1	no	—
287	C₄×C₁₁	#435	1	2	yes	—
288	C₄×C₁₁	#443	1	2	yes	—
289	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
290	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
291	C₄×C₁₁	#575	1	2	yes	—
292	C₂×#41	C₂×Dic₁₁	1	1	yes	characteristic
293	C₂×#41	C₂×Dic₁₁	1	1	yes	characteristic
294	#135	—	2	4	no	—
295	C₂×Q₁₆	C₂×Dic₁₁	1	1	yes	characteristic
296	C₂×SD₁₆	C₂×Dic₁₁	1	1	yes	characteristic
297	C₂×SD₁₆	C₂×Dic₁₁	1	1	yes	characteristic
298	C₂×D₈	C₂×Dic₁₁	1	1	yes	characteristic
299	C₂×M₁₆	—	22	2	no	—
300	C₂²×C₈	—	11	2	no	—
301	C₂²×C₈	—	22	2	no	—
302	C₂²×C₈	—	22	1	no	—
303	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
304	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
305	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
306	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
307	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
308	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
309	C₄×D₄	—	2	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
314	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
315	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
316	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
317	#117	—	2	1	no	—
318	#117	—	2	1	no	—
319	#117	C₂×Dic₁₁	1	1	yes	characteristic
320	#117	C₂×Dic₁₁	1	1	yes	characteristic
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
324	#107	C₂×Dic₁₁	1	1	yes	characteristic
325	#107	C₂×Dic₁₁	1	1	yes	characteristic
326	#106	C₂×Dic₁₁	1	1	yes	characteristic
327	#106	C₂×Dic₁₁	1	1	yes	characteristic
328	C₄⋊C₈	—	11	2	no	—
329	C₄⋊C₈	—	11	2	no	—
330	C₄⋊C₈	—	22	2	no	—
331	C₄⋊C₈	—	22	2	no	—
332	#103	C₂×Dic₁₁	1	1	yes	characteristic
333	#103	C₂×Dic₁₁	1	1	yes	characteristic
334	#103	C₂×Dic₁₁	1	1	yes	characteristic
335	#103	C₂×Dic₁₁	1	1	yes	characteristic
336	#102	C₂×Dic₁₁	1	1	yes	characteristic
337	#102	C₂×Dic₁₁	1	1	yes	characteristic
338	#102	C₂×Dic₁₁	1	1	yes	characteristic
339	#102	C₂×Dic₁₁	1	1	yes	characteristic
340	C₂²⋊C₈	—	22	2	no	—
341	C₂²⋊C₈	—	22	2	no	—
342	C₂²⋊C₈	—	22	1	no	—
343	C₂²⋊C₈	—	22	1	no	—
344	#97	—	22	2	no	—
345	C₄×C₈	—	11	1	no	—
346	C₄×C₈	—	11	1	no	—
347	C₄×C₈	—	11	2	no	—
348	C₄×C₈	—	11	2	no	—
349	C₄×C₈	—	22	2	no	—
350	C₄×C₈	—	22	1	no	—
351	C₄×C₈	—	22	1	no	—
352	C₄×C₈	—	22	1	no	—
353	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
354	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
355	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
356	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
357	C₂×C₁₁	—	2	2	no	—
358	C₂×C₁₁	—	4	2	no	—
359	C₂×C₁₁	—	8	1	no	—
360	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
361	C₂×C₁₁	#2943	1	1	yes	characteristic
362	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	#4318	1	4	yes	complemented
367	C₂×Q₈	C₂²×Dic₁₁	1	1	yes	characteristic
368	C₂×Q₈	C₂²×Dic₁₁	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	C₂²×Dic₁₁	1	1	yes	characteristic
372	C₂×D₄	C₂²×Dic₁₁	1	1	yes	characteristic
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
380	C₂²×C₄	#4341	1	1	yes	characteristic
381	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
382	Q₁₆	—	2	2	no	—
383	SD₁₆	—	2	2	no	—
384	SD₁₆	—	2	2	no	—
385	D₈	—	2	2	no	—
386	M₁₆	—	44	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	11	2	no	—
390	C₂×C₈	—	11	2	no	—
391	C₂×C₈	—	22	4	no	—
392	C₂×C₈	—	22	2	no	—
393	C₂×C₈	—	22	2	no	—
394	C₂×C₈	—	22	2	no	—
395	C₂×C₈	—	44	2	no	—
396	C₂×C₈	—	44	4	no	—
397	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
398	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
399	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
400	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
406	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
407	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
408	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	D₄×D₁₁	1	1	yes	characteristic
422	C₄²	#4341	1	1	yes	characteristic
423	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
424	C₄²	C₂³×D₁₁	1	1	yes	characteristic
425	C₁₁	#17868	1	1	yes	characteristic, complemented, Sylow
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
429	Q₈	—	2	1	no	—
430	Q₈	—	2	1	no	—
431	Q₈	—	2	1	no	—
432	Q₈	C₂×#4318	1	2	yes	—
433	D₄	—	2	4	no	—
434	D₄	—	2	1	no	—
435	D₄	—	2	1	no	—
436	D₄	—	2	1	no	—
437	D₄	—	4	2	no	—
438	D₄	C₂×#4318	1	2	yes	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	C₂×#4318	1	2	yes	—
454	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
455	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
456	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
457	C₂×C₄	#67001	1	2	yes	—
458	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
459	C₂×C₄	C₂×#4341	1	1	yes	characteristic
460	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	22	4	no	—
466	C₈	—	22	2	no	—
467	C₈	—	22	2	no	—
468	C₈	—	44	2	no	—
469	C₈	—	44	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	#10622624	1	2	yes	—
479	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	#10622624	1	2	yes	—
489	C₄	#10622809	1	2	yes	—
490	C₄	#10623299	1	2	yes	—
491	C₄	C₂²×#4318	1	1	yes	characteristic
492	C₄	C₂×#67001	1	1	yes	characteristic
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	8	1	no	—
496	C₂	C₂×#10622624	1	1	yes	characteristic
497	C₂	#13077417	1	1	yes	characteristic
498	C₂	C₂×#10622809	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₄×C₁₁×#135	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₄×#135	D₁₁
hypocenter	C₁₁	#17868
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. #13077583	C₂	semidirect
2. #41×C₁₁⋊C₈	C₂	semidirect
3. #13067495	C₂	semidirect
4. #13067488	C₂	semidirect
5. #13067481	C₂	semidirect
6. #13067474	C₂	semidirect
7. #13067364	C₂	semidirect
8. #13066998	C₂	semidirect
9. #13066998	C₂	semidirect
10. C₂×#10622092	C₂	semidirect
118. C₁₁×#41	M₁₆	semidirect
366. #41	#4318	semidirect
425. C₁₁	#17868	semidirect

Maximal subgroups

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

subgroup	index
#13077583	2
#41×C₁₁⋊C₈	2
#13067495	2
#13067488	2
#13067481	2
#13067474	2
#13067364	2
#13066998	2
C₂×#10622092	2
C₄×C₁₁×#135	2
#17868	11