Subgroups — #14724938

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13078676	C₂	1	1	yes	maximal, characteristic
2	#13077741	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077682	C₂	1	1	yes	maximal, characteristic, complemented
4	#13067503	C₂	1	2	yes	maximal, complemented
5	#13067477	C₂	1	2	yes	maximal, complemented
6	#13067476	C₂	1	2	yes	maximal, complemented
7	#13067408	C₂	1	2	yes	maximal, complemented
8	#13067404	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067068	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066899	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
13	#10623008	C₂²	1	1	yes	characteristic
14	C₁₁×#431	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	#10622851	C₄	1	2	yes	—
17	#10622640	C₄	1	1	yes	characteristic
18	C₄×#4325	C₂²	1	2	yes	—
19	#10622637	C₂²	1	2	yes	—
20	#10622634	C₄	1	1	yes	characteristic
21	#10622628	C₄	1	1	yes	characteristic
22	C₄×#4323	C₂²	1	2	yes	—
23	#10622624	—	2	2	no	—
24	D₄×C₁₁⋊C₈	C₂²	1	2	yes	—
25	#10622621	C₄	1	1	yes	characteristic
26	#10622616	C₄	1	2	yes	—
27	#10622539	—	2	1	no	—
28	#10622538	C₂²	1	1	yes	characteristic
29	#10622538	C₂²	1	1	yes	characteristic
30	#10622537	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
32	#10622451	C₂²	1	2	yes	—
33	#10622447	C₂²	1	2	yes	—
34	#10622340	—	2	2	no	—
35	#10622301	—	2	1	no	—
36	C₈×D₄₄	—	2	1	no	—
37	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
41	#10622118	C₂²	1	2	yes	—
42	#10622117	C₂²	1	2	yes	—
43	#10622097	C₂²	1	2	yes	—
44	#10622097	C₂²	1	2	yes	—
45	#10622093	C₂²	1	2	yes	—
46	C₈×C₁₁⋊C₈	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
48	C₂×#4339	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₄×D₄×C₁₁	—	2	1	no	—
53	C₄×D₄×C₁₁	—	2	1	no	—
54	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
56	C₁₁×#117	—	2	1	no	—
57	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	—	2	1	no	—
59	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×#4325	C₂×C₄	1	2	yes	—
61	C₂×#4323	C₂×C₄	1	2	yes	—
62	#66983	—	2	1	no	—
63	#66983	C₂×C₄	1	2	yes	—
64	C₂×#4318	—	2	1	no	—
65	C₂²×C₁₁⋊C₈	—	2	2	no	—
66	C₂×#4313	—	2	2	no	—
67	C₂×C₈×D₁₁	—	2	2	no	—
68	#66928	—	2	1	no	—
69	#66927	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄₄	—	2	1	no	—
71	C₄×D₄₄	C₂³	1	2	yes	—
72	#66922	C₂×C₄	1	1	yes	characteristic
73	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
74	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
75	C₁₁×C₂²⋊C₈	—	2	1	no	—
76	C₄×C₈×C₁₁	—	2	1	no	—
77	C₄×C₈×C₁₁	—	2	1	no	—
78	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
80	#66899	C₂×C₄	1	2	yes	—
81	#66896	C₂×C₄	1	2	yes	—
82	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
83	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
84	C₂²⋊(C₁₁⋊C₈)	D₄	1	2	yes	—
85	(C₂×D₁₁)⋊C₈	—	2	2	no	—
86	(C₂×D₁₁)⋊C₈	—	2	2	no	—
87	#66873	C₂×C₄	1	2	yes	—
88	#66873	C₂×C₄	1	2	yes	—
89	#66872	C₂×C₄	1	2	yes	—
90	#66871	C₂×C₄	1	2	yes	—
91	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
92	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
93	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
94	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
96	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
97	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
98	#66867	—	2	2	no	—
99	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
100	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
101	#18015	—	11	1	no	maximal, Sylow
102	C₁₁×#41	—	2	2	no	—
103	C₁₁×#41	—	4	1	no	—
104	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×D₄×C₁₁	—	2	1	no	—
106	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	—	2	1	no	—
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₁₁	—	2	2	no	—
114	#4339	—	8	1	no	—
115	#4339	—	8	1	no	—
116	C₂×D₄₄	—	2	1	no	—
117	C₂×D₄₄	—	2	1	no	—
118	C₂×D₄₄	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₁₁	—	2	2	no	—
120	C₂×Dic₂₂	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	4	no	—
122	C₂×C₈×C₁₁	—	2	1	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₁₁×C₄⋊C₄	—	2	1	no	—
127	C₁₁×C₄⋊C₄	—	2	1	no	—
128	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
129	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
130	C₁₁×C₂²⋊C₄	—	2	1	no	—
131	C₁₁×C₂²⋊C₄	—	2	1	no	—
132	C₁₁×C₂²⋊C₄	—	2	1	no	—
133	C₄²×C₁₁	—	2	1	no	—
134	C₄²×C₁₁	—	2	1	no	—
135	C₄²×C₁₁	—	2	1	no	—
136	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₁	#41	1	1	yes	characteristic
139	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
140	#4325	—	4	2	no	—
141	#4323	—	2	4	no	—
142	(C₂×D₁₁)⋊C₄	—	2	2	no	—
143	(C₂×D₁₁)⋊C₄	—	2	2	no	—
144	C₄⋊Dic₁₁	—	2	1	no	—
145	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
146	#4318	—	8	1	no	—
147	C₂×C₁₁⋊C₈	—	2	2	no	—
148	C₂×C₁₁⋊C₈	—	8	2	no	—
149	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
153	#4313	—	8	2	no	—
154	C₈×D₁₁	—	8	2	no	—
155	#3106	—	11	1	no	—
156	#2990	—	11	1	no	—
157	#2979	—	11	1	no	—
158	#1590	—	11	2	no	—
159	#1586	—	11	2	no	—
160	#1585	—	11	2	no	—
161	C₈×D₈	—	11	2	no	—
162	#1574	—	11	1	no	—
163	#1492	—	11	1	no	—
164	#1476	D₁₁	1	1	yes	characteristic, complemented
165	#1450	—	11	1	no	—
166	C₂³×C₁₁	—	2	1	no	—
167	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₁₁	—	2	2	no	—
169	Q₈×C₁₁	—	2	1	no	—
170	Q₈×C₁₁	—	2	1	no	—
171	D₄×C₁₁	—	2	1	no	—
172	D₄×C₁₁	—	4	2	no	—
173	D₄×C₁₁	#131	1	2	yes	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	1	no	—
176	C₂×C₄×C₁₁	—	2	1	no	—
177	C₂×C₄×C₁₁	—	2	1	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	1	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	4	2	no	—
183	C₂×C₄×C₁₁	—	4	1	no	—
184	C₂×C₄×C₁₁	—	4	1	no	—
185	C₂×C₄×C₁₁	—	4	2	no	—
186	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
192	C₂²⋊D₁₁	—	8	2	no	—
193	C₂×Dic₁₁	—	2	2	no	—
194	D₄₄	—	2	2	no	—
195	D₄₄	—	2	2	no	—
196	D₄₄	—	4	2	no	—
197	D₄₄	—	8	1	no	—
198	C₄×D₁₁	—	4	2	no	—
199	C₄×D₁₁	—	4	2	no	—
200	Dic₂₂	—	8	1	no	—
201	C₈×C₁₁	—	2	2	no	—
202	C₈×C₁₁	—	2	2	no	—
203	C₈×C₁₁	—	4	1	no	—
204	C₈×C₁₁	—	4	1	no	—
205	C₁₁⋊C₈	—	2	2	no	—
206	C₁₁⋊C₈	—	2	2	no	—
207	C₁₁⋊C₈	—	2	2	no	—
208	C₁₁⋊C₈	—	2	2	no	—
209	C₁₁⋊C₈	—	4	2	no	—
210	#532	—	11	1	no	—
211	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
212	#482	—	11	2	no	—
213	#477	—	11	1	no	—
214	#476	—	11	1	no	—
215	#460	—	11	1	no	—
216	#459	—	11	1	no	—
217	#449	—	11	2	no	—
218	#446	—	11	2	no	—
219	C₄×SD₁₆	—	11	2	no	—
220	C₄×D₈	—	11	2	no	—
221	#436	—	11	2	no	—
222	#436	—	22	1	no	—
223	#435	—	22	2	no	—
224	C₈×D₄	—	11	2	no	—
225	C₈×D₄	—	11	2	no	—
226	C₈×D₄	—	22	1	no	—
227	#432	—	22	1	no	—
228	#431	—	11	1	no	—
229	#431	—	11	1	no	—
230	#431	C₂×D₁₁	1	1	yes	characteristic
231	#423	—	11	1	no	—
232	C₂×C₄⋊C₈	—	22	1	no	—
233	#408	—	22	2	no	—
234	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
235	#335	—	11	2	no	—
236	#334	—	11	2	no	—
237	Q₈⋊C₈	C₂×D₁₁	1	1	yes	characteristic
238	Q₈⋊C₈	C₂×D₁₁	1	1	yes	characteristic
239	D₄⋊C₈	—	11	2	no	—
240	D₄⋊C₈	—	11	2	no	—
241	D₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
242	D₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
243	#322	—	11	2	no	—
244	C₈²	—	11	2	no	—
245	C₂²×C₁₁	—	2	1	no	—
246	C₂²×C₁₁	—	2	2	no	—
247	C₂²×C₁₁	—	2	1	no	—
248	C₂²×C₁₁	—	2	1	no	—
249	C₂²×C₁₁	—	4	1	no	—
250	C₂²×C₁₁	—	4	1	no	—
251	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂×D₁₁	—	4	2	no	—
253	C₂×D₁₁	—	4	2	no	—
254	C₂×D₁₁	—	4	2	no	—
255	C₄×C₁₁	—	2	1	no	—
256	C₄×C₁₁	—	2	1	no	—
257	C₄×C₁₁	—	2	1	no	—
258	C₄×C₁₁	—	4	1	no	—
259	C₄×C₁₁	—	4	1	no	—
260	C₄×C₁₁	—	4	1	no	—
261	C₄×C₁₁	#443	1	2	yes	—
262	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
263	C₄×C₁₁	#568	1	1	yes	characteristic
264	C₄×C₁₁	#576	1	1	yes	characteristic
265	C₄×C₁₁	#577	1	1	yes	characteristic
266	Dic₁₁	—	4	2	no	—
267	C₂×#41	—	22	1	no	—
268	C₂×#41	C₄×D₁₁	1	1	yes	characteristic
269	C₂×SD₁₆	—	11	2	no	—
270	C₂×D₈	—	11	2	no	—
271	C₂×M₁₆	—	22	2	no	—
272	C₂×M₁₆	—	22	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	22	2	no	—
275	C₂²×C₈	—	22	2	no	—
276	C₄⋊Q₈	—	11	1	no	—
277	#127	—	11	1	no	—
278	#124	—	22	1	no	—
279	#121	—	11	2	no	—
280	#121	—	22	1	no	—
281	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
282	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	11	2	no	—
286	C₄×D₄	—	22	1	no	—
287	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
288	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
289	#117	—	2	1	no	—
290	#117	C₄×D₁₁	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
293	#107	—	11	2	no	—
294	#106	—	11	2	no	—
295	C₄⋊C₈	—	11	1	no	—
296	C₄⋊C₈	—	11	1	no	—
297	C₄⋊C₈	—	11	1	no	—
298	C₄⋊C₈	—	11	1	no	—
299	C₄⋊C₈	—	11	2	no	—
300	C₄⋊C₈	—	22	2	no	—
301	C₄⋊C₈	—	22	1	no	—
302	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
303	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
304	#103	—	11	2	no	—
305	#102	—	11	2	no	—
306	#102	—	11	2	no	—
307	#102	—	11	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	11	2	no	—
310	C₂²⋊C₈	—	11	2	no	—
311	C₂²⋊C₈	—	22	2	no	—
312	C₂²⋊C₈	—	22	2	no	—
313	C₂²⋊C₈	—	22	2	no	—
314	#97	—	22	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	—	11	2	no	—
318	C₄×C₈	—	11	2	no	—
319	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
321	C₂×C₁₁	—	4	1	no	—
322	C₂×C₁₁	—	4	2	no	—
323	C₂×C₁₁	#2933	1	1	yes	characteristic
324	C₂×C₁₁	#2946	1	1	yes	characteristic
325	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
326	D₁₁	—	8	2	no	—
327	#41	—	2	2	no	—
328	#41	—	4	1	no	—
329	#41	—	88	1	no	—
330	#41	—	88	1	no	—
331	C₂×Q₈	—	22	1	no	—
332	C₂×Q₈	C₂×C₄×D₁₁	1	1	yes	characteristic
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	11	2	no	—
335	C₂×D₄	—	22	2	no	—
336	C₂×D₄	—	22	1	no	—
337	C₂×D₄	—	22	1	no	—
338	C₂×D₄	C₂×C₄×D₁₁	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	22	2	no	—
343	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
344	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
345	C₂²×C₄	#4341	1	1	yes	characteristic
346	SD₁₆	—	44	2	no	—
347	D₈	—	22	4	no	—
348	M₁₆	—	88	2	no	—
349	M₁₆	—	88	1	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	11	2	no	—
356	C₂×C₈	—	11	2	no	—
357	C₂×C₈	—	11	2	no	—
358	C₂×C₈	—	11	2	no	—
359	C₂×C₈	—	22	2	no	—
360	C₂×C₈	—	88	2	no	—
361	C₂×C₈	—	88	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	11	2	no	—
365	C₄⋊C₄	—	22	1	no	—
366	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
367	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	22	2	no	—
372	C₂²⋊C₄	—	22	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
377	C₄²	D₄×D₁₁	1	1	yes	characteristic
378	C₄²	#4341	1	1	yes	characteristic
379	C₄²	C₂³×D₁₁	1	1	yes	characteristic
380	C₁₁	#18015	1	1	yes	characteristic, complemented, Sylow
381	C₂³	—	2	1	no	—
382	C₂³	—	22	2	no	—
383	C₂³	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	88	1	no	—
387	D₄	—	2	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	22	2	no	—
390	D₄	—	22	2	no	—
391	D₄	—	44	2	no	—
392	D₄	—	88	1	no	—
393	D₄	—	88	2	no	—
394	D₄	#66954	1	2	yes	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	22	2	no	—
408	C₂×C₄	—	44	2	no	—
409	C₂×C₄	—	44	2	no	—
410	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
411	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
412	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
415	C₂×C₄	C₂×#4341	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	22	2	no	—
421	C₈	—	22	2	no	—
422	C₈	—	22	2	no	—
423	C₈	—	22	2	no	—
424	C₈	—	44	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	44	2	no	—
432	C₂²	—	44	2	no	—
433	C₂²	—	44	2	no	—
434	C₂²	C₂×(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	44	2	no	—
442	C₄	#10622437	1	2	yes	—
443	C₄	C₂×#66954	1	1	yes	characteristic
444	C₄	#10623276	1	1	yes	characteristic
445	C₄	#10623300	1	1	yes	characteristic
446	C₄	#10623301	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	88	2	no	—
450	C₂	#13077337	1	1	yes	characteristic
451	C₂	#13077451	1	1	yes	characteristic
452	C₂	C₂×#10622437	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1476	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	#13078676	C₂
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1476	D₁₁
hypocenter	C₁₁	#18015
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
2. #13077741	C₂	semidirect
3. #13077682	C₂	semidirect
4. #13067503	C₂	semidirect
5. #13067477	C₂	semidirect
6. #13067476	C₂	semidirect
7. #13067408	C₂	semidirect
8. #13067404	C₂	semidirect
9. #13067068	C₂	semidirect
10. #13066899	C₂	semidirect
11. C₁₁×#1476	C₂	semidirect
164. #1476	D₁₁	semidirect
380. C₁₁	#18015	semidirect

Maximal subgroups

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

subgroup	index
#13078676	2
#13077741	2
#13077682	2
#13067503	2
#13067477	2
#13067476	2
#13067408	2
#13067404	2
#13067068	2
#13066899	2
C₁₁×#1476	2
#18015	11