Subgroups — #14761616

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13078406	C₂	1	1	yes	maximal, characteristic
2	#13077550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#66954	C₂	1	1	yes	maximal, characteristic
4	#13069559	C₂	1	1	yes	maximal, characteristic, complemented
5	#13069392	C₂	1	1	yes	maximal, characteristic, complemented
6	#13069216	C₂	1	2	yes	maximal, complemented
7	#13068894	C₂	1	2	yes	maximal
8	#13068637	C₂	1	1	yes	maximal, characteristic
9	#13068500	C₂	1	2	yes	maximal, complemented
10	#13068460	C₂	1	2	yes	maximal
11	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#66954	C₂²	1	1	yes	characteristic
13	C₂×#66954	C₂²	1	1	yes	characteristic
14	C₄×#4339	C₂²	1	1	yes	characteristic
15	#10623001	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#97	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	#10622726	C₂²	1	2	yes	—
21	C₂×#66883	C₂²	1	2	yes	—
22	#10622719	C₂²	1	2	yes	—
23	#10622715	C₂²	1	2	yes	—
24	#10622714	C₂²	1	1	yes	characteristic
25	#10622714	C₂²	1	1	yes	characteristic
26	#10622714	C₂²	1	2	yes	—
27	C₂×#66869	C₂²	1	2	yes	—
28	#10622537	C₂²	1	1	yes	characteristic
29	C₄×#4318	C₂²	1	1	yes	characteristic
30	#10622464	C₄	1	1	yes	characteristic, complemented
31	#10622463	C₄	1	1	yes	characteristic, complemented
32	#10622460	C₄	1	2	yes	complemented
33	#10622459	C₄	1	1	yes	characteristic, complemented
34	#10622455	C₄	1	1	yes	characteristic, complemented
35	#10622442	C₄	1	2	yes	complemented
36	#10622302	—	2	1	no	—
37	#10622302	—	2	1	no	—
38	C₄×#4313	—	2	1	no	—
39	C₄×C₈×D₁₁	—	2	1	no	—
40	#10622292	—	2	1	no	—
41	#10622292	—	2	1	no	—
42	C₈×Dic₂₂	—	2	1	no	—
43	C₈×Dic₂₂	—	2	1	no	—
44	C₁₁×#336	C₂²	1	2	yes	—
45	#10622190	C₂²	1	2	yes	—
46	#10622161	C₂²	1	2	yes	—
47	#10622161	C₂²	1	2	yes	—
48	#10622161	C₂²	1	2	yes	—
49	C₂×#4339	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
54	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₁	—	2	1	no	—
57	C₄×C₂²⋊D₁₁	—	2	1	no	—
58	#66979	C₂³	1	2	yes	—
59	#66979	C₂³	1	1	yes	characteristic
60	#66977	—	2	1	no	—
61	#66977	—	2	1	no	—
62	C₂×#4318	C₂³	1	2	yes	—
63	C₂×#4318	C₂³	1	1	yes	characteristic
64	C₂×#4318	C₂³	1	1	yes	characteristic
65	#66954	—	2	2	no	—
66	#66954	—	2	2	no	—
67	#66954	—	2	2	no	—
68	#66954	Q₈	1	4	yes	complemented
69	C₂×#4313	—	2	1	no	—
70	C₂×#4313	—	2	1	no	—
71	C₂×C₈×D₁₁	—	2	1	no	—
72	C₂×C₈×D₁₁	—	2	1	no	—
73	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
75	#66925	—	2	1	no	—
76	C₄²×D₁₁	—	2	1	no	—
77	#66923	C₂×C₄	1	2	yes	—
78	#66922	C₂×C₄	1	1	yes	characteristic
79	#66922	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₂₂	—	2	1	no	—
81	C₄×Dic₂₂	—	2	1	no	—
82	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
84	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
86	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₁₁×#97	—	2	4	no	—
88	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
92	C₁₁×#95	—	2	1	no	—
93	#66885	C₂×C₄	1	2	yes	—
94	#66885	C₂×C₄	1	2	yes	—
95	#66883	—	2	4	no	—
96	#66882	C₂×C₄	1	2	yes	—
97	#66882	C₂×C₄	1	2	yes	—
98	#66881	C₂×C₄	1	2	yes	—
99	#66881	C₂×C₄	1	2	yes	—
100	#66880	C₂×C₄	1	2	yes	—
101	#66880	C₂×C₄	1	2	yes	—
102	#66879	—	2	2	no	—
103	#66879	—	2	1	no	—
104	#66879	—	2	1	no	—
105	Dic₁₁⋊C₈	—	2	2	no	—
106	Dic₁₁⋊C₈	—	2	2	no	—
107	C₈×Dic₁₁	—	2	2	no	—
108	C₈×Dic₁₁	—	2	1	no	—
109	C₈×Dic₁₁	—	2	1	no	—
110	#66869	—	2	4	no	—
111	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
112	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
113	#66867	—	2	1	no	—
114	C₄×C₁₁⋊C₈	—	2	1	no	—
115	#21628	—	11	1	no	maximal, Sylow
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
120	C₂×C₂²⋊D₁₁	—	2	1	no	—
121	#4339	—	2	1	no	—
122	#4339	—	2	1	no	—
123	#4339	C₂×Q₈	1	2	yes	—
124	#4339	#41	1	2	yes	—
125	C₂×D₄₄	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₁	—	2	1	no	—
127	C₂×C₄×D₁₁	—	2	1	no	—
128	C₂×C₄×D₁₁	—	2	1	no	—
129	C₂×Dic₂₂	—	2	1	no	—
130	C₂×Dic₂₂	—	2	1	no	—
131	C₂×Dic₂₂	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	—	2	2	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
143	C₂×C₈×C₁₁	#41	1	2	yes	—
144	C₁₁×C₄⋊C₄	—	4	2	no	—
145	C₄²×C₁₁	—	2	2	no	—
146	C₄²×C₁₁	—	2	2	no	—
147	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
151	C₂²⋊Dic₁₁	—	2	2	no	—
152	C₂²⋊Dic₁₁	—	2	1	no	—
153	(C₂×D₁₁)⋊C₄	—	2	1	no	—
154	(C₂×D₁₁)⋊C₄	—	2	1	no	—
155	C₄⋊Dic₁₁	—	2	1	no	—
156	C₄⋊Dic₁₁	—	2	1	no	—
157	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
158	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
159	C₄⋊Dic₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊Dic₁₁	C₂²×C₄	1	1	yes	characteristic
161	Dic₁₁⋊C₄	—	2	2	no	—
162	Dic₁₁⋊C₄	—	2	2	no	—
163	Dic₁₁⋊C₄	—	2	1	no	—
164	Dic₁₁⋊C₄	—	2	1	no	—
165	C₄×Dic₁₁	—	2	1	no	—
166	C₄×Dic₁₁	—	2	1	no	—
167	C₄×Dic₁₁	—	2	1	no	—
168	C₄×Dic₁₁	—	2	2	no	—
169	#4318	—	2	1	no	—
170	#4318	—	2	1	no	—
171	#4318	—	2	2	no	—
172	#4318	—	2	2	no	—
173	#4318	C₂×Q₈	1	2	yes	—
174	#4318	#41	1	2	yes	—
175	C₂×C₁₁⋊C₈	—	2	1	no	—
176	C₂×C₁₁⋊C₈	—	2	1	no	—
177	C₂×C₁₁⋊C₈	—	2	2	no	—
178	#4313	—	2	4	no	—
179	#4313	—	2	4	no	—
180	C₈×D₁₁	—	2	4	no	—
181	C₈×D₁₁	—	2	4	no	—
182	#3076	—	11	1	no	—
183	#2960	—	11	1	no	—
184	C₄×#131	—	11	1	no	—
185	#1986	—	11	1	no	—
186	#1950	—	11	1	no	—
187	#1922	—	11	2	no	—
188	#1866	—	11	2	no	—
189	#1806	—	11	1	no	—
190	#1773	—	11	2	no	—
191	#1770	D₁₁	1	1	yes	characteristic, complemented
192	#1765	—	11	2	no	—
193	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
194	C₂²×D₁₁	—	2	1	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	4	1	no	—
197	C₂×C₄×C₁₁	—	4	2	no	—
198	C₂×C₄×C₁₁	—	4	2	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
210	C₂²⋊D₁₁	—	2	2	no	—
211	C₂²⋊D₁₁	—	2	2	no	—
212	C₂×Dic₁₁	—	2	1	no	—
213	C₂×Dic₁₁	—	2	1	no	—
214	C₂×Dic₁₁	—	2	1	no	—
215	C₂×Dic₁₁	—	2	2	no	—
216	C₂×Dic₁₁	—	2	2	no	—
217	D₄₄	—	2	1	no	—
218	D₄₄	C₄×Q₈	1	2	yes	—
219	C₄×D₁₁	—	2	2	no	—
220	C₄×D₁₁	—	2	2	no	—
221	C₄×D₁₁	—	4	2	no	—
222	C₄×D₁₁	—	4	2	no	—
223	Dic₂₂	—	2	1	no	—
224	Dic₂₂	—	4	2	no	—
225	Dic₂₂	—	4	2	no	—
226	Dic₂₂	C₄×Q₈	1	2	yes	—
227	C₈×C₁₁	—	2	2	no	—
228	C₈×C₁₁	—	2	2	no	—
229	C₈×C₁₁	—	2	1	no	—
230	C₈×C₁₁	—	2	1	no	—
231	C₈×C₁₁	C₂²⋊Q₈	1	2	yes	—
232	C₈×C₁₁	C₂²⋊Q₈	1	2	yes	—
233	C₁₁⋊C₈	—	2	2	no	—
234	C₁₁⋊C₈	—	2	2	no	—
235	C₁₁⋊C₈	—	4	2	no	—
236	C₂×#131	—	11	1	no	—
237	C₂×#131	—	11	1	no	—
238	#533	—	11	1	no	—
239	C₄×#41	—	11	1	no	—
240	#479	—	11	2	no	—
241	#478	—	11	2	no	—
242	#477	—	11	1	no	—
243	#476	—	11	1	no	—
244	#475	—	11	1	no	—
245	#474	—	11	1	no	—
246	#446	—	22	1	no	—
247	#446	—	22	1	no	—
248	C₈×Q₈	—	22	1	no	—
249	C₈×Q₈	—	22	1	no	—
250	C₂×#108	—	11	2	no	—
251	#427	—	11	2	no	—
252	#424	—	11	2	no	—
253	#423	—	11	1	no	—
254	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
255	C₂×#104	—	11	2	no	—
256	#416	—	11	2	no	—
257	#405	—	11	1	no	—
258	#405	—	11	1	no	—
259	#405	—	11	2	no	—
260	#405	—	22	1	no	—
261	#405	—	22	1	no	—
262	C₄×M₁₆	—	11	1	no	—
263	C₄×M₁₆	—	22	1	no	—
264	C₂×#97	C₂×D₁₁	1	2	yes	—
265	C₂×C₄×C₈	—	22	1	no	—
266	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
268	#341	—	11	2	no	—
269	#339	—	11	2	no	—
270	#339	—	11	2	no	—
271	#339	—	11	2	no	—
272	#336	C₂×D₁₁	1	2	yes	—
273	C₂²×C₁₁	—	2	1	no	—
274	C₂²×C₁₁	—	2	1	no	—
275	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂²×C₁₁	#529	1	1	yes	characteristic
277	C₂²×C₁₁	#533	1	1	yes	characteristic
278	C₂×D₁₁	—	2	2	no	—
279	C₂×D₁₁	—	4	1	no	—
280	C₂×D₁₁	—	4	1	no	—
281	C₄×C₁₁	—	2	1	no	—
282	C₄×C₁₁	—	2	1	no	—
283	C₄×C₁₁	—	2	1	no	—
284	C₄×C₁₁	—	8	2	no	—
285	C₄×C₁₁	#444	1	2	yes	—
286	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
287	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
288	C₄×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
289	C₄×C₁₁	#525	1	1	yes	characteristic
290	Dic₁₁	—	2	2	no	—
291	Dic₁₁	—	4	2	no	—
292	Dic₁₁	—	4	1	no	—
293	Dic₁₁	—	4	2	no	—
294	Dic₁₁	—	4	1	no	—
295	C₂×#41	—	11	1	no	—
296	#131	—	11	4	no	—
297	#131	—	22	2	no	—
298	#131	—	22	2	no	—
299	#131	—	22	2	no	—
300	C₂×M₁₆	—	11	1	no	—
301	C₂×M₁₆	—	11	1	no	—
302	C₂×M₁₆	—	11	2	no	—
303	C₂×M₁₆	—	22	1	no	—
304	C₂×M₁₆	—	22	1	no	—
305	C₂²×C₈	—	22	1	no	—
306	C₂²×C₈	—	22	1	no	—
307	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
308	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
310	C₄⋊Q₈	—	11	1	no	—
311	C₄⋊Q₈	—	11	1	no	—
312	#125	—	11	2	no	—
313	C₂²⋊Q₈	—	22	1	no	—
314	C₂²⋊Q₈	—	22	1	no	—
315	C₄×Q₈	—	11	1	no	—
316	C₄×Q₈	—	11	1	no	—
317	C₄×Q₈	—	22	1	no	—
318	C₄×Q₈	—	22	1	no	—
319	C₄×D₄	—	11	1	no	—
320	C₄×D₄	—	11	1	no	—
321	C₄×D₄	—	22	1	no	—
322	C₄×D₄	—	22	1	no	—
323	#117	—	11	1	no	—
324	#117	—	11	2	no	—
325	#117	—	22	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄²	—	22	1	no	—
328	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
329	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
330	#108	—	22	4	no	—
331	#107	—	11	2	no	—
332	#107	—	11	2	no	—
333	#106	—	11	2	no	—
334	#106	—	11	2	no	—
335	C₄⋊C₈	—	22	2	no	—
336	C₄⋊C₈	—	22	2	no	—
337	C₄⋊C₈	—	22	1	no	—
338	C₄⋊C₈	—	22	1	no	—
339	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
340	C₄⋊C₈	C₄×D₁₁	1	1	yes	characteristic
341	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
342	#104	—	22	4	no	—
343	#103	—	11	2	no	—
344	#103	—	11	2	no	—
345	#102	—	11	2	no	—
346	#102	—	11	2	no	—
347	#97	—	2	4	no	—
348	#97	—	22	1	no	—
349	#97	—	22	1	no	—
350	#97	—	22	2	no	—
351	#97	—	22	1	no	—
352	C₄×C₈	—	22	1	no	—
353	C₄×C₈	—	22	1	no	—
354	C₄×C₈	—	22	2	no	—
355	C₄×C₈	—	22	1	no	—
356	C₄×C₈	D₄₄	1	1	yes	characteristic
357	C₄×C₈	D₄₄	1	1	yes	characteristic
358	C₄×C₈	D₄₄	1	1	yes	characteristic
359	C₄×C₈	D₄₄	1	1	yes	characteristic
360	#95	—	2	1	no	—
361	C₂×C₁₁	—	2	1	no	—
362	C₂×C₁₁	—	2	1	no	—
363	C₂×C₁₁	C₄×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
365	C₂×C₁₁	#2955	1	1	yes	characteristic
366	D₁₁	—	4	2	no	—
367	#41	—	11	2	no	—
368	#41	—	11	2	no	—
369	#41	—	22	1	no	—
370	#41	—	22	1	no	—
371	C₂×Q₈	—	11	1	no	—
372	C₂×Q₈	—	22	1	no	—
373	C₂×Q₈	—	22	1	no	—
374	C₂×D₄	—	11	1	no	—
375	C₂×D₄	—	22	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	22	1	no	—
378	C₂²×C₄	—	22	1	no	—
379	C₂²×C₄	—	22	1	no	—
380	C₂²×C₄	#4339	1	1	yes	characteristic
381	C₂²×C₄	#4339	1	1	yes	characteristic
382	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
383	M₁₆	—	11	2	no	—
384	M₁₆	—	11	2	no	—
385	M₁₆	—	22	4	no	—
386	M₁₆	—	22	1	no	—
387	M₁₆	—	22	1	no	—
388	M₁₆	—	22	4	no	—
389	M₁₆	—	22	2	no	—
390	M₁₆	—	22	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	22	4	no	—
396	C₂×C₈	—	22	1	no	—
397	C₂×C₈	—	22	1	no	—
398	C₂×C₈	—	22	4	no	—
399	C₂×C₈	—	22	2	no	—
400	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
401	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
402	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
403	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
404	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
405	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
406	C₂×C₈	#4341	1	2	yes	—
407	C₂×C₈	Q₈×D₁₁	1	2	yes	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	11	2	no	—
410	C₄⋊C₄	—	11	2	no	—
411	C₄⋊C₄	—	11	1	no	—
412	C₄⋊C₄	—	11	1	no	—
413	C₄⋊C₄	—	22	1	no	—
414	C₄⋊C₄	—	22	1	no	—
415	C₄⋊C₄	—	22	2	no	—
416	C₄⋊C₄	—	22	2	no	—
417	C₄⋊C₄	—	22	1	no	—
418	C₄⋊C₄	—	22	1	no	—
419	C₂²⋊C₄	—	22	1	no	—
420	C₂²⋊C₄	—	22	2	no	—
421	C₂²⋊C₄	—	22	1	no	—
422	C₂²⋊C₄	—	22	1	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	22	1	no	—
426	C₄²	—	22	1	no	—
427	C₄²	—	22	1	no	—
428	C₄²	—	22	2	no	—
429	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
431	C₄²	C₂×D₄₄	1	1	yes	characteristic
432	C₄²	C₂×D₄₄	1	1	yes	characteristic
433	C₁₁	#21628	1	1	yes	characteristic, complemented, Sylow
434	C₂³	—	22	1	no	—
435	C₂³	C₂×#4339	1	1	yes	characteristic
436	Q₈	—	11	2	no	—
437	Q₈	—	22	1	no	—
438	Q₈	—	44	2	no	—
439	Q₈	—	44	2	no	—
440	D₄	—	11	2	no	—
441	D₄	—	22	2	no	—
442	D₄	—	22	2	no	—
443	D₄	—	22	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	22	1	no	—
450	C₂×C₄	—	22	2	no	—
451	C₂×C₄	—	22	2	no	—
452	C₂×C₄	—	22	1	no	—
453	C₂×C₄	—	22	1	no	—
454	C₂×C₄	—	22	2	no	—
455	C₂×C₄	—	22	2	no	—
456	C₂×C₄	—	44	2	no	—
457	C₂×C₄	—	44	2	no	—
458	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
459	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
460	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
461	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
464	C₂×C₄	C₂×#4341	1	1	yes	characteristic
465	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
466	C₂×C₄	#41×D₁₁	1	1	yes	characteristic
467	C₂×C₄	#41×D₁₁	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	2	no	—
471	C₈	—	2	2	no	—
472	C₈	—	22	2	no	—
473	C₈	—	22	2	no	—
474	C₈	—	44	2	no	—
475	C₈	#66950	1	2	yes	—
476	C₈	#66950	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	22	2	no	—
480	C₂²	—	44	1	no	—
481	C₂²	—	44	1	no	—
482	C₂²	C₂×C₄×D₄₄	1	1	yes	characteristic
483	C₂²	#10623088	1	1	yes	characteristic
484	C₂²	#10623109	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	8	2	no	—
489	C₄	—	22	2	no	—
490	C₄	—	44	1	no	—
491	C₄	—	44	2	no	—
492	C₄	—	44	1	no	—
493	C₄	—	44	2	no	—
494	C₄	#10622330	1	2	yes	—
495	C₄	C₂×#66950	1	1	yes	characteristic
496	C₄	#10623055	1	1	yes	characteristic
497	C₄	C₄×#4341	1	1	yes	characteristic
498	C₄	C₄×Q₈×D₁₁	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	44	2	no	—
502	C₂	C₄×#66950	1	1	yes	characteristic
503	C₂	C₂×#10622330	1	1	yes	characteristic
504	C₂	#13077520	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₁₁×#1770	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×#4339	C₂³
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	#1770	D₁₁
hypocenter	C₁₁	#21628
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1770

Complements

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

N	H ≅ G/N	type
2. #13077550	C₂	semidirect
4. #13069559	C₂	semidirect
5. #13069392	C₂	semidirect
6. #13069216	C₂	semidirect
9. #13068500	C₂	semidirect
11. C₁₁×#1770	C₂	semidirect
30. #10622464	C₄	semidirect
31. #10622463	C₄	semidirect
32. #10622460	C₄	semidirect
33. #10622459	C₄	semidirect
34. #10622455	C₄	semidirect
35. #10622442	C₄	semidirect
68. #66954	Q₈	semidirect
191. #1770	D₁₁	semidirect
433. C₁₁	#21628	semidirect

Maximal subgroups

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

subgroup	index
#13078406	2
#13077550	2
C₄×#66954	2
#13069559	2
#13069392	2
#13069216	2
#13068894	2
#13068637	2
#13068500	2
#13068460	2
C₁₁×#1770	2
#21628	11