Subgroups — #14723556

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#67002	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622301	C₂	1	1	yes	maximal, characteristic, complemented
3	#13067528	C₂	1	2	yes	maximal, complemented
4	#13067516	C₂	1	2	yes	maximal, complemented
5	#13067506	C₂	1	2	yes	maximal, complemented
6	#13067499	C₂	1	2	yes	maximal, complemented
7	#13067369	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067006	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067003	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#4318	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂×#67002	C₄	1	1	yes	characteristic
14	C₂²×#4313	—	2	1	no	—
15	C₂×C₄×D₄₄	C₂²	1	1	yes	characteristic
16	C₁₁×#446	C₂²	1	1	yes	characteristic, complemented
17	C₁₁×#446	C₂²	1	1	yes	characteristic, complemented
18	C₁₁×#436	C₂²	1	1	yes	characteristic, complemented
19	C₁₁×#436	C₂²	1	1	yes	characteristic, complemented
20	C₁₁×#435	—	2	1	no	—
21	C₁₁×#435	—	2	1	no	—
22	C₁₁×#431	—	2	1	no	—
23	C₁₁×#431	C₂²	1	1	yes	characteristic
24	C₄×C₁₁×M₁₆	—	2	1	no	—
25	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	#10622845	C₄	1	1	yes	characteristic
27	C₂×(C₂×D₁₁)⋊C₈	—	2	1	no	—
28	#10622639	C₄	1	2	yes	—
29	C₄×#4325	C₂²	1	2	yes	—
30	#10622627	C₄	1	2	yes	—
31	C₄×#4323	C₂²	1	2	yes	—
32	#10622614	C₄	1	1	yes	characteristic
33	#10622608	C₄	1	1	yes	characteristic
34	#10622538	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
36	C₄×#4318	C₂²	1	1	yes	characteristic
37	#10622301	—	2	1	no	—
38	#10622301	—	2	1	no	—
39	#10622301	C₂²	1	2	yes	—
40	#10622301	C₂²	1	2	yes	—
41	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	complemented
42	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	complemented
43	#10622121	C₂²	1	2	yes	—
44	#10622121	C₂²	1	2	yes	—
45	#10622118	C₂²	1	2	yes	complemented
46	#10622117	C₂²	1	2	yes	complemented
47	#10622092	C₂²	1	2	yes	complemented
48	C₈×C₁₁⋊C₈	C₂²	1	2	yes	complemented
49	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₁₁	—	2	1	no	—
52	C₂×C₁₁×M₁₆	—	2	1	no	—
53	C₂×C₁₁×M₁₆	—	2	1	no	—
54	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
56	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₁	—	2	1	no	—
59	C₄×D₄×C₁₁	—	2	1	no	—
60	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
62	C₁₁×#117	—	2	1	no	—
63	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₁	—	2	1	no	—
65	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
66	#67002	—	2	4	no	—
67	C₂×#4325	C₂×C₄	1	2	yes	—
68	C₂×#4323	C₂×C₄	1	2	yes	—
69	C₂×(C₂×D₁₁)⋊C₄	—	2	1	no	—
70	C₂×C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
71	C₂×#4318	C₂×C₄	1	1	yes	characteristic
72	C₂×#4318	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₁₁⋊C₈	—	2	1	no	—
74	C₂×#4313	—	2	2	no	—
75	C₂×#4313	—	2	2	no	—
76	C₂×#4313	—	4	4	no	—
77	C₄×D₄₄	—	2	1	no	—
78	C₄×D₄₄	—	2	1	no	—
79	C₄×D₄₄	C₂×C₄	1	2	yes	—
80	C₄×D₄₄	C₂³	1	2	yes	—
81	C₁₁×C₄⋊C₈	—	2	1	no	—
82	C₁₁×C₄⋊C₈	—	2	1	no	—
83	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₁×C₂²⋊C₈	—	2	1	no	—
86	C₁₁×C₂²⋊C₈	—	2	1	no	—
87	C₁₁×C₂²⋊C₈	—	2	1	no	—
88	C₁₁×#97	—	2	1	no	—
89	C₁₁×#97	—	2	1	no	—
90	C₄×C₈×C₁₁	—	2	1	no	—
91	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
92	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
93	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
95	#66899	C₂×C₄	1	2	yes	—
96	#66896	C₂×C₄	1	2	yes	—
97	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
98	(C₂×D₁₁)⋊C₈	—	2	2	no	—
99	(C₂×D₁₁)⋊C₈	—	2	2	no	—
100	#66873	C₂×C₄	1	2	yes	—
101	#66873	C₂×C₄	1	2	yes	—
102	#66872	C₂×C₄	1	2	yes	—
103	#66871	C₂×C₄	1	2	yes	—
104	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
105	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
106	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
107	#66867	C₂×C₄	1	2	yes	—
108	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
109	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
110	#17891	—	11	1	no	maximal, Sylow
111	C₂³×D₁₁	—	2	1	no	—
112	C₁₁×#41	—	2	2	no	—
113	C₁₁×#41	—	2	2	no	—
114	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₁	—	2	1	no	—
116	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	—	2	1	no	—
118	C₂²×C₄×C₁₁	—	2	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
123	C₂²×Dic₁₁	—	2	1	no	—
124	C₂×D₄₄	—	2	1	no	—
125	C₂×D₄₄	—	2	2	no	—
126	C₂×D₄₄	—	2	2	no	—
127	C₂×D₄₄	C₂²×C₄	1	2	yes	—
128	C₂×C₄×D₁₁	—	2	2	no	—
129	C₂×C₄×D₁₁	—	2	2	no	—
130	C₂×C₄×D₁₁	—	4	2	no	—
131	C₂×C₄×D₁₁	—	4	2	no	—
132	C₁₁×M₁₆	—	4	2	no	—
133	C₁₁×M₁₆	—	4	2	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	—	2	1	no	—
137	C₂×C₈×C₁₁	—	4	1	no	—
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	C₁₁×C₄⋊C₄	—	2	1	no	—
143	C₁₁×C₄⋊C₄	—	2	1	no	—
144	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
145	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
146	C₁₁×C₂²⋊C₄	—	2	1	no	—
147	C₁₁×C₂²⋊C₄	—	2	1	no	—
148	C₁₁×C₂²⋊C₄	—	2	1	no	—
149	C₄²×C₁₁	—	2	1	no	—
150	C₄²×C₁₁	—	2	1	no	—
151	C₄²×C₁₁	—	2	1	no	—
152	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₁	#41	1	1	yes	characteristic
155	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
156	#4325	—	2	4	no	—
157	#4323	—	2	4	no	—
158	(C₂×D₁₁)⋊C₄	—	2	2	no	—
159	(C₂×D₁₁)⋊C₄	—	2	2	no	—
160	C₄⋊Dic₁₁	—	2	1	no	—
161	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
162	#4318	—	2	2	no	—
163	#4318	M₁₆	1	4	yes	complemented
164	C₂×C₁₁⋊C₈	—	2	2	no	—
165	C₂×C₁₁⋊C₈	—	2	2	no	—
166	C₂×C₁₁⋊C₈	—	4	2	no	—
167	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
169	#4313	—	4	4	no	—
170	#4313	—	4	4	no	—
171	#2965	D₁₁	1	1	yes	characteristic, complemented
172	C₄×AGL(1,ℤ/8)	—	11	1	no	—
173	C₂×#436	—	11	1	no	—
174	#1594	—	11	2	no	—
175	#1592	—	11	2	no	—
176	#1590	—	11	2	no	—
177	#1589	—	11	2	no	—
178	#1565	—	11	1	no	—
179	#1478	—	11	1	no	—
180	#1477	—	11	1	no	—
181	C₈×M₁₆	—	11	1	no	—
182	C₂³×C₁₁	—	2	1	no	—
183	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
184	C₂²×D₁₁	—	2	2	no	—
185	C₂²×D₁₁	—	4	2	no	—
186	C₂²×D₁₁	—	4	2	no	—
187	C₂²×D₁₁	—	4	2	no	—
188	Q₈×C₁₁	—	2	1	no	—
189	Q₈×C₁₁	—	2	1	no	—
190	D₄×C₁₁	—	2	1	no	—
191	D₄×C₁₁	—	2	1	no	—
192	D₄×C₁₁	—	4	2	no	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	1	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	4	1	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	—	4	1	no	—
201	C₂×C₄×C₁₁	—	4	1	no	—
202	C₂×C₄×C₁₁	—	4	2	no	—
203	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
207	C₂×C₄×C₁₁	#131	1	2	yes	—
208	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
211	C₂×Dic₁₁	—	2	2	no	—
212	C₂×Dic₁₁	—	4	2	no	—
213	D₄₄	—	2	2	no	—
214	D₄₄	—	2	2	no	—
215	D₄₄	—	4	2	no	—
216	C₄×D₁₁	—	4	4	no	—
217	C₄×D₁₁	—	4	2	no	—
218	C₄×D₁₁	—	4	2	no	—
219	C₈×C₁₁	—	2	1	no	—
220	C₈×C₁₁	—	2	1	no	—
221	C₈×C₁₁	—	2	1	no	—
222	C₈×C₁₁	—	4	1	no	—
223	C₈×C₁₁	—	4	1	no	—
224	C₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	complemented
225	C₁₁⋊C₈	—	2	2	no	—
226	C₁₁⋊C₈	—	4	2	no	—
227	C₁₁⋊C₈	—	4	2	no	—
228	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	complemented
229	C₂×AGL(1,ℤ/8)	—	11	1	no	—
230	C₂²×M₁₆	—	22	1	no	—
231	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
232	C₂×C₄×D₄	—	11	1	no	—
233	#446	C₂×D₁₁	1	1	yes	characteristic, complemented
234	#446	C₂×D₁₁	1	1	yes	characteristic, complemented
235	#442	—	11	2	no	—
236	#440	—	11	2	no	—
237	C₄×SD₁₆	—	11	2	no	—
238	C₄×D₈	—	11	2	no	—
239	#436	—	11	2	no	—
240	#436	—	11	2	no	—
241	#436	—	22	1	no	—
242	#436	—	22	1	no	—
243	#436	C₂×D₁₁	1	1	yes	characteristic, complemented
244	#436	C₂×D₁₁	1	1	yes	characteristic, complemented
245	#435	—	2	1	no	—
246	#435	—	2	1	no	—
247	#431	—	2	1	no	—
248	#431	—	11	1	no	—
249	#431	C₂×D₁₁	1	1	yes	characteristic
250	#428	—	11	1	no	—
251	C₂×C₄⋊C₈	—	11	1	no	—
252	#418	—	11	1	no	—
253	#417	—	11	1	no	—
254	C₂×C₂²⋊C₈	—	22	1	no	—
255	C₄×M₁₆	—	2	1	no	—
256	C₄×M₁₆	—	11	1	no	—
257	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
258	#335	—	11	2	no	—
259	#334	—	11	2	no	—
260	Q₈⋊C₈	—	11	2	no	—
261	D₄⋊C₈	—	11	2	no	—
262	D₄⋊C₈	—	11	2	no	—
263	D₄⋊C₈	—	11	2	no	—
264	#322	—	11	2	no	—
265	C₈²	—	11	2	no	—
266	C₂²×C₁₁	—	2	1	no	—
267	C₂²×C₁₁	—	2	1	no	—
268	C₂²×C₁₁	—	4	1	no	—
269	C₂²×C₁₁	—	4	1	no	—
270	C₂²×C₁₁	—	4	1	no	—
271	C₂²×C₁₁	#436	1	2	yes	—
272	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×D₁₁	—	4	2	no	—
274	C₂×D₁₁	—	4	2	no	—
275	C₂×D₁₁	—	4	2	no	—
276	C₂×D₁₁	—	8	4	no	—
277	C₄×C₁₁	—	2	1	no	—
278	C₄×C₁₁	—	2	1	no	—
279	C₄×C₁₁	—	2	1	no	—
280	C₄×C₁₁	—	4	1	no	—
281	C₄×C₁₁	—	4	1	no	—
282	C₄×C₁₁	—	4	1	no	—
283	C₄×C₁₁	#436	1	2	yes	—
284	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
285	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
286	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
287	C₄×C₁₁	#575	1	1	yes	characteristic
288	Dic₁₁	—	4	2	no	—
289	C₂×#41	C₄×D₁₁	1	1	yes	characteristic
290	C₂²×D₄	—	11	1	no	—
291	C₂³×C₄	—	22	1	no	—
292	AGL(1,ℤ/8)	—	22	4	no	—
293	C₂×SD₁₆	—	11	2	no	—
294	C₂×D₈	—	11	2	no	—
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	11	1	no	—
298	C₂×M₁₆	—	11	1	no	—
299	C₂×M₁₆	—	22	2	no	—
300	C₂×M₁₆	—	22	2	no	—
301	C₂×M₁₆	—	44	4	no	—
302	C₂²×C₈	—	22	1	no	—
303	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
304	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
305	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
306	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	11	2	no	—
310	C₄×D₄	—	11	2	no	—
311	C₄×D₄	—	22	1	no	—
312	C₄×D₄	—	22	1	no	—
313	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
314	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	C₄×D₁₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	—	11	1	no	—
318	C₂×C₂²⋊C₄	—	22	1	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
321	#107	—	11	2	no	—
322	#106	—	11	2	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	11	2	no	—
326	C₄⋊C₈	—	22	1	no	—
327	C₄⋊C₈	—	22	1	no	—
328	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
329	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
330	#103	—	11	2	no	—
331	#102	—	11	2	no	—
332	#102	—	11	2	no	—
333	#102	—	11	2	no	—
334	C₂²⋊C₈	—	2	1	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	2	1	no	—
337	C₂²⋊C₈	—	22	1	no	—
338	C₂²⋊C₈	—	22	2	no	—
339	C₂²⋊C₈	—	22	2	no	—
340	#97	—	2	1	no	—
341	#97	—	2	1	no	—
342	#97	—	11	2	no	—
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	11	2	no	—
345	C₄×C₈	—	11	2	no	—
346	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
347	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
348	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
349	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
350	C₂×C₁₁	—	2	2	no	—
351	C₂×C₁₁	—	8	1	no	—
352	C₂×C₁₁	C₂×#436	1	1	yes	characteristic
353	C₂×C₁₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
354	C₂×C₁₁	#2955	1	1	yes	characteristic
355	D₁₁	—	8	2	no	—
356	C₂⁴	—	22	1	no	—
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	C₂×Q₈	C₂×C₄×D₁₁	1	1	yes	characteristic
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	11	2	no	—
362	C₂×D₄	—	22	2	no	—
363	C₂×D₄	—	22	2	no	—
364	C₂×D₄	—	22	1	no	—
365	C₂×D₄	C₂×C₄×D₁₁	1	1	yes	characteristic
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	22	1	no	—
370	C₂²×C₄	—	22	2	no	—
371	C₂²×C₄	—	22	2	no	—
372	C₂²×C₄	—	44	2	no	—
373	C₂²×C₄	—	44	2	no	—
374	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
375	C₂²×C₄	#4339	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
377	SD₁₆	—	22	4	no	—
378	D₈	—	22	4	no	—
379	M₁₆	—	4	2	no	—
380	M₁₆	—	4	2	no	—
381	M₁₆	—	11	4	no	—
382	M₁₆	—	22	2	no	—
383	M₁₆	—	44	4	no	—
384	M₁₆	—	44	4	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	4	1	no	—
389	C₂×C₈	—	11	2	no	—
390	C₂×C₈	—	11	2	no	—
391	C₂×C₈	—	22	2	no	—
392	C₂×C₈	—	22	2	no	—
393	C₂×C₈	—	44	2	no	—
394	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
395	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
396	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
397	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	11	2	no	—
401	C₄⋊C₄	—	22	1	no	—
402	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
403	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	22	2	no	—
408	C₂²⋊C₄	—	22	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
413	C₄²	#4339	1	1	yes	characteristic
414	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
415	C₄²	C₂³×D₁₁	1	1	yes	characteristic
416	C₁₁	#17891	1	1	yes	characteristic, complemented, Sylow
417	C₂³	—	2	1	no	—
418	C₂³	—	22	2	no	—
419	C₂³	—	44	2	no	—
420	C₂³	—	44	2	no	—
421	C₂³	—	44	2	no	—
422	C₂³	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	2	1	no	—
427	D₄	—	4	2	no	—
428	D₄	—	22	2	no	—
429	D₄	—	22	2	no	—
430	D₄	—	44	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	22	2	no	—
442	C₂×C₄	—	44	4	no	—
443	C₂×C₄	—	44	2	no	—
444	C₂×C₄	—	44	2	no	—
445	C₂×C₄	—	44	2	no	—
446	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
447	C₂×C₄	#66960	1	2	yes	—
448	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
449	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
450	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#4339	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	11	4	no	—
460	C₈	—	22	2	no	—
461	C₈	—	44	2	no	—
462	C₈	—	44	2	no	—
463	C₈	#67002	1	2	yes	complemented
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	44	2	no	—
470	C₂²	—	44	2	no	—
471	C₂²	—	44	2	no	—
472	C₂²	—	88	4	no	—
473	C₂²	#10622741	1	2	yes	—
474	C₂²	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	44	2	no	—
482	C₄	#10622741	1	2	yes	—
483	C₄	C₂×M₁₆×D₁₁	1	1	yes	characteristic
484	C₄	C₂×#66960	1	1	yes	characteristic
485	C₄	C₂×#67002	1	1	yes	characteristic
486	C₄	#10623353	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	8	1	no	—
489	C₂	—	88	2	no	—
490	C₂	C₂×#10622741	1	1	yes	characteristic
491	C₂	C₄×#67002	1	1	yes	characteristic
492	C₂	#13077517	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#2965	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×#67002	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2965	D₁₁
hypocenter	C₁₁	#17891
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2965

Complements

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

N	H ≅ G/N	type
2. C₂×#10622301	C₂	semidirect
3. #13067528	C₂	semidirect
4. #13067516	C₂	semidirect
5. #13067506	C₂	semidirect
6. #13067499	C₂	semidirect
7. #13067369	C₂	semidirect
8. #13067006	C₂	semidirect
9. #13067003	C₂	semidirect
10. C₈×#4318	C₂	semidirect
11. C₁₁×#2965	C₂	semidirect
16. C₁₁×#446	C₂²	semidirect
17. C₁₁×#446	C₂²	semidirect
18. C₁₁×#436	C₂²	semidirect
19. C₁₁×#436	C₂²	semidirect
41. Q₈⋊(C₁₁⋊C₈)	C₂²	semidirect
42. D₄⋊(C₁₁⋊C₈)	C₂²	semidirect
45. #10622118	C₂²	semidirect
46. #10622117	C₂²	semidirect
47. #10622092	C₂²	semidirect
48. C₈×C₁₁⋊C₈	C₂²	semidirect
163. #4318	M₁₆	semidirect
171. #2965	D₁₁	semidirect
224. C₈×C₁₁	AGL(1,ℤ/8)	semidirect
228. C₁₁⋊C₈	C₂×M₁₆	semidirect
233. #446	C₂×D₁₁	semidirect
234. #446	C₂×D₁₁	semidirect
243. #436	C₂×D₁₁	semidirect
244. #436	C₂×D₁₁	semidirect
416. C₁₁	#17891	semidirect
463. C₈	#67002	semidirect

Maximal subgroups

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

subgroup	index
C₄×#67002	2
C₂×#10622301	2
#13067528	2
#13067516	2
#13067506	2
#13067499	2
#13067369	2
#13067006	2
#13067003	2
C₈×#4318	2
C₁₁×#2965	2
#17891	11