Subgroups — C₁₁×#24267 #14601460

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#466	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2408	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2054	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1999	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1970	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1786	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
11	C₂²×C₁₁×D₈	—	2	8	no	—
12	C₂²×C₁₁×D₈	—	2	4	no	—
13	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
14	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₁×#121	C₂²	1	4	yes	complemented
18	C₂×C₁₁×#120	—	2	2	no	—
19	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#466	—	2	8	no	—
21	C₈×D₄×C₁₁	—	2	4	no	—
22	C₂×C₁₁×#107	C₂²	1	2	yes	complemented
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₁×#102	C₂²	1	4	yes	complemented
25	C₂×C₁₁×#102	C₂²	1	4	yes	complemented
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
29	C₁₁×#394	—	2	2	no	—
30	C₁₁×#392	—	2	2	no	—
31	C₁₁×#390	C₂²	1	4	yes	complemented
32	C₁₁×#380	C₂²	1	2	yes	—
33	C₁₁×#379	—	2	2	no	—
34	C₁₁×#340	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₁	—	2	2	no	—
36	C₂²×D₄×C₁₁	—	2	8	no	—
37	C₂²×D₄×C₁₁	—	2	4	no	—
38	C₂²×D₄×C₁₁	—	2	4	no	—
39	C₂²×D₄×C₁₁	—	2	2	no	—
40	C₂²×D₄×C₁₁	—	2	4	no	—
41	C₂²×D₄×C₁₁	—	4	4	no	—
42	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×C₁₁×D₈	—	2	32	no	—
47	C₂×C₁₁×D₈	—	2	8	no	—
48	C₂×C₁₁×D₈	—	2	4	no	—
49	C₂×C₁₁×D₈	—	2	4	no	—
50	C₂×C₁₁×D₈	—	2	4	no	—
51	C₂×C₁₁×D₈	D₄	1	8	yes	complemented
52	C₂²×C₈×C₁₁	—	2	4	no	—
53	C₂²×C₈×C₁₁	—	2	2	no	—
54	C₂²×C₈×C₁₁	—	2	4	no	—
55	C₂²×C₈×C₁₁	D₄	1	4	yes	complemented
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₁₁×#121	—	2	8	no	—
61	C₁₁×#121	—	4	4	no	—
62	C₁₁×#120	—	4	8	no	—
63	C₄×D₄×C₁₁	—	2	2	no	—
64	C₄×D₄×C₁₁	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
70	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₁₁×C₂²⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₁×C₂²⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×#107	—	2	4	no	—
75	C₁₁×C₄⋊C₈	—	2	2	no	—
76	C₁₁×#102	—	2	8	no	—
77	C₁₁×#102	—	4	4	no	—
78	C₁₁×C₂²⋊C₈	—	2	2	no	—
79	C₁₁×C₂²⋊C₈	—	2	2	no	—
80	C₄×C₈×C₁₁	—	2	2	no	—
81	C₁₁×#95	—	2	2	no	—
82	#24267	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₁	—	2	4	no	—
84	C₂⁴×C₁₁	—	4	8	no	—
85	C₂⁴×C₁₁	—	4	4	no	—
86	C₂⁴×C₁₁	—	4	4	no	—
87	C₂⁴×C₁₁	—	4	4	no	—
88	C₂⁴×C₁₁	—	8	4	no	—
89	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
90	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×C₁₁	—	2	2	no	—
92	C₂×D₄×C₁₁	—	2	2	no	—
93	C₂×D₄×C₁₁	—	2	16	no	—
94	C₂×D₄×C₁₁	—	2	4	no	—
95	C₂×D₄×C₁₁	—	2	4	no	—
96	C₂×D₄×C₁₁	—	2	4	no	—
97	C₂×D₄×C₁₁	—	2	4	no	—
98	C₂×D₄×C₁₁	—	2	4	no	—
99	C₂×D₄×C₁₁	—	4	16	no	—
100	C₂×D₄×C₁₁	—	4	8	no	—
101	C₂×D₄×C₁₁	—	4	8	no	—
102	C₂×D₄×C₁₁	—	4	8	no	—
103	C₂×D₄×C₁₁	—	4	8	no	—
104	C₂×D₄×C₁₁	—	4	4	no	—
105	C₂×D₄×C₁₁	—	8	4	no	—
106	C₂×D₄×C₁₁	D₈	1	4	yes	complemented
107	C₂×D₄×C₁₁	C₂×D₄	1	8	yes	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	—	2	1	no	—
113	C₂²×C₄×C₁₁	—	2	2	no	—
114	C₂²×C₄×C₁₁	—	2	4	no	—
115	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	#41	1	2	yes	—
121	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
122	C₁₁×D₈	—	2	16	no	—
123	C₁₁×D₈	—	2	16	no	—
124	C₂×C₈×C₁₁	—	2	8	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	2	2	no	—
129	C₂×C₈×C₁₁	—	2	2	no	—
130	C₂×C₈×C₁₁	—	4	4	no	—
131	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
134	C₁₁×C₄⋊C₄	—	2	2	no	—
135	C₁₁×C₄⋊C₄	—	2	4	no	—
136	C₁₁×C₄⋊C₄	—	2	4	no	—
137	C₁₁×C₂²⋊C₄	—	2	2	no	—
138	C₁₁×C₂²⋊C₄	—	2	2	no	—
139	C₁₁×C₂²⋊C₄	—	4	8	no	—
140	C₁₁×C₂²⋊C₄	—	4	4	no	—
141	C₁₁×C₂²⋊C₄	—	4	8	no	—
142	C₁₁×C₂²⋊C₄	—	8	4	no	—
143	C₄²×C₁₁	—	2	1	no	—
144	C₄²×C₁₁	—	2	1	no	—
145	C₂³×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
146	C₂×#466	C₂×C₁₁	1	2	yes	complemented
147	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
148	#2408	C₂×C₁₁	1	2	yes	complemented
149	#2054	C₂×C₁₁	1	2	yes	complemented
150	#1999	C₂×C₁₁	1	2	yes	complemented
151	#1970	C₂×C₁₁	1	2	yes	complemented
152	#1808	C₂×C₁₁	1	1	yes	characteristic, complemented
153	#1786	C₂×C₁₁	1	2	yes	complemented
154	C₂³×C₁₁	—	2	2	no	—
155	C₂³×C₁₁	—	2	2	no	—
156	C₂³×C₁₁	—	2	1	no	—
157	C₂³×C₁₁	—	2	2	no	—
158	C₂³×C₁₁	—	2	1	no	—
159	C₂³×C₁₁	—	2	2	no	—
160	C₂³×C₁₁	—	2	8	no	—
161	C₂³×C₁₁	—	4	16	no	—
162	C₂³×C₁₁	—	4	4	no	—
163	C₂³×C₁₁	—	4	4	no	—
164	C₂³×C₁₁	—	4	4	no	—
165	C₂³×C₁₁	—	4	4	no	—
166	C₂³×C₁₁	—	4	4	no	—
167	C₂³×C₁₁	—	4	4	no	—
168	C₂³×C₁₁	—	8	16	no	—
169	C₂³×C₁₁	—	8	16	no	—
170	C₂³×C₁₁	—	8	8	no	—
171	C₂³×C₁₁	—	8	8	no	—
172	C₂³×C₁₁	#121	1	2	yes	—
173	C₂³×C₁₁	C₂×D₈	1	2	yes	—
174	C₂³×C₁₁	C₂×D₈	1	2	yes	complemented
175	C₂³×C₁₁	#135	1	2	yes	—
176	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	D₄×C₁₁	—	2	8	no	—
178	D₄×C₁₁	—	2	8	no	—
179	D₄×C₁₁	—	2	8	no	—
180	D₄×C₁₁	—	4	16	no	—
181	D₄×C₁₁	—	4	4	no	—
182	D₄×C₁₁	—	4	4	no	—
183	D₄×C₁₁	—	8	16	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	2	no	—
189	C₂×C₄×C₁₁	—	2	4	no	—
190	C₂×C₄×C₁₁	—	2	1	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	2	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	4	1	no	—
195	C₂×C₄×C₁₁	—	4	1	no	—
196	C₂×C₄×C₁₁	—	4	2	no	—
197	C₂×C₄×C₁₁	—	4	4	no	—
198	C₂×C₄×C₁₁	—	4	4	no	—
199	C₂×C₄×C₁₁	—	4	4	no	—
200	C₂×C₄×C₁₁	#121	1	2	yes	—
201	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	complemented
202	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
206	C₈×C₁₁	—	2	2	no	—
207	C₈×C₁₁	—	4	1	no	—
208	C₈×C₁₁	—	4	1	no	—
209	C₈×C₁₁	#120	1	4	yes	complemented
210	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
211	C₂²×D₈	—	2	8	no	—
212	C₂²×D₈	—	2	4	no	—
213	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
214	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
215	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
216	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
217	C₂×#121	C₂²×C₁₁	1	4	yes	complemented
218	C₂×#120	—	2	2	no	—
219	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
220	#466	—	2	8	no	—
221	C₈×D₄	—	2	4	no	—
222	C₂×#107	C₂²×C₁₁	1	2	yes	complemented
223	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
224	C₂×#102	C₂²×C₁₁	1	4	yes	complemented
225	C₂×#102	C₂²×C₁₁	1	4	yes	complemented
226	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
228	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
229	#394	—	2	2	no	—
230	#392	—	2	2	no	—
231	#390	C₂²×C₁₁	1	4	yes	complemented
232	#380	C₂²×C₁₁	1	2	yes	—
233	#379	—	2	2	no	—
234	#340	C₂²×C₁₁	1	2	yes	complemented
235	C₂²×C₁₁	—	2	2	no	—
236	C₂²×C₁₁	—	2	4	no	—
237	C₂²×C₁₁	—	2	4	no	—
238	C₂²×C₁₁	—	2	2	no	—
239	C₂²×C₁₁	—	2	4	no	—
240	C₂²×C₁₁	—	2	2	no	—
241	C₂²×C₁₁	—	4	1	no	—
242	C₂²×C₁₁	—	4	2	no	—
243	C₂²×C₁₁	—	4	1	no	—
244	C₂²×C₁₁	—	4	8	no	—
245	C₂²×C₁₁	—	4	8	no	—
246	C₂²×C₁₁	—	4	8	no	—
247	C₂²×C₁₁	—	8	32	no	—
248	C₂²×C₁₁	—	8	4	no	—
249	C₂²×C₁₁	—	8	4	no	—
250	C₂²×C₁₁	—	8	4	no	—
251	C₂²×C₁₁	—	8	4	no	—
252	C₂²×C₁₁	#466	1	4	yes	complemented
253	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
254	C₂²×C₁₁	D₄²	1	2	yes	—
255	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
256	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
257	C₂²×C₁₁	#576	1	2	yes	—
258	C₄×C₁₁	—	2	2	no	—
259	C₄×C₁₁	—	2	2	no	—
260	C₄×C₁₁	—	4	1	no	—
261	C₄×C₁₁	—	4	1	no	—
262	C₄×C₁₁	—	8	4	no	—
263	C₄×C₁₁	C₂×#120	1	1	yes	characteristic
264	C₄×C₁₁	#535	1	1	yes	characteristic
265	C₄×C₁₁	#546	1	2	yes	—
266	C₂⁵	—	2	2	no	—
267	C₂²×D₄	—	2	8	no	—
268	C₂²×D₄	—	2	4	no	—
269	C₂²×D₄	—	2	4	no	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	—	2	4	no	—
272	C₂²×D₄	—	4	4	no	—
273	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
274	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
275	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
277	C₂×D₈	—	2	32	no	—
278	C₂×D₈	—	2	8	no	—
279	C₂×D₈	—	2	4	no	—
280	C₂×D₈	—	2	4	no	—
281	C₂×D₈	—	2	4	no	—
282	C₂×D₈	D₄×C₁₁	1	8	yes	complemented
283	C₂²×C₈	—	2	4	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	4	no	—
286	C₂²×C₈	D₄×C₁₁	1	4	yes	complemented
287	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
291	#121	—	2	8	no	—
292	#121	—	4	4	no	—
293	#120	—	4	8	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	4	no	—
300	C₂×C₂²⋊C₄	—	2	4	no	—
301	C₂×C₂²⋊C₄	—	2	4	no	—
302	C₂×C₂²⋊C₄	D₄×C₁₁	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	D₄×C₁₁	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
305	#107	—	2	4	no	—
306	C₄⋊C₈	—	2	2	no	—
307	#102	—	2	8	no	—
308	#102	—	4	4	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	#95	—	2	2	no	—
313	C₂×C₁₁	—	2	4	no	—
314	C₂×C₁₁	—	4	2	no	—
315	C₂×C₁₁	—	8	8	no	—
316	C₂×C₁₁	#2408	1	1	yes	characteristic
317	C₂×C₁₁	C₂×#466	1	1	yes	characteristic
318	C₂×C₁₁	#3058	1	1	yes	characteristic
319	C₂×C₁₁	D₄×D₈	1	2	yes	—
320	C₂×C₁₁	#3280	1	2	yes	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	4	8	no	—
323	C₂⁴	—	4	4	no	—
324	C₂⁴	—	4	4	no	—
325	C₂⁴	—	4	4	no	—
326	C₂⁴	—	8	4	no	—
327	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
328	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	16	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	4	16	no	—
338	C₂×D₄	—	4	8	no	—
339	C₂×D₄	—	4	8	no	—
340	C₂×D₄	—	4	8	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	8	4	no	—
344	C₂×D₄	C₁₁×D₈	1	4	yes	complemented
345	C₂×D₄	C₂×D₄×C₁₁	1	8	yes	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
358	C₂²×C₄	C₁₁×#41	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
360	D₈	—	2	16	no	—
361	D₈	—	2	16	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	8	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	4	no	—
369	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
371	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	4	8	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	8	no	—
380	C₂²⋊C₄	—	8	4	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₁₁	#24267	1	1	yes	characteristic, direct product factor, Sylow
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	8	no	—
391	C₂³	—	4	16	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	8	16	no	—
399	C₂³	—	8	16	no	—
400	C₂³	—	8	8	no	—
401	C₂³	—	8	8	no	—
402	C₂³	C₁₁×#121	1	2	yes	—
403	C₂³	C₂×C₁₁×D₈	1	2	yes	—
404	C₂³	C₂×C₁₁×D₈	1	2	yes	complemented
405	C₂³	C₁₁×#135	1	2	yes	—
406	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
407	D₄	—	2	8	no	—
408	D₄	—	2	8	no	—
409	D₄	—	2	8	no	—
410	D₄	—	4	16	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	8	16	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	C₁₁×#121	1	2	yes	—
431	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	complemented
432	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
434	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
435	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
436	C₈	—	2	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₈	C₁₁×#120	1	4	yes	complemented
440	C₂²	—	2	2	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	8	no	—
450	C₂²	—	4	8	no	—
451	C₂²	—	4	8	no	—
452	C₂²	—	8	32	no	—
453	C₂²	—	8	4	no	—
454	C₂²	—	8	4	no	—
455	C₂²	—	8	4	no	—
456	C₂²	—	8	4	no	—
457	C₂²	C₁₁×#466	1	4	yes	complemented
458	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
459	C₂²	D₄²×C₁₁	1	2	yes	—
460	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
461	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
462	C₂²	C₁₁×#576	1	2	yes	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	8	4	no	—
468	C₄	C₂×C₁₁×#120	1	1	yes	characteristic
469	C₄	C₁₁×#535	1	1	yes	characteristic
470	C₄	C₁₁×#546	1	2	yes	—
471	C₂	—	2	4	no	—
472	C₂	—	4	2	no	—
473	C₂	—	8	8	no	—
474	C₂	C₁₁×#2408	1	1	yes	characteristic
475	C₂	C₂×C₁₁×#466	1	1	yes	characteristic
476	C₂	C₁₁×#3058	1	1	yes	characteristic
477	C₂	D₄×C₁₁×D₈	1	2	yes	—
478	C₂	C₁₁×#3280	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄×D₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₁×D₈	C₂	semidirect
2. C₂×C₁₁×#466	C₂	semidirect
3. C₂×C₈×D₄×C₁₁	C₂	semidirect
4. C₁₁×#2408	C₂	semidirect
5. C₁₁×#2054	C₂	semidirect
6. C₁₁×#1999	C₂	semidirect
7. C₁₁×#1970	C₂	semidirect
8. C₁₁×#1808	C₂	semidirect
9. C₁₁×#1786	C₂	semidirect
16. C₂³×C₈×C₁₁	C₂²	semidirect
17. C₂×C₁₁×#121	C₂²	semidirect
22. C₂×C₁₁×#107	C₂²	semidirect
23. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
24. C₂×C₁₁×#102	C₂²	semidirect
25. C₂×C₁₁×#102	C₂²	semidirect
27. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
28. C₂×C₄×C₈×C₁₁	C₂²	semidirect
31. C₁₁×#390	C₂²	semidirect
34. C₁₁×#340	C₂²	semidirect
51. C₂×C₁₁×D₈	D₄	semidirect
55. C₂²×C₈×C₁₁	D₄	semidirect
82. #24267	C₁₁	direct (N × H)
106. C₂×D₄×C₁₁	D₈	semidirect
145. C₂³×D₈	C₂×C₁₁	semidirect
146. C₂×#466	C₂×C₁₁	semidirect
147. C₂×C₈×D₄	C₂×C₁₁	semidirect
148. #2408	C₂×C₁₁	semidirect
149. #2054	C₂×C₁₁	semidirect
150. #1999	C₂×C₁₁	semidirect
151. #1970	C₂×C₁₁	semidirect
152. #1808	C₂×C₁₁	semidirect
153. #1786	C₂×C₁₁	semidirect
174. C₂³×C₁₁	C₂×D₈	semidirect
201. C₂×C₄×C₁₁	C₂×D₈	semidirect
209. C₈×C₁₁	#120	semidirect
216. C₂³×C₈	C₂²×C₁₁	semidirect
217. C₂×#121	C₂²×C₁₁	semidirect
222. C₂×#107	C₂²×C₁₁	semidirect
223. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
224. C₂×#102	C₂²×C₁₁	semidirect
225. C₂×#102	C₂²×C₁₁	semidirect
227. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
228. C₂×C₄×C₈	C₂²×C₁₁	semidirect
231. #390	C₂²×C₁₁	semidirect
234. #340	C₂²×C₁₁	semidirect
252. C₂²×C₁₁	#466	semidirect
282. C₂×D₈	D₄×C₁₁	semidirect
286. C₂²×C₈	D₄×C₁₁	semidirect
344. C₂×D₄	C₁₁×D₈	semidirect
383. C₁₁	#24267	direct (N × H)
404. C₂³	C₂×C₁₁×D₈	semidirect
431. C₂×C₄	C₂×C₁₁×D₈	semidirect
439. C₈	C₁₁×#120	semidirect
457. C₂²	C₁₁×#466	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₁×D₈	2
C₂×C₁₁×#466	2
C₂×C₈×D₄×C₁₁	2
C₁₁×#2408	2
C₁₁×#2054	2
C₁₁×#1999	2
C₁₁×#1970	2
C₁₁×#1808	2
C₁₁×#1786	2
#24267	11

Subgroups — C11×#24267 #14601460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#24267 #14601460