Subgroups — C₁₁×#23048 #14600241

Order 2816.

892 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#472	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2946	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2912	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1931	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1883	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1856	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1765	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
15	C₁₁×#520	C₂²	1	2	yes	—
16	C₁₁×#518	C₂²	1	2	yes	—
17	C₁₁×#472	C₄	1	8	yes	complemented
18	C₁₁×#442	—	2	1	no	—
19	C₁₁×#442	—	2	1	no	—
20	C₁₁×#442	—	2	2	no	—
21	C₁₁×#440	—	2	2	no	—
22	C₄×C₁₁×SD₁₆	—	2	2	no	—
23	C₄×C₁₁×D₈	—	2	2	no	—
24	C₄×C₁₁×D₈	—	2	2	no	—
25	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
26	C₁₁×#428	—	2	2	no	—
27	C₁₁×#428	C₂²	1	2	yes	—
28	C₁₁×#428	C₂²	1	2	yes	—
29	C₁₁×#427	—	2	1	no	—
30	C₁₁×#427	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#106	—	2	1	no	—
32	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
34	C₁₁×#418	C₂²	1	2	yes	—
35	C₁₁×#416	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×#102	C₂²	1	2	yes	—
37	C₂×C₁₁×#100	C₂²	1	2	yes	—
38	C₁₁×#405	C₂²	1	2	yes	—
39	C₁₁×#405	C₂²	1	1	yes	characteristic
40	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
41	C₁₁×#390	C₂²	1	2	yes	—
42	C₁₁×#343	C₂²	1	2	yes	—
43	C₁₁×#341	C₂²	1	1	yes	characteristic
44	C₁₁×#339	C₂²	1	2	yes	—
45	C₁₁×#339	C₂²	1	1	yes	characteristic
46	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
48	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
49	C₁₁×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
50	C₂×C₁₁×SD₁₆	—	2	2	no	—
51	C₂×C₁₁×D₈	—	2	2	no	—
52	C₂×C₁₁×D₈	—	2	1	no	—
53	C₂×C₁₁×D₈	—	2	1	no	—
54	C₂×C₁₁×D₈	—	2	2	no	—
55	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
56	C₁₁×#131	—	2	2	no	—
57	C₁₁×#131	C₂×C₄	1	4	yes	complemented
58	C₂×C₁₁×M₁₆	—	2	1	no	—
59	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₁	—	2	1	no	—
63	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₁₁	—	2	2	no	—
66	C₄×D₄×C₁₁	—	2	2	no	—
67	C₄×D₄×C₁₁	—	2	2	no	—
68	C₄×D₄×C₁₁	—	2	2	no	—
69	C₄×D₄×C₁₁	—	2	2	no	—
70	C₄×D₄×C₁₁	—	2	2	no	—
71	C₄×D₄×C₁₁	—	4	2	no	—
72	C₁₁×#117	—	2	2	no	—
73	C₁₁×#117	C₂³	1	1	yes	characteristic
74	C₁₁×#117	C₂³	1	2	yes	—
75	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
78	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
79	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
80	C₁₁×#108	C₂×C₄	1	4	yes	complemented
81	C₁₁×#107	—	2	2	no	—
82	C₁₁×#107	—	2	2	no	—
83	C₁₁×#107	D₄	1	2	yes	—
84	C₁₁×#106	—	2	1	no	—
85	C₁₁×#106	—	2	1	no	—
86	C₁₁×#106	—	2	2	no	—
87	C₁₁×#106	—	2	2	no	—
88	C₁₁×#106	D₄	1	1	yes	characteristic
89	C₁₁×#106	D₄	1	1	yes	characteristic
90	C₁₁×#104	—	2	2	no	—
91	C₁₁×#103	D₄	1	2	yes	—
92	C₁₁×#102	—	2	2	no	—
93	C₁₁×#102	—	2	2	no	—
94	C₁₁×#102	—	2	2	no	—
95	C₁₁×#102	—	2	2	no	—
96	C₁₁×#102	D₄	1	2	yes	—
97	C₁₁×#100	C₂×C₄	1	8	yes	complemented
98	C₁₁×#97	—	2	2	no	—
99	C₁₁×#97	—	2	1	no	—
100	C₁₁×#97	—	2	2	no	—
101	C₄×C₈×C₁₁	—	2	1	no	—
102	C₄×C₈×C₁₁	—	2	2	no	—
103	#23048	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₁	—	2	2	no	—
105	C₁₁×#41	—	2	1	no	—
106	C₁₁×#41	—	2	1	no	—
107	C₁₁×#41	C₂²×C₄	1	2	yes	—
108	C₁₁×#41	#41	1	2	yes	—
109	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₂×D₄×C₁₁	—	2	1	no	—
111	C₂×D₄×C₁₁	—	2	2	no	—
112	C₂×D₄×C₁₁	—	2	2	no	—
113	C₂×D₄×C₁₁	—	2	2	no	—
114	C₂×D₄×C₁₁	—	2	2	no	—
115	C₂×D₄×C₁₁	—	2	2	no	—
116	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
117	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	—	2	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	4	2	no	—
122	C₂²×C₄×C₁₁	—	4	2	no	—
123	C₂²×C₄×C₁₁	—	4	2	no	—
124	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
125	C₁₁×SD₁₆	—	2	8	no	—
126	C₁₁×D₈	—	2	4	no	—
127	C₁₁×D₈	—	2	4	no	—
128	C₁₁×D₈	—	2	8	no	—
129	C₁₁×M₁₆	—	2	4	no	—
130	C₁₁×M₁₆	—	2	1	no	—
131	C₁₁×M₁₆	—	2	2	no	—
132	C₁₁×M₁₆	—	2	1	no	—
133	C₁₁×M₁₆	—	2	1	no	—
134	C₁₁×M₁₆	C₂²×C₄	1	2	yes	—
135	C₁₁×M₁₆	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₁₁	—	2	4	no	—
137	C₂×C₈×C₁₁	—	2	2	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	—	2	1	no	—
141	C₂×C₈×C₁₁	—	2	1	no	—
142	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₁	#41	1	2	yes	—
147	C₁₁×C₄⋊C₄	—	2	2	no	—
148	C₁₁×C₄⋊C₄	—	2	2	no	—
149	C₁₁×C₄⋊C₄	—	4	2	no	—
150	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
151	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
152	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₁×C₂²⋊C₄	—	2	1	no	—
154	C₁₁×C₂²⋊C₄	—	2	2	no	—
155	C₁₁×C₂²⋊C₄	—	4	2	no	—
156	C₁₁×C₂²⋊C₄	—	4	2	no	—
157	C₁₁×C₂²⋊C₄	—	4	2	no	—
158	C₁₁×C₂²⋊C₄	—	8	4	no	—
159	C₄²×C₁₁	—	2	1	no	—
160	C₄²×C₁₁	—	2	2	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	4	2	no	—
164	C₂×#472	C₂×C₁₁	1	1	yes	characteristic
165	#2948	C₂×C₁₁	1	1	yes	characteristic, complemented
166	#2946	C₂×C₁₁	1	2	yes	complemented
167	#2912	C₂×C₁₁	1	1	yes	characteristic, complemented
168	#1972	C₂×C₁₁	1	1	yes	characteristic, complemented
169	#1951	C₂×C₁₁	1	1	yes	characteristic, complemented
170	#1931	C₂×C₁₁	1	2	yes	complemented
171	#1883	C₂×C₁₁	1	2	yes	complemented
172	#1856	C₂×C₁₁	1	2	yes	complemented
173	#1773	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1765	C₂×C₁₁	1	1	yes	characteristic, complemented
175	C₂³×C₁₁	—	2	1	no	—
176	C₂³×C₁₁	—	2	4	no	—
177	C₂³×C₁₁	—	4	2	no	—
178	C₂³×C₁₁	—	4	2	no	—
179	C₂³×C₁₁	—	8	2	no	—
180	C₂³×C₁₁	—	8	2	no	—
181	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
182	Q₈×C₁₁	—	2	1	no	—
183	Q₈×C₁₁	C₄×D₄	1	2	yes	—
184	D₄×C₁₁	—	2	2	no	—
185	D₄×C₁₁	—	2	2	no	—
186	D₄×C₁₁	—	2	4	no	—
187	D₄×C₁₁	—	2	4	no	—
188	D₄×C₁₁	—	2	1	no	—
189	D₄×C₁₁	—	4	2	no	—
190	D₄×C₁₁	—	4	2	no	—
191	D₄×C₁₁	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	2	2	no	—
197	C₂×C₄×C₁₁	—	2	2	no	—
198	C₂×C₄×C₁₁	—	4	2	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	—	4	1	no	—
201	C₂×C₄×C₁₁	—	8	2	no	—
202	C₂×C₄×C₁₁	—	16	2	no	—
203	C₂×C₄×C₁₁	—	16	2	no	—
204	C₂×C₄×C₁₁	—	16	2	no	—
205	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂²×D₄	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	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
211	C₈×C₁₁	—	2	2	no	—
212	C₈×C₁₁	—	2	4	no	—
213	C₈×C₁₁	—	2	2	no	—
214	C₈×C₁₁	—	4	1	no	—
215	C₈×C₁₁	C₄×D₄	1	2	yes	—
216	C₈×C₁₁	C₄×D₄	1	2	yes	—
217	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
218	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
219	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
220	#520	C₂²×C₁₁	1	2	yes	—
221	#518	C₂²×C₁₁	1	2	yes	—
222	#472	C₄×C₁₁	1	8	yes	complemented
223	#442	—	2	1	no	—
224	#442	—	2	1	no	—
225	#442	—	2	2	no	—
226	#440	—	2	2	no	—
227	C₄×SD₁₆	—	2	2	no	—
228	C₄×D₈	—	2	2	no	—
229	C₄×D₈	—	2	2	no	—
230	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
231	#428	—	2	2	no	—
232	#428	C₂²×C₁₁	1	2	yes	—
233	#428	C₂²×C₁₁	1	2	yes	—
234	#427	—	2	1	no	—
235	#427	C₂²×C₁₁	1	1	yes	characteristic
236	C₂×#106	—	2	1	no	—
237	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
238	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
239	#418	C₂²×C₁₁	1	2	yes	—
240	#416	C₂²×C₁₁	1	1	yes	characteristic
241	C₂×#102	C₂²×C₁₁	1	2	yes	—
242	C₂×#100	C₂²×C₁₁	1	2	yes	—
243	#405	C₂²×C₁₁	1	2	yes	—
244	#405	C₂²×C₁₁	1	1	yes	characteristic
245	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
246	#390	C₂²×C₁₁	1	2	yes	—
247	#343	C₂²×C₁₁	1	2	yes	—
248	#341	C₂²×C₁₁	1	1	yes	characteristic
249	#339	C₂²×C₁₁	1	1	yes	characteristic
250	#339	C₂²×C₁₁	1	2	yes	—
251	C₂²×C₁₁	—	2	2	no	—
252	C₂²×C₁₁	—	2	2	no	—
253	C₂²×C₁₁	—	4	2	no	—
254	C₂²×C₁₁	—	4	4	no	—
255	C₂²×C₁₁	—	8	4	no	—
256	C₂²×C₁₁	—	8	2	no	—
257	C₂²×C₁₁	—	8	2	no	—
258	C₂²×C₁₁	—	16	2	no	—
259	C₂²×C₁₁	#520	1	1	yes	characteristic
260	C₂²×C₁₁	D₄²	1	1	yes	characteristic
261	C₂²×C₁₁	#553	1	1	yes	characteristic
262	C₄×C₁₁	—	2	2	no	—
263	C₄×C₁₁	—	4	2	no	—
264	C₄×C₁₁	—	4	2	no	—
265	C₄×C₁₁	—	4	2	no	—
266	C₄×C₁₁	—	8	1	no	—
267	C₄×C₁₁	—	8	2	no	—
268	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
269	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₁₁	#547	1	1	yes	characteristic
271	C₄×C₁₁	#548	1	1	yes	characteristic
272	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
273	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
274	AGL(1,ℤ/8)	—	2	4	no	—
275	AGL(1,ℤ/8)	C₂×C₄×C₁₁	1	8	yes	complemented
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	2	2	no	—
281	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	complemented
282	#131	—	2	2	no	—
283	#131	C₂×C₄×C₁₁	1	4	yes	complemented
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
286	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
287	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
291	C₄×Q₈	—	2	2	no	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	—	4	2	no	—
298	#117	—	2	2	no	—
299	#117	C₂³×C₁₁	1	1	yes	characteristic
300	#117	C₂³×C₁₁	1	2	yes	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
303	C₂×C₂²⋊C₄	—	4	2	no	—
304	C₂×C₂²⋊C₄	—	4	2	no	—
305	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
306	#108	C₂×C₄×C₁₁	1	4	yes	complemented
307	#107	—	2	2	no	—
308	#107	—	2	2	no	—
309	#107	D₄×C₁₁	1	2	yes	—
310	#106	—	2	1	no	—
311	#106	—	2	1	no	—
312	#106	—	2	2	no	—
313	#106	—	2	2	no	—
314	#106	D₄×C₁₁	1	1	yes	characteristic
315	#106	D₄×C₁₁	1	1	yes	characteristic
316	#104	—	2	2	no	—
317	#103	D₄×C₁₁	1	2	yes	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	#102	—	2	2	no	—
321	#102	—	2	2	no	—
322	#102	D₄×C₁₁	1	2	yes	—
323	#100	C₂×C₄×C₁₁	1	8	yes	complemented
324	#97	—	2	2	no	—
325	#97	—	2	1	no	—
326	#97	—	2	2	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	2	2	no	—
329	C₂×C₁₁	—	2	1	no	—
330	C₂×C₁₁	—	2	1	no	—
331	C₂×C₁₁	—	4	2	no	—
332	C₂×C₁₁	—	8	4	no	—
333	C₂×C₁₁	#2361	1	1	yes	characteristic
334	C₂×C₁₁	#3288	1	2	yes	—
335	C₂⁴	—	2	2	no	—
336	#41	—	2	1	no	—
337	#41	—	2	1	no	—
338	#41	C₂²×C₄×C₁₁	1	2	yes	—
339	#41	C₁₁×#41	1	2	yes	—
340	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
348	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
356	SD₁₆	—	2	8	no	—
357	D₈	—	2	8	no	—
358	D₈	—	2	4	no	—
359	D₈	—	2	4	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	C₂²×C₄×C₁₁	1	2	yes	—
366	M₁₆	C₂²×C₄×C₁₁	1	4	yes	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
375	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
376	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
377	C₂×C₈	C₁₁×#41	1	2	yes	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
382	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
383	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	8	4	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	4	2	no	—
395	C₁₁	#23048	1	1	yes	characteristic, direct product factor, Sylow
396	C₂³	—	2	1	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	8	2	no	—
401	C₂³	—	8	2	no	—
402	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
403	Q₈	—	2	1	no	—
404	Q₈	C₄×D₄×C₁₁	1	2	yes	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	1	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	C₄×D₄×C₁₁	1	2	yes	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	8	2	no	—
423	C₂×C₄	—	16	2	no	—
424	C₂×C₄	—	16	2	no	—
425	C₂×C₄	—	16	2	no	—
426	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
429	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
430	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
431	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	4	no	—
434	C₈	—	2	2	no	—
435	C₈	—	4	1	no	—
436	C₈	C₄×D₄×C₁₁	1	2	yes	—
437	C₈	C₄×D₄×C₁₁	1	2	yes	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	8	4	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	16	2	no	—
446	C₂²	C₁₁×#520	1	1	yes	characteristic
447	C₂²	D₄²×C₁₁	1	1	yes	characteristic
448	C₂²	C₁₁×#553	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	2	no	—
455	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
456	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
457	C₄	C₁₁×#547	1	1	yes	characteristic
458	C₄	C₁₁×#548	1	1	yes	characteristic
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	4	2	no	—
462	C₂	—	8	4	no	—
463	C₂	C₁₁×#2361	1	1	yes	characteristic
464	C₂	C₁₁×#3288	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#472	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2948	C₂	semidirect
3. C₁₁×#2946	C₂	semidirect
4. C₁₁×#2912	C₂	semidirect
5. C₁₁×#1972	C₂	semidirect
6. C₁₁×#1951	C₂	semidirect
7. C₁₁×#1931	C₂	semidirect
8. C₁₁×#1883	C₂	semidirect
9. C₁₁×#1856	C₂	semidirect
10. C₁₁×#1773	C₂	semidirect
11. C₁₁×#1765	C₂	semidirect
17. C₁₁×#472	C₄	semidirect
49. C₁₁×AGL(1,ℤ/8)	C₂×C₄	semidirect
55. C₂×C₁₁×D₈	C₂×C₄	semidirect
57. C₁₁×#131	C₂×C₄	semidirect
80. C₁₁×#108	C₂×C₄	semidirect
97. C₁₁×#100	C₂×C₄	semidirect
103. #23048	C₁₁	direct (N × H)
165. #2948	C₂×C₁₁	semidirect
166. #2946	C₂×C₁₁	semidirect
167. #2912	C₂×C₁₁	semidirect
168. #1972	C₂×C₁₁	semidirect
169. #1951	C₂×C₁₁	semidirect
170. #1931	C₂×C₁₁	semidirect
171. #1883	C₂×C₁₁	semidirect
172. #1856	C₂×C₁₁	semidirect
173. #1773	C₂×C₁₁	semidirect
174. #1765	C₂×C₁₁	semidirect
222. #472	C₄×C₁₁	semidirect
275. AGL(1,ℤ/8)	C₂×C₄×C₁₁	semidirect
281. C₂×D₈	C₂×C₄×C₁₁	semidirect
283. #131	C₂×C₄×C₁₁	semidirect
306. #108	C₂×C₄×C₁₁	semidirect
323. #100	C₂×C₄×C₁₁	semidirect
395. C₁₁	#23048	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#472	2
C₁₁×#2948	2
C₁₁×#2946	2
C₁₁×#2912	2
C₁₁×#1972	2
C₁₁×#1951	2
C₁₁×#1931	2
C₁₁×#1883	2
C₁₁×#1856	2
C₁₁×#1773	2
C₁₁×#1765	2
#23048	11

Subgroups — C11×#23048 #14600241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23048 #14600241