Subgroups — C₁₁×#22463 #14599656

Order 2816.

1380 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#576	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2897	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1907	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1883	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1815	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1792	C₂	1	2	yes	maximal, complemented
11	C₁₁×#1765	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	2	yes	—
13	C₁₁×#576	—	2	4	no	—
14	C₁₁×#576	C₄	1	8	yes	complemented
15	C₂×C₁₁×AGL(1,ℤ/8)	—	2	2	no	—
16	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂×C₁₁×#135	—	2	1	no	—
18	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₁₁×D₈	—	2	1	no	—
20	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#131	C₂²	1	2	yes	complemented
23	C₁₁×#520	C₂²	1	2	yes	complemented
24	C₁₁×#444	—	2	4	no	—
25	C₁₁×#442	—	2	1	no	—
26	C₁₁×#441	—	2	1	no	—
27	C₄×C₁₁×SD₁₆	—	2	2	no	—
28	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#104	C₂²	1	2	yes	complemented
32	C₁₁×#418	—	2	2	no	—
33	C₁₁×#418	C₂²	1	2	yes	complemented
34	C₁₁×#417	—	2	2	no	—
35	C₁₁×#417	C₂²	1	2	yes	—
36	C₁₁×#417	C₂²	1	2	yes	complemented
37	C₁₁×#416	—	2	2	no	—
38	C₁₁×#416	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#102	—	2	2	no	—
40	C₂×C₁₁×#102	C₂²	1	2	yes	complemented
41	C₂×C₁₁×#100	C₂²	1	2	yes	complemented
42	C₁₁×#405	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic, complemented
44	C₁₁×#390	C₂²	1	2	yes	complemented
45	C₁₁×#343	C₂²	1	2	yes	complemented
46	C₁₁×#341	C₂²	1	1	yes	characteristic, complemented
47	C₁₁×#339	C₂²	1	1	yes	characteristic, complemented
48	C₁₁×H(5,𝔽₂)	—	2	4	no	—
49	C₁₁×H(5,𝔽₂)	—	2	4	no	—
50	C₁₁×H(5,𝔽₂)	—	4	2	no	—
51	C₁₁×H(5,𝔽₂)	C₂×C₄	1	8	yes	complemented
52	C₂×C₁₁×#41	—	2	2	no	—
53	C₂×C₁₁×#41	—	2	2	no	—
54	C₂×C₁₁×#41	C₂³	1	2	yes	—
55	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₁	—	2	2	no	—
57	C₂²×D₄×C₁₁	—	2	2	no	—
58	C₂²×D₄×C₁₁	—	4	2	no	—
59	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
60	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
61	C₁₁×AGL(1,ℤ/8)	—	2	16	no	—
62	C₁₁×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
63	C₁₁×#135	—	2	8	no	—
64	C₁₁×#135	C₂×C₄	1	4	yes	—
65	C₁₁×#135	D₄	1	4	yes	—
66	C₂×C₁₁×Q₁₆	D₄	1	1	yes	characteristic
67	C₂×C₁₁×SD₁₆	—	2	2	no	—
68	C₂×C₁₁×SD₁₆	D₄	1	2	yes	—
69	C₂×C₁₁×D₈	—	2	2	no	—
70	C₂×C₁₁×D₈	—	2	8	no	—
71	C₂×C₁₁×D₈	—	2	1	no	—
72	C₂×C₁₁×D₈	—	2	1	no	—
73	C₂×C₁₁×D₈	—	2	2	no	—
74	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
75	C₂×C₁₁×D₈	D₄	1	1	yes	characteristic
76	C₁₁×#131	—	2	2	no	—
77	C₁₁×#131	—	2	4	no	—
78	C₁₁×#131	—	4	2	no	—
79	C₁₁×#131	C₂×C₄	1	4	yes	complemented
80	C₂×C₁₁×M₁₆	—	2	1	no	—
81	C₂×C₁₁×M₁₆	—	2	2	no	—
82	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
84	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₁	—	2	1	no	—
86	C₂²×C₈×C₁₁	—	2	2	no	—
87	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
89	C₄×Q₈×C₁₁	—	2	2	no	—
90	C₄×D₄×C₁₁	—	2	2	no	—
91	C₄×D₄×C₁₁	—	4	2	no	—
92	C₁₁×#117	—	2	2	no	—
93	C₁₁×#117	C₂³	1	1	yes	characteristic
94	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
97	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
98	C₁₁×#108	—	2	2	no	—
99	C₁₁×#106	—	2	1	no	—
100	C₁₁×#106	—	2	1	no	—
101	C₁₁×#104	—	2	4	no	—
102	C₁₁×#104	—	2	2	no	—
103	C₁₁×#103	—	2	2	no	—
104	C₁₁×#103	—	2	2	no	—
105	C₁₁×#103	D₄	1	2	yes	—
106	C₁₁×#102	—	2	2	no	—
107	C₁₁×#102	—	2	2	no	—
108	C₁₁×#102	—	2	2	no	—
109	C₁₁×#102	—	2	2	no	—
110	C₁₁×#102	—	2	2	no	—
111	C₁₁×#102	—	2	2	no	—
112	C₁₁×#102	D₄	1	2	yes	—
113	C₁₁×#100	—	4	2	no	—
114	C₁₁×#97	—	2	2	no	—
115	C₁₁×#97	—	2	1	no	—
116	C₄×C₈×C₁₁	—	2	1	no	—
117	#22463	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂⁴×C₁₁	—	2	2	no	—
119	C₂⁴×C₁₁	—	4	2	no	—
120	C₁₁×#41	—	2	1	no	—
121	C₁₁×#41	—	2	2	no	—
122	C₁₁×#41	—	2	2	no	—
123	C₁₁×#41	—	2	1	no	—
124	C₁₁×#41	—	2	8	no	—
125	C₁₁×#41	—	2	8	no	—
126	C₁₁×#41	—	4	4	no	—
127	C₁₁×#41	—	4	4	no	—
128	C₁₁×#41	C₂²×C₄	1	4	yes	—
129	C₁₁×#41	C₂²×C₄	1	2	yes	—
130	C₁₁×#41	C₂×D₄	1	4	yes	—
131	C₁₁×#41	#41	1	2	yes	—
132	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
134	C₂×D₄×C₁₁	—	2	2	no	—
135	C₂×D₄×C₁₁	—	2	1	no	—
136	C₂×D₄×C₁₁	—	2	8	no	—
137	C₂×D₄×C₁₁	—	2	8	no	—
138	C₂×D₄×C₁₁	—	2	2	no	—
139	C₂×D₄×C₁₁	—	2	2	no	—
140	C₂×D₄×C₁₁	—	2	2	no	—
141	C₂×D₄×C₁₁	—	2	2	no	—
142	C₂×D₄×C₁₁	—	2	2	no	—
143	C₂×D₄×C₁₁	—	4	4	no	—
144	C₂×D₄×C₁₁	—	4	4	no	—
145	C₂×D₄×C₁₁	—	4	2	no	—
146	C₂×D₄×C₁₁	—	4	2	no	—
147	C₂×D₄×C₁₁	—	4	8	no	—
148	C₂×D₄×C₁₁	—	4	8	no	—
149	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
150	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₁	—	2	2	no	—
153	C₂²×C₄×C₁₁	—	2	1	no	—
154	C₂²×C₄×C₁₁	—	2	1	no	—
155	C₂²×C₄×C₁₁	—	2	2	no	—
156	C₂²×C₄×C₁₁	—	4	2	no	—
157	C₂²×C₄×C₁₁	—	4	2	no	—
158	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
159	C₁₁×Q₁₆	C₂²⋊C₄	1	4	yes	complemented
160	C₁₁×SD₁₆	—	2	8	no	—
161	C₁₁×SD₁₆	C₂²⋊C₄	1	8	yes	complemented
162	C₁₁×D₈	—	2	4	no	—
163	C₁₁×D₈	—	2	4	no	—
164	C₁₁×D₈	—	2	8	no	—
165	C₁₁×D₈	C₂²⋊C₄	1	4	yes	complemented
166	C₁₁×M₁₆	—	2	4	no	—
167	C₁₁×M₁₆	—	2	1	no	—
168	C₁₁×M₁₆	—	2	2	no	—
169	C₁₁×M₁₆	—	2	1	no	—
170	C₁₁×M₁₆	—	2	1	no	—
171	C₁₁×M₁₆	—	2	2	no	—
172	C₁₁×M₁₆	—	4	4	no	—
173	C₁₁×M₁₆	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₁₁	—	2	4	no	—
175	C₂×C₈×C₁₁	—	2	1	no	—
176	C₂×C₈×C₁₁	—	2	1	no	—
177	C₂×C₈×C₁₁	—	2	1	no	—
178	C₂×C₈×C₁₁	—	2	2	no	—
179	C₂×C₈×C₁₁	—	2	1	no	—
180	C₂×C₈×C₁₁	—	4	4	no	—
181	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
182	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
186	C₁₁×C₄⋊C₄	—	2	2	no	—
187	C₁₁×C₄⋊C₄	—	2	2	no	—
188	C₁₁×C₄⋊C₄	—	4	2	no	—
189	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
190	C₁₁×C₂²⋊C₄	—	2	1	no	—
191	C₁₁×C₂²⋊C₄	—	4	2	no	—
192	C₁₁×C₂²⋊C₄	—	8	4	no	—
193	C₄²×C₁₁	—	2	1	no	—
194	C₄²×C₁₁	—	2	1	no	—
195	C₄²×C₁₁	—	2	1	no	—
196	C₄²×C₁₁	—	4	2	no	—
197	C₂×#576	C₂×C₁₁	1	1	yes	characteristic
198	C₂×#444	C₂×C₁₁	1	1	yes	characteristic, complemented
199	#2952	C₂×C₁₁	1	1	yes	characteristic, complemented
200	#2897	C₂×C₁₁	1	2	yes	complemented
201	#1978	C₂×C₁₁	1	1	yes	characteristic, complemented
202	#1972	C₂×C₁₁	1	1	yes	characteristic, complemented
203	#1907	C₂×C₁₁	1	2	yes	complemented
204	#1883	C₂×C₁₁	1	2	yes	complemented
205	#1815	C₂×C₁₁	1	1	yes	characteristic, complemented
206	#1792	C₂×C₁₁	1	2	yes	complemented
207	#1765	C₂×C₁₁	1	1	yes	characteristic, complemented
208	C₂³×C₁₁	—	2	2	no	—
209	C₂³×C₁₁	—	2	1	no	—
210	C₂³×C₁₁	—	2	4	no	—
211	C₂³×C₁₁	—	4	8	no	—
212	C₂³×C₁₁	—	4	2	no	—
213	C₂³×C₁₁	—	4	2	no	—
214	C₂³×C₁₁	—	8	2	no	—
215	C₂³×C₁₁	—	8	2	no	—
216	C₂³×C₁₁	—	16	2	no	—
217	C₂³×C₁₁	—	16	2	no	—
218	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
219	Q₈×C₁₁	—	2	1	no	—
220	Q₈×C₁₁	—	2	2	no	—
221	Q₈×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
222	Q₈×C₁₁	C₄×D₄	1	2	yes	—
223	D₄×C₁₁	—	2	2	no	—
224	D₄×C₁₁	—	2	4	no	—
225	D₄×C₁₁	—	2	2	no	—
226	D₄×C₁₁	—	2	4	no	—
227	D₄×C₁₁	—	2	4	no	—
228	D₄×C₁₁	—	2	4	no	—
229	D₄×C₁₁	—	2	1	no	—
230	D₄×C₁₁	—	2	2	no	—
231	D₄×C₁₁	—	4	8	no	—
232	D₄×C₁₁	—	4	8	no	—
233	D₄×C₁₁	—	4	2	no	—
234	D₄×C₁₁	—	4	2	no	—
235	D₄×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
236	D₄×C₁₁	C₄×D₄	1	2	yes	—
237	C₂×C₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	2	1	no	—
239	C₂×C₄×C₁₁	—	2	2	no	—
240	C₂×C₄×C₁₁	—	2	4	no	—
241	C₂×C₄×C₁₁	—	2	4	no	—
242	C₂×C₄×C₁₁	—	2	2	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	4	8	no	—
245	C₂×C₄×C₁₁	—	4	2	no	—
246	C₂×C₄×C₁₁	—	4	2	no	—
247	C₂×C₄×C₁₁	—	4	1	no	—
248	C₂×C₄×C₁₁	—	8	2	no	—
249	C₂×C₄×C₁₁	—	16	2	no	—
250	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
256	C₈×C₁₁	—	2	2	no	—
257	C₈×C₁₁	—	2	2	no	—
258	C₈×C₁₁	—	4	2	no	—
259	C₈×C₁₁	—	4	1	no	—
260	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
261	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	2	yes	—
263	#576	—	2	4	no	—
264	#576	C₄×C₁₁	1	8	yes	complemented
265	C₂×AGL(1,ℤ/8)	—	2	2	no	—
266	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
267	C₂×#135	—	2	1	no	—
268	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
269	C₂²×D₈	—	2	1	no	—
270	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
271	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
272	C₂×#131	C₂²×C₁₁	1	2	yes	complemented
273	#520	C₂²×C₁₁	1	2	yes	complemented
274	#444	—	2	4	no	—
275	#442	—	2	1	no	—
276	#441	—	2	1	no	—
277	C₄×SD₁₆	—	2	2	no	—
278	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic, complemented
279	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic, complemented
280	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
281	C₂×#104	C₂²×C₁₁	1	2	yes	complemented
282	#418	—	2	2	no	—
283	#418	C₂²×C₁₁	1	2	yes	complemented
284	#417	—	2	2	no	—
285	#417	C₂²×C₁₁	1	2	yes	—
286	#417	C₂²×C₁₁	1	2	yes	complemented
287	#416	—	2	2	no	—
288	#416	C₂²×C₁₁	1	1	yes	characteristic
289	C₂×#102	—	2	2	no	—
290	C₂×#102	C₂²×C₁₁	1	2	yes	complemented
291	C₂×#100	C₂²×C₁₁	1	2	yes	complemented
292	#405	C₂²×C₁₁	1	1	yes	characteristic, complemented
293	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic, complemented
294	#390	C₂²×C₁₁	1	2	yes	complemented
295	#343	C₂²×C₁₁	1	2	yes	complemented
296	#341	C₂²×C₁₁	1	1	yes	characteristic, complemented
297	#339	C₂²×C₁₁	1	1	yes	characteristic, complemented
298	C₂²×C₁₁	—	2	2	no	—
299	C₂²×C₁₁	—	2	2	no	—
300	C₂²×C₁₁	—	2	4	no	—
301	C₂²×C₁₁	—	4	2	no	—
302	C₂²×C₁₁	—	4	2	no	—
303	C₂²×C₁₁	—	4	2	no	—
304	C₂²×C₁₁	—	4	4	no	—
305	C₂²×C₁₁	—	8	4	no	—
306	C₂²×C₁₁	—	8	2	no	—
307	C₂²×C₁₁	—	8	2	no	—
308	C₂²×C₁₁	—	16	2	no	—
309	C₂²×C₁₁	—	16	8	no	—
310	C₂²×C₁₁	#518	1	1	yes	characteristic
311	C₂²×C₁₁	D₄²	1	1	yes	characteristic
312	C₂²×C₁₁	#546	1	1	yes	characteristic
313	C₄×C₁₁	—	2	2	no	—
314	C₄×C₁₁	—	2	4	no	—
315	C₄×C₁₁	—	4	2	no	—
316	C₄×C₁₁	—	8	1	no	—
317	C₄×C₁₁	—	8	2	no	—
318	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
319	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
320	C₄×C₁₁	D₄²	1	1	yes	characteristic
321	C₄×C₁₁	#546	1	1	yes	characteristic
322	H(5,𝔽₂)	—	2	4	no	—
323	H(5,𝔽₂)	—	2	4	no	—
324	H(5,𝔽₂)	—	4	2	no	—
325	H(5,𝔽₂)	C₂×C₄×C₁₁	1	8	yes	complemented
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	2	no	—
328	C₂×#41	C₂³×C₁₁	1	2	yes	—
329	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	4	2	no	—
333	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
334	AGL(1,ℤ/8)	—	2	4	no	—
335	AGL(1,ℤ/8)	—	2	16	no	—
336	AGL(1,ℤ/8)	C₂×C₄×C₁₁	1	8	yes	complemented
337	#135	—	2	8	no	—
338	#135	C₂×C₄×C₁₁	1	4	yes	—
339	#135	D₄×C₁₁	1	4	yes	—
340	C₂×Q₁₆	D₄×C₁₁	1	1	yes	characteristic
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×SD₁₆	D₄×C₁₁	1	2	yes	—
343	C₂×D₈	—	2	2	no	—
344	C₂×D₈	—	2	8	no	—
345	C₂×D₈	—	2	1	no	—
346	C₂×D₈	—	2	1	no	—
347	C₂×D₈	—	2	2	no	—
348	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	complemented
349	C₂×D₈	D₄×C₁₁	1	1	yes	characteristic
350	#131	—	2	2	no	—
351	#131	—	2	4	no	—
352	#131	—	4	2	no	—
353	#131	C₂×C₄×C₁₁	1	4	yes	complemented
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
357	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
358	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
359	C₂²×C₈	—	2	1	no	—
360	C₂²×C₈	—	2	2	no	—
361	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
363	C₄×Q₈	—	2	2	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	4	2	no	—
366	#117	—	2	2	no	—
367	#117	C₂³×C₁₁	1	1	yes	characteristic
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
370	C₂×C₂²⋊C₄	—	4	2	no	—
371	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
372	#108	—	2	2	no	—
373	#106	—	2	1	no	—
374	#106	—	2	1	no	—
375	#104	—	2	4	no	—
376	#104	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	2	2	no	—
379	#103	D₄×C₁₁	1	2	yes	—
380	#102	—	2	2	no	—
381	#102	—	2	2	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	D₄×C₁₁	1	2	yes	—
387	#100	—	4	2	no	—
388	#97	—	2	2	no	—
389	#97	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₂×C₁₁	—	2	1	no	—
392	C₂×C₁₁	—	2	1	no	—
393	C₂×C₁₁	—	4	4	no	—
394	C₂×C₁₁	—	4	2	no	—
395	C₂×C₁₁	—	8	4	no	—
396	C₂×C₁₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
397	C₂×C₁₁	#3288	1	2	yes	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	4	2	no	—
400	#41	—	2	1	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	2	1	no	—
404	#41	—	2	8	no	—
405	#41	—	2	8	no	—
406	#41	—	4	4	no	—
407	#41	—	4	4	no	—
408	#41	C₂²×C₄×C₁₁	1	4	yes	—
409	#41	C₂²×C₄×C₁₁	1	2	yes	—
410	#41	C₂×D₄×C₁₁	1	4	yes	—
411	#41	C₁₁×#41	1	2	yes	—
412	C₂×Q₈	C₂×D₄×C₁₁	1	2	yes	—
413	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	—	4	8	no	—
428	C₂×D₄	—	4	8	no	—
429	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
430	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
431	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
439	Q₁₆	C₁₁×C₂²⋊C₄	1	4	yes	complemented
440	SD₁₆	—	2	8	no	—
441	SD₁₆	C₁₁×C₂²⋊C₄	1	8	yes	complemented
442	D₈	—	2	8	no	—
443	D₈	—	2	4	no	—
444	D₈	—	2	4	no	—
445	D₈	C₁₁×C₂²⋊C₄	1	4	yes	complemented
446	M₁₆	—	2	1	no	—
447	M₁₆	—	2	4	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	1	no	—
450	M₁₆	—	2	1	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	4	4	no	—
453	M₁₆	C₂²×C₄×C₁₁	1	2	yes	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	4	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	4	4	no	—
461	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
462	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
463	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
464	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
465	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	8	4	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	4	2	no	—
477	C₁₁	#22463	1	1	yes	characteristic, direct product factor, Sylow
478	C₂³	—	2	2	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	8	2	no	—
485	C₂³	—	8	2	no	—
486	C₂³	—	16	2	no	—
487	C₂³	—	16	2	no	—
488	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
489	Q₈	—	2	1	no	—
490	Q₈	—	2	2	no	—
491	Q₈	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
492	Q₈	C₄×D₄×C₁₁	1	2	yes	—
493	D₄	—	2	2	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	4	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	1	no	—
500	D₄	—	2	2	no	—
501	D₄	—	4	8	no	—
502	D₄	—	4	8	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
506	D₄	C₄×D₄×C₁₁	1	2	yes	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	8	2	no	—
519	C₂×C₄	—	16	2	no	—
520	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
524	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
525	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
526	C₈	—	2	2	no	—
527	C₈	—	2	2	no	—
528	C₈	—	4	2	no	—
529	C₈	—	4	1	no	—
530	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
531	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	8	4	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	16	2	no	—
543	C₂²	—	16	8	no	—
544	C₂²	C₁₁×#518	1	1	yes	characteristic
545	C₂²	D₄²×C₁₁	1	1	yes	characteristic
546	C₂²	C₁₁×#546	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	2	4	no	—
549	C₄	—	4	2	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	2	no	—
552	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
553	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
554	C₄	D₄²×C₁₁	1	1	yes	characteristic
555	C₄	C₁₁×#546	1	1	yes	characteristic
556	C₂	—	2	1	no	—
557	C₂	—	2	1	no	—
558	C₂	—	4	2	no	—
559	C₂	—	4	4	no	—
560	C₂	—	8	4	no	—
561	C₂	D₄×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
562	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×#576	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. C₂×C₁₁×#444	C₂	semidirect
3. C₁₁×#2952	C₂	semidirect
4. C₁₁×#2897	C₂	semidirect
5. C₁₁×#1978	C₂	semidirect
6. C₁₁×#1972	C₂	semidirect
7. C₁₁×#1907	C₂	semidirect
8. C₁₁×#1883	C₂	semidirect
9. C₁₁×#1815	C₂	semidirect
10. C₁₁×#1792	C₂	semidirect
11. C₁₁×#1765	C₂	semidirect
14. C₁₁×#576	C₄	semidirect
22. C₂×C₁₁×#131	C₂²	semidirect
23. C₁₁×#520	C₂²	semidirect
28. C₂×C₁₁×#108	C₂²	semidirect
29. C₂×C₁₁×#106	C₂²	semidirect
31. C₂×C₁₁×#104	C₂²	semidirect
33. C₁₁×#418	C₂²	semidirect
36. C₁₁×#417	C₂²	semidirect
40. C₂×C₁₁×#102	C₂²	semidirect
41. C₂×C₁₁×#100	C₂²	semidirect
42. C₁₁×#405	C₂²	semidirect
43. C₂×C₁₁×#97	C₂²	semidirect
44. C₁₁×#390	C₂²	semidirect
45. C₁₁×#343	C₂²	semidirect
46. C₁₁×#341	C₂²	semidirect
47. C₁₁×#339	C₂²	semidirect
51. C₁₁×H(5,𝔽₂)	C₂×C₄	semidirect
62. C₁₁×AGL(1,ℤ/8)	C₂×C₄	semidirect
74. C₂×C₁₁×D₈	C₂×C₄	semidirect
79. C₁₁×#131	C₂×C₄	semidirect
117. #22463	C₁₁	direct (N × H)
159. C₁₁×Q₁₆	C₂²⋊C₄	semidirect
161. C₁₁×SD₁₆	C₂²⋊C₄	semidirect
165. C₁₁×D₈	C₂²⋊C₄	semidirect
198. C₂×#444	C₂×C₁₁	semidirect
199. #2952	C₂×C₁₁	semidirect
200. #2897	C₂×C₁₁	semidirect
201. #1978	C₂×C₁₁	semidirect
202. #1972	C₂×C₁₁	semidirect
203. #1907	C₂×C₁₁	semidirect
204. #1883	C₂×C₁₁	semidirect
205. #1815	C₂×C₁₁	semidirect
206. #1792	C₂×C₁₁	semidirect
207. #1765	C₂×C₁₁	semidirect
264. #576	C₄×C₁₁	semidirect
272. C₂×#131	C₂²×C₁₁	semidirect
273. #520	C₂²×C₁₁	semidirect
278. C₂×#108	C₂²×C₁₁	semidirect
279. C₂×#106	C₂²×C₁₁	semidirect
281. C₂×#104	C₂²×C₁₁	semidirect
283. #418	C₂²×C₁₁	semidirect
286. #417	C₂²×C₁₁	semidirect
290. C₂×#102	C₂²×C₁₁	semidirect
291. C₂×#100	C₂²×C₁₁	semidirect
292. #405	C₂²×C₁₁	semidirect
293. C₂×#97	C₂²×C₁₁	semidirect
294. #390	C₂²×C₁₁	semidirect
295. #343	C₂²×C₁₁	semidirect
296. #341	C₂²×C₁₁	semidirect
297. #339	C₂²×C₁₁	semidirect
325. H(5,𝔽₂)	C₂×C₄×C₁₁	semidirect
336. AGL(1,ℤ/8)	C₂×C₄×C₁₁	semidirect
348. C₂×D₈	C₂×C₄×C₁₁	semidirect
353. #131	C₂×C₄×C₁₁	semidirect
439. Q₁₆	C₁₁×C₂²⋊C₄	semidirect
441. SD₁₆	C₁₁×C₂²⋊C₄	semidirect
445. D₈	C₁₁×C₂²⋊C₄	semidirect
477. C₁₁	#22463	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×#576	2
C₂×C₁₁×#444	2
C₁₁×#2952	2
C₁₁×#2897	2
C₁₁×#1978	2
C₁₁×#1972	2
C₁₁×#1907	2
C₁₁×#1883	2
C₁₁×#1815	2
C₁₁×#1792	2
C₁₁×#1765	2
#22463	11

Subgroups — C11×#22463 #14599656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22463 #14599656