Subgroups — C₁₁×#22286 #14599479

Order 2816.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3155	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1978	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1911	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1910	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1904	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1903	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1833	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
15	C₁₁×#568	C₂²	1	2	yes	—
16	C₁₁×#535	C₂²	1	2	yes	—
17	C₁₁×#518	C₂²	1	2	yes	—
18	C₁₁×#496	C₄	1	4	yes	complemented
19	C₁₁×#495	C₄	1	2	yes	complemented
20	C₁₁×#493	C₄	1	2	yes	complemented
21	C₁₁×#444	—	2	2	no	—
22	C₁₁×#443	—	2	2	no	—
23	C₁₁×#442	—	2	2	no	—
24	C₄×C₁₁×D₈	—	2	2	no	—
25	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
26	C₁₁×#427	C₂²	1	1	yes	characteristic
27	C₁₁×#421	C₂²	1	2	yes	—
28	C₁₁×#421	C₂²	1	2	yes	—
29	C₁₁×#418	C₂²	1	2	yes	—
30	C₁₁×#418	C₂²	1	2	yes	—
31	C₂×C₁₁×#100	C₂²	1	2	yes	—
32	C₁₁×#410	C₂²	1	2	yes	—
33	C₁₁×#405	C₂²	1	1	yes	characteristic
34	C₁₁×#405	C₂²	1	1	yes	characteristic
35	C₁₁×#405	C₂²	1	1	yes	characteristic
36	C₁₁×#344	C₂²	1	2	yes	—
37	C₁₁×#338	C₂²	1	1	yes	characteristic
38	C₁₁×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
39	C₁₁×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
40	C₁₁×H(3,ℤ/4)	C₂²	1	2	yes	—
41	C₁₁×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
42	C₂×C₁₁×#41	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
44	C₁₁×AGL(1,ℤ/8)	—	4	2	no	—
45	C₁₁×AGL(1,ℤ/8)	—	4	2	no	—
46	C₁₁×#135	—	2	1	no	—
47	C₁₁×#135	—	2	1	no	—
48	C₁₁×#135	—	2	1	no	—
49	C₁₁×#135	—	2	1	no	—
50	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	complemented
52	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	complemented
53	C₂×C₁₁×D₈	—	2	1	no	—
54	C₂×C₁₁×D₈	—	2	1	no	—
55	C₂×C₁₁×D₈	—	2	1	no	—
56	C₂×C₁₁×D₈	—	2	1	no	—
57	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
61	C₁₁×#131	—	2	4	no	—
62	C₁₁×#131	—	4	2	no	—
63	C₂×C₁₁×M₁₆	—	4	2	no	—
64	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
66	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₁₁×#127	C₂×C₄	1	4	yes	complemented
70	C₁₁×#124	C₂×C₄	1	4	yes	complemented
71	C₁₁×#121	—	4	2	no	—
72	C₁₁×#120	—	4	2	no	—
73	C₄×D₄×C₁₁	—	2	4	no	—
74	C₄×D₄×C₁₁	—	4	2	no	—
75	C₁₁×#117	C₂³	1	1	yes	characteristic
76	C₁₁×#117	C₂³	1	2	yes	—
77	C₁₁×#117	C₂³	1	1	yes	characteristic
78	C₁₁×#117	C₂³	1	1	yes	characteristic
79	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
80	C₁₁×#108	—	2	1	no	—
81	C₁₁×#108	—	2	1	no	—
82	C₁₁×#107	—	2	1	no	—
83	C₁₁×#106	—	2	1	no	—
84	C₁₁×#104	—	2	4	no	—
85	C₁₁×#104	—	4	2	no	—
86	C₁₁×#102	—	2	4	no	—
87	C₁₁×#102	—	4	2	no	—
88	C₁₁×#100	—	4	2	no	—
89	C₁₁×#99	—	4	2	no	—
90	C₁₁×#97	—	2	1	no	—
91	C₁₁×#97	C₂×C₄	1	2	yes	complemented
92	C₁₁×#97	D₄	1	2	yes	complemented
93	C₄×C₈×C₁₁	—	2	1	no	—
94	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₁₁	D₄	1	2	yes	complemented
96	#22286	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₁	—	2	2	no	—
98	C₁₁×#41	—	2	2	no	—
99	C₁₁×#41	—	2	2	no	—
100	C₁₁×#41	—	2	2	no	—
101	C₁₁×#41	—	2	2	no	—
102	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	—	2	2	no	—
106	C₂×D₄×C₁₁	—	2	2	no	—
107	C₂×D₄×C₁₁	—	2	2	no	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	4	4	no	—
110	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
111	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₁	—	2	2	no	—
113	C₂²×C₄×C₁₁	—	4	4	no	—
114	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
115	C₁₁×Q₁₆	—	2	1	no	—
116	C₁₁×Q₁₆	—	2	1	no	—
117	C₁₁×SD₁₆	—	2	2	no	—
118	C₁₁×SD₁₆	—	2	2	no	—
119	C₁₁×SD₁₆	—	4	4	no	—
120	C₁₁×D₈	—	2	2	no	—
121	C₁₁×D₈	—	2	2	no	—
122	C₁₁×D₈	—	2	2	no	—
123	C₁₁×D₈	—	2	2	no	—
124	C₁₁×D₈	—	2	1	no	—
125	C₁₁×D₈	—	2	1	no	—
126	C₁₁×D₈	—	4	4	no	—
127	C₁₁×M₁₆	—	2	2	no	—
128	C₁₁×M₁₆	—	2	1	no	—
129	C₁₁×M₁₆	—	2	1	no	—
130	C₁₁×M₁₆	—	2	1	no	—
131	C₁₁×M₁₆	—	2	1	no	—
132	C₁₁×M₁₆	—	2	1	no	—
133	C₁₁×M₁₆	—	2	2	no	—
134	C₁₁×M₁₆	—	2	1	no	—
135	C₁₁×M₁₆	—	4	4	no	—
136	C₂×C₈×C₁₁	—	2	1	no	—
137	C₂×C₈×C₁₁	—	2	2	no	—
138	C₂×C₈×C₁₁	—	4	4	no	—
139	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
146	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
147	C₁₁×C₄⋊C₄	—	2	1	no	—
148	C₁₁×C₄⋊C₄	—	2	1	no	—
149	C₁₁×C₄⋊C₄	—	2	2	no	—
150	C₁₁×C₄⋊C₄	—	2	1	no	—
151	C₁₁×C₂²⋊C₄	—	2	1	no	—
152	C₁₁×C₂²⋊C₄	—	2	1	no	—
153	C₁₁×C₂²⋊C₄	—	2	1	no	—
154	C₁₁×C₂²⋊C₄	—	2	2	no	—
155	C₁₁×C₂²⋊C₄	—	4	4	no	—
156	C₁₁×C₂²⋊C₄	—	4	4	no	—
157	C₄²×C₁₁	—	2	1	no	—
158	C₄²×C₁₁	—	2	2	no	—
159	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
160	C₄²×C₁₁	C₂×D₄	1	2	yes	—
161	#3155	C₂×C₁₁	1	1	yes	characteristic
162	#2957	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#2948	C₂×C₁₁	1	1	yes	characteristic, complemented
164	#1978	C₂×C₁₁	1	1	yes	characteristic, complemented
165	#1976	C₂×C₁₁	1	1	yes	characteristic, complemented
166	#1911	C₂×C₁₁	1	2	yes	complemented
167	#1910	C₂×C₁₁	1	2	yes	complemented
168	#1904	C₂×C₁₁	1	2	yes	complemented
169	#1903	C₂×C₁₁	1	2	yes	complemented
170	#1833	C₂×C₁₁	1	1	yes	characteristic, complemented
171	#1747	C₂×C₁₁	1	1	yes	characteristic, complemented
172	C₂³×C₁₁	—	2	4	no	—
173	C₂³×C₁₁	—	2	2	no	—
174	C₂³×C₁₁	—	4	2	no	—
175	C₂³×C₁₁	—	4	2	no	—
176	C₂³×C₁₁	—	16	2	no	—
177	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
178	Q₈×C₁₁	—	2	2	no	—
179	Q₈×C₁₁	—	2	2	no	—
180	D₄×C₁₁	—	2	4	no	—
181	D₄×C₁₁	—	2	2	no	—
182	D₄×C₁₁	—	2	2	no	—
183	D₄×C₁₁	—	2	4	no	—
184	D₄×C₁₁	—	4	2	no	—
185	D₄×C₁₁	—	4	2	no	—
186	D₄×C₁₁	—	4	2	no	—
187	D₄×C₁₁	—	4	2	no	—
188	D₄×C₁₁	—	16	4	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	2	no	—
192	C₂×C₄×C₁₁	—	4	2	no	—
193	C₂×C₄×C₁₁	—	4	2	no	—
194	C₂×C₄×C₁₁	—	4	2	no	—
195	C₂×C₄×C₁₁	—	4	1	no	—
196	C₂×C₄×C₁₁	—	16	4	no	—
197	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
203	C₈×C₁₁	—	2	2	no	—
204	C₈×C₁₁	—	2	2	no	—
205	C₈×C₁₁	—	4	2	no	—
206	C₈×C₁₁	—	4	1	no	—
207	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
208	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
209	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
210	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
211	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
212	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
213	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
214	#568	C₂²×C₁₁	1	2	yes	—
215	#535	C₂²×C₁₁	1	2	yes	—
216	#518	C₂²×C₁₁	1	2	yes	—
217	#496	C₄×C₁₁	1	4	yes	complemented
218	#495	C₄×C₁₁	1	2	yes	complemented
219	#493	C₄×C₁₁	1	2	yes	complemented
220	#444	—	2	2	no	—
221	#443	—	2	2	no	—
222	#442	—	2	2	no	—
223	C₄×D₈	—	2	2	no	—
224	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
225	#427	C₂²×C₁₁	1	1	yes	characteristic
226	#421	C₂²×C₁₁	1	2	yes	—
227	#421	C₂²×C₁₁	1	2	yes	—
228	#418	C₂²×C₁₁	1	2	yes	—
229	#418	C₂²×C₁₁	1	2	yes	—
230	C₂×#100	C₂²×C₁₁	1	2	yes	—
231	#410	C₂²×C₁₁	1	2	yes	—
232	#405	C₂²×C₁₁	1	1	yes	characteristic
233	#405	C₂²×C₁₁	1	1	yes	characteristic
234	#405	C₂²×C₁₁	1	1	yes	characteristic
235	#344	C₂²×C₁₁	1	2	yes	—
236	#338	C₂²×C₁₁	1	1	yes	characteristic
237	H(3,ℤ/4)	C₂²×C₁₁	1	2	yes	—
238	H(3,ℤ/4)	C₂²×C₁₁	1	1	yes	characteristic
239	H(3,ℤ/4)	C₂²×C₁₁	1	1	yes	characteristic
240	H(3,ℤ/4)	C₂²×C₁₁	1	1	yes	characteristic
241	C₂²×C₁₁	—	4	1	no	—
242	C₂²×C₁₁	—	4	2	no	—
243	C₂²×C₁₁	—	4	4	no	—
244	C₂²×C₁₁	—	8	2	no	—
245	C₂²×C₁₁	—	8	4	no	—
246	C₂²×C₁₁	—	8	4	no	—
247	C₂²×C₁₁	—	16	2	no	—
248	C₂²×C₁₁	#518	1	1	yes	characteristic
249	C₂²×C₁₁	#535	1	1	yes	characteristic
250	C₂²×C₁₁	#540	1	1	yes	characteristic
251	C₄×C₁₁	—	4	2	no	—
252	C₄×C₁₁	—	4	2	no	—
253	C₄×C₁₁	—	4	2	no	—
254	C₄×C₁₁	—	8	1	no	—
255	C₄×C₁₁	—	8	2	no	—
256	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₁₁	#518	1	1	yes	characteristic
258	C₄×C₁₁	#535	1	1	yes	characteristic
259	C₄×C₁₁	#540	1	1	yes	characteristic
260	C₂×#41	C₂³×C₁₁	1	2	yes	—
261	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
262	AGL(1,ℤ/8)	—	4	2	no	—
263	AGL(1,ℤ/8)	—	4	2	no	—
264	#135	—	2	1	no	—
265	#135	—	2	1	no	—
266	#135	—	2	1	no	—
267	#135	—	2	1	no	—
268	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
269	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	complemented
270	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
271	C₂×D₈	—	2	1	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×D₈	—	2	1	no	—
275	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
276	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
277	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
278	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	complemented
279	#131	—	2	4	no	—
280	#131	—	4	2	no	—
281	C₂×M₁₆	—	4	2	no	—
282	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
283	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
284	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
285	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
287	#127	C₂×C₄×C₁₁	1	4	yes	complemented
288	#124	C₂×C₄×C₁₁	1	4	yes	complemented
289	#121	—	4	2	no	—
290	#120	—	4	2	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	4	2	no	—
293	#117	C₂³×C₁₁	1	2	yes	—
294	#117	C₂³×C₁₁	1	1	yes	characteristic
295	#117	C₂³×C₁₁	1	1	yes	characteristic
296	#117	C₂³×C₁₁	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	4	2	no	—
298	#108	—	2	1	no	—
299	#108	—	2	1	no	—
300	#107	—	2	1	no	—
301	#106	—	2	1	no	—
302	#104	—	2	4	no	—
303	#104	—	4	2	no	—
304	#102	—	2	4	no	—
305	#102	—	4	2	no	—
306	#100	—	4	2	no	—
307	#99	—	4	2	no	—
308	#97	—	2	1	no	—
309	#97	C₂×C₄×C₁₁	1	2	yes	complemented
310	#97	D₄×C₁₁	1	2	yes	complemented
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	complemented
313	C₄×C₈	D₄×C₁₁	1	2	yes	complemented
314	C₂×C₁₁	—	2	1	no	—
315	C₂×C₁₁	—	2	1	no	—
316	C₂×C₁₁	—	2	1	no	—
317	C₂×C₁₁	—	8	2	no	—
318	C₂×C₁₁	—	8	4	no	—
319	C₂×C₁₁	#2328	1	1	yes	characteristic
320	C₂⁴	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
334	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
338	Q₁₆	—	2	1	no	—
339	Q₁₆	—	2	1	no	—
340	SD₁₆	—	2	2	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	4	4	no	—
343	D₈	—	2	2	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	1	no	—
348	D₈	—	2	1	no	—
349	D₈	—	4	4	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	4	4	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	4	no	—
362	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
363	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
364	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
365	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
366	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
368	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
369	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	2	no	—
382	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
383	C₄²	C₂×D₄×C₁₁	1	2	yes	—
384	C₁₁	#22286	1	1	yes	characteristic, direct product factor, Sylow
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	16	2	no	—
390	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	16	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	16	4	no	—
410	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
412	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
413	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	1	no	—
420	C₈	C₄×D₄×C₁₁	1	1	yes	characteristic
421	C₈	C₄×D₄×C₁₁	1	1	yes	characteristic
422	C₈	C₄×D₄×C₁₁	1	1	yes	characteristic
423	C₈	C₄×D₄×C₁₁	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	16	2	no	—
431	C₂²	C₁₁×#518	1	1	yes	characteristic
432	C₂²	C₁₁×#535	1	1	yes	characteristic
433	C₂²	C₁₁×#540	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	1	no	—
439	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
440	C₄	C₁₁×#518	1	1	yes	characteristic
441	C₄	C₁₁×#535	1	1	yes	characteristic
442	C₄	C₁₁×#540	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	8	2	no	—
448	C₂	C₁₁×#2328	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	#2328
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₁₁×#3155	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2957	C₂	semidirect
3. C₁₁×#2948	C₂	semidirect
4. C₁₁×#1978	C₂	semidirect
5. C₁₁×#1976	C₂	semidirect
6. C₁₁×#1911	C₂	semidirect
7. C₁₁×#1910	C₂	semidirect
8. C₁₁×#1904	C₂	semidirect
9. C₁₁×#1903	C₂	semidirect
10. C₁₁×#1833	C₂	semidirect
11. C₁₁×#1747	C₂	semidirect
18. C₁₁×#496	C₄	semidirect
19. C₁₁×#495	C₄	semidirect
20. C₁₁×#493	C₄	semidirect
50. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
51. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
52. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
59. C₂×C₁₁×D₈	C₂×C₄	semidirect
60. C₂×C₁₁×D₈	C₂×C₄	semidirect
69. C₁₁×#127	C₂×C₄	semidirect
70. C₁₁×#124	C₂×C₄	semidirect
91. C₁₁×#97	C₂×C₄	semidirect
92. C₁₁×#97	D₄	semidirect
94. C₄×C₈×C₁₁	C₂×C₄	semidirect
95. C₄×C₈×C₁₁	D₄	semidirect
96. #22286	C₁₁	direct (N × H)
162. #2957	C₂×C₁₁	semidirect
163. #2948	C₂×C₁₁	semidirect
164. #1978	C₂×C₁₁	semidirect
165. #1976	C₂×C₁₁	semidirect
166. #1911	C₂×C₁₁	semidirect
167. #1910	C₂×C₁₁	semidirect
168. #1904	C₂×C₁₁	semidirect
169. #1903	C₂×C₁₁	semidirect
170. #1833	C₂×C₁₁	semidirect
171. #1747	C₂×C₁₁	semidirect
217. #496	C₄×C₁₁	semidirect
218. #495	C₄×C₁₁	semidirect
219. #493	C₄×C₁₁	semidirect
268. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
269. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
270. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
277. C₂×D₈	C₂×C₄×C₁₁	semidirect
278. C₂×D₈	C₂×C₄×C₁₁	semidirect
287. #127	C₂×C₄×C₁₁	semidirect
288. #124	C₂×C₄×C₁₁	semidirect
309. #97	C₂×C₄×C₁₁	semidirect
310. #97	D₄×C₁₁	semidirect
312. C₄×C₈	C₂×C₄×C₁₁	semidirect
313. C₄×C₈	D₄×C₁₁	semidirect
384. C₁₁	#22286	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3155	2
C₁₁×#2957	2
C₁₁×#2948	2
C₁₁×#1978	2
C₁₁×#1976	2
C₁₁×#1911	2
C₁₁×#1910	2
C₁₁×#1904	2
C₁₁×#1903	2
C₁₁×#1833	2
C₁₁×#1747	2
#22286	11

Subgroups — C11×#22286 #14599479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22286 #14599479