Subgroups — C₁₁×#22285 #14599478

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3156	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2957	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1976	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1912	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1909	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1905	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1902	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×#137	C₂²	1	2	yes	—
13	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
15	C₁₁×#568	C₂²	1	2	yes	—
16	C₁₁×#536	C₂²	1	2	yes	—
17	C₁₁×#519	C₂²	1	2	yes	—
18	C₁₁×#497	C₄	1	4	yes	complemented
19	C₁₁×#495	C₄	1	2	yes	complemented
20	C₁₁×#494	C₄	1	2	yes	complemented
21	C₁₁×#444	—	2	2	no	—
22	C₁₁×#443	—	2	2	no	—
23	C₁₁×#441	—	2	2	no	—
24	C₄×C₁₁×Q₁₆	—	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×#419	C₂²	1	2	yes	—
30	C₁₁×#419	C₂²	1	2	yes	—
31	C₂×C₁₁×#101	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×Q₈×C₁₁	C₂³	1	2	yes	—
44	C₁₁×#137	—	4	2	no	—
45	C₁₁×#137	—	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	—	2	1	no	—
51	C₂×C₁₁×Q₁₆	—	2	1	no	—
52	C₂×C₁₁×Q₁₆	—	2	1	no	—
53	C₂×C₁₁×Q₁₆	—	2	1	no	—
54	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
58	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	—
60	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
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×C₄⋊Q₈	C₂×C₄	1	4	yes	—
70	C₁₁×#124	C₂×C₄	1	4	yes	—
71	C₁₁×#123	—	4	2	no	—
72	C₁₁×C₂²⋊Q₈	—	4	2	no	—
73	C₄×Q₈×C₁₁	—	2	4	no	—
74	C₄×Q₈×C₁₁	—	4	2	no	—
75	C₁₁×#117	—	4	2	no	—
76	C₁₁×#117	C₂³	1	1	yes	characteristic
77	C₁₁×#117	C₂³	1	2	yes	—
78	C₁₁×#117	C₂³	1	1	yes	characteristic
79	C₁₁×#117	C₂³	1	1	yes	characteristic
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×#103	—	2	4	no	—
87	C₁₁×#103	—	4	2	no	—
88	C₁₁×#101	—	4	2	no	—
89	C₁₁×#99	—	4	2	no	—
90	C₁₁×#97	—	2	1	no	—
91	C₁₁×#97	C₂×C₄	1	2	yes	—
92	C₁₁×#97	D₄	1	2	yes	—
93	C₄×C₈×C₁₁	—	2	1	no	—
94	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₁₁	D₄	1	2	yes	—
96	#22285	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₁₁×#41	—	2	2	no	—
98	C₁₁×#41	—	2	2	no	—
99	C₁₁×#41	—	2	2	no	—
100	C₁₁×#41	—	2	2	no	—
101	C₂×Q₈×C₁₁	—	2	2	no	—
102	C₂×Q₈×C₁₁	—	2	2	no	—
103	C₂×Q₈×C₁₁	—	2	2	no	—
104	C₂×Q₈×C₁₁	—	2	2	no	—
105	C₂×Q₈×C₁₁	—	2	2	no	—
106	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
107	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₁₁	—	2	2	no	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
113	C₁₁×Q₁₆	—	2	2	no	—
114	C₁₁×Q₁₆	—	2	2	no	—
115	C₁₁×Q₁₆	—	2	2	no	—
116	C₁₁×Q₁₆	—	2	2	no	—
117	C₁₁×Q₁₆	—	2	1	no	—
118	C₁₁×Q₁₆	—	2	1	no	—
119	C₁₁×Q₁₆	—	4	4	no	—
120	C₁₁×SD₁₆	—	2	2	no	—
121	C₁₁×SD₁₆	—	2	2	no	—
122	C₁₁×SD₁₆	—	4	4	no	—
123	C₁₁×D₈	—	2	1	no	—
124	C₁₁×D₈	—	2	1	no	—
125	C₁₁×M₁₆	—	2	2	no	—
126	C₁₁×M₁₆	—	2	1	no	—
127	C₁₁×M₁₆	—	2	1	no	—
128	C₁₁×M₁₆	—	2	1	no	—
129	C₁₁×M₁₆	—	2	1	no	—
130	C₁₁×M₁₆	—	2	1	no	—
131	C₁₁×M₁₆	—	2	2	no	—
132	C₁₁×M₁₆	—	2	1	no	—
133	C₁₁×M₁₆	—	4	4	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	—	4	4	no	—
137	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
144	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	—	2	1	no	—
147	C₁₁×C₄⋊C₄	—	2	2	no	—
148	C₁₁×C₄⋊C₄	—	2	1	no	—
149	C₁₁×C₄⋊C₄	—	4	4	no	—
150	C₁₁×C₄⋊C₄	—	4	4	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	C₄²×C₁₁	—	2	1	no	—
157	C₄²×C₁₁	—	2	2	no	—
158	C₄²×C₁₁	—	4	4	no	—
159	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
160	C₄²×C₁₁	C₂×D₄	1	2	yes	—
161	#3156	C₂×C₁₁	1	1	yes	characteristic
162	#2957	C₂×C₁₁	1	1	yes	characteristic
163	#2950	C₂×C₁₁	1	1	yes	characteristic, complemented
164	#1979	C₂×C₁₁	1	1	yes	characteristic, complemented
165	#1976	C₂×C₁₁	1	1	yes	characteristic
166	#1912	C₂×C₁₁	1	2	yes	complemented
167	#1909	C₂×C₁₁	1	2	yes	complemented
168	#1905	C₂×C₁₁	1	2	yes	complemented
169	#1902	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	2	no	—
173	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
174	Q₈×C₁₁	—	2	2	no	—
175	Q₈×C₁₁	—	2	4	no	—
176	Q₈×C₁₁	—	2	4	no	—
177	Q₈×C₁₁	—	2	2	no	—
178	Q₈×C₁₁	—	4	2	no	—
179	Q₈×C₁₁	—	4	2	no	—
180	D₄×C₁₁	—	2	2	no	—
181	D₄×C₁₁	—	2	2	no	—
182	D₄×C₁₁	—	4	2	no	—
183	D₄×C₁₁	—	4	2	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	4	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	4	2	no	—
189	C₂×C₄×C₁₁	—	4	2	no	—
190	C₂×C₄×C₁₁	—	4	2	no	—
191	C₂×C₄×C₁₁	—	4	2	no	—
192	C₂×C₄×C₁₁	—	4	2	no	—
193	C₂×C₄×C₁₁	—	4	1	no	—
194	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
200	C₈×C₁₁	—	2	2	no	—
201	C₈×C₁₁	—	2	2	no	—
202	C₈×C₁₁	—	4	2	no	—
203	C₈×C₁₁	—	4	1	no	—
204	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
205	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
206	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
207	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
208	C₂×#137	C₂²×C₁₁	1	2	yes	—
209	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
210	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
211	#568	C₂²×C₁₁	1	2	yes	—
212	#536	C₂²×C₁₁	1	2	yes	—
213	#519	C₂²×C₁₁	1	2	yes	—
214	#497	C₄×C₁₁	1	4	yes	complemented
215	#495	C₄×C₁₁	1	2	yes	complemented
216	#494	C₄×C₁₁	1	2	yes	complemented
217	#444	—	2	2	no	—
218	#443	—	2	2	no	—
219	#441	—	2	2	no	—
220	C₄×Q₁₆	—	2	2	no	—
221	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
222	#427	C₂²×C₁₁	1	1	yes	characteristic
223	#421	C₂²×C₁₁	1	2	yes	—
224	#421	C₂²×C₁₁	1	2	yes	—
225	#419	C₂²×C₁₁	1	2	yes	—
226	#419	C₂²×C₁₁	1	2	yes	—
227	C₂×#101	C₂²×C₁₁	1	2	yes	—
228	#410	C₂²×C₁₁	1	2	yes	—
229	#405	C₂²×C₁₁	1	1	yes	characteristic
230	#405	C₂²×C₁₁	1	1	yes	characteristic
231	#405	C₂²×C₁₁	1	1	yes	characteristic
232	#344	C₂²×C₁₁	1	2	yes	—
233	#338	C₂²×C₁₁	1	1	yes	characteristic
234	H(3,ℤ/4)	C₂²×C₁₁	1	2	yes	—
235	H(3,ℤ/4)	C₂²×C₁₁	1	1	yes	characteristic
236	H(3,ℤ/4)	C₂²×C₁₁	1	1	yes	characteristic
237	H(3,ℤ/4)	C₂²×C₁₁	1	1	yes	characteristic
238	C₂²×C₁₁	—	4	1	no	—
239	C₂²×C₁₁	—	4	2	no	—
240	C₂²×C₁₁	—	8	2	no	—
241	C₂²×C₁₁	#518	1	1	yes	characteristic
242	C₂²×C₁₁	#535	1	1	yes	characteristic
243	C₂²×C₁₁	#540	1	1	yes	characteristic
244	C₄×C₁₁	—	4	2	no	—
245	C₄×C₁₁	—	4	2	no	—
246	C₄×C₁₁	—	4	2	no	—
247	C₄×C₁₁	—	4	4	no	—
248	C₄×C₁₁	—	8	2	no	—
249	C₄×C₁₁	—	8	1	no	—
250	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
251	C₄×C₁₁	#518	1	1	yes	characteristic
252	C₄×C₁₁	#535	1	1	yes	characteristic
253	C₄×C₁₁	#540	1	1	yes	characteristic
254	C₂×#41	C₂³×C₁₁	1	2	yes	—
255	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
256	#137	—	4	2	no	—
257	#137	—	4	2	no	—
258	#135	—	2	1	no	—
259	#135	—	2	1	no	—
260	#135	—	2	1	no	—
261	#135	—	2	1	no	—
262	C₂×Q₁₆	—	2	1	no	—
263	C₂×Q₁₆	—	2	1	no	—
264	C₂×Q₁₆	—	2	1	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
267	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
268	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
269	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
270	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
271	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	—
272	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
273	#131	—	2	4	no	—
274	#131	—	4	2	no	—
275	C₂×M₁₆	—	4	2	no	—
276	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
277	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
278	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
279	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
281	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	—
282	#124	C₂×C₄×C₁₁	1	4	yes	—
283	#123	—	4	2	no	—
284	C₂²⋊Q₈	—	4	2	no	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	—	4	2	no	—
287	#117	—	4	2	no	—
288	#117	C₂³×C₁₁	1	2	yes	—
289	#117	C₂³×C₁₁	1	1	yes	characteristic
290	#117	C₂³×C₁₁	1	1	yes	characteristic
291	#117	C₂³×C₁₁	1	1	yes	characteristic
292	#108	—	2	1	no	—
293	#108	—	2	1	no	—
294	#107	—	2	1	no	—
295	#106	—	2	1	no	—
296	#104	—	2	4	no	—
297	#104	—	4	2	no	—
298	#103	—	2	4	no	—
299	#103	—	4	2	no	—
300	#101	—	4	2	no	—
301	#99	—	4	2	no	—
302	#97	—	2	1	no	—
303	#97	C₂×C₄×C₁₁	1	2	yes	—
304	#97	D₄×C₁₁	1	2	yes	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
307	C₄×C₈	D₄×C₁₁	1	2	yes	—
308	C₂×C₁₁	—	2	1	no	—
309	C₂×C₁₁	—	2	1	no	—
310	C₂×C₁₁	—	2	1	no	—
311	C₂×C₁₁	—	8	2	no	—
312	C₂×C₁₁	#2328	1	1	yes	characteristic
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
323	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
329	Q₁₆	—	2	2	no	—
330	Q₁₆	—	2	2	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	2	1	no	—
334	Q₁₆	—	2	1	no	—
335	Q₁₆	—	4	4	no	—
336	SD₁₆	—	2	2	no	—
337	SD₁₆	—	2	2	no	—
338	SD₁₆	—	4	4	no	—
339	D₈	—	2	1	no	—
340	D₈	—	2	1	no	—
341	M₁₆	—	2	1	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	1	no	—
349	M₁₆	—	4	4	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	4	4	no	—
353	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
355	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
356	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
357	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
358	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
359	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
360	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	4	no	—
375	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
376	C₄²	C₂×D₄×C₁₁	1	2	yes	—
377	C₁₁	#22285	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	2	no	—
379	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	4	no	—
382	Q₈	—	2	4	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
402	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
403	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	1	no	—
410	C₈	C₄×D₄×C₁₁	1	1	yes	characteristic
411	C₈	C₄×D₄×C₁₁	1	1	yes	characteristic
412	C₈	C₄×D₄×C₁₁	1	1	yes	characteristic
413	C₈	C₄×D₄×C₁₁	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₁₁×#518	1	1	yes	characteristic
418	C₂²	C₁₁×#535	1	1	yes	characteristic
419	C₂²	C₁₁×#540	1	1	yes	characteristic
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	1	no	—
426	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
427	C₄	C₁₁×#518	1	1	yes	characteristic
428	C₄	C₁₁×#535	1	1	yes	characteristic
429	C₄	C₁₁×#540	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	8	2	no	—
434	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	C₂×C₁₁×#135	C₂²
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
3. C₁₁×#2950	C₂	semidirect
4. C₁₁×#1979	C₂	semidirect
6. C₁₁×#1912	C₂	semidirect
7. C₁₁×#1909	C₂	semidirect
8. C₁₁×#1905	C₂	semidirect
9. C₁₁×#1902	C₂	semidirect
10. C₁₁×#1833	C₂	semidirect
11. C₁₁×#1747	C₂	semidirect
18. C₁₁×#497	C₄	semidirect
19. C₁₁×#495	C₄	semidirect
20. C₁₁×#494	C₄	semidirect
96. #22285	C₁₁	direct (N × H)
163. #2950	C₂×C₁₁	semidirect
164. #1979	C₂×C₁₁	semidirect
166. #1912	C₂×C₁₁	semidirect
167. #1909	C₂×C₁₁	semidirect
168. #1905	C₂×C₁₁	semidirect
169. #1902	C₂×C₁₁	semidirect
170. #1833	C₂×C₁₁	semidirect
171. #1747	C₂×C₁₁	semidirect
214. #497	C₄×C₁₁	semidirect
215. #495	C₄×C₁₁	semidirect
216. #494	C₄×C₁₁	semidirect
377. C₁₁	#22285	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×#3156	2
C₁₁×#2957	2
C₁₁×#2950	2
C₁₁×#1979	2
C₁₁×#1976	2
C₁₁×#1912	2
C₁₁×#1909	2
C₁₁×#1905	2
C₁₁×#1902	2
C₁₁×#1833	2
C₁₁×#1747	2
#22285	11

Subgroups — C11×#22285 #14599478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22285 #14599478