Subgroups — C₂×C₁₁×#1717 #14596802

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1717	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×SD₁₆	—	2	2	no	—
10	C₂²×C₁₁×D₈	—	2	2	no	—
11	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
15	C₁₁×#493	—	2	2	no	—
16	C₁₁×#493	C₂²	1	4	yes	—
17	C₁₁×#492	—	2	2	no	—
18	C₁₁×#492	C₂²	1	4	yes	complemented
19	C₁₁×#487	—	2	2	no	—
20	C₁₁×#487	C₂²	1	4	yes	complemented
21	C₁₁×#486	—	2	2	no	—
22	C₁₁×#486	—	2	2	no	—
23	C₁₁×#486	—	2	2	no	—
24	C₁₁×#486	C₂²	1	4	yes	complemented
25	C₁₁×#486	C₂²	1	4	yes	complemented
26	C₁₁×#486	C₂²	1	4	yes	complemented
27	C₂×C₁₁×#103	—	2	2	no	—
28	C₂×C₁₁×#102	—	2	2	no	—
29	C₂×C₁₁×#102	—	2	2	no	—
30	C₂×C₁₁×#102	—	2	2	no	—
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#322	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₁₁	—	2	1	no	—
36	C₂²×Q₈×C₁₁	—	2	1	no	—
37	C₂²×D₄×C₁₁	—	2	1	no	—
38	C₂²×D₄×C₁₁	—	2	1	no	—
39	C₂²×D₄×C₁₁	—	2	1	no	—
40	C₂²×D₄×C₁₁	—	2	1	no	—
41	C₂²×D₄×C₁₁	—	2	1	no	—
42	C₂²×D₄×C₁₁	—	2	1	no	—
43	C₂×C₁₁×SD₁₆	—	2	8	no	—
44	C₂×C₁₁×SD₁₆	—	4	8	no	—
45	C₂×C₁₁×D₈	—	2	8	no	—
46	C₂×C₁₁×D₈	—	4	8	no	—
47	C₂²×C₈×C₁₁	D₄	1	2	yes	—
48	C₂²×C₈×C₁₁	D₄	1	2	yes	—
49	C₂²×C₈×C₁₁	D₄	1	2	yes	—
50	C₁₁×C₄⋊Q₈	—	2	1	no	—
51	C₁₁×C₄⋊Q₈	—	2	1	no	—
52	C₁₁×C₄⋊Q₈	—	2	1	no	—
53	C₁₁×C₄⋊Q₈	—	2	1	no	—
54	C₁₁×C₄⋊Q₈	—	2	1	no	—
55	C₁₁×C₄⋊Q₈	—	2	1	no	—
56	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₁×#127	—	2	1	no	—
59	C₁₁×#127	—	2	1	no	—
60	C₁₁×#127	—	2	1	no	—
61	C₁₁×#127	—	2	1	no	—
62	C₁₁×#127	—	2	1	no	—
63	C₁₁×#127	—	2	1	no	—
64	C₁₁×#127	C₂³	1	2	yes	—
65	C₁₁×#127	C₂³	1	2	yes	—
66	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
71	C₁₁×#103	—	2	8	no	—
72	C₁₁×#102	—	2	8	no	—
73	C₁₁×#102	—	2	8	no	—
74	C₁₁×#102	—	2	8	no	—
75	C₄×C₈×C₁₁	D₄	1	2	yes	—
76	C₄×C₈×C₁₁	D₄	1	2	yes	—
77	C₄×C₈×C₁₁	D₄	1	2	yes	—
78	C₄×C₈×C₁₁	C₂³	1	2	yes	—
79	C₄×C₈×C₁₁	C₂³	1	2	yes	—
80	C₄×C₈×C₁₁	C₂³	1	2	yes	—
81	C₂×#1717	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₁	—	4	1	no	—
83	C₂⁴×C₁₁	—	4	1	no	—
84	C₂×Q₈×C₁₁	—	2	2	no	—
85	C₂×Q₈×C₁₁	—	2	2	no	—
86	C₂×Q₈×C₁₁	—	4	1	no	—
87	C₂×Q₈×C₁₁	—	4	1	no	—
88	C₂×Q₈×C₁₁	—	4	4	no	—
89	C₂×Q₈×C₁₁	—	4	4	no	—
90	C₂×D₄×C₁₁	—	2	2	no	—
91	C₂×D₄×C₁₁	—	2	2	no	—
92	C₂×D₄×C₁₁	—	2	2	no	—
93	C₂×D₄×C₁₁	—	2	2	no	—
94	C₂×D₄×C₁₁	—	2	2	no	—
95	C₂×D₄×C₁₁	—	2	2	no	—
96	C₂×D₄×C₁₁	—	4	1	no	—
97	C₂×D₄×C₁₁	—	4	1	no	—
98	C₂×D₄×C₁₁	—	4	1	no	—
99	C₂×D₄×C₁₁	—	4	1	no	—
100	C₂×D₄×C₁₁	—	4	1	no	—
101	C₂×D₄×C₁₁	—	4	1	no	—
102	C₂×D₄×C₁₁	—	4	4	no	—
103	C₂×D₄×C₁₁	—	4	4	no	—
104	C₂×D₄×C₁₁	—	4	4	no	—
105	C₂×D₄×C₁₁	—	4	4	no	—
106	C₂×D₄×C₁₁	—	4	4	no	—
107	C₂×D₄×C₁₁	—	4	4	no	—
108	C₂²×C₄×C₁₁	—	4	1	no	—
109	C₂²×C₄×C₁₁	—	4	1	no	—
110	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₁₁×SD₁₆	—	4	16	no	—
114	C₁₁×D₈	—	4	16	no	—
115	C₂×C₈×C₁₁	—	2	4	no	—
116	C₂×C₈×C₁₁	—	2	4	no	—
117	C₂×C₈×C₁₁	—	2	4	no	—
118	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
120	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
121	C₁₁×C₄⋊C₄	—	2	2	no	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	—	2	2	no	—
124	C₁₁×C₄⋊C₄	—	2	2	no	—
125	C₁₁×C₄⋊C₄	—	4	1	no	—
126	C₁₁×C₄⋊C₄	—	4	1	no	—
127	C₁₁×C₄⋊C₄	—	4	1	no	—
128	C₁₁×C₄⋊C₄	—	4	1	no	—
129	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
133	C₂×#493	C₂×C₁₁	1	1	yes	characteristic
134	C₂×#492	C₂×C₁₁	1	1	yes	characteristic, complemented
135	C₂×#487	C₂×C₁₁	1	1	yes	characteristic, complemented
136	C₂×#486	C₂×C₁₁	1	1	yes	characteristic, complemented
137	C₂×#486	C₂×C₁₁	1	1	yes	characteristic, complemented
138	C₂×#486	C₂×C₁₁	1	1	yes	characteristic, complemented
139	#1717	C₂×C₁₁	1	8	yes	direct product factor
140	C₂×#322	C₂×C₁₁	1	1	yes	characteristic, complemented
141	C₂³×C₁₁	—	4	2	no	—
142	C₂³×C₁₁	—	4	2	no	—
143	C₂³×C₁₁	—	8	2	no	—
144	C₂³×C₁₁	—	8	2	no	—
145	C₂³×C₁₁	—	8	2	no	—
146	C₂³×C₁₁	—	8	2	no	—
147	C₂³×C₁₁	—	8	2	no	—
148	C₂³×C₁₁	—	8	2	no	—
149	C₂³×C₁₁	#127	1	1	yes	characteristic
150	Q₈×C₁₁	—	4	4	no	—
151	Q₈×C₁₁	—	4	4	no	—
152	Q₈×C₁₁	—	8	2	no	—
153	Q₈×C₁₁	—	8	2	no	—
154	D₄×C₁₁	—	4	4	no	—
155	D₄×C₁₁	—	4	4	no	—
156	D₄×C₁₁	—	4	4	no	—
157	D₄×C₁₁	—	4	4	no	—
158	D₄×C₁₁	—	4	4	no	—
159	D₄×C₁₁	—	4	4	no	—
160	D₄×C₁₁	—	8	2	no	—
161	D₄×C₁₁	—	8	2	no	—
162	D₄×C₁₁	—	8	2	no	—
163	D₄×C₁₁	—	8	2	no	—
164	D₄×C₁₁	—	8	2	no	—
165	D₄×C₁₁	—	8	2	no	—
166	C₂×C₄×C₁₁	—	4	2	no	—
167	C₂×C₄×C₁₁	—	4	2	no	—
168	C₂×C₄×C₁₁	—	8	2	no	—
169	C₂×C₄×C₁₁	—	8	2	no	—
170	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
171	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
172	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
173	C₂×C₄×C₁₁	#135	1	4	yes	—
174	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
175	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
176	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₁₁	—	2	4	no	—
180	C₈×C₁₁	—	2	4	no	—
181	C₈×C₁₁	—	2	4	no	—
182	C₂²×SD₁₆	—	2	2	no	—
183	C₂²×D₈	—	2	2	no	—
184	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
185	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
186	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
187	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
188	#493	—	2	2	no	—
189	#493	C₂²×C₁₁	1	4	yes	—
190	#492	—	2	2	no	—
191	#492	C₂²×C₁₁	1	4	yes	complemented
192	#487	—	2	2	no	—
193	#487	C₂²×C₁₁	1	4	yes	complemented
194	#486	—	2	2	no	—
195	#486	—	2	2	no	—
196	#486	—	2	2	no	—
197	#486	C₂²×C₁₁	1	4	yes	complemented
198	#486	C₂²×C₁₁	1	4	yes	complemented
199	#486	C₂²×C₁₁	1	4	yes	complemented
200	C₂×#103	—	2	2	no	—
201	C₂×#102	—	2	2	no	—
202	C₂×#102	—	2	2	no	—
203	C₂×#102	—	2	2	no	—
204	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
207	#322	C₂²×C₁₁	1	4	yes	complemented
208	C₂²×C₁₁	—	8	2	no	—
209	C₂²×C₁₁	—	8	2	no	—
210	C₂²×C₁₁	—	8	2	no	—
211	C₂²×C₁₁	—	8	2	no	—
212	C₂²×C₁₁	—	8	2	no	—
213	C₂²×C₁₁	—	8	2	no	—
214	C₂²×C₁₁	—	16	4	no	—
215	C₂²×C₁₁	—	16	4	no	—
216	C₂²×C₁₁	#495	1	2	yes	—
217	C₂²×C₁₁	#496	1	2	yes	—
218	C₂²×C₁₁	#496	1	2	yes	—
219	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
220	C₄×C₁₁	—	8	2	no	—
221	C₄×C₁₁	—	8	2	no	—
222	C₄×C₁₁	#495	1	2	yes	—
223	C₄×C₁₁	#496	1	2	yes	—
224	C₄×C₁₁	#496	1	2	yes	—
225	C₄×C₁₁	C₂×#135	1	2	yes	—
226	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
227	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	C₂×SD₁₆	—	2	8	no	—
237	C₂×SD₁₆	—	4	8	no	—
238	C₂×D₈	—	2	8	no	—
239	C₂×D₈	—	4	8	no	—
240	C₂²×C₈	D₄×C₁₁	1	2	yes	—
241	C₂²×C₈	D₄×C₁₁	1	2	yes	—
242	C₂²×C₈	D₄×C₁₁	1	2	yes	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
250	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
251	#127	—	2	1	no	—
252	#127	—	2	1	no	—
253	#127	—	2	1	no	—
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	C₂³×C₁₁	1	2	yes	—
258	#127	C₂³×C₁₁	1	2	yes	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
264	#103	—	2	8	no	—
265	#102	—	2	8	no	—
266	#102	—	2	8	no	—
267	#102	—	2	8	no	—
268	C₄×C₈	D₄×C₁₁	1	2	yes	—
269	C₄×C₈	D₄×C₁₁	1	2	yes	—
270	C₄×C₈	D₄×C₁₁	1	2	yes	—
271	C₄×C₈	C₂³×C₁₁	1	2	yes	—
272	C₄×C₈	C₂³×C₁₁	1	2	yes	—
273	C₄×C₈	C₂³×C₁₁	1	2	yes	—
274	C₂×C₁₁	—	16	2	no	—
275	C₂×C₁₁	—	16	2	no	—
276	C₂×C₁₁	#1717	1	4	yes	direct product factor
277	C₂×C₁₁	C₂×#495	1	1	yes	characteristic
278	C₂×C₁₁	C₂×#496	1	1	yes	characteristic
279	C₂×C₁₁	C₂×#496	1	1	yes	characteristic
280	C₂⁴	—	4	1	no	—
281	C₂⁴	—	4	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	4	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	4	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
311	SD₁₆	—	4	16	no	—
312	D₈	—	4	16	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
317	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
318	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
330	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
331	C₁₁	C₂×#1717	1	1	yes	characteristic, direct product factor, Sylow
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	8	2	no	—
336	C₂³	—	8	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	C₁₁×#127	1	1	yes	characteristic
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	8	2	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	8	2	no	—
356	D₄	—	8	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	8	2	no	—
361	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
362	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
363	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
364	C₂×C₄	C₁₁×#135	1	4	yes	—
365	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
366	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₈	—	2	4	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	4	no	—
380	C₂²	—	16	4	no	—
381	C₂²	C₁₁×#495	1	2	yes	—
382	C₂²	C₁₁×#496	1	2	yes	—
383	C₂²	C₁₁×#496	1	2	yes	—
384	C₂²	C₂×C₁₁×#127	1	1	yes	characteristic
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₁₁×#495	1	2	yes	—
388	C₄	C₁₁×#496	1	2	yes	—
389	C₄	C₁₁×#496	1	2	yes	—
390	C₄	C₂×C₁₁×#135	1	2	yes	—
391	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
392	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
393	C₂	—	16	2	no	—
394	C₂	—	16	2	no	—
395	C₂	C₁₁×#1717	1	4	yes	direct product factor
396	C₂	C₂×C₁₁×#495	1	1	yes	characteristic
397	C₂	C₂×C₁₁×#496	1	1	yes	characteristic
398	C₂	C₂×C₁₁×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#492	C₂	semidirect
3. C₂×C₁₁×#487	C₂	semidirect
4. C₂×C₁₁×#486	C₂	semidirect
5. C₂×C₁₁×#486	C₂	semidirect
6. C₂×C₁₁×#486	C₂	semidirect
7. C₁₁×#1717	C₂	direct (N × H)
8. C₂×C₁₁×#322	C₂	semidirect
18. C₁₁×#492	C₂²	semidirect
20. C₁₁×#487	C₂²	semidirect
24. C₁₁×#486	C₂²	semidirect
25. C₁₁×#486	C₂²	semidirect
26. C₁₁×#486	C₂²	semidirect
34. C₁₁×#322	C₂²	semidirect
81. C₂×#1717	C₁₁	direct (N × H)
134. C₂×#492	C₂×C₁₁	semidirect
135. C₂×#487	C₂×C₁₁	semidirect
136. C₂×#486	C₂×C₁₁	semidirect
137. C₂×#486	C₂×C₁₁	semidirect
138. C₂×#486	C₂×C₁₁	semidirect
139. #1717	C₂×C₁₁	direct (N × H)
140. C₂×#322	C₂×C₁₁	semidirect
191. #492	C₂²×C₁₁	semidirect
193. #487	C₂²×C₁₁	semidirect
197. #486	C₂²×C₁₁	semidirect
198. #486	C₂²×C₁₁	semidirect
199. #486	C₂²×C₁₁	semidirect
207. #322	C₂²×C₁₁	semidirect
276. C₂×C₁₁	#1717	direct (N × H)
331. C₁₁	C₂×#1717	direct (N × H)
395. C₂	C₁₁×#1717	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×#493	2
C₂×C₁₁×#492	2
C₂×C₁₁×#487	2
C₂×C₁₁×#486	2
C₁₁×#1717	2
C₂×C₁₁×#322	2
C₂×#1717	11

Subgroups — C2×C11×#1717 #14596802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1717 #14596802