Subgroups — C₁₁×#22804 #14599997

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2943	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2925	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1975	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1974	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1849	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1806	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1773	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	2	yes	—
14	C₁₁×#442	C₄	1	2	yes	complemented
15	C₁₁×#441	C₄	1	2	yes	complemented
16	C₁₁×#440	C₄	1	2	yes	complemented
17	C₁₁×#440	C₄	1	2	yes	complemented
18	C₁₁×#433	—	2	2	no	—
19	C₁₁×#433	—	2	2	no	—
20	C₁₁×#432	—	2	2	no	—
21	C₁₁×#431	—	2	2	no	—
22	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#108	C₂²	1	2	yes	—
25	C₁₁×#427	C₂²	1	1	yes	characteristic
26	C₁₁×#423	C₂²	1	2	yes	—
27	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#104	C₂²	1	2	yes	—
29	C₂×C₁₁×#104	C₂²	1	2	yes	—
30	C₁₁×#416	C₂²	1	2	yes	—
31	C₁₁×#408	C₂²	1	2	yes	—
32	C₁₁×#408	C₂²	1	2	yes	—
33	C₁₁×#405	C₂²	1	2	yes	—
34	C₁₁×#405	C₂²	1	2	yes	—
35	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
38	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₁×#339	C₂²	1	2	yes	—
40	C₁₁×#339	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	1	yes	characteristic
42	C₁₁×#336	C₂²	1	1	yes	characteristic
43	C₂×C₁₁×#41	C₂³	1	2	yes	—
44	C₁₁×#135	—	2	2	no	—
45	C₁₁×#135	—	2	2	no	—
46	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
50	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
57	C₄×D₄×C₁₁	—	2	2	no	—
58	C₄×D₄×C₁₁	—	2	2	no	—
59	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
61	C₁₁×#117	—	2	2	no	—
62	C₁₁×#117	C₂³	1	2	yes	—
63	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
64	C₂×C₄²×C₁₁	—	2	2	no	—
65	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
68	C₁₁×#108	—	2	2	no	—
69	C₁₁×#108	—	2	2	no	—
70	C₁₁×#108	—	4	2	no	—
71	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
72	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
73	C₁₁×#106	C₂×C₄	1	2	yes	—
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×C₄⋊C₈	—	2	2	no	—
76	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
77	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
78	C₁₁×#104	—	4	2	no	—
79	C₁₁×#104	—	4	2	no	—
80	C₁₁×#103	C₂×C₄	1	2	yes	—
81	C₁₁×#103	C₂×C₄	1	2	yes	—
82	C₁₁×#102	C₂×C₄	1	2	yes	—
83	C₁₁×#102	C₂×C₄	1	2	yes	—
84	C₁₁×C₂²⋊C₈	—	2	2	no	—
85	C₁₁×C₂²⋊C₈	—	2	2	no	—
86	C₁₁×C₂²⋊C₈	—	2	2	no	—
87	C₁₁×C₂²⋊C₈	—	2	2	no	—
88	C₁₁×#97	—	2	2	no	—
89	C₁₁×#97	—	2	2	no	—
90	C₁₁×#97	—	2	2	no	—
91	C₁₁×#97	C₂×C₄	1	2	yes	—
92	C₁₁×#97	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₁₁	—	2	2	no	—
94	C₄×C₈×C₁₁	—	2	2	no	—
95	C₄×C₈×C₁₁	—	2	2	no	—
96	C₁₁×#95	—	2	1	no	—
97	#22804	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₁	—	2	1	no	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
113	C₁₁×Q₁₆	—	2	2	no	—
114	C₁₁×SD₁₆	—	2	4	no	—
115	C₁₁×D₈	—	2	2	no	—
116	C₁₁×M₁₆	—	2	2	no	—
117	C₁₁×M₁₆	—	2	2	no	—
118	C₁₁×M₁₆	—	2	2	no	—
119	C₁₁×M₁₆	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	1	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₁	#41	1	2	yes	—
135	C₂×C₈×C₁₁	#41	1	2	yes	—
136	C₁₁×C₄⋊C₄	—	2	2	no	—
137	C₁₁×C₄⋊C₄	—	2	2	no	—
138	C₁₁×C₄⋊C₄	—	4	2	no	—
139	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
140	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
141	C₁₁×C₂²⋊C₄	—	2	2	no	—
142	C₁₁×C₂²⋊C₄	—	2	2	no	—
143	C₁₁×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₁₁	—	2	2	no	—
145	C₄²×C₁₁	—	2	2	no	—
146	C₄²×C₁₁	—	2	2	no	—
147	C₄²×C₁₁	—	2	1	no	—
148	C₄²×C₁₁	—	2	1	no	—
149	C₄²×C₁₁	—	2	1	no	—
150	C₄²×C₁₁	—	2	1	no	—
151	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
152	C₄²×C₁₁	C₂×D₄	1	2	yes	—
153	#2943	C₂×C₁₁	1	1	yes	characteristic
154	#2925	C₂×C₁₁	1	2	yes	complemented
155	#1975	C₂×C₁₁	1	1	yes	characteristic
156	#1974	C₂×C₁₁	1	1	yes	characteristic
157	#1929	C₂×C₁₁	1	2	yes	complemented
158	#1929	C₂×C₁₁	1	2	yes	complemented
159	#1849	C₂×C₁₁	1	1	yes	characteristic, complemented
160	#1806	C₂×C₁₁	1	2	yes	complemented
161	#1773	C₂×C₁₁	1	1	yes	characteristic, complemented
162	#1772	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#1771	C₂×C₁₁	1	1	yes	characteristic, complemented
164	C₂³×C₁₁	—	2	2	no	—
165	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
166	Q₈×C₁₁	—	2	2	no	—
167	Q₈×C₁₁	—	2	2	no	—
168	D₄×C₁₁	—	2	2	no	—
169	D₄×C₁₁	—	2	2	no	—
170	D₄×C₁₁	—	4	2	no	—
171	D₄×C₁₁	—	4	2	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	4	1	no	—
177	C₂×C₄×C₁₁	—	4	1	no	—
178	C₂×C₄×C₁₁	—	4	4	no	—
179	C₂×C₄×C₁₁	—	4	1	no	—
180	C₂×C₄×C₁₁	—	4	1	no	—
181	C₂×C₄×C₁₁	—	4	2	no	—
182	C₂×C₄×C₁₁	—	4	2	no	—
183	C₂×C₄×C₁₁	—	4	1	no	—
184	C₂×C₄×C₁₁	—	4	1	no	—
185	C₂×C₄×C₁₁	—	4	1	no	—
186	C₂×C₄×C₁₁	—	8	2	no	—
187	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₁₁	—	2	2	no	—
196	C₈×C₁₁	—	2	1	no	—
197	C₈×C₁₁	—	2	1	no	—
198	C₈×C₁₁	—	2	2	no	—
199	C₈×C₁₁	—	4	2	no	—
200	C₈×C₁₁	—	4	2	no	—
201	C₈×C₁₁	#117	1	2	yes	—
202	C₈×C₁₁	#117	1	2	yes	—
203	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
204	C₄×#41	C₂²×C₁₁	1	2	yes	—
205	#442	C₄×C₁₁	1	2	yes	complemented
206	#441	C₄×C₁₁	1	2	yes	complemented
207	#440	C₄×C₁₁	1	2	yes	complemented
208	#440	C₄×C₁₁	1	2	yes	complemented
209	#433	—	2	2	no	—
210	#433	—	2	2	no	—
211	#432	—	2	2	no	—
212	#431	—	2	2	no	—
213	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
214	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
215	C₂×#108	C₂²×C₁₁	1	2	yes	—
216	#427	C₂²×C₁₁	1	1	yes	characteristic
217	#423	C₂²×C₁₁	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
219	C₂×#104	C₂²×C₁₁	1	2	yes	—
220	C₂×#104	C₂²×C₁₁	1	2	yes	—
221	#416	C₂²×C₁₁	1	2	yes	—
222	#408	C₂²×C₁₁	1	2	yes	—
223	#408	C₂²×C₁₁	1	2	yes	—
224	#405	C₂²×C₁₁	1	2	yes	—
225	#405	C₂²×C₁₁	1	2	yes	—
226	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
227	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
230	#339	C₂²×C₁₁	1	2	yes	—
231	#339	C₂²×C₁₁	1	2	yes	—
232	#336	C₂²×C₁₁	1	1	yes	characteristic
233	#336	C₂²×C₁₁	1	1	yes	characteristic
234	C₂²×C₁₁	—	2	1	no	—
235	C₂²×C₁₁	—	2	1	no	—
236	C₂²×C₁₁	—	4	2	no	—
237	C₂²×C₁₁	—	4	2	no	—
238	C₂²×C₁₁	—	4	2	no	—
239	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂²×C₁₁	#555	1	1	yes	characteristic
241	C₂²×C₁₁	#556	1	1	yes	characteristic
242	C₄×C₁₁	—	2	2	no	—
243	C₄×C₁₁	—	2	2	no	—
244	C₄×C₁₁	—	4	2	no	—
245	C₄×C₁₁	—	4	2	no	—
246	C₄×C₁₁	—	4	2	no	—
247	C₄×C₁₁	—	4	2	no	—
248	C₄×C₁₁	—	8	1	no	—
249	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
250	C₄×C₁₁	#520	1	1	yes	characteristic
251	C₄×C₁₁	#547	1	1	yes	characteristic
252	C₄×C₁₁	#550	1	1	yes	characteristic
253	C₂×#41	C₂³×C₁₁	1	2	yes	—
254	#135	—	2	2	no	—
255	#135	—	2	2	no	—
256	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
257	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
258	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
259	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
260	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
265	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
266	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
270	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
271	#117	—	2	2	no	—
272	#117	C₂³×C₁₁	1	2	yes	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
278	#108	—	2	2	no	—
279	#108	—	2	2	no	—
280	#108	—	4	2	no	—
281	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
282	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
283	#106	C₂×C₄×C₁₁	1	2	yes	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
287	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
288	#104	—	4	2	no	—
289	#104	—	4	2	no	—
290	#103	C₂×C₄×C₁₁	1	2	yes	—
291	#103	C₂×C₄×C₁₁	1	2	yes	—
292	#102	C₂×C₄×C₁₁	1	2	yes	—
293	#102	C₂×C₄×C₁₁	1	2	yes	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	C₂²⋊C₈	—	2	2	no	—
298	#97	—	2	2	no	—
299	#97	—	2	2	no	—
300	#97	—	2	2	no	—
301	#97	C₂×C₄×C₁₁	1	2	yes	—
302	#97	C₂×C₄×C₁₁	1	2	yes	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	2	2	no	—
306	#95	—	2	1	no	—
307	C₂×C₁₁	—	2	1	no	—
308	C₂×C₁₁	—	2	1	no	—
309	C₂×C₁₁	—	8	2	no	—
310	C₂×C₁₁	#2354	1	1	yes	characteristic
311	C₂×C₁₁	#2955	1	1	yes	characteristic
312	C₂×C₁₁	#2956	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	C₂²×C₄×C₁₁	1	2	yes	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
326	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
328	Q₁₆	—	2	2	no	—
329	SD₁₆	—	2	4	no	—
330	D₈	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
344	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
345	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
346	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
347	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
348	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
349	C₂×C₈	C₁₁×#41	1	2	yes	—
350	C₂×C₈	C₁₁×#41	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
355	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
367	C₄²	C₂×D₄×C₁₁	1	2	yes	—
368	C₁₁	#22804	1	1	yes	characteristic, direct product factor, Sylow
369	C₂³	—	2	2	no	—
370	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
393	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
394	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
397	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
398	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	2	no	—
406	C₈	C₁₁×#117	1	2	yes	—
407	C₈	C₁₁×#117	1	2	yes	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
414	C₂²	C₁₁×#555	1	1	yes	characteristic
415	C₂²	C₁₁×#556	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
424	C₄	C₁₁×#520	1	1	yes	characteristic
425	C₄	C₁₁×#547	1	1	yes	characteristic
426	C₄	C₁₁×#550	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	8	2	no	—
430	C₂	C₁₁×#2354	1	1	yes	characteristic
431	C₂	C₁₁×#2955	1	1	yes	characteristic
432	C₂	C₁₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2925	C₂	semidirect
5. C₁₁×#1929	C₂	semidirect
6. C₁₁×#1929	C₂	semidirect
7. C₁₁×#1849	C₂	semidirect
8. C₁₁×#1806	C₂	semidirect
9. C₁₁×#1773	C₂	semidirect
10. C₁₁×#1772	C₂	semidirect
11. C₁₁×#1771	C₂	semidirect
14. C₁₁×#442	C₄	semidirect
15. C₁₁×#441	C₄	semidirect
16. C₁₁×#440	C₄	semidirect
17. C₁₁×#440	C₄	semidirect
97. #22804	C₁₁	direct (N × H)
154. #2925	C₂×C₁₁	semidirect
157. #1929	C₂×C₁₁	semidirect
158. #1929	C₂×C₁₁	semidirect
159. #1849	C₂×C₁₁	semidirect
160. #1806	C₂×C₁₁	semidirect
161. #1773	C₂×C₁₁	semidirect
162. #1772	C₂×C₁₁	semidirect
163. #1771	C₂×C₁₁	semidirect
205. #442	C₄×C₁₁	semidirect
206. #441	C₄×C₁₁	semidirect
207. #440	C₄×C₁₁	semidirect
208. #440	C₄×C₁₁	semidirect
368. C₁₁	#22804	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×#2943	2
C₁₁×#2925	2
C₁₁×#1975	2
C₁₁×#1974	2
C₁₁×#1929	2
C₁₁×#1849	2
C₁₁×#1806	2
C₁₁×#1773	2
C₁₁×#1772	2
C₁₁×#1771	2
#22804	11

Subgroups — C11×#22804 #14599997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22804 #14599997