Subgroups — C₁₁×#22105 #14599298

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#433	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2396	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1940	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1924	C₂	1	2	yes	maximal
8	C₁₁×#1924	C₂	1	2	yes	maximal
9	C₁₁×#1917	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1798	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
14	C₁₁×#446	—	2	4	no	—
15	C₁₁×#433	—	2	4	no	—
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×#97	C₂²	1	2	yes	—
27	C₂×C₁₁×#97	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₁₁×#400	C₄	1	1	yes	characteristic
30	C₁₁×#399	C₄	1	1	yes	characteristic
31	C₁₁×#398	C₄	1	2	yes	—
32	C₁₁×#396	C₄	1	2	yes	—
33	C₁₁×#395	C₄	1	1	yes	characteristic
34	C₁₁×#393	C₄	1	1	yes	characteristic
35	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₄×Q₈×C₁₁	—	2	2	no	—
52	C₄×Q₈×C₁₁	—	2	2	no	—
53	C₁₁×#117	—	2	2	no	—
54	C₁₁×#117	—	2	2	no	—
55	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×C₄⋊C₈	—	2	2	no	—
71	C₁₁×C₄⋊C₈	—	2	2	no	—
72	C₁₁×C₄⋊C₈	—	2	4	no	—
73	C₁₁×C₄⋊C₈	—	2	2	no	—
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×C₄⋊C₈	—	4	2	no	—
76	C₁₁×C₂²⋊C₈	—	2	2	no	—
77	C₁₁×C₂²⋊C₈	—	2	2	no	—
78	C₁₁×C₂²⋊C₈	—	4	2	no	—
79	C₁₁×#97	—	2	4	no	—
80	C₁₁×#97	—	2	2	no	—
81	C₁₁×#97	—	4	2	no	—
82	C₄×C₈×C₁₁	D₄	1	4	yes	—
83	C₁₁×#95	C₂×C₄	1	2	yes	—
84	C₁₁×#95	C₂×C₄	1	2	yes	—
85	C₁₁×#95	C₂×C₄	1	2	yes	—
86	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
87	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#95	C₂×C₄	1	2	yes	—
89	#22105	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
91	C₂×Q₈×C₁₁	—	2	2	no	—
92	C₂×Q₈×C₁₁	—	4	2	no	—
93	C₂²×C₄×C₁₁	—	2	1	no	—
94	C₂²×C₄×C₁₁	—	2	1	no	—
95	C₂²×C₄×C₁₁	—	2	1	no	—
96	C₂²×C₄×C₁₁	—	2	1	no	—
97	C₂²×C₄×C₁₁	—	2	1	no	—
98	C₂²×C₄×C₁₁	—	2	1	no	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₁₁	—	2	1	no	—
110	C₂×C₈×C₁₁	—	2	1	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	2	no	—
115	C₂×C₈×C₁₁	—	2	2	no	—
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	—	2	1	no	—
118	C₂×C₈×C₁₁	—	2	1	no	—
119	C₂×C₈×C₁₁	—	2	1	no	—
120	C₂×C₈×C₁₁	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
127	C₁₁×C₄⋊C₄	—	2	2	no	—
128	C₁₁×C₄⋊C₄	—	2	2	no	—
129	C₁₁×C₄⋊C₄	—	2	2	no	—
130	C₁₁×C₄⋊C₄	—	2	4	no	—
131	C₁₁×C₄⋊C₄	—	4	2	no	—
132	C₁₁×C₄⋊C₄	—	4	2	no	—
133	C₁₁×C₄⋊C₄	—	4	2	no	—
134	C₁₁×C₂²⋊C₄	—	2	2	no	—
135	C₁₁×C₂²⋊C₄	—	2	2	no	—
136	C₁₁×C₂²⋊C₄	—	4	2	no	—
137	C₁₁×C₂²⋊C₄	—	4	2	no	—
138	C₄²×C₁₁	—	2	2	no	—
139	C₄²×C₁₁	—	2	1	no	—
140	C₄²×C₁₁	—	2	1	no	—
141	C₄²×C₁₁	—	2	2	no	—
142	C₄²×C₁₁	—	2	2	no	—
143	C₄²×C₁₁	—	2	2	no	—
144	C₄²×C₁₁	C₂×D₄	1	2	yes	—
145	C₄²×C₁₁	#41	1	2	yes	—
146	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
147	C₂×#433	C₂×C₁₁	1	1	yes	characteristic
148	#2396	C₂×C₁₁	1	1	yes	characteristic
149	#1985	C₂×C₁₁	1	1	yes	characteristic, complemented
150	#1940	C₂×C₁₁	1	2	yes	complemented
151	#1940	C₂×C₁₁	1	1	yes	characteristic, complemented
152	#1924	C₂×C₁₁	1	2	yes	—
153	#1924	C₂×C₁₁	1	2	yes	—
154	#1917	C₂×C₁₁	1	2	yes	complemented
155	#1798	C₂×C₁₁	1	1	yes	characteristic
156	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
157	C₂³×C₁₁	—	2	1	no	—
158	C₂³×C₁₁	—	2	1	no	—
159	C₂³×C₁₁	—	2	1	no	—
160	C₂³×C₁₁	—	2	2	no	—
161	C₂³×C₁₁	—	2	2	no	—
162	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
163	Q₈×C₁₁	—	4	4	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	1	no	—
171	C₂×C₄×C₁₁	—	2	1	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	2	2	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	4	1	no	—
186	C₂×C₄×C₁₁	—	4	1	no	—
187	C₂×C₄×C₁₁	—	4	1	no	—
188	C₂×C₄×C₁₁	—	4	1	no	—
189	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₁₁	C₂²×D₄	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	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
197	C₈×C₁₁	—	2	2	no	—
198	C₈×C₁₁	—	2	2	no	—
199	C₈×C₁₁	—	4	1	no	—
200	C₈×C₁₁	—	4	1	no	—
201	C₈×C₁₁	—	4	2	no	—
202	C₈×C₁₁	—	4	2	no	—
203	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
204	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
205	#446	—	2	4	no	—
206	#433	—	2	4	no	—
207	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
211	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
212	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
213	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
214	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
215	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
216	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
217	C₂×#97	C₂²×C₁₁	1	2	yes	—
218	C₂×#97	C₂²×C₁₁	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
220	#400	C₄×C₁₁	1	1	yes	characteristic
221	#399	C₄×C₁₁	1	1	yes	characteristic
222	#398	C₄×C₁₁	1	2	yes	—
223	#396	C₄×C₁₁	1	2	yes	—
224	#395	C₄×C₁₁	1	1	yes	characteristic
225	#393	C₄×C₁₁	1	1	yes	characteristic
226	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
227	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
228	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
229	#336	C₂²×C₁₁	1	2	yes	—
230	#336	C₂²×C₁₁	1	2	yes	—
231	#336	C₂²×C₁₁	1	2	yes	—
232	#336	C₂²×C₁₁	1	2	yes	—
233	#336	C₂²×C₁₁	1	2	yes	—
234	C₂²×C₁₁	—	4	1	no	—
235	C₂²×C₁₁	—	4	1	no	—
236	C₂²×C₁₁	—	4	1	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	#519	1	1	yes	characteristic
241	C₂²×C₁₁	#520	1	1	yes	characteristic
242	C₂²×C₁₁	#568	1	2	yes	—
243	C₂²×C₁₁	#568	1	2	yes	—
244	C₄×C₁₁	—	2	2	no	—
245	C₄×C₁₁	—	2	2	no	—
246	C₄×C₁₁	—	4	1	no	—
247	C₄×C₁₁	—	4	1	no	—
248	C₄×C₁₁	—	4	2	no	—
249	C₄×C₁₁	—	4	1	no	—
250	C₄×C₁₁	—	4	2	no	—
251	C₄×C₁₁	—	4	2	no	—
252	C₄×C₁₁	—	4	2	no	—
253	C₄×C₁₁	#536	1	1	yes	characteristic
254	C₄×C₁₁	#537	1	1	yes	characteristic
255	C₄×C₁₁	#541	1	1	yes	characteristic
256	C₄×C₁₁	#542	1	1	yes	characteristic
257	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
263	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	#117	—	2	2	no	—
268	#117	—	2	2	no	—
269	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
275	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
280	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
282	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
283	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	2	4	no	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	4	2	no	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	—	4	2	no	—
293	#97	—	2	4	no	—
294	#97	—	2	2	no	—
295	#97	—	4	2	no	—
296	C₄×C₈	D₄×C₁₁	1	4	yes	—
297	#95	C₂×C₄×C₁₁	1	2	yes	—
298	#95	C₂×C₄×C₁₁	1	2	yes	—
299	#95	C₂×C₄×C₁₁	1	2	yes	—
300	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
301	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
302	#95	C₂×C₄×C₁₁	1	2	yes	—
303	C₂×C₁₁	—	8	1	no	—
304	C₂×C₁₁	#2323	1	1	yes	characteristic
305	C₂×C₁₁	#2930	1	1	yes	characteristic
306	C₂×C₁₁	#2932	1	1	yes	characteristic
307	C₂×C₁₁	#2987	1	2	yes	—
308	C₂×C₁₁	#2995	1	2	yes	—
309	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
319	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
322	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
323	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
325	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
327	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
345	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	C₂×D₄×C₁₁	1	2	yes	—
364	C₄²	C₁₁×#41	1	2	yes	—
365	C₁₁	#22105	1	1	yes	characteristic, direct product factor, Sylow
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
372	Q₈	—	4	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
399	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
401	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
402	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
404	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
405	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	1	no	—
417	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
418	C₂²	C₁₁×#519	1	1	yes	characteristic
419	C₂²	C₁₁×#520	1	1	yes	characteristic
420	C₂²	C₁₁×#568	1	2	yes	—
421	C₂²	C₁₁×#568	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	1	no	—
431	C₄	C₁₁×#536	1	1	yes	characteristic
432	C₄	C₁₁×#537	1	1	yes	characteristic
433	C₄	C₁₁×#541	1	1	yes	characteristic
434	C₄	C₁₁×#542	1	1	yes	characteristic
435	C₂	—	8	1	no	—
436	C₂	C₁₁×#2323	1	1	yes	characteristic
437	C₂	C₁₁×#2930	1	1	yes	characteristic
438	C₂	C₁₁×#2932	1	1	yes	characteristic
439	C₂	C₁₁×#2987	1	2	yes	—
440	C₂	C₁₁×#2995	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#446	C₂	semidirect
4. C₁₁×#1985	C₂	semidirect
5. C₁₁×#1940	C₂	semidirect
6. C₁₁×#1940	C₂	semidirect
9. C₁₁×#1917	C₂	semidirect
11. C₁₁×#1770	C₂	semidirect
89. #22105	C₁₁	direct (N × H)
146. C₂×#446	C₂×C₁₁	semidirect
149. #1985	C₂×C₁₁	semidirect
150. #1940	C₂×C₁₁	semidirect
151. #1940	C₂×C₁₁	semidirect
154. #1917	C₂×C₁₁	semidirect
156. #1770	C₂×C₁₁	semidirect
365. C₁₁	#22105	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×#446	2
C₂×C₁₁×#433	2
C₁₁×#2396	2
C₁₁×#1985	2
C₁₁×#1940	2
C₁₁×#1924	2
C₁₁×#1917	2
C₁₁×#1798	2
C₁₁×#1770	2
#22105	11

Subgroups — C11×#22105 #14599298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22105 #14599298