Subgroups — C₁₁×#22798 #14599991

Order 2816.

808 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#433	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2293	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1955	C₂	1	2	yes	maximal
4	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1923	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1798	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1771	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#117	C₂²	1	2	yes	—
12	C₁₁×#433	—	2	8	no	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
19	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₁×#97	C₂²	1	2	yes	—
24	C₂×C₁₁×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
26	C₁₁×#390	C₄	1	1	yes	characteristic
27	C₁₁×#390	C₄	1	1	yes	characteristic
28	C₁₁×#389	C₄	1	1	yes	characteristic
29	C₁₁×#389	C₄	1	1	yes	characteristic
30	C₁₁×#388	C₄	1	2	yes	—
31	C₁₁×#388	C₄	1	2	yes	—
32	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₄³×C₁₁	C₂²	1	1	yes	characteristic
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	2	yes	—
37	C₁₁×#336	C₂²	1	2	yes	—
38	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
44	C₄×D₄×C₁₁	—	2	2	no	—
45	C₄×D₄×C₁₁	—	2	2	no	—
46	C₁₁×#117	—	2	4	no	—
47	C₁₁×#117	—	2	4	no	—
48	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
66	C₁₁×C₄⋊C₈	—	2	4	no	—
67	C₁₁×C₄⋊C₈	—	2	4	no	—
68	C₁₁×C₄⋊C₈	—	2	2	no	—
69	C₁₁×C₄⋊C₈	—	4	1	no	—
70	C₁₁×C₄⋊C₈	—	4	1	no	—
71	C₁₁×C₄⋊C₈	D₄	1	4	yes	complemented
72	C₁₁×C₂²⋊C₈	—	2	4	no	—
73	C₁₁×C₂²⋊C₈	—	2	4	no	—
74	C₁₁×C₂²⋊C₈	—	4	2	no	—
75	C₁₁×C₂²⋊C₈	—	4	2	no	—
76	C₁₁×#97	—	2	4	no	—
77	C₁₁×#97	—	2	4	no	—
78	C₄×C₈×C₁₁	—	2	4	no	—
79	C₁₁×#95	C₂×C₄	1	2	yes	—
80	C₁₁×#95	C₂×C₄	1	2	yes	—
81	C₁₁×#95	C₂×C₄	1	2	yes	—
82	#22798	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
84	C₂×D₄×C₁₁	—	2	2	no	—
85	C₂×D₄×C₁₁	—	4	1	no	—
86	C₂×D₄×C₁₁	—	4	1	no	—
87	C₂²×C₄×C₁₁	—	2	2	no	—
88	C₂²×C₄×C₁₁	—	2	2	no	—
89	C₂²×C₄×C₁₁	—	2	2	no	—
90	C₂²×C₄×C₁₁	—	2	2	no	—
91	C₂²×C₄×C₁₁	—	2	2	no	—
92	C₂²×C₄×C₁₁	—	2	2	no	—
93	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₁	—	2	2	no	—
104	C₂×C₈×C₁₁	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	—	2	2	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	2	2	no	—
114	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
115	C₁₁×C₄⋊C₄	—	2	2	no	—
116	C₁₁×C₄⋊C₄	—	2	4	no	—
117	C₁₁×C₄⋊C₄	—	2	4	no	—
118	C₁₁×C₄⋊C₄	—	4	1	no	—
119	C₁₁×C₄⋊C₄	—	4	1	no	—
120	C₁₁×C₂²⋊C₄	—	2	4	no	—
121	C₁₁×C₂²⋊C₄	—	2	4	no	—
122	C₁₁×C₂²⋊C₄	—	2	4	no	—
123	C₁₁×C₂²⋊C₄	—	2	4	no	—
124	C₁₁×C₂²⋊C₄	—	4	2	no	—
125	C₄²×C₁₁	—	2	2	no	—
126	C₄²×C₁₁	—	2	2	no	—
127	C₄²×C₁₁	—	2	2	no	—
128	C₄²×C₁₁	—	2	1	no	—
129	C₄²×C₁₁	—	2	1	no	—
130	C₄²×C₁₁	—	4	1	no	—
131	C₄²×C₁₁	—	4	1	no	—
132	C₄²×C₁₁	—	4	1	no	—
133	C₄²×C₁₁	C₂×D₄	1	2	yes	—
134	C₄²×C₁₁	#41	1	2	yes	—
135	C₄²×C₁₁	#41	1	2	yes	—
136	C₄²×C₁₁	#41	1	2	yes	—
137	C₂×#433	C₂×C₁₁	1	2	yes	complemented
138	#2293	C₂×C₁₁	1	1	yes	characteristic
139	#1955	C₂×C₁₁	1	2	yes	—
140	#1924	C₂×C₁₁	1	2	yes	complemented
141	#1923	C₂×C₁₁	1	2	yes	complemented
142	#1842	C₂×C₁₁	1	1	yes	characteristic, complemented
143	#1798	C₂×C₁₁	1	2	yes	complemented
144	#1771	C₂×C₁₁	1	2	yes	complemented
145	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
146	C₂³×C₁₁	—	2	2	no	—
147	C₂³×C₁₁	—	2	2	no	—
148	C₂³×C₁₁	—	2	2	no	—
149	C₂³×C₁₁	—	2	2	no	—
150	C₂³×C₁₁	—	2	2	no	—
151	C₂³×C₁₁	—	2	2	no	—
152	C₂³×C₁₁	—	2	2	no	—
153	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
154	D₄×C₁₁	—	4	4	no	—
155	C₂×C₄×C₁₁	—	2	1	no	—
156	C₂×C₄×C₁₁	—	2	1	no	—
157	C₂×C₄×C₁₁	—	2	1	no	—
158	C₂×C₄×C₁₁	—	2	1	no	—
159	C₂×C₄×C₁₁	—	2	1	no	—
160	C₂×C₄×C₁₁	—	2	1	no	—
161	C₂×C₄×C₁₁	—	2	1	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	1	no	—
165	C₂×C₄×C₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	1	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	—	4	2	no	—
178	C₂×C₄×C₁₁	—	4	2	no	—
179	C₂×C₄×C₁₁	—	4	2	no	—
180	C₂×C₄×C₁₁	—	4	2	no	—
181	C₂×C₄×C₁₁	#117	1	2	yes	—
182	C₂×C₄×C₁₁	#117	1	2	yes	—
183	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₁	#131	1	2	yes	—
186	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
192	C₈×C₁₁	—	2	4	no	—
193	C₈×C₁₁	—	4	2	no	—
194	C₈×C₁₁	—	4	2	no	—
195	C₈×C₁₁	—	4	2	no	—
196	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
197	C₂×#117	C₂²×C₁₁	1	2	yes	—
198	#433	—	2	8	no	—
199	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
204	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
206	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
207	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
208	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
209	C₂×#97	C₂²×C₁₁	1	2	yes	—
210	C₂×#97	C₂²×C₁₁	1	2	yes	—
211	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
212	#390	C₄×C₁₁	1	1	yes	characteristic
213	#390	C₄×C₁₁	1	1	yes	characteristic
214	#389	C₄×C₁₁	1	1	yes	characteristic
215	#389	C₄×C₁₁	1	1	yes	characteristic
216	#388	C₄×C₁₁	1	2	yes	—
217	#388	C₄×C₁₁	1	2	yes	—
218	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
219	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
220	C₄³	C₂²×C₁₁	1	1	yes	characteristic
221	#336	C₂²×C₁₁	1	2	yes	—
222	#336	C₂²×C₁₁	1	2	yes	—
223	#336	C₂²×C₁₁	1	2	yes	—
224	C₂²×C₁₁	—	4	2	no	—
225	C₂²×C₁₁	—	4	2	no	—
226	C₂²×C₁₁	—	4	2	no	—
227	C₂²×C₁₁	—	4	2	no	—
228	C₂²×C₁₁	—	4	2	no	—
229	C₂²×C₁₁	—	4	2	no	—
230	C₂²×C₁₁	—	4	2	no	—
231	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
232	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
233	C₂²×C₁₁	#520	1	1	yes	characteristic
234	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
235	C₂²×C₁₁	#568	1	1	yes	characteristic
236	C₂²×C₁₁	#568	1	1	yes	characteristic
237	C₂²×C₁₁	#568	1	1	yes	characteristic
238	C₄×C₁₁	—	2	2	no	—
239	C₄×C₁₁	—	2	2	no	—
240	C₄×C₁₁	—	2	2	no	—
241	C₄×C₁₁	—	2	2	no	—
242	C₄×C₁₁	—	2	2	no	—
243	C₄×C₁₁	—	4	2	no	—
244	C₄×C₁₁	—	4	2	no	—
245	C₄×C₁₁	—	4	2	no	—
246	C₄×C₁₁	—	4	1	no	—
247	C₄×C₁₁	#547	1	1	yes	characteristic
248	C₄×C₁₁	#550	1	1	yes	characteristic
249	C₄×C₁₁	#555	1	1	yes	characteristic
250	C₄×C₁₁	#556	1	1	yes	characteristic
251	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
253	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	#117	—	2	4	no	—
260	#117	—	2	4	no	—
261	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
262	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
271	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
272	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
273	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
274	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
276	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
279	C₄⋊C₈	—	2	4	no	—
280	C₄⋊C₈	—	2	4	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	4	1	no	—
283	C₄⋊C₈	—	4	1	no	—
284	C₄⋊C₈	D₄×C₁₁	1	4	yes	complemented
285	C₂²⋊C₈	—	2	4	no	—
286	C₂²⋊C₈	—	2	4	no	—
287	C₂²⋊C₈	—	4	2	no	—
288	C₂²⋊C₈	—	4	2	no	—
289	#97	—	2	4	no	—
290	#97	—	2	4	no	—
291	C₄×C₈	—	2	4	no	—
292	#95	C₂×C₄×C₁₁	1	2	yes	—
293	#95	C₂×C₄×C₁₁	1	2	yes	—
294	#95	C₂×C₄×C₁₁	1	2	yes	—
295	C₂×C₁₁	—	8	2	no	—
296	C₂×C₁₁	#2354	1	1	yes	characteristic
297	C₂×C₁₁	#2921	1	1	yes	characteristic
298	C₂×C₁₁	#2925	1	1	yes	characteristic
299	C₂×C₁₁	#2932	1	1	yes	characteristic
300	C₂×C₁₁	#2935	1	1	yes	characteristic
301	C₂×C₁₁	#2992	1	1	yes	characteristic
302	C₂×C₁₁	#2995	1	1	yes	characteristic
303	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
317	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
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	C₂⁴×C₁₁	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	—	4	1	no	—
353	C₄²	C₂×D₄×C₁₁	1	2	yes	—
354	C₄²	C₁₁×#41	1	2	yes	—
355	C₄²	C₁₁×#41	1	2	yes	—
356	C₄²	C₁₁×#41	1	2	yes	—
357	C₁₁	#22798	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
366	D₄	—	4	4	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	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	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	C₁₁×#117	1	2	yes	—
394	C₂×C₄	C₁₁×#117	1	2	yes	—
395	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
396	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
397	C₂×C₄	C₁₁×#131	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
399	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
400	C₂×C₄	C₂×C₁₁×#41	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	C₈	—	2	4	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
416	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
417	C₂²	C₁₁×#520	1	1	yes	characteristic
418	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
419	C₂²	C₁₁×#568	1	1	yes	characteristic
420	C₂²	C₁₁×#568	1	1	yes	characteristic
421	C₂²	C₁₁×#568	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	2	no	—
431	C₄	C₁₁×#547	1	1	yes	characteristic
432	C₄	C₁₁×#550	1	1	yes	characteristic
433	C₄	C₁₁×#555	1	1	yes	characteristic
434	C₄	C₁₁×#556	1	1	yes	characteristic
435	C₂	—	8	2	no	—
436	C₂	C₁₁×#2354	1	1	yes	characteristic
437	C₂	C₁₁×#2921	1	1	yes	characteristic
438	C₂	C₁₁×#2925	1	1	yes	characteristic
439	C₂	C₁₁×#2932	1	1	yes	characteristic
440	C₂	C₁₁×#2935	1	1	yes	characteristic
441	C₂	C₁₁×#2992	1	1	yes	characteristic
442	C₂	C₁₁×#2995	1	1	yes	characteristic

	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	C₂²×D₄×C₁₁	C₂×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×#433	C₂	semidirect
4. C₁₁×#1924	C₂	semidirect
5. C₁₁×#1923	C₂	semidirect
6. C₁₁×#1842	C₂	semidirect
7. C₁₁×#1798	C₂	semidirect
8. C₁₁×#1771	C₂	semidirect
9. C₁₁×#1767	C₂	semidirect
71. C₁₁×C₄⋊C₈	D₄	semidirect
82. #22798	C₁₁	direct (N × H)
137. C₂×#433	C₂×C₁₁	semidirect
140. #1924	C₂×C₁₁	semidirect
141. #1923	C₂×C₁₁	semidirect
142. #1842	C₂×C₁₁	semidirect
143. #1798	C₂×C₁₁	semidirect
144. #1771	C₂×C₁₁	semidirect
145. #1767	C₂×C₁₁	semidirect
284. C₄⋊C₈	D₄×C₁₁	semidirect
357. C₁₁	#22798	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×#433	2
C₁₁×#2293	2
C₁₁×#1955	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1842	2
C₁₁×#1798	2
C₁₁×#1771	2
C₁₁×#1767	2
#22798	11

Subgroups — C11×#22798 #14599991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22798 #14599991