Subgroups — C₁₁×#33361 #14610554

Order 2816.

1252 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3500	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2883	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2129	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2127	C₂	1	4	yes	maximal, complemented
5	C₁₁×#2126	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#354	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₁×2₋¹⁺⁴	C₄	1	1	yes	characteristic, complemented
8	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
9	C₁₁×#548	—	2	2	no	—
10	C₁₁×#546	—	2	4	no	—
11	C₁₁×#546	—	2	2	no	—
12	C₁₁×#536	C₄	1	2	yes	complemented
13	C₁₁×#536	C₂²	1	1	yes	characteristic
14	C₁₁×#535	C₄	1	1	yes	characteristic, complemented
15	C₁₁×#535	C₂²	1	2	yes	—
16	C₁₁×#532	C₄	1	2	yes	complemented
17	C₁₁×#532	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#124	C₄	1	1	yes	characteristic, complemented
19	C₂×C₁₁×#124	C₂²	1	2	yes	—
20	C₁₁×#518	—	2	2	no	—
21	C₄×C₁₁×#41	C₄	1	1	yes	characteristic, complemented
22	C₁₁×#410	—	2	2	no	—
23	C₁₁×#410	C₂²	1	4	yes	—
24	C₂×C₁₁×#99	—	2	4	no	—
25	C₂×C₁₁×#99	C₂²	1	8	yes	—
26	C₁₁×#354	C₂²	1	4	yes	complemented
27	C₁₁×#354	C₂²	1	8	yes	complemented
28	C₁₁×#353	C₂²	1	4	yes	complemented
29	C₁₁×2₋¹⁺⁴	—	4	4	no	—
30	C₁₁×H(5,𝔽₂)	—	4	4	no	—
31	C₂×C₁₁×#41	—	2	2	no	—
32	C₂×C₁₁×#41	—	2	1	no	—
33	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
34	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
35	C₂×C₁₁×#41	C₂×C₄	1	2	yes	complemented
36	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic, complemented
37	C₂×C₁₁×#41	D₄	1	2	yes	—
38	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
39	C₂²×Q₈×C₁₁	—	2	1	no	—
40	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	complemented
42	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₁	D₄	1	4	yes	—
44	C₂²×D₄×C₁₁	D₄	1	2	yes	—
45	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
46	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
47	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
48	C₁₁×#127	C₂×C₄	1	2	yes	complemented
49	C₁₁×#127	C₂³	1	1	yes	characteristic
50	C₁₁×#124	—	2	2	no	—
51	C₁₁×#124	—	2	4	no	—
52	C₁₁×#124	C₂×C₄	1	2	yes	complemented
53	C₁₁×#124	C₂×C₄	1	2	yes	complemented
54	C₁₁×#124	C₂×C₄	1	2	yes	complemented
55	C₁₁×#124	C₂×C₄	1	1	yes	characteristic, complemented
56	C₁₁×#124	C₂³	1	1	yes	characteristic
57	C₁₁×#124	C₂³	1	2	yes	—
58	C₁₁×#123	—	2	4	no	—
59	C₁₁×#123	—	2	2	no	—
60	C₁₁×C₂²⋊Q₈	—	2	4	no	—
61	C₁₁×C₂²⋊Q₈	—	2	2	no	—
62	C₁₁×#121	—	2	4	no	—
63	C₁₁×#121	—	2	2	no	—
64	C₁₁×#121	—	2	2	no	—
65	C₁₁×#121	—	2	4	no	—
66	C₁₁×#120	—	2	2	no	—
67	C₁₁×#120	—	2	4	no	—
68	C₄×Q₈×C₁₁	—	2	1	no	—
69	C₄×D₄×C₁₁	—	2	2	no	—
70	C₄×D₄×C₁₁	—	2	1	no	—
71	C₄×D₄×C₁₁	—	2	4	no	—
72	C₄×D₄×C₁₁	—	2	2	no	—
73	C₄×D₄×C₁₁	—	4	8	no	—
74	C₁₁×#117	—	2	4	no	—
75	C₁₁×#117	C₂×C₄	1	1	yes	characteristic, complemented
76	C₁₁×#117	C₂×C₄	1	2	yes	complemented
77	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
79	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
80	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic, complemented
81	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	complemented
82	C₁₁×#99	—	2	4	no	—
83	C₁₁×#99	—	2	8	no	—
84	C₁₁×#99	C₂³	1	8	yes	—
85	#33361	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₁	C₂²⋊C₄	1	2	yes	—
87	C₂⁴×C₁₁	C₂×D₄	1	4	yes	—
88	C₁₁×#41	—	2	4	no	—
89	C₁₁×#41	—	4	2	no	—
90	C₁₁×#41	—	4	4	no	—
91	C₁₁×#41	—	4	4	no	—
92	C₁₁×#41	—	4	4	no	—
93	C₁₁×#41	—	4	2	no	—
94	C₁₁×#41	—	4	8	no	—
95	C₁₁×#41	—	4	4	no	—
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×Q₈×C₁₁	—	2	1	no	—
98	C₂×Q₈×C₁₁	—	4	2	no	—
99	C₂×Q₈×C₁₁	—	4	4	no	—
100	C₂×Q₈×C₁₁	—	4	4	no	—
101	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×D₄×C₁₁	—	2	8	no	—
106	C₂×D₄×C₁₁	—	2	1	no	—
107	C₂×D₄×C₁₁	—	2	2	no	—
108	C₂×D₄×C₁₁	—	2	4	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	4	2	no	—
111	C₂×D₄×C₁₁	—	4	4	no	—
112	C₂×D₄×C₁₁	—	4	8	no	—
113	C₂×D₄×C₁₁	C₂²⋊C₄	1	2	yes	—
114	C₂×D₄×C₁₁	C₂²⋊C₄	1	4	yes	—
115	C₂×D₄×C₁₁	C₂²⋊C₄	1	2	yes	—
116	C₂×D₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
119	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
120	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
121	C₂×D₄×C₁₁	C₂⁴	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	—	2	1	no	—
123	C₂²×C₄×C₁₁	—	2	2	no	—
124	C₂²×C₄×C₁₁	—	2	1	no	—
125	C₂²×C₄×C₁₁	—	2	2	no	—
126	C₂²×C₄×C₁₁	—	2	2	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	4	8	no	—
129	C₂²×C₄×C₁₁	C₂²⋊C₄	1	4	yes	—
130	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
133	C₁₁×C₄⋊C₄	—	2	2	no	—
134	C₁₁×C₄⋊C₄	—	2	1	no	—
135	C₁₁×C₄⋊C₄	—	2	4	no	—
136	C₁₁×C₄⋊C₄	—	2	2	no	—
137	C₁₁×C₄⋊C₄	—	4	4	no	—
138	C₁₁×C₂²⋊C₄	—	2	4	no	—
139	C₁₁×C₂²⋊C₄	—	2	4	no	—
140	C₁₁×C₂²⋊C₄	—	2	4	no	—
141	C₁₁×C₂²⋊C₄	—	2	1	no	—
142	C₁₁×C₂²⋊C₄	—	2	2	no	—
143	C₁₁×C₂²⋊C₄	—	2	2	no	—
144	C₁₁×C₂²⋊C₄	—	2	4	no	—
145	C₁₁×C₂²⋊C₄	—	2	2	no	—
146	C₁₁×C₂²⋊C₄	—	2	8	no	—
147	C₁₁×C₂²⋊C₄	—	4	8	no	—
148	C₄²×C₁₁	—	2	2	no	—
149	C₄²×C₁₁	—	2	1	no	—
150	C₄²×C₁₁	—	4	4	no	—
151	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
154	#3500	C₂×C₁₁	1	1	yes	characteristic
155	#2883	C₂×C₁₁	1	2	yes	complemented
156	#2129	C₂×C₁₁	1	2	yes	complemented
157	#2127	C₂×C₁₁	1	4	yes	complemented
158	#2126	C₂×C₁₁	1	2	yes	complemented
159	C₂×#354	C₂×C₁₁	1	4	yes	complemented
160	C₂³×C₁₁	—	2	8	no	—
161	C₂³×C₁₁	—	2	1	no	—
162	C₂³×C₁₁	—	4	2	no	—
163	C₂³×C₁₁	—	8	4	no	—
164	C₂³×C₁₁	—	8	2	no	—
165	C₂³×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
166	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂³×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
169	Q₈×C₁₁	—	2	2	no	—
170	Q₈×C₁₁	—	4	1	no	—
171	Q₈×C₁₁	—	4	2	no	—
172	Q₈×C₁₁	—	4	1	no	—
173	Q₈×C₁₁	—	4	4	no	—
174	Q₈×C₁₁	—	4	2	no	—
175	D₄×C₁₁	—	2	8	no	—
176	D₄×C₁₁	—	2	4	no	—
177	D₄×C₁₁	—	2	4	no	—
178	D₄×C₁₁	—	4	2	no	—
179	D₄×C₁₁	—	4	4	no	—
180	D₄×C₁₁	—	4	2	no	—
181	D₄×C₁₁	—	4	1	no	—
182	D₄×C₁₁	—	4	1	no	—
183	D₄×C₁₁	—	4	2	no	—
184	D₄×C₁₁	—	4	4	no	—
185	D₄×C₁₁	—	8	4	no	—
186	D₄×C₁₁	—	8	2	no	—
187	D₄×C₁₁	#99	1	4	yes	—
188	C₂×C₄×C₁₁	—	2	4	no	—
189	C₂×C₄×C₁₁	—	2	4	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	4	4	no	—
197	C₂×C₄×C₁₁	—	4	4	no	—
198	C₂×C₄×C₁₁	—	4	2	no	—
199	C₂×C₄×C₁₁	—	4	4	no	—
200	C₂×C₄×C₁₁	—	4	2	no	—
201	C₂×C₄×C₁₁	—	4	8	no	—
202	C₂×C₄×C₁₁	—	8	2	no	—
203	C₂×C₄×C₁₁	—	8	1	no	—
204	C₂×C₄×C₁₁	—	16	8	no	—
205	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
209	C₂×2₋¹⁺⁴	C₄×C₁₁	1	1	yes	characteristic, complemented
210	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	1	yes	characteristic
211	#548	—	2	2	no	—
212	#546	—	2	4	no	—
213	#546	—	2	2	no	—
214	#536	C₄×C₁₁	1	2	yes	complemented
215	#536	C₂²×C₁₁	1	1	yes	characteristic
216	#535	C₄×C₁₁	1	1	yes	characteristic, complemented
217	#535	C₂²×C₁₁	1	2	yes	—
218	#532	C₄×C₁₁	1	2	yes	complemented
219	#532	C₂²×C₁₁	1	1	yes	characteristic
220	C₂×#124	C₄×C₁₁	1	1	yes	characteristic, complemented
221	C₂×#124	C₂²×C₁₁	1	2	yes	—
222	#518	—	2	2	no	—
223	C₄×#41	C₄×C₁₁	1	1	yes	characteristic, complemented
224	#410	—	2	2	no	—
225	#410	C₂²×C₁₁	1	4	yes	—
226	C₂×#99	—	2	4	no	—
227	C₂×#99	C₂²×C₁₁	1	8	yes	—
228	#354	C₂²×C₁₁	1	4	yes	complemented
229	#354	C₂²×C₁₁	1	8	yes	complemented
230	#353	C₂²×C₁₁	1	4	yes	complemented
231	C₂²×C₁₁	—	2	2	no	—
232	C₂²×C₁₁	—	2	1	no	—
233	C₂²×C₁₁	—	2	4	no	—
234	C₂²×C₁₁	—	4	2	no	—
235	C₂²×C₁₁	—	4	1	no	—
236	C₂²×C₁₁	—	4	4	no	—
237	C₂²×C₁₁	—	4	2	no	—
238	C₂²×C₁₁	—	4	2	no	—
239	C₂²×C₁₁	—	4	1	no	—
240	C₂²×C₁₁	—	8	8	no	—
241	C₂²×C₁₁	—	16	2	no	—
242	C₂²×C₁₁	C₂×#99	1	4	yes	—
243	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
244	C₄×C₁₁	—	2	1	no	—
245	C₄×C₁₁	—	2	2	no	—
246	C₄×C₁₁	—	2	2	no	—
247	C₄×C₁₁	—	4	1	no	—
248	C₄×C₁₁	—	4	1	no	—
249	C₄×C₁₁	—	4	2	no	—
250	C₄×C₁₁	—	4	2	no	—
251	C₄×C₁₁	—	4	1	no	—
252	C₄×C₁₁	—	8	8	no	—
253	C₄×C₁₁	C₂×#99	1	2	yes	—
254	2₋¹⁺⁴	—	4	4	no	—
255	H(5,𝔽₂)	—	4	4	no	—
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	1	no	—
258	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
259	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
260	C₂×#41	C₂×C₄×C₁₁	1	2	yes	complemented
261	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
262	C₂×#41	D₄×C₁₁	1	2	yes	—
263	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
266	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	complemented
267	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
268	C₂²×D₄	D₄×C₁₁	1	4	yes	—
269	C₂²×D₄	D₄×C₁₁	1	2	yes	—
270	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
271	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	complemented
272	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
273	#127	C₂×C₄×C₁₁	1	2	yes	complemented
274	#127	C₂³×C₁₁	1	1	yes	characteristic
275	#124	—	2	2	no	—
276	#124	—	2	4	no	—
277	#124	C₂×C₄×C₁₁	1	2	yes	complemented
278	#124	C₂×C₄×C₁₁	1	2	yes	complemented
279	#124	C₂×C₄×C₁₁	1	2	yes	complemented
280	#124	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
281	#124	C₂³×C₁₁	1	1	yes	characteristic
282	#124	C₂³×C₁₁	1	2	yes	—
283	#123	—	2	4	no	—
284	#123	—	2	2	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	#121	—	2	4	no	—
288	#121	—	2	2	no	—
289	#121	—	2	2	no	—
290	#121	—	2	4	no	—
291	#120	—	2	2	no	—
292	#120	—	2	4	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	4	8	no	—
299	#117	—	2	4	no	—
300	#117	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
301	#117	C₂×C₄×C₁₁	1	2	yes	complemented
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	4	no	—
304	C₂×C₂²⋊C₄	—	2	8	no	—
305	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
306	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	complemented
307	#99	—	2	4	no	—
308	#99	—	2	8	no	—
309	#99	C₂³×C₁₁	1	8	yes	—
310	C₂×C₁₁	—	2	1	no	—
311	C₂×C₁₁	—	2	4	no	—
312	C₂×C₁₁	—	4	2	no	—
313	C₂×C₁₁	—	4	4	no	—
314	C₂×C₁₁	—	4	1	no	—
315	C₂×C₁₁	—	8	1	no	—
316	C₂×C₁₁	C₂²×#99	1	1	yes	characteristic
317	C₂⁴	C₁₁×C₂²⋊C₄	1	2	yes	—
318	C₂⁴	C₂×D₄×C₁₁	1	4	yes	—
319	#41	—	2	4	no	—
320	#41	—	4	2	no	—
321	#41	—	4	4	no	—
322	#41	—	4	4	no	—
323	#41	—	4	4	no	—
324	#41	—	4	2	no	—
325	#41	—	4	8	no	—
326	#41	—	4	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	4	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
333	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
334	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
335	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	8	no	—
344	C₂×D₄	C₁₁×C₂²⋊C₄	1	2	yes	—
345	C₂×D₄	C₁₁×C₂²⋊C₄	1	4	yes	—
346	C₂×D₄	C₁₁×C₂²⋊C₄	1	2	yes	—
347	C₂×D₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
349	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
350	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
351	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
352	C₂×D₄	C₂⁴×C₁₁	1	1	yes	characteristic
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	4	8	no	—
360	C₂²×C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	4	8	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	4	4	no	—
382	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
383	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
384	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
385	C₁₁	#33361	1	1	yes	characteristic, direct product factor, Sylow
386	C₂³	—	2	8	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	8	4	no	—
390	C₂³	—	8	2	no	—
391	C₂³	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
392	C₂³	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
393	C₂³	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
395	Q₈	—	2	2	no	—
396	Q₈	—	4	1	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	4	1	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	2	8	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	1	no	—
408	D₄	—	4	1	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	4	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	2	no	—
413	D₄	C₁₁×#99	1	4	yes	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	1	no	—
430	C₂×C₄	—	16	8	no	—
431	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
432	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
433	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
434	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	8	8	no	—
445	C₂²	—	16	2	no	—
446	C₂²	C₂×C₁₁×#99	1	4	yes	—
447	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	8	8	no	—
457	C₄	C₂×C₁₁×#99	1	2	yes	—
458	C₂	—	2	1	no	—
459	C₂	—	2	4	no	—
460	C₂	—	4	2	no	—
461	C₂	—	4	4	no	—
462	C₂	—	4	1	no	—
463	C₂	—	8	1	no	—
464	C₂	C₂²×C₁₁×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	C₂²×#99
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×D₄	C₂⁴×C₁₁
prime radical	C₁₁×#3500	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×D₄×C₁₁ ◁ C₂×C₁₁×H(5,𝔽₂) ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2883	C₂	semidirect
3. C₁₁×#2129	C₂	semidirect
4. C₁₁×#2127	C₂	semidirect
5. C₁₁×#2126	C₂	semidirect
6. C₂×C₁₁×#354	C₂	semidirect
7. C₂×C₁₁×2₋¹⁺⁴	C₄	semidirect
12. C₁₁×#536	C₄	semidirect
14. C₁₁×#535	C₄	semidirect
16. C₁₁×#532	C₄	semidirect
18. C₂×C₁₁×#124	C₄	semidirect
21. C₄×C₁₁×#41	C₄	semidirect
26. C₁₁×#354	C₂²	semidirect
27. C₁₁×#354	C₂²	semidirect
28. C₁₁×#353	C₂²	semidirect
35. C₂×C₁₁×#41	C₂×C₄	semidirect
36. C₂×C₁₁×#41	C₂×C₄	semidirect
40. C₂²×Q₈×C₁₁	C₂×C₄	semidirect
41. C₂²×Q₈×C₁₁	C₂×C₄	semidirect
46. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
47. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
48. C₁₁×#127	C₂×C₄	semidirect
52. C₁₁×#124	C₂×C₄	semidirect
53. C₁₁×#124	C₂×C₄	semidirect
54. C₁₁×#124	C₂×C₄	semidirect
55. C₁₁×#124	C₂×C₄	semidirect
75. C₁₁×#117	C₂×C₄	semidirect
76. C₁₁×#117	C₂×C₄	semidirect
80. C₂×C₄²×C₁₁	C₂×C₄	semidirect
81. C₂×C₄²×C₁₁	C₂×C₄	semidirect
85. #33361	C₁₁	direct (N × H)
155. #2883	C₂×C₁₁	semidirect
156. #2129	C₂×C₁₁	semidirect
157. #2127	C₂×C₁₁	semidirect
158. #2126	C₂×C₁₁	semidirect
159. C₂×#354	C₂×C₁₁	semidirect
209. C₂×2₋¹⁺⁴	C₄×C₁₁	semidirect
214. #536	C₄×C₁₁	semidirect
216. #535	C₄×C₁₁	semidirect
218. #532	C₄×C₁₁	semidirect
220. C₂×#124	C₄×C₁₁	semidirect
223. C₄×#41	C₄×C₁₁	semidirect
228. #354	C₂²×C₁₁	semidirect
229. #354	C₂²×C₁₁	semidirect
230. #353	C₂²×C₁₁	semidirect
260. C₂×#41	C₂×C₄×C₁₁	semidirect
261. C₂×#41	C₂×C₄×C₁₁	semidirect
265. C₂²×Q₈	C₂×C₄×C₁₁	semidirect
266. C₂²×Q₈	C₂×C₄×C₁₁	semidirect
271. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
272. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
273. #127	C₂×C₄×C₁₁	semidirect
277. #124	C₂×C₄×C₁₁	semidirect
278. #124	C₂×C₄×C₁₁	semidirect
279. #124	C₂×C₄×C₁₁	semidirect
280. #124	C₂×C₄×C₁₁	semidirect
300. #117	C₂×C₄×C₁₁	semidirect
301. #117	C₂×C₄×C₁₁	semidirect
305. C₂×C₄²	C₂×C₄×C₁₁	semidirect
306. C₂×C₄²	C₂×C₄×C₁₁	semidirect
385. C₁₁	#33361	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×#3500	2
C₁₁×#2883	2
C₁₁×#2129	2
C₁₁×#2127	2
C₁₁×#2126	2
C₂×C₁₁×#354	2
#33361	11

Subgroups — C11×#33361 #14610554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33361 #14610554