Subgroups — C₁₁×#33359 #14610552

Order 2816.

1356 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3498	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2883	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2128	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×#353	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₁×H(5,𝔽₂)	C₄	1	1	yes	characteristic, complemented
8	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
9	C₁₁×#550	—	2	2	no	—
10	D₄²×C₁₁	—	2	4	no	—
11	D₄²×C₁₁	—	2	2	no	—
12	C₁₁×#535	C₄	1	1	yes	characteristic, complemented
13	C₁₁×#535	C₄	1	2	yes	complemented
14	C₁₁×#535	C₂²	1	1	yes	characteristic
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×#127	C₄	1	1	yes	characteristic, complemented
19	C₂×C₁₁×#127	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	complemented
24	C₂×C₁₁×#99	—	2	4	no	—
25	C₂×C₁₁×#99	C₂²	1	8	yes	complemented
26	C₁₁×#354	C₂²	1	4	yes	complemented
27	C₁₁×#353	C₂²	1	4	yes	complemented
28	C₁₁×#353	C₂²	1	8	yes	complemented
29	C₁₁×H(5,𝔽₂)	—	4	4	no	—
30	C₁₁×H(5,𝔽₂)	—	4	4	no	—
31	C₂×C₁₁×#41	—	2	1	no	—
32	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
33	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
34	C₂×C₁₁×#41	C₂×C₄	1	2	yes	complemented
35	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic, complemented
36	C₂×C₁₁×#41	D₄	1	2	yes	—
37	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₁	—	2	2	no	—
39	C₂²×D₄×C₁₁	—	2	4	no	—
40	C₂²×D₄×C₁₁	—	2	2	no	—
41	C₂²×D₄×C₁₁	—	2	1	no	—
42	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic, complemented
44	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	complemented
45	C₂²×D₄×C₁₁	D₄	1	4	yes	—
46	C₂²×D₄×C₁₁	D₄	1	2	yes	—
47	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
48	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
49	C₁₁×#127	—	2	2	no	—
50	C₁₁×#127	—	2	4	no	—
51	C₁₁×#127	C₂×C₄	1	2	yes	complemented
52	C₁₁×#127	C₂×C₄	1	2	yes	complemented
53	C₁₁×#127	C₂×C₄	1	2	yes	complemented
54	C₁₁×#127	C₂³	1	1	yes	characteristic
55	C₁₁×#127	C₂³	1	2	yes	—
56	C₁₁×#124	C₂×C₄	1	2	yes	complemented
57	C₁₁×#124	C₂×C₄	1	2	yes	complemented
58	C₁₁×#124	C₂×C₄	1	1	yes	characteristic, complemented
59	C₁₁×#124	C₂³	1	1	yes	characteristic
60	C₁₁×#121	—	2	4	no	—
61	C₁₁×#121	—	2	2	no	—
62	C₁₁×#121	—	2	2	no	—
63	C₁₁×#121	—	2	4	no	—
64	C₁₁×#121	—	2	4	no	—
65	C₁₁×#121	—	2	2	no	—
66	C₁₁×#120	—	2	2	no	—
67	C₁₁×#120	—	2	4	no	—
68	C₁₁×#120	—	2	4	no	—
69	C₁₁×#120	—	2	2	no	—
70	C₄×Q₈×C₁₁	—	2	1	no	—
71	C₄×D₄×C₁₁	—	2	2	no	—
72	C₄×D₄×C₁₁	—	2	1	no	—
73	C₄×D₄×C₁₁	—	2	4	no	—
74	C₄×D₄×C₁₁	—	2	2	no	—
75	C₄×D₄×C₁₁	—	4	8	no	—
76	C₁₁×#117	—	2	4	no	—
77	C₁₁×#117	C₂×C₄	1	1	yes	characteristic, complemented
78	C₁₁×#117	C₂×C₄	1	2	yes	complemented
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	#33359	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₁	—	2	1	no	—
87	C₂⁴×C₁₁	—	2	2	no	—
88	C₂⁴×C₁₁	C₂²⋊C₄	1	2	yes	—
89	C₂⁴×C₁₁	C₂×D₄	1	4	yes	—
90	C₁₁×#41	—	2	4	no	—
91	C₁₁×#41	—	4	2	no	—
92	C₁₁×#41	—	4	4	no	—
93	C₁₁×#41	—	4	4	no	—
94	C₁₁×#41	—	4	4	no	—
95	C₁₁×#41	—	4	2	no	—
96	C₁₁×#41	—	4	4	no	—
97	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×D₄×C₁₁	—	2	8	no	—
101	C₂×D₄×C₁₁	—	2	4	no	—
102	C₂×D₄×C₁₁	—	2	1	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	—	2	4	no	—
106	C₂×D₄×C₁₁	—	2	4	no	—
107	C₂×D₄×C₁₁	—	2	4	no	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	2	1	no	—
110	C₂×D₄×C₁₁	—	4	2	no	—
111	C₂×D₄×C₁₁	—	4	4	no	—
112	C₂×D₄×C₁₁	—	4	4	no	—
113	C₂×D₄×C₁₁	—	4	2	no	—
114	C₂×D₄×C₁₁	—	4	8	no	—
115	C₂×D₄×C₁₁	—	4	8	no	—
116	C₂×D₄×C₁₁	—	4	4	no	—
117	C₂×D₄×C₁₁	—	8	8	no	—
118	C₂×D₄×C₁₁	—	8	4	no	—
119	C₂×D₄×C₁₁	C₂²⋊C₄	1	2	yes	—
120	C₂×D₄×C₁₁	C₂²⋊C₄	1	4	yes	—
121	C₂×D₄×C₁₁	C₂²⋊C₄	1	2	yes	—
122	C₂×D₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
126	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₁₁	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	—	2	1	no	—
130	C₂²×C₄×C₁₁	—	2	2	no	—
131	C₂²×C₄×C₁₁	—	2	2	no	—
132	C₂²×C₄×C₁₁	—	2	1	no	—
133	C₂²×C₄×C₁₁	—	4	8	no	—
134	C₂²×C₄×C₁₁	C₂²⋊C₄	1	4	yes	—
135	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
138	C₁₁×C₄⋊C₄	—	2	2	no	—
139	C₁₁×C₄⋊C₄	—	2	1	no	—
140	C₁₁×C₄⋊C₄	—	2	2	no	—
141	C₁₁×C₄⋊C₄	—	4	4	no	—
142	C₁₁×C₂²⋊C₄	—	2	1	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	4	no	—
147	C₁₁×C₂²⋊C₄	—	2	2	no	—
148	C₁₁×C₂²⋊C₄	—	2	8	no	—
149	C₁₁×C₂²⋊C₄	—	4	8	no	—
150	C₄²×C₁₁	—	2	2	no	—
151	C₄²×C₁₁	—	2	1	no	—
152	C₄²×C₁₁	—	4	4	no	—
153	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
155	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
156	#3498	C₂×C₁₁	1	1	yes	characteristic
157	#2883	C₂×C₁₁	1	2	yes	complemented
158	#2128	C₂×C₁₁	1	2	yes	complemented
159	#2127	C₂×C₁₁	1	4	yes	complemented
160	#2126	C₂×C₁₁	1	2	yes	complemented
161	C₂×#353	C₂×C₁₁	1	4	yes	complemented
162	C₂³×C₁₁	—	2	8	no	—
163	C₂³×C₁₁	—	2	2	no	—
164	C₂³×C₁₁	—	2	1	no	—
165	C₂³×C₁₁	—	4	2	no	—
166	C₂³×C₁₁	—	4	2	no	—
167	C₂³×C₁₁	—	4	4	no	—
168	C₂³×C₁₁	—	8	4	no	—
169	C₂³×C₁₁	—	8	2	no	—
170	C₂³×C₁₁	—	8	4	no	—
171	C₂³×C₁₁	—	8	2	no	—
172	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂³×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
174	C₂³×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
176	Q₈×C₁₁	—	2	2	no	—
177	Q₈×C₁₁	—	4	1	no	—
178	Q₈×C₁₁	—	4	1	no	—
179	D₄×C₁₁	—	2	8	no	—
180	D₄×C₁₁	—	2	4	no	—
181	D₄×C₁₁	—	2	4	no	—
182	D₄×C₁₁	—	4	2	no	—
183	D₄×C₁₁	—	4	4	no	—
184	D₄×C₁₁	—	4	2	no	—
185	D₄×C₁₁	—	4	1	no	—
186	D₄×C₁₁	—	4	1	no	—
187	D₄×C₁₁	—	4	2	no	—
188	D₄×C₁₁	—	4	4	no	—
189	D₄×C₁₁	—	4	8	no	—
190	D₄×C₁₁	—	4	4	no	—
191	D₄×C₁₁	—	4	2	no	—
192	D₄×C₁₁	—	4	4	no	—
193	D₄×C₁₁	—	4	2	no	—
194	D₄×C₁₁	—	8	4	no	—
195	D₄×C₁₁	—	8	4	no	—
196	D₄×C₁₁	—	8	4	no	—
197	D₄×C₁₁	#99	1	4	yes	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	4	no	—
200	C₂×C₄×C₁₁	—	2	4	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	2	1	no	—
204	C₂×C₄×C₁₁	—	2	1	no	—
205	C₂×C₄×C₁₁	—	4	4	no	—
206	C₂×C₄×C₁₁	—	4	4	no	—
207	C₂×C₄×C₁₁	—	4	4	no	—
208	C₂×C₄×C₁₁	—	4	2	no	—
209	C₂×C₄×C₁₁	—	4	2	no	—
210	C₂×C₄×C₁₁	—	4	8	no	—
211	C₂×C₄×C₁₁	—	16	8	no	—
212	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
216	C₂×H(5,𝔽₂)	C₄×C₁₁	1	1	yes	characteristic, complemented
217	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	1	yes	characteristic
218	#550	—	2	2	no	—
219	D₄²	—	2	4	no	—
220	D₄²	—	2	2	no	—
221	#535	C₄×C₁₁	1	1	yes	characteristic, complemented
222	#535	C₄×C₁₁	1	2	yes	complemented
223	#535	C₂²×C₁₁	1	1	yes	characteristic
224	#535	C₂²×C₁₁	1	2	yes	—
225	#532	C₄×C₁₁	1	2	yes	complemented
226	#532	C₂²×C₁₁	1	1	yes	characteristic
227	C₂×#127	C₄×C₁₁	1	1	yes	characteristic, complemented
228	C₂×#127	C₂²×C₁₁	1	2	yes	—
229	#518	—	2	2	no	—
230	C₄×#41	C₄×C₁₁	1	1	yes	characteristic, complemented
231	#410	—	2	2	no	—
232	#410	C₂²×C₁₁	1	4	yes	complemented
233	C₂×#99	—	2	4	no	—
234	C₂×#99	C₂²×C₁₁	1	8	yes	complemented
235	#354	C₂²×C₁₁	1	4	yes	complemented
236	#353	C₂²×C₁₁	1	4	yes	complemented
237	#353	C₂²×C₁₁	1	8	yes	complemented
238	C₂²×C₁₁	—	2	2	no	—
239	C₂²×C₁₁	—	2	1	no	—
240	C₂²×C₁₁	—	2	4	no	—
241	C₂²×C₁₁	—	4	2	no	—
242	C₂²×C₁₁	—	4	1	no	—
243	C₂²×C₁₁	—	4	4	no	—
244	C₂²×C₁₁	—	4	2	no	—
245	C₂²×C₁₁	—	4	2	no	—
246	C₂²×C₁₁	—	4	4	no	—
247	C₂²×C₁₁	—	4	2	no	—
248	C₂²×C₁₁	—	4	1	no	—
249	C₂²×C₁₁	—	8	8	no	—
250	C₂²×C₁₁	—	16	4	no	—
251	C₂²×C₁₁	—	16	2	no	—
252	C₂²×C₁₁	—	16	2	no	—
253	C₂²×C₁₁	C₂×#99	1	4	yes	—
254	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
255	C₄×C₁₁	—	2	2	no	—
256	C₄×C₁₁	—	2	1	no	—
257	C₄×C₁₁	—	2	2	no	—
258	C₄×C₁₁	—	2	2	no	—
259	C₄×C₁₁	—	4	2	no	—
260	C₄×C₁₁	—	4	1	no	—
261	C₄×C₁₁	—	4	1	no	—
262	C₄×C₁₁	—	8	8	no	—
263	C₄×C₁₁	C₂×#99	1	2	yes	—
264	H(5,𝔽₂)	—	4	4	no	—
265	H(5,𝔽₂)	—	4	4	no	—
266	C₂×#41	—	2	1	no	—
267	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
268	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
269	C₂×#41	C₂×C₄×C₁₁	1	2	yes	complemented
270	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
271	C₂×#41	D₄×C₁₁	1	2	yes	—
272	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	4	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
278	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
279	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	complemented
280	C₂²×D₄	D₄×C₁₁	1	4	yes	—
281	C₂²×D₄	D₄×C₁₁	1	2	yes	—
282	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
283	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
284	#127	—	2	2	no	—
285	#127	—	2	4	no	—
286	#127	C₂×C₄×C₁₁	1	2	yes	complemented
287	#127	C₂×C₄×C₁₁	1	2	yes	complemented
288	#127	C₂×C₄×C₁₁	1	2	yes	complemented
289	#127	C₂³×C₁₁	1	1	yes	characteristic
290	#127	C₂³×C₁₁	1	2	yes	—
291	#124	C₂×C₄×C₁₁	1	2	yes	complemented
292	#124	C₂×C₄×C₁₁	1	2	yes	complemented
293	#124	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
294	#124	C₂³×C₁₁	1	1	yes	characteristic
295	#121	—	2	4	no	—
296	#121	—	2	2	no	—
297	#121	—	2	2	no	—
298	#121	—	2	4	no	—
299	#121	—	2	4	no	—
300	#121	—	2	2	no	—
301	#120	—	2	2	no	—
302	#120	—	2	4	no	—
303	#120	—	2	4	no	—
304	#120	—	2	2	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	4	8	no	—
311	#117	—	2	4	no	—
312	#117	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
313	#117	C₂×C₄×C₁₁	1	2	yes	complemented
314	C₂×C₂²⋊C₄	—	2	8	no	—
315	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
316	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	complemented
317	#99	—	2	4	no	—
318	#99	—	2	8	no	—
319	#99	C₂³×C₁₁	1	8	yes	—
320	C₂×C₁₁	—	2	1	no	—
321	C₂×C₁₁	—	2	4	no	—
322	C₂×C₁₁	—	4	2	no	—
323	C₂×C₁₁	—	4	4	no	—
324	C₂×C₁₁	—	4	1	no	—
325	C₂×C₁₁	—	8	1	no	—
326	C₂×C₁₁	—	8	2	no	—
327	C₂×C₁₁	C₂²×#99	1	1	yes	characteristic
328	C₂⁴	—	2	1	no	—
329	C₂⁴	—	2	2	no	—
330	C₂⁴	C₁₁×C₂²⋊C₄	1	2	yes	—
331	C₂⁴	C₂×D₄×C₁₁	1	4	yes	—
332	#41	—	2	4	no	—
333	#41	—	4	2	no	—
334	#41	—	4	4	no	—
335	#41	—	4	4	no	—
336	#41	—	4	4	no	—
337	#41	—	4	2	no	—
338	#41	—	4	4	no	—
339	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
341	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	4	8	no	—
357	C₂×D₄	—	4	8	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	8	8	no	—
360	C₂×D₄	—	8	4	no	—
361	C₂×D₄	C₁₁×C₂²⋊C₄	1	2	yes	—
362	C₂×D₄	C₁₁×C₂²⋊C₄	1	4	yes	—
363	C₂×D₄	C₁₁×C₂²⋊C₄	1	2	yes	—
364	C₂×D₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
365	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
366	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
367	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
368	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
369	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
370	C₂×D₄	C₂⁴×C₁₁	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	4	8	no	—
376	C₂²×C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
377	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	4	8	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	4	4	no	—
395	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
396	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
397	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
398	C₁₁	#33359	1	1	yes	characteristic, direct product factor, Sylow
399	C₂³	—	2	8	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	8	4	no	—
406	C₂³	—	8	2	no	—
407	C₂³	—	8	4	no	—
408	C₂³	—	8	2	no	—
409	C₂³	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
410	C₂³	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
411	C₂³	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
412	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
413	Q₈	—	2	2	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	4	1	no	—
416	D₄	—	2	8	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	4	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	8	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	8	4	no	—
432	D₄	—	8	4	no	—
433	D₄	—	8	4	no	—
434	D₄	C₁₁×#99	1	4	yes	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	—	16	8	no	—
449	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
450	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
451	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
452	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
453	C₂²	—	2	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	8	8	no	—
465	C₂²	—	16	4	no	—
466	C₂²	—	16	2	no	—
467	C₂²	—	16	2	no	—
468	C₂²	C₂×C₁₁×#99	1	4	yes	—
469	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	8	8	no	—
478	C₄	C₂×C₁₁×#99	1	2	yes	—
479	C₂	—	2	1	no	—
480	C₂	—	2	4	no	—
481	C₂	—	4	2	no	—
482	C₂	—	4	4	no	—
483	C₂	—	4	1	no	—
484	C₂	—	8	1	no	—
485	C₂	—	8	2	no	—
486	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×#3498	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×#2128	C₂	semidirect
4. C₁₁×#2127	C₂	semidirect
5. C₁₁×#2126	C₂	semidirect
6. C₂×C₁₁×#353	C₂	semidirect
7. C₂×C₁₁×H(5,𝔽₂)	C₄	semidirect
12. C₁₁×#535	C₄	semidirect
13. C₁₁×#535	C₄	semidirect
16. C₁₁×#532	C₄	semidirect
18. C₂×C₁₁×#127	C₄	semidirect
21. C₄×C₁₁×#41	C₄	semidirect
23. C₁₁×#410	C₂²	semidirect
25. C₂×C₁₁×#99	C₂²	semidirect
26. C₁₁×#354	C₂²	semidirect
27. C₁₁×#353	C₂²	semidirect
28. C₁₁×#353	C₂²	semidirect
34. C₂×C₁₁×#41	C₂×C₄	semidirect
35. C₂×C₁₁×#41	C₂×C₄	semidirect
43. C₂²×D₄×C₁₁	C₂×C₄	semidirect
44. C₂²×D₄×C₁₁	C₂×C₄	semidirect
48. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
51. C₁₁×#127	C₂×C₄	semidirect
52. C₁₁×#127	C₂×C₄	semidirect
53. C₁₁×#127	C₂×C₄	semidirect
56. C₁₁×#124	C₂×C₄	semidirect
57. C₁₁×#124	C₂×C₄	semidirect
58. C₁₁×#124	C₂×C₄	semidirect
77. C₁₁×#117	C₂×C₄	semidirect
78. C₁₁×#117	C₂×C₄	semidirect
80. C₂×C₄²×C₁₁	C₂×C₄	semidirect
81. C₂×C₄²×C₁₁	C₂×C₄	semidirect
85. #33359	C₁₁	direct (N × H)
157. #2883	C₂×C₁₁	semidirect
158. #2128	C₂×C₁₁	semidirect
159. #2127	C₂×C₁₁	semidirect
160. #2126	C₂×C₁₁	semidirect
161. C₂×#353	C₂×C₁₁	semidirect
216. C₂×H(5,𝔽₂)	C₄×C₁₁	semidirect
221. #535	C₄×C₁₁	semidirect
222. #535	C₄×C₁₁	semidirect
225. #532	C₄×C₁₁	semidirect
227. C₂×#127	C₄×C₁₁	semidirect
230. C₄×#41	C₄×C₁₁	semidirect
232. #410	C₂²×C₁₁	semidirect
234. C₂×#99	C₂²×C₁₁	semidirect
235. #354	C₂²×C₁₁	semidirect
236. #353	C₂²×C₁₁	semidirect
237. #353	C₂²×C₁₁	semidirect
269. C₂×#41	C₂×C₄×C₁₁	semidirect
270. C₂×#41	C₂×C₄×C₁₁	semidirect
278. C₂²×D₄	C₂×C₄×C₁₁	semidirect
279. C₂²×D₄	C₂×C₄×C₁₁	semidirect
283. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
286. #127	C₂×C₄×C₁₁	semidirect
287. #127	C₂×C₄×C₁₁	semidirect
288. #127	C₂×C₄×C₁₁	semidirect
291. #124	C₂×C₄×C₁₁	semidirect
292. #124	C₂×C₄×C₁₁	semidirect
293. #124	C₂×C₄×C₁₁	semidirect
312. #117	C₂×C₄×C₁₁	semidirect
313. #117	C₂×C₄×C₁₁	semidirect
315. C₂×C₄²	C₂×C₄×C₁₁	semidirect
316. C₂×C₄²	C₂×C₄×C₁₁	semidirect
398. C₁₁	#33359	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×#3498	2
C₁₁×#2883	2
C₁₁×#2128	2
C₁₁×#2127	2
C₁₁×#2126	2
C₂×C₁₁×#353	2
#33359	11

Subgroups — C11×#33359 #14610552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33359 #14610552