Subgroups — C₁₁×#22983 #14600176

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3076	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2906	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1946	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1922	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1866	C₂	1	2	yes	maximal
9	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1765	C₂	1	2	yes	maximal
11	C₄×C₁₁×#104	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×#131	C₂²	1	2	yes	—
13	C₁₁×#533	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
15	C₁₁×#479	C₄	1	2	yes	complemented
16	C₁₁×#478	C₄	1	2	yes	complemented
17	C₁₁×#477	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#476	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#475	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#474	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#446	—	2	2	no	—
22	C₁₁×#446	—	2	1	no	—
23	C₈×Q₈×C₁₁	—	2	1	no	—
24	C₂×C₁₁×#108	C₂²	1	2	yes	—
25	C₁₁×#427	C₂²	1	2	yes	—
26	C₁₁×#424	—	2	2	no	—
27	C₁₁×#424	C₂²	1	2	yes	—
28	C₁₁×#424	C₂²	1	2	yes	—
29	C₁₁×#423	—	2	1	no	—
30	C₁₁×#423	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
32	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
36	C₁₁×#416	C₂²	1	2	yes	—
37	C₁₁×#405	C₂²	1	2	yes	—
38	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#97	C₂²	1	2	yes	—
40	C₄³×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#341	C₂²	1	2	yes	—
42	C₁₁×#339	C₂²	1	2	yes	—
43	C₁₁×#339	C₂²	1	1	yes	characteristic
44	C₁₁×#339	C₂²	1	1	yes	characteristic
45	C₁₁×#339	C₂²	1	2	yes	—
46	C₁₁×#336	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
48	C₁₁×#131	—	2	4	no	—
49	C₁₁×#131	—	4	2	no	—
50	C₂×C₁₁×M₁₆	—	2	2	no	—
51	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
52	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	—	2	2	no	—
55	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
57	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
58	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
59	C₁₁×#125	C₂×C₄	1	2	yes	—
60	C₁₁×C₂²⋊Q₈	—	2	1	no	—
61	C₁₁×C₂²⋊Q₈	—	2	1	no	—
62	C₄×Q₈×C₁₁	—	2	1	no	—
63	C₄×Q₈×C₁₁	—	2	1	no	—
64	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄×C₁₁	—	2	1	no	—
67	C₄×D₄×C₁₁	—	2	1	no	—
68	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₁₁×#117	—	2	1	no	—
71	C₁₁×#117	C₂³	1	1	yes	characteristic
72	C₁₁×#117	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₁	—	2	1	no	—
74	C₂×C₄²×C₁₁	—	2	1	no	—
75	C₂×C₄²×C₁₁	—	2	1	no	—
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
79	C₁₁×#108	—	4	2	no	—
80	C₁₁×#107	C₂×C₄	1	2	yes	—
81	C₁₁×#107	C₂×C₄	1	2	yes	—
82	C₁₁×#106	C₂×C₄	1	2	yes	—
83	C₁₁×#106	C₂×C₄	1	2	yes	—
84	C₁₁×C₄⋊C₈	—	2	2	no	—
85	C₁₁×C₄⋊C₈	—	2	2	no	—
86	C₁₁×C₄⋊C₈	—	2	2	no	—
87	C₁₁×C₄⋊C₈	—	2	2	no	—
88	C₁₁×C₄⋊C₈	—	2	1	no	—
89	C₁₁×C₄⋊C₈	—	2	1	no	—
90	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
94	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
95	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
96	C₁₁×#104	—	2	2	no	—
97	C₁₁×#104	Q₈	1	4	yes	complemented
98	C₁₁×#103	C₂×C₄	1	2	yes	—
99	C₁₁×#103	C₂×C₄	1	2	yes	—
100	C₁₁×#102	C₂×C₄	1	2	yes	—
101	C₁₁×#102	C₂×C₄	1	2	yes	—
102	C₁₁×#97	—	2	2	no	—
103	C₁₁×#97	—	2	1	no	—
104	C₁₁×#97	—	4	2	no	—
105	C₄×C₈×C₁₁	—	2	2	no	—
106	C₄×C₈×C₁₁	—	2	1	no	—
107	#22983	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₁₁×#41	—	2	1	no	—
109	C₁₁×#41	—	2	1	no	—
110	C₁₁×#41	C₂×Q₈	1	2	yes	—
111	C₁₁×#41	#41	1	2	yes	—
112	C₂×Q₈×C₁₁	—	2	1	no	—
113	C₂×Q₈×C₁₁	—	2	1	no	—
114	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₁	—	2	1	no	—
116	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	—	2	1	no	—
118	C₂²×C₄×C₁₁	—	2	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	—	2	1	no	—
121	C₂²×C₄×C₁₁	—	2	1	no	—
122	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
125	C₁₁×M₁₆	—	2	1	no	—
126	C₁₁×M₁₆	—	2	2	no	—
127	C₁₁×M₁₆	—	2	1	no	—
128	C₁₁×M₁₆	—	2	2	no	—
129	C₁₁×M₁₆	—	2	1	no	—
130	C₁₁×M₁₆	—	4	4	no	—
131	C₁₁×M₁₆	C₂×Q₈	1	2	yes	—
132	C₂×C₈×C₁₁	—	2	1	no	—
133	C₂×C₈×C₁₁	—	2	1	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	2	2	no	—
138	C₂×C₈×C₁₁	—	2	2	no	—
139	C₂×C₈×C₁₁	—	4	4	no	—
140	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
144	C₁₁×C₄⋊C₄	—	2	1	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	—	2	2	no	—
147	C₁₁×C₄⋊C₄	—	2	2	no	—
148	C₁₁×C₄⋊C₄	—	2	1	no	—
149	C₁₁×C₄⋊C₄	—	2	1	no	—
150	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
151	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
152	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
154	C₁₁×C₂²⋊C₄	—	2	1	no	—
155	C₁₁×C₂²⋊C₄	—	2	2	no	—
156	C₁₁×C₂²⋊C₄	—	2	1	no	—
157	C₁₁×C₂²⋊C₄	—	2	1	no	—
158	C₄²×C₁₁	—	2	1	no	—
159	C₄²×C₁₁	—	2	1	no	—
160	C₄²×C₁₁	—	2	2	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	2	1	no	—
164	C₄²×C₁₁	—	2	1	no	—
165	C₄²×C₁₁	—	4	2	no	—
166	C₄²×C₁₁	—	4	2	no	—
167	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
172	#3076	C₂×C₁₁	1	1	yes	characteristic
173	#2962	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#2906	C₂×C₁₁	1	1	yes	characteristic
175	#1994	C₂×C₁₁	1	1	yes	characteristic, complemented
176	#1950	C₂×C₁₁	1	1	yes	characteristic, complemented
177	#1946	C₂×C₁₁	1	2	yes	complemented
178	#1922	C₂×C₁₁	1	2	yes	complemented
179	#1866	C₂×C₁₁	1	2	yes	—
180	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
181	#1765	C₂×C₁₁	1	2	yes	—
182	C₄×#104	C₂×C₁₁	1	1	yes	characteristic
183	C₂³×C₁₁	—	2	1	no	—
184	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
185	Q₈×C₁₁	—	2	1	no	—
186	Q₈×C₁₁	—	4	2	no	—
187	Q₈×C₁₁	—	8	1	no	—
188	Q₈×C₁₁	C₄×Q₈	1	2	yes	—
189	D₄×C₁₁	—	2	2	no	—
190	D₄×C₁₁	—	2	2	no	—
191	D₄×C₁₁	—	2	1	no	—
192	D₄×C₁₁	C₄×Q₈	1	2	yes	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	2	2	no	—
197	C₂×C₄×C₁₁	—	2	2	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	4	1	no	—
204	C₂×C₄×C₁₁	—	4	1	no	—
205	C₂×C₄×C₁₁	—	4	1	no	—
206	C₂×C₄×C₁₁	—	4	1	no	—
207	C₂×C₄×C₁₁	—	4	1	no	—
208	C₂×C₄×C₁₁	—	4	2	no	—
209	C₂×C₄×C₁₁	—	8	1	no	—
210	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
220	C₈×C₁₁	—	2	2	no	—
221	C₈×C₁₁	—	2	2	no	—
222	C₈×C₁₁	—	2	2	no	—
223	C₈×C₁₁	—	2	2	no	—
224	C₈×C₁₁	—	2	2	no	—
225	C₈×C₁₁	—	4	2	no	—
226	C₈×C₁₁	—	4	1	no	—
227	C₂×#131	C₂²×C₁₁	1	2	yes	—
228	#533	C₂²×C₁₁	1	1	yes	characteristic
229	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
230	#479	C₄×C₁₁	1	2	yes	complemented
231	#478	C₄×C₁₁	1	2	yes	complemented
232	#477	C₄×C₁₁	1	1	yes	characteristic, complemented
233	#476	C₄×C₁₁	1	1	yes	characteristic, complemented
234	#475	C₄×C₁₁	1	1	yes	characteristic, complemented
235	#474	C₄×C₁₁	1	1	yes	characteristic, complemented
236	#446	—	2	2	no	—
237	#446	—	2	1	no	—
238	C₈×Q₈	—	2	1	no	—
239	C₂×#108	C₂²×C₁₁	1	2	yes	—
240	#427	C₂²×C₁₁	1	2	yes	—
241	#424	—	2	2	no	—
242	#424	C₂²×C₁₁	1	2	yes	—
243	#424	C₂²×C₁₁	1	2	yes	—
244	#423	—	2	1	no	—
245	#423	C₂²×C₁₁	1	1	yes	characteristic
246	C₂×C₄⋊C₈	—	2	1	no	—
247	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
249	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
251	#416	C₂²×C₁₁	1	2	yes	—
252	#405	C₂²×C₁₁	1	2	yes	—
253	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
254	C₂×#97	C₂²×C₁₁	1	2	yes	—
255	C₄³	C₂²×C₁₁	1	1	yes	characteristic
256	#341	C₂²×C₁₁	1	2	yes	—
257	#339	C₂²×C₁₁	1	2	yes	—
258	#339	C₂²×C₁₁	1	1	yes	characteristic
259	#339	C₂²×C₁₁	1	1	yes	characteristic
260	#339	C₂²×C₁₁	1	2	yes	—
261	#336	C₂²×C₁₁	1	2	yes	—
262	C₂²×C₁₁	—	2	1	no	—
263	C₂²×C₁₁	—	2	1	no	—
264	C₂²×C₁₁	—	2	2	no	—
265	C₂²×C₁₁	—	4	1	no	—
266	C₂²×C₁₁	—	4	1	no	—
267	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
268	C₂²×C₁₁	#552	1	1	yes	characteristic
269	C₂²×C₁₁	#554	1	1	yes	characteristic
270	C₄×C₁₁	—	2	2	no	—
271	C₄×C₁₁	—	2	1	no	—
272	C₄×C₁₁	—	2	1	no	—
273	C₄×C₁₁	—	2	1	no	—
274	C₄×C₁₁	—	4	2	no	—
275	C₄×C₁₁	—	4	2	no	—
276	C₄×C₁₁	—	4	1	no	—
277	C₄×C₁₁	—	4	2	no	—
278	C₄×C₁₁	—	4	1	no	—
279	C₄×C₁₁	—	4	2	no	—
280	C₄×C₁₁	#444	1	2	yes	—
281	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
282	C₄×C₁₁	#520	1	1	yes	characteristic
283	C₄×C₁₁	#546	1	1	yes	characteristic
284	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
285	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
286	#131	—	2	4	no	—
287	#131	—	4	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
290	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
291	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
295	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
296	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
297	#125	C₂×C₄×C₁₁	1	2	yes	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
303	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
307	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
308	#117	—	2	1	no	—
309	#117	C₂³×C₁₁	1	1	yes	characteristic
310	#117	C₂³×C₁₁	1	2	yes	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
317	#108	—	4	2	no	—
318	#107	C₂×C₄×C₁₁	1	2	yes	—
319	#107	C₂×C₄×C₁₁	1	2	yes	—
320	#106	C₂×C₄×C₁₁	1	2	yes	—
321	#106	C₂×C₄×C₁₁	1	2	yes	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	2	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
329	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
330	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
331	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
332	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
333	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
334	#104	—	2	2	no	—
335	#104	Q₈×C₁₁	1	4	yes	complemented
336	#103	C₂×C₄×C₁₁	1	2	yes	—
337	#103	C₂×C₄×C₁₁	1	2	yes	—
338	#102	C₂×C₄×C₁₁	1	2	yes	—
339	#102	C₂×C₄×C₁₁	1	2	yes	—
340	#97	—	2	2	no	—
341	#97	—	2	1	no	—
342	#97	—	4	2	no	—
343	C₄×C₈	—	2	2	no	—
344	C₄×C₈	—	2	1	no	—
345	C₂×C₁₁	—	2	1	no	—
346	C₂×C₁₁	—	2	1	no	—
347	C₂×C₁₁	—	4	2	no	—
348	C₂×C₁₁	#2360	1	1	yes	characteristic
349	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
350	C₂×C₁₁	#2956	1	1	yes	characteristic
351	#41	—	2	1	no	—
352	#41	—	2	1	no	—
353	#41	C₂×Q₈×C₁₁	1	2	yes	—
354	#41	C₁₁×#41	1	2	yes	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
366	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
368	M₁₆	—	2	1	no	—
369	M₁₆	—	2	1	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	4	4	no	—
374	M₁₆	C₂×Q₈×C₁₁	1	2	yes	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	4	no	—
383	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
384	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
385	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
394	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
395	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	4	2	no	—
409	C₄²	—	4	2	no	—
410	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
411	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
414	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
415	C₁₁	#22983	1	1	yes	characteristic, direct product factor, Sylow
416	C₂³	—	2	1	no	—
417	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	8	1	no	—
421	Q₈	C₄×Q₈×C₁₁	1	2	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	C₄×Q₈×C₁₁	1	2	yes	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	1	no	—
443	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
444	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
445	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
446	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
447	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
449	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
450	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
451	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
466	C₂²	C₁₁×#552	1	1	yes	characteristic
467	C₂²	C₁₁×#554	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	2	no	—
478	C₄	C₁₁×#444	1	2	yes	—
479	C₄	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
480	C₄	C₁₁×#520	1	1	yes	characteristic
481	C₄	C₁₁×#546	1	1	yes	characteristic
482	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	C₁₁×#2360	1	1	yes	characteristic
487	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
488	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×#41	C₂³
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×#2962	C₂	semidirect
4. C₁₁×#1994	C₂	semidirect
5. C₁₁×#1950	C₂	semidirect
6. C₁₁×#1946	C₂	semidirect
7. C₁₁×#1922	C₂	semidirect
9. C₁₁×#1767	C₂	semidirect
15. C₁₁×#479	C₄	semidirect
16. C₁₁×#478	C₄	semidirect
17. C₁₁×#477	C₄	semidirect
18. C₁₁×#476	C₄	semidirect
19. C₁₁×#475	C₄	semidirect
20. C₁₁×#474	C₄	semidirect
97. C₁₁×#104	Q₈	semidirect
107. #22983	C₁₁	direct (N × H)
173. #2962	C₂×C₁₁	semidirect
175. #1994	C₂×C₁₁	semidirect
176. #1950	C₂×C₁₁	semidirect
177. #1946	C₂×C₁₁	semidirect
178. #1922	C₂×C₁₁	semidirect
180. #1767	C₂×C₁₁	semidirect
230. #479	C₄×C₁₁	semidirect
231. #478	C₄×C₁₁	semidirect
232. #477	C₄×C₁₁	semidirect
233. #476	C₄×C₁₁	semidirect
234. #475	C₄×C₁₁	semidirect
235. #474	C₄×C₁₁	semidirect
335. #104	Q₈×C₁₁	semidirect
415. C₁₁	#22983	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×#3076	2
C₁₁×#2962	2
C₁₁×#2906	2
C₁₁×#1994	2
C₁₁×#1950	2
C₁₁×#1946	2
C₁₁×#1922	2
C₁₁×#1866	2
C₁₁×#1767	2
C₁₁×#1765	2
C₄×C₁₁×#104	2
#22983	11

Subgroups — C11×#22983 #14600176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22983 #14600176