Subgroups — C₁₁×#24288 #14601481

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3067	C₂	1	2	yes	maximal, complemented
3	C₁₁×#3018	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2932	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2050	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2017	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1975	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1813	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1791	C₂	1	2	yes	maximal, complemented
10	C₁₁×#585	C₂²	1	2	yes	—
11	C₁₁×#578	—	2	2	no	—
12	C₁₁×#577	—	2	4	no	—
13	C₁₁×#576	—	2	2	no	—
14	C₁₁×#575	—	2	2	no	—
15	C₁₁×#575	C₂²	1	2	yes	—
16	C₁₁×#575	C₂²	1	4	yes	complemented
17	C₂×C₁₁×#135	—	2	2	no	—
18	C₂×C₁₁×#135	C₂²	1	2	yes	—
19	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic, complemented
21	C₁₁×#532	C₂²	1	1	yes	characteristic
22	C₁₁×#473	—	2	2	no	—
23	C₁₁×#472	—	2	2	no	—
24	C₁₁×#471	—	2	4	no	—
25	C₁₁×#456	—	2	2	no	—
26	C₁₁×#455	—	2	2	no	—
27	C₁₁×#454	—	2	2	no	—
28	C₁₁×#453	—	2	2	no	—
29	C₁₁×#435	—	2	2	no	—
30	C₁₁×#435	—	2	2	no	—
31	C₂×C₁₁×#108	C₂²	1	2	yes	complemented
32	C₁₁×#423	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₁×#104	C₂²	1	4	yes	complemented
34	C₁₁×#413	C₂²	1	2	yes	—
35	C₁₁×#413	C₂²	1	4	yes	complemented
36	C₁₁×#408	C₂²	1	1	yes	characteristic
37	C₁₁×#408	C₂²	1	1	yes	characteristic, complemented
38	C₁₁×#408	C₂²	1	4	yes	complemented
39	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic, complemented
40	C₁₁×#338	C₂²	1	2	yes	complemented
41	C₁₁×2₋¹⁺⁴	—	2	4	no	—
42	C₁₁×2₋¹⁺⁴	—	2	2	no	—
43	C₁₁×H(5,𝔽₂)	—	2	4	no	—
44	C₁₁×H(5,𝔽₂)	—	2	4	no	—
45	C₁₁×H(5,𝔽₂)	—	2	2	no	—
46	C₂×C₁₁×#41	—	2	4	no	—
47	C₂×C₁₁×#41	—	4	4	no	—
48	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
49	C₂×C₁₁×#41	C₂³	1	4	yes	—
50	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
51	C₁₁×#137	—	2	8	no	—
52	C₁₁×#137	—	2	4	no	—
53	C₁₁×#137	—	2	4	no	—
54	C₁₁×#137	—	2	4	no	—
55	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
56	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
57	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
58	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
59	C₁₁×#135	—	2	4	no	—
60	C₁₁×#135	—	2	4	no	—
61	C₁₁×#135	—	2	2	no	—
62	C₁₁×#135	—	2	4	no	—
63	C₁₁×#135	—	2	2	no	—
64	C₁₁×#135	—	2	2	no	—
65	C₁₁×#135	—	2	2	no	—
66	C₁₁×#135	—	4	4	no	—
67	C₂×C₁₁×Q₁₆	—	2	2	no	—
68	C₂×C₁₁×Q₁₆	D₄	1	2	yes	complemented
69	C₂×C₁₁×SD₁₆	—	2	4	no	—
70	C₂×C₁₁×SD₁₆	D₄	1	4	yes	complemented
71	C₂×C₁₁×D₈	—	2	2	no	—
72	C₂×C₁₁×D₈	D₄	1	2	yes	complemented
73	C₁₁×#131	—	2	2	no	—
74	C₁₁×#131	—	2	2	no	—
75	C₁₁×#131	—	2	2	no	—
76	C₁₁×#131	—	2	2	no	—
77	C₂×C₁₁×M₁₆	—	2	1	no	—
78	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
79	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
80	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₁	—	2	1	no	—
83	C₂²×C₈×C₁₁	D₄	1	2	yes	—
84	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
86	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₁×#127	D₄	1	1	yes	characteristic
88	C₁₁×#124	D₄	1	1	yes	characteristic
89	C₁₁×#124	D₄	1	1	yes	characteristic
90	C₁₁×#121	—	2	2	no	—
91	C₄×D₄×C₁₁	—	2	2	no	—
92	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
93	C₁₁×#108	—	2	2	no	—
94	C₁₁×#108	—	2	2	no	—
95	C₁₁×C₄⋊C₈	—	2	2	no	—
96	C₁₁×#104	—	2	4	no	—
97	C₁₁×#104	—	2	4	no	—
98	C₁₁×#101	—	2	2	no	—
99	C₁₁×#101	—	2	4	no	—
100	C₁₁×#100	—	2	2	no	—
101	C₁₁×#100	—	2	4	no	—
102	C₁₁×C₂²⋊C₈	—	2	2	no	—
103	C₁₁×C₂²⋊C₈	—	2	2	no	—
104	C₁₁×C₂²⋊C₈	—	4	4	no	—
105	C₁₁×#97	—	2	1	no	—
106	C₁₁×#97	—	2	1	no	—
107	#24288	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₁₁×#41	—	2	2	no	—
109	C₁₁×#41	—	2	2	no	—
110	C₁₁×#41	—	2	8	no	—
111	C₁₁×#41	—	2	4	no	—
112	C₁₁×#41	—	2	2	no	—
113	C₁₁×#41	—	2	4	no	—
114	C₁₁×#41	—	2	4	no	—
115	C₁₁×#41	—	2	2	no	—
116	C₁₁×#41	—	2	4	no	—
117	C₁₁×#41	—	4	8	no	—
118	C₁₁×#41	—	4	4	no	—
119	C₁₁×#41	—	4	4	no	—
120	C₁₁×#41	—	4	4	no	—
121	C₁₁×#41	—	4	4	no	—
122	C₂×Q₈×C₁₁	—	2	4	no	—
123	C₂×Q₈×C₁₁	—	4	4	no	—
124	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
127	C₂×D₄×C₁₁	—	2	4	no	—
128	C₂×D₄×C₁₁	—	2	1	no	—
129	C₂×D₄×C₁₁	—	2	4	no	—
130	C₂×D₄×C₁₁	—	2	2	no	—
131	C₂×D₄×C₁₁	—	4	4	no	—
132	C₂×D₄×C₁₁	—	4	8	no	—
133	C₂×D₄×C₁₁	—	4	4	no	—
134	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
135	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
137	C₂×D₄×C₁₁	#41	1	2	yes	—
138	C₂²×C₄×C₁₁	—	2	1	no	—
139	C₂²×C₄×C₁₁	—	2	1	no	—
140	C₂²×C₄×C₁₁	—	2	4	no	—
141	C₂²×C₄×C₁₁	—	4	4	no	—
142	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
144	C₁₁×Q₁₆	—	2	4	no	—
145	C₁₁×Q₁₆	—	2	2	no	—
146	C₁₁×Q₁₆	—	2	2	no	—
147	C₁₁×Q₁₆	—	4	4	no	—
148	C₁₁×SD₁₆	—	2	8	no	—
149	C₁₁×SD₁₆	—	2	4	no	—
150	C₁₁×SD₁₆	—	2	4	no	—
151	C₁₁×SD₁₆	—	4	4	no	—
152	C₁₁×SD₁₆	—	4	4	no	—
153	C₁₁×D₈	—	2	4	no	—
154	C₁₁×D₈	—	2	2	no	—
155	C₁₁×D₈	—	2	2	no	—
156	C₁₁×D₈	—	4	4	no	—
157	C₁₁×M₁₆	—	2	4	no	—
158	C₁₁×M₁₆	—	2	2	no	—
159	C₁₁×M₁₆	—	2	2	no	—
160	C₁₁×M₁₆	—	2	4	no	—
161	C₁₁×M₁₆	—	2	4	no	—
162	C₁₁×M₁₆	—	4	1	no	—
163	C₁₁×M₁₆	—	4	1	no	—
164	C₂×C₈×C₁₁	—	2	2	no	—
165	C₂×C₈×C₁₁	—	2	2	no	—
166	C₂×C₈×C₁₁	—	2	1	no	—
167	C₂×C₈×C₁₁	—	2	1	no	—
168	C₂×C₈×C₁₁	—	2	2	no	—
169	C₂×C₈×C₁₁	—	2	4	no	—
170	C₂×C₈×C₁₁	—	4	2	no	—
171	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
176	C₁₁×C₄⋊C₄	—	2	2	no	—
177	C₁₁×C₂²⋊C₄	—	2	2	no	—
178	C₁₁×C₂²⋊C₄	—	2	2	no	—
179	C₄²×C₁₁	—	2	1	no	—
180	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
182	#3584	C₂×C₁₁	1	1	yes	characteristic, complemented
183	#3067	C₂×C₁₁	1	2	yes	complemented
184	#3018	C₂×C₁₁	1	2	yes	complemented
185	#2932	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#2050	C₂×C₁₁	1	2	yes	complemented
187	#2017	C₂×C₁₁	1	2	yes	complemented
188	#1975	C₂×C₁₁	1	2	yes	complemented
189	#1813	C₂×C₁₁	1	1	yes	characteristic, complemented
190	#1791	C₂×C₁₁	1	2	yes	complemented
191	C₂³×C₁₁	—	2	1	no	—
192	C₂³×C₁₁	—	2	4	no	—
193	C₂³×C₁₁	—	4	4	no	—
194	C₂³×C₁₁	#121	1	2	yes	—
195	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
196	Q₈×C₁₁	—	2	2	no	—
197	Q₈×C₁₁	—	2	4	no	—
198	Q₈×C₁₁	—	2	2	no	—
199	Q₈×C₁₁	—	2	4	no	—
200	Q₈×C₁₁	—	4	4	no	—
201	D₄×C₁₁	—	2	4	no	—
202	D₄×C₁₁	—	2	4	no	—
203	D₄×C₁₁	—	2	2	no	—
204	D₄×C₁₁	—	2	2	no	—
205	D₄×C₁₁	—	2	4	no	—
206	D₄×C₁₁	—	4	4	no	—
207	D₄×C₁₁	—	4	8	no	—
208	D₄×C₁₁	—	4	4	no	—
209	D₄×C₁₁	—	4	4	no	—
210	D₄×C₁₁	—	4	2	no	—
211	D₄×C₁₁	—	8	2	no	—
212	C₂×C₄×C₁₁	—	2	2	no	—
213	C₂×C₄×C₁₁	—	2	2	no	—
214	C₂×C₄×C₁₁	—	2	1	no	—
215	C₂×C₄×C₁₁	—	2	1	no	—
216	C₂×C₄×C₁₁	—	2	1	no	—
217	C₂×C₄×C₁₁	—	2	4	no	—
218	C₂×C₄×C₁₁	—	4	8	no	—
219	C₂×C₄×C₁₁	—	4	4	no	—
220	C₂×C₄×C₁₁	—	4	1	no	—
221	C₂×C₄×C₁₁	—	4	4	no	—
222	C₂×C₄×C₁₁	—	4	1	no	—
223	C₂×C₄×C₁₁	—	4	4	no	—
224	C₂×C₄×C₁₁	—	8	1	no	—
225	C₂×C₄×C₁₁	#121	1	2	yes	—
226	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
230	C₈×C₁₁	—	2	2	no	—
231	C₈×C₁₁	—	4	1	no	—
232	C₈×C₁₁	—	4	1	no	—
233	C₈×C₁₁	—	4	4	no	—
234	C₈×C₁₁	#120	1	1	yes	characteristic
235	C₈×C₁₁	#120	1	1	yes	characteristic
236	C₈×C₁₁	#120	1	2	yes	—
237	#585	C₂²×C₁₁	1	2	yes	—
238	#578	—	2	2	no	—
239	#577	—	2	4	no	—
240	#576	—	2	2	no	—
241	#575	—	2	2	no	—
242	#575	C₂²×C₁₁	1	2	yes	—
243	#575	C₂²×C₁₁	1	4	yes	complemented
244	C₂×#135	—	2	2	no	—
245	C₂×#135	C₂²×C₁₁	1	2	yes	—
246	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
247	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic, complemented
248	#532	C₂²×C₁₁	1	1	yes	characteristic
249	#473	—	2	2	no	—
250	#472	—	2	2	no	—
251	#471	—	2	4	no	—
252	#456	—	2	2	no	—
253	#455	—	2	2	no	—
254	#454	—	2	2	no	—
255	#453	—	2	2	no	—
256	#435	—	2	2	no	—
257	#435	—	2	2	no	—
258	C₂×#108	C₂²×C₁₁	1	2	yes	complemented
259	#423	C₂²×C₁₁	1	1	yes	characteristic, complemented
260	C₂×#104	C₂²×C₁₁	1	4	yes	complemented
261	#413	C₂²×C₁₁	1	2	yes	—
262	#413	C₂²×C₁₁	1	4	yes	complemented
263	#408	C₂²×C₁₁	1	1	yes	characteristic
264	#408	C₂²×C₁₁	1	1	yes	characteristic, complemented
265	#408	C₂²×C₁₁	1	4	yes	complemented
266	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic, complemented
267	#338	C₂²×C₁₁	1	2	yes	complemented
268	C₂²×C₁₁	—	2	2	no	—
269	C₂²×C₁₁	—	4	1	no	—
270	C₂²×C₁₁	—	4	2	no	—
271	C₂²×C₁₁	—	4	2	no	—
272	C₂²×C₁₁	—	4	4	no	—
273	C₂²×C₁₁	—	4	1	no	—
274	C₂²×C₁₁	—	8	4	no	—
275	C₂²×C₁₁	—	16	4	no	—
276	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
277	C₂²×C₁₁	#546	1	2	yes	—
278	C₄×C₁₁	—	2	2	no	—
279	C₄×C₁₁	—	4	1	no	—
280	C₄×C₁₁	—	4	1	no	—
281	C₄×C₁₁	—	4	4	no	—
282	C₄×C₁₁	—	4	1	no	—
283	C₄×C₁₁	C₂×#120	1	1	yes	characteristic
284	C₄×C₁₁	#535	1	1	yes	characteristic
285	C₄×C₁₁	D₄²	1	2	yes	—
286	2₋¹⁺⁴	—	2	4	no	—
287	2₋¹⁺⁴	—	2	2	no	—
288	H(5,𝔽₂)	—	2	4	no	—
289	H(5,𝔽₂)	—	2	4	no	—
290	H(5,𝔽₂)	—	2	2	no	—
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	4	4	no	—
293	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
294	C₂×#41	C₂³×C₁₁	1	4	yes	—
295	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
296	#137	—	2	8	no	—
297	#137	—	2	4	no	—
298	#137	—	2	4	no	—
299	#137	—	2	4	no	—
300	AGL(1,ℤ/8)	—	2	8	no	—
301	AGL(1,ℤ/8)	—	2	4	no	—
302	AGL(1,ℤ/8)	—	2	4	no	—
303	AGL(1,ℤ/8)	—	2	4	no	—
304	#135	—	2	4	no	—
305	#135	—	2	4	no	—
306	#135	—	2	2	no	—
307	#135	—	2	4	no	—
308	#135	—	2	2	no	—
309	#135	—	2	2	no	—
310	#135	—	2	2	no	—
311	#135	—	4	4	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×Q₁₆	D₄×C₁₁	1	2	yes	complemented
314	C₂×SD₁₆	—	2	4	no	—
315	C₂×SD₁₆	D₄×C₁₁	1	4	yes	complemented
316	C₂×D₈	—	2	2	no	—
317	C₂×D₈	D₄×C₁₁	1	2	yes	complemented
318	#131	—	2	2	no	—
319	#131	—	2	2	no	—
320	#131	—	2	2	no	—
321	#131	—	2	2	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
324	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
325	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
326	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
327	C₂²×C₈	—	2	1	no	—
328	C₂²×C₈	D₄×C₁₁	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
331	C₄⋊Q₈	D₄×C₁₁	1	1	yes	characteristic
332	#127	D₄×C₁₁	1	1	yes	characteristic
333	#124	D₄×C₁₁	1	1	yes	characteristic
334	#124	D₄×C₁₁	1	1	yes	characteristic
335	#121	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
338	#108	—	2	2	no	—
339	#108	—	2	2	no	—
340	C₄⋊C₈	—	2	2	no	—
341	#104	—	2	4	no	—
342	#104	—	2	4	no	—
343	#101	—	2	2	no	—
344	#101	—	2	4	no	—
345	#100	—	2	2	no	—
346	#100	—	2	4	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	4	4	no	—
350	#97	—	2	1	no	—
351	#97	—	2	1	no	—
352	C₂×C₁₁	—	2	1	no	—
353	C₂×C₁₁	—	2	2	no	—
354	C₂×C₁₁	—	4	2	no	—
355	C₂×C₁₁	—	8	1	no	—
356	C₂×C₁₁	—	8	4	no	—
357	C₂×C₁₁	#2408	1	1	yes	characteristic
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	#41	—	2	8	no	—
361	#41	—	2	4	no	—
362	#41	—	2	2	no	—
363	#41	—	2	4	no	—
364	#41	—	2	4	no	—
365	#41	—	2	2	no	—
366	#41	—	2	4	no	—
367	#41	—	4	8	no	—
368	#41	—	4	4	no	—
369	#41	—	4	4	no	—
370	#41	—	4	4	no	—
371	#41	—	4	4	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	4	4	no	—
374	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
375	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
376	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
385	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
386	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
387	C₂×D₄	C₁₁×#41	1	2	yes	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
394	Q₁₆	—	2	4	no	—
395	Q₁₆	—	2	2	no	—
396	Q₁₆	—	2	2	no	—
397	Q₁₆	—	4	4	no	—
398	SD₁₆	—	2	8	no	—
399	SD₁₆	—	2	4	no	—
400	SD₁₆	—	2	4	no	—
401	SD₁₆	—	4	4	no	—
402	SD₁₆	—	4	4	no	—
403	D₈	—	2	4	no	—
404	D₈	—	2	2	no	—
405	D₈	—	2	2	no	—
406	D₈	—	4	4	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	4	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	4	no	—
411	M₁₆	—	2	4	no	—
412	M₁₆	—	4	1	no	—
413	M₁₆	—	4	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
422	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
423	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
424	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
425	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
426	C₄⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₄²	—	2	1	no	—
430	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
432	C₁₁	#24288	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	1	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	4	4	no	—
436	C₂³	C₁₁×#121	1	2	yes	—
437	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	2	4	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	4	4	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	8	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	2	no	—
453	D₄	—	8	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	8	1	no	—
467	C₂×C₄	C₁₁×#121	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
471	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
472	C₈	—	2	2	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	1	no	—
475	C₈	—	4	4	no	—
476	C₈	C₁₁×#120	1	1	yes	characteristic
477	C₈	C₁₁×#120	1	1	yes	characteristic
478	C₈	C₁₁×#120	1	2	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	8	4	no	—
486	C₂²	—	16	4	no	—
487	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
488	C₂²	C₁₁×#546	1	2	yes	—
489	C₄	—	2	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	4	no	—
493	C₄	—	4	1	no	—
494	C₄	C₂×C₁₁×#120	1	1	yes	characteristic
495	C₄	C₁₁×#535	1	1	yes	characteristic
496	C₄	D₄²×C₁₁	1	2	yes	—
497	C₂	—	2	1	no	—
498	C₂	—	2	2	no	—
499	C₂	—	4	2	no	—
500	C₂	—	8	1	no	—
501	C₂	—	8	4	no	—
502	C₂	C₁₁×#2408	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	#535
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂×C₁₁	#2408
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3584	C₂	semidirect
2. C₁₁×#3067	C₂	semidirect
3. C₁₁×#3018	C₂	semidirect
4. C₁₁×#2932	C₂	semidirect
5. C₁₁×#2050	C₂	semidirect
6. C₁₁×#2017	C₂	semidirect
7. C₁₁×#1975	C₂	semidirect
8. C₁₁×#1813	C₂	semidirect
9. C₁₁×#1791	C₂	semidirect
16. C₁₁×#575	C₂²	semidirect
20. C₂×C₁₁×#131	C₂²	semidirect
31. C₂×C₁₁×#108	C₂²	semidirect
32. C₁₁×#423	C₂²	semidirect
33. C₂×C₁₁×#104	C₂²	semidirect
35. C₁₁×#413	C₂²	semidirect
37. C₁₁×#408	C₂²	semidirect
38. C₁₁×#408	C₂²	semidirect
39. C₂×C₁₁×#97	C₂²	semidirect
40. C₁₁×#338	C₂²	semidirect
68. C₂×C₁₁×Q₁₆	D₄	semidirect
70. C₂×C₁₁×SD₁₆	D₄	semidirect
72. C₂×C₁₁×D₈	D₄	semidirect
107. #24288	C₁₁	direct (N × H)
182. #3584	C₂×C₁₁	semidirect
183. #3067	C₂×C₁₁	semidirect
184. #3018	C₂×C₁₁	semidirect
185. #2932	C₂×C₁₁	semidirect
186. #2050	C₂×C₁₁	semidirect
187. #2017	C₂×C₁₁	semidirect
188. #1975	C₂×C₁₁	semidirect
189. #1813	C₂×C₁₁	semidirect
190. #1791	C₂×C₁₁	semidirect
243. #575	C₂²×C₁₁	semidirect
247. C₂×#131	C₂²×C₁₁	semidirect
258. C₂×#108	C₂²×C₁₁	semidirect
259. #423	C₂²×C₁₁	semidirect
260. C₂×#104	C₂²×C₁₁	semidirect
262. #413	C₂²×C₁₁	semidirect
264. #408	C₂²×C₁₁	semidirect
265. #408	C₂²×C₁₁	semidirect
266. C₂×#97	C₂²×C₁₁	semidirect
267. #338	C₂²×C₁₁	semidirect
313. C₂×Q₁₆	D₄×C₁₁	semidirect
315. C₂×SD₁₆	D₄×C₁₁	semidirect
317. C₂×D₈	D₄×C₁₁	semidirect
432. C₁₁	#24288	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×#3584	2
C₁₁×#3067	2
C₁₁×#3018	2
C₁₁×#2932	2
C₁₁×#2050	2
C₁₁×#2017	2
C₁₁×#1975	2
C₁₁×#1813	2
C₁₁×#1791	2
#24288	11

Subgroups — C11×#24288 #14601481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#24288 #14601481