Subgroups — C₁₁×#24988 #14602181

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#472	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2081	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2048	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1904	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1829	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1814	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1757	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
15	C₁₁×#518	C₂²	1	2	yes	—
16	C₁₁×#472	—	2	2	no	—
17	C₁₁×#472	—	2	2	no	—
18	C₁₁×#442	—	2	2	no	—
19	C₄×C₁₁×D₈	—	2	2	no	—
20	C₁₁×#430	C₂²	1	2	yes	—
21	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
23	C₁₁×#427	C₂²	1	1	yes	characteristic
24	C₁₁×#421	C₂²	1	2	yes	—
25	C₁₁×#418	C₂²	1	2	yes	—
26	C₁₁×#418	C₂²	1	2	yes	—
27	C₁₁×#413	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#100	C₂²	1	2	yes	—
29	C₂×C₁₁×#100	C₂²	1	2	yes	—
30	C₁₁×#410	C₂²	1	1	yes	characteristic
31	C₁₁×#405	C₂²	1	1	yes	characteristic
32	C₁₁×#405	C₂²	1	1	yes	characteristic
33	C₁₁×#344	C₂²	1	2	yes	—
34	C₁₁×#344	C₂²	1	1	yes	characteristic
35	C₁₁×#344	C₂²	1	1	yes	characteristic
36	C₁₁×#344	C₂²	1	2	yes	—
37	C₁₁×#344	C₂²	1	2	yes	—
38	C₁₁×H(3,ℤ/4)	C₂²	1	2	yes	—
39	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
41	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
42	C₁₁×AGL(1,ℤ/8)	—	4	2	no	—
43	C₂×C₁₁×SD₁₆	—	2	2	no	—
44	C₂×C₁₁×D₈	—	2	2	no	—
45	C₂×C₁₁×D₈	—	2	1	no	—
46	C₂×C₁₁×D₈	—	2	1	no	—
47	C₂×C₁₁×D₈	—	2	1	no	—
48	C₂×C₁₁×D₈	—	2	1	no	—
49	C₂×C₁₁×D₈	D₄	1	2	yes	—
50	C₂×C₁₁×D₈	D₄	1	2	yes	—
51	C₁₁×#131	—	2	1	no	—
52	C₁₁×#131	—	2	1	no	—
53	C₁₁×#131	—	2	1	no	—
54	C₁₁×#131	—	2	1	no	—
55	C₂×C₁₁×M₁₆	—	2	1	no	—
56	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
60	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	—	2	1	no	—
62	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₁	—	2	4	no	—
64	C₄×D₄×C₁₁	—	4	2	no	—
65	C₁₁×#117	C₂³	1	1	yes	characteristic
66	C₁₁×#117	C₂³	1	2	yes	—
67	C₁₁×#117	C₂³	1	1	yes	characteristic
68	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
69	C₁₁×#108	—	2	1	no	—
70	C₁₁×#108	—	2	1	no	—
71	C₁₁×#108	—	2	1	no	—
72	C₁₁×#108	—	2	1	no	—
73	C₁₁×#108	—	4	2	no	—
74	C₁₁×#107	—	2	1	no	—
75	C₁₁×#106	—	2	1	no	—
76	C₁₁×#104	—	4	2	no	—
77	C₁₁×#102	—	2	4	no	—
78	C₁₁×#102	—	4	2	no	—
79	C₁₁×#101	—	2	1	no	—
80	C₁₁×#100	—	2	4	no	—
81	C₁₁×#100	—	2	1	no	—
82	C₁₁×#100	—	4	2	no	—
83	C₁₁×#99	—	2	2	no	—
84	C₁₁×#97	—	2	1	no	—
85	C₁₁×#97	—	2	1	no	—
86	C₄×C₈×C₁₁	—	2	1	no	—
87	C₄×C₈×C₁₁	—	2	1	no	—
88	#24988	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₁	—	2	2	no	—
90	C₁₁×#41	—	2	1	no	—
91	C₁₁×#41	—	2	1	no	—
92	C₁₁×#41	—	2	1	no	—
93	C₁₁×#41	—	2	1	no	—
94	C₂×Q₈×C₁₁	#41	1	1	yes	characteristic
95	C₂×D₄×C₁₁	—	2	1	no	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	—	2	2	no	—
98	C₂×D₄×C₁₁	—	2	2	no	—
99	C₂×D₄×C₁₁	—	2	2	no	—
100	C₂×D₄×C₁₁	—	2	2	no	—
101	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
102	C₂×D₄×C₁₁	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	—	2	1	no	—
104	C₂²×C₄×C₁₁	—	4	4	no	—
105	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
106	C₁₁×SD₁₆	—	4	4	no	—
107	C₁₁×D₈	—	2	2	no	—
108	C₁₁×D₈	—	2	2	no	—
109	C₁₁×D₈	—	2	2	no	—
110	C₁₁×D₈	—	2	2	no	—
111	C₁₁×D₈	—	4	4	no	—
112	C₁₁×M₁₆	—	2	1	no	—
113	C₁₁×M₁₆	—	2	2	no	—
114	C₁₁×M₁₆	—	2	1	no	—
115	C₁₁×M₁₆	—	2	1	no	—
116	C₁₁×M₁₆	—	2	2	no	—
117	C₁₁×M₁₆	—	2	1	no	—
118	C₁₁×M₁₆	—	2	1	no	—
119	C₁₁×M₁₆	—	2	2	no	—
120	C₁₁×M₁₆	—	2	1	no	—
121	C₁₁×M₁₆	—	2	2	no	—
122	C₁₁×M₁₆	—	4	1	no	—
123	C₁₁×M₁₆	—	4	1	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	—	2	2	no	—
129	C₂×C₈×C₁₁	—	4	1	no	—
130	C₂×C₈×C₁₁	—	4	1	no	—
131	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
134	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
135	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
136	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
137	C₁₁×C₄⋊C₄	—	2	1	no	—
138	C₁₁×C₄⋊C₄	—	2	2	no	—
139	C₁₁×C₄⋊C₄	—	2	1	no	—
140	C₁₁×C₂²⋊C₄	—	2	1	no	—
141	C₁₁×C₂²⋊C₄	—	2	2	no	—
142	C₁₁×C₂²⋊C₄	—	4	4	no	—
143	C₁₁×C₂²⋊C₄	#41	1	2	yes	—
144	C₄²×C₁₁	—	2	1	no	—
145	C₄²×C₁₁	—	2	1	no	—
146	C₄²×C₁₁	—	2	2	no	—
147	C₂×#472	C₂×C₁₁	1	1	yes	characteristic
148	#2948	C₂×C₁₁	1	1	yes	characteristic, complemented
149	#2081	C₂×C₁₁	1	2	yes	complemented
150	#2048	C₂×C₁₁	1	2	yes	complemented
151	#1978	C₂×C₁₁	1	1	yes	characteristic, complemented
152	#1953	C₂×C₁₁	1	1	yes	characteristic, complemented
153	#1904	C₂×C₁₁	1	2	yes	complemented
154	#1833	C₂×C₁₁	1	1	yes	characteristic, complemented
155	#1829	C₂×C₁₁	1	2	yes	complemented
156	#1814	C₂×C₁₁	1	1	yes	characteristic, complemented
157	#1757	C₂×C₁₁	1	1	yes	characteristic, complemented
158	C₂³×C₁₁	—	2	1	no	—
159	C₂³×C₁₁	—	2	4	no	—
160	C₂³×C₁₁	—	4	2	no	—
161	C₂³×C₁₁	—	4	2	no	—
162	C₂³×C₁₁	—	16	2	no	—
163	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
164	Q₈×C₁₁	—	2	1	no	—
165	Q₈×C₁₁	—	2	1	no	—
166	D₄×C₁₁	—	2	4	no	—
167	D₄×C₁₁	—	2	1	no	—
168	D₄×C₁₁	—	2	4	no	—
169	D₄×C₁₁	—	2	1	no	—
170	D₄×C₁₁	—	4	1	no	—
171	D₄×C₁₁	—	4	1	no	—
172	D₄×C₁₁	—	4	2	no	—
173	D₄×C₁₁	—	4	2	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	4	1	no	—
177	C₂×C₄×C₁₁	—	4	1	no	—
178	C₂×C₄×C₁₁	—	4	2	no	—
179	C₂×C₄×C₁₁	—	4	1	no	—
180	C₂×C₄×C₁₁	—	16	4	no	—
181	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
187	C₈×C₁₁	—	4	1	no	—
188	C₈×C₁₁	—	4	2	no	—
189	C₈×C₁₁	—	4	1	no	—
190	C₈×C₁₁	—	4	2	no	—
191	C₈×C₁₁	—	4	1	no	—
192	C₈×C₁₁	#123	1	1	yes	characteristic
193	C₈×C₁₁	#123	1	1	yes	characteristic
194	C₈×C₁₁	#123	1	1	yes	characteristic
195	C₈×C₁₁	#123	1	1	yes	characteristic
196	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
197	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
199	#518	C₂²×C₁₁	1	2	yes	—
200	#472	—	2	2	no	—
201	#472	—	2	2	no	—
202	#442	—	2	2	no	—
203	C₄×D₈	—	2	2	no	—
204	#430	C₂²×C₁₁	1	2	yes	—
205	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
206	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
207	#427	C₂²×C₁₁	1	1	yes	characteristic
208	#421	C₂²×C₁₁	1	2	yes	—
209	#418	C₂²×C₁₁	1	2	yes	—
210	#418	C₂²×C₁₁	1	2	yes	—
211	#413	C₂²×C₁₁	1	1	yes	characteristic
212	C₂×#100	C₂²×C₁₁	1	2	yes	—
213	C₂×#100	C₂²×C₁₁	1	2	yes	—
214	#410	C₂²×C₁₁	1	1	yes	characteristic
215	#405	C₂²×C₁₁	1	1	yes	characteristic
216	#405	C₂²×C₁₁	1	1	yes	characteristic
217	#344	C₂²×C₁₁	1	2	yes	—
218	#344	C₂²×C₁₁	1	2	yes	—
219	#344	C₂²×C₁₁	1	1	yes	characteristic
220	#344	C₂²×C₁₁	1	1	yes	characteristic
221	#344	C₂²×C₁₁	1	2	yes	—
222	H(3,ℤ/4)	C₂²×C₁₁	1	2	yes	—
223	C₂²×C₁₁	—	4	1	no	—
224	C₂²×C₁₁	—	4	1	no	—
225	C₂²×C₁₁	—	4	4	no	—
226	C₂²×C₁₁	—	8	4	no	—
227	C₂²×C₁₁	—	8	1	no	—
228	C₂²×C₁₁	—	16	2	no	—
229	C₂²×C₁₁	—	16	2	no	—
230	C₂²×C₁₁	#529	1	1	yes	characteristic
231	C₂²×C₁₁	#546	1	1	yes	characteristic
232	C₂²×C₁₁	#555	1	1	yes	characteristic
233	C₄×C₁₁	—	4	2	no	—
234	C₄×C₁₁	—	4	1	no	—
235	C₄×C₁₁	—	8	1	no	—
236	C₄×C₁₁	—	8	2	no	—
237	C₄×C₁₁	C₂×#123	1	1	yes	characteristic
238	C₄×C₁₁	#540	1	1	yes	characteristic
239	C₄×C₁₁	#546	1	1	yes	characteristic
240	C₄×C₁₁	#553	1	1	yes	characteristic
241	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
242	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
243	AGL(1,ℤ/8)	—	2	4	no	—
244	AGL(1,ℤ/8)	—	4	2	no	—
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×D₈	—	2	2	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂×D₈	—	2	1	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	D₄×C₁₁	1	2	yes	—
252	C₂×D₈	D₄×C₁₁	1	2	yes	—
253	#131	—	2	1	no	—
254	#131	—	2	1	no	—
255	#131	—	2	1	no	—
256	#131	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
259	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
260	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
262	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
265	C₄×D₄	—	2	4	no	—
266	C₄×D₄	—	4	2	no	—
267	#117	C₂³×C₁₁	1	2	yes	—
268	#117	C₂³×C₁₁	1	1	yes	characteristic
269	#117	C₂³×C₁₁	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	#108	—	2	1	no	—
272	#108	—	2	1	no	—
273	#108	—	2	1	no	—
274	#108	—	2	1	no	—
275	#108	—	4	2	no	—
276	#107	—	2	1	no	—
277	#106	—	2	1	no	—
278	#104	—	4	2	no	—
279	#102	—	2	4	no	—
280	#102	—	4	2	no	—
281	#101	—	2	1	no	—
282	#100	—	2	4	no	—
283	#100	—	2	1	no	—
284	#100	—	4	2	no	—
285	#99	—	2	2	no	—
286	#97	—	2	1	no	—
287	#97	—	2	1	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₂×C₁₁	—	2	1	no	—
291	C₂×C₁₁	—	2	1	no	—
292	C₂×C₁₁	—	2	1	no	—
293	C₂×C₁₁	—	8	1	no	—
294	C₂×C₁₁	—	8	4	no	—
295	C₂×C₁₁	#2420	1	1	yes	characteristic
296	C₂⁴	—	2	2	no	—
297	#41	—	2	1	no	—
298	#41	—	2	1	no	—
299	#41	—	2	1	no	—
300	#41	—	2	1	no	—
301	C₂×Q₈	C₁₁×#41	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
309	C₂×D₄	C₁₁×#41	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	4	no	—
312	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
313	SD₁₆	—	4	4	no	—
314	D₈	—	2	2	no	—
315	D₈	—	2	2	no	—
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	4	4	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	2	1	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	1	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	1	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
340	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
341	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
342	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
343	C₂×C₈	C₁₁×#41	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	C₁₁×#41	1	2	yes	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	2	no	—
354	C₁₁	#24988	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	—	2	1	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	16	2	no	—
360	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
361	Q₈	—	2	1	no	—
362	Q₈	—	2	1	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	1	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	16	4	no	—
378	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
379	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
380	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
381	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
382	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
384	C₈	—	4	1	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	1	no	—
389	C₈	C₁₁×#123	1	1	yes	characteristic
390	C₈	C₁₁×#123	1	1	yes	characteristic
391	C₈	C₁₁×#123	1	1	yes	characteristic
392	C₈	C₁₁×#123	1	1	yes	characteristic
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	8	4	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	16	2	no	—
399	C₂²	—	16	2	no	—
400	C₂²	C₁₁×#529	1	1	yes	characteristic
401	C₂²	C₁₁×#546	1	1	yes	characteristic
402	C₂²	C₁₁×#555	1	1	yes	characteristic
403	C₄	—	4	2	no	—
404	C₄	—	4	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	1	no	—
407	C₄	C₂×C₁₁×#123	1	1	yes	characteristic
408	C₄	C₁₁×#540	1	1	yes	characteristic
409	C₄	C₁₁×#546	1	1	yes	characteristic
410	C₄	C₁₁×#553	1	1	yes	characteristic
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	8	4	no	—
415	C₂	—	8	1	no	—
416	C₂	C₁₁×#2420	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	#2420
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#472	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2948	C₂	semidirect
3. C₁₁×#2081	C₂	semidirect
4. C₁₁×#2048	C₂	semidirect
5. C₁₁×#1978	C₂	semidirect
6. C₁₁×#1953	C₂	semidirect
7. C₁₁×#1904	C₂	semidirect
8. C₁₁×#1833	C₂	semidirect
9. C₁₁×#1829	C₂	semidirect
10. C₁₁×#1814	C₂	semidirect
11. C₁₁×#1757	C₂	semidirect
88. #24988	C₁₁	direct (N × H)
148. #2948	C₂×C₁₁	semidirect
149. #2081	C₂×C₁₁	semidirect
150. #2048	C₂×C₁₁	semidirect
151. #1978	C₂×C₁₁	semidirect
152. #1953	C₂×C₁₁	semidirect
153. #1904	C₂×C₁₁	semidirect
154. #1833	C₂×C₁₁	semidirect
155. #1829	C₂×C₁₁	semidirect
156. #1814	C₂×C₁₁	semidirect
157. #1757	C₂×C₁₁	semidirect
354. C₁₁	#24988	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×#472	2
C₁₁×#2948	2
C₁₁×#2081	2
C₁₁×#2048	2
C₁₁×#1978	2
C₁₁×#1953	2
C₁₁×#1904	2
C₁₁×#1833	2
C₁₁×#1829	2
C₁₁×#1814	2
C₁₁×#1757	2
#24988	11

Subgroups — C11×#24988 #14602181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#24988 #14602181