Subgroups — C₁₁×#24282 #14601475

Order 2816.

1308 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#473	C₂	1	2	yes	maximal, complemented
3	C₁₁×#3004	C₂	1	2	yes	maximal
4	C₁₁×#2929	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#2047	C₂	1	2	yes	maximal, complemented
6	C₁₁×#2020	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1979	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1784	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×#137	C₂²	1	4	yes	—
12	C₂²×C₁₁×Q₁₆	—	2	8	no	—
13	C₂²×C₁₁×Q₁₆	—	2	2	no	—
14	C₂²×C₁₁×Q₁₆	—	2	2	no	—
15	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₁₁×#525	C₂²	1	1	yes	characteristic
20	C₁₁×#473	—	2	8	no	—
21	C₁₁×#451	—	2	4	no	—
22	C₁₁×#448	—	2	4	no	—
23	C₁₁×#435	—	2	2	no	—
24	C₈×D₄×C₁₁	—	2	2	no	—
25	C₂×C₁₁×#108	C₂²	1	2	yes	—
26	C₁₁×#424	C₂²	1	1	yes	characteristic
27	C₁₁×#419	C₂²	1	4	yes	—
28	C₂×C₁₁×#101	C₂²	1	4	yes	—
29	C₂×C₁₁×#101	C₂²	1	4	yes	—
30	C₁₁×#408	C₂²	1	1	yes	characteristic
31	C₁₁×#407	C₂²	1	1	yes	characteristic
32	C₁₁×#407	C₂²	1	2	yes	—
33	C₁₁×#405	C₂²	1	1	yes	characteristic
34	C₁₁×#341	C₂²	1	2	yes	—
35	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
36	C₂²×Q₈×C₁₁	—	2	2	no	—
37	C₂²×Q₈×C₁₁	—	2	8	no	—
38	C₂²×Q₈×C₁₁	—	2	4	no	—
39	C₂²×Q₈×C₁₁	—	2	4	no	—
40	C₂²×Q₈×C₁₁	—	4	4	no	—
41	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₁	—	2	2	no	—
43	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×#137	—	2	8	no	—
45	C₁₁×#137	—	4	4	no	—
46	C₂×C₁₁×Q₁₆	—	2	16	no	—
47	C₂×C₁₁×Q₁₆	—	2	16	no	—
48	C₂×C₁₁×Q₁₆	—	2	8	no	—
49	C₂×C₁₁×Q₁₆	—	2	4	no	—
50	C₂×C₁₁×Q₁₆	—	2	4	no	—
51	C₂×C₁₁×Q₁₆	—	2	2	no	—
52	C₂×C₁₁×Q₁₆	—	2	2	no	—
53	C₂×C₁₁×Q₁₆	—	2	4	no	—
54	C₂×C₁₁×Q₁₆	D₄	1	8	yes	complemented
55	C₂×C₁₁×SD₁₆	—	2	4	no	—
56	C₁₁×#131	—	2	4	no	—
57	C₂×C₁₁×M₁₆	—	2	1	no	—
58	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
59	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	—	2	4	no	—
62	C₂²×C₈×C₁₁	—	2	1	no	—
63	C₂²×C₈×C₁₁	D₄	1	2	yes	—
64	C₂²×C₈×C₁₁	D₄	1	2	yes	—
65	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×#123	—	2	1	no	—
68	C₁₁×C₂²⋊Q₈	D₄	1	2	yes	—
69	C₁₁×#121	D₄	1	2	yes	—
70	C₁₁×#120	—	2	1	no	—
71	C₄×D₄×C₁₁	—	2	2	no	—
72	C₁₁×#117	C₂³	1	1	yes	characteristic
73	C₁₁×#108	—	2	4	no	—
74	C₁₁×C₄⋊C₈	—	2	2	no	—
75	C₁₁×#103	—	2	8	no	—
76	C₁₁×#101	—	2	8	no	—
77	C₁₁×#101	—	4	4	no	—
78	C₁₁×C₂²⋊C₈	—	2	2	no	—
79	C₁₁×C₂²⋊C₈	—	2	4	no	—
80	C₁₁×C₂²⋊C₈	—	2	2	no	—
81	C₁₁×#97	—	2	1	no	—
82	C₄×C₈×C₁₁	—	2	1	no	—
83	#24282	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₁	#41	1	1	yes	characteristic
85	C₁₁×#41	—	2	2	no	—
86	C₁₁×#41	—	2	2	no	—
87	C₂×Q₈×C₁₁	—	2	4	no	—
88	C₂×Q₈×C₁₁	—	2	16	no	—
89	C₂×Q₈×C₁₁	—	2	4	no	—
90	C₂×Q₈×C₁₁	—	2	4	no	—
91	C₂×Q₈×C₁₁	—	2	4	no	—
92	C₂×Q₈×C₁₁	—	2	4	no	—
93	C₂×Q₈×C₁₁	—	4	8	no	—
94	C₂×Q₈×C₁₁	—	4	16	no	—
95	C₂×Q₈×C₁₁	—	4	8	no	—
96	C₂×Q₈×C₁₁	—	4	4	no	—
97	C₂×Q₈×C₁₁	C₂×D₄	1	8	yes	—
98	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₁₁	—	2	2	no	—
100	C₂×D₄×C₁₁	—	2	1	no	—
101	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	—	2	2	no	—
103	C₂²×C₄×C₁₁	—	2	2	no	—
104	C₂²×C₄×C₁₁	—	2	4	no	—
105	C₂²×C₄×C₁₁	—	2	1	no	—
106	C₂²×C₄×C₁₁	—	4	8	no	—
107	C₂²×C₄×C₁₁	—	4	4	no	—
108	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
112	C₁₁×Q₁₆	—	2	16	no	—
113	C₁₁×Q₁₆	—	2	8	no	—
114	C₁₁×Q₁₆	—	2	8	no	—
115	C₁₁×Q₁₆	—	4	8	no	—
116	C₁₁×SD₁₆	—	4	8	no	—
117	C₁₁×M₁₆	—	2	2	no	—
118	C₁₁×M₁₆	—	2	4	no	—
119	C₁₁×M₁₆	—	2	2	no	—
120	C₁₁×M₁₆	—	2	4	no	—
121	C₁₁×M₁₆	—	4	2	no	—
122	C₂×C₈×C₁₁	—	2	4	no	—
123	C₂×C₈×C₁₁	—	2	4	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	4	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	4	2	no	—
129	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
133	C₁₁×C₄⋊C₄	—	2	2	no	—
134	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
135	C₁₁×C₂²⋊C₄	—	2	2	no	—
136	C₁₁×C₂²⋊C₄	—	2	1	no	—
137	C₁₁×C₂²⋊C₄	—	2	2	no	—
138	C₄²×C₁₁	—	2	1	no	—
139	C₂³×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
140	C₂×#473	C₂×C₁₁	1	2	yes	complemented
141	#3004	C₂×C₁₁	1	2	yes	—
142	#2929	C₂×C₁₁	1	1	yes	characteristic
143	#2047	C₂×C₁₁	1	2	yes	complemented
144	#2020	C₂×C₁₁	1	2	yes	complemented
145	#1979	C₂×C₁₁	1	2	yes	complemented
146	#1810	C₂×C₁₁	1	1	yes	characteristic, complemented
147	#1784	C₂×C₁₁	1	2	yes	complemented
148	C₂³×C₁₁	—	2	2	no	—
149	C₂³×C₁₁	—	2	4	no	—
150	C₂³×C₁₁	—	2	1	no	—
151	C₂³×C₁₁	#121	1	2	yes	—
152	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
153	Q₈×C₁₁	—	2	8	no	—
154	Q₈×C₁₁	—	2	8	no	—
155	Q₈×C₁₁	—	2	2	no	—
156	Q₈×C₁₁	—	4	16	no	—
157	Q₈×C₁₁	—	4	4	no	—
158	Q₈×C₁₁	—	4	4	no	—
159	D₄×C₁₁	—	2	2	no	—
160	D₄×C₁₁	—	4	2	no	—
161	D₄×C₁₁	—	4	4	no	—
162	C₂×C₄×C₁₁	—	2	2	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	4	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	8	no	—
169	C₂×C₄×C₁₁	—	4	16	no	—
170	C₂×C₄×C₁₁	—	4	4	no	—
171	C₂×C₄×C₁₁	—	4	4	no	—
172	C₂×C₄×C₁₁	—	4	1	no	—
173	C₂×C₄×C₁₁	—	4	1	no	—
174	C₂×C₄×C₁₁	#121	1	2	yes	—
175	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
179	C₈×C₁₁	—	2	2	no	—
180	C₈×C₁₁	—	4	1	no	—
181	C₈×C₁₁	—	4	1	no	—
182	C₈×C₁₁	—	4	4	no	—
183	C₈×C₁₁	#120	1	2	yes	—
184	C₈×C₁₁	#120	1	2	yes	—
185	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
186	C₂×#137	C₂²×C₁₁	1	4	yes	—
187	C₂²×Q₁₆	—	2	8	no	—
188	C₂²×Q₁₆	—	2	2	no	—
189	C₂²×Q₁₆	—	2	2	no	—
190	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
191	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
192	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
194	#525	C₂²×C₁₁	1	1	yes	characteristic
195	#473	—	2	8	no	—
196	#451	—	2	4	no	—
197	#448	—	2	4	no	—
198	#435	—	2	2	no	—
199	C₈×D₄	—	2	2	no	—
200	C₂×#108	C₂²×C₁₁	1	2	yes	—
201	#424	C₂²×C₁₁	1	1	yes	characteristic
202	#419	C₂²×C₁₁	1	4	yes	—
203	C₂×#101	C₂²×C₁₁	1	4	yes	—
204	C₂×#101	C₂²×C₁₁	1	4	yes	—
205	#408	C₂²×C₁₁	1	1	yes	characteristic
206	#407	C₂²×C₁₁	1	2	yes	—
207	#407	C₂²×C₁₁	1	1	yes	characteristic
208	#405	C₂²×C₁₁	1	1	yes	characteristic
209	#341	C₂²×C₁₁	1	2	yes	—
210	C₂²×C₁₁	—	2	8	no	—
211	C₂²×C₁₁	—	2	2	no	—
212	C₂²×C₁₁	—	2	2	no	—
213	C₂²×C₁₁	—	2	2	no	—
214	C₂²×C₁₁	—	4	1	no	—
215	C₂²×C₁₁	—	4	2	no	—
216	C₂²×C₁₁	#473	1	4	yes	complemented
217	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
218	C₂²×C₁₁	#546	1	2	yes	—
219	C₄×C₁₁	—	2	2	no	—
220	C₄×C₁₁	—	4	8	no	—
221	C₄×C₁₁	—	4	1	no	—
222	C₄×C₁₁	—	4	2	no	—
223	C₄×C₁₁	C₂×#120	1	1	yes	characteristic
224	C₄×C₁₁	#535	1	1	yes	characteristic
225	C₄×C₁₁	D₄²	1	2	yes	—
226	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	—	2	8	no	—
229	C₂²×Q₈	—	2	4	no	—
230	C₂²×Q₈	—	2	4	no	—
231	C₂²×Q₈	—	4	4	no	—
232	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
235	#137	—	2	8	no	—
236	#137	—	4	4	no	—
237	C₂×Q₁₆	—	2	16	no	—
238	C₂×Q₁₆	—	2	16	no	—
239	C₂×Q₁₆	—	2	8	no	—
240	C₂×Q₁₆	—	2	4	no	—
241	C₂×Q₁₆	—	2	4	no	—
242	C₂×Q₁₆	—	2	2	no	—
243	C₂×Q₁₆	—	2	2	no	—
244	C₂×Q₁₆	—	2	4	no	—
245	C₂×Q₁₆	D₄×C₁₁	1	8	yes	complemented
246	C₂×SD₁₆	—	2	4	no	—
247	#131	—	2	4	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
250	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
251	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
252	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	D₄×C₁₁	1	2	yes	—
255	C₂²×C₈	D₄×C₁₁	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
258	#123	—	2	1	no	—
259	C₂²⋊Q₈	D₄×C₁₁	1	2	yes	—
260	#121	D₄×C₁₁	1	2	yes	—
261	#120	—	2	1	no	—
262	C₄×D₄	—	2	2	no	—
263	#117	C₂³×C₁₁	1	1	yes	characteristic
264	#108	—	2	4	no	—
265	C₄⋊C₈	—	2	2	no	—
266	#103	—	2	8	no	—
267	#101	—	2	8	no	—
268	#101	—	4	4	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	—	2	4	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	#97	—	2	1	no	—
273	C₄×C₈	—	2	1	no	—
274	C₂×C₁₁	—	2	2	no	—
275	C₂×C₁₁	—	2	4	no	—
276	C₂×C₁₁	—	8	1	no	—
277	C₂×C₁₁	#2408	1	1	yes	characteristic
278	C₂×C₁₁	C₂×#473	1	2	yes	—
279	C₂⁴	C₁₁×#41	1	1	yes	characteristic
280	#41	—	2	2	no	—
281	#41	—	2	2	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	16	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	4	8	no	—
289	C₂×Q₈	—	4	16	no	—
290	C₂×Q₈	—	4	8	no	—
291	C₂×Q₈	—	4	4	no	—
292	C₂×Q₈	C₂×D₄×C₁₁	1	8	yes	—
293	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
305	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
307	Q₁₆	—	2	16	no	—
308	Q₁₆	—	2	8	no	—
309	Q₁₆	—	2	8	no	—
310	Q₁₆	—	4	8	no	—
311	SD₁₆	—	4	8	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	4	no	—
316	M₁₆	—	4	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
325	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₄²	—	2	1	no	—
334	C₁₁	#24282	1	1	yes	characteristic, direct product factor, Sylow
335	C₂³	—	2	2	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	1	no	—
338	C₂³	C₁₁×#121	1	2	yes	—
339	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
340	Q₈	—	2	8	no	—
341	Q₈	—	2	8	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	16	no	—
344	Q₈	—	4	4	no	—
345	Q₈	—	4	4	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	C₁₁×#121	1	2	yes	—
362	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
363	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
364	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
365	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
366	C₈	—	2	2	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	1	no	—
369	C₈	—	4	4	no	—
370	C₈	C₁₁×#120	1	2	yes	—
371	C₈	C₁₁×#120	1	2	yes	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	C₁₁×#473	1	4	yes	complemented
379	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
380	C₂²	C₁₁×#546	1	2	yes	—
381	C₄	—	2	2	no	—
382	C₄	—	4	8	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	2	no	—
385	C₄	C₂×C₁₁×#120	1	1	yes	characteristic
386	C₄	C₁₁×#535	1	1	yes	characteristic
387	C₄	D₄²×C₁₁	1	2	yes	—
388	C₂	—	2	2	no	—
389	C₂	—	2	4	no	—
390	C₂	—	8	1	no	—
391	C₂	C₁₁×#2408	1	1	yes	characteristic
392	C₂	C₂×C₁₁×#473	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₁₁×#525	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₁×Q₁₆	C₂	semidirect
2. C₂×C₁₁×#473	C₂	semidirect
5. C₁₁×#2047	C₂	semidirect
6. C₁₁×#2020	C₂	semidirect
7. C₁₁×#1979	C₂	semidirect
8. C₁₁×#1810	C₂	semidirect
9. C₁₁×#1784	C₂	semidirect
54. C₂×C₁₁×Q₁₆	D₄	semidirect
83. #24282	C₁₁	direct (N × H)
139. C₂³×Q₁₆	C₂×C₁₁	semidirect
140. C₂×#473	C₂×C₁₁	semidirect
143. #2047	C₂×C₁₁	semidirect
144. #2020	C₂×C₁₁	semidirect
145. #1979	C₂×C₁₁	semidirect
146. #1810	C₂×C₁₁	semidirect
147. #1784	C₂×C₁₁	semidirect
216. C₂²×C₁₁	#473	semidirect
245. C₂×Q₁₆	D₄×C₁₁	semidirect
334. C₁₁	#24282	direct (N × H)
378. C₂²	C₁₁×#473	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₁×Q₁₆	2
C₂×C₁₁×#473	2
C₁₁×#3004	2
C₁₁×#2929	2
C₁₁×#2047	2
C₁₁×#2020	2
C₁₁×#1979	2
C₁₁×#1810	2
C₁₁×#1784	2
#24282	11

Subgroups — C11×#24282 #14601475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#24282 #14601475