Subgroups — #14725796

Order 2816.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079175	C₂	1	1	yes	maximal, characteristic
2	#13077717	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077682	C₂	1	1	yes	maximal, characteristic
4	#13067520	C₂	1	2	yes	maximal, complemented
5	#13067461	C₂	1	2	yes	maximal, complemented
6	#13067454	C₂	1	2	yes	maximal, complemented
7	#13067430	C₂	1	2	yes	maximal, complemented
8	#13067364	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067038	C₂	1	1	yes	maximal, characteristic, complemented
10	#13067034	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	#10623008	C₂²	1	1	yes	characteristic
13	#10623001	C₂²	1	1	yes	characteristic
14	C₁₁×#431	C₂²	1	1	yes	characteristic
15	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	#10622727	C₄	1	2	yes	—
18	#10622727	C₄	1	2	yes	—
19	#10622538	C₂²	1	1	yes	characteristic
20	#10622538	C₂²	1	1	yes	characteristic
21	#10622451	—	2	1	no	—
22	#10622447	—	2	1	no	—
23	#10622444	—	2	1	no	—
24	#10622443	—	2	1	no	—
25	#10622340	—	2	2	no	—
26	#10622333	—	2	2	no	—
27	#10622307	C₄	1	1	yes	characteristic
28	#10622306	C₄	1	1	yes	characteristic
29	C₄×#4314	C₂²	1	2	yes	—
30	C₄×#4314	C₂²	1	2	yes	—
31	#10622301	C₂²	1	2	yes	—
32	C₈×D₄₄	C₂²	1	2	yes	—
33	#10622294	C₄	1	1	yes	characteristic
34	#10622293	C₄	1	1	yes	characteristic
35	#10622292	C₂²	1	2	yes	—
36	C₈×Dic₂₂	C₂²	1	2	yes	—
37	C₁₁×#322	C₂²	1	2	yes	—
38	C₁₁×#322	C₂²	1	2	yes	—
39	#10622097	C₂²	1	2	yes	—
40	#10622097	C₂²	1	2	yes	—
41	#10622096	C₂²	1	1	yes	characteristic
42	#10622096	C₂²	1	1	yes	characteristic
43	#10622095	C₂²	1	1	yes	characteristic
44	#10622095	C₂²	1	1	yes	characteristic
45	#10622094	C₂²	1	2	yes	—
46	#10622094	C₂²	1	2	yes	—
47	C₂×#4339	—	2	1	no	—
48	C₂×C₁₁×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
52	#66983	—	2	1	no	—
53	#66983	C₂×C₄	1	2	yes	—
54	#66979	—	2	1	no	—
55	#66977	—	2	1	no	—
56	#66977	C₂×C₄	1	2	yes	—
57	C₂×#4314	C₂×C₄	1	2	yes	—
58	C₂×#4314	C₂×C₄	1	2	yes	—
59	C₂×#4313	—	2	2	no	—
60	C₂×C₈×D₁₁	—	2	2	no	—
61	#66928	—	2	1	no	—
62	#66927	C₂×C₄	1	1	yes	characteristic
63	C₄×D₄₄	—	2	1	no	—
64	C₄×D₄₄	C₂³	1	2	yes	—
65	#66923	—	2	1	no	—
66	#66922	C₂×C₄	1	1	yes	characteristic
67	#66922	C₂×C₄	1	1	yes	characteristic
68	#66922	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₂₂	—	2	1	no	—
70	C₄×Dic₂₂	C₂³	1	2	yes	—
71	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
72	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
73	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
74	C₁₁×#97	—	2	1	no	—
75	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₁	C₂³	1	2	yes	—
78	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₁	C₂³	1	2	yes	—
81	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
82	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
83	#66885	C₂×C₄	1	2	yes	—
84	#66885	C₂×C₄	1	2	yes	—
85	(C₂×D₁₁)⋊C₈	—	2	2	no	—
86	(C₂×D₁₁)⋊C₈	—	2	2	no	—
87	#66881	C₂×C₄	1	2	yes	—
88	#66881	C₂×C₄	1	2	yes	—
89	#66880	C₂×C₄	1	2	yes	—
90	#66880	C₂×C₄	1	2	yes	—
91	#66879	—	2	2	no	—
92	Dic₁₁⋊C₈	—	2	2	no	—
93	Dic₁₁⋊C₈	—	2	2	no	—
94	C₈×Dic₁₁	—	2	2	no	—
95	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
96	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
97	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
98	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
99	C₄×C₁₁⋊C₈	—	2	1	no	—
100	C₄×C₁₁⋊C₈	—	2	1	no	—
101	#18089	—	11	1	no	maximal, Sylow
102	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₁	—	2	2	no	—
106	#4339	—	8	1	no	—
107	#4339	—	8	1	no	—
108	C₂×D₄₄	—	2	1	no	—
109	C₂×D₄₄	—	2	1	no	—
110	C₂×D₄₄	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₁₁	—	2	2	no	—
112	C₂×Dic₂₂	—	2	1	no	—
113	C₂×Dic₂₂	—	2	1	no	—
114	C₂×Dic₂₂	C₂²×C₄	1	2	yes	—
115	C₁₁×M₁₆	—	4	2	no	—
116	C₂×C₈×C₁₁	—	2	2	no	—
117	C₂×C₈×C₁₁	—	2	2	no	—
118	C₂×C₈×C₁₁	—	4	1	no	—
119	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
125	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₁	#41	1	1	yes	characteristic
128	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
129	C₂²⋊Dic₁₁	—	2	2	no	—
130	(C₂×D₁₁)⋊C₄	—	2	2	no	—
131	(C₂×D₁₁)⋊C₄	—	2	2	no	—
132	C₄⋊Dic₁₁	—	2	1	no	—
133	C₄⋊Dic₁₁	—	2	1	no	—
134	C₄⋊Dic₁₁	—	2	1	no	—
135	C₄⋊Dic₁₁	—	2	1	no	—
136	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
137	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
138	Dic₁₁⋊C₄	—	2	2	no	—
139	Dic₁₁⋊C₄	—	2	2	no	—
140	C₄×Dic₁₁	—	2	2	no	—
141	C₂×C₁₁⋊C₈	—	2	1	no	—
142	C₂×C₁₁⋊C₈	—	2	1	no	—
143	C₂×C₁₁⋊C₈	—	2	1	no	—
144	C₂×C₁₁⋊C₈	—	2	1	no	—
145	#4314	—	2	4	no	—
146	#4314	—	4	2	no	—
147	#4313	—	8	2	no	—
148	C₈×D₁₁	—	8	2	no	—
149	#3167	—	11	1	no	—
150	#2986	—	11	1	no	—
151	#2979	—	11	1	no	—
152	#1592	—	11	2	no	—
153	#1583	—	11	2	no	—
154	#1582	—	11	2	no	—
155	SD₁₆⋊C₈	—	11	2	no	—
156	#1564	—	11	1	no	—
157	#1485	—	11	1	no	—
158	#1484	—	11	1	no	—
159	#1451	D₁₁	1	1	yes	characteristic, complemented
160	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	1	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
173	C₂²⋊D₁₁	—	8	2	no	—
174	C₂×Dic₁₁	—	2	2	no	—
175	C₂×Dic₁₁	—	2	2	no	—
176	C₂×Dic₁₁	—	2	2	no	—
177	D₄₄	—	2	2	no	—
178	D₄₄	—	2	2	no	—
179	D₄₄	—	4	2	no	—
180	D₄₄	—	8	1	no	—
181	C₄×D₁₁	—	4	2	no	—
182	C₄×D₁₁	—	4	2	no	—
183	Dic₂₂	—	2	2	no	—
184	Dic₂₂	—	2	2	no	—
185	Dic₂₂	—	4	2	no	—
186	Dic₂₂	—	8	1	no	—
187	C₈×C₁₁	—	2	1	no	—
188	C₈×C₁₁	—	2	1	no	—
189	C₈×C₁₁	—	2	1	no	—
190	C₈×C₁₁	—	2	2	no	—
191	C₈×C₁₁	—	2	2	no	—
192	C₈×C₁₁	—	4	2	no	—
193	C₈×C₁₁	#131	1	2	yes	—
194	C₁₁⋊C₈	—	4	1	no	—
195	C₁₁⋊C₈	—	4	1	no	—
196	C₁₁⋊C₈	—	4	1	no	—
197	C₁₁⋊C₈	—	4	1	no	—
198	#533	—	11	1	no	—
199	#532	—	11	1	no	—
200	#498	—	11	1	no	—
201	#492	—	11	1	no	—
202	#487	—	11	1	no	—
203	#486	—	11	1	no	—
204	#465	—	11	2	no	—
205	#465	—	11	2	no	—
206	#446	—	11	2	no	—
207	#446	—	22	1	no	—
208	C₈×Q₈	—	11	2	no	—
209	C₈×Q₈	—	22	1	no	—
210	C₄×SD₁₆	—	11	2	no	—
211	C₄×SD₁₆	—	11	2	no	—
212	#436	—	11	2	no	—
213	#436	—	22	1	no	—
214	C₈×D₄	—	11	2	no	—
215	C₈×D₄	—	22	1	no	—
216	#433	—	22	2	no	—
217	#431	—	11	1	no	—
218	#431	—	11	1	no	—
219	#431	C₂×D₁₁	1	1	yes	characteristic
220	#408	—	22	2	no	—
221	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
223	#335	—	11	1	no	—
224	#335	—	11	1	no	—
225	#334	—	11	1	no	—
226	#334	—	11	1	no	—
227	Q₈⋊C₈	—	11	2	no	—
228	Q₈⋊C₈	—	11	2	no	—
229	D₄⋊C₈	—	11	2	no	—
230	D₄⋊C₈	—	11	2	no	—
231	#322	C₂×D₁₁	1	2	yes	—
232	#322	C₂×D₁₁	1	2	yes	—
233	C₂²×C₁₁	—	2	1	no	—
234	C₂²×C₁₁	—	2	1	no	—
235	C₂²×C₁₁	—	2	1	no	—
236	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂×D₁₁	—	4	2	no	—
238	C₂×D₁₁	—	4	2	no	—
239	C₂×D₁₁	—	4	2	no	—
240	C₄×C₁₁	—	2	1	no	—
241	C₄×C₁₁	—	2	1	no	—
242	C₄×C₁₁	—	2	1	no	—
243	C₄×C₁₁	#444	1	2	yes	—
244	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
245	C₄×C₁₁	#568	1	1	yes	characteristic
246	C₄×C₁₁	#577	1	1	yes	characteristic
247	C₄×C₁₁	#577	1	1	yes	characteristic
248	Dic₁₁	—	4	2	no	—
249	Dic₁₁	—	4	2	no	—
250	Dic₁₁	—	4	2	no	—
251	C₂×#41	—	22	1	no	—
252	C₂×SD₁₆	—	11	2	no	—
253	C₂×SD₁₆	—	11	2	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	22	2	no	—
256	C₂²×C₈	—	22	2	no	—
257	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
258	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
259	C₄⋊Q₈	—	11	1	no	—
260	C₄⋊Q₈	—	11	1	no	—
261	C₄⋊Q₈	—	11	1	no	—
262	#127	—	11	1	no	—
263	#125	—	22	1	no	—
264	#124	—	22	1	no	—
265	C₂²⋊Q₈	—	11	2	no	—
266	C₂²⋊Q₈	—	22	1	no	—
267	#121	—	11	2	no	—
268	#121	—	22	1	no	—
269	C₄×Q₈	—	11	2	no	—
270	C₄×Q₈	—	22	1	no	—
271	C₄×D₄	—	11	2	no	—
272	C₄×D₄	—	22	1	no	—
273	#117	—	22	1	no	—
274	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
275	#106	—	11	2	no	—
276	#106	—	11	2	no	—
277	C₄⋊C₈	—	11	1	no	—
278	C₄⋊C₈	—	11	1	no	—
279	C₄⋊C₈	—	11	1	no	—
280	C₄⋊C₈	—	11	1	no	—
281	C₄⋊C₈	—	22	2	no	—
282	C₄⋊C₈	—	22	2	no	—
283	C₄⋊C₈	D₄₄	1	1	yes	characteristic
284	C₄⋊C₈	D₄₄	1	1	yes	characteristic
285	#103	—	11	2	no	—
286	#103	—	11	2	no	—
287	#102	—	11	2	no	—
288	#102	—	11	2	no	—
289	C₂²⋊C₈	—	22	1	no	—
290	C₂²⋊C₈	—	22	1	no	—
291	C₂²⋊C₈	—	22	2	no	—
292	C₂²⋊C₈	—	22	2	no	—
293	C₂²⋊C₈	D₄₄	1	2	yes	—
294	#97	—	2	1	no	—
295	#97	—	22	2	no	—
296	C₄×C₈	—	22	2	no	—
297	C₄×C₈	—	22	1	no	—
298	C₄×C₈	—	22	1	no	—
299	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
300	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₁₁	1	2	yes	—
302	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₁₁	1	2	yes	—
305	C₂×C₁₁	—	4	1	no	—
306	C₂×C₁₁	#2935	1	1	yes	characteristic
307	C₂×C₁₁	#2949	1	1	yes	characteristic
308	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
309	D₁₁	—	8	2	no	—
310	#41	—	88	1	no	—
311	#41	—	88	1	no	—
312	C₂×Q₈	—	11	2	no	—
313	C₂×Q₈	—	22	1	no	—
314	C₂×Q₈	—	22	1	no	—
315	C₂×D₄	—	11	2	no	—
316	C₂×D₄	—	22	2	no	—
317	C₂×D₄	—	22	1	no	—
318	C₂×D₄	—	22	1	no	—
319	C₂²×C₄	—	22	2	no	—
320	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
322	C₂²×C₄	#4339	1	1	yes	characteristic
323	SD₁₆	—	22	4	no	—
324	SD₁₆	—	44	2	no	—
325	M₁₆	—	4	2	no	—
326	M₁₆	—	88	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	22	1	no	—
331	C₂×C₈	—	22	1	no	—
332	C₂×C₈	—	22	1	no	—
333	C₂×C₈	—	22	1	no	—
334	C₂×C₈	—	88	2	no	—
335	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄₄	1	2	yes	—
340	C₂×C₈	C₂×D₄₄	1	2	yes	—
341	C₄⋊C₄	—	11	2	no	—
342	C₄⋊C₄	—	11	2	no	—
343	C₄⋊C₄	—	22	1	no	—
344	C₄⋊C₄	—	22	1	no	—
345	C₄⋊C₄	—	22	1	no	—
346	C₄⋊C₄	—	22	2	no	—
347	C₄⋊C₄	—	22	1	no	—
348	C₄⋊C₄	—	22	2	no	—
349	C₂²⋊C₄	—	22	2	no	—
350	C₂²⋊C₄	—	22	2	no	—
351	C₂²⋊C₄	—	22	2	no	—
352	C₄²	—	22	2	no	—
353	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
354	C₄²	C₂×D₄₄	1	1	yes	characteristic
355	C₄²	#4339	1	1	yes	characteristic
356	C₄²	C₂³×D₁₁	1	1	yes	characteristic
357	C₁₁	#18089	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	22	2	no	—
359	C₂³	C₄×D₄₄	1	1	yes	characteristic
360	Q₈	—	22	2	no	—
361	Q₈	—	22	2	no	—
362	Q₈	—	44	2	no	—
363	Q₈	—	88	1	no	—
364	D₄	—	22	2	no	—
365	D₄	—	22	2	no	—
366	D₄	—	44	2	no	—
367	D₄	—	88	1	no	—
368	D₄	—	88	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	22	2	no	—
375	C₂×C₄	—	22	2	no	—
376	C₂×C₄	—	22	2	no	—
377	C₂×C₄	—	44	2	no	—
378	C₂×C₄	—	44	2	no	—
379	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
380	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
381	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
384	C₂×C₄	C₂×#4339	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	44	1	no	—
392	C₈	—	44	1	no	—
393	C₈	—	44	1	no	—
394	C₈	—	44	1	no	—
395	C₈	#66960	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	44	2	no	—
400	C₂²	—	44	2	no	—
401	C₂²	—	44	2	no	—
402	C₂²	C₂×C₄×D₄₄	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	44	2	no	—
407	C₄	—	44	2	no	—
408	C₄	—	44	2	no	—
409	C₄	#10622330	1	2	yes	—
410	C₄	C₂×#66960	1	1	yes	characteristic
411	C₄	#10623276	1	1	yes	characteristic
412	C₄	#10623282	1	1	yes	characteristic
413	C₄	#10623282	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	88	2	no	—
416	C₂	#13077362	1	1	yes	characteristic
417	C₂	#13077477	1	1	yes	characteristic
418	C₂	C₂×#10622330	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1451	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	#10623008	C₂²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1451	D₁₁
hypocenter	C₁₁	#18089
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1451

Complements

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

N	H ≅ G/N	type
2. #13077717	C₂	semidirect
4. #13067520	C₂	semidirect
5. #13067461	C₂	semidirect
6. #13067454	C₂	semidirect
7. #13067430	C₂	semidirect
8. #13067364	C₂	semidirect
9. #13067038	C₂	semidirect
11. C₁₁×#1451	C₂	semidirect
159. #1451	D₁₁	semidirect
357. C₁₁	#18089	semidirect

Maximal subgroups

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

subgroup	index
#13079175	2
#13077717	2
#13077682	2
#13067520	2
#13067461	2
#13067454	2
#13067430	2
#13067364	2
#13067038	2
#13067034	2
C₁₁×#1451	2
#18089	11