Subgroups — C₁₁×#22460 #14599653

Order 2816.

1286 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#578	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2957	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2889	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1979	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1902	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1813	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1796	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1757	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×2₋¹⁺⁴	C₂²	1	2	yes	—
10	C₁₁×#578	—	2	4	no	—
11	C₁₁×#578	—	2	4	no	—
12	C₂×C₁₁×#137	C₄	1	4	yes	complemented
13	C₂×C₁₁×#137	C₂²	1	2	yes	—
14	C₂×C₁₁×#135	C₄	1	2	yes	complemented
15	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁×Q₁₆	C₄	1	2	yes	complemented
17	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
18	C₁₁×#568	C₂²	1	4	yes	—
19	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
20	C₁₁×#444	—	2	4	no	—
21	C₁₁×#443	—	2	4	no	—
22	C₂×C₁₁×#108	C₂²	1	2	yes	—
23	C₁₁×#421	C₂²	1	4	yes	—
24	C₁₁×#419	C₂²	1	4	yes	—
25	C₁₁×#413	—	2	4	no	—
26	C₁₁×#413	C₂²	1	2	yes	—
27	C₁₁×#413	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#101	—	2	4	no	—
29	C₂×C₁₁×#101	C₂²	1	4	yes	—
30	C₁₁×#410	C₂²	1	1	yes	characteristic
31	C₁₁×#405	C₂²	1	2	yes	—
32	C₁₁×#344	C₂²	1	2	yes	—
33	C₁₁×#338	C₂²	1	2	yes	—
34	C₁₁×2₋¹⁺⁴	—	2	8	no	—
35	C₁₁×2₋¹⁺⁴	—	4	4	no	—
36	C₂×C₁₁×#41	—	2	2	no	—
37	C₂×C₁₁×#41	—	2	4	no	—
38	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
39	C₂×C₁₁×#41	C₂³	1	2	yes	—
40	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
41	C₂²×Q₈×C₁₁	—	2	2	no	—
42	C₂²×Q₈×C₁₁	C₂×C₄	1	4	yes	—
43	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
44	C₁₁×#137	—	2	8	no	—
45	C₁₁×#137	—	2	16	no	—
46	C₁₁×#135	—	2	4	no	—
47	C₁₁×#135	—	2	4	no	—
48	C₁₁×#135	D₄	1	4	yes	—
49	C₁₁×#135	D₄	1	4	yes	—
50	C₂×C₁₁×Q₁₆	—	2	4	no	—
51	C₂×C₁₁×Q₁₆	—	2	4	no	—
52	C₂×C₁₁×Q₁₆	—	2	2	no	—
53	C₂×C₁₁×Q₁₆	—	2	2	no	—
54	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
56	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	—
59	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
60	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
61	C₁₁×#131	—	2	2	no	—
62	C₁₁×#131	—	2	2	no	—
63	C₁₁×#131	—	2	8	no	—
64	C₁₁×#131	—	4	4	no	—
65	C₂×C₁₁×M₁₆	—	2	8	no	—
66	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
68	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₁₁×#117	C₂³	1	2	yes	—
73	C₁₁×#108	—	2	2	no	—
74	C₁₁×#108	—	2	2	no	—
75	C₁₁×#104	—	2	8	no	—
76	C₁₁×#103	—	4	4	no	—
77	C₁₁×#101	—	2	2	no	—
78	C₁₁×#101	—	2	8	no	—
79	C₁₁×#101	D₄	1	2	yes	—
80	C₁₁×#100	—	2	2	no	—
81	C₁₁×#100	D₄	1	2	yes	—
82	C₁₁×#99	—	2	2	no	—
83	C₁₁×#97	—	2	2	no	—
84	C₄×C₈×C₁₁	—	2	2	no	—
85	#22460	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₁₁×#41	—	2	2	no	—
87	C₁₁×#41	—	2	4	no	—
88	C₁₁×#41	—	2	2	no	—
89	C₁₁×#41	—	2	8	no	—
90	C₁₁×#41	—	4	4	no	—
91	C₁₁×#41	—	4	8	no	—
92	C₁₁×#41	—	4	16	no	—
93	C₁₁×#41	C₂×D₄	1	8	yes	—
94	C₂×Q₈×C₁₁	—	2	4	no	—
95	C₂×Q₈×C₁₁	—	2	2	no	—
96	C₂×Q₈×C₁₁	—	2	8	no	—
97	C₂×Q₈×C₁₁	—	2	4	no	—
98	C₂×Q₈×C₁₁	—	2	4	no	—
99	C₂×Q₈×C₁₁	—	4	4	no	—
100	C₂×Q₈×C₁₁	—	4	8	no	—
101	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
102	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
103	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	—	2	4	no	—
106	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₂×D₄×C₁₁	#41	1	2	yes	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	2	4	no	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	—	2	4	no	—
113	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
115	C₁₁×Q₁₆	—	2	2	no	—
116	C₁₁×Q₁₆	—	2	2	no	—
117	C₁₁×Q₁₆	—	2	4	no	—
118	C₁₁×Q₁₆	—	2	8	no	—
119	C₁₁×Q₁₆	C₂²⋊C₄	1	2	yes	—
120	C₁₁×Q₁₆	C₂²⋊C₄	1	2	yes	—
121	C₁₁×SD₁₆	—	2	8	no	—
122	C₁₁×SD₁₆	C₂²⋊C₄	1	8	yes	—
123	C₁₁×D₈	C₂²⋊C₄	1	2	yes	—
124	C₁₁×D₈	C₂²⋊C₄	1	2	yes	—
125	C₁₁×M₁₆	—	2	4	no	—
126	C₁₁×M₁₆	—	2	2	no	—
127	C₁₁×M₁₆	—	2	4	no	—
128	C₁₁×M₁₆	—	2	4	no	—
129	C₁₁×M₁₆	—	2	2	no	—
130	C₁₁×M₁₆	—	4	8	no	—
131	C₁₁×M₁₆	C₂×D₄	1	4	yes	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	—	2	2	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	4	no	—
136	C₂×C₈×C₁₁	—	4	8	no	—
137	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
142	C₁₁×C₄⋊C₄	—	2	2	no	—
143	C₁₁×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₁₁	—	2	2	no	—
145	C₂×#578	C₂×C₁₁	1	1	yes	characteristic
146	#2957	C₂×C₁₁	1	2	yes	complemented
147	#2889	C₂×C₁₁	1	2	yes	complemented
148	#1979	C₂×C₁₁	1	2	yes	complemented
149	#1902	C₂×C₁₁	1	4	yes	complemented
150	#1813	C₂×C₁₁	1	1	yes	characteristic, complemented
151	#1796	C₂×C₁₁	1	2	yes	complemented
152	#1757	C₂×C₁₁	1	1	yes	characteristic, complemented
153	C₂³×C₁₁	—	2	2	no	—
154	C₂³×C₁₁	C₄×D₄	1	2	yes	—
155	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
156	Q₈×C₁₁	—	2	2	no	—
157	Q₈×C₁₁	—	2	2	no	—
158	Q₈×C₁₁	—	2	4	no	—
159	Q₈×C₁₁	—	2	4	no	—
160	Q₈×C₁₁	—	4	8	no	—
161	Q₈×C₁₁	—	4	4	no	—
162	Q₈×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
163	D₄×C₁₁	—	2	8	no	—
164	D₄×C₁₁	—	2	4	no	—
165	D₄×C₁₁	—	2	2	no	—
166	D₄×C₁₁	—	2	2	no	—
167	D₄×C₁₁	—	4	8	no	—
168	D₄×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	8	no	—
173	C₂×C₄×C₁₁	—	2	4	no	—
174	C₂×C₄×C₁₁	—	4	8	no	—
175	C₂×C₄×C₁₁	—	4	8	no	—
176	C₂×C₄×C₁₁	—	4	4	no	—
177	C₂×C₄×C₁₁	—	4	2	no	—
178	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
183	C₈×C₁₁	—	2	2	no	—
184	C₈×C₁₁	—	2	4	no	—
185	C₈×C₁₁	—	4	4	no	—
186	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×2₋¹⁺⁴	C₂²×C₁₁	1	2	yes	—
190	#578	—	2	4	no	—
191	#578	—	2	4	no	—
192	C₂×#137	C₄×C₁₁	1	4	yes	complemented
193	C₂×#137	C₂²×C₁₁	1	2	yes	—
194	C₂×#135	C₄×C₁₁	1	2	yes	complemented
195	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
196	C₂²×Q₁₆	C₄×C₁₁	1	2	yes	complemented
197	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
198	#568	C₂²×C₁₁	1	4	yes	—
199	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
200	#444	—	2	4	no	—
201	#443	—	2	4	no	—
202	C₂×#108	C₂²×C₁₁	1	2	yes	—
203	#421	C₂²×C₁₁	1	4	yes	—
204	#419	C₂²×C₁₁	1	4	yes	—
205	#413	—	2	4	no	—
206	#413	C₂²×C₁₁	1	2	yes	—
207	#413	C₂²×C₁₁	1	1	yes	characteristic
208	C₂×#101	—	2	4	no	—
209	C₂×#101	C₂²×C₁₁	1	4	yes	—
210	#410	C₂²×C₁₁	1	1	yes	characteristic
211	#405	C₂²×C₁₁	1	2	yes	—
212	#344	C₂²×C₁₁	1	2	yes	—
213	#338	C₂²×C₁₁	1	2	yes	—
214	C₂²×C₁₁	—	2	2	no	—
215	C₂²×C₁₁	—	2	4	no	—
216	C₂²×C₁₁	—	4	1	no	—
217	C₂²×C₁₁	—	4	2	no	—
218	C₂²×C₁₁	—	8	2	no	—
219	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₁₁	#546	1	2	yes	—
221	C₄×C₁₁	—	2	4	no	—
222	C₄×C₁₁	—	2	2	no	—
223	C₄×C₁₁	—	4	4	no	—
224	C₄×C₁₁	—	8	2	no	—
225	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
226	C₄×C₁₁	#518	1	1	yes	characteristic
227	C₄×C₁₁	D₄²	1	2	yes	—
228	2₋¹⁺⁴	—	2	8	no	—
229	2₋¹⁺⁴	—	4	4	no	—
230	C₂×#41	—	2	2	no	—
231	C₂×#41	—	2	4	no	—
232	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
233	C₂×#41	C₂³×C₁₁	1	2	yes	—
234	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	C₂×C₄×C₁₁	1	4	yes	—
237	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
238	#137	—	2	8	no	—
239	#137	—	2	16	no	—
240	#135	—	2	4	no	—
241	#135	—	2	4	no	—
242	#135	D₄×C₁₁	1	4	yes	—
243	#135	D₄×C₁₁	1	4	yes	—
244	C₂×Q₁₆	—	2	4	no	—
245	C₂×Q₁₆	—	2	4	no	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×Q₁₆	—	2	2	no	—
248	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
249	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
250	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
251	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
252	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	—
253	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
254	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
255	#131	—	2	2	no	—
256	#131	—	2	2	no	—
257	#131	—	2	8	no	—
258	#131	—	4	4	no	—
259	C₂×M₁₆	—	2	8	no	—
260	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
261	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
262	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
263	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
264	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
266	#117	C₂³×C₁₁	1	2	yes	—
267	#108	—	2	2	no	—
268	#108	—	2	2	no	—
269	#104	—	2	8	no	—
270	#103	—	4	4	no	—
271	#101	—	2	2	no	—
272	#101	—	2	8	no	—
273	#101	D₄×C₁₁	1	2	yes	—
274	#100	—	2	2	no	—
275	#100	D₄×C₁₁	1	2	yes	—
276	#99	—	2	2	no	—
277	#97	—	2	2	no	—
278	C₄×C₈	—	2	2	no	—
279	C₂×C₁₁	—	2	2	no	—
280	C₂×C₁₁	—	2	1	no	—
281	C₂×C₁₁	—	4	2	no	—
282	C₂×C₁₁	—	4	4	no	—
283	C₂×C₁₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
284	#41	—	2	2	no	—
285	#41	—	2	4	no	—
286	#41	—	2	2	no	—
287	#41	—	2	8	no	—
288	#41	—	4	4	no	—
289	#41	—	4	8	no	—
290	#41	—	4	16	no	—
291	#41	C₂×D₄×C₁₁	1	8	yes	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	8	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×Q₈	—	4	8	no	—
299	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
300	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
301	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
305	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
306	C₂×D₄	C₁₁×#41	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
313	Q₁₆	—	2	8	no	—
314	Q₁₆	—	2	2	no	—
315	Q₁₆	—	2	2	no	—
316	Q₁₆	—	2	4	no	—
317	Q₁₆	C₁₁×C₂²⋊C₄	1	2	yes	—
318	Q₁₆	C₁₁×C₂²⋊C₄	1	2	yes	—
319	SD₁₆	—	2	8	no	—
320	SD₁₆	C₁₁×C₂²⋊C₄	1	8	yes	—
321	D₈	C₁₁×C₂²⋊C₄	1	2	yes	—
322	D₈	C₁₁×C₂²⋊C₄	1	2	yes	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	4	no	—
326	M₁₆	—	2	4	no	—
327	M₁₆	—	2	4	no	—
328	M₁₆	—	4	8	no	—
329	M₁₆	C₂×D₄×C₁₁	1	4	yes	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	4	8	no	—
335	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
336	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
337	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
338	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
340	C₄⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₁₁	#22460	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	—	2	2	no	—
345	C₂³	C₄×D₄×C₁₁	1	2	yes	—
346	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
347	Q₈	—	2	2	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	2	4	no	—
350	Q₈	—	2	4	no	—
351	Q₈	—	4	8	no	—
352	Q₈	—	4	4	no	—
353	Q₈	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
354	D₄	—	2	8	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	8	no	—
359	D₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
370	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
372	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
373	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
374	C₈	—	2	2	no	—
375	C₈	—	2	4	no	—
376	C₈	—	4	4	no	—
377	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
378	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
379	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
386	C₂²	C₁₁×#546	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	8	2	no	—
391	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
392	C₄	C₁₁×#518	1	1	yes	characteristic
393	C₄	D₄²×C₁₁	1	2	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	2	1	no	—
396	C₂	—	4	2	no	—
397	C₂	—	4	4	no	—
398	C₂	D₄×C₁₁×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	D₄×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#578	C₂
LCS	G ▷ C₂×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×#2957	C₂	semidirect
3. C₁₁×#2889	C₂	semidirect
4. C₁₁×#1979	C₂	semidirect
5. C₁₁×#1902	C₂	semidirect
6. C₁₁×#1813	C₂	semidirect
7. C₁₁×#1796	C₂	semidirect
8. C₁₁×#1757	C₂	semidirect
12. C₂×C₁₁×#137	C₄	semidirect
14. C₂×C₁₁×#135	C₄	semidirect
16. C₂²×C₁₁×Q₁₆	C₄	semidirect
85. #22460	C₁₁	direct (N × H)
146. #2957	C₂×C₁₁	semidirect
147. #2889	C₂×C₁₁	semidirect
148. #1979	C₂×C₁₁	semidirect
149. #1902	C₂×C₁₁	semidirect
150. #1813	C₂×C₁₁	semidirect
151. #1796	C₂×C₁₁	semidirect
152. #1757	C₂×C₁₁	semidirect
192. C₂×#137	C₄×C₁₁	semidirect
194. C₂×#135	C₄×C₁₁	semidirect
196. C₂²×Q₁₆	C₄×C₁₁	semidirect
343. C₁₁	#22460	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×#578	2
C₁₁×#2957	2
C₁₁×#2889	2
C₁₁×#1979	2
C₁₁×#1902	2
C₁₁×#1813	2
C₁₁×#1796	2
C₁₁×#1757	2
#22460	11

Subgroups — C11×#22460 #14599653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22460 #14599653