Subgroups — C₁₁×#22802 #14599995

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2925	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1974	C₂	1	2	yes	maximal
4	C₁₁×#1929	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1806	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1772	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
10	C₄×C₁₁×#41	C₂²	1	2	yes	—
11	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic, complemented
12	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic, complemented
13	C₄×C₁₁×SD₁₆	C₄	1	2	yes	complemented
14	C₄×C₁₁×SD₁₆	C₄	1	2	yes	complemented
15	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic, complemented
16	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#433	—	2	4	no	—
18	C₁₁×#432	—	2	2	no	—
19	C₁₁×#431	—	2	2	no	—
20	C₂×C₁₁×#108	C₂²	1	2	yes	—
21	C₂×C₁₁×#108	C₂²	1	2	yes	—
22	C₁₁×#427	C₂²	1	1	yes	characteristic
23	C₁₁×#423	C₂²	1	2	yes	—
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#104	C₂²	1	4	yes	—
26	C₁₁×#416	C₂²	1	2	yes	—
27	C₁₁×#408	C₂²	1	4	yes	—
28	C₁₁×#405	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₁₁×#339	C₂²	1	4	yes	—
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₂×C₁₁×#41	C₂³	1	2	yes	—
35	C₁₁×#135	—	2	2	no	—
36	C₁₁×#135	—	2	2	no	—
37	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
39	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
44	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
45	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₁₁	—	2	2	no	—
47	C₄×D₄×C₁₁	—	2	2	no	—
48	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
50	C₁₁×#117	—	2	2	no	—
51	C₁₁×#117	C₂³	1	2	yes	—
52	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
53	C₂×C₄²×C₁₁	—	2	2	no	—
54	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₁₁×#108	—	2	4	no	—
57	C₁₁×#108	—	4	2	no	—
58	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
59	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
60	C₁₁×#106	C₂×C₄	1	2	yes	—
61	C₁₁×C₄⋊C₈	—	2	2	no	—
62	C₁₁×C₄⋊C₈	—	2	2	no	—
63	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
64	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
65	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
66	C₁₁×#104	—	4	4	no	—
67	C₁₁×#103	C₂×C₄	1	2	yes	—
68	C₁₁×#103	C₂×C₄	1	2	yes	—
69	C₁₁×#102	C₂×C₄	1	2	yes	—
70	C₁₁×#102	C₂×C₄	1	2	yes	—
71	C₁₁×C₂²⋊C₈	—	2	4	no	—
72	C₁₁×C₂²⋊C₈	—	2	4	no	—
73	C₁₁×#97	—	2	4	no	—
74	C₄×C₈×C₁₁	—	2	4	no	—
75	C₄×C₈×C₁₁	—	2	4	no	—
76	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
80	C₁₁×#95	—	2	1	no	—
81	#22802	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₁₁×#41	—	2	2	no	—
83	C₁₁×#41	—	2	2	no	—
84	C₁₁×#41	—	2	2	no	—
85	C₁₁×#41	—	2	2	no	—
86	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
87	C₂×D₄×C₁₁	—	2	2	no	—
88	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₁	—	2	2	no	—
90	C₂²×C₄×C₁₁	—	2	2	no	—
91	C₂²×C₄×C₁₁	—	2	2	no	—
92	C₂²×C₄×C₁₁	—	2	2	no	—
93	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
96	C₁₁×Q₁₆	—	2	2	no	—
97	C₁₁×SD₁₆	—	2	4	no	—
98	C₁₁×D₈	—	2	2	no	—
99	C₁₁×M₁₆	—	2	4	no	—
100	C₁₁×M₁₆	—	2	4	no	—
101	C₂×C₈×C₁₁	—	2	4	no	—
102	C₂×C₈×C₁₁	—	2	2	no	—
103	C₂×C₈×C₁₁	—	2	1	no	—
104	C₂×C₈×C₁₁	—	2	1	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₁	#41	1	2	yes	—
113	C₂×C₈×C₁₁	#41	1	2	yes	—
114	C₁₁×C₄⋊C₄	—	2	4	no	—
115	C₁₁×C₄⋊C₄	—	2	2	no	—
116	C₁₁×C₄⋊C₄	—	2	2	no	—
117	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
118	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
119	C₁₁×C₂²⋊C₄	—	2	2	no	—
120	C₁₁×C₂²⋊C₄	—	2	2	no	—
121	C₁₁×C₂²⋊C₄	—	2	2	no	—
122	C₄²×C₁₁	—	2	2	no	—
123	C₄²×C₁₁	—	2	2	no	—
124	C₄²×C₁₁	—	2	2	no	—
125	C₄²×C₁₁	—	2	2	no	—
126	C₄²×C₁₁	—	2	2	no	—
127	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
132	#2925	C₂×C₁₁	1	2	yes	complemented
133	#1974	C₂×C₁₁	1	2	yes	—
134	#1929	C₂×C₁₁	1	4	yes	complemented
135	#1848	C₂×C₁₁	1	1	yes	characteristic, complemented
136	#1806	C₂×C₁₁	1	2	yes	complemented
137	#1772	C₂×C₁₁	1	2	yes	complemented
138	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
139	C₂³×C₁₁	—	2	2	no	—
140	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
141	Q₈×C₁₁	—	2	2	no	—
142	Q₈×C₁₁	—	2	2	no	—
143	D₄×C₁₁	—	2	2	no	—
144	D₄×C₁₁	—	2	2	no	—
145	D₄×C₁₁	—	4	2	no	—
146	D₄×C₁₁	—	4	2	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	4	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	2	2	no	—
152	C₂×C₄×C₁₁	—	4	1	no	—
153	C₂×C₄×C₁₁	—	4	2	no	—
154	C₂×C₄×C₁₁	—	4	2	no	—
155	C₂×C₄×C₁₁	—	4	2	no	—
156	C₂×C₄×C₁₁	—	4	2	no	—
157	C₂×C₄×C₁₁	—	4	4	no	—
158	C₂×C₄×C₁₁	—	8	2	no	—
159	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
169	C₈×C₁₁	—	2	1	no	—
170	C₈×C₁₁	—	2	1	no	—
171	C₈×C₁₁	—	2	2	no	—
172	C₈×C₁₁	—	2	2	no	—
173	C₈×C₁₁	—	4	4	no	—
174	C₈×C₁₁	#117	1	2	yes	—
175	C₈×C₁₁	#117	1	2	yes	—
176	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
177	C₄×#41	C₂²×C₁₁	1	2	yes	—
178	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
179	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
180	C₄×SD₁₆	C₄×C₁₁	1	2	yes	complemented
181	C₄×SD₁₆	C₄×C₁₁	1	2	yes	complemented
182	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
183	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
184	#433	—	2	4	no	—
185	#432	—	2	2	no	—
186	#431	—	2	2	no	—
187	C₂×#108	C₂²×C₁₁	1	2	yes	—
188	C₂×#108	C₂²×C₁₁	1	2	yes	—
189	#427	C₂²×C₁₁	1	1	yes	characteristic
190	#423	C₂²×C₁₁	1	2	yes	—
191	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
192	C₂×#104	C₂²×C₁₁	1	4	yes	—
193	#416	C₂²×C₁₁	1	2	yes	—
194	#408	C₂²×C₁₁	1	4	yes	—
195	#405	C₂²×C₁₁	1	4	yes	—
196	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
198	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
199	#339	C₂²×C₁₁	1	4	yes	—
200	#336	C₂²×C₁₁	1	2	yes	—
201	C₂²×C₁₁	—	2	1	no	—
202	C₂²×C₁₁	—	2	1	no	—
203	C₂²×C₁₁	—	4	2	no	—
204	C₂²×C₁₁	—	4	2	no	—
205	C₂²×C₁₁	—	4	2	no	—
206	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₁₁	#555	1	1	yes	characteristic
208	C₂²×C₁₁	#556	1	1	yes	characteristic
209	C₄×C₁₁	—	2	1	no	—
210	C₄×C₁₁	—	2	1	no	—
211	C₄×C₁₁	—	2	1	no	—
212	C₄×C₁₁	—	4	4	no	—
213	C₄×C₁₁	—	4	2	no	—
214	C₄×C₁₁	—	4	2	no	—
215	C₄×C₁₁	—	4	2	no	—
216	C₄×C₁₁	#443	1	2	yes	—
217	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
218	C₄×C₁₁	#520	1	1	yes	characteristic
219	C₄×C₁₁	#547	1	1	yes	characteristic
220	C₄×C₁₁	#550	1	1	yes	characteristic
221	C₂×#41	C₂³×C₁₁	1	2	yes	—
222	#135	—	2	2	no	—
223	#135	—	2	2	no	—
224	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
225	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
226	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
227	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
228	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
230	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
231	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
232	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	—	2	2	no	—
235	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
236	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
237	#117	—	2	2	no	—
238	#117	C₂³×C₁₁	1	2	yes	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
242	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
243	#108	—	2	4	no	—
244	#108	—	4	2	no	—
245	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
246	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
247	#106	C₂×C₄×C₁₁	1	2	yes	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
251	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
252	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
253	#104	—	4	4	no	—
254	#103	C₂×C₄×C₁₁	1	2	yes	—
255	#103	C₂×C₄×C₁₁	1	2	yes	—
256	#102	C₂×C₄×C₁₁	1	2	yes	—
257	#102	C₂×C₄×C₁₁	1	2	yes	—
258	C₂²⋊C₈	—	2	4	no	—
259	C₂²⋊C₈	—	2	4	no	—
260	#97	—	2	4	no	—
261	C₄×C₈	—	2	4	no	—
262	C₄×C₈	—	2	4	no	—
263	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
264	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
265	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
266	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
267	#95	—	2	1	no	—
268	C₂×C₁₁	—	2	1	no	—
269	C₂×C₁₁	—	2	1	no	—
270	C₂×C₁₁	—	8	2	no	—
271	C₂×C₁₁	#2354	1	1	yes	characteristic
272	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
273	C₂×C₁₁	#2957	1	1	yes	characteristic
274	#41	—	2	2	no	—
275	#41	—	2	2	no	—
276	#41	—	2	2	no	—
277	#41	—	2	2	no	—
278	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
286	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
288	Q₁₆	—	2	2	no	—
289	SD₁₆	—	2	4	no	—
290	D₈	—	2	2	no	—
291	M₁₆	—	2	4	no	—
292	M₁₆	—	2	4	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
299	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
300	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
302	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
303	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
304	C₂×C₈	C₁₁×#41	1	2	yes	—
305	C₂×C₈	C₁₁×#41	1	2	yes	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
310	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
320	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
323	C₁₁	#22802	1	1	yes	characteristic, direct product factor, Sylow
324	C₂³	—	2	2	no	—
325	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	8	2	no	—
344	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
345	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
346	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
347	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
348	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
350	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
351	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
352	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	2	2	no	—
357	C₈	—	2	2	no	—
358	C₈	—	4	4	no	—
359	C₈	C₁₁×#117	1	2	yes	—
360	C₈	C₁₁×#117	1	2	yes	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
367	C₂²	C₁₁×#555	1	1	yes	characteristic
368	C₂²	C₁₁×#556	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	C₁₁×#443	1	2	yes	—
377	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
378	C₄	C₁₁×#520	1	1	yes	characteristic
379	C₄	C₁₁×#547	1	1	yes	characteristic
380	C₄	C₁₁×#550	1	1	yes	characteristic
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	8	2	no	—
384	C₂	C₁₁×#2354	1	1	yes	characteristic
385	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
386	C₂	C₁₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2925	C₂	semidirect
4. C₁₁×#1929	C₂	semidirect
5. C₁₁×#1848	C₂	semidirect
6. C₁₁×#1806	C₂	semidirect
7. C₁₁×#1772	C₂	semidirect
8. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
11. C₄×C₁₁×Q₁₆	C₄	semidirect
12. C₄×C₁₁×Q₁₆	C₄	semidirect
13. C₄×C₁₁×SD₁₆	C₄	semidirect
14. C₄×C₁₁×SD₁₆	C₄	semidirect
15. C₄×C₁₁×D₈	C₄	semidirect
16. C₄×C₁₁×D₈	C₄	semidirect
81. #22802	C₁₁	direct (N × H)
132. #2925	C₂×C₁₁	semidirect
134. #1929	C₂×C₁₁	semidirect
135. #1848	C₂×C₁₁	semidirect
136. #1806	C₂×C₁₁	semidirect
137. #1772	C₂×C₁₁	semidirect
138. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
178. C₄×Q₁₆	C₄×C₁₁	semidirect
179. C₄×Q₁₆	C₄×C₁₁	semidirect
180. C₄×SD₁₆	C₄×C₁₁	semidirect
181. C₄×SD₁₆	C₄×C₁₁	semidirect
182. C₄×D₈	C₄×C₁₁	semidirect
183. C₄×D₈	C₄×C₁₁	semidirect
323. C₁₁	#22802	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#135	2
C₁₁×#2925	2
C₁₁×#1974	2
C₁₁×#1929	2
C₁₁×#1848	2
C₁₁×#1806	2
C₁₁×#1772	2
C₈×C₁₁×C₄⋊C₄	2
#22802	11

Subgroups — C11×#22802 #14599995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22802 #14599995