Subgroups — C₁₁×#22803 #14599996

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 382 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×#1975	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×#1773	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1770	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×C₁₁×#97	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	2	yes	—
64	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
65	C₁₁×#104	—	4	4	no	—
66	C₁₁×#103	C₂×C₄	1	2	yes	—
67	C₁₁×#103	C₂×C₄	1	2	yes	—
68	C₁₁×#102	C₂×C₄	1	2	yes	—
69	C₁₁×#102	C₂×C₄	1	2	yes	—
70	C₁₁×C₂²⋊C₈	—	2	4	no	—
71	C₁₁×C₂²⋊C₈	—	2	4	no	—
72	C₁₁×#97	—	2	4	no	—
73	C₁₁×#97	—	2	4	no	—
74	C₄×C₈×C₁₁	—	2	4	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	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
79	C₁₁×#95	—	2	1	no	—
80	#22803	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₁₁×#41	—	2	2	no	—
82	C₁₁×#41	—	2	2	no	—
83	C₁₁×#41	—	2	2	no	—
84	C₁₁×#41	—	2	2	no	—
85	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
86	C₂×D₄×C₁₁	—	2	2	no	—
87	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₁	—	2	2	no	—
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	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
95	C₁₁×Q₁₆	—	2	2	no	—
96	C₁₁×SD₁₆	—	2	4	no	—
97	C₁₁×D₈	—	2	2	no	—
98	C₁₁×M₁₆	—	2	4	no	—
99	C₁₁×M₁₆	—	2	4	no	—
100	C₂×C₈×C₁₁	—	2	4	no	—
101	C₂×C₈×C₁₁	—	2	2	no	—
102	C₂×C₈×C₁₁	—	2	1	no	—
103	C₂×C₈×C₁₁	—	2	1	no	—
104	C₂×C₈×C₁₁	—	2	2	no	—
105	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₁₁	#41	1	2	yes	—
111	C₂×C₈×C₁₁	#41	1	2	yes	—
112	C₁₁×C₄⋊C₄	—	2	2	no	—
113	C₁₁×C₄⋊C₄	—	2	2	no	—
114	C₁₁×C₄⋊C₄	—	4	2	no	—
115	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
116	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
117	C₁₁×C₂²⋊C₄	—	2	2	no	—
118	C₁₁×C₂²⋊C₄	—	2	2	no	—
119	C₁₁×C₂²⋊C₄	—	2	2	no	—
120	C₄²×C₁₁	—	2	2	no	—
121	C₄²×C₁₁	—	2	2	no	—
122	C₄²×C₁₁	—	2	2	no	—
123	C₄²×C₁₁	—	2	2	no	—
124	C₄²×C₁₁	—	2	2	no	—
125	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₄×#135	C₂×C₁₁	1	1	yes	characteristic
130	#2925	C₂×C₁₁	1	2	yes	complemented
131	#1975	C₂×C₁₁	1	2	yes	—
132	#1929	C₂×C₁₁	1	4	yes	complemented
133	#1848	C₂×C₁₁	1	1	yes	characteristic, complemented
134	#1806	C₂×C₁₁	1	2	yes	complemented
135	#1773	C₂×C₁₁	1	2	yes	complemented
136	#1770	C₂×C₁₁	1	1	yes	characteristic, complemented
137	C₂³×C₁₁	—	2	2	no	—
138	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
139	Q₈×C₁₁	—	2	2	no	—
140	Q₈×C₁₁	—	2	2	no	—
141	D₄×C₁₁	—	2	2	no	—
142	D₄×C₁₁	—	2	2	no	—
143	D₄×C₁₁	—	4	2	no	—
144	D₄×C₁₁	—	4	2	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	2	2	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	4	1	no	—
150	C₂×C₄×C₁₁	—	4	2	no	—
151	C₂×C₄×C₁₁	—	4	2	no	—
152	C₂×C₄×C₁₁	—	4	4	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	—	8	2	no	—
157	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
167	C₈×C₁₁	—	2	1	no	—
168	C₈×C₁₁	—	2	1	no	—
169	C₈×C₁₁	—	2	4	no	—
170	C₈×C₁₁	—	4	4	no	—
171	C₈×C₁₁	#117	1	2	yes	—
172	C₈×C₁₁	#117	1	2	yes	—
173	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
174	C₄×#41	C₂²×C₁₁	1	2	yes	—
175	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
176	C₄×Q₁₆	C₄×C₁₁	1	1	yes	characteristic, complemented
177	C₄×SD₁₆	C₄×C₁₁	1	2	yes	complemented
178	C₄×SD₁₆	C₄×C₁₁	1	2	yes	complemented
179	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
180	C₄×D₈	C₄×C₁₁	1	1	yes	characteristic, complemented
181	#433	—	2	4	no	—
182	#432	—	2	2	no	—
183	#431	—	2	2	no	—
184	C₂×#108	C₂²×C₁₁	1	2	yes	—
185	C₂×#108	C₂²×C₁₁	1	2	yes	—
186	#427	C₂²×C₁₁	1	1	yes	characteristic
187	#423	C₂²×C₁₁	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
189	C₂×#104	C₂²×C₁₁	1	4	yes	—
190	#416	C₂²×C₁₁	1	2	yes	—
191	#408	C₂²×C₁₁	1	4	yes	—
192	#405	C₂²×C₁₁	1	4	yes	—
193	C₂×#97	C₂²×C₁₁	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
195	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
196	#339	C₂²×C₁₁	1	4	yes	—
197	#336	C₂²×C₁₁	1	2	yes	—
198	C₂²×C₁₁	—	2	1	no	—
199	C₂²×C₁₁	—	2	1	no	—
200	C₂²×C₁₁	—	4	2	no	—
201	C₂²×C₁₁	—	4	2	no	—
202	C₂²×C₁₁	—	4	2	no	—
203	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₁₁	#555	1	1	yes	characteristic
205	C₂²×C₁₁	#556	1	1	yes	characteristic
206	C₄×C₁₁	—	2	1	no	—
207	C₄×C₁₁	—	2	1	no	—
208	C₄×C₁₁	—	2	1	no	—
209	C₄×C₁₁	—	4	2	no	—
210	C₄×C₁₁	—	4	2	no	—
211	C₄×C₁₁	—	4	2	no	—
212	C₄×C₁₁	—	8	2	no	—
213	C₄×C₁₁	#444	1	2	yes	—
214	C₄×C₁₁	C₂×#117	1	1	yes	characteristic
215	C₄×C₁₁	#520	1	1	yes	characteristic
216	C₄×C₁₁	#547	1	1	yes	characteristic
217	C₄×C₁₁	#550	1	1	yes	characteristic
218	C₂×#41	C₂³×C₁₁	1	2	yes	—
219	#135	—	2	2	no	—
220	#135	—	2	2	no	—
221	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
222	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
223	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
224	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
225	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
228	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
229	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
230	C₄×D₄	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
233	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
234	#117	—	2	2	no	—
235	#117	C₂³×C₁₁	1	2	yes	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
239	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
240	#108	—	2	4	no	—
241	#108	—	4	2	no	—
242	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
243	#107	C₂×C₄×C₁₁	1	1	yes	characteristic
244	#106	C₂×C₄×C₁₁	1	2	yes	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
248	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
249	#104	—	4	4	no	—
250	#103	C₂×C₄×C₁₁	1	2	yes	—
251	#103	C₂×C₄×C₁₁	1	2	yes	—
252	#102	C₂×C₄×C₁₁	1	2	yes	—
253	#102	C₂×C₄×C₁₁	1	2	yes	—
254	C₂²⋊C₈	—	2	4	no	—
255	C₂²⋊C₈	—	2	4	no	—
256	#97	—	2	4	no	—
257	#97	—	2	4	no	—
258	C₄×C₈	—	2	4	no	—
259	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
260	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
261	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
262	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
263	#95	—	2	1	no	—
264	C₂×C₁₁	—	2	1	no	—
265	C₂×C₁₁	—	2	1	no	—
266	C₂×C₁₁	—	8	2	no	—
267	C₂×C₁₁	#2354	1	1	yes	characteristic
268	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
269	C₂×C₁₁	#2957	1	1	yes	characteristic
270	#41	—	2	2	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
282	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
284	Q₁₆	—	2	2	no	—
285	SD₁₆	—	2	4	no	—
286	D₈	—	2	2	no	—
287	M₁₆	—	2	4	no	—
288	M₁₆	—	2	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
295	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
296	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
297	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
299	C₂×C₈	C₁₁×#41	1	2	yes	—
300	C₂×C₈	C₁₁×#41	1	2	yes	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
305	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
315	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
317	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
318	C₁₁	#22803	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	2	no	—
320	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
341	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
343	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
346	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
347	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	2	4	no	—
352	C₈	—	4	4	no	—
353	C₈	C₁₁×#117	1	2	yes	—
354	C₈	C₁₁×#117	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
361	C₂²	C₁₁×#555	1	1	yes	characteristic
362	C₂²	C₁₁×#556	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	8	2	no	—
370	C₄	C₁₁×#444	1	2	yes	—
371	C₄	C₂×C₁₁×#117	1	1	yes	characteristic
372	C₄	C₁₁×#520	1	1	yes	characteristic
373	C₄	C₁₁×#547	1	1	yes	characteristic
374	C₄	C₁₁×#550	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	8	2	no	—
378	C₂	C₁₁×#2354	1	1	yes	characteristic
379	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
380	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×#1773	C₂	semidirect
8. C₁₁×#1770	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
80. #22803	C₁₁	direct (N × H)
130. #2925	C₂×C₁₁	semidirect
132. #1929	C₂×C₁₁	semidirect
133. #1848	C₂×C₁₁	semidirect
134. #1806	C₂×C₁₁	semidirect
135. #1773	C₂×C₁₁	semidirect
136. #1770	C₂×C₁₁	semidirect
175. C₄×Q₁₆	C₄×C₁₁	semidirect
176. C₄×Q₁₆	C₄×C₁₁	semidirect
177. C₄×SD₁₆	C₄×C₁₁	semidirect
178. C₄×SD₁₆	C₄×C₁₁	semidirect
179. C₄×D₈	C₄×C₁₁	semidirect
180. C₄×D₈	C₄×C₁₁	semidirect
318. C₁₁	#22803	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×#1975	2
C₁₁×#1929	2
C₁₁×#1848	2
C₁₁×#1806	2
C₁₁×#1773	2
C₁₁×#1770	2
#22803	11

Subgroups — C11×#22803 #14599996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22803 #14599996