Subgroups — C₁₁×#17876 #14595069

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2988	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₁×#137	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1587	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1585	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1584	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1582	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#137	C₄	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#446	—	2	1	no	—
16	C₁₁×#446	—	2	1	no	—
17	C₁₁×#446	C₂²	1	2	yes	—
18	C₁₁×#446	C₂²	1	2	yes	—
19	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
20	C₁₁×#441	C₄	1	2	yes	—
21	C₁₁×#440	C₄	1	2	yes	—
22	C₄×C₁₁×Q₁₆	C₂²	1	2	yes	—
23	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
24	C₈×D₄×C₁₁	—	2	2	no	—
25	C₈×D₄×C₁₁	C₂²	1	2	yes	—
26	C₁₁×#432	—	2	2	no	—
27	C₁₁×#431	—	2	1	no	—
28	C₁₁×#431	C₂²	1	1	yes	characteristic
29	C₁₁×#431	C₂²	1	1	yes	characteristic
30	C₁₁×#428	C₄	1	1	yes	characteristic
31	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
32	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₁×#419	C₄	1	1	yes	characteristic
34	C₁₁×#417	C₄	1	1	yes	characteristic
35	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#335	C₂²	1	2	yes	—
38	C₁₁×#334	C₂²	1	2	yes	—
39	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
40	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	—
41	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₁×#322	C₂²	1	2	yes	—
46	C₁₁×#322	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
48	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₁₁×#137	—	2	4	no	—
50	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	—	2	1	no	—
55	C₂²×C₈×C₁₁	—	2	1	no	—
56	C₂²×C₈×C₁₁	—	2	2	no	—
57	C₄×Q₈×C₁₁	—	2	1	no	—
58	C₄×Q₈×C₁₁	—	2	1	no	—
59	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
62	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	—	2	1	no	—
65	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×#117	—	2	1	no	—
68	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₁	—	2	1	no	—
72	C₂×C₄²×C₁₁	—	2	1	no	—
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×#107	C₂×C₄	1	2	yes	—
75	C₁₁×#106	C₂×C₄	1	2	yes	—
76	C₁₁×C₄⋊C₈	—	2	2	no	—
77	C₁₁×C₄⋊C₈	—	2	2	no	—
78	C₁₁×C₄⋊C₈	—	2	2	no	—
79	C₁₁×C₄⋊C₈	—	2	1	no	—
80	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
81	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
85	C₁₁×#103	C₂×C₄	1	2	yes	—
86	C₁₁×#103	C₂×C₄	1	2	yes	—
87	C₁₁×#103	C₂×C₄	1	2	yes	—
88	C₁₁×#102	C₂×C₄	1	2	yes	—
89	C₁₁×C₂²⋊C₈	—	2	1	no	—
90	C₁₁×C₂²⋊C₈	—	2	2	no	—
91	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
92	C₁₁×#97	—	2	2	no	—
93	C₁₁×#97	—	2	2	no	—
94	C₁₁×#97	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₁₁	—	2	2	no	—
96	C₄×C₈×C₁₁	—	2	1	no	—
97	C₄×C₈×C₁₁	—	2	1	no	—
98	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₁	C₂³	1	2	yes	—
101	C₄×C₈×C₁₁	C₂³	1	2	yes	—
102	#17876	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₁₁×#41	—	2	2	no	—
104	C₁₁×#41	M₁₆	1	4	yes	—
105	C₂×Q₈×C₁₁	—	2	1	no	—
106	C₂×Q₈×C₁₁	—	2	2	no	—
107	C₂×Q₈×C₁₁	—	2	2	no	—
108	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
109	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₄×C₁₁	—	2	1	no	—
111	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	—	2	1	no	—
113	C₂²×C₄×C₁₁	—	2	1	no	—
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	—	2	1	no	—
116	C₂²×C₄×C₁₁	—	2	1	no	—
117	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
120	C₁₁×Q₁₆	—	2	4	no	—
121	C₁₁×SD₁₆	—	2	4	no	—
122	C₁₁×M₁₆	—	2	2	no	—
123	C₁₁×M₁₆	—	2	2	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	2	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	—	4	2	no	—
130	C₂×C₈×C₁₁	—	8	1	no	—
131	C₂×C₈×C₁₁	—	8	2	no	—
132	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
136	C₁₁×C₄⋊C₄	—	2	2	no	—
137	C₁₁×C₄⋊C₄	—	2	1	no	—
138	C₁₁×C₄⋊C₄	—	2	1	no	—
139	C₁₁×C₄⋊C₄	—	2	2	no	—
140	C₁₁×C₄⋊C₄	—	2	1	no	—
141	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
142	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
143	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
144	C₁₁×C₂²⋊C₄	—	2	1	no	—
145	C₁₁×C₂²⋊C₄	—	2	1	no	—
146	C₁₁×C₂²⋊C₄	—	2	1	no	—
147	C₄²×C₁₁	—	2	1	no	—
148	C₄²×C₁₁	—	2	1	no	—
149	C₄²×C₁₁	—	2	2	no	—
150	C₄²×C₁₁	—	2	1	no	—
151	C₄²×C₁₁	—	2	2	no	—
152	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₁	#41	1	1	yes	characteristic
155	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
156	#2988	C₂×C₁₁	1	1	yes	characteristic
157	#2983	C₂×C₁₁	1	1	yes	characteristic, complemented
158	C₄×#137	C₂×C₁₁	1	1	yes	characteristic
159	#1587	C₂×C₁₁	1	2	yes	complemented
160	#1585	C₂×C₁₁	1	2	yes	complemented
161	#1584	C₂×C₁₁	1	2	yes	complemented
162	#1582	C₂×C₁₁	1	2	yes	complemented
163	#1565	C₂×C₁₁	1	1	yes	characteristic, complemented
164	#1476	C₂×C₁₁	1	1	yes	characteristic
165	C₂×Q₈⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
166	#1451	C₂×C₁₁	1	1	yes	characteristic, complemented
167	C₂³×C₁₁	—	2	1	no	—
168	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
169	Q₈×C₁₁	—	2	1	no	—
170	Q₈×C₁₁	—	2	2	no	—
171	Q₈×C₁₁	—	2	2	no	—
172	Q₈×C₁₁	—	4	2	no	—
173	Q₈×C₁₁	C₂×M₁₆	1	2	yes	—
174	D₄×C₁₁	—	2	4	no	—
175	D₄×C₁₁	—	2	1	no	—
176	D₄×C₁₁	C₂×M₁₆	1	2	yes	—
177	C₂×C₄×C₁₁	—	2	1	no	—
178	C₂×C₄×C₁₁	—	2	1	no	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	4	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	4	1	no	—
186	C₂×C₄×C₁₁	—	4	2	no	—
187	C₂×C₄×C₁₁	—	4	1	no	—
188	C₂×C₄×C₁₁	—	4	1	no	—
189	C₂×C₄×C₁₁	—	8	1	no	—
190	C₂×C₄×C₁₁	—	8	1	no	—
191	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₁₁	#131	1	2	yes	—
196	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
199	C₈×C₁₁	—	2	2	no	—
200	C₈×C₁₁	—	2	2	no	—
201	C₈×C₁₁	—	2	2	no	—
202	C₈×C₁₁	—	2	2	no	—
203	C₈×C₁₁	—	2	2	no	—
204	C₈×C₁₁	—	4	1	no	—
205	C₈×C₁₁	—	4	1	no	—
206	C₈×C₁₁	—	4	2	no	—
207	C₈×C₁₁	—	4	1	no	—
208	C₂×#137	C₄×C₁₁	1	1	yes	characteristic
209	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
210	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
211	#446	—	2	1	no	—
212	#446	—	2	1	no	—
213	#446	C₂²×C₁₁	1	2	yes	—
214	#446	C₂²×C₁₁	1	2	yes	—
215	C₈×Q₈	C₂²×C₁₁	1	2	yes	—
216	#441	C₄×C₁₁	1	2	yes	—
217	#440	C₄×C₁₁	1	2	yes	—
218	C₄×Q₁₆	C₂²×C₁₁	1	2	yes	—
219	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
220	C₈×D₄	—	2	2	no	—
221	C₈×D₄	C₂²×C₁₁	1	2	yes	—
222	#432	—	2	2	no	—
223	#431	—	2	1	no	—
224	#431	C₂²×C₁₁	1	1	yes	characteristic
225	#431	C₂²×C₁₁	1	1	yes	characteristic
226	#428	C₄×C₁₁	1	1	yes	characteristic
227	C₂×C₄⋊C₈	—	2	1	no	—
228	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
229	#419	C₄×C₁₁	1	1	yes	characteristic
230	#417	C₄×C₁₁	1	1	yes	characteristic
231	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
233	#335	C₂²×C₁₁	1	2	yes	—
234	#334	C₂²×C₁₁	1	2	yes	—
235	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
236	Q₈⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
237	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	—
238	Q₈⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
239	D₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
240	D₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
241	#322	C₂²×C₁₁	1	2	yes	—
242	#322	C₂²×C₁₁	1	2	yes	—
243	C₂²×C₁₁	—	2	1	no	—
244	C₂²×C₁₁	—	2	1	no	—
245	C₂²×C₁₁	—	2	2	no	—
246	C₂²×C₁₁	—	4	1	no	—
247	C₂²×C₁₁	—	4	1	no	—
248	C₂²×C₁₁	#435	1	2	yes	—
249	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
250	C₄×C₁₁	—	2	2	no	—
251	C₄×C₁₁	—	2	1	no	—
252	C₄×C₁₁	—	2	1	no	—
253	C₄×C₁₁	—	2	1	no	—
254	C₄×C₁₁	—	4	2	no	—
255	C₄×C₁₁	—	4	1	no	—
256	C₄×C₁₁	—	4	1	no	—
257	C₄×C₁₁	—	4	2	no	—
258	C₄×C₁₁	#435	1	2	yes	—
259	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
260	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
261	C₄×C₁₁	#577	1	1	yes	characteristic
262	C₄×C₁₁	#578	1	1	yes	characteristic
263	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
264	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
265	#137	—	2	4	no	—
266	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
267	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
268	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
269	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
276	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
277	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
278	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
282	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
283	#117	—	2	1	no	—
284	#117	C₂×C₄×C₁₁	1	1	yes	characteristic
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
290	#107	C₂×C₄×C₁₁	1	2	yes	—
291	#106	C₂×C₄×C₁₁	1	2	yes	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
297	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
298	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
301	#103	C₂×C₄×C₁₁	1	2	yes	—
302	#103	C₂×C₄×C₁₁	1	2	yes	—
303	#103	C₂×C₄×C₁₁	1	2	yes	—
304	#102	C₂×C₄×C₁₁	1	2	yes	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	D₄×C₁₁	1	2	yes	—
308	#97	—	2	2	no	—
309	#97	—	2	2	no	—
310	#97	C₂×C₄×C₁₁	1	2	yes	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
315	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
316	C₄×C₈	C₂³×C₁₁	1	2	yes	—
317	C₄×C₈	C₂³×C₁₁	1	2	yes	—
318	C₂×C₁₁	—	2	2	no	—
319	C₂×C₁₁	—	4	2	no	—
320	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
321	C₂×C₁₁	#2947	1	1	yes	characteristic
322	C₂×C₁₁	#2956	1	1	yes	characteristic
323	#41	—	2	2	no	—
324	#41	C₁₁×M₁₆	1	4	yes	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
329	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
339	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
340	Q₁₆	—	2	4	no	—
341	SD₁₆	—	2	4	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	—	8	2	no	—
351	C₂×C₈	—	8	1	no	—
352	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
353	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
354	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
362	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
374	C₄²	C₁₁×#41	1	1	yes	characteristic
375	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
376	C₁₁	#17876	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	2	1	no	—
378	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
379	Q₈	—	2	1	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	C₂×C₁₁×M₁₆	1	2	yes	—
384	D₄	—	2	4	no	—
385	D₄	—	2	1	no	—
386	D₄	C₂×C₁₁×M₁₆	1	2	yes	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	—	8	1	no	—
401	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
402	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
403	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
404	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
405	C₂×C₄	C₁₁×#131	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
408	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	C₁₁×#435	1	2	yes	—
424	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	2	no	—
433	C₄	C₁₁×#435	1	2	yes	—
434	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
435	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
436	C₄	C₁₁×#577	1	1	yes	characteristic
437	C₄	C₁₁×#578	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	4	2	no	—
440	C₂	C₂×C₁₁×#435	1	1	yes	characteristic
441	C₂	C₁₁×#2947	1	1	yes	characteristic
442	C₂	C₁₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#41	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2983	C₂	semidirect
4. C₁₁×#1587	C₂	semidirect
5. C₁₁×#1585	C₂	semidirect
6. C₁₁×#1584	C₂	semidirect
7. C₁₁×#1582	C₂	semidirect
8. C₁₁×#1565	C₂	semidirect
10. C₂×C₁₁×Q₈⋊C₈	C₂	semidirect
11. C₁₁×#1451	C₂	semidirect
102. #17876	C₁₁	direct (N × H)
157. #2983	C₂×C₁₁	semidirect
159. #1587	C₂×C₁₁	semidirect
160. #1585	C₂×C₁₁	semidirect
161. #1584	C₂×C₁₁	semidirect
162. #1582	C₂×C₁₁	semidirect
163. #1565	C₂×C₁₁	semidirect
165. C₂×Q₈⋊C₈	C₂×C₁₁	semidirect
166. #1451	C₂×C₁₁	semidirect
376. C₁₁	#17876	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#2988	2
C₁₁×#2983	2
C₄×C₁₁×#137	2
C₁₁×#1587	2
C₁₁×#1585	2
C₁₁×#1584	2
C₁₁×#1582	2
C₁₁×#1565	2
C₁₁×#1476	2
C₂×C₁₁×Q₈⋊C₈	2
C₁₁×#1451	2
#17876	11

Subgroups — C11×#17876 #14595069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17876 #14595069