Subgroups — C₁₁×#22455 #14599648

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#576	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2948	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2883	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1976	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1904	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1812	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1795	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1757	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	2	yes	—
10	C₁₁×#576	—	2	4	no	—
11	C₁₁×#576	—	2	4	no	—
12	C₂×C₁₁×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
13	C₂×C₁₁×AGL(1,ℤ/8)	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×D₈	C₄	1	2	yes	complemented
17	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
19	C₁₁×#518	C₂²	1	4	yes	complemented
20	C₁₁×#442	—	2	4	no	—
21	C₄×C₁₁×D₈	—	2	4	no	—
22	C₁₁×#427	C₂²	1	2	yes	complemented
23	C₁₁×#421	C₂²	1	4	yes	complemented
24	C₁₁×#418	C₂²	1	4	yes	complemented
25	C₁₁×#413	C₂²	1	1	yes	characteristic
26	C₁₁×#410	C₂²	1	2	yes	—
27	C₁₁×#410	C₂²	1	1	yes	characteristic
28	C₁₁×#410	C₂²	1	4	yes	complemented
29	C₂×C₁₁×#99	—	2	8	no	—
30	C₁₁×#405	C₂²	1	2	yes	complemented
31	C₁₁×#344	C₂²	1	2	yes	complemented
32	C₁₁×H(3,ℤ/4)	C₂²	1	2	yes	complemented
33	C₁₁×H(5,𝔽₂)	—	2	8	no	—
34	C₁₁×H(5,𝔽₂)	—	4	4	no	—
35	C₂×C₁₁×#41	—	2	2	no	—
36	C₂×C₁₁×#41	C₂×C₄	1	4	yes	complemented
37	C₂×C₁₁×#41	C₂³	1	2	yes	—
38	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₁₁	—	2	4	no	—
40	C₂²×D₄×C₁₁	—	2	2	no	—
41	C₂²×D₄×C₁₁	C₂×C₄	1	4	yes	complemented
42	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
43	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
44	C₁₁×AGL(1,ℤ/8)	—	2	16	no	—
45	C₁₁×#135	—	2	4	no	—
46	C₁₁×#135	—	2	4	no	—
47	C₁₁×#135	—	2	2	no	—
48	C₁₁×#135	—	2	2	no	—
49	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	complemented
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	complemented
52	C₂×C₁₁×D₈	—	2	4	no	—
53	C₂×C₁₁×D₈	—	2	4	no	—
54	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic, complemented
57	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₁₁×D₈	D₄	1	4	yes	—
59	C₂×C₁₁×D₈	D₄	1	4	yes	—
60	C₁₁×#131	—	2	2	no	—
61	C₁₁×#131	—	2	2	no	—
62	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	complemented
63	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	complemented
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₁₁	—	2	8	no	—
68	C₄×D₄×C₁₁	—	4	4	no	—
69	C₁₁×#117	C₂³	1	4	yes	—
70	C₁₁×#117	C₂³	1	2	yes	—
71	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
72	C₁₁×#107	—	2	2	no	—
73	C₁₁×#106	—	2	2	no	—
74	C₁₁×#104	—	4	4	no	—
75	C₁₁×#102	—	2	8	no	—
76	C₁₁×#101	—	2	1	no	—
77	C₁₁×#100	—	2	1	no	—
78	C₁₁×#99	—	2	4	no	—
79	C₁₁×#99	—	2	8	no	—
80	C₁₁×#99	D₄	1	4	yes	—
81	C₁₁×#97	—	2	2	no	—
82	C₄×C₈×C₁₁	—	2	2	no	—
83	#22455	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₁	—	2	2	no	—
85	C₂⁴×C₁₁	—	2	4	no	—
86	C₁₁×#41	—	2	2	no	—
87	C₁₁×#41	—	2	2	no	—
88	C₁₁×#41	—	2	8	no	—
89	C₁₁×#41	—	2	4	no	—
90	C₁₁×#41	—	2	4	no	—
91	C₁₁×#41	—	4	4	no	—
92	C₁₁×#41	—	4	8	no	—
93	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
94	C₂×Q₈×C₁₁	#41	1	1	yes	characteristic
95	C₂×D₄×C₁₁	—	2	8	no	—
96	C₂×D₄×C₁₁	—	2	4	no	—
97	C₂×D₄×C₁₁	—	2	2	no	—
98	C₂×D₄×C₁₁	—	2	4	no	—
99	C₂×D₄×C₁₁	—	2	2	no	—
100	C₂×D₄×C₁₁	—	2	4	no	—
101	C₂×D₄×C₁₁	—	4	4	no	—
102	C₂×D₄×C₁₁	—	4	8	no	—
103	C₂×D₄×C₁₁	—	4	16	no	—
104	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
105	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
106	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₁₁	C₂×D₄	1	8	yes	—
108	C₂×D₄×C₁₁	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	—	2	4	no	—
110	C₂²×C₄×C₁₁	—	2	2	no	—
111	C₂²×C₄×C₁₁	—	4	8	no	—
112	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
114	C₁₁×Q₁₆	—	2	1	no	—
115	C₁₁×Q₁₆	—	2	1	no	—
116	C₁₁×SD₁₆	—	2	4	no	—
117	C₁₁×SD₁₆	—	2	8	no	—
118	C₁₁×D₈	—	2	1	no	—
119	C₁₁×D₈	—	2	1	no	—
120	C₁₁×D₈	—	2	8	no	—
121	C₁₁×D₈	C₂²⋊C₄	1	4	yes	—
122	C₁₁×D₈	C₂²⋊C₄	1	4	yes	—
123	C₁₁×D₈	C₂²⋊C₄	1	8	yes	—
124	C₁₁×M₁₆	—	2	4	no	—
125	C₁₁×M₁₆	—	2	2	no	—
126	C₁₁×M₁₆	—	2	2	no	—
127	C₁₁×M₁₆	—	2	2	no	—
128	C₂×C₈×C₁₁	—	2	2	no	—
129	C₂×C₈×C₁₁	—	2	2	no	—
130	C₂×C₈×C₁₁	—	2	2	no	—
131	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	4	no	—
138	C₁₁×C₂²⋊C₄	—	2	4	no	—
139	C₁₁×C₂²⋊C₄	—	4	8	no	—
140	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
141	C₄²×C₁₁	—	2	2	no	—
142	C₄²×C₁₁	—	2	4	no	—
143	C₂×#576	C₂×C₁₁	1	1	yes	characteristic
144	#2948	C₂×C₁₁	1	2	yes	complemented
145	#2883	C₂×C₁₁	1	2	yes	complemented
146	#1976	C₂×C₁₁	1	2	yes	complemented
147	#1904	C₂×C₁₁	1	4	yes	complemented
148	#1812	C₂×C₁₁	1	1	yes	characteristic, complemented
149	#1795	C₂×C₁₁	1	2	yes	complemented
150	#1757	C₂×C₁₁	1	1	yes	characteristic, complemented
151	C₂³×C₁₁	—	2	4	no	—
152	C₂³×C₁₁	—	2	8	no	—
153	C₂³×C₁₁	—	2	2	no	—
154	C₂³×C₁₁	—	4	8	no	—
155	C₂³×C₁₁	—	16	2	no	—
156	C₂³×C₁₁	—	16	4	no	—
157	C₂³×C₁₁	C₄×D₄	1	2	yes	—
158	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₁₁	—	2	2	no	—
160	Q₈×C₁₁	—	2	2	no	—
161	Q₈×C₁₁	—	2	2	no	—
162	D₄×C₁₁	—	2	4	no	—
163	D₄×C₁₁	—	2	2	no	—
164	D₄×C₁₁	—	2	4	no	—
165	D₄×C₁₁	—	2	2	no	—
166	D₄×C₁₁	—	2	8	no	—
167	D₄×C₁₁	—	2	2	no	—
168	D₄×C₁₁	—	4	8	no	—
169	D₄×C₁₁	—	4	8	no	—
170	D₄×C₁₁	—	4	4	no	—
171	D₄×C₁₁	C₂×C₂²⋊C₄	1	8	yes	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	2	no	—
175	C₂×C₄×C₁₁	—	2	4	no	—
176	C₂×C₄×C₁₁	—	4	8	no	—
177	C₂×C₄×C₁₁	—	4	4	no	—
178	C₂×C₄×C₁₁	—	4	4	no	—
179	C₂×C₄×C₁₁	—	16	8	no	—
180	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
185	C₈×C₁₁	—	2	2	no	—
186	C₈×C₁₁	—	4	2	no	—
187	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	2	yes	—
191	#576	—	2	4	no	—
192	#576	—	2	4	no	—
193	C₂×AGL(1,ℤ/8)	C₄×C₁₁	1	4	yes	complemented
194	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
195	C₂×#135	C₄×C₁₁	1	2	yes	complemented
196	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
197	C₂²×D₈	C₄×C₁₁	1	2	yes	complemented
198	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
199	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
200	#518	C₂²×C₁₁	1	4	yes	complemented
201	#442	—	2	4	no	—
202	C₄×D₈	—	2	4	no	—
203	#427	C₂²×C₁₁	1	2	yes	complemented
204	#421	C₂²×C₁₁	1	4	yes	complemented
205	#418	C₂²×C₁₁	1	4	yes	complemented
206	#413	C₂²×C₁₁	1	1	yes	characteristic
207	#410	C₂²×C₁₁	1	2	yes	—
208	#410	C₂²×C₁₁	1	1	yes	characteristic
209	#410	C₂²×C₁₁	1	4	yes	complemented
210	C₂×#99	—	2	8	no	—
211	#405	C₂²×C₁₁	1	2	yes	complemented
212	#344	C₂²×C₁₁	1	2	yes	complemented
213	H(3,ℤ/4)	C₂²×C₁₁	1	2	yes	complemented
214	C₂²×C₁₁	—	2	2	no	—
215	C₂²×C₁₁	—	2	8	no	—
216	C₂²×C₁₁	—	4	1	no	—
217	C₂²×C₁₁	—	4	2	no	—
218	C₂²×C₁₁	—	4	2	no	—
219	C₂²×C₁₁	—	8	8	no	—
220	C₂²×C₁₁	—	8	4	no	—
221	C₂²×C₁₁	—	8	2	no	—
222	C₂²×C₁₁	—	16	8	no	—
223	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₁₁	D₄²	1	2	yes	—
225	C₄×C₁₁	—	2	2	no	—
226	C₄×C₁₁	—	4	4	no	—
227	C₄×C₁₁	—	4	2	no	—
228	C₄×C₁₁	—	8	4	no	—
229	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
230	C₄×C₁₁	#518	1	1	yes	characteristic
231	C₄×C₁₁	#546	1	2	yes	—
232	H(5,𝔽₂)	—	2	8	no	—
233	H(5,𝔽₂)	—	4	4	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	C₂×C₄×C₁₁	1	4	yes	complemented
236	C₂×#41	C₂³×C₁₁	1	2	yes	—
237	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	C₂×C₄×C₁₁	1	4	yes	complemented
241	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
242	AGL(1,ℤ/8)	—	2	8	no	—
243	AGL(1,ℤ/8)	—	2	16	no	—
244	#135	—	2	4	no	—
245	#135	—	2	4	no	—
246	#135	—	2	2	no	—
247	#135	—	2	2	no	—
248	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
249	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
250	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	complemented
251	C₂×D₈	—	2	4	no	—
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
254	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
255	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
256	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	complemented
257	C₂×D₈	D₄×C₁₁	1	4	yes	—
258	C₂×D₈	D₄×C₁₁	1	4	yes	—
259	#131	—	2	2	no	—
260	#131	—	2	2	no	—
261	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	complemented
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	complemented
265	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
266	C₄×D₄	—	2	8	no	—
267	C₄×D₄	—	4	4	no	—
268	#117	C₂³×C₁₁	1	4	yes	—
269	#117	C₂³×C₁₁	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	8	no	—
271	#107	—	2	2	no	—
272	#106	—	2	2	no	—
273	#104	—	4	4	no	—
274	#102	—	2	8	no	—
275	#101	—	2	1	no	—
276	#100	—	2	1	no	—
277	#99	—	2	4	no	—
278	#99	—	2	8	no	—
279	#99	D₄×C₁₁	1	4	yes	—
280	#97	—	2	2	no	—
281	C₄×C₈	—	2	2	no	—
282	C₂×C₁₁	—	2	2	no	—
283	C₂×C₁₁	—	2	1	no	—
284	C₂×C₁₁	—	4	2	no	—
285	C₂×C₁₁	—	4	8	no	—
286	C₂×C₁₁	—	8	2	no	—
287	C₂×C₁₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
288	C₂⁴	—	2	2	no	—
289	C₂⁴	—	2	4	no	—
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	2	8	no	—
293	#41	—	2	4	no	—
294	#41	—	2	4	no	—
295	#41	—	4	4	no	—
296	#41	—	4	8	no	—
297	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
298	C₂×Q₈	C₁₁×#41	1	1	yes	characteristic
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	—	4	8	no	—
307	C₂×D₄	—	4	16	no	—
308	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
309	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
310	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
311	C₂×D₄	C₂×D₄×C₁₁	1	8	yes	—
312	C₂×D₄	C₁₁×#41	1	1	yes	characteristic
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	4	8	no	—
316	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
318	Q₁₆	—	2	1	no	—
319	Q₁₆	—	2	1	no	—
320	SD₁₆	—	2	8	no	—
321	SD₁₆	—	2	4	no	—
322	D₈	—	2	8	no	—
323	D₈	—	2	1	no	—
324	D₈	—	2	1	no	—
325	D₈	C₁₁×C₂²⋊C₄	1	4	yes	—
326	D₈	C₁₁×C₂²⋊C₄	1	4	yes	—
327	D₈	C₁₁×C₂²⋊C₄	1	8	yes	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	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	C₄⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	4	8	no	—
344	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	4	no	—
347	C₁₁	#22455	1	1	yes	characteristic, direct product factor, Sylow
348	C₂³	—	2	4	no	—
349	C₂³	—	2	8	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	16	2	no	—
353	C₂³	—	16	4	no	—
354	C₂³	C₄×D₄×C₁₁	1	2	yes	—
355	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
356	Q₈	—	2	2	no	—
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	D₄	—	2	4	no	—
360	D₄	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	8	no	—
364	D₄	—	2	2	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	4	no	—
368	D₄	C₂×C₁₁×C₂²⋊C₄	1	8	yes	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	4	8	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	16	8	no	—
377	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
378	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
380	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
381	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
385	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
386	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	8	no	—
393	C₂²	—	8	4	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	16	8	no	—
396	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
397	C₂²	D₄²×C₁₁	1	2	yes	—
398	C₄	—	2	2	no	—
399	C₄	—	4	4	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	4	no	—
402	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
403	C₄	C₁₁×#518	1	1	yes	characteristic
404	C₄	C₁₁×#546	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	2	1	no	—
407	C₂	—	4	2	no	—
408	C₂	—	4	8	no	—
409	C₂	—	8	2	no	—
410	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×#576	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×#2948	C₂	semidirect
3. C₁₁×#2883	C₂	semidirect
4. C₁₁×#1976	C₂	semidirect
5. C₁₁×#1904	C₂	semidirect
6. C₁₁×#1812	C₂	semidirect
7. C₁₁×#1795	C₂	semidirect
8. C₁₁×#1757	C₂	semidirect
12. C₂×C₁₁×AGL(1,ℤ/8)	C₄	semidirect
14. C₂×C₁₁×#135	C₄	semidirect
16. C₂²×C₁₁×D₈	C₄	semidirect
19. C₁₁×#518	C₂²	semidirect
22. C₁₁×#427	C₂²	semidirect
23. C₁₁×#421	C₂²	semidirect
24. C₁₁×#418	C₂²	semidirect
28. C₁₁×#410	C₂²	semidirect
30. C₁₁×#405	C₂²	semidirect
31. C₁₁×#344	C₂²	semidirect
32. C₁₁×H(3,ℤ/4)	C₂²	semidirect
36. C₂×C₁₁×#41	C₂×C₄	semidirect
41. C₂²×D₄×C₁₁	C₂×C₄	semidirect
49. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
50. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
51. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
56. C₂×C₁₁×D₈	C₂×C₄	semidirect
57. C₂×C₁₁×D₈	C₂×C₄	semidirect
62. C₂×C₁₁×M₁₆	C₂×C₄	semidirect
65. C₂²×C₈×C₁₁	C₂×C₄	semidirect
83. #22455	C₁₁	direct (N × H)
144. #2948	C₂×C₁₁	semidirect
145. #2883	C₂×C₁₁	semidirect
146. #1976	C₂×C₁₁	semidirect
147. #1904	C₂×C₁₁	semidirect
148. #1812	C₂×C₁₁	semidirect
149. #1795	C₂×C₁₁	semidirect
150. #1757	C₂×C₁₁	semidirect
193. C₂×AGL(1,ℤ/8)	C₄×C₁₁	semidirect
195. C₂×#135	C₄×C₁₁	semidirect
197. C₂²×D₈	C₄×C₁₁	semidirect
200. #518	C₂²×C₁₁	semidirect
203. #427	C₂²×C₁₁	semidirect
204. #421	C₂²×C₁₁	semidirect
205. #418	C₂²×C₁₁	semidirect
209. #410	C₂²×C₁₁	semidirect
211. #405	C₂²×C₁₁	semidirect
212. #344	C₂²×C₁₁	semidirect
213. H(3,ℤ/4)	C₂²×C₁₁	semidirect
235. C₂×#41	C₂×C₄×C₁₁	semidirect
240. C₂²×D₄	C₂×C₄×C₁₁	semidirect
248. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
249. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
250. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
255. C₂×D₈	C₂×C₄×C₁₁	semidirect
256. C₂×D₈	C₂×C₄×C₁₁	semidirect
261. C₂×M₁₆	C₂×C₄×C₁₁	semidirect
264. C₂²×C₈	C₂×C₄×C₁₁	semidirect
347. C₁₁	#22455	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×#576	2
C₁₁×#2948	2
C₁₁×#2883	2
C₁₁×#1976	2
C₁₁×#1904	2
C₁₁×#1812	2
C₁₁×#1795	2
C₁₁×#1757	2
#22455	11

Subgroups — C11×#22455 #14599648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22455 #14599648