Subgroups — C₂×C₁₁×#3151 #14637829

Order 2816.

3950 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	C₂²×C₁₁×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
2	C₂×C₁₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3151	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₁×#496	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#493	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#492	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×#41	C₂²	1	2	yes	—
10	C₂³×D₄×C₁₁	—	2	2	no	—
11	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
12	C₂×C₁₁×AGL(1,ℤ/8)	—	2	32	no	—
13	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	32	yes	complemented
14	C₂²×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
15	C₂²×C₁₁×D₈	C₂²	1	8	yes	complemented
16	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
17	C₁₁×#532	—	2	4	no	—
18	C₁₁×#532	C₂²	1	8	yes	complemented
19	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₁×#127	—	2	2	no	—
21	C₂×C₁₁×#127	—	2	4	no	—
22	C₂×C₁₁×#127	C₂²	1	2	yes	—
23	C₂×C₁₁×#127	C₂²	1	2	yes	—
24	C₂×C₁₁×#127	C₂²	1	8	yes	complemented
25	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₁₁×#124	C₂²	1	2	yes	complemented
27	C₂×C₁₁×#121	—	2	2	no	—
28	C₂×C₄×D₄×C₁₁	—	2	2	no	—
29	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#496	C₂²	1	32	yes	complemented
31	C₁₁×#493	C₂²	1	16	yes	complemented
32	C₁₁×#492	C₂²	1	16	yes	complemented
33	C₄×C₁₁×M₁₆	C₂²	1	8	yes	complemented
34	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
35	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
36	C₂⁵×C₁₁	—	2	2	no	—
37	C₂×C₁₁×#41	—	2	4	no	—
38	C₂×C₁₁×#41	—	2	16	no	—
39	C₂×C₁₁×#41	C₂³	1	8	yes	—
40	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
41	C₂²×D₄×C₁₁	—	2	2	no	—
42	C₂²×D₄×C₁₁	—	2	16	no	—
43	C₂²×D₄×C₁₁	—	2	2	no	—
44	C₂²×D₄×C₁₁	—	2	4	no	—
45	C₂²×D₄×C₁₁	—	2	2	no	—
46	C₂²×D₄×C₁₁	—	2	4	no	—
47	C₂²×D₄×C₁₁	—	2	4	no	—
48	C₂²×D₄×C₁₁	—	2	16	no	—
49	C₂²×D₄×C₁₁	—	4	16	no	—
50	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₁	C₂³	1	8	yes	—
53	C₂³×C₄×C₁₁	—	2	2	no	—
54	C₂³×C₄×C₁₁	D₄	1	2	yes	—
55	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
56	C₁₁×AGL(1,ℤ/8)	—	2	128	no	—
57	C₂×C₁₁×SD₁₆	—	2	32	no	—
58	C₂×C₁₁×SD₁₆	C₂³	1	32	yes	complemented
59	C₂×C₁₁×D₈	—	2	32	no	—
60	C₂×C₁₁×D₈	C₂³	1	32	yes	complemented
61	C₂×C₁₁×M₁₆	D₄	1	16	yes	complemented
62	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
63	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
64	C₁₁×C₄⋊Q₈	—	2	2	no	—
65	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	complemented
66	C₁₁×#127	—	2	4	no	—
67	C₁₁×#127	—	2	4	no	—
68	C₁₁×#127	—	2	16	no	—
69	C₁₁×#127	—	2	2	no	—
70	C₁₁×#127	C₂³	1	8	yes	—
71	C₁₁×#127	C₂³	1	8	yes	—
72	C₁₁×#127	C₂³	1	4	yes	complemented
73	C₁₁×#124	—	2	4	no	—
74	C₁₁×#124	C₂³	1	8	yes	complemented
75	C₁₁×#121	—	2	16	no	—
76	C₄×D₄×C₁₁	—	2	16	no	—
77	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
79	C₂×C₄²×C₁₁	D₄	1	2	yes	—
80	C₂×C₄²×C₁₁	D₄	1	4	yes	—
81	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
84	C₁₁×#97	C₂³	1	8	yes	complemented
85	C₄×C₈×C₁₁	C₂³	1	8	yes	complemented
86	C₂×#3151	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₁	—	2	8	no	—
88	C₂⁴×C₁₁	—	2	2	no	—
89	C₂⁴×C₁₁	—	2	4	no	—
90	C₂⁴×C₁₁	—	4	16	no	—
91	C₂⁴×C₁₁	—	4	8	no	—
92	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₁₁×#41	—	2	32	no	—
94	C₁₁×#41	—	4	16	no	—
95	C₂×Q₈×C₁₁	—	2	2	no	—
96	C₂×Q₈×C₁₁	—	2	8	no	—
97	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
98	C₂×D₄×C₁₁	—	2	8	no	—
99	C₂×D₄×C₁₁	—	2	8	no	—
100	C₂×D₄×C₁₁	—	2	16	no	—
101	C₂×D₄×C₁₁	—	2	32	no	—
102	C₂×D₄×C₁₁	—	2	8	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	8	no	—
105	C₂×D₄×C₁₁	—	2	4	no	—
106	C₂×D₄×C₁₁	—	2	16	no	—
107	C₂×D₄×C₁₁	—	2	16	no	—
108	C₂×D₄×C₁₁	—	4	16	no	—
109	C₂×D₄×C₁₁	—	4	64	no	—
110	C₂×D₄×C₁₁	—	4	8	no	—
111	C₂×D₄×C₁₁	—	4	8	no	—
112	C₂×D₄×C₁₁	—	4	16	no	—
113	C₂×D₄×C₁₁	—	4	8	no	—
114	C₂×D₄×C₁₁	—	4	16	no	—
115	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
116	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₁₁	—	2	8	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	2	8	no	—
120	C₂²×C₄×C₁₁	—	4	8	no	—
121	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
122	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
126	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
129	C₁₁×SD₁₆	—	2	64	no	—
130	C₁₁×D₈	—	2	64	no	—
131	C₁₁×M₁₆	C₂×D₄	1	32	yes	complemented
132	C₂×C₈×C₁₁	C₂×D₄	1	16	yes	complemented
133	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
134	C₁₁×C₄⋊C₄	—	2	8	no	—
135	C₁₁×C₂²⋊C₄	—	2	16	no	—
136	C₄²×C₁₁	C₂×D₄	1	8	yes	—
137	C₄²×C₁₁	C₂×D₄	1	2	yes	—
138	C₄²×C₁₁	C₂×D₄	1	2	yes	—
139	C₄²×C₁₁	C₂⁴	1	2	yes	—
140	C₄²×C₁₁	C₂⁴	1	2	yes	—
141	C₂²×AGL(1,ℤ/8)	C₂×C₁₁	1	4	yes	complemented
142	C₂×#532	C₂×C₁₁	1	1	yes	characteristic, complemented
143	C₂²×#127	C₂×C₁₁	1	1	yes	characteristic, complemented
144	#3151	C₂×C₁₁	1	16	yes	direct product factor
145	C₂×#496	C₂×C₁₁	1	4	yes	complemented
146	C₂×#493	C₂×C₁₁	1	2	yes	complemented
147	C₂×#492	C₂×C₁₁	1	2	yes	complemented
148	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
149	C₂³×C₁₁	—	2	4	no	—
150	C₂³×C₁₁	—	2	4	no	—
151	C₂³×C₁₁	—	2	8	no	—
152	C₂³×C₁₁	—	4	32	no	—
153	C₂³×C₁₁	—	4	4	no	—
154	C₂³×C₁₁	—	4	16	no	—
155	C₂³×C₁₁	—	4	8	no	—
156	C₂³×C₁₁	—	4	16	no	—
157	C₂³×C₁₁	—	4	8	no	—
158	C₂³×C₁₁	—	8	32	no	—
159	C₂³×C₁₁	#127	1	4	yes	—
160	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
161	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₁	—	2	8	no	—
163	Q₈×C₁₁	—	4	4	no	—
164	D₄×C₁₁	—	2	8	no	—
165	D₄×C₁₁	—	2	16	no	—
166	D₄×C₁₁	—	4	32	no	—
167	D₄×C₁₁	—	4	16	no	—
168	D₄×C₁₁	—	4	16	no	—
169	D₄×C₁₁	—	4	8	no	—
170	D₄×C₁₁	—	4	4	no	—
171	D₄×C₁₁	—	4	16	no	—
172	D₄×C₁₁	—	4	32	no	—
173	C₂×C₄×C₁₁	—	2	4	no	—
174	C₂×C₄×C₁₁	—	2	16	no	—
175	C₂×C₄×C₁₁	—	2	4	no	—
176	C₂×C₄×C₁₁	—	4	4	no	—
177	C₂×C₄×C₁₁	—	4	16	no	—
178	C₂×C₄×C₁₁	#127	1	4	yes	—
179	C₂×C₄×C₁₁	#127	1	8	yes	—
180	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	8	yes	complemented
181	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
185	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
186	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
188	C₈×C₁₁	C₂²×D₄	1	16	yes	complemented
189	C₂²×#41	C₂²×C₁₁	1	2	yes	—
190	C₂³×D₄	—	2	2	no	—
191	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
192	C₂×AGL(1,ℤ/8)	—	2	32	no	—
193	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	32	yes	complemented
194	C₂²×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
195	C₂²×D₈	C₂²×C₁₁	1	8	yes	complemented
196	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
197	#532	—	2	4	no	—
198	#532	C₂²×C₁₁	1	8	yes	complemented
199	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
200	C₂×#127	—	2	2	no	—
201	C₂×#127	—	2	4	no	—
202	C₂×#127	C₂²×C₁₁	1	2	yes	—
203	C₂×#127	C₂²×C₁₁	1	2	yes	—
204	C₂×#127	C₂²×C₁₁	1	8	yes	complemented
205	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic, complemented
206	C₂×#124	C₂²×C₁₁	1	2	yes	complemented
207	C₂×#121	—	2	2	no	—
208	C₂×C₄×D₄	—	2	2	no	—
209	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
210	#496	C₂²×C₁₁	1	32	yes	complemented
211	#493	C₂²×C₁₁	1	16	yes	complemented
212	#492	C₂²×C₁₁	1	16	yes	complemented
213	C₄×M₁₆	C₂²×C₁₁	1	8	yes	complemented
214	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
215	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
216	C₂²×C₁₁	—	2	8	no	—
217	C₂²×C₁₁	—	2	4	no	—
218	C₂²×C₁₁	—	4	4	no	—
219	C₂²×C₁₁	—	4	8	no	—
220	C₂²×C₁₁	—	4	16	no	—
221	C₂²×C₁₁	—	4	8	no	—
222	C₂²×C₁₁	—	8	32	no	—
223	C₂²×C₁₁	—	8	8	no	—
224	C₂²×C₁₁	—	8	16	no	—
225	C₂²×C₁₁	C₂×#127	1	4	yes	—
226	C₂²×C₁₁	C₂×#127	1	2	yes	—
227	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
228	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
229	C₄×C₁₁	—	2	4	no	—
230	C₄×C₁₁	—	4	4	no	—
231	C₄×C₁₁	C₂×#127	1	4	yes	—
232	C₄×C₁₁	C₂×#127	1	2	yes	—
233	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	8	yes	complemented
234	C₄×C₁₁	C₂³×D₄	1	2	yes	—
235	C₂⁵	—	2	2	no	—
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	16	no	—
238	C₂×#41	C₂³×C₁₁	1	8	yes	—
239	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	16	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	4	no	—
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	2	4	no	—
247	C₂²×D₄	—	2	16	no	—
248	C₂²×D₄	—	4	16	no	—
249	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
250	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
251	C₂²×D₄	C₂³×C₁₁	1	8	yes	—
252	C₂³×C₄	—	2	2	no	—
253	C₂³×C₄	D₄×C₁₁	1	2	yes	—
254	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
255	AGL(1,ℤ/8)	—	2	128	no	—
256	C₂×SD₁₆	—	2	32	no	—
257	C₂×SD₁₆	C₂³×C₁₁	1	32	yes	complemented
258	C₂×D₈	—	2	32	no	—
259	C₂×D₈	C₂³×C₁₁	1	32	yes	complemented
260	C₂×M₁₆	D₄×C₁₁	1	16	yes	complemented
261	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
262	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	complemented
265	#127	—	2	4	no	—
266	#127	—	2	4	no	—
267	#127	—	2	16	no	—
268	#127	—	2	2	no	—
269	#127	C₂³×C₁₁	1	8	yes	—
270	#127	C₂³×C₁₁	1	8	yes	—
271	#127	C₂³×C₁₁	1	4	yes	complemented
272	#124	—	2	4	no	—
273	#124	C₂³×C₁₁	1	8	yes	complemented
274	#121	—	2	16	no	—
275	C₄×D₄	—	2	16	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	4	no	—
278	C₂×C₄²	D₄×C₁₁	1	2	yes	—
279	C₂×C₄²	D₄×C₁₁	1	4	yes	—
280	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
283	#97	C₂³×C₁₁	1	8	yes	complemented
284	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
285	C₂×C₁₁	—	2	4	no	—
286	C₂×C₁₁	—	8	4	no	—
287	C₂×C₁₁	—	8	8	no	—
288	C₂×C₁₁	#3151	1	4	yes	direct product factor
289	C₂×C₁₁	C₂²×#127	1	1	yes	characteristic
290	C₂×C₁₁	C₂²×AGL(1,ℤ/8)	1	2	yes	—
291	C₂⁴	—	2	2	no	—
292	C₂⁴	—	2	8	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	4	16	no	—
295	C₂⁴	—	4	8	no	—
296	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
297	#41	—	2	32	no	—
298	#41	—	4	16	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	8	no	—
301	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	8	no	—
304	C₂×D₄	—	2	16	no	—
305	C₂×D₄	—	2	32	no	—
306	C₂×D₄	—	2	8	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	16	no	—
311	C₂×D₄	—	2	16	no	—
312	C₂×D₄	—	4	16	no	—
313	C₂×D₄	—	4	64	no	—
314	C₂×D₄	—	4	8	no	—
315	C₂×D₄	—	4	8	no	—
316	C₂×D₄	—	4	16	no	—
317	C₂×D₄	—	4	16	no	—
318	C₂×D₄	—	4	8	no	—
319	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
320	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	4	8	no	—
325	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
327	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
330	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
333	SD₁₆	—	2	64	no	—
334	D₈	—	2	64	no	—
335	M₁₆	C₂×D₄×C₁₁	1	32	yes	complemented
336	C₂×C₈	C₂×D₄×C₁₁	1	16	yes	complemented
337	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
338	C₄⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	16	no	—
340	C₄²	C₂×D₄×C₁₁	1	8	yes	—
341	C₄²	C₂×D₄×C₁₁	1	2	yes	—
342	C₄²	C₂×D₄×C₁₁	1	2	yes	—
343	C₄²	C₂⁴×C₁₁	1	2	yes	—
344	C₄²	C₂⁴×C₁₁	1	2	yes	—
345	C₁₁	C₂×#3151	1	1	yes	characteristic, direct product factor, Sylow
346	C₂³	—	2	4	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	4	32	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	16	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	16	no	—
354	C₂³	—	4	8	no	—
355	C₂³	—	8	32	no	—
356	C₂³	C₁₁×#127	1	4	yes	—
357	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
358	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
359	Q₈	—	2	8	no	—
360	Q₈	—	4	4	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	16	no	—
363	D₄	—	4	32	no	—
364	D₄	—	4	16	no	—
365	D₄	—	4	16	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	16	no	—
369	D₄	—	4	32	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	16	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	C₁₁×#127	1	4	yes	—
376	C₂×C₄	C₁₁×#127	1	8	yes	—
377	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	8	yes	complemented
378	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
379	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
382	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
383	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
384	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
385	C₈	C₂²×D₄×C₁₁	1	16	yes	complemented
386	C₂²	—	2	8	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	16	no	—
391	C₂²	—	4	8	no	—
392	C₂²	—	8	32	no	—
393	C₂²	—	8	16	no	—
394	C₂²	—	8	8	no	—
395	C₂²	C₂×C₁₁×#127	1	4	yes	—
396	C₂²	C₂×C₁₁×#127	1	2	yes	—
397	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	4	yes	—
398	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
399	C₄	—	2	4	no	—
400	C₄	—	4	4	no	—
401	C₄	C₂×C₁₁×#127	1	4	yes	—
402	C₄	C₂×C₁₁×#127	1	2	yes	—
403	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	8	yes	complemented
404	C₄	C₂³×D₄×C₁₁	1	2	yes	—
405	C₂	—	2	4	no	—
406	C₂	—	8	8	no	—
407	C₂	—	8	4	no	—
408	C₂	C₁₁×#3151	1	4	yes	direct product factor
409	C₂	C₂²×C₁₁×#127	1	1	yes	characteristic
410	C₂	C₂²×C₁₁×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₁×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₁₁×#532	C₂	semidirect
3. C₂²×C₁₁×#127	C₂	semidirect
4. C₁₁×#3151	C₂	direct (N × H)
5. C₂×C₁₁×#496	C₂	semidirect
6. C₂×C₁₁×#493	C₂	semidirect
7. C₂×C₁₁×#492	C₂	semidirect
8. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
13. C₂×C₁₁×AGL(1,ℤ/8)	C₂²	semidirect
14. C₂²×C₁₁×SD₁₆	C₂²	semidirect
15. C₂²×C₁₁×D₈	C₂²	semidirect
18. C₁₁×#532	C₂²	semidirect
19. C₂×C₁₁×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₁₁×#127	C₂²	semidirect
25. C₂×C₁₁×#127	C₂²	semidirect
26. C₂×C₁₁×#124	C₂²	semidirect
30. C₁₁×#496	C₂²	semidirect
31. C₁₁×#493	C₂²	semidirect
32. C₁₁×#492	C₂²	semidirect
33. C₄×C₁₁×M₁₆	C₂²	semidirect
34. C₂×C₁₁×#97	C₂²	semidirect
35. C₂×C₄×C₈×C₁₁	C₂²	semidirect
58. C₂×C₁₁×SD₁₆	C₂³	semidirect
60. C₂×C₁₁×D₈	C₂³	semidirect
61. C₂×C₁₁×M₁₆	D₄	semidirect
65. C₁₁×C₄⋊Q₈	C₂³	semidirect
72. C₁₁×#127	C₂³	semidirect
74. C₁₁×#124	C₂³	semidirect
84. C₁₁×#97	C₂³	semidirect
85. C₄×C₈×C₁₁	C₂³	semidirect
86. C₂×#3151	C₁₁	direct (N × H)
131. C₁₁×M₁₆	C₂×D₄	semidirect
132. C₂×C₈×C₁₁	C₂×D₄	semidirect
141. C₂²×AGL(1,ℤ/8)	C₂×C₁₁	semidirect
142. C₂×#532	C₂×C₁₁	semidirect
143. C₂²×#127	C₂×C₁₁	semidirect
144. #3151	C₂×C₁₁	direct (N × H)
145. C₂×#496	C₂×C₁₁	semidirect
146. C₂×#493	C₂×C₁₁	semidirect
147. C₂×#492	C₂×C₁₁	semidirect
148. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
180. C₂×C₄×C₁₁	AGL(1,ℤ/8)	semidirect
188. C₈×C₁₁	C₂²×D₄	semidirect
193. C₂×AGL(1,ℤ/8)	C₂²×C₁₁	semidirect
194. C₂²×SD₁₆	C₂²×C₁₁	semidirect
195. C₂²×D₈	C₂²×C₁₁	semidirect
198. #532	C₂²×C₁₁	semidirect
199. C₂×C₄⋊Q₈	C₂²×C₁₁	semidirect
204. C₂×#127	C₂²×C₁₁	semidirect
205. C₂×#127	C₂²×C₁₁	semidirect
206. C₂×#124	C₂²×C₁₁	semidirect
210. #496	C₂²×C₁₁	semidirect
211. #493	C₂²×C₁₁	semidirect
212. #492	C₂²×C₁₁	semidirect
213. C₄×M₁₆	C₂²×C₁₁	semidirect
214. C₂×#97	C₂²×C₁₁	semidirect
215. C₂×C₄×C₈	C₂²×C₁₁	semidirect
233. C₄×C₁₁	C₂×AGL(1,ℤ/8)	semidirect
257. C₂×SD₁₆	C₂³×C₁₁	semidirect
259. C₂×D₈	C₂³×C₁₁	semidirect
260. C₂×M₁₆	D₄×C₁₁	semidirect
264. C₄⋊Q₈	C₂³×C₁₁	semidirect
271. #127	C₂³×C₁₁	semidirect
273. #124	C₂³×C₁₁	semidirect
283. #97	C₂³×C₁₁	semidirect
284. C₄×C₈	C₂³×C₁₁	semidirect
288. C₂×C₁₁	#3151	direct (N × H)
335. M₁₆	C₂×D₄×C₁₁	semidirect
336. C₂×C₈	C₂×D₄×C₁₁	semidirect
345. C₁₁	C₂×#3151	direct (N × H)
377. C₂×C₄	C₁₁×AGL(1,ℤ/8)	semidirect
385. C₈	C₂²×D₄×C₁₁	semidirect
403. C₄	C₂×C₁₁×AGL(1,ℤ/8)	semidirect
408. C₂	C₁₁×#3151	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×AGL(1,ℤ/8)	2
C₂×C₁₁×#532	2
C₂²×C₁₁×#127	2
C₁₁×#3151	2
C₂×C₁₁×#496	2
C₂×C₁₁×#493	2
C₂×C₁₁×#492	2
C₂×C₄×C₁₁×M₁₆	2
C₂×#3151	11

Subgroups — C2×C11×#3151 #14637829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3151 #14637829