Subgroups — C₂×C₁₁×#3155 #14637834

Order 2816.

3534 conjugacy classes of subgroups.

The subgroup lattice has 446 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	2	yes	maximal, complemented
2	C₂²×C₁₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×#535	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3155	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₁×#496	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₁×#495	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#493	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×#41	C₂²	1	2	yes	—
11	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
12	C₂×C₁₁×AGL(1,ℤ/8)	—	2	16	no	—
13	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
14	C₂×C₁₁×#135	—	2	8	no	—
15	C₂×C₁₁×#135	C₂²	1	8	yes	complemented
16	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
18	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₁₁×D₈	—	2	8	no	—
20	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
21	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
22	C₂²×C₁₁×D₈	C₂²	1	8	yes	complemented
23	C₂²×C₁₁×D₈	C₂²	1	4	yes	complemented
24	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×#535	—	2	8	no	—
28	C₁₁×#535	C₂²	1	16	yes	complemented
29	C₂×C₁₁×#127	C₂²	1	4	yes	complemented
30	C₂×C₁₁×#124	C₂²	1	4	yes	complemented
31	C₂×C₁₁×#121	—	2	4	no	—
32	C₂×C₁₁×#120	—	2	4	no	—
33	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
34	C₁₁×#496	C₂²	1	32	yes	complemented
35	C₁₁×#495	C₂²	1	16	yes	complemented
36	C₁₁×#493	C₂²	1	16	yes	complemented
37	C₁₁×#405	C₂²	1	8	yes	complemented
38	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
39	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
40	C₂⁵×C₁₁	—	2	2	no	—
41	C₂×C₁₁×#41	—	2	4	no	—
42	C₂×C₁₁×#41	—	2	8	no	—
43	C₂×C₁₁×#41	—	2	8	no	—
44	C₂×C₁₁×#41	C₂³	1	8	yes	—
45	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₁	—	2	2	no	—
47	C₂²×D₄×C₁₁	—	2	8	no	—
48	C₂²×D₄×C₁₁	—	2	8	no	—
49	C₂²×D₄×C₁₁	—	2	2	no	—
50	C₂²×D₄×C₁₁	—	2	4	no	—
51	C₂²×D₄×C₁₁	—	2	8	no	—
52	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₁	C₂³	1	8	yes	—
55	C₂³×C₄×C₁₁	—	2	2	no	—
56	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×AGL(1,ℤ/8)	—	2	64	no	—
58	C₁₁×#135	—	2	32	no	—
59	C₂×C₁₁×Q₁₆	—	2	4	no	—
60	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	complemented
61	C₂×C₁₁×SD₁₆	—	2	8	no	—
62	C₂×C₁₁×SD₁₆	—	2	16	no	—
63	C₂×C₁₁×SD₁₆	C₂³	1	16	yes	complemented
64	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	complemented
65	C₂×C₁₁×D₈	—	2	8	no	—
66	C₂×C₁₁×D₈	—	2	8	no	—
67	C₂×C₁₁×D₈	—	2	4	no	—
68	C₂×C₁₁×D₈	—	2	16	no	—
69	C₂×C₁₁×D₈	—	2	32	no	—
70	C₂×C₁₁×D₈	C₂³	1	8	yes	—
71	C₂×C₁₁×D₈	C₂³	1	8	yes	—
72	C₂×C₁₁×D₈	C₂³	1	4	yes	complemented
73	C₂×C₁₁×D₈	C₂³	1	16	yes	complemented
74	C₂×C₁₁×M₁₆	D₄	1	8	yes	complemented
75	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
76	C₂²×C₈×C₁₁	D₄	1	8	yes	complemented
77	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
81	C₁₁×#127	—	2	8	no	—
82	C₁₁×#127	C₂³	1	16	yes	complemented
83	C₁₁×#124	—	2	8	no	—
84	C₁₁×#124	C₂³	1	16	yes	complemented
85	C₁₁×#121	—	2	32	no	—
86	C₁₁×#120	—	2	32	no	—
87	C₁₁×#117	D₄	1	4	yes	—
88	C₁₁×#117	C₂³	1	4	yes	—
89	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
90	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
91	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
92	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
93	C₁₁×#97	C₂³	1	8	yes	complemented
94	C₄×C₈×C₁₁	C₂³	1	8	yes	complemented
95	C₂×#3155	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₁	—	2	4	no	—
97	C₂⁴×C₁₁	—	2	2	no	—
98	C₂⁴×C₁₁	—	2	8	no	—
99	C₂⁴×C₁₁	—	4	8	no	—
100	C₂⁴×C₁₁	—	8	8	no	—
101	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₁₁×#41	—	2	16	no	—
103	C₁₁×#41	—	2	16	no	—
104	C₁₁×#41	—	4	16	no	—
105	C₂×Q₈×C₁₁	—	2	2	no	—
106	C₂×Q₈×C₁₁	—	2	4	no	—
107	C₂×Q₈×C₁₁	—	2	4	no	—
108	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
109	C₂×D₄×C₁₁	—	2	8	no	—
110	C₂×D₄×C₁₁	—	2	8	no	—
111	C₂×D₄×C₁₁	—	2	16	no	—
112	C₂×D₄×C₁₁	—	2	4	no	—
113	C₂×D₄×C₁₁	—	2	8	no	—
114	C₂×D₄×C₁₁	—	2	4	no	—
115	C₂×D₄×C₁₁	—	2	16	no	—
116	C₂×D₄×C₁₁	—	2	8	no	—
117	C₂×D₄×C₁₁	—	2	4	no	—
118	C₂×D₄×C₁₁	—	2	2	no	—
119	C₂×D₄×C₁₁	—	2	32	no	—
120	C₂×D₄×C₁₁	—	4	8	no	—
121	C₂×D₄×C₁₁	—	4	8	no	—
122	C₂×D₄×C₁₁	—	4	16	no	—
123	C₂×D₄×C₁₁	—	8	16	no	—
124	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
125	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₁	—	2	2	no	—
127	C₂²×C₄×C₁₁	—	2	8	no	—
128	C₂²×C₄×C₁₁	—	4	8	no	—
129	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
136	C₁₁×Q₁₆	—	2	8	no	—
137	C₁₁×SD₁₆	—	2	16	no	—
138	C₁₁×SD₁₆	—	2	32	no	—
139	C₁₁×D₈	—	2	16	no	—
140	C₁₁×D₈	—	2	16	no	—
141	C₁₁×D₈	—	2	8	no	—
142	C₁₁×D₈	—	2	32	no	—
143	C₁₁×M₁₆	C₂×D₄	1	16	yes	complemented
144	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
145	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
146	C₂×C₈×C₁₁	C₂×D₄	1	8	yes	—
147	C₂×C₈×C₁₁	C₂×D₄	1	16	yes	complemented
148	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
149	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
150	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
151	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
152	C₁₁×C₂²⋊C₄	—	2	32	no	—
153	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
154	C₄²×C₁₁	C₂×D₄	1	4	yes	—
155	C₄²×C₁₁	C₂⁴	1	4	yes	—
156	C₂²×AGL(1,ℤ/8)	C₂×C₁₁	1	2	yes	complemented
157	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic, complemented
158	C₂³×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
159	C₂×#535	C₂×C₁₁	1	2	yes	complemented
160	#3155	C₂×C₁₁	1	16	yes	direct product factor
161	C₂×#496	C₂×C₁₁	1	4	yes	complemented
162	C₂×#495	C₂×C₁₁	1	2	yes	complemented
163	C₂×#493	C₂×C₁₁	1	2	yes	complemented
164	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
165	C₂³×C₁₁	—	2	4	no	—
166	C₂³×C₁₁	—	2	8	no	—
167	C₂³×C₁₁	—	2	4	no	—
168	C₂³×C₁₁	—	4	4	no	—
169	C₂³×C₁₁	—	4	16	no	—
170	C₂³×C₁₁	—	4	8	no	—
171	C₂³×C₁₁	—	4	8	no	—
172	C₂³×C₁₁	—	4	16	no	—
173	C₂³×C₁₁	—	8	16	no	—
174	C₂³×C₁₁	—	8	32	no	—
175	C₂³×C₁₁	#127	1	4	yes	—
176	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
177	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₁₁	—	2	4	no	—
179	Q₈×C₁₁	—	2	4	no	—
180	Q₈×C₁₁	—	4	4	no	—
181	D₄×C₁₁	—	2	8	no	—
182	D₄×C₁₁	—	2	4	no	—
183	D₄×C₁₁	—	2	8	no	—
184	D₄×C₁₁	—	2	4	no	—
185	D₄×C₁₁	—	4	16	no	—
186	D₄×C₁₁	—	4	16	no	—
187	D₄×C₁₁	—	4	8	no	—
188	D₄×C₁₁	—	4	4	no	—
189	D₄×C₁₁	—	8	32	no	—
190	C₂×C₄×C₁₁	—	2	8	no	—
191	C₂×C₄×C₁₁	—	2	4	no	—
192	C₂×C₄×C₁₁	—	4	4	no	—
193	C₂×C₄×C₁₁	—	4	16	no	—
194	C₂×C₄×C₁₁	#127	1	4	yes	—
195	C₂×C₄×C₁₁	#127	1	8	yes	—
196	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
197	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
204	C₈×C₁₁	C₂²×D₄	1	4	yes	—
205	C₈×C₁₁	C₂²×D₄	1	4	yes	—
206	C₈×C₁₁	C₂²×D₄	1	8	yes	—
207	C₂²×#41	C₂²×C₁₁	1	2	yes	—
208	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
209	C₂×AGL(1,ℤ/8)	—	2	16	no	—
210	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	16	yes	complemented
211	C₂×#135	—	2	8	no	—
212	C₂×#135	C₂²×C₁₁	1	8	yes	complemented
213	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
214	C₂²×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
215	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	complemented
216	C₂²×D₈	—	2	8	no	—
217	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
218	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
219	C₂²×D₈	C₂²×C₁₁	1	8	yes	complemented
220	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
221	C₂²×D₈	C₂²×C₁₁	1	4	yes	complemented
222	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
223	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
224	#535	—	2	8	no	—
225	#535	C₂²×C₁₁	1	16	yes	complemented
226	C₂×#127	C₂²×C₁₁	1	4	yes	complemented
227	C₂×#124	C₂²×C₁₁	1	4	yes	complemented
228	C₂×#121	—	2	4	no	—
229	C₂×#120	—	2	4	no	—
230	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
231	#496	C₂²×C₁₁	1	32	yes	complemented
232	#495	C₂²×C₁₁	1	16	yes	complemented
233	#493	C₂²×C₁₁	1	16	yes	complemented
234	#405	C₂²×C₁₁	1	8	yes	complemented
235	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
236	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
237	C₂²×C₁₁	—	2	8	no	—
238	C₂²×C₁₁	—	2	4	no	—
239	C₂²×C₁₁	—	4	4	no	—
240	C₂²×C₁₁	—	4	8	no	—
241	C₂²×C₁₁	—	4	8	no	—
242	C₂²×C₁₁	—	4	16	no	—
243	C₂²×C₁₁	—	8	32	no	—
244	C₂²×C₁₁	—	8	8	no	—
245	C₂²×C₁₁	—	8	16	no	—
246	C₂²×C₁₁	C₂×#127	1	4	yes	—
247	C₂²×C₁₁	C₂×#127	1	2	yes	—
248	C₂²×C₁₁	#576	1	4	yes	—
249	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
250	C₄×C₁₁	—	2	8	no	—
251	C₄×C₁₁	—	4	4	no	—
252	C₄×C₁₁	C₂×#127	1	4	yes	—
253	C₄×C₁₁	C₂×#127	1	2	yes	—
254	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
255	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
256	C₂⁵	—	2	2	no	—
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	2	8	no	—
259	C₂×#41	—	2	8	no	—
260	C₂×#41	C₂³×C₁₁	1	8	yes	—
261	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	2	8	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	4	no	—
267	C₂²×D₄	—	2	8	no	—
268	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
269	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
270	C₂²×D₄	C₂³×C₁₁	1	8	yes	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
273	AGL(1,ℤ/8)	—	2	64	no	—
274	#135	—	2	32	no	—
275	C₂×Q₁₆	—	2	4	no	—
276	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	complemented
277	C₂×SD₁₆	—	2	8	no	—
278	C₂×SD₁₆	—	2	16	no	—
279	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	complemented
280	C₂×SD₁₆	C₂³×C₁₁	1	16	yes	complemented
281	C₂×D₈	—	2	8	no	—
282	C₂×D₈	—	2	8	no	—
283	C₂×D₈	—	2	4	no	—
284	C₂×D₈	—	2	16	no	—
285	C₂×D₈	—	2	32	no	—
286	C₂×D₈	C₂³×C₁₁	1	8	yes	—
287	C₂×D₈	C₂³×C₁₁	1	8	yes	—
288	C₂×D₈	C₂³×C₁₁	1	4	yes	complemented
289	C₂×D₈	C₂³×C₁₁	1	16	yes	complemented
290	C₂×M₁₆	D₄×C₁₁	1	8	yes	complemented
291	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
292	C₂²×C₈	D₄×C₁₁	1	8	yes	complemented
293	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
297	#127	—	2	8	no	—
298	#127	C₂³×C₁₁	1	16	yes	complemented
299	#124	—	2	8	no	—
300	#124	C₂³×C₁₁	1	16	yes	complemented
301	#121	—	2	32	no	—
302	#120	—	2	32	no	—
303	#117	D₄×C₁₁	1	4	yes	—
304	#117	C₂³×C₁₁	1	4	yes	—
305	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	8	no	—
307	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
308	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
309	#97	C₂³×C₁₁	1	8	yes	complemented
310	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
311	C₂×C₁₁	—	2	4	no	—
312	C₂×C₁₁	—	8	4	no	—
313	C₂×C₁₁	—	8	8	no	—
314	C₂×C₁₁	#3155	1	4	yes	direct product factor
315	C₂×C₁₁	C₂²×#127	1	1	yes	characteristic
316	C₂×C₁₁	C₂×#576	1	2	yes	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	2	8	no	—
320	C₂⁴	—	4	8	no	—
321	C₂⁴	—	8	8	no	—
322	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
323	#41	—	2	16	no	—
324	#41	—	2	16	no	—
325	#41	—	4	16	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	16	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	16	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	32	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	—	4	8	no	—
343	C₂×D₄	—	4	16	no	—
344	C₂×D₄	—	8	16	no	—
345	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
346	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	4	8	no	—
350	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
351	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
354	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
355	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
357	Q₁₆	—	2	8	no	—
358	SD₁₆	—	2	16	no	—
359	SD₁₆	—	2	32	no	—
360	D₈	—	2	16	no	—
361	D₈	—	2	16	no	—
362	D₈	—	2	8	no	—
363	D₈	—	2	32	no	—
364	M₁₆	C₂×D₄×C₁₁	1	16	yes	complemented
365	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
366	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
367	C₂×C₈	C₂×D₄×C₁₁	1	8	yes	—
368	C₂×C₈	C₂×D₄×C₁₁	1	16	yes	complemented
369	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
370	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
371	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
372	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
373	C₂²⋊C₄	—	2	32	no	—
374	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
375	C₄²	C₂×D₄×C₁₁	1	4	yes	—
376	C₄²	C₂⁴×C₁₁	1	4	yes	—
377	C₁₁	C₂×#3155	1	1	yes	characteristic, direct product factor, Sylow
378	C₂³	—	2	4	no	—
379	C₂³	—	2	8	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	16	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	4	16	no	—
386	C₂³	—	8	16	no	—
387	C₂³	—	8	32	no	—
388	C₂³	C₁₁×#127	1	4	yes	—
389	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
390	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
391	Q₈	—	2	4	no	—
392	Q₈	—	2	4	no	—
393	Q₈	—	4	4	no	—
394	D₄	—	2	8	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	2	4	no	—
398	D₄	—	4	16	no	—
399	D₄	—	4	16	no	—
400	D₄	—	4	8	no	—
401	D₄	—	4	4	no	—
402	D₄	—	8	32	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	16	no	—
407	C₂×C₄	C₁₁×#127	1	4	yes	—
408	C₂×C₄	C₁₁×#127	1	8	yes	—
409	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
410	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
415	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
416	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
417	C₈	C₂²×D₄×C₁₁	1	4	yes	—
418	C₈	C₂²×D₄×C₁₁	1	4	yes	—
419	C₈	C₂²×D₄×C₁₁	1	8	yes	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	8	no	—
424	C₂²	—	4	8	no	—
425	C₂²	—	4	16	no	—
426	C₂²	—	8	32	no	—
427	C₂²	—	8	16	no	—
428	C₂²	—	8	8	no	—
429	C₂²	C₂×C₁₁×#127	1	4	yes	—
430	C₂²	C₂×C₁₁×#127	1	2	yes	—
431	C₂²	C₁₁×#576	1	4	yes	—
432	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
433	C₄	—	2	8	no	—
434	C₄	—	4	4	no	—
435	C₄	C₂×C₁₁×#127	1	4	yes	—
436	C₄	C₂×C₁₁×#127	1	2	yes	—
437	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
438	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
439	C₂	—	2	4	no	—
440	C₂	—	8	8	no	—
441	C₂	—	8	4	no	—
442	C₂	C₁₁×#3155	1	4	yes	direct product factor
443	C₂	C₂²×C₁₁×#127	1	1	yes	characteristic
444	C₂	C₂×C₁₁×#576	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 ◁ C₂×C₁₁×#117 ◁ 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. C₂²×C₁₁×#135	C₂	semidirect
3. C₂³×C₁₁×D₈	C₂	semidirect
4. C₂×C₁₁×#535	C₂	semidirect
5. C₁₁×#3155	C₂	direct (N × H)
6. C₂×C₁₁×#496	C₂	semidirect
7. C₂×C₁₁×#495	C₂	semidirect
8. C₂×C₁₁×#493	C₂	semidirect
9. C₂×C₁₁×#405	C₂	semidirect
13. C₂×C₁₁×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂×C₁₁×#135	C₂²	semidirect
16. C₂²×C₁₁×Q₁₆	C₂²	semidirect
17. C₂²×C₁₁×SD₁₆	C₂²	semidirect
18. C₂²×C₁₁×SD₁₆	C₂²	semidirect
22. C₂²×C₁₁×D₈	C₂²	semidirect
23. C₂²×C₁₁×D₈	C₂²	semidirect
24. C₂²×C₁₁×D₈	C₂²	semidirect
28. C₁₁×#535	C₂²	semidirect
29. C₂×C₁₁×#127	C₂²	semidirect
30. C₂×C₁₁×#124	C₂²	semidirect
34. C₁₁×#496	C₂²	semidirect
35. C₁₁×#495	C₂²	semidirect
36. C₁₁×#493	C₂²	semidirect
37. C₁₁×#405	C₂²	semidirect
38. C₂×C₁₁×#97	C₂²	semidirect
39. C₂×C₄×C₈×C₁₁	C₂²	semidirect
60. C₂×C₁₁×Q₁₆	C₂³	semidirect
63. C₂×C₁₁×SD₁₆	C₂³	semidirect
64. C₂×C₁₁×SD₁₆	C₂³	semidirect
72. C₂×C₁₁×D₈	C₂³	semidirect
73. C₂×C₁₁×D₈	C₂³	semidirect
74. C₂×C₁₁×M₁₆	D₄	semidirect
76. C₂²×C₈×C₁₁	D₄	semidirect
82. C₁₁×#127	C₂³	semidirect
84. C₁₁×#124	C₂³	semidirect
93. C₁₁×#97	C₂³	semidirect
94. C₄×C₈×C₁₁	C₂³	semidirect
95. C₂×#3155	C₁₁	direct (N × H)
143. C₁₁×M₁₆	C₂×D₄	semidirect
147. C₂×C₈×C₁₁	C₂×D₄	semidirect
156. C₂²×AGL(1,ℤ/8)	C₂×C₁₁	semidirect
157. C₂²×#135	C₂×C₁₁	semidirect
158. C₂³×D₈	C₂×C₁₁	semidirect
159. C₂×#535	C₂×C₁₁	semidirect
160. #3155	C₂×C₁₁	direct (N × H)
161. C₂×#496	C₂×C₁₁	semidirect
162. C₂×#495	C₂×C₁₁	semidirect
163. C₂×#493	C₂×C₁₁	semidirect
164. C₂×#405	C₂×C₁₁	semidirect
210. C₂×AGL(1,ℤ/8)	C₂²×C₁₁	semidirect
212. C₂×#135	C₂²×C₁₁	semidirect
213. C₂²×Q₁₆	C₂²×C₁₁	semidirect
214. C₂²×SD₁₆	C₂²×C₁₁	semidirect
215. C₂²×SD₁₆	C₂²×C₁₁	semidirect
219. C₂²×D₈	C₂²×C₁₁	semidirect
220. C₂²×D₈	C₂²×C₁₁	semidirect
221. C₂²×D₈	C₂²×C₁₁	semidirect
225. #535	C₂²×C₁₁	semidirect
226. C₂×#127	C₂²×C₁₁	semidirect
227. C₂×#124	C₂²×C₁₁	semidirect
231. #496	C₂²×C₁₁	semidirect
232. #495	C₂²×C₁₁	semidirect
233. #493	C₂²×C₁₁	semidirect
234. #405	C₂²×C₁₁	semidirect
235. C₂×#97	C₂²×C₁₁	semidirect
236. C₂×C₄×C₈	C₂²×C₁₁	semidirect
276. C₂×Q₁₆	C₂³×C₁₁	semidirect
279. C₂×SD₁₆	C₂³×C₁₁	semidirect
280. C₂×SD₁₆	C₂³×C₁₁	semidirect
288. C₂×D₈	C₂³×C₁₁	semidirect
289. C₂×D₈	C₂³×C₁₁	semidirect
290. C₂×M₁₆	D₄×C₁₁	semidirect
292. C₂²×C₈	D₄×C₁₁	semidirect
298. #127	C₂³×C₁₁	semidirect
300. #124	C₂³×C₁₁	semidirect
309. #97	C₂³×C₁₁	semidirect
310. C₄×C₈	C₂³×C₁₁	semidirect
314. C₂×C₁₁	#3155	direct (N × H)
364. M₁₆	C₂×D₄×C₁₁	semidirect
368. C₂×C₈	C₂×D₄×C₁₁	semidirect
377. C₁₁	C₂×#3155	direct (N × H)
442. C₂	C₁₁×#3155	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
C₂²×C₁₁×#135	2
C₂³×C₁₁×D₈	2
C₂×C₁₁×#535	2
C₁₁×#3155	2
C₂×C₁₁×#496	2
C₂×C₁₁×#495	2
C₂×C₁₁×#493	2
C₂×C₁₁×#405	2
C₂×#3155	11

Subgroups — C2×C11×#3155 #14637834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3155 #14637834