Subgroups — C₂×C₁₁×#2955 #14637372

Order 2816.

2666 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#575	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×#131	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2955	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#444	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#443	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#421	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₁×#41	C₂²	1	2	yes	—
10	C₁₁×#575	C₄	1	8	yes	complemented
11	C₁₁×#575	C₂²	1	8	yes	—
12	C₂×C₁₁×#137	C₄	1	4	yes	complemented
13	C₂×C₁₁×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
14	C₂×C₁₁×#135	C₂²	1	4	yes	—
15	C₂×C₁₁×#131	—	2	2	no	—
16	C₂×C₁₁×#131	—	2	8	no	—
17	C₂×C₁₁×#131	—	2	2	no	—
18	C₂×C₁₁×#131	C₂²	1	4	yes	complemented
19	C₂×C₁₁×#131	C₂²	1	4	yes	complemented
20	C₂×C₁₁×#131	C₂²	1	16	yes	complemented
21	C₂²×C₁₁×M₁₆	—	2	2	no	—
22	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
23	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₁₁	—	2	2	no	—
25	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
27	C₁₁×#444	C₂²	1	32	yes	complemented
28	C₁₁×#443	C₂²	1	32	yes	complemented
29	C₁₁×#430	C₂²	1	8	yes	complemented
30	C₂×C₁₁×#108	C₂²	1	4	yes	complemented
31	C₁₁×#421	C₂²	1	16	yes	complemented
32	C₂×C₁₁×#104	C₂²	1	8	yes	complemented
33	C₁₁×#405	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	C₂×C₁₁×#41	—	2	2	no	—
37	C₂×C₁₁×#41	—	2	4	no	—
38	C₂×C₁₁×#41	—	2	2	no	—
39	C₂×C₁₁×#41	—	2	4	no	—
40	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
41	C₂×C₁₁×#41	C₂×C₄	1	8	yes	—
42	C₂×C₁₁×#41	C₂³	1	4	yes	—
43	C₂×C₁₁×#41	C₂³	1	8	yes	—
44	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₁	—	2	2	no	—
46	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₁₁	—	2	2	no	—
48	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
49	C₁₁×#137	C₂×C₄	1	32	yes	complemented
50	C₁₁×AGL(1,ℤ/8)	C₂×C₄	1	32	yes	complemented
51	C₁₁×#135	C₂×C₄	1	16	yes	—
52	C₁₁×#135	C₂³	1	16	yes	—
53	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
54	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	—
55	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
56	C₁₁×#131	—	2	16	no	—
57	C₁₁×#131	—	2	16	no	—
58	C₁₁×#131	—	2	8	no	—
59	C₁₁×#131	—	2	8	no	—
60	C₁₁×#131	C₂³	1	16	yes	complemented
61	C₁₁×#131	C₂³	1	16	yes	complemented
62	C₂×C₁₁×M₁₆	—	2	2	no	—
63	C₂×C₁₁×M₁₆	—	2	4	no	—
64	C₂×C₁₁×M₁₆	—	2	4	no	—
65	C₂×C₁₁×M₁₆	—	2	4	no	—
66	C₂×C₁₁×M₁₆	—	2	16	no	—
67	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
68	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
69	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
70	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
71	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₁	—	2	2	no	—
73	C₂²×C₈×C₁₁	—	2	4	no	—
74	C₂²×C₈×C₁₁	—	2	16	no	—
75	C₂²×C₈×C₁₁	—	2	4	no	—
76	C₂²×C₈×C₁₁	D₄	1	2	yes	—
77	C₂²×C₈×C₁₁	D₄	1	4	yes	—
78	C₂²×C₈×C₁₁	D₄	1	2	yes	—
79	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
82	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
83	C₁₁×#117	—	2	2	no	—
84	C₁₁×#117	C₂³	1	4	yes	—
85	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
88	C₁₁×#108	C₂³	1	16	yes	complemented
89	C₁₁×#104	C₂³	1	32	yes	complemented
90	C₁₁×#97	C₂³	1	8	yes	complemented
91	C₄×C₈×C₁₁	C₂³	1	8	yes	complemented
92	C₂×#2955	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₁	—	2	2	no	—
94	C₂⁴×C₁₁	#41	1	1	yes	characteristic
95	C₁₁×#41	—	2	8	no	—
96	C₁₁×#41	—	2	8	no	—
97	C₁₁×#41	—	2	8	no	—
98	C₁₁×#41	—	2	8	no	—
99	C₁₁×#41	—	2	4	no	—
100	C₁₁×#41	—	2	4	no	—
101	C₁₁×#41	—	2	8	no	—
102	C₁₁×#41	C₂²×C₄	1	8	yes	—
103	C₁₁×#41	C₂²×C₄	1	16	yes	—
104	C₁₁×#41	C₂⁴	1	8	yes	—
105	C₂×Q₈×C₁₁	—	2	2	no	—
106	C₂×Q₈×C₁₁	—	2	4	no	—
107	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
108	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
109	C₂×D₄×C₁₁	—	2	4	no	—
110	C₂×D₄×C₁₁	—	2	8	no	—
111	C₂×D₄×C₁₁	—	2	4	no	—
112	C₂×D₄×C₁₁	—	2	8	no	—
113	C₂×D₄×C₁₁	—	2	2	no	—
114	C₂×D₄×C₁₁	—	2	4	no	—
115	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
116	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	4	no	—
119	C₂²×C₄×C₁₁	—	2	8	no	—
120	C₂²×C₄×C₁₁	—	2	4	no	—
121	C₂²×C₄×C₁₁	—	2	8	no	—
122	C₂²×C₄×C₁₁	—	2	2	no	—
123	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	#41	1	2	yes	—
129	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
131	C₁₁×Q₁₆	C₂²×C₄	1	16	yes	—
132	C₁₁×SD₁₆	C₂²×C₄	1	32	yes	—
133	C₁₁×D₈	C₂²×C₄	1	16	yes	—
134	C₁₁×M₁₆	—	2	16	no	—
135	C₁₁×M₁₆	—	2	16	no	—
136	C₁₁×M₁₆	—	2	8	no	—
137	C₁₁×M₁₆	—	2	4	no	—
138	C₁₁×M₁₆	C₂²×C₄	1	16	yes	—
139	C₁₁×M₁₆	C₂⁴	1	8	yes	—
140	C₂×C₈×C₁₁	—	2	16	no	—
141	C₂×C₈×C₁₁	—	2	16	no	—
142	C₂×C₈×C₁₁	—	2	4	no	—
143	C₂×C₈×C₁₁	—	2	8	no	—
144	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
145	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
146	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₁₁	C₂×D₄	1	8	yes	—
148	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₁₁	C₂×D₄	1	8	yes	—
150	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
154	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
155	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
156	C₁₁×C₄⋊C₄	—	2	4	no	—
157	C₁₁×C₂²⋊C₄	—	2	4	no	—
158	C₄²×C₁₁	—	2	2	no	—
159	C₄²×C₁₁	C₂⁴	1	4	yes	—
160	C₂×#575	C₂×C₁₁	1	1	yes	characteristic
161	C₂²×#131	C₂×C₁₁	1	2	yes	complemented
162	#2955	C₂×C₁₁	1	16	yes	direct product factor
163	C₂×#444	C₂×C₁₁	1	4	yes	complemented
164	C₂×#443	C₂×C₁₁	1	4	yes	complemented
165	C₂×#430	C₂×C₁₁	1	1	yes	characteristic, complemented
166	C₂×#421	C₂×C₁₁	1	2	yes	complemented
167	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
168	C₂³×C₁₁	—	2	8	no	—
169	C₂³×C₁₁	—	2	4	no	—
170	C₂³×C₁₁	—	4	2	no	—
171	C₂³×C₁₁	—	4	8	no	—
172	C₂³×C₁₁	C₄×D₄	1	2	yes	—
173	C₂³×C₁₁	C₄×D₄	1	2	yes	—
174	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
175	C₂³×C₁₁	C₂×#41	1	2	yes	—
176	Q₈×C₁₁	—	2	8	no	—
177	Q₈×C₁₁	—	2	4	no	—
178	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
179	D₄×C₁₁	—	2	16	no	—
180	D₄×C₁₁	—	2	8	no	—
181	D₄×C₁₁	—	2	8	no	—
182	D₄×C₁₁	—	2	8	no	—
183	D₄×C₁₁	—	2	4	no	—
184	D₄×C₁₁	C₂³×C₄	1	8	yes	—
185	C₂×C₄×C₁₁	—	2	8	no	—
186	C₂×C₄×C₁₁	—	2	4	no	—
187	C₂×C₄×C₁₁	—	2	8	no	—
188	C₂×C₄×C₁₁	—	2	16	no	—
189	C₂×C₄×C₁₁	—	2	8	no	—
190	C₂×C₄×C₁₁	—	2	4	no	—
191	C₂×C₄×C₁₁	—	4	4	no	—
192	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
194	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
195	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
199	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
204	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
205	C₈×C₁₁	—	2	8	no	—
206	C₈×C₁₁	C₂³×C₄	1	8	yes	—
207	C₈×C₁₁	C₂²×D₄	1	2	yes	—
208	C₈×C₁₁	C₂²×D₄	1	4	yes	—
209	C₈×C₁₁	C₂²×D₄	1	2	yes	—
210	C₂²×#41	C₂²×C₁₁	1	2	yes	—
211	#575	C₄×C₁₁	1	8	yes	complemented
212	#575	C₂²×C₁₁	1	8	yes	—
213	C₂×#137	C₄×C₁₁	1	4	yes	complemented
214	C₂×AGL(1,ℤ/8)	C₄×C₁₁	1	4	yes	complemented
215	C₂×#135	C₂²×C₁₁	1	4	yes	—
216	C₂×#131	—	2	2	no	—
217	C₂×#131	—	2	2	no	—
218	C₂×#131	—	2	8	no	—
219	C₂×#131	C₂²×C₁₁	1	4	yes	complemented
220	C₂×#131	C₂²×C₁₁	1	4	yes	complemented
221	C₂×#131	C₂²×C₁₁	1	16	yes	complemented
222	C₂²×M₁₆	—	2	2	no	—
223	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
224	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
225	C₂³×C₈	—	2	2	no	—
226	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
227	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
228	#444	C₂²×C₁₁	1	32	yes	complemented
229	#443	C₂²×C₁₁	1	32	yes	complemented
230	#430	C₂²×C₁₁	1	8	yes	complemented
231	C₂×#108	C₂²×C₁₁	1	4	yes	complemented
232	#421	C₂²×C₁₁	1	16	yes	complemented
233	C₂×#104	C₂²×C₁₁	1	8	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	2	no	—
238	C₂²×C₁₁	—	2	4	no	—
239	C₂²×C₁₁	—	2	8	no	—
240	C₂²×C₁₁	—	4	2	no	—
241	C₂²×C₁₁	—	4	2	no	—
242	C₂²×C₁₁	—	4	16	no	—
243	C₂²×C₁₁	—	4	8	no	—
244	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
245	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
248	C₄×C₁₁	—	2	8	no	—
249	C₄×C₁₁	—	4	4	no	—
250	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
251	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
252	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
254	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	4	no	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	4	no	—
259	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
260	C₂×#41	C₂×C₄×C₁₁	1	8	yes	—
261	C₂×#41	C₂³×C₁₁	1	4	yes	—
262	C₂×#41	C₂³×C₁₁	1	8	yes	—
263	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
268	#137	C₂×C₄×C₁₁	1	32	yes	complemented
269	AGL(1,ℤ/8)	C₂×C₄×C₁₁	1	32	yes	complemented
270	#135	C₂×C₄×C₁₁	1	16	yes	—
271	#135	C₂³×C₁₁	1	16	yes	—
272	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
273	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	—
274	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
275	#131	—	2	16	no	—
276	#131	—	2	16	no	—
277	#131	—	2	8	no	—
278	#131	—	2	8	no	—
279	#131	C₂³×C₁₁	1	16	yes	complemented
280	#131	C₂³×C₁₁	1	16	yes	complemented
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	4	no	—
283	C₂×M₁₆	—	2	4	no	—
284	C₂×M₁₆	—	2	4	no	—
285	C₂×M₁₆	—	2	16	no	—
286	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
287	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
288	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
289	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
290	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	4	no	—
293	C₂²×C₈	—	2	4	no	—
294	C₂²×C₈	—	2	16	no	—
295	C₂²×C₈	D₄×C₁₁	1	2	yes	—
296	C₂²×C₈	D₄×C₁₁	1	2	yes	—
297	C₂²×C₈	D₄×C₁₁	1	4	yes	—
298	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
299	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
302	#117	—	2	2	no	—
303	#117	C₂³×C₁₁	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
307	#108	C₂³×C₁₁	1	16	yes	complemented
308	#104	C₂³×C₁₁	1	32	yes	complemented
309	#97	C₂³×C₁₁	1	8	yes	complemented
310	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
311	C₂×C₁₁	—	2	1	no	—
312	C₂×C₁₁	—	2	4	no	—
313	C₂×C₁₁	—	2	1	no	—
314	C₂×C₁₁	—	4	8	no	—
315	C₂×C₁₁	#2955	1	2	yes	direct product factor
316	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
317	C₂⁴	—	2	2	no	—
318	C₂⁴	C₁₁×#41	1	1	yes	characteristic
319	#41	—	2	8	no	—
320	#41	—	2	8	no	—
321	#41	—	2	8	no	—
322	#41	—	2	8	no	—
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	8	no	—
326	#41	C₂²×C₄×C₁₁	1	8	yes	—
327	#41	C₂²×C₄×C₁₁	1	16	yes	—
328	#41	C₂⁴×C₁₁	1	8	yes	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
332	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
340	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
351	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
352	C₂²×C₄	C₁₁×#41	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
355	Q₁₆	C₂²×C₄×C₁₁	1	16	yes	—
356	SD₁₆	C₂²×C₄×C₁₁	1	32	yes	—
357	D₈	C₂²×C₄×C₁₁	1	16	yes	—
358	M₁₆	—	2	8	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	16	no	—
361	M₁₆	—	2	16	no	—
362	M₁₆	C₂²×C₄×C₁₁	1	16	yes	—
363	M₁₆	C₂⁴×C₁₁	1	8	yes	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	8	no	—
366	C₂×C₈	—	2	16	no	—
367	C₂×C₈	—	2	16	no	—
368	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
369	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
370	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
371	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
372	C₂×C₈	C₂×D₄×C₁₁	1	8	yes	—
373	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
374	C₂×C₈	C₂×D₄×C₁₁	1	8	yes	—
375	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
376	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
377	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
378	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
379	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	C₂⁴×C₁₁	1	4	yes	—
384	C₁₁	C₂×#2955	1	1	yes	characteristic, direct product factor, Sylow
385	C₂³	—	2	8	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	8	no	—
389	C₂³	C₄×D₄×C₁₁	1	2	yes	—
390	C₂³	C₄×D₄×C₁₁	1	2	yes	—
391	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
392	C₂³	C₂×C₁₁×#41	1	2	yes	—
393	Q₈	—	2	8	no	—
394	Q₈	—	2	4	no	—
395	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
396	D₄	—	2	16	no	—
397	D₄	—	2	8	no	—
398	D₄	—	2	8	no	—
399	D₄	—	2	8	no	—
400	D₄	—	2	4	no	—
401	D₄	C₂³×C₄×C₁₁	1	8	yes	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	16	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
410	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
411	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
412	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
413	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
414	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
415	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
416	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
418	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
421	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
422	C₈	—	2	8	no	—
423	C₈	C₂³×C₄×C₁₁	1	8	yes	—
424	C₈	C₂²×D₄×C₁₁	1	2	yes	—
425	C₈	C₂²×D₄×C₁₁	1	4	yes	—
426	C₈	C₂²×D₄×C₁₁	1	2	yes	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	16	no	—
433	C₂²	—	4	8	no	—
434	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
435	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
436	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
437	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
438	C₄	—	2	8	no	—
439	C₄	—	4	4	no	—
440	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
441	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
442	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
443	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
444	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	4	no	—
447	C₂	—	2	1	no	—
448	C₂	—	4	8	no	—
449	C₂	C₁₁×#2955	1	2	yes	direct product factor
450	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₁×#131	C₂	semidirect
3. C₁₁×#2955	C₂	direct (N × H)
4. C₂×C₁₁×#444	C₂	semidirect
5. C₂×C₁₁×#443	C₂	semidirect
6. C₂×C₁₁×#430	C₂	semidirect
7. C₂×C₁₁×#421	C₂	semidirect
8. C₂×C₁₁×#405	C₂	semidirect
10. C₁₁×#575	C₄	semidirect
12. C₂×C₁₁×#137	C₄	semidirect
13. C₂×C₁₁×AGL(1,ℤ/8)	C₄	semidirect
18. C₂×C₁₁×#131	C₂²	semidirect
19. C₂×C₁₁×#131	C₂²	semidirect
20. C₂×C₁₁×#131	C₂²	semidirect
27. C₁₁×#444	C₂²	semidirect
28. C₁₁×#443	C₂²	semidirect
29. C₁₁×#430	C₂²	semidirect
30. C₂×C₁₁×#108	C₂²	semidirect
31. C₁₁×#421	C₂²	semidirect
32. C₂×C₁₁×#104	C₂²	semidirect
33. C₁₁×#405	C₂²	semidirect
34. C₂×C₁₁×#97	C₂²	semidirect
35. C₂×C₄×C₈×C₁₁	C₂²	semidirect
49. C₁₁×#137	C₂×C₄	semidirect
50. C₁₁×AGL(1,ℤ/8)	C₂×C₄	semidirect
60. C₁₁×#131	C₂³	semidirect
61. C₁₁×#131	C₂³	semidirect
88. C₁₁×#108	C₂³	semidirect
89. C₁₁×#104	C₂³	semidirect
90. C₁₁×#97	C₂³	semidirect
91. C₄×C₈×C₁₁	C₂³	semidirect
92. C₂×#2955	C₁₁	direct (N × H)
161. C₂²×#131	C₂×C₁₁	semidirect
162. #2955	C₂×C₁₁	direct (N × H)
163. C₂×#444	C₂×C₁₁	semidirect
164. C₂×#443	C₂×C₁₁	semidirect
165. C₂×#430	C₂×C₁₁	semidirect
166. C₂×#421	C₂×C₁₁	semidirect
167. C₂×#405	C₂×C₁₁	semidirect
211. #575	C₄×C₁₁	semidirect
213. C₂×#137	C₄×C₁₁	semidirect
214. C₂×AGL(1,ℤ/8)	C₄×C₁₁	semidirect
219. C₂×#131	C₂²×C₁₁	semidirect
220. C₂×#131	C₂²×C₁₁	semidirect
221. C₂×#131	C₂²×C₁₁	semidirect
228. #444	C₂²×C₁₁	semidirect
229. #443	C₂²×C₁₁	semidirect
230. #430	C₂²×C₁₁	semidirect
231. C₂×#108	C₂²×C₁₁	semidirect
232. #421	C₂²×C₁₁	semidirect
233. C₂×#104	C₂²×C₁₁	semidirect
234. #405	C₂²×C₁₁	semidirect
235. C₂×#97	C₂²×C₁₁	semidirect
236. C₂×C₄×C₈	C₂²×C₁₁	semidirect
268. #137	C₂×C₄×C₁₁	semidirect
269. AGL(1,ℤ/8)	C₂×C₄×C₁₁	semidirect
279. #131	C₂³×C₁₁	semidirect
280. #131	C₂³×C₁₁	semidirect
307. #108	C₂³×C₁₁	semidirect
308. #104	C₂³×C₁₁	semidirect
309. #97	C₂³×C₁₁	semidirect
310. C₄×C₈	C₂³×C₁₁	semidirect
315. C₂×C₁₁	#2955	direct (N × H)
384. C₁₁	C₂×#2955	direct (N × H)
449. C₂	C₁₁×#2955	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×#575	2
C₂²×C₁₁×#131	2
C₁₁×#2955	2
C₂×C₁₁×#444	2
C₂×C₁₁×#443	2
C₂×C₁₁×#430	2
C₂×C₁₁×#421	2
C₂×C₁₁×#405	2
C₂×#2955	11

Subgroups — C2×C11×#2955 #14637372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2955 #14637372