Subgroups — C₂×C₁₁×#2956 #14637373

Order 2816.

2674 conjugacy classes of subgroups.

The subgroup lattice has 434 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	C₂×C₁₁×#568	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2956	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	C₂²×C₁₁×#104	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	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	C₁₁×#568	—	2	8	no	—
16	C₁₁×#568	C₂²	1	16	yes	complemented
17	C₂×C₁₁×#131	—	2	4	no	—
18	C₂×C₁₁×#131	C₂²	1	8	yes	complemented
19	C₂²×C₁₁×M₁₆	—	2	4	no	—
20	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
21	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#444	C₂²	1	32	yes	complemented
25	C₁₁×#443	C₂²	1	32	yes	complemented
26	C₁₁×#430	C₂²	1	8	yes	complemented
27	C₂×C₁₁×#108	C₂²	1	4	yes	complemented
28	C₂×C₁₁×#104	C₂²	1	4	yes	complemented
29	C₂×C₁₁×#104	C₂²	1	4	yes	complemented
30	C₂×C₁₁×#104	C₂²	1	16	yes	complemented
31	C₄×C₁₁×M₁₆	C₂²	1	8	yes	complemented
32	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
33	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
34	C₂×C₁₁×#41	—	2	2	no	—
35	C₂×C₁₁×#41	—	2	4	no	—
36	C₂×C₁₁×#41	—	2	2	no	—
37	C₂×C₁₁×#41	—	2	4	no	—
38	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
39	C₂×C₁₁×#41	C₂×C₄	1	8	yes	—
40	C₂×C₁₁×#41	C₂³	1	4	yes	—
41	C₂×C₁₁×#41	C₂³	1	8	yes	—
42	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₁	—	2	2	no	—
44	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₁₁	—	2	2	no	—
46	C₂³×C₄×C₁₁	—	2	1	no	—
47	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
48	C₁₁×#137	C₂×C₄	1	32	yes	complemented
49	C₁₁×AGL(1,ℤ/8)	C₂×C₄	1	32	yes	complemented
50	C₁₁×#135	C₂×C₄	1	16	yes	complemented
51	C₁₁×#135	C₂³	1	16	yes	—
52	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
54	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
55	C₁₁×#131	—	2	32	no	—
56	C₁₁×#131	—	2	16	no	—
57	C₁₁×#131	C₂³	1	32	yes	complemented
58	C₂×C₁₁×M₁₆	—	2	2	no	—
59	C₂×C₁₁×M₁₆	—	2	4	no	—
60	C₂×C₁₁×M₁₆	—	2	32	no	—
61	C₂×C₁₁×M₁₆	—	2	8	no	—
62	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
63	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
64	C₂×C₁₁×M₁₆	D₄	1	4	yes	—
65	C₂×C₁₁×M₁₆	D₄	1	4	yes	—
66	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
67	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
68	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
69	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₁	—	2	2	no	—
71	C₂²×C₈×C₁₁	—	2	8	no	—
72	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₁	—	2	1	no	—
75	C₂×C₄²×C₁₁	—	2	2	no	—
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
79	C₁₁×#108	C₂³	1	16	yes	complemented
80	C₁₁×#104	C₂³	1	16	yes	complemented
81	C₁₁×#104	C₂³	1	16	yes	complemented
82	C₁₁×#97	C₂³	1	8	yes	complemented
83	C₄×C₈×C₁₁	C₂³	1	8	yes	complemented
84	C₂×#2956	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₁	—	2	2	no	—
86	C₂⁴×C₁₁	#41	1	1	yes	characteristic
87	C₁₁×#41	—	2	8	no	—
88	C₁₁×#41	—	2	8	no	—
89	C₁₁×#41	—	2	8	no	—
90	C₁₁×#41	—	2	8	no	—
91	C₁₁×#41	—	2	4	no	—
92	C₁₁×#41	—	2	4	no	—
93	C₁₁×#41	—	2	8	no	—
94	C₁₁×#41	C₂²×C₄	1	8	yes	—
95	C₁₁×#41	C₂²×C₄	1	16	yes	—
96	C₁₁×#41	C₂⁴	1	8	yes	—
97	C₂×Q₈×C₁₁	—	2	2	no	—
98	C₂×Q₈×C₁₁	—	2	4	no	—
99	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
101	C₂×D₄×C₁₁	—	2	4	no	—
102	C₂×D₄×C₁₁	—	2	8	no	—
103	C₂×D₄×C₁₁	—	2	4	no	—
104	C₂×D₄×C₁₁	—	2	8	no	—
105	C₂×D₄×C₁₁	—	2	2	no	—
106	C₂×D₄×C₁₁	—	2	4	no	—
107	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
108	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	2	4	no	—
112	C₂²×C₄×C₁₁	—	2	8	no	—
113	C₂²×C₄×C₁₁	—	2	8	no	—
114	C₂²×C₄×C₁₁	—	2	4	no	—
115	C₂²×C₄×C₁₁	—	2	4	no	—
116	C₂²×C₄×C₁₁	—	2	1	no	—
117	C₂²×C₄×C₁₁	—	4	4	no	—
118	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	#41	1	2	yes	—
124	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
126	C₁₁×Q₁₆	C₂²×C₄	1	16	yes	complemented
127	C₁₁×SD₁₆	C₂²×C₄	1	32	yes	complemented
128	C₁₁×D₈	C₂²×C₄	1	16	yes	complemented
129	C₁₁×M₁₆	—	2	32	no	—
130	C₁₁×M₁₆	—	2	8	no	—
131	C₁₁×M₁₆	—	2	4	no	—
132	C₁₁×M₁₆	C₂²×C₄	1	16	yes	—
133	C₁₁×M₁₆	C₂×D₄	1	16	yes	—
134	C₁₁×M₁₆	C₂⁴	1	8	yes	—
135	C₂×C₈×C₁₁	—	2	32	no	—
136	C₂×C₈×C₁₁	—	2	8	no	—
137	C₂×C₈×C₁₁	—	2	4	no	—
138	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
139	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
140	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
141	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
142	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
143	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
144	C₄²×C₁₁	—	2	1	no	—
145	C₄²×C₁₁	—	2	4	no	—
146	C₄²×C₁₁	—	2	1	no	—
147	C₄²×C₁₁	C₂⁴	1	2	yes	—
148	C₄²×C₁₁	C₂⁴	1	2	yes	—
149	C₂×#575	C₂×C₁₁	1	1	yes	characteristic
150	C₂×#568	C₂×C₁₁	1	2	yes	complemented
151	#2956	C₂×C₁₁	1	16	yes	direct product factor
152	C₂×#444	C₂×C₁₁	1	4	yes	complemented
153	C₂×#443	C₂×C₁₁	1	4	yes	complemented
154	C₂×#430	C₂×C₁₁	1	1	yes	characteristic, complemented
155	C₂²×#104	C₂×C₁₁	1	2	yes	complemented
156	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
157	C₂³×C₁₁	—	2	4	no	—
158	C₂³×C₁₁	—	2	8	no	—
159	C₂³×C₁₁	—	4	2	no	—
160	C₂³×C₁₁	—	8	4	no	—
161	C₂³×C₁₁	C₄×D₄	1	2	yes	—
162	C₂³×C₁₁	C₄×D₄	1	2	yes	—
163	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
164	C₂³×C₁₁	C₂×#41	1	2	yes	—
165	Q₈×C₁₁	—	2	8	no	—
166	Q₈×C₁₁	—	2	4	no	—
167	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
168	D₄×C₁₁	—	2	16	no	—
169	D₄×C₁₁	—	2	8	no	—
170	D₄×C₁₁	—	2	8	no	—
171	D₄×C₁₁	—	2	8	no	—
172	D₄×C₁₁	—	2	4	no	—
173	D₄×C₁₁	C₂³×C₄	1	8	yes	—
174	C₂×C₄×C₁₁	—	2	4	no	—
175	C₂×C₄×C₁₁	—	2	8	no	—
176	C₂×C₄×C₁₁	—	2	4	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	2	8	no	—
179	C₂×C₄×C₁₁	—	2	16	no	—
180	C₂×C₄×C₁₁	—	2	8	no	—
181	C₂×C₄×C₁₁	—	2	2	no	—
182	C₂×C₄×C₁₁	—	4	8	no	—
183	C₂×C₄×C₁₁	—	4	2	no	—
184	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
186	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
187	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
191	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
196	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
197	C₈×C₁₁	—	2	8	no	—
198	C₈×C₁₁	C₂³×C₄	1	8	yes	—
199	C₈×C₁₁	C₂²×D₄	1	8	yes	—
200	C₂²×#41	C₂²×C₁₁	1	2	yes	—
201	#575	C₄×C₁₁	1	8	yes	complemented
202	#575	C₂²×C₁₁	1	8	yes	—
203	C₂×#137	C₄×C₁₁	1	4	yes	complemented
204	C₂×AGL(1,ℤ/8)	C₄×C₁₁	1	4	yes	complemented
205	C₂×#135	C₂²×C₁₁	1	4	yes	—
206	#568	—	2	8	no	—
207	#568	C₂²×C₁₁	1	16	yes	complemented
208	C₂×#131	—	2	4	no	—
209	C₂×#131	C₂²×C₁₁	1	8	yes	complemented
210	C₂²×M₁₆	—	2	4	no	—
211	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
212	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
215	#444	C₂²×C₁₁	1	32	yes	complemented
216	#443	C₂²×C₁₁	1	32	yes	complemented
217	#430	C₂²×C₁₁	1	8	yes	complemented
218	C₂×#108	C₂²×C₁₁	1	4	yes	complemented
219	C₂×#104	C₂²×C₁₁	1	4	yes	complemented
220	C₂×#104	C₂²×C₁₁	1	4	yes	complemented
221	C₂×#104	C₂²×C₁₁	1	16	yes	complemented
222	C₄×M₁₆	C₂²×C₁₁	1	8	yes	complemented
223	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
224	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
225	C₂²×C₁₁	—	2	2	no	—
226	C₂²×C₁₁	—	2	4	no	—
227	C₂²×C₁₁	—	2	8	no	—
228	C₂²×C₁₁	—	4	2	no	—
229	C₂²×C₁₁	—	4	2	no	—
230	C₂²×C₁₁	—	4	8	no	—
231	C₂²×C₁₁	—	8	8	no	—
232	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
233	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
236	C₄×C₁₁	—	2	4	no	—
237	C₄×C₁₁	—	2	8	no	—
238	C₄×C₁₁	—	4	2	no	—
239	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
241	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
242	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
243	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	4	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
249	C₂×#41	C₂×C₄×C₁₁	1	8	yes	—
250	C₂×#41	C₂³×C₁₁	1	4	yes	—
251	C₂×#41	C₂³×C₁₁	1	8	yes	—
252	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	—	2	1	no	—
257	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
258	#137	C₂×C₄×C₁₁	1	32	yes	complemented
259	AGL(1,ℤ/8)	C₂×C₄×C₁₁	1	32	yes	complemented
260	#135	C₂×C₄×C₁₁	1	16	yes	complemented
261	#135	C₂³×C₁₁	1	16	yes	—
262	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
263	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
264	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	complemented
265	#131	—	2	32	no	—
266	#131	—	2	16	no	—
267	#131	C₂³×C₁₁	1	32	yes	complemented
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	4	no	—
270	C₂×M₁₆	—	2	32	no	—
271	C₂×M₁₆	—	2	8	no	—
272	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
273	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
274	C₂×M₁₆	D₄×C₁₁	1	4	yes	—
275	C₂×M₁₆	D₄×C₁₁	1	4	yes	—
276	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
277	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
278	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
279	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	8	no	—
282	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
283	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
289	#108	C₂³×C₁₁	1	16	yes	complemented
290	#104	C₂³×C₁₁	1	16	yes	complemented
291	#104	C₂³×C₁₁	1	16	yes	complemented
292	#97	C₂³×C₁₁	1	8	yes	complemented
293	C₄×C₈	C₂³×C₁₁	1	8	yes	complemented
294	C₂×C₁₁	—	2	1	no	—
295	C₂×C₁₁	—	2	4	no	—
296	C₂×C₁₁	—	2	1	no	—
297	C₂×C₁₁	—	4	8	no	—
298	C₂×C₁₁	#2956	1	2	yes	direct product factor
299	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
300	C₂⁴	—	2	2	no	—
301	C₂⁴	C₁₁×#41	1	1	yes	characteristic
302	#41	—	2	8	no	—
303	#41	—	2	8	no	—
304	#41	—	2	8	no	—
305	#41	—	2	8	no	—
306	#41	—	2	4	no	—
307	#41	—	2	4	no	—
308	#41	—	2	8	no	—
309	#41	C₂²×C₄×C₁₁	1	8	yes	—
310	#41	C₂²×C₄×C₁₁	1	16	yes	—
311	#41	C₂⁴×C₁₁	1	8	yes	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
315	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	8	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
323	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
337	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
338	C₂²×C₄	C₁₁×#41	1	2	yes	—
339	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
341	Q₁₆	C₂²×C₄×C₁₁	1	16	yes	complemented
342	SD₁₆	C₂²×C₄×C₁₁	1	32	yes	complemented
343	D₈	C₂²×C₄×C₁₁	1	16	yes	complemented
344	M₁₆	—	2	8	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	32	no	—
347	M₁₆	C₂²×C₄×C₁₁	1	16	yes	—
348	M₁₆	C₂×D₄×C₁₁	1	16	yes	—
349	M₁₆	C₂⁴×C₁₁	1	8	yes	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	8	no	—
352	C₂×C₈	—	2	32	no	—
353	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
354	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
355	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
356	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
357	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
358	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	C₂⁴×C₁₁	1	2	yes	—
363	C₄²	C₂⁴×C₁₁	1	2	yes	—
364	C₁₁	C₂×#2956	1	1	yes	characteristic, direct product factor, Sylow
365	C₂³	—	2	4	no	—
366	C₂³	—	2	8	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	8	4	no	—
369	C₂³	C₄×D₄×C₁₁	1	2	yes	—
370	C₂³	C₄×D₄×C₁₁	1	2	yes	—
371	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
372	C₂³	C₂×C₁₁×#41	1	2	yes	—
373	Q₈	—	2	8	no	—
374	Q₈	—	2	4	no	—
375	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
376	D₄	—	2	16	no	—
377	D₄	—	2	8	no	—
378	D₄	—	2	8	no	—
379	D₄	—	2	8	no	—
380	D₄	—	2	4	no	—
381	D₄	C₂³×C₄×C₁₁	1	8	yes	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	16	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	8	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
393	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
394	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
395	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
397	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
398	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
399	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
400	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
402	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
403	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
404	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
405	C₈	—	2	8	no	—
406	C₈	C₂³×C₄×C₁₁	1	8	yes	—
407	C₈	C₂²×D₄×C₁₁	1	8	yes	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	8	no	—
414	C₂²	—	8	8	no	—
415	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
416	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
417	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
418	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
419	C₄	—	2	4	no	—
420	C₄	—	2	8	no	—
421	C₄	—	4	2	no	—
422	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
423	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
424	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
425	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
426	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	1	no	—
430	C₂	—	4	8	no	—
431	C₂	C₁₁×#2956	1	2	yes	direct product factor
432	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×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×C₄×C₁₁ ◁ C₂²×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#568	C₂	semidirect
3. C₁₁×#2956	C₂	direct (N × H)
4. C₂×C₁₁×#444	C₂	semidirect
5. C₂×C₁₁×#443	C₂	semidirect
6. C₂×C₁₁×#430	C₂	semidirect
7. C₂²×C₁₁×#104	C₂	semidirect
8. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
10. C₁₁×#575	C₄	semidirect
12. C₂×C₁₁×#137	C₄	semidirect
13. C₂×C₁₁×AGL(1,ℤ/8)	C₄	semidirect
16. C₁₁×#568	C₂²	semidirect
18. C₂×C₁₁×#131	C₂²	semidirect
24. C₁₁×#444	C₂²	semidirect
25. C₁₁×#443	C₂²	semidirect
26. C₁₁×#430	C₂²	semidirect
27. C₂×C₁₁×#108	C₂²	semidirect
28. C₂×C₁₁×#104	C₂²	semidirect
29. C₂×C₁₁×#104	C₂²	semidirect
30. C₂×C₁₁×#104	C₂²	semidirect
31. C₄×C₁₁×M₁₆	C₂²	semidirect
32. C₂×C₁₁×#97	C₂²	semidirect
33. C₂×C₄×C₈×C₁₁	C₂²	semidirect
48. C₁₁×#137	C₂×C₄	semidirect
49. C₁₁×AGL(1,ℤ/8)	C₂×C₄	semidirect
50. C₁₁×#135	C₂×C₄	semidirect
52. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
53. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
54. C₂×C₁₁×D₈	C₂×C₄	semidirect
57. C₁₁×#131	C₂³	semidirect
79. C₁₁×#108	C₂³	semidirect
80. C₁₁×#104	C₂³	semidirect
81. C₁₁×#104	C₂³	semidirect
82. C₁₁×#97	C₂³	semidirect
83. C₄×C₈×C₁₁	C₂³	semidirect
84. C₂×#2956	C₁₁	direct (N × H)
126. C₁₁×Q₁₆	C₂²×C₄	semidirect
127. C₁₁×SD₁₆	C₂²×C₄	semidirect
128. C₁₁×D₈	C₂²×C₄	semidirect
150. C₂×#568	C₂×C₁₁	semidirect
151. #2956	C₂×C₁₁	direct (N × H)
152. C₂×#444	C₂×C₁₁	semidirect
153. C₂×#443	C₂×C₁₁	semidirect
154. C₂×#430	C₂×C₁₁	semidirect
155. C₂²×#104	C₂×C₁₁	semidirect
156. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
201. #575	C₄×C₁₁	semidirect
203. C₂×#137	C₄×C₁₁	semidirect
204. C₂×AGL(1,ℤ/8)	C₄×C₁₁	semidirect
207. #568	C₂²×C₁₁	semidirect
209. C₂×#131	C₂²×C₁₁	semidirect
215. #444	C₂²×C₁₁	semidirect
216. #443	C₂²×C₁₁	semidirect
217. #430	C₂²×C₁₁	semidirect
218. C₂×#108	C₂²×C₁₁	semidirect
219. C₂×#104	C₂²×C₁₁	semidirect
220. C₂×#104	C₂²×C₁₁	semidirect
221. C₂×#104	C₂²×C₁₁	semidirect
222. C₄×M₁₆	C₂²×C₁₁	semidirect
223. C₂×#97	C₂²×C₁₁	semidirect
224. C₂×C₄×C₈	C₂²×C₁₁	semidirect
258. #137	C₂×C₄×C₁₁	semidirect
259. AGL(1,ℤ/8)	C₂×C₄×C₁₁	semidirect
260. #135	C₂×C₄×C₁₁	semidirect
262. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
263. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
264. C₂×D₈	C₂×C₄×C₁₁	semidirect
267. #131	C₂³×C₁₁	semidirect
289. #108	C₂³×C₁₁	semidirect
290. #104	C₂³×C₁₁	semidirect
291. #104	C₂³×C₁₁	semidirect
292. #97	C₂³×C₁₁	semidirect
293. C₄×C₈	C₂³×C₁₁	semidirect
298. C₂×C₁₁	#2956	direct (N × H)
341. Q₁₆	C₂²×C₄×C₁₁	semidirect
342. SD₁₆	C₂²×C₄×C₁₁	semidirect
343. D₈	C₂²×C₄×C₁₁	semidirect
364. C₁₁	C₂×#2956	direct (N × H)
431. C₂	C₁₁×#2956	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
C₂×C₁₁×#568	2
C₁₁×#2956	2
C₂×C₁₁×#444	2
C₂×C₁₁×#443	2
C₂×C₁₁×#430	2
C₂²×C₁₁×#104	2
C₂×C₄×C₁₁×M₁₆	2
C₂×#2956	11

Subgroups — C2×C11×#2956 #14637373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2956 #14637373