Subgroups — C₂²×C₁₁×#435 #14637324

Order 2816.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#435	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₁	C₄	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂²×C₁₁×M₁₆	—	2	8	no	—
13	C₂²×C₁₁×M₁₆	C₂²	1	12	yes	complemented
14	C₂³×C₈×C₁₁	—	2	8	no	—
15	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₁	C₂²	1	12	yes	complemented
20	C₂×C₄×D₄×C₁₁	C₄	1	12	yes	—
21	C₂×C₄×D₄×C₁₁	C₂²	1	12	yes	—
22	C₂²×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₂²×C₁₁×C₂²⋊C₄	C₄	1	1	yes	characteristic
24	C₂²×C₁₁×C₂²⋊C₄	C₄	1	1	yes	characteristic
25	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
26	C₁₁×#435	C₂²	1	64	yes	direct product factor
27	C₂×C₁₁×C₄⋊C₈	C₂²	1	12	yes	complemented
28	C₂×C₁₁×C₂²⋊C₈	C₂²	1	12	yes	complemented
29	C₂×C₁₁×C₂²⋊C₈	C₂²	1	12	yes	complemented
30	C₂×C₁₁×#97	C₂²	1	12	yes	complemented
31	C₂⁵×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂⁵×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₁	—	2	8	no	—
34	C₂²×D₄×C₁₁	C₂×C₄	1	12	yes	—
35	C₂³×C₄×C₁₁	—	2	4	no	—
36	C₂³×C₄×C₁₁	—	2	4	no	—
37	C₂³×C₄×C₁₁	—	2	4	no	—
38	C₂³×C₄×C₁₁	—	2	4	no	—
39	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₁	C₂×C₄	1	6	yes	—
44	C₂³×C₄×C₁₁	C₂×C₄	1	6	yes	—
45	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
46	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
47	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×C₁₁×M₁₆	—	2	48	no	—
49	C₂×C₁₁×M₁₆	C₂³	1	16	yes	complemented
50	C₂²×C₈×C₁₁	—	2	4	no	—
51	C₂²×C₈×C₁₁	—	2	4	no	—
52	C₂²×C₈×C₁₁	—	2	4	no	—
53	C₂²×C₈×C₁₁	—	2	48	no	—
54	C₂²×C₈×C₁₁	D₄	1	8	yes	complemented
55	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
56	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
57	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
58	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
59	C₂²×C₈×C₁₁	C₂³	1	16	yes	complemented
60	C₄×D₄×C₁₁	C₂×C₄	1	48	yes	—
61	C₄×D₄×C₁₁	C₂³	1	16	yes	—
62	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	12	yes	—
63	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	12	yes	—
64	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	12	yes	—
65	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
66	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
67	C₁₁×C₄⋊C₈	C₂³	1	16	yes	complemented
68	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
69	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
70	C₁₁×#97	C₂³	1	16	yes	complemented
71	C₂²×#435	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₁	—	2	4	no	—
73	C₂⁴×C₁₁	—	2	4	no	—
74	C₂⁴×C₁₁	—	2	4	no	—
75	C₂⁴×C₁₁	—	2	4	no	—
76	C₂⁴×C₁₁	—	2	4	no	—
77	C₂⁴×C₁₁	M₁₆	1	8	yes	complemented
78	C₂⁴×C₁₁	C₂²×C₄	1	6	yes	—
79	C₂⁴×C₁₁	C₂²×C₄	1	6	yes	—
80	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₂×D₄×C₁₁	—	2	48	no	—
82	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
83	C₂²×C₄×C₁₁	—	2	4	no	—
84	C₂²×C₄×C₁₁	—	2	4	no	—
85	C₂²×C₄×C₁₁	—	2	4	no	—
86	C₂²×C₄×C₁₁	—	2	4	no	—
87	C₂²×C₄×C₁₁	—	2	24	no	—
88	C₂²×C₄×C₁₁	—	2	24	no	—
89	C₂²×C₄×C₁₁	—	2	12	no	—
90	C₂²×C₄×C₁₁	—	2	12	no	—
91	C₂²×C₄×C₁₁	—	2	12	no	—
92	C₂²×C₄×C₁₁	—	2	12	no	—
93	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
95	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
96	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
98	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
100	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₁	#41	1	4	yes	—
102	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
105	C₁₁×M₁₆	—	2	32	no	—
106	C₂×C₈×C₁₁	—	2	32	no	—
107	C₂×C₈×C₁₁	—	2	12	no	—
108	C₂×C₈×C₁₁	—	2	12	no	—
109	C₂×C₈×C₁₁	—	2	12	no	—
110	C₂×C₈×C₁₁	C₂×D₄	1	24	yes	complemented
111	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
112	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
113	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
114	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
115	C₁₁×C₄⋊C₄	C₂²×C₄	1	16	yes	—
116	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
117	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
118	C₄²×C₁₁	C₂²×C₄	1	12	yes	—
119	C₄²×C₁₁	C₂⁴	1	4	yes	—
120	C₂³×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
121	C₂⁴×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
122	C₂²×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic
123	C₂×#435	C₂×C₁₁	1	24	yes	direct product factor
124	C₂²×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
125	C₂²×C₂²⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
126	C₂²×C₂²⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
127	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic, complemented
128	C₂³×C₁₁	—	2	12	no	—
129	C₂³×C₁₁	—	2	12	no	—
130	C₂³×C₁₁	—	2	32	no	—
131	C₂³×C₁₁	—	2	12	no	—
132	C₂³×C₁₁	—	2	12	no	—
133	C₂³×C₁₁	—	2	12	no	—
134	C₂³×C₁₁	—	4	16	no	—
135	C₂³×C₁₁	C₄×D₄	1	4	yes	—
136	C₂³×C₁₁	C₂×M₁₆	1	4	yes	—
137	C₂³×C₁₁	C₂×M₁₆	1	24	yes	complemented
138	C₂³×C₁₁	#131	1	4	yes	—
139	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
140	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
141	C₂³×C₁₁	C₂³×C₄	1	3	yes	—
142	D₄×C₁₁	—	2	32	no	—
143	C₂×C₄×C₁₁	—	2	12	no	—
144	C₂×C₄×C₁₁	—	2	12	no	—
145	C₂×C₄×C₁₁	—	2	12	no	—
146	C₂×C₄×C₁₁	—	2	12	no	—
147	C₂×C₄×C₁₁	—	2	24	no	—
148	C₂×C₄×C₁₁	—	2	24	no	—
149	C₂×C₄×C₁₁	—	2	4	no	—
150	C₂×C₄×C₁₁	—	2	4	no	—
151	C₂×C₄×C₁₁	—	2	4	no	—
152	C₂×C₄×C₁₁	—	2	4	no	—
153	C₂×C₄×C₁₁	C₄×D₄	1	12	yes	—
154	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
155	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
156	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
157	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
158	C₂×C₄×C₁₁	C₂³×C₄	1	3	yes	—
159	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
160	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
161	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
162	C₈×C₁₁	—	2	4	no	—
163	C₈×C₁₁	—	2	4	no	—
164	C₈×C₁₁	—	2	4	no	—
165	C₈×C₁₁	C₂²×D₄	1	8	yes	complemented
166	C₂³×D₄	C₄×C₁₁	1	1	yes	characteristic
167	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
168	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
169	C₂²×M₁₆	—	2	8	no	—
170	C₂²×M₁₆	C₂²×C₁₁	1	12	yes	complemented
171	C₂³×C₈	—	2	8	no	—
172	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
173	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
174	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
175	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
176	C₂³×C₈	C₂²×C₁₁	1	12	yes	complemented
177	C₂×C₄×D₄	C₄×C₁₁	1	12	yes	—
178	C₂×C₄×D₄	C₂²×C₁₁	1	12	yes	—
179	C₂²×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
180	C₂²×C₂²⋊C₄	C₄×C₁₁	1	1	yes	characteristic
181	C₂²×C₂²⋊C₄	C₄×C₁₁	1	1	yes	characteristic
182	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
183	#435	C₂²×C₁₁	1	64	yes	direct product factor
184	C₂×C₄⋊C₈	C₂²×C₁₁	1	12	yes	complemented
185	C₂×C₂²⋊C₈	C₂²×C₁₁	1	12	yes	complemented
186	C₂×C₂²⋊C₈	C₂²×C₁₁	1	12	yes	complemented
187	C₂×#97	C₂²×C₁₁	1	12	yes	complemented
188	C₂²×C₁₁	—	2	4	no	—
189	C₂²×C₁₁	—	2	48	no	—
190	C₂²×C₁₁	—	2	4	no	—
191	C₂²×C₁₁	—	2	4	no	—
192	C₂²×C₁₁	—	2	4	no	—
193	C₂²×C₁₁	—	2	4	no	—
194	C₂²×C₁₁	—	4	24	no	—
195	C₂²×C₁₁	#435	1	16	yes	direct product factor
196	C₂²×C₁₁	C₂×C₄×D₄	1	6	yes	—
197	C₂²×C₁₁	C₂²×M₁₆	1	6	yes	—
198	C₂²×C₁₁	C₂²×M₁₆	1	8	yes	complemented
199	C₂²×C₁₁	C₂×#131	1	6	yes	—
200	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
201	C₄×C₁₁	—	2	4	no	—
202	C₄×C₁₁	—	2	4	no	—
203	C₄×C₁₁	—	2	4	no	—
204	C₄×C₁₁	—	2	4	no	—
205	C₄×C₁₁	C₂×C₄×D₄	1	6	yes	—
206	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
207	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
208	C₂⁵	C₂×C₄×C₁₁	1	1	yes	characteristic
209	C₂⁵	C₂×C₄×C₁₁	1	1	yes	characteristic
210	C₂²×D₄	—	2	8	no	—
211	C₂²×D₄	C₂×C₄×C₁₁	1	12	yes	—
212	C₂³×C₄	—	2	4	no	—
213	C₂³×C₄	—	2	4	no	—
214	C₂³×C₄	—	2	4	no	—
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
217	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
220	C₂³×C₄	C₂×C₄×C₁₁	1	6	yes	—
221	C₂³×C₄	C₂×C₄×C₁₁	1	6	yes	—
222	C₂³×C₄	C₂³×C₁₁	1	6	yes	—
223	C₂³×C₄	C₂³×C₁₁	1	6	yes	—
224	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
225	C₂×M₁₆	—	2	48	no	—
226	C₂×M₁₆	C₂³×C₁₁	1	16	yes	complemented
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	—	2	48	no	—
231	C₂²×C₈	D₄×C₁₁	1	8	yes	complemented
232	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
233	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
234	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
235	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
236	C₂²×C₈	C₂³×C₁₁	1	16	yes	complemented
237	C₄×D₄	C₂×C₄×C₁₁	1	48	yes	—
238	C₄×D₄	C₂³×C₁₁	1	16	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	12	yes	—
240	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	12	yes	—
241	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	12	yes	—
242	C₂×C₄²	C₂×C₄×C₁₁	1	6	yes	—
243	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
244	C₄⋊C₈	C₂³×C₁₁	1	16	yes	complemented
245	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	complemented
246	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	complemented
247	#97	C₂³×C₁₁	1	16	yes	complemented
248	C₂×C₁₁	—	2	8	no	—
249	C₂×C₁₁	—	4	4	no	—
250	C₂×C₁₁	C₂×#435	1	12	yes	direct product factor
251	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
252	C₂×C₁₁	C₂³×M₁₆	1	1	yes	characteristic
253	C₂×C₁₁	C₂²×#131	1	1	yes	characteristic
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	C₁₁×M₁₆	1	8	yes	complemented
260	C₂⁴	C₂²×C₄×C₁₁	1	6	yes	—
261	C₂⁴	C₂²×C₄×C₁₁	1	6	yes	—
262	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
263	C₂×D₄	—	2	48	no	—
264	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	24	no	—
270	C₂²×C₄	—	2	24	no	—
271	C₂²×C₄	—	2	12	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	12	no	—
274	C₂²×C₄	—	2	12	no	—
275	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
276	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
278	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
279	C₂²×C₄	C₂²×C₄×C₁₁	1	12	yes	—
280	C₂²×C₄	C₂²×C₄×C₁₁	1	12	yes	—
281	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
282	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
283	C₂²×C₄	C₁₁×#41	1	4	yes	—
284	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
287	M₁₆	—	2	32	no	—
288	C₂×C₈	—	2	12	no	—
289	C₂×C₈	—	2	12	no	—
290	C₂×C₈	—	2	12	no	—
291	C₂×C₈	—	2	32	no	—
292	C₂×C₈	C₂×D₄×C₁₁	1	24	yes	complemented
293	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
294	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
295	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
296	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
297	C₄⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
298	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
299	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
300	C₄²	C₂²×C₄×C₁₁	1	12	yes	—
301	C₄²	C₂⁴×C₁₁	1	4	yes	—
302	C₁₁	C₂²×#435	1	1	yes	characteristic, direct product factor, Sylow
303	C₂³	—	2	12	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	32	no	—
306	C₂³	—	2	12	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	2	12	no	—
309	C₂³	—	4	16	no	—
310	C₂³	C₄×D₄×C₁₁	1	4	yes	—
311	C₂³	C₂×C₁₁×M₁₆	1	4	yes	—
312	C₂³	C₂×C₁₁×M₁₆	1	24	yes	complemented
313	C₂³	C₁₁×#131	1	4	yes	—
314	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
315	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
316	C₂³	C₂³×C₄×C₁₁	1	3	yes	—
317	D₄	—	2	32	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	24	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	C₄×D₄×C₁₁	1	12	yes	—
329	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
330	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
331	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
332	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
333	C₂×C₄	C₂³×C₄×C₁₁	1	3	yes	—
334	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
335	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
336	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₈	—	2	4	no	—
339	C₈	—	2	4	no	—
340	C₈	C₂²×D₄×C₁₁	1	8	yes	complemented
341	C₂²	—	2	4	no	—
342	C₂²	—	2	48	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	24	no	—
348	C₂²	C₁₁×#435	1	16	yes	direct product factor
349	C₂²	C₂×C₄×D₄×C₁₁	1	6	yes	—
350	C₂²	C₂²×C₁₁×M₁₆	1	6	yes	—
351	C₂²	C₂²×C₁₁×M₁₆	1	8	yes	complemented
352	C₂²	C₂×C₁₁×#131	1	6	yes	—
353	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	C₂×C₄×D₄×C₁₁	1	6	yes	—
359	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
360	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	4	4	no	—
363	C₂	C₂×C₁₁×#435	1	12	yes	direct product factor
364	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
365	C₂	C₂³×C₁₁×M₁₆	1	1	yes	characteristic
366	C₂	C₂²×C₁₁×#131	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₁×M₁₆	C₂	semidirect
2. C₂⁴×C₈×C₁₁	C₂	semidirect
4. C₂×C₁₁×#435	C₂	direct (N × H)
5. C₂²×C₁₁×C₄⋊C₈	C₂	semidirect
6. C₂²×C₁₁×C₂²⋊C₈	C₂	semidirect
7. C₂²×C₁₁×C₂²⋊C₈	C₂	semidirect
8. C₂²×C₁₁×#97	C₂	semidirect
13. C₂²×C₁₁×M₁₆	C₂²	semidirect
19. C₂³×C₈×C₁₁	C₂²	semidirect
26. C₁₁×#435	C₂²	direct (N × H)
27. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
28. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
29. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
30. C₂×C₁₁×#97	C₂²	semidirect
49. C₂×C₁₁×M₁₆	C₂³	semidirect
54. C₂²×C₈×C₁₁	D₄	semidirect
59. C₂²×C₈×C₁₁	C₂³	semidirect
67. C₁₁×C₄⋊C₈	C₂³	semidirect
68. C₁₁×C₂²⋊C₈	C₂³	semidirect
69. C₁₁×C₂²⋊C₈	C₂³	semidirect
70. C₁₁×#97	C₂³	semidirect
71. C₂²×#435	C₁₁	direct (N × H)
77. C₂⁴×C₁₁	M₁₆	semidirect
110. C₂×C₈×C₁₁	C₂×D₄	semidirect
120. C₂³×M₁₆	C₂×C₁₁	semidirect
121. C₂⁴×C₈	C₂×C₁₁	semidirect
123. C₂×#435	C₂×C₁₁	direct (N × H)
124. C₂²×C₄⋊C₈	C₂×C₁₁	semidirect
125. C₂²×C₂²⋊C₈	C₂×C₁₁	semidirect
126. C₂²×C₂²⋊C₈	C₂×C₁₁	semidirect
127. C₂²×#97	C₂×C₁₁	semidirect
137. C₂³×C₁₁	C₂×M₁₆	semidirect
165. C₈×C₁₁	C₂²×D₄	semidirect
170. C₂²×M₁₆	C₂²×C₁₁	semidirect
176. C₂³×C₈	C₂²×C₁₁	semidirect
183. #435	C₂²×C₁₁	direct (N × H)
184. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
185. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
186. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
187. C₂×#97	C₂²×C₁₁	semidirect
195. C₂²×C₁₁	#435	direct (N × H)
198. C₂²×C₁₁	C₂²×M₁₆	semidirect
226. C₂×M₁₆	C₂³×C₁₁	semidirect
231. C₂²×C₈	D₄×C₁₁	semidirect
236. C₂²×C₈	C₂³×C₁₁	semidirect
244. C₄⋊C₈	C₂³×C₁₁	semidirect
245. C₂²⋊C₈	C₂³×C₁₁	semidirect
246. C₂²⋊C₈	C₂³×C₁₁	semidirect
247. #97	C₂³×C₁₁	semidirect
250. C₂×C₁₁	C₂×#435	direct (N × H)
259. C₂⁴	C₁₁×M₁₆	semidirect
292. C₂×C₈	C₂×D₄×C₁₁	semidirect
302. C₁₁	C₂²×#435	direct (N × H)
312. C₂³	C₂×C₁₁×M₁₆	semidirect
340. C₈	C₂²×D₄×C₁₁	semidirect
348. C₂²	C₁₁×#435	direct (N × H)
351. C₂²	C₂²×C₁₁×M₁₆	semidirect
363. C₂	C₂×C₁₁×#435	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₁×M₁₆	2
C₂⁴×C₈×C₁₁	2
C₂²×C₄×D₄×C₁₁	2
C₂×C₁₁×#435	2
C₂²×C₁₁×C₄⋊C₈	2
C₂²×C₁₁×C₂²⋊C₈	2
C₂²×C₁₁×#97	2
C₂²×#435	11

Subgroups — C22×C11×#435 #14637324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#435 #14637324