Subgroups — C₂×C₁₁×#2357 #14611313

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2357	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#390	C₂	1	2	yes	maximal
4	C₂×C₁₁×#388	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#381	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₁×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₁×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₁	C₄	1	16	yes	complemented
13	C₂×C₄×D₄×C₁₁	C₂²	1	8	yes	—
14	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
18	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
19	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₁	C₂²	1	4	yes	—
22	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#390	C₂²	1	16	yes	—
24	C₁₁×#388	C₂²	1	32	yes	complemented
25	C₁₁×#382	C₂²	1	8	yes	complemented
26	C₁₁×#381	C₂²	1	16	yes	complemented
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	8	yes	complemented
28	C₄×C₁₁×C₄⋊C₄	C₂²	1	16	yes	complemented
29	C₄×C₁₁×C₂²⋊C₄	C₂²	1	16	yes	complemented
30	C₂×C₁₁×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#95	C₂²	1	2	yes	—
32	C₂×C₁₁×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×#95	C₂²	1	4	yes	—
34	C₂×C₁₁×#95	C₂²	1	2	yes	—
35	C₂⁵×C₁₁	C₂³	1	2	yes	—
36	C₂²×D₄×C₁₁	—	2	4	no	—
37	C₂²×D₄×C₁₁	—	2	4	no	—
38	C₂²×D₄×C₁₁	C₂×C₄	1	8	yes	—
39	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₁	—	4	8	no	—
41	C₂³×C₄×C₁₁	C₂×C₄	1	16	yes	—
42	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₁	C₂³	1	8	yes	—
49	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
50	C₄×D₄×C₁₁	C₂×C₄	1	64	yes	complemented
51	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
52	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
53	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	—
54	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
55	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
56	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
57	C₂×C₁₁×C₂²⋊C₄	—	2	16	no	—
58	C₂×C₁₁×C₂²⋊C₄	—	4	8	no	—
59	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	16	yes	—
60	C₂×C₁₁×C₂²⋊C₄	C₂³	1	16	yes	—
61	C₂×C₁₁×C₂²⋊C₄	C₂³	1	16	yes	—
62	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
63	C₂×C₄²×C₁₁	—	2	8	no	—
64	C₂×C₄²×C₁₁	—	4	8	no	—
65	C₂×C₄²×C₁₁	C₂×C₄	1	8	yes	—
66	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
67	C₂×C₄²×C₁₁	C₂³	1	16	yes	—
68	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
69	C₁₁×#95	C₂³	1	4	yes	—
70	C₁₁×#95	C₂³	1	8	yes	—
71	C₁₁×#95	C₂³	1	4	yes	—
72	C₁₁×#95	C₂³	1	16	yes	—
73	C₁₁×#95	C₂³	1	8	yes	—
74	C₂×#2357	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₁	—	2	8	no	—
76	C₂⁴×C₁₁	—	2	4	no	—
77	C₂⁴×C₁₁	—	2	4	no	—
78	C₂⁴×C₁₁	—	2	8	no	—
79	C₂⁴×C₁₁	C₂²×C₄	1	8	yes	—
80	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
81	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
82	C₂×D₄×C₁₁	—	2	32	no	—
83	C₂×D₄×C₁₁	—	2	8	no	—
84	C₂×D₄×C₁₁	—	2	8	no	—
85	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
86	C₂²×C₄×C₁₁	—	2	4	no	—
87	C₂²×C₄×C₁₁	—	2	4	no	—
88	C₂²×C₄×C₁₁	—	2	4	no	—
89	C₂²×C₄×C₁₁	—	2	8	no	—
90	C₂²×C₄×C₁₁	—	2	4	no	—
91	C₂²×C₄×C₁₁	—	2	4	no	—
92	C₂²×C₄×C₁₁	—	2	8	no	—
93	C₂²×C₄×C₁₁	—	2	4	no	—
94	C₂²×C₄×C₁₁	—	2	8	no	—
95	C₂²×C₄×C₁₁	—	2	8	no	—
96	C₂²×C₄×C₁₁	—	2	4	no	—
97	C₂²×C₄×C₁₁	—	4	32	no	—
98	C₂²×C₄×C₁₁	—	4	16	no	—
99	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
102	C₂²×C₄×C₁₁	C₂²×C₄	1	32	yes	—
103	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₁₁	#41	1	8	yes	—
105	C₂²×C₄×C₁₁	#41	1	4	yes	—
106	C₂²×C₄×C₁₁	#41	1	4	yes	—
107	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
110	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
114	C₁₁×C₄⋊C₄	—	2	16	no	—
115	C₁₁×C₄⋊C₄	—	2	16	no	—
116	C₁₁×C₄⋊C₄	C₂²×C₄	1	16	yes	—
117	C₁₁×C₂²⋊C₄	—	2	32	no	—
118	C₁₁×C₂²⋊C₄	—	4	16	no	—
119	C₁₁×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
120	C₄²×C₁₁	—	2	16	no	—
121	C₄²×C₁₁	—	4	16	no	—
122	C₄²×C₁₁	C₂²×C₄	1	16	yes	—
123	C₂²×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic
124	#2357	C₂×C₁₁	1	16	yes	direct product factor
125	C₂×#390	C₂×C₁₁	1	2	yes	—
126	C₂×#388	C₂×C₁₁	1	4	yes	complemented
127	C₂×#382	C₂×C₁₁	1	1	yes	characteristic, complemented
128	C₂×#381	C₂×C₁₁	1	2	yes	complemented
129	C₂×C₄×C₄⋊C₄	C₂×C₁₁	1	2	yes	complemented
130	C₂×C₄×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
131	C₂×C₄×C₂²⋊C₄	C₂×C₁₁	1	2	yes	complemented
132	C₂³×C₁₁	—	2	16	no	—
133	C₂³×C₁₁	—	2	16	no	—
134	C₂³×C₁₁	—	2	16	no	—
135	C₂³×C₁₁	—	2	8	no	—
136	C₂³×C₁₁	—	2	4	no	—
137	C₂³×C₁₁	—	2	4	no	—
138	C₂³×C₁₁	—	2	8	no	—
139	C₂³×C₁₁	—	4	16	no	—
140	C₂³×C₁₁	—	4	16	no	—
141	C₂³×C₁₁	C₂³×C₄	1	8	yes	—
142	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
143	C₂³×C₁₁	C₂×#41	1	2	yes	—
144	C₂³×C₁₁	C₂×#41	1	2	yes	—
145	C₂³×C₁₁	C₂×#41	1	4	yes	—
146	C₂³×C₁₁	H(5,𝔽₂)	1	4	yes	—
147	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
148	D₄×C₁₁	—	2	32	no	—
149	C₂×C₄×C₁₁	—	2	8	no	—
150	C₂×C₄×C₁₁	—	2	8	no	—
151	C₂×C₄×C₁₁	—	2	16	no	—
152	C₂×C₄×C₁₁	—	2	16	no	—
153	C₂×C₄×C₁₁	—	2	4	no	—
154	C₂×C₄×C₁₁	—	2	4	no	—
155	C₂×C₄×C₁₁	—	2	4	no	—
156	C₂×C₄×C₁₁	—	2	8	no	—
157	C₂×C₄×C₁₁	—	2	4	no	—
158	C₂×C₄×C₁₁	—	2	4	no	—
159	C₂×C₄×C₁₁	—	2	8	no	—
160	C₂×C₄×C₁₁	—	2	4	no	—
161	C₂×C₄×C₁₁	—	2	8	no	—
162	C₂×C₄×C₁₁	—	2	8	no	—
163	C₂×C₄×C₁₁	—	2	4	no	—
164	C₂×C₄×C₁₁	—	4	32	no	—
165	C₂×C₄×C₁₁	—	4	8	no	—
166	C₂×C₄×C₁₁	—	4	16	no	—
167	C₂×C₄×C₁₁	#117	1	16	yes	—
168	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
169	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
170	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
171	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
172	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
173	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
174	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
175	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
176	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	—
177	C₂×C₄×D₄	C₄×C₁₁	1	16	yes	complemented
178	C₂×C₄×D₄	C₂²×C₁₁	1	8	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
181	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
182	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
184	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
185	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
186	C₂²×C₄²	C₂²×C₁₁	1	4	yes	—
187	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
188	#390	C₂²×C₁₁	1	16	yes	—
189	#388	C₂²×C₁₁	1	32	yes	complemented
190	#382	C₂²×C₁₁	1	8	yes	complemented
191	#381	C₂²×C₁₁	1	16	yes	complemented
192	C₄×C₄⋊C₄	C₂²×C₁₁	1	8	yes	complemented
193	C₄×C₄⋊C₄	C₂²×C₁₁	1	16	yes	complemented
194	C₄×C₂²⋊C₄	C₂²×C₁₁	1	16	yes	complemented
195	C₂×#95	C₂²×C₁₁	1	1	yes	characteristic
196	C₂×#95	C₂²×C₁₁	1	2	yes	—
197	C₂×#95	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×#95	C₂²×C₁₁	1	4	yes	—
199	C₂×#95	C₂²×C₁₁	1	2	yes	—
200	C₂²×C₁₁	—	2	8	no	—
201	C₂²×C₁₁	—	2	8	no	—
202	C₂²×C₁₁	—	2	8	no	—
203	C₂²×C₁₁	—	4	32	no	—
204	C₂²×C₁₁	—	4	8	no	—
205	C₂²×C₁₁	—	4	8	no	—
206	C₂²×C₁₁	C₂×#117	1	4	yes	—
207	C₂²×C₁₁	C₄×#41	1	4	yes	—
208	C₂²×C₁₁	#518	1	4	yes	—
209	C₂²×C₁₁	#553	1	8	yes	—
210	C₂²×C₁₁	#559	1	8	yes	—
211	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
212	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
213	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
214	C₂²×C₁₁	C₂²×#41	1	2	yes	—
215	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
216	C₄×C₁₁	—	2	4	no	—
217	C₄×C₁₁	—	2	4	no	—
218	C₄×C₁₁	—	2	8	no	—
219	C₄×C₁₁	—	2	8	no	—
220	C₄×C₁₁	—	4	4	no	—
221	C₄×C₁₁	—	4	8	no	—
222	C₄×C₁₁	C₂×#117	1	8	yes	—
223	C₂⁵	C₂³×C₁₁	1	2	yes	—
224	C₂²×D₄	—	2	4	no	—
225	C₂²×D₄	—	2	4	no	—
226	C₂²×D₄	C₂×C₄×C₁₁	1	8	yes	—
227	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
228	C₂³×C₄	—	4	8	no	—
229	C₂³×C₄	C₂×C₄×C₁₁	1	16	yes	—
230	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
231	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
232	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
233	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
234	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
236	C₂³×C₄	C₂³×C₁₁	1	8	yes	—
237	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
238	C₄×D₄	C₂×C₄×C₁₁	1	64	yes	complemented
239	C₂×C₄⋊C₄	—	2	8	no	—
240	C₂×C₄⋊C₄	—	2	8	no	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
244	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
245	C₂×C₂²⋊C₄	—	2	16	no	—
246	C₂×C₂²⋊C₄	—	4	8	no	—
247	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	16	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₁₁	1	16	yes	—
249	C₂×C₂²⋊C₄	C₂³×C₁₁	1	16	yes	—
250	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
251	C₂×C₄²	—	2	8	no	—
252	C₂×C₄²	—	4	8	no	—
253	C₂×C₄²	C₂×C₄×C₁₁	1	8	yes	—
254	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
255	C₂×C₄²	C₂³×C₁₁	1	16	yes	—
256	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
257	#95	C₂³×C₁₁	1	4	yes	—
258	#95	C₂³×C₁₁	1	8	yes	—
259	#95	C₂³×C₁₁	1	4	yes	—
260	#95	C₂³×C₁₁	1	16	yes	—
261	#95	C₂³×C₁₁	1	8	yes	—
262	C₂×C₁₁	—	4	8	no	—
263	C₂×C₁₁	#2357	1	8	yes	direct product factor
264	C₂×C₁₁	C₂²×#117	1	1	yes	characteristic
265	C₂×C₁₁	C₂×C₄×#41	1	1	yes	characteristic
266	C₂×C₁₁	C₂×#518	1	1	yes	characteristic
267	C₂×C₁₁	C₂×#553	1	2	yes	—
268	C₂×C₁₁	C₂×#559	1	2	yes	—
269	C₂⁴	—	2	8	no	—
270	C₂⁴	—	2	4	no	—
271	C₂⁴	—	2	4	no	—
272	C₂⁴	—	2	8	no	—
273	C₂⁴	C₂²×C₄×C₁₁	1	8	yes	—
274	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
275	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
276	C₂×D₄	—	2	32	no	—
277	C₂×D₄	—	2	8	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	8	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	32	no	—
292	C₂²×C₄	—	4	16	no	—
293	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
294	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
296	C₂²×C₄	C₂²×C₄×C₁₁	1	32	yes	—
297	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
298	C₂²×C₄	C₁₁×#41	1	8	yes	—
299	C₂²×C₄	C₁₁×#41	1	4	yes	—
300	C₂²×C₄	C₁₁×#41	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
302	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
303	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
305	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
308	C₄⋊C₄	—	2	16	no	—
309	C₄⋊C₄	—	2	16	no	—
310	C₄⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
311	C₂²⋊C₄	—	2	32	no	—
312	C₂²⋊C₄	—	4	16	no	—
313	C₂²⋊C₄	C₂²×C₄×C₁₁	1	32	yes	—
314	C₄²	—	2	16	no	—
315	C₄²	—	4	16	no	—
316	C₄²	C₂²×C₄×C₁₁	1	16	yes	—
317	C₁₁	C₂×#2357	1	1	yes	characteristic, direct product factor, Sylow
318	C₂³	—	2	16	no	—
319	C₂³	—	2	16	no	—
320	C₂³	—	2	16	no	—
321	C₂³	—	2	8	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	8	no	—
325	C₂³	—	4	16	no	—
326	C₂³	—	4	16	no	—
327	C₂³	C₂³×C₄×C₁₁	1	8	yes	—
328	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
329	C₂³	C₂×C₁₁×#41	1	2	yes	—
330	C₂³	C₂×C₁₁×#41	1	2	yes	—
331	C₂³	C₂×C₁₁×#41	1	4	yes	—
332	C₂³	C₁₁×H(5,𝔽₂)	1	4	yes	—
333	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
334	D₄	—	2	32	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	16	no	—
338	C₂×C₄	—	2	16	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	4	32	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	—	4	16	no	—
353	C₂×C₄	C₁₁×#117	1	16	yes	—
354	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
355	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
356	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
357	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
358	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
359	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
360	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
361	C₂²	—	2	8	no	—
362	C₂²	—	2	8	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	4	8	no	—
365	C₂²	—	4	8	no	—
366	C₂²	—	4	32	no	—
367	C₂²	C₂×C₁₁×#117	1	4	yes	—
368	C₂²	C₄×C₁₁×#41	1	4	yes	—
369	C₂²	C₁₁×#518	1	4	yes	—
370	C₂²	C₁₁×#553	1	8	yes	—
371	C₂²	C₁₁×#559	1	8	yes	—
372	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
373	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
374	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
375	C₂²	C₂²×C₁₁×#41	1	2	yes	—
376	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
377	C₄	—	2	4	no	—
378	C₄	—	2	4	no	—
379	C₄	—	2	8	no	—
380	C₄	—	2	8	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	8	no	—
383	C₄	C₂×C₁₁×#117	1	8	yes	—
384	C₂	—	4	8	no	—
385	C₂	C₁₁×#2357	1	8	yes	direct product factor
386	C₂	C₂²×C₁₁×#117	1	1	yes	characteristic
387	C₂	C₂×C₄×C₁₁×#41	1	1	yes	characteristic
388	C₂	C₂×C₁₁×#518	1	1	yes	characteristic
389	C₂	C₂×C₁₁×#553	1	2	yes	—
390	C₂	C₂×C₁₁×#559	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2357	C₂	direct (N × H)
4. C₂×C₁₁×#388	C₂	semidirect
5. C₂×C₁₁×#382	C₂	semidirect
6. C₂×C₁₁×#381	C₂	semidirect
7. C₂×C₄×C₁₁×C₄⋊C₄	C₂	semidirect
8. C₂×C₄×C₁₁×C₄⋊C₄	C₂	semidirect
9. C₂×C₄×C₁₁×C₂²⋊C₄	C₂	semidirect
12. C₂×C₄×D₄×C₁₁	C₄	semidirect
24. C₁₁×#388	C₂²	semidirect
25. C₁₁×#382	C₂²	semidirect
26. C₁₁×#381	C₂²	semidirect
27. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
28. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
29. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
50. C₄×D₄×C₁₁	C₂×C₄	semidirect
74. C₂×#2357	C₁₁	direct (N × H)
124. #2357	C₂×C₁₁	direct (N × H)
126. C₂×#388	C₂×C₁₁	semidirect
127. C₂×#382	C₂×C₁₁	semidirect
128. C₂×#381	C₂×C₁₁	semidirect
129. C₂×C₄×C₄⋊C₄	C₂×C₁₁	semidirect
130. C₂×C₄×C₄⋊C₄	C₂×C₁₁	semidirect
131. C₂×C₄×C₂²⋊C₄	C₂×C₁₁	semidirect
177. C₂×C₄×D₄	C₄×C₁₁	semidirect
189. #388	C₂²×C₁₁	semidirect
190. #382	C₂²×C₁₁	semidirect
191. #381	C₂²×C₁₁	semidirect
192. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
193. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
194. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
238. C₄×D₄	C₂×C₄×C₁₁	semidirect
263. C₂×C₁₁	#2357	direct (N × H)
317. C₁₁	C₂×#2357	direct (N × H)
385. C₂	C₁₁×#2357	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×C₄×D₄×C₁₁	2
C₁₁×#2357	2
C₂×C₁₁×#390	2
C₂×C₁₁×#388	2
C₂×C₁₁×#382	2
C₂×C₁₁×#381	2
C₂×C₄×C₁₁×C₄⋊C₄	2
C₂×C₄×C₁₁×C₂²⋊C₄	2
C₂×#2357	11

Subgroups — C2×C11×#2357 #14611313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2357 #14611313