Subgroups — C₂×C₁₁×#2952 #14637359

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#520	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2952	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#442	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#441	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₁₁×SD₁₆	C₂	1	4	yes	maximal, complemented
7	C₂²×C₁₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#417	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	C₂×C₁₁×#135	C₄	1	16	yes	complemented
12	C₂×C₁₁×#135	C₂²	1	8	yes	—
13	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#520	—	2	8	no	—
19	C₁₁×#520	C₂²	1	16	yes	complemented
20	C₂×C₄×Q₈×C₁₁	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₁	—	2	4	no	—
22	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
23	C₂×C₁₁×#117	—	2	2	no	—
24	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₁₁×C₄⋊C₄	—	2	2	no	—
26	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
27	C₁₁×#442	C₂²	1	16	yes	complemented
28	C₁₁×#441	C₂²	1	16	yes	complemented
29	C₄×C₁₁×SD₁₆	C₂²	1	32	yes	complemented
30	C₂×C₁₁×#106	C₂²	1	2	yes	—
31	C₂×C₁₁×#106	C₂²	1	2	yes	—
32	C₂×C₁₁×#106	C₂²	1	8	yes	complemented
33	C₁₁×#417	C₂²	1	16	yes	complemented
34	C₂×C₁₁×#103	C₂²	1	4	yes	—
35	C₂×C₁₁×#102	C₂²	1	4	yes	—
36	C₁₁×#405	C₂²	1	8	yes	complemented
37	C₂×C₁₁×#97	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
39	C₂×C₁₁×#41	—	2	4	no	—
40	C₂×C₁₁×#41	—	2	8	no	—
41	C₂×C₁₁×#41	C₂×C₄	1	16	yes	complemented
42	C₂×C₁₁×#41	C₂³	1	8	yes	—
43	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₁	—	2	2	no	—
45	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₁	—	2	2	no	—
47	C₂³×C₄×C₁₁	—	2	2	no	—
48	C₂³×C₄×C₁₁	—	2	4	no	—
49	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
50	C₁₁×#135	C₂×C₄	1	64	yes	complemented
51	C₂×C₁₁×Q₁₆	C₂×C₄	1	8	yes	complemented
52	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	16	yes	complemented
54	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
55	C₂×C₁₁×D₈	C₂×C₄	1	8	yes	complemented
56	C₂×C₁₁×D₈	C₂³	1	4	yes	—
57	C₂×C₁₁×M₁₆	—	2	4	no	—
58	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
59	C₂²×C₈×C₁₁	C₂×C₄	1	8	yes	complemented
60	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
64	C₄×Q₈×C₁₁	—	2	8	no	—
65	C₄×Q₈×C₁₁	C₂³	1	16	yes	—
66	C₄×D₄×C₁₁	—	2	32	no	—
67	C₄×D₄×C₁₁	—	2	8	no	—
68	C₄×D₄×C₁₁	C₂³	1	16	yes	—
69	C₁₁×#117	—	2	16	no	—
70	C₁₁×#117	D₄	1	4	yes	—
71	C₁₁×#117	C₂³	1	4	yes	—
72	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
73	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
74	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
75	C₂×C₁₁×C₄⋊C₄	—	2	16	no	—
76	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
77	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
80	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
81	C₂×C₄²×C₁₁	—	2	4	no	—
82	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
83	C₁₁×#106	C₂³	1	8	yes	—
84	C₁₁×#106	C₂³	1	8	yes	—
85	C₁₁×#103	C₂³	1	16	yes	—
86	C₁₁×#102	C₂³	1	16	yes	—
87	C₁₁×#97	C₂³	1	8	yes	—
88	C₄×C₈×C₁₁	C₂³	1	8	yes	—
89	C₂×#2952	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₁	—	2	2	no	—
91	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
92	C₁₁×#41	—	2	32	no	—
93	C₁₁×#41	—	2	16	no	—
94	C₁₁×#41	C₂²×C₄	1	32	yes	complemented
95	C₂×Q₈×C₁₁	—	2	2	no	—
96	C₂×Q₈×C₁₁	—	2	4	no	—
97	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
98	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
99	C₂×D₄×C₁₁	—	2	16	no	—
100	C₂×D₄×C₁₁	—	2	8	no	—
101	C₂×D₄×C₁₁	—	2	2	no	—
102	C₂×D₄×C₁₁	—	2	4	no	—
103	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
104	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₁₁	—	2	2	no	—
106	C₂²×C₄×C₁₁	—	2	16	no	—
107	C₂²×C₄×C₁₁	—	2	8	no	—
108	C₂²×C₄×C₁₁	—	2	4	no	—
109	C₂²×C₄×C₁₁	—	2	8	no	—
110	C₂²×C₄×C₁₁	—	2	16	no	—
111	C₂²×C₄×C₁₁	—	8	8	no	—
112	C₂²×C₄×C₁₁	—	8	4	no	—
113	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
114	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	#41	1	4	yes	—
118	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
120	C₁₁×Q₁₆	C₂²×C₄	1	16	yes	complemented
121	C₁₁×SD₁₆	C₂²×C₄	1	32	yes	complemented
122	C₁₁×D₈	C₂²×C₄	1	16	yes	complemented
123	C₁₁×M₁₆	—	2	8	no	—
124	C₂×C₈×C₁₁	—	2	4	no	—
125	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	16	yes	complemented
128	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
129	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
130	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
131	C₁₁×C₄⋊C₄	—	2	8	no	—
132	C₁₁×C₄⋊C₄	—	2	16	no	—
133	C₁₁×C₄⋊C₄	—	2	4	no	—
134	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
135	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
136	C₁₁×C₂²⋊C₄	—	2	16	no	—
137	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
138	C₄²×C₁₁	—	2	16	no	—
139	C₄²×C₁₁	C₂×D₄	1	4	yes	—
140	C₄²×C₁₁	C₂⁴	1	4	yes	—
141	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic
142	C₂×#520	C₂×C₁₁	1	2	yes	complemented
143	#2952	C₂×C₁₁	1	16	yes	direct product factor
144	C₂×#442	C₂×C₁₁	1	2	yes	complemented
145	C₂×#441	C₂×C₁₁	1	2	yes	complemented
146	C₂×C₄×SD₁₆	C₂×C₁₁	1	4	yes	complemented
147	C₂²×#106	C₂×C₁₁	1	1	yes	characteristic, complemented
148	C₂×#417	C₂×C₁₁	1	2	yes	complemented
149	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
150	C₂³×C₁₁	—	2	4	no	—
151	C₂³×C₁₁	—	2	8	no	—
152	C₂³×C₁₁	—	2	4	no	—
153	C₂³×C₁₁	—	4	4	no	—
154	C₂³×C₁₁	—	4	4	no	—
155	C₂³×C₁₁	C₄×D₄	1	4	yes	—
156	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
157	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₁₁	—	2	8	no	—
159	Q₈×C₁₁	—	2	4	no	—
160	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
161	D₄×C₁₁	—	2	32	no	—
162	D₄×C₁₁	—	2	8	no	—
163	D₄×C₁₁	—	2	4	no	—
164	D₄×C₁₁	C₂³×C₄	1	8	yes	—
165	C₂×C₄×C₁₁	—	2	8	no	—
166	C₂×C₄×C₁₁	—	2	8	no	—
167	C₂×C₄×C₁₁	—	2	4	no	—
168	C₂×C₄×C₁₁	—	2	32	no	—
169	C₂×C₄×C₁₁	—	2	8	no	—
170	C₂×C₄×C₁₁	—	4	8	no	—
171	C₂×C₄×C₁₁	—	8	16	no	—
172	C₂×C₄×C₁₁	—	8	8	no	—
173	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
174	C₂×C₄×C₁₁	C₄×D₄	1	8	yes	—
175	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
176	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
177	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
178	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
181	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
182	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
183	C₈×C₁₁	—	2	4	no	—
184	C₈×C₁₁	C₂³×C₄	1	4	yes	—
185	C₈×C₁₁	C₂³×C₄	1	4	yes	—
186	C₂²×#41	C₂²×C₁₁	1	2	yes	—
187	C₂×#135	C₄×C₁₁	1	16	yes	complemented
188	C₂×#135	C₂²×C₁₁	1	8	yes	—
189	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
190	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
191	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
192	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
194	#520	—	2	8	no	—
195	#520	C₂²×C₁₁	1	16	yes	complemented
196	C₂×C₄×Q₈	C₂²×C₁₁	1	4	yes	—
197	C₂×C₄×D₄	—	2	4	no	—
198	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
199	C₂×#117	—	2	2	no	—
200	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
201	C₂²×C₄⋊C₄	—	2	2	no	—
202	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
203	#442	C₂²×C₁₁	1	16	yes	complemented
204	#441	C₂²×C₁₁	1	16	yes	complemented
205	C₄×SD₁₆	C₂²×C₁₁	1	32	yes	complemented
206	C₂×#106	C₂²×C₁₁	1	2	yes	—
207	C₂×#106	C₂²×C₁₁	1	2	yes	—
208	C₂×#106	C₂²×C₁₁	1	8	yes	complemented
209	#417	C₂²×C₁₁	1	16	yes	complemented
210	C₂×#103	C₂²×C₁₁	1	4	yes	—
211	C₂×#102	C₂²×C₁₁	1	4	yes	—
212	#405	C₂²×C₁₁	1	8	yes	complemented
213	C₂×#97	C₂²×C₁₁	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
215	C₂²×C₁₁	—	2	8	no	—
216	C₂²×C₁₁	—	2	4	no	—
217	C₂²×C₁₁	—	2	8	no	—
218	C₂²×C₁₁	—	4	16	no	—
219	C₂²×C₁₁	—	4	4	no	—
220	C₂²×C₁₁	—	4	4	no	—
221	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
222	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
223	C₂²×C₁₁	#577	1	4	yes	—
224	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
225	C₄×C₁₁	—	2	8	no	—
226	C₄×C₁₁	—	2	8	no	—
227	C₄×C₁₁	—	4	8	no	—
228	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
229	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
230	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
231	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
232	C₂×#41	—	2	4	no	—
233	C₂×#41	—	2	8	no	—
234	C₂×#41	C₂×C₄×C₁₁	1	16	yes	complemented
235	C₂×#41	C₂³×C₁₁	1	8	yes	—
236	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
237	C₂²×D₄	—	2	2	no	—
238	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
239	C₂³×C₄	—	2	2	no	—
240	C₂³×C₄	—	2	2	no	—
241	C₂³×C₄	—	2	4	no	—
242	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
243	#135	C₂×C₄×C₁₁	1	64	yes	complemented
244	C₂×Q₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
245	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
246	C₂×SD₁₆	C₂×C₄×C₁₁	1	16	yes	complemented
247	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
248	C₂×D₈	C₂×C₄×C₁₁	1	8	yes	complemented
249	C₂×D₈	C₂³×C₁₁	1	4	yes	—
250	C₂×M₁₆	—	2	4	no	—
251	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
252	C₂²×C₈	C₂×C₄×C₁₁	1	8	yes	complemented
253	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
254	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
257	C₄×Q₈	—	2	8	no	—
258	C₄×Q₈	C₂³×C₁₁	1	16	yes	—
259	C₄×D₄	—	2	32	no	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	C₂³×C₁₁	1	16	yes	—
262	#117	—	2	16	no	—
263	#117	D₄×C₁₁	1	4	yes	—
264	#117	C₂³×C₁₁	1	4	yes	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	16	no	—
269	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
274	C₂×C₄²	—	2	4	no	—
275	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
276	#106	C₂³×C₁₁	1	8	yes	—
277	#106	C₂³×C₁₁	1	8	yes	—
278	#103	C₂³×C₁₁	1	16	yes	—
279	#102	C₂³×C₁₁	1	16	yes	—
280	#97	C₂³×C₁₁	1	8	yes	—
281	C₄×C₈	C₂³×C₁₁	1	8	yes	—
282	C₂×C₁₁	—	2	4	no	—
283	C₂×C₁₁	—	4	8	no	—
284	C₂×C₁₁	#2952	1	4	yes	direct product factor
285	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
286	C₂×C₁₁	C₂×#577	1	2	yes	—
287	C₂⁴	—	2	2	no	—
288	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
289	#41	—	2	32	no	—
290	#41	—	2	16	no	—
291	#41	C₂²×C₄×C₁₁	1	32	yes	complemented
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
295	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
296	C₂×D₄	—	2	16	no	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
301	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	16	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	16	no	—
308	C₂²×C₄	—	8	8	no	—
309	C₂²×C₄	—	8	4	no	—
310	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
311	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
314	C₂²×C₄	C₁₁×#41	1	4	yes	—
315	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
317	Q₁₆	C₂²×C₄×C₁₁	1	16	yes	complemented
318	SD₁₆	C₂²×C₄×C₁₁	1	32	yes	complemented
319	D₈	C₂²×C₄×C₁₁	1	16	yes	complemented
320	M₁₆	—	2	8	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
323	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
324	C₂×C₈	C₂²×C₄×C₁₁	1	16	yes	complemented
325	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
326	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
327	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	16	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
332	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
333	C₂²⋊C₄	—	2	16	no	—
334	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
335	C₄²	—	2	16	no	—
336	C₄²	C₂×D₄×C₁₁	1	4	yes	—
337	C₄²	C₂⁴×C₁₁	1	4	yes	—
338	C₁₁	C₂×#2952	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	2	4	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	C₄×D₄×C₁₁	1	4	yes	—
345	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
346	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
347	Q₈	—	2	8	no	—
348	Q₈	—	2	4	no	—
349	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
350	D₄	—	2	32	no	—
351	D₄	—	2	8	no	—
352	D₄	—	2	4	no	—
353	D₄	C₂³×C₄×C₁₁	1	8	yes	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	32	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	8	16	no	—
361	C₂×C₄	—	8	8	no	—
362	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
363	C₂×C₄	C₄×D₄×C₁₁	1	8	yes	—
364	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
365	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
366	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
367	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
369	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
370	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
371	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₈	C₂³×C₄×C₁₁	1	4	yes	—
374	C₈	C₂³×C₄×C₁₁	1	4	yes	—
375	C₂²	—	2	8	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	4	16	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
382	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
383	C₂²	C₁₁×#577	1	4	yes	—
384	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
385	C₄	—	2	8	no	—
386	C₄	—	2	8	no	—
387	C₄	—	4	8	no	—
388	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
389	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
390	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
391	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
392	C₂	—	2	4	no	—
393	C₂	—	4	8	no	—
394	C₂	C₁₁×#2952	1	4	yes	direct product factor
395	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
396	C₂	C₂×C₁₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂²×C₁₁×#135	C₂
LCS	G ▷ 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
2. C₂×C₁₁×#520	C₂	semidirect
3. C₁₁×#2952	C₂	direct (N × H)
4. C₂×C₁₁×#442	C₂	semidirect
5. C₂×C₁₁×#441	C₂	semidirect
6. C₂×C₄×C₁₁×SD₁₆	C₂	semidirect
7. C₂²×C₁₁×#106	C₂	semidirect
8. C₂×C₁₁×#417	C₂	semidirect
9. C₂×C₁₁×#405	C₂	semidirect
11. C₂×C₁₁×#135	C₄	semidirect
19. C₁₁×#520	C₂²	semidirect
27. C₁₁×#442	C₂²	semidirect
28. C₁₁×#441	C₂²	semidirect
29. C₄×C₁₁×SD₁₆	C₂²	semidirect
32. C₂×C₁₁×#106	C₂²	semidirect
33. C₁₁×#417	C₂²	semidirect
36. C₁₁×#405	C₂²	semidirect
41. C₂×C₁₁×#41	C₂×C₄	semidirect
50. C₁₁×#135	C₂×C₄	semidirect
51. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
53. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
55. C₂×C₁₁×D₈	C₂×C₄	semidirect
59. C₂²×C₈×C₁₁	C₂×C₄	semidirect
89. C₂×#2952	C₁₁	direct (N × H)
94. C₁₁×#41	C₂²×C₄	semidirect
120. C₁₁×Q₁₆	C₂²×C₄	semidirect
121. C₁₁×SD₁₆	C₂²×C₄	semidirect
122. C₁₁×D₈	C₂²×C₄	semidirect
127. C₂×C₈×C₁₁	C₂²×C₄	semidirect
142. C₂×#520	C₂×C₁₁	semidirect
143. #2952	C₂×C₁₁	direct (N × H)
144. C₂×#442	C₂×C₁₁	semidirect
145. C₂×#441	C₂×C₁₁	semidirect
146. C₂×C₄×SD₁₆	C₂×C₁₁	semidirect
147. C₂²×#106	C₂×C₁₁	semidirect
148. C₂×#417	C₂×C₁₁	semidirect
149. C₂×#405	C₂×C₁₁	semidirect
187. C₂×#135	C₄×C₁₁	semidirect
195. #520	C₂²×C₁₁	semidirect
203. #442	C₂²×C₁₁	semidirect
204. #441	C₂²×C₁₁	semidirect
205. C₄×SD₁₆	C₂²×C₁₁	semidirect
208. C₂×#106	C₂²×C₁₁	semidirect
209. #417	C₂²×C₁₁	semidirect
212. #405	C₂²×C₁₁	semidirect
234. C₂×#41	C₂×C₄×C₁₁	semidirect
243. #135	C₂×C₄×C₁₁	semidirect
244. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
246. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
248. C₂×D₈	C₂×C₄×C₁₁	semidirect
252. C₂²×C₈	C₂×C₄×C₁₁	semidirect
284. C₂×C₁₁	#2952	direct (N × H)
291. #41	C₂²×C₄×C₁₁	semidirect
317. Q₁₆	C₂²×C₄×C₁₁	semidirect
318. SD₁₆	C₂²×C₄×C₁₁	semidirect
319. D₈	C₂²×C₄×C₁₁	semidirect
324. C₂×C₈	C₂²×C₄×C₁₁	semidirect
338. C₁₁	C₂×#2952	direct (N × H)
394. C₂	C₁₁×#2952	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×#135	2
C₂×C₁₁×#520	2
C₁₁×#2952	2
C₂×C₁₁×#442	2
C₂×C₁₁×#441	2
C₂×C₄×C₁₁×SD₁₆	2
C₂²×C₁₁×#106	2
C₂×C₁₁×#417	2
C₂×C₁₁×#405	2
C₂×#2952	11

Subgroups — C2×C11×#2952 #14637359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2952 #14637359