Subgroups — C₂×C₁₁×#3152 #14637830

Order 2816.

3262 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#137	C₂	1	4	yes	maximal, complemented
2	C₂×C₁₁×#532	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#3152	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₁×#497	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#494	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#492	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	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×#137	—	2	32	no	—
12	C₂×C₁₁×#137	C₂²	1	32	yes	complemented
13	C₂²×C₁₁×Q₁₆	C₂²	1	8	yes	—
14	C₂²×C₁₁×SD₁₆	C₂²	1	8	yes	—
15	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
16	C₁₁×#532	—	2	4	no	—
17	C₁₁×#532	C₂²	1	8	yes	—
18	C₂×C₁₁×C₄⋊Q₈	—	2	2	no	—
19	C₂×C₁₁×C₄⋊Q₈	—	2	4	no	—
20	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊Q₈	C₂²	1	8	yes	complemented
24	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#124	C₂²	1	2	yes	—
26	C₂×C₁₁×#121	—	2	2	no	—
27	C₂×C₄×D₄×C₁₁	—	2	2	no	—
28	C₂²×C₁₁×C₄⋊C₄	—	2	2	no	—
29	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#497	C₂²	1	32	yes	complemented
31	C₁₁×#494	C₂²	1	16	yes	complemented
32	C₁₁×#492	C₂²	1	16	yes	complemented
33	C₄×C₁₁×M₁₆	C₂²	1	8	yes	complemented
34	C₂×C₁₁×#97	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
36	C₂×C₁₁×#41	—	2	4	no	—
37	C₂×C₁₁×#41	—	2	16	no	—
38	C₂×C₁₁×#41	C₂³	1	8	yes	—
39	C₂²×Q₈×C₁₁	—	2	4	no	—
40	C₂²×Q₈×C₁₁	—	2	2	no	—
41	C₂²×Q₈×C₁₁	—	2	16	no	—
42	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
44	C₂²×Q₈×C₁₁	C₂³	1	8	yes	—
45	C₂²×D₄×C₁₁	—	2	2	no	—
46	C₂²×D₄×C₁₁	—	2	2	no	—
47	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₁	—	2	2	no	—
49	C₂³×C₄×C₁₁	—	2	2	no	—
50	C₂³×C₄×C₁₁	D₄	1	2	yes	—
51	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
52	C₁₁×#137	—	2	128	no	—
53	C₂×C₁₁×Q₁₆	—	2	32	no	—
54	C₂×C₁₁×Q₁₆	C₂³	1	32	yes	—
55	C₂×C₁₁×SD₁₆	—	2	32	no	—
56	C₂×C₁₁×SD₁₆	C₂³	1	32	yes	—
57	C₂×C₁₁×M₁₆	D₄	1	16	yes	complemented
58	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
59	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
60	C₁₁×C₄⋊Q₈	—	2	4	no	—
61	C₁₁×C₄⋊Q₈	—	2	4	no	—
62	C₁₁×C₄⋊Q₈	—	2	16	no	—
63	C₁₁×C₄⋊Q₈	—	2	2	no	—
64	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
65	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
66	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
67	C₁₁×#127	—	2	2	no	—
68	C₁₁×#127	C₂³	1	4	yes	—
69	C₁₁×#124	—	2	4	no	—
70	C₁₁×#124	C₂³	1	8	yes	—
71	C₁₁×#121	—	2	16	no	—
72	C₄×D₄×C₁₁	—	2	16	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	—	2	2	no	—
77	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
78	C₂×C₄²×C₁₁	D₄	1	2	yes	—
79	C₂×C₄²×C₁₁	D₄	1	4	yes	—
80	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
83	C₁₁×#97	C₂³	1	8	yes	—
84	C₄×C₈×C₁₁	C₂³	1	8	yes	—
85	C₂×#3152	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₁	—	2	2	no	—
87	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₁₁×#41	—	2	32	no	—
89	C₁₁×#41	—	4	16	no	—
90	C₂×Q₈×C₁₁	—	2	2	no	—
91	C₂×Q₈×C₁₁	—	2	8	no	—
92	C₂×Q₈×C₁₁	—	2	4	no	—
93	C₂×Q₈×C₁₁	—	2	16	no	—
94	C₂×Q₈×C₁₁	—	2	8	no	—
95	C₂×Q₈×C₁₁	—	2	32	no	—
96	C₂×Q₈×C₁₁	—	4	8	no	—
97	C₂×Q₈×C₁₁	—	4	16	no	—
98	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
99	C₂×Q₈×C₁₁	C₂⁴	1	8	yes	—
100	C₂×D₄×C₁₁	—	2	8	no	—
101	C₂×D₄×C₁₁	—	2	8	no	—
102	C₂×D₄×C₁₁	—	2	8	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	4	8	no	—
105	C₂×D₄×C₁₁	—	4	8	no	—
106	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₁₁	—	2	8	no	—
108	C₂²×C₄×C₁₁	—	2	8	no	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	2	4	no	—
111	C₂²×C₄×C₁₁	—	2	8	no	—
112	C₂²×C₄×C₁₁	—	4	8	no	—
113	C₂²×C₄×C₁₁	—	4	8	no	—
114	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
115	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
119	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
122	C₁₁×Q₁₆	—	2	64	no	—
123	C₁₁×SD₁₆	—	2	64	no	—
124	C₁₁×M₁₆	C₂×D₄	1	32	yes	complemented
125	C₂×C₈×C₁₁	C₂×D₄	1	16	yes	—
126	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
127	C₁₁×C₄⋊C₄	—	2	16	no	—
128	C₁₁×C₄⋊C₄	—	2	16	no	—
129	C₁₁×C₄⋊C₄	—	2	8	no	—
130	C₁₁×C₂²⋊C₄	—	2	16	no	—
131	C₄²×C₁₁	C₂×D₄	1	8	yes	—
132	C₄²×C₁₁	C₂×D₄	1	2	yes	—
133	C₄²×C₁₁	C₂×D₄	1	2	yes	—
134	C₄²×C₁₁	C₂⁴	1	2	yes	—
135	C₄²×C₁₁	C₂⁴	1	2	yes	—
136	C₂²×#137	C₂×C₁₁	1	4	yes	complemented
137	C₂×#532	C₂×C₁₁	1	1	yes	characteristic
138	C₂²×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
139	#3152	C₂×C₁₁	1	16	yes	direct product factor
140	C₂×#497	C₂×C₁₁	1	4	yes	complemented
141	C₂×#494	C₂×C₁₁	1	2	yes	complemented
142	C₂×#492	C₂×C₁₁	1	2	yes	complemented
143	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
144	C₂³×C₁₁	—	2	4	no	—
145	C₂³×C₁₁	—	2	4	no	—
146	C₂³×C₁₁	—	4	4	no	—
147	C₂³×C₁₁	—	4	8	no	—
148	C₂³×C₁₁	#127	1	4	yes	—
149	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
150	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₁	—	2	16	no	—
152	Q₈×C₁₁	—	2	8	no	—
153	Q₈×C₁₁	—	4	16	no	—
154	Q₈×C₁₁	—	4	8	no	—
155	Q₈×C₁₁	—	4	4	no	—
156	D₄×C₁₁	—	2	8	no	—
157	D₄×C₁₁	—	4	16	no	—
158	D₄×C₁₁	—	4	4	no	—
159	D₄×C₁₁	—	4	16	no	—
160	C₂×C₄×C₁₁	—	2	4	no	—
161	C₂×C₄×C₁₁	—	2	16	no	—
162	C₂×C₄×C₁₁	—	2	4	no	—
163	C₂×C₄×C₁₁	—	2	8	no	—
164	C₂×C₄×C₁₁	—	4	4	no	—
165	C₂×C₄×C₁₁	—	4	16	no	—
166	C₂×C₄×C₁₁	—	4	8	no	—
167	C₂×C₄×C₁₁	—	4	16	no	—
168	C₂×C₄×C₁₁	#127	1	4	yes	—
169	C₂×C₄×C₁₁	#127	1	8	yes	—
170	C₂×C₄×C₁₁	#137	1	8	yes	complemented
171	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
176	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
177	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
178	C₈×C₁₁	C₂²×D₄	1	16	yes	—
179	C₂²×#41	C₂²×C₁₁	1	2	yes	—
180	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
181	C₂×#137	—	2	32	no	—
182	C₂×#137	C₂²×C₁₁	1	32	yes	complemented
183	C₂²×Q₁₆	C₂²×C₁₁	1	8	yes	—
184	C₂²×SD₁₆	C₂²×C₁₁	1	8	yes	—
185	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
186	#532	—	2	4	no	—
187	#532	C₂²×C₁₁	1	8	yes	—
188	C₂×C₄⋊Q₈	—	2	2	no	—
189	C₂×C₄⋊Q₈	—	2	4	no	—
190	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
191	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
192	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
193	C₂×C₄⋊Q₈	C₂²×C₁₁	1	8	yes	complemented
194	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
195	C₂×#124	C₂²×C₁₁	1	2	yes	—
196	C₂×#121	—	2	2	no	—
197	C₂×C₄×D₄	—	2	2	no	—
198	C₂²×C₄⋊C₄	—	2	2	no	—
199	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
200	#497	C₂²×C₁₁	1	32	yes	complemented
201	#494	C₂²×C₁₁	1	16	yes	complemented
202	#492	C₂²×C₁₁	1	16	yes	complemented
203	C₄×M₁₆	C₂²×C₁₁	1	8	yes	complemented
204	C₂×#97	C₂²×C₁₁	1	2	yes	—
205	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
206	C₂²×C₁₁	—	2	8	no	—
207	C₂²×C₁₁	—	2	4	no	—
208	C₂²×C₁₁	—	4	4	no	—
209	C₂²×C₁₁	—	4	8	no	—
210	C₂²×C₁₁	—	8	8	no	—
211	C₂²×C₁₁	C₂×#127	1	4	yes	—
212	C₂²×C₁₁	C₂×#127	1	2	yes	—
213	C₂²×C₁₁	C₂×#137	1	4	yes	—
214	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
215	C₄×C₁₁	—	2	4	no	—
216	C₄×C₁₁	—	4	4	no	—
217	C₄×C₁₁	—	4	8	no	—
218	C₄×C₁₁	C₂×#127	1	4	yes	—
219	C₄×C₁₁	C₂×#127	1	2	yes	—
220	C₄×C₁₁	C₂×#137	1	8	yes	complemented
221	C₄×C₁₁	C₂³×D₄	1	2	yes	—
222	C₂×#41	—	2	4	no	—
223	C₂×#41	—	2	16	no	—
224	C₂×#41	C₂³×C₁₁	1	8	yes	—
225	C₂²×Q₈	—	2	2	no	—
226	C₂²×Q₈	—	2	4	no	—
227	C₂²×Q₈	—	2	16	no	—
228	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
229	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
230	C₂²×Q₈	C₂³×C₁₁	1	8	yes	—
231	C₂²×D₄	—	2	2	no	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	D₄×C₁₁	1	2	yes	—
237	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
238	#137	—	2	128	no	—
239	C₂×Q₁₆	—	2	32	no	—
240	C₂×Q₁₆	C₂³×C₁₁	1	32	yes	—
241	C₂×SD₁₆	—	2	32	no	—
242	C₂×SD₁₆	C₂³×C₁₁	1	32	yes	—
243	C₂×M₁₆	D₄×C₁₁	1	16	yes	complemented
244	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
245	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
246	C₄⋊Q₈	—	2	4	no	—
247	C₄⋊Q₈	—	2	4	no	—
248	C₄⋊Q₈	—	2	16	no	—
249	C₄⋊Q₈	—	2	2	no	—
250	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
251	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
252	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
253	#127	—	2	2	no	—
254	#127	C₂³×C₁₁	1	4	yes	—
255	#124	—	2	4	no	—
256	#124	C₂³×C₁₁	1	8	yes	—
257	#121	—	2	16	no	—
258	C₄×D₄	—	2	16	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	16	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₄²	D₄×C₁₁	1	2	yes	—
265	C₂×C₄²	D₄×C₁₁	1	4	yes	—
266	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
269	#97	C₂³×C₁₁	1	8	yes	—
270	C₄×C₈	C₂³×C₁₁	1	8	yes	—
271	C₂×C₁₁	—	2	4	no	—
272	C₂×C₁₁	—	8	4	no	—
273	C₂×C₁₁	#3152	1	4	yes	direct product factor
274	C₂×C₁₁	C₂²×#127	1	1	yes	characteristic
275	C₂×C₁₁	C₂²×#137	1	2	yes	—
276	C₂⁴	—	2	2	no	—
277	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
278	#41	—	2	32	no	—
279	#41	—	4	16	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	16	no	—
284	C₂×Q₈	—	2	8	no	—
285	C₂×Q₈	—	2	32	no	—
286	C₂×Q₈	—	4	8	no	—
287	C₂×Q₈	—	4	16	no	—
288	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
289	C₂×Q₈	C₂⁴×C₁₁	1	8	yes	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	8	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	—	4	8	no	—
304	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
306	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
309	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
312	Q₁₆	—	2	64	no	—
313	SD₁₆	—	2	64	no	—
314	M₁₆	C₂×D₄×C₁₁	1	32	yes	complemented
315	C₂×C₈	C₂×D₄×C₁₁	1	16	yes	—
316	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
317	C₄⋊C₄	—	2	16	no	—
318	C₄⋊C₄	—	2	16	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	2	16	no	—
321	C₄²	C₂×D₄×C₁₁	1	8	yes	—
322	C₄²	C₂×D₄×C₁₁	1	2	yes	—
323	C₄²	C₂×D₄×C₁₁	1	2	yes	—
324	C₄²	C₂⁴×C₁₁	1	2	yes	—
325	C₄²	C₂⁴×C₁₁	1	2	yes	—
326	C₁₁	C₂×#3152	1	1	yes	characteristic, direct product factor, Sylow
327	C₂³	—	2	4	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	4	4	no	—
330	C₂³	—	4	8	no	—
331	C₂³	C₁₁×#127	1	4	yes	—
332	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
333	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
334	Q₈	—	2	16	no	—
335	Q₈	—	2	8	no	—
336	Q₈	—	4	16	no	—
337	Q₈	—	4	8	no	—
338	Q₈	—	4	4	no	—
339	D₄	—	2	8	no	—
340	D₄	—	4	16	no	—
341	D₄	—	4	4	no	—
342	D₄	—	4	16	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	16	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	16	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	16	no	—
351	C₂×C₄	C₁₁×#127	1	4	yes	—
352	C₂×C₄	C₁₁×#127	1	8	yes	—
353	C₂×C₄	C₁₁×#137	1	8	yes	complemented
354	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
355	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
357	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
359	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
360	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
361	C₈	C₂²×D₄×C₁₁	1	16	yes	—
362	C₂²	—	2	8	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	8	no	—
366	C₂²	—	8	8	no	—
367	C₂²	C₂×C₁₁×#127	1	4	yes	—
368	C₂²	C₂×C₁₁×#127	1	2	yes	—
369	C₂²	C₂×C₁₁×#137	1	4	yes	—
370	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	8	no	—
374	C₄	C₂×C₁₁×#127	1	4	yes	—
375	C₄	C₂×C₁₁×#127	1	2	yes	—
376	C₄	C₂×C₁₁×#137	1	8	yes	complemented
377	C₄	C₂³×D₄×C₁₁	1	2	yes	—
378	C₂	—	2	4	no	—
379	C₂	—	8	4	no	—
380	C₂	C₁₁×#3152	1	4	yes	direct product factor
381	C₂	C₂²×C₁₁×#127	1	1	yes	characteristic
382	C₂	C₂²×C₁₁×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₁×#137	C₂	semidirect
3. C₂²×C₁₁×C₄⋊Q₈	C₂	semidirect
4. C₁₁×#3152	C₂	direct (N × H)
5. C₂×C₁₁×#497	C₂	semidirect
6. C₂×C₁₁×#494	C₂	semidirect
7. C₂×C₁₁×#492	C₂	semidirect
8. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
12. C₂×C₁₁×#137	C₂²	semidirect
23. C₂×C₁₁×C₄⋊Q₈	C₂²	semidirect
30. C₁₁×#497	C₂²	semidirect
31. C₁₁×#494	C₂²	semidirect
32. C₁₁×#492	C₂²	semidirect
33. C₄×C₁₁×M₁₆	C₂²	semidirect
57. C₂×C₁₁×M₁₆	D₄	semidirect
85. C₂×#3152	C₁₁	direct (N × H)
124. C₁₁×M₁₆	C₂×D₄	semidirect
136. C₂²×#137	C₂×C₁₁	semidirect
138. C₂²×C₄⋊Q₈	C₂×C₁₁	semidirect
139. #3152	C₂×C₁₁	direct (N × H)
140. C₂×#497	C₂×C₁₁	semidirect
141. C₂×#494	C₂×C₁₁	semidirect
142. C₂×#492	C₂×C₁₁	semidirect
143. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
170. C₂×C₄×C₁₁	#137	semidirect
182. C₂×#137	C₂²×C₁₁	semidirect
193. C₂×C₄⋊Q₈	C₂²×C₁₁	semidirect
200. #497	C₂²×C₁₁	semidirect
201. #494	C₂²×C₁₁	semidirect
202. #492	C₂²×C₁₁	semidirect
203. C₄×M₁₆	C₂²×C₁₁	semidirect
220. C₄×C₁₁	C₂×#137	semidirect
243. C₂×M₁₆	D₄×C₁₁	semidirect
273. C₂×C₁₁	#3152	direct (N × H)
314. M₁₆	C₂×D₄×C₁₁	semidirect
326. C₁₁	C₂×#3152	direct (N × H)
353. C₂×C₄	C₁₁×#137	semidirect
376. C₄	C₂×C₁₁×#137	semidirect
380. C₂	C₁₁×#3152	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×#137	2
C₂×C₁₁×#532	2
C₂²×C₁₁×C₄⋊Q₈	2
C₁₁×#3152	2
C₂×C₁₁×#497	2
C₂×C₁₁×#494	2
C₂×C₁₁×#492	2
C₂×C₄×C₁₁×M₁₆	2
C₂×#3152	11

Subgroups — C2×C11×#3152 #14637830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3152 #14637830