Subgroups — C₂×C₁₁×#3186 #14637921

Order 2816.

3042 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#121	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3186	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#480	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#466	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#447	C₂	1	4	yes	maximal, complemented
6	C₂²×C₁₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₁₁	—	2	2	no	—
8	C₂³×D₄×C₁₁	C₂²	1	2	yes	complemented
9	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁×D₈	C₂²	1	4	yes	complemented
11	C₂³×C₈×C₁₁	C₂²	1	2	yes	complemented
12	C₂×C₁₁×#121	—	2	2	no	—
13	C₂×C₁₁×#121	—	2	8	no	—
14	C₂×C₁₁×#121	—	2	2	no	—
15	C₂×C₁₁×#121	C₂²	1	4	yes	—
16	C₂×C₁₁×#121	C₂²	1	4	yes	complemented
17	C₂×C₁₁×#121	C₂²	1	16	yes	complemented
18	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
19	C₂²×C₁₁×C₂²⋊C₄	—	2	2	no	—
20	C₁₁×#480	C₂²	1	32	yes	complemented
21	C₁₁×#466	C₂²	1	32	yes	complemented
22	C₁₁×#447	C₂²	1	32	yes	complemented
23	C₂×C₁₁×#107	C₂²	1	4	yes	complemented
24	C₂×C₁₁×#102	C₂²	1	8	yes	complemented
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	complemented
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₁	—	2	2	no	—
28	C₂⁵×C₁₁	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₁	—	2	4	no	—
30	C₂²×D₄×C₁₁	—	2	16	no	—
31	C₂²×D₄×C₁₁	—	2	4	no	—
32	C₂²×D₄×C₁₁	—	2	4	no	—
33	C₂²×D₄×C₁₁	—	2	2	no	—
34	C₂²×D₄×C₁₁	—	4	8	no	—
35	C₂²×D₄×C₁₁	—	4	16	no	—
36	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
37	C₂²×D₄×C₁₁	C₂³	1	8	yes	complemented
38	C₂³×C₄×C₁₁	—	2	2	no	—
39	C₂³×C₄×C₁₁	—	4	4	no	—
40	C₂³×C₄×C₁₁	D₄	1	2	yes	—
41	C₂³×C₄×C₁₁	D₄	1	4	yes	—
42	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
46	C₂×C₁₁×D₈	—	4	8	no	—
47	C₂×C₁₁×D₈	C₂³	1	16	yes	complemented
48	C₂²×C₈×C₁₁	—	4	4	no	—
49	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
50	C₂²×C₈×C₁₁	C₂³	1	8	yes	complemented
51	C₁₁×#121	—	2	8	no	—
52	C₁₁×#121	—	2	16	no	—
53	C₁₁×#121	—	2	8	no	—
54	C₁₁×#121	—	2	16	no	—
55	C₁₁×#121	C₂³	1	16	yes	—
56	C₁₁×#121	C₂³	1	16	yes	complemented
57	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
58	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
60	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	complemented
61	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
62	C₂×C₁₁×C₂²⋊C₄	—	2	16	no	—
63	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
64	C₁₁×#107	C₂³	1	16	yes	complemented
65	C₁₁×#102	C₂³	1	32	yes	complemented
66	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
67	C₂×#3186	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₁	—	2	8	no	—
69	C₂⁴×C₁₁	—	2	4	no	—
70	C₂⁴×C₁₁	—	4	2	no	—
71	C₂⁴×C₁₁	—	4	2	no	—
72	C₂⁴×C₁₁	—	4	8	no	—
73	C₂⁴×C₁₁	—	4	8	no	—
74	C₂⁴×C₁₁	—	4	8	no	—
75	C₂⁴×C₁₁	D₈	1	8	yes	complemented
76	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
77	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂⁴×C₁₁	C₂×D₄	1	4	yes	—
79	C₂×D₄×C₁₁	—	2	16	no	—
80	C₂×D₄×C₁₁	—	2	16	no	—
81	C₂×D₄×C₁₁	—	2	4	no	—
82	C₂×D₄×C₁₁	—	2	8	no	—
83	C₂×D₄×C₁₁	—	2	16	no	—
84	C₂×D₄×C₁₁	—	4	16	no	—
85	C₂×D₄×C₁₁	—	4	8	no	—
86	C₂×D₄×C₁₁	—	4	16	no	—
87	C₂×D₄×C₁₁	—	4	16	no	—
88	C₂×D₄×C₁₁	—	4	16	no	—
89	C₂×D₄×C₁₁	—	4	64	no	—
90	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
91	C₂²×C₄×C₁₁	—	2	4	no	—
92	C₂²×C₄×C₁₁	—	2	8	no	—
93	C₂²×C₄×C₁₁	—	2	8	no	—
94	C₂²×C₄×C₁₁	—	2	4	no	—
95	C₂²×C₄×C₁₁	—	4	8	no	—
96	C₂²×C₄×C₁₁	—	4	8	no	—
97	C₂²×C₄×C₁₁	—	4	4	no	—
98	C₂²×C₄×C₁₁	—	4	2	no	—
99	C₂²×C₄×C₁₁	—	4	8	no	—
100	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
105	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
109	C₁₁×D₈	—	4	16	no	—
110	C₂×C₈×C₁₁	—	2	8	no	—
111	C₂×C₈×C₁₁	—	4	8	no	—
112	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
113	C₁₁×C₄⋊C₄	—	2	4	no	—
114	C₁₁×C₄⋊C₄	—	2	8	no	—
115	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
116	C₁₁×C₂²⋊C₄	—	2	16	no	—
117	C₁₁×C₂²⋊C₄	—	2	16	no	—
118	C₂²×#121	C₂×C₁₁	1	2	yes	complemented
119	#3186	C₂×C₁₁	1	16	yes	direct product factor
120	C₂×#480	C₂×C₁₁	1	4	yes	complemented
121	C₂×#466	C₂×C₁₁	1	4	yes	complemented
122	C₂×#447	C₂×C₁₁	1	4	yes	complemented
123	C₂²×C₂²⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
124	C₂³×C₁₁	—	2	4	no	—
125	C₂³×C₁₁	—	2	2	no	—
126	C₂³×C₁₁	—	2	4	no	—
127	C₂³×C₁₁	—	2	2	no	—
128	C₂³×C₁₁	—	2	8	no	—
129	C₂³×C₁₁	—	4	4	no	—
130	C₂³×C₁₁	—	4	16	no	—
131	C₂³×C₁₁	—	4	4	no	—
132	C₂³×C₁₁	—	4	16	no	—
133	C₂³×C₁₁	—	4	16	no	—
134	C₂³×C₁₁	—	4	8	no	—
135	C₂³×C₁₁	—	4	16	no	—
136	C₂³×C₁₁	—	4	8	no	—
137	C₂³×C₁₁	—	4	8	no	—
138	C₂³×C₁₁	—	8	32	no	—
139	C₂³×C₁₁	C₂×D₈	1	8	yes	—
140	C₂³×C₁₁	C₂×D₈	1	4	yes	—
141	C₂³×C₁₁	C₂×D₈	1	16	yes	complemented
142	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
143	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
144	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
145	D₄×C₁₁	—	2	16	no	—
146	D₄×C₁₁	—	4	16	no	—
147	D₄×C₁₁	—	4	32	no	—
148	D₄×C₁₁	—	4	32	no	—
149	D₄×C₁₁	—	4	8	no	—
150	C₂×C₄×C₁₁	—	2	2	no	—
151	C₂×C₄×C₁₁	—	2	4	no	—
152	C₂×C₄×C₁₁	—	2	4	no	—
153	C₂×C₄×C₁₁	—	2	8	no	—
154	C₂×C₄×C₁₁	—	2	4	no	—
155	C₂×C₄×C₁₁	—	2	8	no	—
156	C₂×C₄×C₁₁	—	2	8	no	—
157	C₂×C₄×C₁₁	—	4	8	no	—
158	C₂×C₄×C₁₁	—	4	4	no	—
159	C₂×C₄×C₁₁	—	4	16	no	—
160	C₂×C₄×C₁₁	—	4	8	no	—
161	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
162	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
163	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
165	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
166	C₈×C₁₁	—	2	8	no	—
167	C₂³×D₄	—	2	2	no	—
168	C₂³×D₄	C₂²×C₁₁	1	2	yes	complemented
169	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
170	C₂²×D₈	C₂²×C₁₁	1	4	yes	complemented
171	C₂³×C₈	C₂²×C₁₁	1	2	yes	complemented
172	C₂×#121	—	2	2	no	—
173	C₂×#121	—	2	8	no	—
174	C₂×#121	—	2	2	no	—
175	C₂×#121	C₂²×C₁₁	1	4	yes	—
176	C₂×#121	C₂²×C₁₁	1	4	yes	complemented
177	C₂×#121	C₂²×C₁₁	1	16	yes	complemented
178	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
179	C₂²×C₂²⋊C₄	—	2	2	no	—
180	#480	C₂²×C₁₁	1	32	yes	complemented
181	#466	C₂²×C₁₁	1	32	yes	complemented
182	#447	C₂²×C₁₁	1	32	yes	complemented
183	C₂×#107	C₂²×C₁₁	1	4	yes	complemented
184	C₂×#102	C₂²×C₁₁	1	8	yes	complemented
185	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	complemented
186	C₂×C₂²⋊C₈	C₂²×C₁₁	1	8	yes	complemented
187	C₂²×C₁₁	—	2	16	no	—
188	C₂²×C₁₁	—	2	8	no	—
189	C₂²×C₁₁	—	2	4	no	—
190	C₂²×C₁₁	—	2	2	no	—
191	C₂²×C₁₁	—	2	4	no	—
192	C₂²×C₁₁	—	2	2	no	—
193	C₂²×C₁₁	—	4	16	no	—
194	C₂²×C₁₁	—	4	8	no	—
195	C₂²×C₁₁	—	4	8	no	—
196	C₂²×C₁₁	—	4	8	no	—
197	C₂²×C₁₁	—	8	32	no	—
198	C₂²×C₁₁	—	8	16	no	—
199	C₂²×C₁₁	#534	1	2	yes	—
200	C₂²×C₁₁	C₂²×D₈	1	8	yes	—
201	C₂²×C₁₁	C₂²×D₈	1	4	yes	—
202	C₂²×C₁₁	C₂²×D₈	1	2	yes	—
203	C₂²×C₁₁	#575	1	2	yes	—
204	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
205	C₄×C₁₁	—	2	2	no	—
206	C₄×C₁₁	—	2	4	no	—
207	C₄×C₁₁	—	4	8	no	—
208	C₄×C₁₁	#534	1	2	yes	—
209	C₄×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
210	C₂⁵	—	2	2	no	—
211	C₂⁵	D₄×C₁₁	1	1	yes	characteristic
212	C₂²×D₄	—	2	4	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	2	16	no	—
215	C₂²×D₄	—	2	2	no	—
216	C₂²×D₄	—	2	4	no	—
217	C₂²×D₄	—	4	8	no	—
218	C₂²×D₄	—	4	16	no	—
219	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
220	C₂²×D₄	C₂³×C₁₁	1	8	yes	complemented
221	C₂³×C₄	—	2	2	no	—
222	C₂³×C₄	—	4	4	no	—
223	C₂³×C₄	D₄×C₁₁	1	2	yes	—
224	C₂³×C₄	D₄×C₁₁	1	4	yes	—
225	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
226	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
227	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
229	C₂×D₈	—	4	8	no	—
230	C₂×D₈	C₂³×C₁₁	1	16	yes	complemented
231	C₂²×C₈	—	4	4	no	—
232	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
233	C₂²×C₈	C₂³×C₁₁	1	8	yes	complemented
234	#121	—	2	8	no	—
235	#121	—	2	16	no	—
236	#121	—	2	8	no	—
237	#121	—	2	16	no	—
238	#121	C₂³×C₁₁	1	16	yes	—
239	#121	C₂³×C₁₁	1	16	yes	complemented
240	C₂×C₄⋊C₄	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
243	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	complemented
244	C₂×C₂²⋊C₄	—	2	4	no	—
245	C₂×C₂²⋊C₄	—	2	16	no	—
246	C₂×C₂²⋊C₄	—	2	4	no	—
247	#107	C₂³×C₁₁	1	16	yes	complemented
248	#102	C₂³×C₁₁	1	32	yes	complemented
249	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	complemented
250	C₂×C₁₁	—	2	8	no	—
251	C₂×C₁₁	—	2	4	no	—
252	C₂×C₁₁	—	8	8	no	—
253	C₂×C₁₁	#3186	1	4	yes	direct product factor
254	C₂×C₁₁	C₂×#534	1	1	yes	characteristic
255	C₂×C₁₁	C₂³×D₈	1	1	yes	characteristic
256	C₂×C₁₁	C₂×#575	1	1	yes	characteristic
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	4	2	no	—
260	C₂⁴	—	4	2	no	—
261	C₂⁴	—	4	8	no	—
262	C₂⁴	—	4	8	no	—
263	C₂⁴	—	4	8	no	—
264	C₂⁴	C₁₁×D₈	1	8	yes	complemented
265	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
266	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
267	C₂⁴	C₂×D₄×C₁₁	1	4	yes	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	8	no	—
272	C₂×D₄	—	2	16	no	—
273	C₂×D₄	—	4	16	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	16	no	—
276	C₂×D₄	—	4	16	no	—
277	C₂×D₄	—	4	16	no	—
278	C₂×D₄	—	4	64	no	—
279	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	8	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	—	4	8	no	—
286	C₂²×C₄	—	4	4	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	8	no	—
289	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
292	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
294	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
295	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
297	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
298	D₈	—	4	16	no	—
299	C₂×C₈	—	2	8	no	—
300	C₂×C₈	—	4	8	no	—
301	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
305	C₂²⋊C₄	—	2	16	no	—
306	C₂²⋊C₄	—	2	16	no	—
307	C₁₁	C₂×#3186	1	1	yes	characteristic, direct product factor, Sylow
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	8	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	16	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	16	no	—
317	C₂³	—	4	16	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	16	no	—
320	C₂³	—	4	8	no	—
321	C₂³	—	4	8	no	—
322	C₂³	—	8	32	no	—
323	C₂³	C₂×C₁₁×D₈	1	8	yes	—
324	C₂³	C₂×C₁₁×D₈	1	4	yes	—
325	C₂³	C₂×C₁₁×D₈	1	16	yes	complemented
326	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
327	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
328	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
329	D₄	—	2	16	no	—
330	D₄	—	4	16	no	—
331	D₄	—	4	32	no	—
332	D₄	—	4	32	no	—
333	D₄	—	4	8	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	16	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
346	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
347	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
348	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
349	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
350	C₈	—	2	8	no	—
351	C₂²	—	2	16	no	—
352	C₂²	—	2	8	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	4	16	no	—
358	C₂²	—	4	8	no	—
359	C₂²	—	4	8	no	—
360	C₂²	—	4	8	no	—
361	C₂²	—	8	32	no	—
362	C₂²	—	8	16	no	—
363	C₂²	C₁₁×#534	1	2	yes	—
364	C₂²	C₂²×C₁₁×D₈	1	8	yes	—
365	C₂²	C₂²×C₁₁×D₈	1	4	yes	—
366	C₂²	C₂²×C₁₁×D₈	1	2	yes	—
367	C₂²	C₁₁×#575	1	2	yes	—
368	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	2	no	—
371	C₄	—	4	8	no	—
372	C₄	C₁₁×#534	1	2	yes	—
373	C₄	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
374	C₂	—	2	8	no	—
375	C₂	—	2	4	no	—
376	C₂	—	8	8	no	—
377	C₂	C₁₁×#3186	1	4	yes	direct product factor
378	C₂	C₂×C₁₁×#534	1	1	yes	characteristic
379	C₂	C₂³×C₁₁×D₈	1	1	yes	characteristic
380	C₂	C₂×C₁₁×#575	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₁×#121	C₂	semidirect
2. C₁₁×#3186	C₂	direct (N × H)
3. C₂×C₁₁×#480	C₂	semidirect
4. C₂×C₁₁×#466	C₂	semidirect
5. C₂×C₁₁×#447	C₂	semidirect
6. C₂²×C₁₁×C₂²⋊C₈	C₂	semidirect
8. C₂³×D₄×C₁₁	C₂²	semidirect
10. C₂²×C₁₁×D₈	C₂²	semidirect
11. C₂³×C₈×C₁₁	C₂²	semidirect
16. C₂×C₁₁×#121	C₂²	semidirect
17. C₂×C₁₁×#121	C₂²	semidirect
18. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
20. C₁₁×#480	C₂²	semidirect
21. C₁₁×#466	C₂²	semidirect
22. C₁₁×#447	C₂²	semidirect
23. C₂×C₁₁×#107	C₂²	semidirect
24. C₂×C₁₁×#102	C₂²	semidirect
25. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
26. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
37. C₂²×D₄×C₁₁	C₂³	semidirect
47. C₂×C₁₁×D₈	C₂³	semidirect
50. C₂²×C₈×C₁₁	C₂³	semidirect
56. C₁₁×#121	C₂³	semidirect
60. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
64. C₁₁×#107	C₂³	semidirect
65. C₁₁×#102	C₂³	semidirect
66. C₁₁×C₂²⋊C₈	C₂³	semidirect
67. C₂×#3186	C₁₁	direct (N × H)
75. C₂⁴×C₁₁	D₈	semidirect
118. C₂²×#121	C₂×C₁₁	semidirect
119. #3186	C₂×C₁₁	direct (N × H)
120. C₂×#480	C₂×C₁₁	semidirect
121. C₂×#466	C₂×C₁₁	semidirect
122. C₂×#447	C₂×C₁₁	semidirect
123. C₂²×C₂²⋊C₈	C₂×C₁₁	semidirect
141. C₂³×C₁₁	C₂×D₈	semidirect
168. C₂³×D₄	C₂²×C₁₁	semidirect
170. C₂²×D₈	C₂²×C₁₁	semidirect
171. C₂³×C₈	C₂²×C₁₁	semidirect
176. C₂×#121	C₂²×C₁₁	semidirect
177. C₂×#121	C₂²×C₁₁	semidirect
178. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
180. #480	C₂²×C₁₁	semidirect
181. #466	C₂²×C₁₁	semidirect
182. #447	C₂²×C₁₁	semidirect
183. C₂×#107	C₂²×C₁₁	semidirect
184. C₂×#102	C₂²×C₁₁	semidirect
185. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
186. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
220. C₂²×D₄	C₂³×C₁₁	semidirect
230. C₂×D₈	C₂³×C₁₁	semidirect
233. C₂²×C₈	C₂³×C₁₁	semidirect
239. #121	C₂³×C₁₁	semidirect
243. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
247. #107	C₂³×C₁₁	semidirect
248. #102	C₂³×C₁₁	semidirect
249. C₂²⋊C₈	C₂³×C₁₁	semidirect
253. C₂×C₁₁	#3186	direct (N × H)
264. C₂⁴	C₁₁×D₈	semidirect
307. C₁₁	C₂×#3186	direct (N × H)
325. C₂³	C₂×C₁₁×D₈	semidirect
377. C₂	C₁₁×#3186	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×#121	2
C₁₁×#3186	2
C₂×C₁₁×#480	2
C₂×C₁₁×#466	2
C₂×C₁₁×#447	2
C₂²×C₁₁×C₂²⋊C₈	2
C₂×#3186	11

Subgroups — C2×C11×#3186 #14637921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3186 #14637921