Subgroups — C₂×C₁₁×#3192 #14637928

Order 2816.

3010 conjugacy classes of subgroups.

The subgroup lattice has 370 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×#3192	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#481	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#469	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#447	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#407	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	C₂²×C₁₁×M₁₆	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×#481	C₂²	1	32	yes	complemented
21	C₁₁×#469	C₂²	1	32	yes	complemented
22	C₁₁×#447	C₂²	1	32	yes	complemented
23	C₂×C₁₁×#106	C₂²	1	4	yes	complemented
24	C₂×C₁₁×#102	C₂²	1	8	yes	complemented
25	C₁₁×#407	C₂²	1	8	yes	complemented
26	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	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	C₂×C₁₁×M₁₆	—	4	4	no	—
49	C₂×C₁₁×M₁₆	C₂³	1	8	yes	complemented
50	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
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×#106	C₂³	1	16	yes	complemented
65	C₁₁×#102	C₂³	1	32	yes	complemented
66	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
67	C₂×#3192	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₁	—	2	8	no	—
69	C₂⁴×C₁₁	—	2	8	no	—
70	C₂⁴×C₁₁	—	2	4	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	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×C₁₁	C₂×D₄	1	4	yes	—
77	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
78	C₂×D₄×C₁₁	—	2	16	no	—
79	C₂×D₄×C₁₁	—	2	16	no	—
80	C₂×D₄×C₁₁	—	2	4	no	—
81	C₂×D₄×C₁₁	—	2	8	no	—
82	C₂×D₄×C₁₁	—	2	16	no	—
83	C₂×D₄×C₁₁	—	4	16	no	—
84	C₂×D₄×C₁₁	—	4	8	no	—
85	C₂×D₄×C₁₁	—	4	16	no	—
86	C₂×D₄×C₁₁	—	4	64	no	—
87	C₂×D₄×C₁₁	—	4	16	no	—
88	C₂×D₄×C₁₁	—	4	16	no	—
89	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
90	C₂²×C₄×C₁₁	—	2	4	no	—
91	C₂²×C₄×C₁₁	—	2	8	no	—
92	C₂²×C₄×C₁₁	—	2	8	no	—
93	C₂²×C₄×C₁₁	—	2	4	no	—
94	C₂²×C₄×C₁₁	—	4	8	no	—
95	C₂²×C₄×C₁₁	—	4	8	no	—
96	C₂²×C₄×C₁₁	—	4	4	no	—
97	C₂²×C₄×C₁₁	—	4	2	no	—
98	C₂²×C₄×C₁₁	—	4	8	no	—
99	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
108	C₁₁×D₈	—	4	16	no	—
109	C₁₁×M₁₆	—	4	8	no	—
110	C₂×C₈×C₁₁	—	2	8	no	—
111	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
112	C₁₁×C₄⋊C₄	—	2	4	no	—
113	C₁₁×C₄⋊C₄	—	2	8	no	—
114	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
115	C₁₁×C₂²⋊C₄	—	2	16	no	—
116	C₁₁×C₂²⋊C₄	—	2	16	no	—
117	C₂²×#121	C₂×C₁₁	1	2	yes	complemented
118	#3192	C₂×C₁₁	1	16	yes	direct product factor
119	C₂×#481	C₂×C₁₁	1	4	yes	complemented
120	C₂×#469	C₂×C₁₁	1	4	yes	complemented
121	C₂×#447	C₂×C₁₁	1	4	yes	complemented
122	C₂×#407	C₂×C₁₁	1	1	yes	characteristic, complemented
123	C₂³×C₁₁	—	2	4	no	—
124	C₂³×C₁₁	—	2	4	no	—
125	C₂³×C₁₁	—	2	2	no	—
126	C₂³×C₁₁	—	2	16	no	—
127	C₂³×C₁₁	—	2	4	no	—
128	C₂³×C₁₁	—	2	8	no	—
129	C₂³×C₁₁	—	4	4	no	—
130	C₂³×C₁₁	—	4	16	no	—
131	C₂³×C₁₁	—	4	16	no	—
132	C₂³×C₁₁	—	4	16	no	—
133	C₂³×C₁₁	—	4	8	no	—
134	C₂³×C₁₁	—	4	8	no	—
135	C₂³×C₁₁	—	4	16	no	—
136	C₂³×C₁₁	—	4	8	no	—
137	C₂³×C₁₁	—	8	32	no	—
138	C₂³×C₁₁	AGL(1,ℤ/8)	1	8	yes	—
139	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
140	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
141	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₁₁	—	2	16	no	—
143	D₄×C₁₁	—	4	16	no	—
144	D₄×C₁₁	—	4	32	no	—
145	D₄×C₁₁	—	4	32	no	—
146	D₄×C₁₁	—	4	8	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	4	no	—
149	C₂×C₄×C₁₁	—	2	4	no	—
150	C₂×C₄×C₁₁	—	2	8	no	—
151	C₂×C₄×C₁₁	—	2	4	no	—
152	C₂×C₄×C₁₁	—	2	8	no	—
153	C₂×C₄×C₁₁	—	2	8	no	—
154	C₂×C₄×C₁₁	—	4	8	no	—
155	C₂×C₄×C₁₁	—	4	4	no	—
156	C₂×C₄×C₁₁	—	4	16	no	—
157	C₂×C₄×C₁₁	—	4	8	no	—
158	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
160	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
162	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
163	C₈×C₁₁	—	2	8	no	—
164	C₂³×D₄	—	2	2	no	—
165	C₂³×D₄	C₂²×C₁₁	1	2	yes	complemented
166	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
167	C₂²×D₈	C₂²×C₁₁	1	4	yes	complemented
168	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	complemented
169	C₂×#121	—	2	2	no	—
170	C₂×#121	—	2	8	no	—
171	C₂×#121	—	2	2	no	—
172	C₂×#121	C₂²×C₁₁	1	4	yes	—
173	C₂×#121	C₂²×C₁₁	1	4	yes	complemented
174	C₂×#121	C₂²×C₁₁	1	16	yes	complemented
175	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
176	C₂²×C₂²⋊C₄	—	2	2	no	—
177	#481	C₂²×C₁₁	1	32	yes	complemented
178	#469	C₂²×C₁₁	1	32	yes	complemented
179	#447	C₂²×C₁₁	1	32	yes	complemented
180	C₂×#106	C₂²×C₁₁	1	4	yes	complemented
181	C₂×#102	C₂²×C₁₁	1	8	yes	complemented
182	#407	C₂²×C₁₁	1	8	yes	complemented
183	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	complemented
184	C₂²×C₁₁	—	2	4	no	—
185	C₂²×C₁₁	—	2	16	no	—
186	C₂²×C₁₁	—	2	4	no	—
187	C₂²×C₁₁	—	2	2	no	—
188	C₂²×C₁₁	—	2	4	no	—
189	C₂²×C₁₁	—	4	16	no	—
190	C₂²×C₁₁	—	4	4	no	—
191	C₂²×C₁₁	—	4	8	no	—
192	C₂²×C₁₁	—	4	8	no	—
193	C₂²×C₁₁	—	4	8	no	—
194	C₂²×C₁₁	—	8	32	no	—
195	C₂²×C₁₁	—	8	16	no	—
196	C₂²×C₁₁	#534	1	2	yes	—
197	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	8	yes	—
198	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
199	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
200	C₄×C₁₁	—	2	2	no	—
201	C₄×C₁₁	—	2	4	no	—
202	C₄×C₁₁	—	4	8	no	—
203	C₄×C₁₁	#534	1	2	yes	—
204	C₄×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
205	C₂⁵	—	2	2	no	—
206	C₂⁵	D₄×C₁₁	1	1	yes	characteristic
207	C₂²×D₄	—	2	4	no	—
208	C₂²×D₄	—	2	4	no	—
209	C₂²×D₄	—	2	16	no	—
210	C₂²×D₄	—	2	2	no	—
211	C₂²×D₄	—	2	4	no	—
212	C₂²×D₄	—	4	8	no	—
213	C₂²×D₄	—	4	16	no	—
214	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
215	C₂²×D₄	C₂³×C₁₁	1	8	yes	complemented
216	C₂³×C₄	—	2	2	no	—
217	C₂³×C₄	—	4	4	no	—
218	C₂³×C₄	D₄×C₁₁	1	2	yes	—
219	C₂³×C₄	D₄×C₁₁	1	4	yes	—
220	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
222	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
224	C₂×D₈	—	4	8	no	—
225	C₂×D₈	C₂³×C₁₁	1	16	yes	complemented
226	C₂×M₁₆	—	4	4	no	—
227	C₂×M₁₆	C₂³×C₁₁	1	8	yes	complemented
228	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
229	#121	—	2	8	no	—
230	#121	—	2	16	no	—
231	#121	—	2	8	no	—
232	#121	—	2	16	no	—
233	#121	C₂³×C₁₁	1	16	yes	—
234	#121	C₂³×C₁₁	1	16	yes	complemented
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	complemented
239	C₂×C₂²⋊C₄	—	2	4	no	—
240	C₂×C₂²⋊C₄	—	2	16	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	#106	C₂³×C₁₁	1	16	yes	complemented
243	#102	C₂³×C₁₁	1	32	yes	complemented
244	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	complemented
245	C₂×C₁₁	—	2	8	no	—
246	C₂×C₁₁	—	4	2	no	—
247	C₂×C₁₁	—	8	8	no	—
248	C₂×C₁₁	#3192	1	4	yes	direct product factor
249	C₂×C₁₁	C₂×#534	1	1	yes	characteristic
250	C₂×C₁₁	C₂²×AGL(1,ℤ/8)	1	2	yes	—
251	C₂⁴	—	2	8	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	2	8	no	—
254	C₂⁴	—	4	2	no	—
255	C₂⁴	—	4	8	no	—
256	C₂⁴	—	4	8	no	—
257	C₂⁴	—	4	8	no	—
258	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
259	C₂⁴	C₂×D₄×C₁₁	1	4	yes	—
260	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
261	C₂×D₄	—	2	16	no	—
262	C₂×D₄	—	2	16	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	4	16	no	—
267	C₂×D₄	—	4	8	no	—
268	C₂×D₄	—	4	16	no	—
269	C₂×D₄	—	4	64	no	—
270	C₂×D₄	—	4	16	no	—
271	C₂×D₄	—	4	16	no	—
272	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	4	8	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	—	4	4	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	8	no	—
282	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
285	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
287	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
288	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
291	D₈	—	4	16	no	—
292	M₁₆	—	4	8	no	—
293	C₂×C₈	—	2	8	no	—
294	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
298	C₂²⋊C₄	—	2	16	no	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₁₁	C₂×#3192	1	1	yes	characteristic, direct product factor, Sylow
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	8	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	16	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	16	no	—
314	C₂³	—	4	8	no	—
315	C₂³	—	8	32	no	—
316	C₂³	C₁₁×AGL(1,ℤ/8)	1	8	yes	—
317	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
318	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
319	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
320	D₄	—	2	16	no	—
321	D₄	—	4	16	no	—
322	D₄	—	4	32	no	—
323	D₄	—	4	32	no	—
324	D₄	—	4	8	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
337	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
339	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
340	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
341	C₈	—	2	8	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	16	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	16	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	8	32	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₁₁×#534	1	2	yes	—
355	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	8	yes	—
356	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	4	yes	—
357	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	8	no	—
361	C₄	C₁₁×#534	1	2	yes	—
362	C₄	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
363	C₂	—	2	8	no	—
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₁₁×#3192	1	4	yes	direct product factor
367	C₂	C₂×C₁₁×#534	1	1	yes	characteristic
368	C₂	C₂²×C₁₁×AGL(1,ℤ/8)	1	2	yes	—

	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×#3192	C₂	direct (N × H)
3. C₂×C₁₁×#481	C₂	semidirect
4. C₂×C₁₁×#469	C₂	semidirect
5. C₂×C₁₁×#447	C₂	semidirect
6. C₂×C₁₁×#407	C₂	semidirect
8. C₂³×D₄×C₁₁	C₂²	semidirect
10. C₂²×C₁₁×D₈	C₂²	semidirect
11. C₂²×C₁₁×M₁₆	C₂²	semidirect
16. C₂×C₁₁×#121	C₂²	semidirect
17. C₂×C₁₁×#121	C₂²	semidirect
18. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
20. C₁₁×#481	C₂²	semidirect
21. C₁₁×#469	C₂²	semidirect
22. C₁₁×#447	C₂²	semidirect
23. C₂×C₁₁×#106	C₂²	semidirect
24. C₂×C₁₁×#102	C₂²	semidirect
25. C₁₁×#407	C₂²	semidirect
26. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
37. C₂²×D₄×C₁₁	C₂³	semidirect
47. C₂×C₁₁×D₈	C₂³	semidirect
49. C₂×C₁₁×M₁₆	C₂³	semidirect
56. C₁₁×#121	C₂³	semidirect
60. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
64. C₁₁×#106	C₂³	semidirect
65. C₁₁×#102	C₂³	semidirect
66. C₁₁×C₂²⋊C₈	C₂³	semidirect
67. C₂×#3192	C₁₁	direct (N × H)
117. C₂²×#121	C₂×C₁₁	semidirect
118. #3192	C₂×C₁₁	direct (N × H)
119. C₂×#481	C₂×C₁₁	semidirect
120. C₂×#469	C₂×C₁₁	semidirect
121. C₂×#447	C₂×C₁₁	semidirect
122. C₂×#407	C₂×C₁₁	semidirect
165. C₂³×D₄	C₂²×C₁₁	semidirect
167. C₂²×D₈	C₂²×C₁₁	semidirect
168. C₂²×M₁₆	C₂²×C₁₁	semidirect
173. C₂×#121	C₂²×C₁₁	semidirect
174. C₂×#121	C₂²×C₁₁	semidirect
175. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
177. #481	C₂²×C₁₁	semidirect
178. #469	C₂²×C₁₁	semidirect
179. #447	C₂²×C₁₁	semidirect
180. C₂×#106	C₂²×C₁₁	semidirect
181. C₂×#102	C₂²×C₁₁	semidirect
182. #407	C₂²×C₁₁	semidirect
183. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
215. C₂²×D₄	C₂³×C₁₁	semidirect
225. C₂×D₈	C₂³×C₁₁	semidirect
227. C₂×M₁₆	C₂³×C₁₁	semidirect
234. #121	C₂³×C₁₁	semidirect
238. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
242. #106	C₂³×C₁₁	semidirect
243. #102	C₂³×C₁₁	semidirect
244. C₂²⋊C₈	C₂³×C₁₁	semidirect
248. C₂×C₁₁	#3192	direct (N × H)
300. C₁₁	C₂×#3192	direct (N × H)
366. C₂	C₁₁×#3192	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×#3192	2
C₂×C₁₁×#481	2
C₂×C₁₁×#469	2
C₂×C₁₁×#447	2
C₂×C₁₁×#407	2
C₂×#3192	11

Subgroups — C2×C11×#3192 #14637928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3192 #14637928