Subgroups — C₂×C₁₁×#3199 #14637936

Order 2816.

2506 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#535	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3199	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#482	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#469	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#466	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#447	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₁	C₂²	1	2	yes	complemented
10	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
11	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
12	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
14	C₁₁×#535	—	2	8	no	—
15	C₁₁×#535	C₂²	1	16	yes	complemented
16	C₂×C₁₁×#127	—	2	2	no	—
17	C₂×C₁₁×#124	—	2	2	no	—
18	C₂×C₁₁×#121	C₂²	1	4	yes	—
19	C₂×C₁₁×#121	C₂²	1	4	yes	complemented
20	C₂×C₁₁×#120	—	2	2	no	—
21	C₂×C₁₁×#120	—	2	2	no	—
22	C₂×C₁₁×#117	C₂²	1	2	yes	complemented
23	C₁₁×#482	C₂²	1	32	yes	complemented
24	C₁₁×#469	C₂²	1	16	yes	complemented
25	C₁₁×#466	C₂²	1	16	yes	complemented
26	C₁₁×#447	C₂²	1	32	yes	complemented
27	C₂×C₁₁×#107	C₂²	1	2	yes	complemented
28	C₂×C₁₁×#106	C₂²	1	2	yes	complemented
29	C₂×C₁₁×#102	C₂²	1	4	yes	complemented
30	C₂×C₁₁×#102	C₂²	1	4	yes	complemented
31	C₁₁×#408	C₂²	1	8	yes	complemented
32	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	complemented
33	C₂⁵×C₁₁	—	2	2	no	—
34	C₂×C₁₁×#41	—	4	2	no	—
35	C₂×C₁₁×#41	—	4	2	no	—
36	C₂×C₁₁×#41	D₄	1	4	yes	—
37	C₂×C₁₁×#41	C₂³	1	4	yes	—
38	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₁	—	2	4	no	—
40	C₂²×D₄×C₁₁	—	2	4	no	—
41	C₂²×D₄×C₁₁	—	2	2	no	—
42	C₂²×D₄×C₁₁	—	2	4	no	—
43	C₂²×D₄×C₁₁	—	4	4	no	—
44	C₂²×D₄×C₁₁	—	4	4	no	—
45	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₁	D₄	1	2	yes	—
47	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
48	C₂²×D₄×C₁₁	C₂³	1	8	yes	complemented
49	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
51	C₂×C₁₁×D₈	—	4	4	no	—
52	C₂×C₁₁×D₈	—	4	4	no	—
53	C₂×C₁₁×D₈	C₂³	1	8	yes	—
54	C₂×C₁₁×D₈	C₂³	1	8	yes	—
55	C₂×C₁₁×M₁₆	—	4	2	no	—
56	C₂×C₁₁×M₁₆	C₂³	1	4	yes	complemented
57	C₂²×C₈×C₁₁	—	4	2	no	—
58	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₁	C₂³	1	4	yes	complemented
61	C₁₁×#127	—	2	16	no	—
62	C₁₁×#124	—	2	16	no	—
63	C₁₁×#121	—	2	8	no	—
64	C₁₁×#121	—	2	8	no	—
65	C₁₁×#121	C₂³	1	16	yes	—
66	C₁₁×#121	C₂³	1	16	yes	complemented
67	C₁₁×#120	—	2	16	no	—
68	C₁₁×#120	—	2	16	no	—
69	C₁₁×#117	—	2	4	no	—
70	C₁₁×#117	C₂³	1	8	yes	complemented
71	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₄²×C₁₁	—	2	2	no	—
76	C₁₁×#107	C₂³	1	8	yes	complemented
77	C₁₁×#106	C₂³	1	8	yes	complemented
78	C₁₁×#102	C₂³	1	16	yes	complemented
79	C₁₁×#102	C₂³	1	16	yes	complemented
80	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
81	C₂×#3199	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₁	—	2	4	no	—
83	C₂⁴×C₁₁	—	2	8	no	—
84	C₂⁴×C₁₁	—	4	8	no	—
85	C₂⁴×C₁₁	—	8	8	no	—
86	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
87	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₁₁×#41	—	4	8	no	—
89	C₁₁×#41	—	4	4	no	—
90	C₁₁×#41	—	4	4	no	—
91	C₂×Q₈×C₁₁	—	4	2	no	—
92	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
93	C₂×D₄×C₁₁	—	2	16	no	—
94	C₂×D₄×C₁₁	—	2	16	no	—
95	C₂×D₄×C₁₁	—	2	4	no	—
96	C₂×D₄×C₁₁	—	2	8	no	—
97	C₂×D₄×C₁₁	—	2	8	no	—
98	C₂×D₄×C₁₁	—	2	8	no	—
99	C₂×D₄×C₁₁	—	4	8	no	—
100	C₂×D₄×C₁₁	—	4	8	no	—
101	C₂×D₄×C₁₁	—	4	4	no	—
102	C₂×D₄×C₁₁	—	4	2	no	—
103	C₂×D₄×C₁₁	—	4	8	no	—
104	C₂×D₄×C₁₁	—	4	16	no	—
105	C₂×D₄×C₁₁	—	8	8	no	—
106	C₂×D₄×C₁₁	—	8	8	no	—
107	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
108	C₂×D₄×C₁₁	C₂×D₄	1	8	yes	—
109	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
110	C₂²×C₄×C₁₁	—	2	2	no	—
111	C₂²×C₄×C₁₁	—	2	2	no	—
112	C₂²×C₄×C₁₁	—	2	4	no	—
113	C₂²×C₄×C₁₁	—	2	4	no	—
114	C₂²×C₄×C₁₁	—	2	4	no	—
115	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
122	C₁₁×D₈	—	4	8	no	—
123	C₁₁×D₈	—	4	8	no	—
124	C₁₁×M₁₆	—	4	4	no	—
125	C₂×C₈×C₁₁	—	2	4	no	—
126	C₂×C₈×C₁₁	—	2	4	no	—
127	C₂×C₈×C₁₁	—	4	4	no	—
128	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
129	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
130	C₁₁×C₄⋊C₄	—	2	4	no	—
131	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
132	C₁₁×C₂²⋊C₄	—	2	8	no	—
133	C₁₁×C₂²⋊C₄	—	2	16	no	—
134	C₁₁×C₂²⋊C₄	—	2	16	no	—
135	C₄²×C₁₁	—	2	8	no	—
136	C₂×#535	C₂×C₁₁	1	2	yes	complemented
137	#3199	C₂×C₁₁	1	16	yes	direct product factor
138	C₂×#482	C₂×C₁₁	1	4	yes	complemented
139	C₂×#469	C₂×C₁₁	1	2	yes	complemented
140	C₂×#466	C₂×C₁₁	1	2	yes	complemented
141	C₂×#447	C₂×C₁₁	1	4	yes	complemented
142	C₂×#408	C₂×C₁₁	1	1	yes	characteristic, complemented
143	C₂³×C₁₁	—	2	4	no	—
144	C₂³×C₁₁	—	2	2	no	—
145	C₂³×C₁₁	—	2	4	no	—
146	C₂³×C₁₁	—	2	8	no	—
147	C₂³×C₁₁	—	2	8	no	—
148	C₂³×C₁₁	—	4	16	no	—
149	C₂³×C₁₁	—	4	8	no	—
150	C₂³×C₁₁	—	4	8	no	—
151	C₂³×C₁₁	—	4	8	no	—
152	C₂³×C₁₁	—	8	16	no	—
153	C₂³×C₁₁	—	8	32	no	—
154	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
155	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
156	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₁	—	4	4	no	—
158	D₄×C₁₁	—	2	8	no	—
159	D₄×C₁₁	—	2	8	no	—
160	D₄×C₁₁	—	4	8	no	—
161	D₄×C₁₁	—	4	4	no	—
162	D₄×C₁₁	—	4	16	no	—
163	D₄×C₁₁	—	4	8	no	—
164	D₄×C₁₁	—	8	16	no	—
165	D₄×C₁₁	—	8	16	no	—
166	C₂×C₄×C₁₁	—	2	4	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	8	no	—
169	C₂×C₄×C₁₁	—	2	4	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	4	no	—
173	C₂×C₄×C₁₁	—	2	4	no	—
174	C₂×C₄×C₁₁	—	2	8	no	—
175	C₂×C₄×C₁₁	—	4	8	no	—
176	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
177	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
180	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
181	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
182	C₈×C₁₁	—	2	4	no	—
183	C₈×C₁₁	—	2	4	no	—
184	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
185	C₂³×D₄	C₂²×C₁₁	1	2	yes	complemented
186	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
187	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
188	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
189	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
190	#535	—	2	8	no	—
191	#535	C₂²×C₁₁	1	16	yes	complemented
192	C₂×#127	—	2	2	no	—
193	C₂×#124	—	2	2	no	—
194	C₂×#121	C₂²×C₁₁	1	4	yes	—
195	C₂×#121	C₂²×C₁₁	1	4	yes	complemented
196	C₂×#120	—	2	2	no	—
197	C₂×#120	—	2	2	no	—
198	C₂×#117	C₂²×C₁₁	1	2	yes	complemented
199	#482	C₂²×C₁₁	1	32	yes	complemented
200	#469	C₂²×C₁₁	1	16	yes	complemented
201	#466	C₂²×C₁₁	1	16	yes	complemented
202	#447	C₂²×C₁₁	1	32	yes	complemented
203	C₂×#107	C₂²×C₁₁	1	2	yes	complemented
204	C₂×#106	C₂²×C₁₁	1	2	yes	complemented
205	C₂×#102	C₂²×C₁₁	1	4	yes	complemented
206	C₂×#102	C₂²×C₁₁	1	4	yes	complemented
207	#408	C₂²×C₁₁	1	8	yes	complemented
208	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	complemented
209	C₂²×C₁₁	—	2	4	no	—
210	C₂²×C₁₁	—	2	2	no	—
211	C₂²×C₁₁	—	2	4	no	—
212	C₂²×C₁₁	—	2	8	no	—
213	C₂²×C₁₁	—	4	4	no	—
214	C₂²×C₁₁	—	4	8	no	—
215	C₂²×C₁₁	—	4	8	no	—
216	C₂²×C₁₁	—	4	8	no	—
217	C₂²×C₁₁	—	4	8	no	—
218	C₂²×C₁₁	—	8	32	no	—
219	C₂²×C₁₁	—	8	16	no	—
220	C₂²×C₁₁	#534	1	2	yes	—
221	C₂²×C₁₁	#576	1	4	yes	—
222	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
223	C₄×C₁₁	—	2	4	no	—
224	C₄×C₁₁	—	2	2	no	—
225	C₄×C₁₁	—	4	8	no	—
226	C₄×C₁₁	#534	1	2	yes	—
227	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
228	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂⁵	—	2	2	no	—
230	C₂×#41	—	4	2	no	—
231	C₂×#41	—	4	2	no	—
232	C₂×#41	D₄×C₁₁	1	4	yes	—
233	C₂×#41	C₂³×C₁₁	1	4	yes	—
234	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
235	C₂²×D₄	—	2	4	no	—
236	C₂²×D₄	—	2	4	no	—
237	C₂²×D₄	—	2	2	no	—
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	4	4	no	—
240	C₂²×D₄	—	4	4	no	—
241	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
242	C₂²×D₄	D₄×C₁₁	1	2	yes	—
243	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
244	C₂²×D₄	C₂³×C₁₁	1	8	yes	complemented
245	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
246	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
247	C₂×D₈	—	4	4	no	—
248	C₂×D₈	—	4	4	no	—
249	C₂×D₈	C₂³×C₁₁	1	8	yes	—
250	C₂×D₈	C₂³×C₁₁	1	8	yes	—
251	C₂×M₁₆	—	4	2	no	—
252	C₂×M₁₆	C₂³×C₁₁	1	4	yes	complemented
253	C₂²×C₈	—	4	2	no	—
254	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
256	C₂²×C₈	C₂³×C₁₁	1	4	yes	complemented
257	#127	—	2	16	no	—
258	#124	—	2	16	no	—
259	#121	—	2	8	no	—
260	#121	—	2	8	no	—
261	#121	C₂³×C₁₁	1	16	yes	—
262	#121	C₂³×C₁₁	1	16	yes	complemented
263	#120	—	2	16	no	—
264	#120	—	2	16	no	—
265	#117	—	2	4	no	—
266	#117	C₂³×C₁₁	1	8	yes	complemented
267	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	4	no	—
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	C₂×C₄²	—	2	2	no	—
272	#107	C₂³×C₁₁	1	8	yes	complemented
273	#106	C₂³×C₁₁	1	8	yes	complemented
274	#102	C₂³×C₁₁	1	16	yes	complemented
275	#102	C₂³×C₁₁	1	16	yes	complemented
276	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	complemented
277	C₂×C₁₁	—	4	2	no	—
278	C₂×C₁₁	—	4	4	no	—
279	C₂×C₁₁	—	8	8	no	—
280	C₂×C₁₁	#3199	1	4	yes	direct product factor
281	C₂×C₁₁	C₂×#534	1	1	yes	characteristic
282	C₂×C₁₁	C₂×#576	1	2	yes	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	—	2	8	no	—
285	C₂⁴	—	4	8	no	—
286	C₂⁴	—	8	8	no	—
287	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
288	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
289	#41	—	4	8	no	—
290	#41	—	4	4	no	—
291	#41	—	4	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
294	C₂×D₄	—	2	16	no	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	4	8	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	8	no	—
305	C₂×D₄	—	4	16	no	—
306	C₂×D₄	—	8	8	no	—
307	C₂×D₄	—	8	8	no	—
308	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
309	C₂×D₄	C₂×D₄×C₁₁	1	8	yes	—
310	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
319	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
321	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
322	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
323	D₈	—	4	8	no	—
324	D₈	—	4	8	no	—
325	M₁₆	—	4	4	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	4	4	no	—
329	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
330	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
333	C₂²⋊C₄	—	2	8	no	—
334	C₂²⋊C₄	—	2	16	no	—
335	C₂²⋊C₄	—	2	16	no	—
336	C₄²	—	2	8	no	—
337	C₁₁	C₂×#3199	1	1	yes	characteristic, direct product factor, Sylow
338	C₂³	—	2	4	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	4	16	no	—
344	C₂³	—	4	8	no	—
345	C₂³	—	4	8	no	—
346	C₂³	—	4	8	no	—
347	C₂³	—	8	16	no	—
348	C₂³	—	8	32	no	—
349	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
350	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
351	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
352	Q₈	—	4	4	no	—
353	D₄	—	2	8	no	—
354	D₄	—	2	8	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	D₄	—	4	16	no	—
358	D₄	—	4	8	no	—
359	D₄	—	8	16	no	—
360	D₄	—	8	16	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
372	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
374	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
376	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	8	no	—
383	C₂²	—	4	8	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	8	32	no	—
389	C₂²	—	8	16	no	—
390	C₂²	C₁₁×#534	1	2	yes	—
391	C₂²	C₁₁×#576	1	4	yes	—
392	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	8	no	—
396	C₄	C₁₁×#534	1	2	yes	—
397	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
398	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂	—	4	4	no	—
400	C₂	—	4	2	no	—
401	C₂	—	8	8	no	—
402	C₂	C₁₁×#3199	1	4	yes	direct product factor
403	C₂	C₂×C₁₁×#534	1	1	yes	characteristic
404	C₂	C₂×C₁₁×#576	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 ◁ C₂²×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#535	C₂	semidirect
2. C₁₁×#3199	C₂	direct (N × H)
3. C₂×C₁₁×#482	C₂	semidirect
4. C₂×C₁₁×#469	C₂	semidirect
5. C₂×C₁₁×#466	C₂	semidirect
6. C₂×C₁₁×#447	C₂	semidirect
7. C₂×C₁₁×#408	C₂	semidirect
9. C₂³×D₄×C₁₁	C₂²	semidirect
12. C₂²×C₁₁×M₁₆	C₂²	semidirect
13. C₂³×C₈×C₁₁	C₂²	semidirect
15. C₁₁×#535	C₂²	semidirect
19. C₂×C₁₁×#121	C₂²	semidirect
22. C₂×C₁₁×#117	C₂²	semidirect
23. C₁₁×#482	C₂²	semidirect
24. C₁₁×#469	C₂²	semidirect
25. C₁₁×#466	C₂²	semidirect
26. C₁₁×#447	C₂²	semidirect
27. C₂×C₁₁×#107	C₂²	semidirect
28. C₂×C₁₁×#106	C₂²	semidirect
29. C₂×C₁₁×#102	C₂²	semidirect
30. C₂×C₁₁×#102	C₂²	semidirect
31. C₁₁×#408	C₂²	semidirect
32. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
48. C₂²×D₄×C₁₁	C₂³	semidirect
56. C₂×C₁₁×M₁₆	C₂³	semidirect
60. C₂²×C₈×C₁₁	C₂³	semidirect
66. C₁₁×#121	C₂³	semidirect
70. C₁₁×#117	C₂³	semidirect
76. C₁₁×#107	C₂³	semidirect
77. C₁₁×#106	C₂³	semidirect
78. C₁₁×#102	C₂³	semidirect
79. C₁₁×#102	C₂³	semidirect
80. C₁₁×C₂²⋊C₈	C₂³	semidirect
81. C₂×#3199	C₁₁	direct (N × H)
136. C₂×#535	C₂×C₁₁	semidirect
137. #3199	C₂×C₁₁	direct (N × H)
138. C₂×#482	C₂×C₁₁	semidirect
139. C₂×#469	C₂×C₁₁	semidirect
140. C₂×#466	C₂×C₁₁	semidirect
141. C₂×#447	C₂×C₁₁	semidirect
142. C₂×#408	C₂×C₁₁	semidirect
185. C₂³×D₄	C₂²×C₁₁	semidirect
188. C₂²×M₁₆	C₂²×C₁₁	semidirect
189. C₂³×C₈	C₂²×C₁₁	semidirect
191. #535	C₂²×C₁₁	semidirect
195. C₂×#121	C₂²×C₁₁	semidirect
198. C₂×#117	C₂²×C₁₁	semidirect
199. #482	C₂²×C₁₁	semidirect
200. #469	C₂²×C₁₁	semidirect
201. #466	C₂²×C₁₁	semidirect
202. #447	C₂²×C₁₁	semidirect
203. C₂×#107	C₂²×C₁₁	semidirect
204. C₂×#106	C₂²×C₁₁	semidirect
205. C₂×#102	C₂²×C₁₁	semidirect
206. C₂×#102	C₂²×C₁₁	semidirect
207. #408	C₂²×C₁₁	semidirect
208. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
244. C₂²×D₄	C₂³×C₁₁	semidirect
252. C₂×M₁₆	C₂³×C₁₁	semidirect
256. C₂²×C₈	C₂³×C₁₁	semidirect
262. #121	C₂³×C₁₁	semidirect
266. #117	C₂³×C₁₁	semidirect
272. #107	C₂³×C₁₁	semidirect
273. #106	C₂³×C₁₁	semidirect
274. #102	C₂³×C₁₁	semidirect
275. #102	C₂³×C₁₁	semidirect
276. C₂²⋊C₈	C₂³×C₁₁	semidirect
280. C₂×C₁₁	#3199	direct (N × H)
337. C₁₁	C₂×#3199	direct (N × H)
402. C₂	C₁₁×#3199	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₁×#535	2
C₁₁×#3199	2
C₂×C₁₁×#482	2
C₂×C₁₁×#469	2
C₂×C₁₁×#466	2
C₂×C₁₁×#447	2
C₂×C₁₁×#408	2
C₂×#3199	11

Subgroups — C2×C11×#3199 #14637936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3199 #14637936