Subgroups — C₂×C₁₁×#3200 #14637937

Order 2816.

2314 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#535	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3200	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#485	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#468	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#448	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#450	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
18	C₁₁×#536	—	2	4	no	—
19	C₁₁×#536	C₂²	1	8	yes	complemented
20	C₁₁×#535	—	2	4	no	—
21	C₁₁×#535	C₂²	1	8	yes	—
22	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
23	C₂×C₁₁×#127	—	2	1	no	—
24	C₂×C₁₁×#124	—	2	1	no	—
25	C₂×C₁₁×#124	—	2	1	no	—
26	C₂×C₁₁×#123	—	2	1	no	—
27	C₂×C₁₁×#123	—	2	1	no	—
28	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
30	C₂×C₁₁×#121	C₂²	1	2	yes	—
31	C₂×C₁₁×#121	C₂²	1	2	yes	—
32	C₂×C₁₁×#120	—	2	1	no	—
33	C₂×C₁₁×#120	—	2	1	no	—
34	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic, complemented
36	C₁₁×#485	C₂²	1	16	yes	complemented
37	C₁₁×#482	C₂²	1	16	yes	complemented
38	C₁₁×#468	C₂²	1	16	yes	complemented
39	C₁₁×#465	C₂²	1	16	yes	complemented
40	C₁₁×#450	C₂²	1	16	yes	complemented
41	C₁₁×#448	C₂²	1	16	yes	complemented
42	C₂×C₁₁×#107	C₂²	1	2	yes	complemented
43	C₂×C₁₁×#106	C₂²	1	2	yes	complemented
44	C₂×C₁₁×#103	C₂²	1	2	yes	complemented
45	C₂×C₁₁×#103	C₂²	1	2	yes	complemented
46	C₂×C₁₁×#102	C₂²	1	2	yes	—
47	C₂×C₁₁×#102	C₂²	1	2	yes	—
48	C₁₁×#408	C₂²	1	8	yes	complemented
49	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
50	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
51	C₂⁵×C₁₁	—	2	1	no	—
52	C₂×C₁₁×#41	—	4	2	no	—
53	C₂×C₁₁×#41	—	4	2	no	—
54	C₂×C₁₁×#41	D₄	1	4	yes	—
55	C₂×C₁₁×#41	C₂³	1	4	yes	—
56	C₂²×Q₈×C₁₁	—	2	1	no	—
57	C₂²×Q₈×C₁₁	—	2	2	no	—
58	C₂²×Q₈×C₁₁	—	4	2	no	—
59	C₂²×Q₈×C₁₁	—	4	2	no	—
60	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
61	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
62	C₂²×Q₈×C₁₁	C₂³	1	4	yes	complemented
63	C₂²×D₄×C₁₁	—	2	2	no	—
64	C₂²×D₄×C₁₁	—	2	2	no	—
65	C₂²×D₄×C₁₁	—	2	1	no	—
66	C₂²×D₄×C₁₁	—	2	2	no	—
67	C₂²×D₄×C₁₁	—	4	2	no	—
68	C₂²×D₄×C₁₁	—	4	2	no	—
69	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
70	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₁	—	2	1	no	—
75	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
78	C₂×C₁₁×SD₁₆	—	4	4	no	—
79	C₂×C₁₁×SD₁₆	—	4	4	no	—
80	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
81	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
82	C₂×C₁₁×M₁₆	—	4	2	no	—
83	C₂×C₁₁×M₁₆	C₂³	1	4	yes	complemented
84	C₂²×C₈×C₁₁	—	4	2	no	—
85	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
86	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
87	C₂²×C₈×C₁₁	C₂³	1	4	yes	complemented
88	C₁₁×C₄⋊Q₈	—	2	8	no	—
89	C₁₁×#127	—	2	8	no	—
90	C₁₁×#124	—	2	8	no	—
91	C₁₁×#124	—	2	8	no	—
92	C₁₁×#123	—	2	8	no	—
93	C₁₁×#123	—	2	8	no	—
94	C₁₁×C₂²⋊Q₈	—	2	4	no	—
95	C₁₁×C₂²⋊Q₈	—	2	4	no	—
96	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
97	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	complemented
98	C₁₁×#121	—	2	4	no	—
99	C₁₁×#121	—	2	4	no	—
100	C₁₁×#121	C₂³	1	8	yes	—
101	C₁₁×#121	C₂³	1	8	yes	—
102	C₁₁×#120	—	2	8	no	—
103	C₁₁×#120	—	2	8	no	—
104	C₁₁×#117	—	2	2	no	—
105	C₁₁×#117	—	2	2	no	—
106	C₁₁×#117	C₂³	1	4	yes	—
107	C₁₁×#117	C₂³	1	4	yes	complemented
108	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
109	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₄²×C₁₁	—	2	1	no	—
119	C₂×C₄²×C₁₁	—	2	1	no	—
120	C₁₁×#107	C₂³	1	8	yes	complemented
121	C₁₁×#106	C₂³	1	8	yes	complemented
122	C₁₁×#103	C₂³	1	8	yes	complemented
123	C₁₁×#103	C₂³	1	8	yes	complemented
124	C₁₁×#102	C₂³	1	8	yes	—
125	C₁₁×#102	C₂³	1	8	yes	—
126	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
127	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	complemented
128	C₂×#3200	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₁	—	2	2	no	—
130	C₂⁴×C₁₁	—	2	4	no	—
131	C₂⁴×C₁₁	—	4	4	no	—
132	C₂⁴×C₁₁	—	8	4	no	—
133	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
135	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₁₁×#41	—	4	8	no	—
137	C₁₁×#41	—	4	4	no	—
138	C₁₁×#41	—	4	4	no	—
139	C₂×Q₈×C₁₁	—	2	2	no	—
140	C₂×Q₈×C₁₁	—	2	4	no	—
141	C₂×Q₈×C₁₁	—	2	4	no	—
142	C₂×Q₈×C₁₁	—	2	4	no	—
143	C₂×Q₈×C₁₁	—	4	2	no	—
144	C₂×Q₈×C₁₁	—	4	4	no	—
145	C₂×Q₈×C₁₁	—	4	4	no	—
146	C₂×Q₈×C₁₁	—	4	4	no	—
147	C₂×Q₈×C₁₁	—	4	8	no	—
148	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
149	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
150	C₂×D₄×C₁₁	—	2	8	no	—
151	C₂×D₄×C₁₁	—	2	8	no	—
152	C₂×D₄×C₁₁	—	2	2	no	—
153	C₂×D₄×C₁₁	—	2	4	no	—
154	C₂×D₄×C₁₁	—	2	4	no	—
155	C₂×D₄×C₁₁	—	2	4	no	—
156	C₂×D₄×C₁₁	—	4	4	no	—
157	C₂×D₄×C₁₁	—	4	4	no	—
158	C₂×D₄×C₁₁	—	4	2	no	—
159	C₂×D₄×C₁₁	—	4	2	no	—
160	C₂×D₄×C₁₁	—	4	2	no	—
161	C₂×D₄×C₁₁	—	4	4	no	—
162	C₂×D₄×C₁₁	—	4	8	no	—
163	C₂×D₄×C₁₁	—	8	4	no	—
164	C₂×D₄×C₁₁	—	8	4	no	—
165	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
166	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
167	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
168	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₁₁	—	2	2	no	—
170	C₂²×C₄×C₁₁	—	2	2	no	—
171	C₂²×C₄×C₁₁	—	2	2	no	—
172	C₂²×C₄×C₁₁	—	2	2	no	—
173	C₂²×C₄×C₁₁	—	2	2	no	—
174	C₂²×C₄×C₁₁	—	2	2	no	—
175	C₂²×C₄×C₁₁	—	2	4	no	—
176	C₂²×C₄×C₁₁	—	2	2	no	—
177	C₂²×C₄×C₁₁	—	2	2	no	—
178	C₂²×C₄×C₁₁	—	2	2	no	—
179	C₂²×C₄×C₁₁	—	4	4	no	—
180	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
190	C₁₁×SD₁₆	—	4	8	no	—
191	C₁₁×SD₁₆	—	4	8	no	—
192	C₁₁×M₁₆	—	4	4	no	—
193	C₂×C₈×C₁₁	—	2	4	no	—
194	C₂×C₈×C₁₁	—	2	4	no	—
195	C₂×C₈×C₁₁	—	4	4	no	—
196	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
197	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
198	C₁₁×C₄⋊C₄	—	2	8	no	—
199	C₁₁×C₄⋊C₄	—	2	8	no	—
200	C₁₁×C₄⋊C₄	—	2	2	no	—
201	C₁₁×C₄⋊C₄	—	2	2	no	—
202	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
203	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
204	C₁₁×C₂²⋊C₄	—	2	4	no	—
205	C₁₁×C₂²⋊C₄	—	2	4	no	—
206	C₁₁×C₂²⋊C₄	—	2	8	no	—
207	C₁₁×C₂²⋊C₄	—	2	8	no	—
208	C₁₁×C₂²⋊C₄	—	2	8	no	—
209	C₁₁×C₂²⋊C₄	—	2	8	no	—
210	C₄²×C₁₁	—	2	4	no	—
211	C₄²×C₁₁	—	2	4	no	—
212	C₂×#536	C₂×C₁₁	1	1	yes	characteristic, complemented
213	C₂×#535	C₂×C₁₁	1	1	yes	characteristic
214	#3200	C₂×C₁₁	1	16	yes	direct product factor
215	C₂×#485	C₂×C₁₁	1	2	yes	complemented
216	C₂×#482	C₂×C₁₁	1	2	yes	complemented
217	C₂×#468	C₂×C₁₁	1	2	yes	complemented
218	C₂×#465	C₂×C₁₁	1	2	yes	complemented
219	C₂×#448	C₂×C₁₁	1	2	yes	complemented
220	C₂×#450	C₂×C₁₁	1	2	yes	complemented
221	C₂×#408	C₂×C₁₁	1	1	yes	characteristic, complemented
222	C₂³×C₁₁	—	2	2	no	—
223	C₂³×C₁₁	—	2	2	no	—
224	C₂³×C₁₁	—	2	2	no	—
225	C₂³×C₁₁	—	2	4	no	—
226	C₂³×C₁₁	—	2	4	no	—
227	C₂³×C₁₁	—	2	4	no	—
228	C₂³×C₁₁	—	2	4	no	—
229	C₂³×C₁₁	—	4	8	no	—
230	C₂³×C₁₁	—	4	4	no	—
231	C₂³×C₁₁	—	4	4	no	—
232	C₂³×C₁₁	—	4	4	no	—
233	C₂³×C₁₁	—	8	8	no	—
234	C₂³×C₁₁	—	8	16	no	—
235	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
236	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
237	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
238	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₁	—	2	4	no	—
240	Q₈×C₁₁	—	2	4	no	—
241	Q₈×C₁₁	—	4	4	no	—
242	Q₈×C₁₁	—	4	8	no	—
243	Q₈×C₁₁	—	4	4	no	—
244	D₄×C₁₁	—	2	4	no	—
245	D₄×C₁₁	—	2	4	no	—
246	D₄×C₁₁	—	4	4	no	—
247	D₄×C₁₁	—	4	4	no	—
248	D₄×C₁₁	—	4	4	no	—
249	D₄×C₁₁	—	4	8	no	—
250	D₄×C₁₁	—	4	4	no	—
251	D₄×C₁₁	—	8	8	no	—
252	D₄×C₁₁	—	8	8	no	—
253	C₂×C₄×C₁₁	—	2	2	no	—
254	C₂×C₄×C₁₁	—	2	2	no	—
255	C₂×C₄×C₁₁	—	2	2	no	—
256	C₂×C₄×C₁₁	—	2	4	no	—
257	C₂×C₄×C₁₁	—	2	4	no	—
258	C₂×C₄×C₁₁	—	2	4	no	—
259	C₂×C₄×C₁₁	—	2	2	no	—
260	C₂×C₄×C₁₁	—	2	2	no	—
261	C₂×C₄×C₁₁	—	2	2	no	—
262	C₂×C₄×C₁₁	—	2	2	no	—
263	C₂×C₄×C₁₁	—	2	2	no	—
264	C₂×C₄×C₁₁	—	2	2	no	—
265	C₂×C₄×C₁₁	—	2	4	no	—
266	C₂×C₄×C₁₁	—	2	4	no	—
267	C₂×C₄×C₁₁	—	2	4	no	—
268	C₂×C₄×C₁₁	—	4	8	no	—
269	C₂×C₄×C₁₁	—	4	4	no	—
270	C₂×C₄×C₁₁	—	4	4	no	—
271	C₂×C₄×C₁₁	—	4	4	no	—
272	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
277	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
278	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
279	C₈×C₁₁	—	2	4	no	—
280	C₈×C₁₁	—	2	4	no	—
281	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
282	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
283	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
284	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
285	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
286	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
287	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
288	#536	—	2	4	no	—
289	#536	C₂²×C₁₁	1	8	yes	complemented
290	#535	—	2	4	no	—
291	#535	C₂²×C₁₁	1	8	yes	—
292	C₂×C₄⋊Q₈	—	2	1	no	—
293	C₂×#127	—	2	1	no	—
294	C₂×#124	—	2	1	no	—
295	C₂×#124	—	2	1	no	—
296	C₂×#123	—	2	1	no	—
297	C₂×#123	—	2	1	no	—
298	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
299	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
300	C₂×#121	C₂²×C₁₁	1	2	yes	—
301	C₂×#121	C₂²×C₁₁	1	2	yes	—
302	C₂×#120	—	2	1	no	—
303	C₂×#120	—	2	1	no	—
304	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
305	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic, complemented
306	#485	C₂²×C₁₁	1	16	yes	complemented
307	#482	C₂²×C₁₁	1	16	yes	complemented
308	#468	C₂²×C₁₁	1	16	yes	complemented
309	#465	C₂²×C₁₁	1	16	yes	complemented
310	#450	C₂²×C₁₁	1	16	yes	complemented
311	#448	C₂²×C₁₁	1	16	yes	complemented
312	C₂×#107	C₂²×C₁₁	1	2	yes	complemented
313	C₂×#106	C₂²×C₁₁	1	2	yes	complemented
314	C₂×#103	C₂²×C₁₁	1	2	yes	complemented
315	C₂×#103	C₂²×C₁₁	1	2	yes	complemented
316	C₂×#102	C₂²×C₁₁	1	2	yes	—
317	C₂×#102	C₂²×C₁₁	1	2	yes	—
318	#408	C₂²×C₁₁	1	8	yes	complemented
319	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
320	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	complemented
321	C₂²×C₁₁	—	2	2	no	—
322	C₂²×C₁₁	—	2	2	no	—
323	C₂²×C₁₁	—	2	2	no	—
324	C₂²×C₁₁	—	2	4	no	—
325	C₂²×C₁₁	—	2	4	no	—
326	C₂²×C₁₁	—	2	4	no	—
327	C₂²×C₁₁	—	4	4	no	—
328	C₂²×C₁₁	—	4	4	no	—
329	C₂²×C₁₁	—	4	4	no	—
330	C₂²×C₁₁	—	4	4	no	—
331	C₂²×C₁₁	—	4	4	no	—
332	C₂²×C₁₁	—	4	4	no	—
333	C₂²×C₁₁	—	8	16	no	—
334	C₂²×C₁₁	—	8	8	no	—
335	C₂²×C₁₁	#534	1	2	yes	—
336	C₂²×C₁₁	#577	1	4	yes	—
337	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
338	C₄×C₁₁	—	2	2	no	—
339	C₄×C₁₁	—	2	2	no	—
340	C₄×C₁₁	—	2	2	no	—
341	C₄×C₁₁	—	4	4	no	—
342	C₄×C₁₁	—	4	4	no	—
343	C₄×C₁₁	—	4	4	no	—
344	C₄×C₁₁	#534	1	2	yes	—
345	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂⁵	—	2	1	no	—
348	C₂×#41	—	4	2	no	—
349	C₂×#41	—	4	2	no	—
350	C₂×#41	D₄×C₁₁	1	4	yes	—
351	C₂×#41	C₂³×C₁₁	1	4	yes	—
352	C₂²×Q₈	—	2	1	no	—
353	C₂²×Q₈	—	2	2	no	—
354	C₂²×Q₈	—	4	2	no	—
355	C₂²×Q₈	—	4	2	no	—
356	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
357	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
358	C₂²×Q₈	C₂³×C₁₁	1	4	yes	complemented
359	C₂²×D₄	—	2	2	no	—
360	C₂²×D₄	—	2	2	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	—	2	2	no	—
363	C₂²×D₄	—	4	2	no	—
364	C₂²×D₄	—	4	2	no	—
365	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
366	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
367	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
369	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
374	C₂×SD₁₆	—	4	4	no	—
375	C₂×SD₁₆	—	4	4	no	—
376	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
377	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
378	C₂×M₁₆	—	4	2	no	—
379	C₂×M₁₆	C₂³×C₁₁	1	4	yes	complemented
380	C₂²×C₈	—	4	2	no	—
381	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
382	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
383	C₂²×C₈	C₂³×C₁₁	1	4	yes	complemented
384	C₄⋊Q₈	—	2	8	no	—
385	#127	—	2	8	no	—
386	#124	—	2	8	no	—
387	#124	—	2	8	no	—
388	#123	—	2	8	no	—
389	#123	—	2	8	no	—
390	C₂²⋊Q₈	—	2	4	no	—
391	C₂²⋊Q₈	—	2	4	no	—
392	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
393	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	complemented
394	#121	—	2	4	no	—
395	#121	—	2	4	no	—
396	#121	C₂³×C₁₁	1	8	yes	—
397	#121	C₂³×C₁₁	1	8	yes	—
398	#120	—	2	8	no	—
399	#120	—	2	8	no	—
400	#117	—	2	2	no	—
401	#117	—	2	2	no	—
402	#117	C₂³×C₁₁	1	4	yes	—
403	#117	C₂³×C₁₁	1	4	yes	complemented
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	2	no	—
411	C₂×C₂²⋊C₄	—	2	2	no	—
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	—	2	2	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	#107	C₂³×C₁₁	1	8	yes	complemented
417	#106	C₂³×C₁₁	1	8	yes	complemented
418	#103	C₂³×C₁₁	1	8	yes	complemented
419	#103	C₂³×C₁₁	1	8	yes	complemented
420	#102	C₂³×C₁₁	1	8	yes	—
421	#102	C₂³×C₁₁	1	8	yes	—
422	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
423	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	complemented
424	C₂×C₁₁	—	4	2	no	—
425	C₂×C₁₁	—	4	2	no	—
426	C₂×C₁₁	—	4	2	no	—
427	C₂×C₁₁	—	8	4	no	—
428	C₂×C₁₁	#3200	1	4	yes	direct product factor
429	C₂×C₁₁	C₂×#534	1	1	yes	characteristic
430	C₂×C₁₁	C₂×#577	1	2	yes	—
431	C₂⁴	—	2	2	no	—
432	C₂⁴	—	2	4	no	—
433	C₂⁴	—	4	4	no	—
434	C₂⁴	—	8	4	no	—
435	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
436	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
437	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
438	#41	—	4	8	no	—
439	#41	—	4	4	no	—
440	#41	—	4	4	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	4	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	—	4	4	no	—
447	C₂×Q₈	—	4	4	no	—
448	C₂×Q₈	—	4	4	no	—
449	C₂×Q₈	—	4	8	no	—
450	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
451	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	4	2	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	—	4	2	no	—
463	C₂×D₄	—	4	4	no	—
464	C₂×D₄	—	4	8	no	—
465	C₂×D₄	—	8	4	no	—
466	C₂×D₄	—	8	4	no	—
467	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
468	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
469	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
470	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
486	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
487	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
492	SD₁₆	—	4	8	no	—
493	SD₁₆	—	4	8	no	—
494	M₁₆	—	4	4	no	—
495	C₂×C₈	—	2	4	no	—
496	C₂×C₈	—	2	4	no	—
497	C₂×C₈	—	4	4	no	—
498	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
499	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
500	C₄⋊C₄	—	2	8	no	—
501	C₄⋊C₄	—	2	8	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
505	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	8	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₄²	—	2	4	no	—
513	C₄²	—	2	4	no	—
514	C₁₁	C₂×#3200	1	1	yes	characteristic, direct product factor, Sylow
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	4	8	no	—
523	C₂³	—	4	4	no	—
524	C₂³	—	4	4	no	—
525	C₂³	—	4	4	no	—
526	C₂³	—	8	8	no	—
527	C₂³	—	8	16	no	—
528	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
529	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
530	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
531	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
532	Q₈	—	2	4	no	—
533	Q₈	—	2	4	no	—
534	Q₈	—	4	4	no	—
535	Q₈	—	4	8	no	—
536	Q₈	—	4	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	4	4	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	4	no	—
542	D₄	—	4	8	no	—
543	D₄	—	4	4	no	—
544	D₄	—	8	8	no	—
545	D₄	—	8	8	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	4	8	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
568	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
569	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
570	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
571	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
572	C₈	—	2	4	no	—
573	C₈	—	2	4	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	8	16	no	—
587	C₂²	—	8	8	no	—
588	C₂²	C₁₁×#534	1	2	yes	—
589	C₂²	C₁₁×#577	1	4	yes	—
590	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	4	no	—
596	C₄	—	4	4	no	—
597	C₄	C₁₁×#534	1	2	yes	—
598	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
599	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂	—	4	2	no	—
601	C₂	—	4	2	no	—
602	C₂	—	4	2	no	—
603	C₂	—	8	4	no	—
604	C₂	C₁₁×#3200	1	4	yes	direct product factor
605	C₂	C₂×C₁₁×#534	1	1	yes	characteristic
606	C₂	C₂×C₁₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#535	C₂
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×#536	C₂	semidirect
3. C₁₁×#3200	C₂	direct (N × H)
4. C₂×C₁₁×#485	C₂	semidirect
5. C₂×C₁₁×#482	C₂	semidirect
6. C₂×C₁₁×#468	C₂	semidirect
7. C₂×C₁₁×#465	C₂	semidirect
8. C₂×C₁₁×#448	C₂	semidirect
9. C₂×C₁₁×#450	C₂	semidirect
10. C₂×C₁₁×#408	C₂	semidirect
12. C₂³×Q₈×C₁₁	C₂²	semidirect
16. C₂²×C₁₁×M₁₆	C₂²	semidirect
17. C₂³×C₈×C₁₁	C₂²	semidirect
19. C₁₁×#536	C₂²	semidirect
29. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
35. C₂×C₁₁×#117	C₂²	semidirect
36. C₁₁×#485	C₂²	semidirect
37. C₁₁×#482	C₂²	semidirect
38. C₁₁×#468	C₂²	semidirect
39. C₁₁×#465	C₂²	semidirect
40. C₁₁×#450	C₂²	semidirect
41. C₁₁×#448	C₂²	semidirect
42. C₂×C₁₁×#107	C₂²	semidirect
43. C₂×C₁₁×#106	C₂²	semidirect
44. C₂×C₁₁×#103	C₂²	semidirect
45. C₂×C₁₁×#103	C₂²	semidirect
48. C₁₁×#408	C₂²	semidirect
50. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
62. C₂²×Q₈×C₁₁	C₂³	semidirect
83. C₂×C₁₁×M₁₆	C₂³	semidirect
87. C₂²×C₈×C₁₁	C₂³	semidirect
97. C₁₁×C₂²⋊Q₈	C₂³	semidirect
107. C₁₁×#117	C₂³	semidirect
120. C₁₁×#107	C₂³	semidirect
121. C₁₁×#106	C₂³	semidirect
122. C₁₁×#103	C₂³	semidirect
123. C₁₁×#103	C₂³	semidirect
127. C₁₁×C₂²⋊C₈	C₂³	semidirect
128. C₂×#3200	C₁₁	direct (N × H)
212. C₂×#536	C₂×C₁₁	semidirect
214. #3200	C₂×C₁₁	direct (N × H)
215. C₂×#485	C₂×C₁₁	semidirect
216. C₂×#482	C₂×C₁₁	semidirect
217. C₂×#468	C₂×C₁₁	semidirect
218. C₂×#465	C₂×C₁₁	semidirect
219. C₂×#448	C₂×C₁₁	semidirect
220. C₂×#450	C₂×C₁₁	semidirect
221. C₂×#408	C₂×C₁₁	semidirect
282. C₂³×Q₈	C₂²×C₁₁	semidirect
286. C₂²×M₁₆	C₂²×C₁₁	semidirect
287. C₂³×C₈	C₂²×C₁₁	semidirect
289. #536	C₂²×C₁₁	semidirect
299. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
305. C₂×#117	C₂²×C₁₁	semidirect
306. #485	C₂²×C₁₁	semidirect
307. #482	C₂²×C₁₁	semidirect
308. #468	C₂²×C₁₁	semidirect
309. #465	C₂²×C₁₁	semidirect
310. #450	C₂²×C₁₁	semidirect
311. #448	C₂²×C₁₁	semidirect
312. C₂×#107	C₂²×C₁₁	semidirect
313. C₂×#106	C₂²×C₁₁	semidirect
314. C₂×#103	C₂²×C₁₁	semidirect
315. C₂×#103	C₂²×C₁₁	semidirect
318. #408	C₂²×C₁₁	semidirect
320. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
358. C₂²×Q₈	C₂³×C₁₁	semidirect
379. C₂×M₁₆	C₂³×C₁₁	semidirect
383. C₂²×C₈	C₂³×C₁₁	semidirect
393. C₂²⋊Q₈	C₂³×C₁₁	semidirect
403. #117	C₂³×C₁₁	semidirect
416. #107	C₂³×C₁₁	semidirect
417. #106	C₂³×C₁₁	semidirect
418. #103	C₂³×C₁₁	semidirect
419. #103	C₂³×C₁₁	semidirect
423. C₂²⋊C₈	C₂³×C₁₁	semidirect
428. C₂×C₁₁	#3200	direct (N × H)
514. C₁₁	C₂×#3200	direct (N × H)
604. C₂	C₁₁×#3200	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×#536	2
C₂×C₁₁×#535	2
C₁₁×#3200	2
C₂×C₁₁×#485	2
C₂×C₁₁×#482	2
C₂×C₁₁×#468	2
C₂×C₁₁×#465	2
C₂×C₁₁×#448	2
C₂×C₁₁×#450	2
C₂×C₁₁×#408	2
C₂×#3200	11

Subgroups — C2×C11×#3200 #14637937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3200 #14637937