Subgroups — C₁₁×#60597 #14637790

Order 2816.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₁×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3125	C₂	1	4	yes	maximal, complemented
4	C₁₁×#3118	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3116	C₂	1	2	yes	maximal, complemented
6	C₁₁×#3109	C₂	1	2	yes	maximal, complemented
7	C₁₁×#3106	C₂	1	2	yes	maximal, complemented
8	C₁₁×#3101	C₂	1	2	yes	maximal, complemented
9	C₁₁×#3099	C₂	1	2	yes	maximal, complemented
10	C₁₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#3012	C₂	1	2	yes	maximal, complemented
15	C₁₁×#2952	C₂	1	2	yes	maximal, complemented
16	C₁₁×#2946	C₂	1	2	yes	maximal, complemented
17	C₁₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₁₁×#135	C₂²	1	2	yes	—
21	C₁₁×#556	—	2	1	no	—
22	C₁₁×#555	—	2	1	no	—
23	C₁₁×#554	—	2	1	no	—
24	C₁₁×#553	—	2	2	no	—
25	C₁₁×#548	—	2	2	no	—
26	C₁₁×#547	—	2	1	no	—
27	C₁₁×#542	C₂²	1	4	yes	complemented
28	C₁₁×#537	C₂²	1	2	yes	—
29	C₁₁×#533	C₂²	1	2	yes	complemented
30	C₁₁×#532	C₂²	1	1	yes	characteristic, complemented
31	C₁₁×#532	C₂²	1	2	yes	complemented
32	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₁×#520	—	2	1	no	—
34	C₁₁×#520	C₂²	1	1	yes	characteristic
35	C₁₁×#520	C₂²	1	2	yes	—
36	C₁₁×#520	C₂²	1	1	yes	characteristic
37	C₁₁×#520	C₂²	1	2	yes	complemented
38	C₁₁×#518	—	2	1	no	—
39	C₁₁×#518	—	2	2	no	—
40	C₁₁×#518	C₂²	1	1	yes	characteristic
41	C₁₁×#518	C₂²	1	2	yes	—
42	C₄×C₁₁×#41	—	2	1	no	—
43	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
44	C₄×C₁₁×#41	C₂²	1	2	yes	—
45	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₁₁	—	2	2	no	—
47	C₂×C₄×D₄×C₁₁	—	2	1	no	—
48	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
50	C₁₁×#485	C₂²	1	4	yes	complemented
51	C₁₁×#483	C₂²	1	4	yes	complemented
52	C₁₁×#482	C₂²	1	4	yes	complemented
53	C₁₁×#481	C₂²	1	4	yes	complemented
54	C₁₁×#477	C₂²	1	2	yes	complemented
55	C₁₁×#476	C₂²	1	2	yes	complemented
56	C₁₁×#476	C₂²	1	2	yes	complemented
57	C₁₁×#476	C₂²	1	4	yes	complemented
58	C₁₁×#476	C₂²	1	2	yes	complemented
59	C₁₁×#475	C₂²	1	2	yes	complemented
60	C₁₁×#474	C₂²	1	2	yes	complemented
61	C₁₁×#464	C₂²	1	2	yes	complemented
62	C₁₁×#463	C₂²	1	2	yes	complemented
63	C₁₁×#463	C₂²	1	4	yes	complemented
64	C₁₁×#462	C₂²	1	1	yes	characteristic, complemented
65	C₁₁×#461	C₂²	1	1	yes	characteristic, complemented
66	C₁₁×#461	C₂²	1	2	yes	complemented
67	C₁₁×#460	C₂²	1	1	yes	characteristic, complemented
68	C₁₁×#459	C₂²	1	1	yes	characteristic, complemented
69	C₁₁×#459	C₂²	1	2	yes	complemented
70	C₁₁×#452	C₂²	1	4	yes	—
71	C₁₁×#450	C₂²	1	4	yes	—
72	C₁₁×#449	C₂²	1	4	yes	—
73	C₁₁×#447	C₂²	1	4	yes	—
74	C₁₁×#442	C₂²	1	4	yes	complemented
75	C₁₁×#442	C₂²	1	4	yes	complemented
76	C₁₁×#441	C₂²	1	4	yes	complemented
77	C₁₁×#440	C₂²	1	4	yes	complemented
78	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
79	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
80	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
81	C₄×C₁₁×D₈	C₂²	1	4	yes	complemented
82	C₁₁×#433	C₂²	1	4	yes	complemented
83	C₁₁×#432	C₂²	1	2	yes	complemented
84	C₁₁×#431	C₂²	1	2	yes	complemented
85	C₁₁×#428	C₂²	1	2	yes	complemented
86	C₂×C₁₁×#106	C₂²	1	2	yes	complemented
87	C₁₁×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₁₁×#417	C₂²	1	2	yes	—
90	C₁₁×#417	C₂²	1	2	yes	complemented
91	C₁₁×#416	C₂²	1	2	yes	complemented
92	C₂×C₁₁×#102	C₂²	1	2	yes	—
93	C₁₁×#408	C₂²	1	2	yes	—
94	C₁₁×#405	C₂²	1	2	yes	complemented
95	C₁₁×H(5,𝔽₂)	—	2	4	no	—
96	C₁₁×H(5,𝔽₂)	—	2	4	no	—
97	C₂×C₁₁×#41	—	2	1	no	—
98	C₂×C₁₁×#41	—	2	2	no	—
99	C₂×C₁₁×#41	C₂³	1	2	yes	—
100	C₂×C₁₁×#41	C₂³	1	2	yes	—
101	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
102	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₁₁	—	2	1	no	—
104	C₂²×D₄×C₁₁	—	2	2	no	—
105	C₂²×D₄×C₁₁	—	2	1	no	—
106	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
107	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₁	—	2	1	no	—
109	C₂³×C₄×C₁₁	—	2	2	no	—
110	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
111	C₁₁×#135	—	2	8	no	—
112	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
113	C₂×C₁₁×SD₁₆	C₂³	1	2	yes	—
114	C₂×C₁₁×SD₁₆	C₂³	1	2	yes	—
115	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₁×D₈	C₂³	1	2	yes	—
117	C₂×C₁₁×D₈	C₂³	1	4	yes	—
118	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
119	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
120	C₁₁×C₄⋊Q₈	—	2	1	no	—
121	C₁₁×C₄⋊Q₈	—	2	1	no	—
122	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₁₁×#127	C₂³	1	1	yes	characteristic
126	C₁₁×#126	—	2	4	no	—
127	C₁₁×#125	—	2	2	no	—
128	C₁₁×#124	—	2	4	no	—
129	C₁₁×#124	—	2	2	no	—
130	C₁₁×#124	C₂³	1	2	yes	—
131	C₁₁×#123	—	2	4	no	—
132	C₁₁×C₂²⋊Q₈	—	2	2	no	—
133	C₁₁×C₂²⋊Q₈	—	2	2	no	—
134	C₁₁×C₂²⋊Q₈	—	2	4	no	—
135	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₁₁×#121	—	2	2	no	—
137	C₁₁×#121	—	2	4	no	—
138	C₁₁×#121	—	2	1	no	—
139	C₁₁×#121	—	2	1	no	—
140	C₁₁×#121	—	2	2	no	—
141	C₁₁×#121	C₂³	1	4	yes	—
142	C₄×Q₈×C₁₁	—	2	1	no	—
143	C₄×Q₈×C₁₁	—	2	2	no	—
144	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
145	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
146	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
147	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
149	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
150	C₄×D₄×C₁₁	—	2	2	no	—
151	C₄×D₄×C₁₁	—	2	1	no	—
152	C₄×D₄×C₁₁	—	2	1	no	—
153	C₄×D₄×C₁₁	—	2	2	no	—
154	C₄×D₄×C₁₁	—	2	1	no	—
155	C₄×D₄×C₁₁	—	2	2	no	—
156	C₄×D₄×C₁₁	—	2	1	no	—
157	C₄×D₄×C₁₁	—	2	2	no	—
158	C₄×D₄×C₁₁	—	2	1	no	—
159	C₄×D₄×C₁₁	—	2	2	no	—
160	C₄×D₄×C₁₁	—	2	2	no	—
161	C₄×D₄×C₁₁	—	2	2	no	—
162	C₄×D₄×C₁₁	—	2	2	no	—
163	C₄×D₄×C₁₁	—	2	4	no	—
164	C₄×D₄×C₁₁	—	2	2	no	—
165	C₄×D₄×C₁₁	—	2	1	no	—
166	C₄×D₄×C₁₁	—	2	1	no	—
167	C₄×D₄×C₁₁	—	2	2	no	—
168	C₄×D₄×C₁₁	—	2	1	no	—
169	C₄×D₄×C₁₁	—	2	2	no	—
170	C₄×D₄×C₁₁	—	2	1	no	—
171	C₄×D₄×C₁₁	D₄	1	2	yes	—
172	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
173	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
174	C₄×D₄×C₁₁	D₄	1	2	yes	—
175	C₄×D₄×C₁₁	C₂³	1	2	yes	—
176	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₁₁	C₂³	1	2	yes	—
178	C₄×D₄×C₁₁	C₂³	1	2	yes	—
179	C₄×D₄×C₁₁	C₂³	1	2	yes	—
180	C₄×D₄×C₁₁	C₂³	1	2	yes	—
181	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₁₁	C₂³	1	4	yes	—
183	C₁₁×#117	—	2	2	no	—
184	C₁₁×#117	—	2	1	no	—
185	C₁₁×#117	—	2	2	no	—
186	C₁₁×#117	—	2	2	no	—
187	C₁₁×#117	—	2	1	no	—
188	C₁₁×#117	—	2	2	no	—
189	C₁₁×#117	C₂³	1	1	yes	characteristic
190	C₁₁×#117	C₂³	1	2	yes	—
191	C₁₁×#117	C₂³	1	1	yes	characteristic
192	C₁₁×#117	C₂³	1	2	yes	—
193	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
194	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
195	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
196	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
197	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₄²×C₁₁	—	2	2	no	—
206	C₂×C₄²×C₁₁	—	2	1	no	—
207	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
209	C₁₁×#107	C₂³	1	4	yes	—
210	C₁₁×#106	C₂³	1	4	yes	—
211	C₁₁×#106	C₂³	1	4	yes	—
212	C₁₁×#106	C₂³	1	4	yes	—
213	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₁×#103	C₂³	1	2	yes	—
219	C₁₁×#103	C₂³	1	2	yes	—
220	C₁₁×#103	C₂³	1	4	yes	—
221	C₁₁×#103	C₂³	1	4	yes	—
222	C₁₁×#102	C₂³	1	4	yes	—
223	C₁₁×#102	C₂³	1	4	yes	—
224	C₁₁×#102	C₂³	1	2	yes	—
225	C₁₁×#102	C₂³	1	2	yes	—
226	C₁₁×#102	C₂³	1	4	yes	—
227	C₁₁×#102	C₂³	1	4	yes	—
228	C₁₁×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₁₁×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₁₁×#97	C₂³	1	4	yes	—
231	C₄×C₈×C₁₁	C₂³	1	4	yes	—
232	#60597	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂⁴×C₁₁	—	2	2	no	—
234	C₂⁴×C₁₁	—	2	1	no	—
235	C₁₁×#41	—	2	8	no	—
236	C₁₁×#41	—	2	4	no	—
237	C₁₁×#41	—	2	4	no	—
238	C₁₁×#41	—	2	2	no	—
239	C₁₁×#41	—	2	2	no	—
240	C₁₁×#41	—	2	2	no	—
241	C₁₁×#41	—	2	4	no	—
242	C₁₁×#41	—	2	4	no	—
243	C₁₁×#41	—	8	4	no	—
244	C₁₁×#41	#41	1	4	yes	complemented
245	C₂×Q₈×C₁₁	—	2	2	no	—
246	C₂×Q₈×C₁₁	—	2	2	no	—
247	C₂×Q₈×C₁₁	—	8	2	no	—
248	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
249	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
250	C₂×Q₈×C₁₁	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₁₁	—	2	16	no	—
252	C₂×D₄×C₁₁	—	2	8	no	—
253	C₂×D₄×C₁₁	—	2	2	no	—
254	C₂×D₄×C₁₁	—	2	1	no	—
255	C₂×D₄×C₁₁	—	2	4	no	—
256	C₂×D₄×C₁₁	—	2	4	no	—
257	C₂×D₄×C₁₁	—	2	2	no	—
258	C₂×D₄×C₁₁	—	2	4	no	—
259	C₂×D₄×C₁₁	—	2	2	no	—
260	C₂×D₄×C₁₁	—	2	1	no	—
261	C₂×D₄×C₁₁	—	2	1	no	—
262	C₂×D₄×C₁₁	—	2	1	no	—
263	C₂×D₄×C₁₁	—	2	2	no	—
264	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
265	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₁₁	#41	1	4	yes	complemented
267	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
268	C₂×D₄×C₁₁	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₁₁	—	2	2	no	—
271	C₂²×C₄×C₁₁	—	2	1	no	—
272	C₂²×C₄×C₁₁	—	2	2	no	—
273	C₂²×C₄×C₁₁	—	2	1	no	—
274	C₂²×C₄×C₁₁	—	2	2	no	—
275	C₂²×C₄×C₁₁	—	2	2	no	—
276	C₂²×C₄×C₁₁	—	2	1	no	—
277	C₂²×C₄×C₁₁	—	2	2	no	—
278	C₂²×C₄×C₁₁	—	2	1	no	—
279	C₂²×C₄×C₁₁	—	2	2	no	—
280	C₂²×C₄×C₁₁	—	2	2	no	—
281	C₂²×C₄×C₁₁	—	2	2	no	—
282	C₂²×C₄×C₁₁	—	2	2	no	—
283	C₂²×C₄×C₁₁	—	2	4	no	—
284	C₂²×C₄×C₁₁	—	8	2	no	—
285	C₂²×C₄×C₁₁	—	8	4	no	—
286	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
292	C₁₁×Q₁₆	—	2	4	no	—
293	C₁₁×SD₁₆	—	2	4	no	—
294	C₁₁×SD₁₆	—	2	4	no	—
295	C₁₁×SD₁₆	—	2	8	no	—
296	C₁₁×D₈	—	2	4	no	—
297	C₁₁×D₈	—	2	8	no	—
298	C₁₁×M₁₆	—	2	4	no	—
299	C₂×C₈×C₁₁	—	2	4	no	—
300	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
301	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
302	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
303	C₁₁×C₄⋊C₄	—	2	2	no	—
304	C₁₁×C₄⋊C₄	—	2	1	no	—
305	C₁₁×C₄⋊C₄	—	2	2	no	—
306	C₁₁×C₄⋊C₄	—	2	1	no	—
307	C₁₁×C₄⋊C₄	—	2	2	no	—
308	C₁₁×C₄⋊C₄	—	2	2	no	—
309	C₁₁×C₄⋊C₄	—	2	4	no	—
310	C₁₁×C₄⋊C₄	—	2	2	no	—
311	C₁₁×C₄⋊C₄	—	2	1	no	—
312	C₁₁×C₄⋊C₄	—	2	1	no	—
313	C₁₁×C₄⋊C₄	—	2	1	no	—
314	C₁₁×C₄⋊C₄	—	2	4	no	—
315	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
316	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
317	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
318	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
320	C₁₁×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
321	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
322	C₁₁×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₁₁×C₂²⋊C₄	—	2	2	no	—
324	C₁₁×C₂²⋊C₄	—	2	1	no	—
325	C₁₁×C₂²⋊C₄	—	2	4	no	—
326	C₁₁×C₂²⋊C₄	—	2	2	no	—
327	C₁₁×C₂²⋊C₄	—	2	1	no	—
328	C₁₁×C₂²⋊C₄	—	2	2	no	—
329	C₁₁×C₂²⋊C₄	—	2	2	no	—
330	C₁₁×C₂²⋊C₄	—	2	2	no	—
331	C₁₁×C₂²⋊C₄	—	2	2	no	—
332	C₁₁×C₂²⋊C₄	—	2	1	no	—
333	C₁₁×C₂²⋊C₄	—	2	4	no	—
334	C₁₁×C₂²⋊C₄	—	2	4	no	—
335	C₁₁×C₂²⋊C₄	—	2	2	no	—
336	C₁₁×C₂²⋊C₄	—	2	2	no	—
337	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
339	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
340	C₄²×C₁₁	—	2	1	no	—
341	C₄²×C₁₁	—	2	1	no	—
342	C₄²×C₁₁	—	2	2	no	—
343	C₄²×C₁₁	—	2	2	no	—
344	C₄²×C₁₁	—	2	1	no	—
345	C₄²×C₁₁	—	2	4	no	—
346	C₄²×C₁₁	C₂×D₄	1	2	yes	—
347	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₁₁	C₂×D₄	1	2	yes	—
350	C₄²×C₁₁	C₂⁴	1	2	yes	—
351	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
352	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
353	#3511	C₂×C₁₁	1	1	yes	characteristic, complemented
354	C₄×H(5,𝔽₂)	C₂×C₁₁	1	1	yes	characteristic, complemented
355	#3125	C₂×C₁₁	1	4	yes	complemented
356	#3118	C₂×C₁₁	1	4	yes	complemented
357	#3116	C₂×C₁₁	1	2	yes	complemented
358	#3109	C₂×C₁₁	1	2	yes	complemented
359	#3106	C₂×C₁₁	1	2	yes	complemented
360	#3101	C₂×C₁₁	1	2	yes	complemented
361	#3099	C₂×C₁₁	1	2	yes	complemented
362	#3079	C₂×C₁₁	1	1	yes	characteristic, complemented
363	C₂×#476	C₂×C₁₁	1	1	yes	characteristic, complemented
364	#3036	C₂×C₁₁	1	1	yes	characteristic, complemented
365	#3035	C₂×C₁₁	1	1	yes	characteristic, complemented
366	#3012	C₂×C₁₁	1	2	yes	complemented
367	#2952	C₂×C₁₁	1	2	yes	complemented
368	#2946	C₂×C₁₁	1	2	yes	complemented
369	#2925	C₂×C₁₁	1	1	yes	characteristic, complemented
370	C₂³×C₁₁	—	2	8	no	—
371	C₂³×C₁₁	—	2	2	no	—
372	C₂³×C₁₁	—	2	1	no	—
373	C₂³×C₁₁	—	2	4	no	—
374	C₂³×C₁₁	—	2	2	no	—
375	C₂³×C₁₁	—	8	1	no	—
376	C₂³×C₁₁	—	8	2	no	—
377	C₂³×C₁₁	—	8	1	no	—
378	C₂³×C₁₁	—	8	2	no	—
379	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
380	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
381	Q₈×C₁₁	—	2	2	no	—
382	Q₈×C₁₁	—	2	1	no	—
383	Q₈×C₁₁	—	2	2	no	—
384	Q₈×C₁₁	—	2	2	no	—
385	Q₈×C₁₁	—	4	4	no	—
386	Q₈×C₁₁	—	8	2	no	—
387	Q₈×C₁₁	C₂×#41	1	2	yes	—
388	D₄×C₁₁	—	2	8	no	—
389	D₄×C₁₁	—	2	8	no	—
390	D₄×C₁₁	—	2	4	no	—
391	D₄×C₁₁	—	2	4	no	—
392	D₄×C₁₁	—	2	2	no	—
393	D₄×C₁₁	—	2	4	no	—
394	D₄×C₁₁	—	2	2	no	—
395	D₄×C₁₁	—	2	1	no	—
396	D₄×C₁₁	—	2	2	no	—
397	D₄×C₁₁	—	2	2	no	—
398	D₄×C₁₁	—	4	2	no	—
399	D₄×C₁₁	—	4	4	no	—
400	D₄×C₁₁	—	4	2	no	—
401	D₄×C₁₁	—	8	4	no	—
402	D₄×C₁₁	C₂×#41	1	2	yes	—
403	D₄×C₁₁	C₂×#41	1	4	yes	—
404	C₂×C₄×C₁₁	—	2	8	no	—
405	C₂×C₄×C₁₁	—	2	1	no	—
406	C₂×C₄×C₁₁	—	2	4	no	—
407	C₂×C₄×C₁₁	—	2	2	no	—
408	C₂×C₄×C₁₁	—	2	4	no	—
409	C₂×C₄×C₁₁	—	2	2	no	—
410	C₂×C₄×C₁₁	—	2	2	no	—
411	C₂×C₄×C₁₁	—	2	1	no	—
412	C₂×C₄×C₁₁	—	2	2	no	—
413	C₂×C₄×C₁₁	—	2	1	no	—
414	C₂×C₄×C₁₁	—	2	2	no	—
415	C₂×C₄×C₁₁	—	2	4	no	—
416	C₂×C₄×C₁₁	—	4	1	no	—
417	C₂×C₄×C₁₁	—	4	2	no	—
418	C₂×C₄×C₁₁	—	4	4	no	—
419	C₂×C₄×C₁₁	—	4	4	no	—
420	C₂×C₄×C₁₁	—	4	2	no	—
421	C₂×C₄×C₁₁	—	8	2	no	—
422	C₂×C₄×C₁₁	—	8	1	no	—
423	C₂×C₄×C₁₁	—	8	2	no	—
424	C₂×C₄×C₁₁	—	8	2	no	—
425	C₂×C₄×C₁₁	—	8	2	no	—
426	C₂×C₄×C₁₁	—	8	4	no	—
427	C₂×C₄×C₁₁	—	8	1	no	—
428	C₂×C₄×C₁₁	—	8	2	no	—
429	C₂×C₄×C₁₁	—	8	2	no	—
430	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
431	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
434	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
439	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
440	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
441	C₈×C₁₁	—	2	2	no	—
442	C₈×C₁₁	—	2	2	no	—
443	C₈×C₁₁	—	2	4	no	—
444	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	1	yes	characteristic
445	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
446	C₂×#135	C₂²×C₁₁	1	2	yes	—
447	#556	—	2	1	no	—
448	#555	—	2	1	no	—
449	#554	—	2	1	no	—
450	#553	—	2	2	no	—
451	#548	—	2	2	no	—
452	#547	—	2	1	no	—
453	#542	C₂²×C₁₁	1	4	yes	complemented
454	#537	C₂²×C₁₁	1	2	yes	—
455	#533	C₂²×C₁₁	1	2	yes	complemented
456	#532	C₂²×C₁₁	1	1	yes	characteristic, complemented
457	#532	C₂²×C₁₁	1	2	yes	complemented
458	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
459	#520	—	2	1	no	—
460	#520	C₂²×C₁₁	1	2	yes	—
461	#520	C₂²×C₁₁	1	1	yes	characteristic
462	#520	C₂²×C₁₁	1	1	yes	characteristic
463	#520	C₂²×C₁₁	1	2	yes	complemented
464	#518	—	2	1	no	—
465	#518	—	2	2	no	—
466	#518	C₂²×C₁₁	1	2	yes	—
467	#518	C₂²×C₁₁	1	1	yes	characteristic
468	C₄×#41	—	2	1	no	—
469	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
470	C₄×#41	C₂²×C₁₁	1	2	yes	—
471	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
472	C₂×C₄×D₄	—	2	2	no	—
473	C₂×C₄×D₄	—	2	1	no	—
474	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
475	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
476	#485	C₂²×C₁₁	1	4	yes	complemented
477	#483	C₂²×C₁₁	1	4	yes	complemented
478	#482	C₂²×C₁₁	1	4	yes	complemented
479	#481	C₂²×C₁₁	1	4	yes	complemented
480	#477	C₂²×C₁₁	1	2	yes	complemented
481	#476	C₂²×C₁₁	1	2	yes	complemented
482	#476	C₂²×C₁₁	1	2	yes	complemented
483	#476	C₂²×C₁₁	1	2	yes	complemented
484	#476	C₂²×C₁₁	1	4	yes	complemented
485	#475	C₂²×C₁₁	1	2	yes	complemented
486	#474	C₂²×C₁₁	1	2	yes	complemented
487	#464	C₂²×C₁₁	1	2	yes	complemented
488	#463	C₂²×C₁₁	1	2	yes	complemented
489	#463	C₂²×C₁₁	1	4	yes	complemented
490	#462	C₂²×C₁₁	1	1	yes	characteristic, complemented
491	#461	C₂²×C₁₁	1	1	yes	characteristic, complemented
492	#461	C₂²×C₁₁	1	2	yes	complemented
493	#460	C₂²×C₁₁	1	1	yes	characteristic, complemented
494	#459	C₂²×C₁₁	1	2	yes	complemented
495	#459	C₂²×C₁₁	1	1	yes	characteristic, complemented
496	#452	C₂²×C₁₁	1	4	yes	—
497	#450	C₂²×C₁₁	1	4	yes	—
498	#449	C₂²×C₁₁	1	4	yes	—
499	#447	C₂²×C₁₁	1	4	yes	—
500	#442	C₂²×C₁₁	1	4	yes	complemented
501	#442	C₂²×C₁₁	1	4	yes	complemented
502	#441	C₂²×C₁₁	1	4	yes	complemented
503	#440	C₂²×C₁₁	1	4	yes	complemented
504	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
505	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
506	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
507	C₄×D₈	C₂²×C₁₁	1	4	yes	complemented
508	#433	C₂²×C₁₁	1	4	yes	complemented
509	#432	C₂²×C₁₁	1	2	yes	complemented
510	#431	C₂²×C₁₁	1	2	yes	complemented
511	#428	C₂²×C₁₁	1	2	yes	complemented
512	C₂×#106	C₂²×C₁₁	1	2	yes	complemented
513	#423	C₂²×C₁₁	1	1	yes	characteristic, complemented
514	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
515	#417	C₂²×C₁₁	1	2	yes	—
516	#417	C₂²×C₁₁	1	2	yes	complemented
517	#416	C₂²×C₁₁	1	2	yes	complemented
518	C₂×#102	C₂²×C₁₁	1	2	yes	—
519	#408	C₂²×C₁₁	1	2	yes	—
520	#405	C₂²×C₁₁	1	2	yes	complemented
521	C₂²×C₁₁	—	2	1	no	—
522	C₂²×C₁₁	—	2	1	no	—
523	C₂²×C₁₁	—	2	2	no	—
524	C₂²×C₁₁	—	2	2	no	—
525	C₂²×C₁₁	—	2	4	no	—
526	C₂²×C₁₁	—	2	2	no	—
527	C₂²×C₁₁	—	2	2	no	—
528	C₂²×C₁₁	—	4	2	no	—
529	C₂²×C₁₁	—	4	1	no	—
530	C₂²×C₁₁	—	4	2	no	—
531	C₂²×C₁₁	—	4	1	no	—
532	C₂²×C₁₁	—	4	2	no	—
533	C₂²×C₁₁	—	4	2	no	—
534	C₂²×C₁₁	—	4	2	no	—
535	C₂²×C₁₁	—	8	4	no	—
536	C₂²×C₁₁	—	8	8	no	—
537	C₂²×C₁₁	#525	1	2	yes	—
538	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₁₁	—	2	1	no	—
540	C₄×C₁₁	—	2	2	no	—
541	C₄×C₁₁	—	2	1	no	—
542	C₄×C₁₁	—	2	2	no	—
543	C₄×C₁₁	—	2	2	no	—
544	C₄×C₁₁	—	2	2	no	—
545	C₄×C₁₁	—	2	1	no	—
546	C₄×C₁₁	—	4	1	no	—
547	C₄×C₁₁	—	4	4	no	—
548	C₄×C₁₁	—	4	2	no	—
549	C₄×C₁₁	—	4	2	no	—
550	C₄×C₁₁	—	4	1	no	—
551	C₄×C₁₁	#525	1	2	yes	—
552	C₄×C₁₁	#577	1	2	yes	—
553	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
554	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
555	H(5,𝔽₂)	—	2	4	no	—
556	H(5,𝔽₂)	—	2	4	no	—
557	C₂×#41	—	2	1	no	—
558	C₂×#41	—	2	2	no	—
559	C₂×#41	C₂³×C₁₁	1	2	yes	—
560	C₂×#41	C₂³×C₁₁	1	2	yes	—
561	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
562	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
563	C₂²×Q₈	—	2	1	no	—
564	C₂²×D₄	—	2	2	no	—
565	C₂²×D₄	—	2	1	no	—
566	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
567	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	—	2	2	no	—
570	AGL(1,ℤ/8)	—	2	8	no	—
571	#135	—	2	8	no	—
572	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
573	C₂×SD₁₆	C₂³×C₁₁	1	2	yes	—
574	C₂×SD₁₆	C₂³×C₁₁	1	2	yes	—
575	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
576	C₂×D₈	C₂³×C₁₁	1	2	yes	—
577	C₂×D₈	C₂³×C₁₁	1	4	yes	—
578	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
579	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
580	C₄⋊Q₈	—	2	1	no	—
581	C₄⋊Q₈	—	2	1	no	—
582	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
584	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
585	#127	C₂³×C₁₁	1	1	yes	characteristic
586	#126	—	2	4	no	—
587	#125	—	2	2	no	—
588	#124	—	2	4	no	—
589	#124	—	2	2	no	—
590	#124	C₂³×C₁₁	1	2	yes	—
591	#123	—	2	4	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	4	no	—
595	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
596	#121	—	2	2	no	—
597	#121	—	2	4	no	—
598	#121	—	2	1	no	—
599	#121	—	2	1	no	—
600	#121	—	2	2	no	—
601	#121	C₂³×C₁₁	1	4	yes	—
602	C₄×Q₈	—	2	1	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
605	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
608	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	4	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	D₄×C₁₁	1	2	yes	—
632	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
633	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
634	C₄×D₄	D₄×C₁₁	1	2	yes	—
635	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₁₁	1	2	yes	—
637	C₄×D₄	C₂³×C₁₁	1	2	yes	—
638	C₄×D₄	C₂³×C₁₁	1	2	yes	—
639	C₄×D₄	C₂³×C₁₁	1	2	yes	—
640	C₄×D₄	C₂³×C₁₁	1	2	yes	—
641	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
642	C₄×D₄	C₂³×C₁₁	1	4	yes	—
643	#117	—	2	2	no	—
644	#117	—	2	1	no	—
645	#117	—	2	2	no	—
646	#117	—	2	2	no	—
647	#117	—	2	1	no	—
648	#117	—	2	2	no	—
649	#117	C₂³×C₁₁	1	1	yes	characteristic
650	#117	C₂³×C₁₁	1	2	yes	—
651	#117	C₂³×C₁₁	1	1	yes	characteristic
652	#117	C₂³×C₁₁	1	2	yes	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	—	2	2	no	—
656	C₂×C₄⋊C₄	—	2	2	no	—
657	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	2	no	—
662	C₂×C₂²⋊C₄	—	2	2	no	—
663	C₂×C₂²⋊C₄	—	2	2	no	—
664	C₂×C₂²⋊C₄	—	2	2	no	—
665	C₂×C₄²	—	2	2	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
669	#107	C₂³×C₁₁	1	4	yes	—
670	#106	C₂³×C₁₁	1	4	yes	—
671	#106	C₂³×C₁₁	1	4	yes	—
672	#106	C₂³×C₁₁	1	4	yes	—
673	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
674	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
675	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
676	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
677	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
678	#103	C₂³×C₁₁	1	2	yes	—
679	#103	C₂³×C₁₁	1	2	yes	—
680	#103	C₂³×C₁₁	1	4	yes	—
681	#103	C₂³×C₁₁	1	4	yes	—
682	#102	C₂³×C₁₁	1	4	yes	—
683	#102	C₂³×C₁₁	1	4	yes	—
684	#102	C₂³×C₁₁	1	2	yes	—
685	#102	C₂³×C₁₁	1	2	yes	—
686	#102	C₂³×C₁₁	1	4	yes	—
687	#102	C₂³×C₁₁	1	4	yes	—
688	C₂²⋊C₈	C₂³×C₁₁	1	4	yes	—
689	C₂²⋊C₈	C₂³×C₁₁	1	4	yes	—
690	#97	C₂³×C₁₁	1	4	yes	—
691	C₄×C₈	C₂³×C₁₁	1	4	yes	—
692	C₂×C₁₁	—	2	2	no	—
693	C₂×C₁₁	—	4	2	no	—
694	C₂×C₁₁	—	4	4	no	—
695	C₂×C₁₁	—	4	2	no	—
696	C₂×C₁₁	—	8	2	no	—
697	C₂×C₁₁	C₂×#525	1	1	yes	characteristic
698	C₂×C₁₁	C₂×#577	1	1	yes	characteristic
699	C₂×C₁₁	#3585	1	1	yes	characteristic
700	C₂⁴	—	2	2	no	—
701	C₂⁴	—	2	1	no	—
702	#41	—	2	8	no	—
703	#41	—	2	4	no	—
704	#41	—	2	4	no	—
705	#41	—	2	2	no	—
706	#41	—	2	2	no	—
707	#41	—	2	2	no	—
708	#41	—	2	4	no	—
709	#41	—	2	4	no	—
710	#41	—	8	4	no	—
711	#41	C₁₁×#41	1	4	yes	complemented
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	8	2	no	—
715	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
716	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
717	C₂×Q₈	C₂⁴×C₁₁	1	1	yes	characteristic
718	C₂×D₄	—	2	16	no	—
719	C₂×D₄	—	2	8	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
732	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
733	C₂×D₄	C₁₁×#41	1	4	yes	complemented
734	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
735	C₂×D₄	C₂⁴×C₁₁	1	1	yes	characteristic
736	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	8	2	no	—
752	C₂²×C₄	—	8	4	no	—
753	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
754	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
759	Q₁₆	—	2	4	no	—
760	SD₁₆	—	2	4	no	—
761	SD₁₆	—	2	4	no	—
762	SD₁₆	—	2	8	no	—
763	D₈	—	2	4	no	—
764	D₈	—	2	8	no	—
765	M₁₆	—	2	4	no	—
766	C₂×C₈	—	2	4	no	—
767	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
768	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
769	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
783	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
784	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
785	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
786	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
787	C₄⋊C₄	C₂⁴×C₁₁	1	1	yes	characteristic
788	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
789	C₄⋊C₄	C₂⁴×C₁₁	1	1	yes	characteristic
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	1	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
805	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
807	C₄²	—	2	1	no	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	1	no	—
812	C₄²	—	2	4	no	—
813	C₄²	C₂×D₄×C₁₁	1	2	yes	—
814	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
815	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
816	C₄²	C₂×D₄×C₁₁	1	2	yes	—
817	C₄²	C₂⁴×C₁₁	1	2	yes	—
818	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
819	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
820	C₁₁	#60597	1	1	yes	characteristic, direct product factor, Sylow
821	C₂³	—	2	8	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	8	1	no	—
827	C₂³	—	8	2	no	—
828	C₂³	—	8	1	no	—
829	C₂³	—	8	2	no	—
830	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
831	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
832	Q₈	—	2	2	no	—
833	Q₈	—	2	1	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	4	4	no	—
837	Q₈	—	8	2	no	—
838	Q₈	C₂×C₁₁×#41	1	2	yes	—
839	D₄	—	2	8	no	—
840	D₄	—	2	8	no	—
841	D₄	—	2	4	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	4	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	1	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	2	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	2	no	—
852	D₄	—	8	4	no	—
853	D₄	C₂×C₁₁×#41	1	2	yes	—
854	D₄	C₂×C₁₁×#41	1	4	yes	—
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	4	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	—	4	4	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	—	8	1	no	—
874	C₂×C₄	—	8	2	no	—
875	C₂×C₄	—	8	2	no	—
876	C₂×C₄	—	8	2	no	—
877	C₂×C₄	—	8	4	no	—
878	C₂×C₄	—	8	1	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	—	8	2	no	—
881	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
882	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
883	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
884	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
889	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
890	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
891	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	2	no	—
894	C₈	—	2	4	no	—
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	8	4	no	—
910	C₂²	—	8	8	no	—
911	C₂²	C₁₁×#525	1	2	yes	—
912	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
913	C₄	—	2	2	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	4	no	—
925	C₄	C₁₁×#525	1	2	yes	—
926	C₄	C₁₁×#577	1	2	yes	—
927	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
928	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
929	C₂	—	2	2	no	—
930	C₂	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₂×C₁₁×#525	1	1	yes	characteristic
935	C₂	C₂×C₁₁×#577	1	1	yes	characteristic
936	C₂	C₁₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3511	C₂	semidirect
2. C₄×C₁₁×H(5,𝔽₂)	C₂	semidirect
3. C₁₁×#3125	C₂	semidirect
4. C₁₁×#3118	C₂	semidirect
5. C₁₁×#3116	C₂	semidirect
6. C₁₁×#3109	C₂	semidirect
7. C₁₁×#3106	C₂	semidirect
8. C₁₁×#3101	C₂	semidirect
9. C₁₁×#3099	C₂	semidirect
10. C₁₁×#3079	C₂	semidirect
11. C₂×C₁₁×#476	C₂	semidirect
12. C₁₁×#3036	C₂	semidirect
13. C₁₁×#3035	C₂	semidirect
14. C₁₁×#3012	C₂	semidirect
15. C₁₁×#2952	C₂	semidirect
16. C₁₁×#2946	C₂	semidirect
17. C₁₁×#2925	C₂	semidirect
27. C₁₁×#542	C₂²	semidirect
29. C₁₁×#533	C₂²	semidirect
30. C₁₁×#532	C₂²	semidirect
31. C₁₁×#532	C₂²	semidirect
32. C₂×C₁₁×C₄⋊Q₈	C₂²	semidirect
37. C₁₁×#520	C₂²	semidirect
50. C₁₁×#485	C₂²	semidirect
51. C₁₁×#483	C₂²	semidirect
52. C₁₁×#482	C₂²	semidirect
53. C₁₁×#481	C₂²	semidirect
54. C₁₁×#477	C₂²	semidirect
55. C₁₁×#476	C₂²	semidirect
56. C₁₁×#476	C₂²	semidirect
57. C₁₁×#476	C₂²	semidirect
58. C₁₁×#476	C₂²	semidirect
59. C₁₁×#475	C₂²	semidirect
60. C₁₁×#474	C₂²	semidirect
61. C₁₁×#464	C₂²	semidirect
62. C₁₁×#463	C₂²	semidirect
63. C₁₁×#463	C₂²	semidirect
64. C₁₁×#462	C₂²	semidirect
65. C₁₁×#461	C₂²	semidirect
66. C₁₁×#461	C₂²	semidirect
67. C₁₁×#460	C₂²	semidirect
68. C₁₁×#459	C₂²	semidirect
69. C₁₁×#459	C₂²	semidirect
74. C₁₁×#442	C₂²	semidirect
75. C₁₁×#442	C₂²	semidirect
76. C₁₁×#441	C₂²	semidirect
77. C₁₁×#440	C₂²	semidirect
78. C₄×C₁₁×SD₁₆	C₂²	semidirect
79. C₄×C₁₁×SD₁₆	C₂²	semidirect
80. C₄×C₁₁×SD₁₆	C₂²	semidirect
81. C₄×C₁₁×D₈	C₂²	semidirect
82. C₁₁×#433	C₂²	semidirect
83. C₁₁×#432	C₂²	semidirect
84. C₁₁×#431	C₂²	semidirect
85. C₁₁×#428	C₂²	semidirect
86. C₂×C₁₁×#106	C₂²	semidirect
87. C₁₁×#423	C₂²	semidirect
88. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
90. C₁₁×#417	C₂²	semidirect
91. C₁₁×#416	C₂²	semidirect
94. C₁₁×#405	C₂²	semidirect
232. #60597	C₁₁	direct (N × H)
244. C₁₁×#41	#41	semidirect
266. C₂×D₄×C₁₁	#41	semidirect
353. #3511	C₂×C₁₁	semidirect
354. C₄×H(5,𝔽₂)	C₂×C₁₁	semidirect
355. #3125	C₂×C₁₁	semidirect
356. #3118	C₂×C₁₁	semidirect
357. #3116	C₂×C₁₁	semidirect
358. #3109	C₂×C₁₁	semidirect
359. #3106	C₂×C₁₁	semidirect
360. #3101	C₂×C₁₁	semidirect
361. #3099	C₂×C₁₁	semidirect
362. #3079	C₂×C₁₁	semidirect
363. C₂×#476	C₂×C₁₁	semidirect
364. #3036	C₂×C₁₁	semidirect
365. #3035	C₂×C₁₁	semidirect
366. #3012	C₂×C₁₁	semidirect
367. #2952	C₂×C₁₁	semidirect
368. #2946	C₂×C₁₁	semidirect
369. #2925	C₂×C₁₁	semidirect
453. #542	C₂²×C₁₁	semidirect
455. #533	C₂²×C₁₁	semidirect
456. #532	C₂²×C₁₁	semidirect
457. #532	C₂²×C₁₁	semidirect
458. C₂×C₄⋊Q₈	C₂²×C₁₁	semidirect
463. #520	C₂²×C₁₁	semidirect
476. #485	C₂²×C₁₁	semidirect
477. #483	C₂²×C₁₁	semidirect
478. #482	C₂²×C₁₁	semidirect
479. #481	C₂²×C₁₁	semidirect
480. #477	C₂²×C₁₁	semidirect
481. #476	C₂²×C₁₁	semidirect
482. #476	C₂²×C₁₁	semidirect
483. #476	C₂²×C₁₁	semidirect
484. #476	C₂²×C₁₁	semidirect
485. #475	C₂²×C₁₁	semidirect
486. #474	C₂²×C₁₁	semidirect
487. #464	C₂²×C₁₁	semidirect
488. #463	C₂²×C₁₁	semidirect
489. #463	C₂²×C₁₁	semidirect
490. #462	C₂²×C₁₁	semidirect
491. #461	C₂²×C₁₁	semidirect
492. #461	C₂²×C₁₁	semidirect
493. #460	C₂²×C₁₁	semidirect
494. #459	C₂²×C₁₁	semidirect
495. #459	C₂²×C₁₁	semidirect
500. #442	C₂²×C₁₁	semidirect
501. #442	C₂²×C₁₁	semidirect
502. #441	C₂²×C₁₁	semidirect
503. #440	C₂²×C₁₁	semidirect
504. C₄×SD₁₆	C₂²×C₁₁	semidirect
505. C₄×SD₁₆	C₂²×C₁₁	semidirect
506. C₄×SD₁₆	C₂²×C₁₁	semidirect
507. C₄×D₈	C₂²×C₁₁	semidirect
508. #433	C₂²×C₁₁	semidirect
509. #432	C₂²×C₁₁	semidirect
510. #431	C₂²×C₁₁	semidirect
511. #428	C₂²×C₁₁	semidirect
512. C₂×#106	C₂²×C₁₁	semidirect
513. #423	C₂²×C₁₁	semidirect
514. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
516. #417	C₂²×C₁₁	semidirect
517. #416	C₂²×C₁₁	semidirect
520. #405	C₂²×C₁₁	semidirect
711. #41	C₁₁×#41	semidirect
733. C₂×D₄	C₁₁×#41	semidirect
820. C₁₁	#60597	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3511	2
C₄×C₁₁×H(5,𝔽₂)	2
C₁₁×#3125	2
C₁₁×#3118	2
C₁₁×#3116	2
C₁₁×#3109	2
C₁₁×#3106	2
C₁₁×#3101	2
C₁₁×#3099	2
C₁₁×#3079	2
C₂×C₁₁×#476	2
C₁₁×#3036	2
C₁₁×#3035	2
C₁₁×#3012	2
C₁₁×#2952	2
C₁₁×#2946	2
C₁₁×#2925	2
#60597	11

Subgroups — C11×#60597 #14637790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60597 #14637790