Subgroups — #576×AGL(1,𝔽₁₁) #72269602

Order 7040.

3024 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72269581	C₂	1	3	yes	maximal, complemented
2	#72269567	C₂	1	2	yes	maximal, complemented
3	#72269559	C₂	1	1	yes	maximal, characteristic, complemented
4	#72269550	C₂	1	6	yes	maximal, complemented
5	#72269543	C₂	1	3	yes	maximal, complemented
6	C₁₁⋊C₅×#576	C₂	1	1	yes	maximal, characteristic, complemented
7	#131×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
8	#135×AGL(1,𝔽₁₁)	C₂	1	3	yes	maximal, complemented
9	H(5,𝔽₂)×AGL(1,𝔽₁₁)	C₂	1	2	yes	maximal, complemented
10	AGL(1,ℤ/8)×AGL(1,𝔽₁₁)	C₂	1	6	yes	maximal, complemented
11	C₂×D₈×AGL(1,𝔽₁₁)	C₂	1	3	yes	maximal, complemented
12	H(5,𝔽₂)×C₁₁⋊C₅	C₂²	1	2	yes	complemented
13	#67042⋊C₅	—	2	2	no	—
14	#67042⋊C₅	C₂²	1	6	yes	complemented
15	#67042⋊C₅	C₂²	1	2	yes	complemented
16	#41×AGL(1,𝔽₁₁)	—	2	2	no	—
17	#41×AGL(1,𝔽₁₁)	C₂²	1	1	yes	characteristic
18	#41×AGL(1,𝔽₁₁)	C₂²	1	6	yes	complemented
19	#67037⋊C₅	—	2	6	no	—
20	#67037⋊C₅	C₂²	1	6	yes	complemented
21	C₂×D₄×AGL(1,𝔽₁₁)	—	2	6	no	—
22	C₂×D₄×AGL(1,𝔽₁₁)	C₂²	1	6	yes	complemented
23	AGL(1,ℤ/8)×C₁₁⋊C₅	C₂²	1	6	yes	complemented
24	#135×C₁₁⋊C₅	C₂²	1	3	yes	complemented
25	C₂×D₈×C₁₁⋊C₅	C₂²	1	3	yes	complemented
26	#131×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented
27	#67003⋊C₅	C₂²	1	6	yes	complemented
28	#67002⋊C₅	C₂²	1	6	yes	complemented
29	#67001⋊C₅	C₂²	1	1	yes	characteristic, complemented
30	#66985⋊C₅	C₂²	1	6	yes	complemented
31	C₂×#4323⋊C₅	C₂²	1	6	yes	complemented
32	#66972⋊C₅	C₂²	1	3	yes	complemented
33	Q₁₆×AGL(1,𝔽₁₁)	C₂²	1	1	yes	characteristic, complemented
34	#66969⋊C₅	C₂²	1	6	yes	complemented
35	#66967⋊C₅	C₂²	1	12	yes	complemented
36	SD₁₆×AGL(1,𝔽₁₁)	C₂²	1	6	yes	complemented
37	#66965⋊C₅	C₂²	1	3	yes	complemented
38	#66964⋊C₅	C₂²	1	12	yes	complemented
39	D₈×AGL(1,𝔽₁₁)	C₂²	1	3	yes	complemented
40	D₈×AGL(1,𝔽₁₁)	C₂²	1	6	yes	complemented
41	D₈×AGL(1,𝔽₁₁)	C₂²	1	6	yes	complemented
42	D₈×AGL(1,𝔽₁₁)	C₂²	1	6	yes	complemented
43	#66961⋊C₅	C₂²	1	6	yes	complemented
44	#66960⋊C₅	C₂²	1	3	yes	complemented
45	M₁₆×AGL(1,𝔽₁₁)	C₂²	1	3	yes	complemented
46	#66957⋊C₅	C₂²	1	3	yes	complemented
47	C₂×D₈₈⋊C₅	C₂²	1	3	yes	complemented
48	#66954⋊C₅	C₂²	1	3	yes	complemented
49	C₂×C₈×AGL(1,𝔽₁₁)	C₂²	1	3	yes	complemented
50	D₁₁×#576	C₅	1	1	yes	maximal, characteristic, complemented, Hall
51	C₂³×AGL(1,𝔽₁₁)	—	2	6	no	—
52	#41×C₁₁⋊C₅	—	2	2	no	—
53	#41×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
54	#41×C₁₁⋊C₅	C₂³	1	6	yes	complemented
55	C₂×D₄×C₁₁⋊C₅	—	2	6	no	—
56	C₂×D₄×C₁₁⋊C₅	C₂³	1	6	yes	complemented
57	C₂×C₂²⋊AGL(1,𝔽₁₁)	—	2	12	no	—
58	C₂×C₂²⋊AGL(1,𝔽₁₁)	—	2	6	no	—
59	#4343⋊C₅	—	2	2	no	—
60	#4343⋊C₅	D₄	1	1	yes	characteristic
61	#4343⋊C₅	C₂³	1	6	yes	complemented
62	Q₈×AGL(1,𝔽₁₁)	D₄	1	1	yes	characteristic
63	Q₈×AGL(1,𝔽₁₁)	C₂³	1	2	yes	—
64	#4341⋊C₅	—	2	6	no	—
65	#4341⋊C₅	—	2	6	no	—
66	#4341⋊C₅	D₄	1	3	yes	—
67	#4341⋊C₅	C₂³	1	6	yes	complemented
68	D₄×AGL(1,𝔽₁₁)	—	2	6	no	—
69	D₄×AGL(1,𝔽₁₁)	—	2	6	no	—
70	D₄×AGL(1,𝔽₁₁)	—	2	12	no	—
71	D₄×AGL(1,𝔽₁₁)	—	2	6	no	—
72	D₄×AGL(1,𝔽₁₁)	—	2	6	no	—
73	D₄×AGL(1,𝔽₁₁)	—	2	6	no	—
74	D₄×AGL(1,𝔽₁₁)	D₄	1	3	yes	—
75	D₄×AGL(1,𝔽₁₁)	C₂³	1	6	yes	—
76	D₄×AGL(1,𝔽₁₁)	C₂³	1	12	yes	complemented
77	#4339⋊C₅	—	2	6	no	—
78	#4339⋊C₅	—	2	6	no	—
79	#4339⋊C₅	C₂³	1	3	yes	—
80	#4339⋊C₅	C₂³	1	6	yes	complemented
81	C₂×C₄⋊AGL(1,𝔽₁₁)	—	2	6	no	—
82	C₂×C₄⋊AGL(1,𝔽₁₁)	C₂³	1	6	yes	complemented
83	C₂×C₄×AGL(1,𝔽₁₁)	—	2	6	no	—
84	C₂×C₄×AGL(1,𝔽₁₁)	C₂³	1	3	yes	—
85	Q₁₆×C₁₁⋊C₅	C₂³	1	1	yes	characteristic, complemented
86	SD₁₆×C₁₁⋊C₅	C₂³	1	6	yes	complemented
87	D₈×C₁₁⋊C₅	C₂³	1	3	yes	complemented
88	D₈×C₁₁⋊C₅	C₂³	1	6	yes	complemented
89	M₁₆×C₁₁⋊C₅	C₂³	1	3	yes	complemented
90	C₂×C₈×C₁₁⋊C₅	C₂³	1	3	yes	complemented
91	#4326⋊C₅	C₂³	1	2	yes	complemented
92	#4325⋊C₅	C₂³	1	6	yes	complemented
93	#4324⋊C₅	C₂³	1	6	yes	complemented
94	#4323⋊C₅	C₂³	1	6	yes	complemented
95	#4323⋊C₅	C₂³	1	12	yes	complemented
96	#4318⋊C₅	C₂³	1	3	yes	complemented
97	C₂×(C₁₁⋊C₅)⋊C₈	C₂³	1	3	yes	complemented
98	Dic₄₄⋊C₅	C₂³	1	1	yes	characteristic, complemented
99	D₈₈⋊C₅	C₂³	1	3	yes	complemented
100	D₈₈⋊C₅	C₂³	1	6	yes	complemented
101	#4314⋊C₅	C₂³	1	6	yes	complemented
102	#4313⋊C₅	C₂³	1	6	yes	complemented
103	C₈×AGL(1,𝔽₁₁)	C₂³	1	1	yes	characteristic
104	C₈×AGL(1,𝔽₁₁)	C₂³	1	3	yes	—
105	C₈×AGL(1,𝔽₁₁)	C₂³	1	3	yes	complemented
106	C₈×AGL(1,𝔽₁₁)	C₂³	1	3	yes	complemented
107	D₁₁×H(5,𝔽₂)	C₂×C₅	1	2	yes	complemented
108	C₁₁×#576	C₂×C₅	1	1	yes	characteristic, complemented
109	#10623366	C₂×C₅	1	2	yes	complemented
110	#10623305	C₂×C₅	1	6	yes	complemented
111	D₁₁×AGL(1,ℤ/8)	C₂×C₅	1	6	yes	complemented
112	#10623300	C₂×C₅	1	3	yes	complemented
113	D₁₁×#135	C₂×C₅	1	3	yes	complemented
114	#10623288	C₂×C₅	1	3	yes	complemented
115	C₂×D₈×D₁₁	C₂×C₅	1	3	yes	complemented
116	#10623283	C₂×C₅	1	1	yes	characteristic, complemented
117	D₁₁×#131	C₂×C₅	1	1	yes	characteristic, complemented
118	C₂×C₅×#576	—	11	1	no	maximal, Hall
119	C₂³×C₁₁⋊C₅	—	2	6	no	—
120	C₂²×AGL(1,𝔽₁₁)	—	2	6	no	—
121	C₂²×AGL(1,𝔽₁₁)	—	2	6	no	—
122	C₂²×AGL(1,𝔽₁₁)	—	2	12	no	—
123	C₂²×AGL(1,𝔽₁₁)	—	8	12	no	—
124	C₂²×AGL(1,𝔽₁₁)	C₂×D₄	1	3	yes	—
125	Q₈×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
126	Q₈×C₁₁⋊C₅	C₂⁴	1	2	yes	—
127	D₄×C₁₁⋊C₅	—	2	6	no	—
128	D₄×C₁₁⋊C₅	—	2	6	no	—
129	D₄×C₁₁⋊C₅	C₂×D₄	1	3	yes	—
130	D₄×C₁₁⋊C₅	C₂⁴	1	6	yes	—
131	C₂×C₄×C₁₁⋊C₅	—	2	6	no	—
132	C₂×C₄×C₁₁⋊C₅	C₂⁴	1	3	yes	—
133	C₂²⋊AGL(1,𝔽₁₁)	—	2	6	no	—
134	C₂²⋊AGL(1,𝔽₁₁)	—	2	6	no	—
135	C₂²⋊AGL(1,𝔽₁₁)	—	2	6	no	—
136	C₂²⋊AGL(1,𝔽₁₁)	—	2	12	no	—
137	C₂²⋊AGL(1,𝔽₁₁)	C₂×D₄	1	6	yes	—
138	C₂×Dic₁₁⋊C₅	—	2	6	no	—
139	C₂×Dic₁₁⋊C₅	C₂×D₄	1	3	yes	—
140	C₄⋊AGL(1,𝔽₁₁)	—	2	6	no	—
141	C₄⋊AGL(1,𝔽₁₁)	—	2	6	no	—
142	C₄⋊AGL(1,𝔽₁₁)	C₂×D₄	1	3	yes	—
143	C₄⋊AGL(1,𝔽₁₁)	C₂⁴	1	6	yes	—
144	C₄×AGL(1,𝔽₁₁)	—	2	2	no	—
145	C₄×AGL(1,𝔽₁₁)	—	2	6	no	—
146	C₄×AGL(1,𝔽₁₁)	—	2	6	no	—
147	C₄×AGL(1,𝔽₁₁)	C₂×D₄	1	3	yes	—
148	C₄×AGL(1,𝔽₁₁)	C₂×D₄	1	3	yes	—
149	C₄×AGL(1,𝔽₁₁)	C₂⁴	1	1	yes	characteristic
150	C₄×AGL(1,𝔽₁₁)	C₂⁴	1	3	yes	—
151	(C₁₁⋊C₅)⋊Q₈	—	2	2	no	—
152	(C₁₁⋊C₅)⋊Q₈	C₂×D₄	1	3	yes	—
153	(C₁₁⋊C₅)⋊Q₈	C₂⁴	1	2	yes	—
154	C₈×C₁₁⋊C₅	C₂⁴	1	1	yes	characteristic
155	C₈×C₁₁⋊C₅	C₂⁴	1	3	yes	—
156	(C₁₁⋊C₅)⋊C₈	C₂⁴	1	1	yes	characteristic
157	(C₁₁⋊C₅)⋊C₈	C₂⁴	1	3	yes	—
158	C₁₁×H(5,𝔽₂)	C₂²×C₅	1	2	yes	complemented
159	#67042	—	2	2	no	—
160	#67042	C₂²×C₅	1	6	yes	complemented
161	#67042	C₂²×C₅	1	2	yes	complemented
162	#41×D₁₁	—	2	2	no	—
163	#41×D₁₁	C₂²×C₅	1	1	yes	characteristic
164	#41×D₁₁	C₂²×C₅	1	6	yes	complemented
165	#67037	—	2	6	no	—
166	#67037	C₂²×C₅	1	6	yes	complemented
167	C₂×D₄×D₁₁	—	2	6	no	—
168	C₂×D₄×D₁₁	C₂²×C₅	1	6	yes	complemented
169	C₁₁×AGL(1,ℤ/8)	C₂²×C₅	1	6	yes	complemented
170	C₁₁×#135	C₂²×C₅	1	3	yes	complemented
171	C₂×C₁₁×D₈	C₂²×C₅	1	3	yes	complemented
172	C₁₁×#131	C₂²×C₅	1	1	yes	characteristic, complemented
173	#67003	C₂²×C₅	1	6	yes	complemented
174	#67002	C₂²×C₅	1	6	yes	complemented
175	#67001	C₂²×C₅	1	1	yes	characteristic, complemented
176	#66985	C₂²×C₅	1	6	yes	complemented
177	C₂×#4323	C₂²×C₅	1	6	yes	complemented
178	#66972	C₂²×C₅	1	3	yes	complemented
179	Q₁₆×D₁₁	C₂²×C₅	1	1	yes	characteristic, complemented
180	#66969	C₂²×C₅	1	6	yes	complemented
181	#66967	C₂²×C₅	1	12	yes	complemented
182	SD₁₆×D₁₁	C₂²×C₅	1	6	yes	complemented
183	#66965	C₂²×C₅	1	3	yes	complemented
184	#66964	C₂²×C₅	1	12	yes	complemented
185	D₈×D₁₁	C₂²×C₅	1	3	yes	complemented
186	D₈×D₁₁	C₂²×C₅	1	6	yes	complemented
187	D₈×D₁₁	C₂²×C₅	1	6	yes	complemented
188	D₈×D₁₁	C₂²×C₅	1	6	yes	complemented
189	#66961	C₂²×C₅	1	6	yes	complemented
190	#66960	C₂²×C₅	1	3	yes	complemented
191	M₁₆×D₁₁	C₂²×C₅	1	3	yes	complemented
192	#66957	C₂²×C₅	1	3	yes	complemented
193	C₂×D₈₈	C₂²×C₅	1	3	yes	complemented
194	#66954	C₂²×C₅	1	3	yes	complemented
195	C₂×C₈×D₁₁	C₂²×C₅	1	3	yes	complemented
196	C₂×C₅×H(5,𝔽₂)	—	11	2	no	—
197	C₅×#576	—	11	2	no	—
198	C₅×#576	—	11	6	no	—
199	C₅×#576	—	11	3	no	—
200	C₅×#576	—	11	3	no	—
201	C₅×#576	—	11	1	no	—
202	C₅×#576	—	22	1	no	—
203	C₂×C₅×AGL(1,ℤ/8)	—	11	6	no	—
204	C₂×C₅×#135	—	11	3	no	—
205	C₂²×C₅×D₈	—	11	3	no	—
206	C₂×C₅×#131	—	11	1	no	—
207	C₂²×C₁₁⋊C₅	—	2	6	no	—
208	C₂²×C₁₁⋊C₅	—	8	6	no	—
209	C₂²×C₁₁⋊C₅	C₂²×D₄	1	3	yes	—
210	C₂×AGL(1,𝔽₁₁)	—	2	6	no	—
211	C₂×AGL(1,𝔽₁₁)	—	2	6	no	—
212	C₂×AGL(1,𝔽₁₁)	—	4	12	no	—
213	C₂×AGL(1,𝔽₁₁)	—	8	12	no	—
214	C₂×AGL(1,𝔽₁₁)	—	8	6	no	—
215	C₂×AGL(1,𝔽₁₁)	C₂²×D₄	1	3	yes	—
216	C₂×AGL(1,𝔽₁₁)	C₂²×D₄	1	1	yes	characteristic
217	C₄×C₁₁⋊C₅	—	2	2	no	—
218	C₄×C₁₁⋊C₅	C₂²×D₄	1	3	yes	—
219	C₄×C₁₁⋊C₅	C₂⁵	1	1	yes	characteristic
220	Dic₁₁⋊C₅	—	2	2	no	—
221	Dic₁₁⋊C₅	C₂²×D₄	1	1	yes	characteristic
222	Dic₁₁⋊C₅	C₂²×D₄	1	3	yes	—
223	C₂³×D₁₁	—	2	6	no	—
224	C₁₁×#41	—	2	2	no	—
225	C₁₁×#41	C₂³×C₅	1	1	yes	characteristic
226	C₁₁×#41	C₂³×C₅	1	6	yes	complemented
227	C₂×D₄×C₁₁	—	2	6	no	—
228	C₂×D₄×C₁₁	C₂³×C₅	1	6	yes	complemented
229	C₂×C₂²⋊D₁₁	—	2	12	no	—
230	C₂×C₂²⋊D₁₁	—	2	6	no	—
231	#4343	—	2	2	no	—
232	#4343	C₅×D₄	1	1	yes	characteristic
233	#4343	C₂³×C₅	1	6	yes	complemented
234	Q₈×D₁₁	C₅×D₄	1	1	yes	characteristic
235	Q₈×D₁₁	C₂³×C₅	1	2	yes	—
236	#4341	—	2	6	no	—
237	#4341	—	2	6	no	—
238	#4341	C₅×D₄	1	3	yes	—
239	#4341	C₂³×C₅	1	6	yes	complemented
240	D₄×D₁₁	—	2	12	no	—
241	D₄×D₁₁	—	2	6	no	—
242	D₄×D₁₁	—	2	6	no	—
243	D₄×D₁₁	—	2	6	no	—
244	D₄×D₁₁	—	2	6	no	—
245	D₄×D₁₁	—	2	6	no	—
246	D₄×D₁₁	C₅×D₄	1	3	yes	—
247	D₄×D₁₁	C₂³×C₅	1	6	yes	—
248	D₄×D₁₁	C₂³×C₅	1	12	yes	complemented
249	#4339	—	2	6	no	—
250	#4339	—	2	6	no	—
251	#4339	C₂³×C₅	1	3	yes	—
252	#4339	C₂³×C₅	1	6	yes	complemented
253	C₂×D₄₄	—	2	6	no	—
254	C₂×D₄₄	C₂³×C₅	1	6	yes	complemented
255	C₂×C₄×D₁₁	—	2	6	no	—
256	C₂×C₄×D₁₁	C₂³×C₅	1	3	yes	—
257	C₁₁×Q₁₆	C₂³×C₅	1	1	yes	characteristic, complemented
258	C₁₁×SD₁₆	C₂³×C₅	1	6	yes	complemented
259	C₁₁×D₈	C₂³×C₅	1	3	yes	complemented
260	C₁₁×D₈	C₂³×C₅	1	6	yes	complemented
261	C₁₁×M₁₆	C₂³×C₅	1	3	yes	complemented
262	C₂×C₈×C₁₁	C₂³×C₅	1	3	yes	complemented
263	#4326	C₂³×C₅	1	2	yes	complemented
264	#4325	C₂³×C₅	1	6	yes	complemented
265	#4324	C₂³×C₅	1	6	yes	complemented
266	#4323	C₂³×C₅	1	6	yes	complemented
267	#4323	C₂³×C₅	1	12	yes	complemented
268	#4318	C₂³×C₅	1	3	yes	complemented
269	C₂×C₁₁⋊C₈	C₂³×C₅	1	3	yes	complemented
270	Dic₄₄	C₂³×C₅	1	1	yes	characteristic, complemented
271	D₈₈	C₂³×C₅	1	3	yes	complemented
272	D₈₈	C₂³×C₅	1	6	yes	complemented
273	#4314	C₂³×C₅	1	6	yes	complemented
274	#4313	C₂³×C₅	1	6	yes	complemented
275	C₈×D₁₁	C₂³×C₅	1	1	yes	characteristic
276	C₈×D₁₁	C₂³×C₅	1	3	yes	—
277	C₈×D₁₁	C₂³×C₅	1	3	yes	complemented
278	C₈×D₁₁	C₂³×C₅	1	3	yes	complemented
279	C₅×H(5,𝔽₂)	—	11	2	no	—
280	C₅×H(5,𝔽₂)	—	11	6	no	—
281	C₅×H(5,𝔽₂)	—	11	6	no	—
282	C₅×H(5,𝔽₂)	—	22	2	no	—
283	C₅×H(5,𝔽₂)	—	22	6	no	—
284	C₅×H(5,𝔽₂)	—	22	2	no	—
285	C₂×C₅×#41	—	11	1	no	—
286	C₂×C₅×#41	—	11	6	no	—
287	C₂×C₅×#41	—	22	2	no	—
288	C₂²×C₅×D₄	—	11	6	no	—
289	C₂²×C₅×D₄	—	22	6	no	—
290	C₅×AGL(1,ℤ/8)	—	11	6	no	—
291	C₅×AGL(1,ℤ/8)	—	11	6	no	—
292	C₅×AGL(1,ℤ/8)	—	11	12	no	—
293	C₅×AGL(1,ℤ/8)	—	11	12	no	—
294	C₅×AGL(1,ℤ/8)	—	11	6	no	—
295	C₅×AGL(1,ℤ/8)	—	22	6	no	—
296	C₅×#135	—	11	6	no	—
297	C₅×#135	—	11	3	no	—
298	C₅×#135	—	11	6	no	—
299	C₅×#135	—	11	3	no	—
300	C₅×#135	—	11	3	no	—
301	C₅×#135	—	22	3	no	—
302	C₂×C₅×Q₁₆	—	11	1	no	—
303	C₂×C₅×SD₁₆	—	11	6	no	—
304	C₂×C₅×D₈	—	11	6	no	—
305	C₂×C₅×D₈	—	11	3	no	—
306	C₂×C₅×D₈	—	11	6	no	—
307	C₂×C₅×D₈	—	11	6	no	—
308	C₂×C₅×D₈	—	11	6	no	—
309	C₂×C₅×D₈	—	11	3	no	—
310	C₂×C₅×D₈	—	22	3	no	—
311	C₅×#131	—	11	1	no	—
312	C₅×#131	—	11	3	no	—
313	C₅×#131	—	11	3	no	—
314	C₅×#131	—	22	1	no	—
315	C₂×C₅×M₁₆	—	11	3	no	—
316	C₂²×C₅×C₈	—	11	3	no	—
317	C₂×#576	—	11	1	no	Sylow
318	C₂×C₁₁⋊C₅	—	2	3	no	—
319	C₂×C₁₁⋊C₅	—	4	6	no	—
320	C₂×C₁₁⋊C₅	C₂³×D₄	1	1	yes	characteristic
321	AGL(1,𝔽₁₁)	—	2	3	no	—
322	AGL(1,𝔽₁₁)	—	4	6	no	—
323	AGL(1,𝔽₁₁)	#576	1	2	yes	direct product factor
324	C₂³×C₁₁	—	2	6	no	—
325	C₂²×D₁₁	—	2	6	no	—
326	C₂²×D₁₁	—	2	6	no	—
327	C₂²×D₁₁	—	2	12	no	—
328	C₂²×D₁₁	—	8	12	no	—
329	C₂²×D₁₁	C₂×C₅×D₄	1	3	yes	—
330	Q₈×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
331	Q₈×C₁₁	C₂⁴×C₅	1	2	yes	—
332	D₄×C₁₁	—	2	6	no	—
333	D₄×C₁₁	—	2	6	no	—
334	D₄×C₁₁	C₂×C₅×D₄	1	3	yes	—
335	D₄×C₁₁	C₂⁴×C₅	1	6	yes	—
336	C₂×C₄×C₁₁	—	2	6	no	—
337	C₂×C₄×C₁₁	C₂⁴×C₅	1	3	yes	—
338	C₂²⋊D₁₁	—	2	6	no	—
339	C₂²⋊D₁₁	—	2	6	no	—
340	C₂²⋊D₁₁	—	2	6	no	—
341	C₂²⋊D₁₁	—	2	12	no	—
342	C₂²⋊D₁₁	C₂×C₅×D₄	1	6	yes	—
343	C₂×Dic₁₁	—	2	6	no	—
344	C₂×Dic₁₁	C₂×C₅×D₄	1	3	yes	—
345	D₄₄	—	2	6	no	—
346	D₄₄	—	2	6	no	—
347	D₄₄	C₂×C₅×D₄	1	3	yes	—
348	D₄₄	C₂⁴×C₅	1	6	yes	—
349	C₄×D₁₁	—	2	2	no	—
350	C₄×D₁₁	—	2	6	no	—
351	C₄×D₁₁	—	2	6	no	—
352	C₄×D₁₁	C₂×C₅×D₄	1	3	yes	—
353	C₄×D₁₁	C₂×C₅×D₄	1	3	yes	—
354	C₄×D₁₁	C₂⁴×C₅	1	1	yes	characteristic
355	C₄×D₁₁	C₂⁴×C₅	1	3	yes	—
356	Dic₂₂	—	2	2	no	—
357	Dic₂₂	C₂×C₅×D₄	1	3	yes	—
358	Dic₂₂	C₂⁴×C₅	1	2	yes	—
359	C₈×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
360	C₈×C₁₁	C₂⁴×C₅	1	3	yes	—
361	C₁₁⋊C₈	C₂⁴×C₅	1	1	yes	characteristic
362	C₁₁⋊C₈	C₂⁴×C₅	1	3	yes	—
363	C₂⁴×C₅	—	22	6	no	—
364	C₅×#41	—	11	1	no	—
365	C₅×#41	—	11	3	no	—
366	C₅×#41	—	11	3	no	—
367	C₅×#41	—	11	6	no	—
368	C₅×#41	—	11	6	no	—
369	C₅×#41	—	11	6	no	—
370	C₅×#41	—	22	6	no	—
371	C₅×#41	—	22	6	no	—
372	C₅×#41	—	22	2	no	—
373	C₅×#41	—	22	6	no	—
374	C₅×#41	—	22	6	no	—
375	C₅×#41	—	22	1	no	—
376	C₅×#41	—	22	6	no	—
377	C₅×#41	—	44	2	no	—
378	C₂×C₅×Q₈	—	11	1	no	—
379	C₂×C₅×Q₈	—	11	2	no	—
380	C₂×C₅×D₄	—	11	3	no	—
381	C₂×C₅×D₄	—	11	6	no	—
382	C₂×C₅×D₄	—	11	12	no	—
383	C₂×C₅×D₄	—	11	6	no	—
384	C₂×C₅×D₄	—	22	6	no	—
385	C₂×C₅×D₄	—	22	6	no	—
386	C₂×C₅×D₄	—	22	6	no	—
387	C₂×C₅×D₄	—	22	12	no	—
388	C₂×C₅×D₄	—	22	12	no	—
389	C₂×C₅×D₄	—	22	6	no	—
390	C₂×C₅×D₄	—	22	6	no	—
391	C₂×C₅×D₄	—	22	6	no	—
392	C₂×C₅×D₄	—	22	6	no	—
393	C₂×C₅×D₄	—	22	6	no	—
394	C₂×C₅×D₄	—	44	6	no	—
395	C₂²×C₄×C₅	—	11	3	no	—
396	C₂²×C₄×C₅	—	22	6	no	—
397	C₅×Q₁₆	—	11	2	no	—
398	C₅×Q₁₆	—	11	1	no	—
399	C₅×Q₁₆	—	22	1	no	—
400	C₅×SD₁₆	—	11	6	no	—
401	C₅×SD₁₆	—	11	6	no	—
402	C₅×SD₁₆	—	11	6	no	—
403	C₅×SD₁₆	—	22	6	no	—
404	C₅×D₈	—	11	6	no	—
405	C₅×D₈	—	11	12	no	—
406	C₅×D₈	—	11	3	no	—
407	C₅×D₈	—	11	6	no	—
408	C₅×D₈	—	22	3	no	—
409	C₅×D₈	—	22	6	no	—
410	C₅×M₁₆	—	11	3	no	—
411	C₅×M₁₆	—	11	6	no	—
412	C₅×M₁₆	—	22	3	no	—
413	C₂×C₅×C₈	—	11	3	no	—
414	C₂×C₅×C₈	—	11	1	no	—
415	C₂×C₅×C₈	—	11	3	no	—
416	C₂×C₅×C₈	—	11	3	no	—
417	C₂×C₅×C₈	—	11	3	no	—
418	C₂×C₅×C₈	—	22	3	no	—
419	C₂×H(5,𝔽₂)	—	11	2	no	—
420	#576	—	11	2	no	—
421	#576	—	11	6	no	—
422	#576	—	11	3	no	—
423	#576	—	11	3	no	—
424	#576	—	11	1	no	—
425	#576	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
426	C₂×AGL(1,ℤ/8)	—	11	6	no	—
427	C₂×#135	—	11	3	no	—
428	C₂²×D₈	—	11	3	no	—
429	C₂×#131	—	11	1	no	—
430	C₁₁⋊C₅	C₂×#576	1	1	yes	characteristic, complemented, Hall
431	C₂²×C₁₁	—	2	6	no	—
432	C₂²×C₁₁	—	8	6	no	—
433	C₂²×C₁₁	C₂²×C₅×D₄	1	3	yes	—
434	C₂×D₁₁	—	2	6	no	—
435	C₂×D₁₁	—	2	6	no	—
436	C₂×D₁₁	—	4	12	no	—
437	C₂×D₁₁	—	8	12	no	—
438	C₂×D₁₁	—	8	6	no	—
439	C₂×D₁₁	C₂²×C₅×D₄	1	3	yes	—
440	C₂×D₁₁	C₂²×C₅×D₄	1	1	yes	characteristic
441	C₄×C₁₁	—	2	2	no	—
442	C₄×C₁₁	C₂²×C₅×D₄	1	3	yes	—
443	C₄×C₁₁	C₂⁵×C₅	1	1	yes	characteristic
444	Dic₁₁	—	2	2	no	—
445	Dic₁₁	C₂²×C₅×D₄	1	1	yes	characteristic
446	Dic₁₁	C₂²×C₅×D₄	1	3	yes	—
447	C₂³×C₅	—	11	3	no	—
448	C₂³×C₅	—	22	6	no	—
449	C₂³×C₅	—	22	12	no	—
450	C₂³×C₅	—	22	6	no	—
451	C₂³×C₅	—	44	6	no	—
452	C₂³×C₅	—	88	12	no	—
453	C₅×Q₈	—	11	3	no	—
454	C₅×Q₈	—	11	2	no	—
455	C₅×Q₈	—	22	2	no	—
456	C₅×Q₈	—	22	1	no	—
457	C₅×Q₈	—	22	2	no	—
458	C₅×D₄	—	11	6	no	—
459	C₅×D₄	—	11	3	no	—
460	C₅×D₄	—	11	6	no	—
461	C₅×D₄	—	22	6	no	—
462	C₅×D₄	—	22	12	no	—
463	C₅×D₄	—	22	6	no	—
464	C₅×D₄	—	22	6	no	—
465	C₅×D₄	—	22	6	no	—
466	C₅×D₄	—	22	6	no	—
467	C₅×D₄	—	22	3	no	—
468	C₅×D₄	—	22	6	no	—
469	C₅×D₄	—	44	6	no	—
470	C₅×D₄	—	44	6	no	—
471	C₂×C₄×C₅	—	11	3	no	—
472	C₂×C₄×C₅	—	11	3	no	—
473	C₂×C₄×C₅	—	11	3	no	—
474	C₂×C₄×C₅	—	11	1	no	—
475	C₂×C₄×C₅	—	11	3	no	—
476	C₂×C₄×C₅	—	22	6	no	—
477	C₂×C₄×C₅	—	22	6	no	—
478	C₂×C₄×C₅	—	22	6	no	—
479	C₂×C₄×C₅	—	22	2	no	—
480	C₂×C₄×C₅	—	22	3	no	—
481	C₂×C₄×C₅	—	44	6	no	—
482	C₅×C₈	—	11	1	no	—
483	C₅×C₈	—	11	3	no	—
484	C₅×C₈	—	22	1	no	—
485	C₅×C₈	—	22	3	no	—
486	H(5,𝔽₂)	—	11	2	no	—
487	H(5,𝔽₂)	—	11	6	no	—
488	H(5,𝔽₂)	—	11	6	no	—
489	H(5,𝔽₂)	—	22	6	no	—
490	H(5,𝔽₂)	—	22	2	no	—
491	H(5,𝔽₂)	C₂×AGL(1,𝔽₁₁)	1	2	yes	complemented
492	C₂×#41	—	11	1	no	—
493	C₂×#41	—	11	6	no	—
494	C₂×#41	—	22	2	no	—
495	C₂²×D₄	—	11	6	no	—
496	C₂²×D₄	—	22	6	no	—
497	AGL(1,ℤ/8)	—	11	6	no	—
498	AGL(1,ℤ/8)	—	11	6	no	—
499	AGL(1,ℤ/8)	—	11	12	no	—
500	AGL(1,ℤ/8)	—	11	12	no	—
501	AGL(1,ℤ/8)	—	11	6	no	—
502	AGL(1,ℤ/8)	C₂×AGL(1,𝔽₁₁)	1	6	yes	complemented
503	#135	—	11	6	no	—
504	#135	—	11	3	no	—
505	#135	—	11	6	no	—
506	#135	—	11	3	no	—
507	#135	—	11	3	no	—
508	#135	C₂×AGL(1,𝔽₁₁)	1	3	yes	complemented
509	C₂×Q₁₆	—	11	1	no	—
510	C₂×SD₁₆	—	11	6	no	—
511	C₂×D₈	—	11	6	no	—
512	C₂×D₈	—	11	3	no	—
513	C₂×D₈	—	11	6	no	—
514	C₂×D₈	—	11	6	no	—
515	C₂×D₈	—	11	6	no	—
516	C₂×D₈	—	11	3	no	—
517	C₂×D₈	C₂×AGL(1,𝔽₁₁)	1	3	yes	complemented
518	#131	—	11	1	no	—
519	#131	—	11	3	no	—
520	#131	—	11	3	no	—
521	#131	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
522	C₂×M₁₆	—	11	3	no	—
523	C₂²×C₈	—	11	3	no	—
524	C₂×C₁₁	—	2	3	no	—
525	C₂×C₁₁	—	4	6	no	—
526	C₂×C₁₁	C₂³×C₅×D₄	1	1	yes	characteristic
527	D₁₁	—	2	3	no	—
528	D₁₁	—	4	6	no	—
529	D₁₁	C₅×#576	1	2	yes	complemented
530	C₂²×C₅	—	11	1	no	—
531	C₂²×C₅	—	11	3	no	—
532	C₂²×C₅	—	22	6	no	—
533	C₂²×C₅	—	22	6	no	—
534	C₂²×C₅	—	22	3	no	—
535	C₂²×C₅	—	44	6	no	—
536	C₂²×C₅	—	44	12	no	—
537	C₂²×C₅	—	88	12	no	—
538	C₂²×C₅	—	88	6	no	—
539	C₂²×C₅	—	176	6	no	—
540	C₄×C₅	—	11	1	no	—
541	C₄×C₅	—	11	3	no	—
542	C₄×C₅	—	22	2	no	—
543	C₄×C₅	—	22	3	no	—
544	C₄×C₅	—	22	1	no	—
545	C₄×C₅	—	44	2	no	—
546	C₂⁴	—	22	6	no	—
547	#41	—	2	2	no	—
548	#41	—	11	1	no	—
549	#41	—	11	3	no	—
550	#41	—	11	3	no	—
551	#41	—	11	6	no	—
552	#41	—	11	6	no	—
553	#41	—	11	6	no	—
554	#41	—	22	6	no	—
555	#41	—	22	6	no	—
556	#41	—	22	6	no	—
557	#41	—	22	6	no	—
558	#41	—	22	2	no	—
559	#41	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
560	#41	C₂²×AGL(1,𝔽₁₁)	1	6	yes	complemented
561	C₂×Q₈	—	11	1	no	—
562	C₂×Q₈	—	11	2	no	—
563	C₂×D₄	—	2	6	no	—
564	C₂×D₄	—	11	3	no	—
565	C₂×D₄	—	11	6	no	—
566	C₂×D₄	—	11	12	no	—
567	C₂×D₄	—	11	6	no	—
568	C₂×D₄	—	22	6	no	—
569	C₂×D₄	—	22	6	no	—
570	C₂×D₄	—	22	6	no	—
571	C₂×D₄	—	22	6	no	—
572	C₂×D₄	—	22	12	no	—
573	C₂×D₄	—	22	6	no	—
574	C₂×D₄	—	22	6	no	—
575	C₂×D₄	—	22	12	no	—
576	C₂×D₄	—	22	6	no	—
577	C₂×D₄	C₂²×AGL(1,𝔽₁₁)	1	6	yes	complemented
578	C₂²×C₄	—	11	3	no	—
579	C₂²×C₄	—	22	6	no	—
580	Q₁₆	—	11	2	no	—
581	Q₁₆	—	11	1	no	—
582	Q₁₆	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
583	SD₁₆	—	11	6	no	—
584	SD₁₆	—	11	6	no	—
585	SD₁₆	—	11	6	no	—
586	SD₁₆	C₂²×AGL(1,𝔽₁₁)	1	6	yes	complemented
587	D₈	—	11	6	no	—
588	D₈	—	11	12	no	—
589	D₈	—	11	3	no	—
590	D₈	—	11	6	no	—
591	D₈	C₂²×AGL(1,𝔽₁₁)	1	3	yes	complemented
592	D₈	C₂²×AGL(1,𝔽₁₁)	1	6	yes	complemented
593	M₁₆	—	11	3	no	—
594	M₁₆	—	11	6	no	—
595	M₁₆	C₂²×AGL(1,𝔽₁₁)	1	3	yes	complemented
596	C₂×C₈	—	11	3	no	—
597	C₂×C₈	—	11	1	no	—
598	C₂×C₈	—	11	3	no	—
599	C₂×C₈	—	11	3	no	—
600	C₂×C₈	—	11	3	no	—
601	C₂×C₈	C₂²×AGL(1,𝔽₁₁)	1	3	yes	complemented
602	C₁₁	C₂×C₅×#576	1	1	yes	characteristic, complemented, Sylow
603	C₂×C₅	—	11	2	no	—
604	C₂×C₅	—	22	3	no	—
605	C₂×C₅	—	22	1	no	—
606	C₂×C₅	—	44	3	no	—
607	C₂×C₅	—	44	6	no	—
608	C₂×C₅	—	88	6	no	—
609	C₂³	—	2	6	no	—
610	C₂³	—	11	3	no	—
611	C₂³	—	22	6	no	—
612	C₂³	—	22	12	no	—
613	C₂³	—	22	6	no	—
614	C₂³	—	88	12	no	—
615	Q₈	—	11	3	no	—
616	Q₈	—	11	2	no	—
617	Q₈	—	22	2	no	—
618	Q₈	D₄×AGL(1,𝔽₁₁)	1	1	yes	characteristic
619	Q₈	C₂³×AGL(1,𝔽₁₁)	1	2	yes	—
620	D₄	—	2	6	no	—
621	D₄	—	2	6	no	—
622	D₄	—	11	6	no	—
623	D₄	—	11	3	no	—
624	D₄	—	11	6	no	—
625	D₄	—	22	6	no	—
626	D₄	—	22	6	no	—
627	D₄	—	22	12	no	—
628	D₄	—	22	6	no	—
629	D₄	—	22	6	no	—
630	D₄	—	22	6	no	—
631	D₄	D₄×AGL(1,𝔽₁₁)	1	3	yes	—
632	D₄	C₂³×AGL(1,𝔽₁₁)	1	6	yes	—
633	C₂×C₄	—	2	6	no	—
634	C₂×C₄	—	11	3	no	—
635	C₂×C₄	—	11	3	no	—
636	C₂×C₄	—	11	3	no	—
637	C₂×C₄	—	11	1	no	—
638	C₂×C₄	—	11	3	no	—
639	C₂×C₄	—	22	6	no	—
640	C₂×C₄	—	22	2	no	—
641	C₂×C₄	—	22	6	no	—
642	C₂×C₄	—	22	6	no	—
643	C₂×C₄	C₂³×AGL(1,𝔽₁₁)	1	3	yes	—
644	C₈	—	11	1	no	—
645	C₈	—	11	3	no	—
646	C₈	C₂³×AGL(1,𝔽₁₁)	1	1	yes	characteristic
647	C₈	C₂³×AGL(1,𝔽₁₁)	1	3	yes	—
648	C₅	—	22	1	no	Sylow
649	C₂²	—	2	6	no	—
650	C₂²	—	8	6	no	—
651	C₂²	—	11	1	no	—
652	C₂²	—	11	3	no	—
653	C₂²	—	22	6	no	—
654	C₂²	—	22	6	no	—
655	C₂²	—	44	12	no	—
656	C₂²	—	88	6	no	—
657	C₂²	—	88	12	no	—
658	C₂²	C₂×D₄×AGL(1,𝔽₁₁)	1	3	yes	—
659	C₄	—	2	2	no	—
660	C₄	—	11	1	no	—
661	C₄	—	11	3	no	—
662	C₄	—	22	2	no	—
663	C₄	C₂×D₄×AGL(1,𝔽₁₁)	1	3	yes	—
664	C₄	C₂⁴×AGL(1,𝔽₁₁)	1	1	yes	characteristic
665	C₂	—	2	3	no	—
666	C₂	—	4	6	no	—
667	C₂	—	11	2	no	—
668	C₂	—	22	3	no	—
669	C₂	—	44	6	no	—
670	C₂	C₂²×D₄×AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×AGL(1,𝔽₁₁)
commutator, cosocle	C₄×C₁₁	C₂⁵×C₅
Frattini	C₄	C₂⁴×AGL(1,𝔽₁₁)
Fitting	C₁₁×#576	C₂×C₅
socle	C₂×C₁₁	C₂³×C₅×D₄
hypercenter	#576	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₂×C₅×#576
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. #72269581	C₂	semidirect
2. #72269567	C₂	semidirect
3. #72269559	C₂	semidirect
4. #72269550	C₂	semidirect
5. #72269543	C₂	semidirect
6. C₁₁⋊C₅×#576	C₂	semidirect
7. #131×AGL(1,𝔽₁₁)	C₂	semidirect
8. #135×AGL(1,𝔽₁₁)	C₂	semidirect
9. H(5,𝔽₂)×AGL(1,𝔽₁₁)	C₂	semidirect
10. AGL(1,ℤ/8)×AGL(1,𝔽₁₁)	C₂	semidirect
11. C₂×D₈×AGL(1,𝔽₁₁)	C₂	semidirect
12. H(5,𝔽₂)×C₁₁⋊C₅	C₂²	semidirect
14. #67042⋊C₅	C₂²	semidirect
15. #67042⋊C₅	C₂²	semidirect
18. #41×AGL(1,𝔽₁₁)	C₂²	semidirect
20. #67037⋊C₅	C₂²	semidirect
22. C₂×D₄×AGL(1,𝔽₁₁)	C₂²	semidirect
23. AGL(1,ℤ/8)×C₁₁⋊C₅	C₂²	semidirect
24. #135×C₁₁⋊C₅	C₂²	semidirect
25. C₂×D₈×C₁₁⋊C₅	C₂²	semidirect
26. #131×C₁₁⋊C₅	C₂²	semidirect
27. #67003⋊C₅	C₂²	semidirect
28. #67002⋊C₅	C₂²	semidirect
29. #67001⋊C₅	C₂²	semidirect
30. #66985⋊C₅	C₂²	semidirect
31. C₂×#4323⋊C₅	C₂²	semidirect
32. #66972⋊C₅	C₂²	semidirect
33. Q₁₆×AGL(1,𝔽₁₁)	C₂²	semidirect
34. #66969⋊C₅	C₂²	semidirect
35. #66967⋊C₅	C₂²	semidirect
36. SD₁₆×AGL(1,𝔽₁₁)	C₂²	semidirect
37. #66965⋊C₅	C₂²	semidirect
38. #66964⋊C₅	C₂²	semidirect
39. D₈×AGL(1,𝔽₁₁)	C₂²	semidirect
40. D₈×AGL(1,𝔽₁₁)	C₂²	semidirect
41. D₈×AGL(1,𝔽₁₁)	C₂²	semidirect
42. D₈×AGL(1,𝔽₁₁)	C₂²	semidirect
43. #66961⋊C₅	C₂²	semidirect
44. #66960⋊C₅	C₂²	semidirect
45. M₁₆×AGL(1,𝔽₁₁)	C₂²	semidirect
46. #66957⋊C₅	C₂²	semidirect
47. C₂×D₈₈⋊C₅	C₂²	semidirect
48. #66954⋊C₅	C₂²	semidirect
49. C₂×C₈×AGL(1,𝔽₁₁)	C₂²	semidirect
50. D₁₁×#576	C₅	semidirect
54. #41×C₁₁⋊C₅	C₂³	semidirect
56. C₂×D₄×C₁₁⋊C₅	C₂³	semidirect
61. #4343⋊C₅	C₂³	semidirect
67. #4341⋊C₅	C₂³	semidirect
76. D₄×AGL(1,𝔽₁₁)	C₂³	semidirect
80. #4339⋊C₅	C₂³	semidirect
82. C₂×C₄⋊AGL(1,𝔽₁₁)	C₂³	semidirect
85. Q₁₆×C₁₁⋊C₅	C₂³	semidirect
86. SD₁₆×C₁₁⋊C₅	C₂³	semidirect
87. D₈×C₁₁⋊C₅	C₂³	semidirect
88. D₈×C₁₁⋊C₅	C₂³	semidirect
89. M₁₆×C₁₁⋊C₅	C₂³	semidirect
90. C₂×C₈×C₁₁⋊C₅	C₂³	semidirect
91. #4326⋊C₅	C₂³	semidirect
92. #4325⋊C₅	C₂³	semidirect
93. #4324⋊C₅	C₂³	semidirect
94. #4323⋊C₅	C₂³	semidirect
95. #4323⋊C₅	C₂³	semidirect
96. #4318⋊C₅	C₂³	semidirect
97. C₂×(C₁₁⋊C₅)⋊C₈	C₂³	semidirect
98. Dic₄₄⋊C₅	C₂³	semidirect
99. D₈₈⋊C₅	C₂³	semidirect
100. D₈₈⋊C₅	C₂³	semidirect
101. #4314⋊C₅	C₂³	semidirect
102. #4313⋊C₅	C₂³	semidirect
105. C₈×AGL(1,𝔽₁₁)	C₂³	semidirect
106. C₈×AGL(1,𝔽₁₁)	C₂³	semidirect
107. D₁₁×H(5,𝔽₂)	C₂×C₅	semidirect
108. C₁₁×#576	C₂×C₅	semidirect
109. #10623366	C₂×C₅	semidirect
110. #10623305	C₂×C₅	semidirect
111. D₁₁×AGL(1,ℤ/8)	C₂×C₅	semidirect
112. #10623300	C₂×C₅	semidirect
113. D₁₁×#135	C₂×C₅	semidirect
114. #10623288	C₂×C₅	semidirect
115. C₂×D₈×D₁₁	C₂×C₅	semidirect
116. #10623283	C₂×C₅	semidirect
117. D₁₁×#131	C₂×C₅	semidirect
158. C₁₁×H(5,𝔽₂)	C₂²×C₅	semidirect
160. #67042	C₂²×C₅	semidirect
161. #67042	C₂²×C₅	semidirect
164. #41×D₁₁	C₂²×C₅	semidirect
166. #67037	C₂²×C₅	semidirect
168. C₂×D₄×D₁₁	C₂²×C₅	semidirect
169. C₁₁×AGL(1,ℤ/8)	C₂²×C₅	semidirect
170. C₁₁×#135	C₂²×C₅	semidirect
171. C₂×C₁₁×D₈	C₂²×C₅	semidirect
172. C₁₁×#131	C₂²×C₅	semidirect
173. #67003	C₂²×C₅	semidirect
174. #67002	C₂²×C₅	semidirect
175. #67001	C₂²×C₅	semidirect
176. #66985	C₂²×C₅	semidirect
177. C₂×#4323	C₂²×C₅	semidirect
178. #66972	C₂²×C₅	semidirect
179. Q₁₆×D₁₁	C₂²×C₅	semidirect
180. #66969	C₂²×C₅	semidirect
181. #66967	C₂²×C₅	semidirect
182. SD₁₆×D₁₁	C₂²×C₅	semidirect
183. #66965	C₂²×C₅	semidirect
184. #66964	C₂²×C₅	semidirect
185. D₈×D₁₁	C₂²×C₅	semidirect
186. D₈×D₁₁	C₂²×C₅	semidirect
187. D₈×D₁₁	C₂²×C₅	semidirect
188. D₈×D₁₁	C₂²×C₅	semidirect
189. #66961	C₂²×C₅	semidirect
190. #66960	C₂²×C₅	semidirect
191. M₁₆×D₁₁	C₂²×C₅	semidirect
192. #66957	C₂²×C₅	semidirect
193. C₂×D₈₈	C₂²×C₅	semidirect
194. #66954	C₂²×C₅	semidirect
195. C₂×C₈×D₁₁	C₂²×C₅	semidirect
226. C₁₁×#41	C₂³×C₅	semidirect
228. C₂×D₄×C₁₁	C₂³×C₅	semidirect
233. #4343	C₂³×C₅	semidirect
239. #4341	C₂³×C₅	semidirect
248. D₄×D₁₁	C₂³×C₅	semidirect
252. #4339	C₂³×C₅	semidirect
254. C₂×D₄₄	C₂³×C₅	semidirect
257. C₁₁×Q₁₆	C₂³×C₅	semidirect
258. C₁₁×SD₁₆	C₂³×C₅	semidirect
259. C₁₁×D₈	C₂³×C₅	semidirect
260. C₁₁×D₈	C₂³×C₅	semidirect
261. C₁₁×M₁₆	C₂³×C₅	semidirect
262. C₂×C₈×C₁₁	C₂³×C₅	semidirect
263. #4326	C₂³×C₅	semidirect
264. #4325	C₂³×C₅	semidirect
265. #4324	C₂³×C₅	semidirect
266. #4323	C₂³×C₅	semidirect
267. #4323	C₂³×C₅	semidirect
268. #4318	C₂³×C₅	semidirect
269. C₂×C₁₁⋊C₈	C₂³×C₅	semidirect
270. Dic₄₄	C₂³×C₅	semidirect
271. D₈₈	C₂³×C₅	semidirect
272. D₈₈	C₂³×C₅	semidirect
273. #4314	C₂³×C₅	semidirect
274. #4313	C₂³×C₅	semidirect
277. C₈×D₁₁	C₂³×C₅	semidirect
278. C₈×D₁₁	C₂³×C₅	semidirect
323. AGL(1,𝔽₁₁)	#576	direct (N × H)
425. #576	AGL(1,𝔽₁₁)	direct (N × H)
430. C₁₁⋊C₅	C₂×#576	semidirect
491. H(5,𝔽₂)	C₂×AGL(1,𝔽₁₁)	semidirect
502. AGL(1,ℤ/8)	C₂×AGL(1,𝔽₁₁)	semidirect
508. #135	C₂×AGL(1,𝔽₁₁)	semidirect
517. C₂×D₈	C₂×AGL(1,𝔽₁₁)	semidirect
521. #131	C₂×AGL(1,𝔽₁₁)	semidirect
529. D₁₁	C₅×#576	semidirect
560. #41	C₂²×AGL(1,𝔽₁₁)	semidirect
577. C₂×D₄	C₂²×AGL(1,𝔽₁₁)	semidirect
582. Q₁₆	C₂²×AGL(1,𝔽₁₁)	semidirect
586. SD₁₆	C₂²×AGL(1,𝔽₁₁)	semidirect
591. D₈	C₂²×AGL(1,𝔽₁₁)	semidirect
592. D₈	C₂²×AGL(1,𝔽₁₁)	semidirect
595. M₁₆	C₂²×AGL(1,𝔽₁₁)	semidirect
601. C₂×C₈	C₂²×AGL(1,𝔽₁₁)	semidirect
602. C₁₁	C₂×C₅×#576	semidirect

Maximal subgroups

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

subgroup	index
#72269581	2
#72269567	2
#72269559	2
#72269550	2
#72269543	2
C₁₁⋊C₅×#576	2
#131×AGL(1,𝔽₁₁)	2
#135×AGL(1,𝔽₁₁)	2
H(5,𝔽₂)×AGL(1,𝔽₁₁)	2
AGL(1,ℤ/8)×AGL(1,𝔽₁₁)	2
C₂×D₈×AGL(1,𝔽₁₁)	2
D₁₁×#576	5
C₂×C₅×#576	11

Subgroups — #576×AGL(1,𝔽11) #72269602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #576×AGL(1,𝔽₁₁) #72269602