Subgroups — C₁₁×#60126 #14637319

Order 2816.

2042 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3428	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2925	C₂	1	8	yes	maximal, complemented
3	C₁₁×#2924	C₂	1	8	yes	maximal, complemented
4	C₁₁×#2923	C₂	1	4	yes	maximal, complemented
5	C₁₁×#2922	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#2879	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₁×#408	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#520	C₄	1	4	yes	—
18	C₁₁×#520	C₄	1	4	yes	—
19	C₁₁×#519	C₄	1	2	yes	—
20	C₁₁×#518	C₄	1	2	yes	—
21	C₁₁×#518	C₄	1	4	yes	—
22	C₄×C₁₁×#41	C₂²	1	4	yes	—
23	C₄×C₁₁×#41	C₂²	1	4	yes	—
24	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#117	C₂²	1	4	yes	—
26	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
27	C₁₁×#433	C₂²	1	16	yes	complemented
28	C₁₁×#433	C₂²	1	16	yes	complemented
29	C₁₁×#432	C₂²	1	16	yes	complemented
30	C₁₁×#431	C₂²	1	16	yes	complemented
31	C₁₁×#424	C₂²	1	4	yes	—
32	C₁₁×#424	C₂²	1	4	yes	—
33	C₁₁×#424	C₂²	1	2	yes	complemented
34	C₁₁×#424	C₂²	1	2	yes	complemented
35	C₁₁×#424	C₂²	1	4	yes	complemented
36	C₁₁×#423	C₂²	1	4	yes	complemented
37	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	complemented
38	C₁₁×#408	C₂²	1	2	yes	—
39	C₁₁×#408	C₂²	1	4	yes	—
40	C₁₁×#408	C₂²	1	2	yes	—
41	C₁₁×#408	C₂²	1	4	yes	—
42	C₁₁×#408	C₂²	1	4	yes	—
43	C₁₁×#407	C₂²	1	4	yes	—
44	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
45	C₁₁×#405	C₂²	1	4	yes	—
46	C₁₁×#405	C₂²	1	4	yes	—
47	C₁₁×#405	C₂²	1	4	yes	complemented
48	C₁₁×#405	C₂²	1	4	yes	complemented
49	C₄×C₁₁×M₁₆	C₂²	1	4	yes	complemented
50	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
51	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
52	C₂×C₁₁×#41	—	2	4	no	—
53	C₂×C₁₁×#41	—	2	4	no	—
54	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×#41	C₂³	1	2	yes	—
57	C₂×C₁₁×#41	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
60	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
63	C₂×C₁₁×M₁₆	—	2	4	no	—
64	C₂×C₁₁×M₁₆	—	2	4	no	—
65	C₂×C₁₁×M₁₆	—	2	4	no	—
66	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
67	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
70	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
71	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
72	C₂²×C₈×C₁₁	—	2	4	no	—
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
77	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
78	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
80	C₄×Q₈×C₁₁	C₂×C₄	1	8	yes	—
81	C₄×Q₈×C₁₁	C₂×C₄	1	8	yes	—
82	C₄×D₄×C₁₁	C₂×C₄	1	16	yes	—
83	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
84	C₄×D₄×C₁₁	C₂×C₄	1	16	yes	—
85	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
86	C₁₁×#117	C₂×C₄	1	8	yes	—
87	C₁₁×#117	C₂×C₄	1	2	yes	—
88	C₁₁×#117	C₂×C₄	1	2	yes	—
89	C₁₁×#117	C₂×C₄	1	8	yes	—
90	C₁₁×#117	C₂×C₄	1	2	yes	—
91	C₁₁×#117	C₂×C₄	1	2	yes	—
92	C₁₁×#117	C₂³	1	2	yes	—
93	C₁₁×#117	C₂³	1	2	yes	—
94	C₁₁×#117	C₂³	1	2	yes	—
95	C₁₁×#117	C₂³	1	2	yes	—
96	C₁₁×#117	C₂³	1	8	yes	—
97	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	—
98	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
99	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
100	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	8	yes	—
101	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
102	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
103	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
104	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
106	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
107	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
108	C₁₁×C₄⋊C₈	C₂³	1	16	yes	—
109	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
110	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
111	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	—
112	C₁₁×#97	C₂³	1	8	yes	—
113	C₁₁×#97	C₂³	1	8	yes	—
114	C₄×C₈×C₁₁	C₂³	1	8	yes	—
115	C₄×C₈×C₁₁	C₂³	1	8	yes	—
116	#60126	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
118	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₁₁×#41	—	2	8	no	—
120	C₁₁×#41	—	2	8	no	—
121	C₁₁×#41	—	2	4	no	—
122	C₁₁×#41	—	2	4	no	—
123	C₁₁×#41	—	2	4	no	—
124	C₁₁×#41	—	2	4	no	—
125	C₂×Q₈×C₁₁	—	2	4	no	—
126	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
128	C₂×D₄×C₁₁	—	2	8	no	—
129	C₂×D₄×C₁₁	—	2	4	no	—
130	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
131	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
132	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₁	—	2	4	no	—
135	C₂²×C₄×C₁₁	—	2	4	no	—
136	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₁	C₂²×C₄	1	16	yes	—
139	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₁	#41	1	4	yes	—
145	C₂²×C₄×C₁₁	#41	1	4	yes	—
146	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
150	C₁₁×M₁₆	—	2	4	no	—
151	C₁₁×M₁₆	—	2	4	no	—
152	C₁₁×M₁₆	—	2	4	no	—
153	C₁₁×M₁₆	—	2	4	no	—
154	C₁₁×M₁₆	—	2	4	no	—
155	C₁₁×M₁₆	—	2	4	no	—
156	C₂×C₈×C₁₁	—	2	4	no	—
157	C₂×C₈×C₁₁	—	2	4	no	—
158	C₂×C₈×C₁₁	—	2	2	no	—
159	C₂×C₈×C₁₁	—	2	2	no	—
160	C₂×C₈×C₁₁	—	2	4	no	—
161	C₂×C₈×C₁₁	—	2	4	no	—
162	C₂×C₈×C₁₁	—	2	4	no	—
163	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
164	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
165	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
166	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
167	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
168	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
169	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
170	C₁₁×C₄⋊C₄	C₂²×C₄	1	16	yes	—
171	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
172	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
173	C₁₁×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
174	C₁₁×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
175	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
176	C₁₁×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
177	C₁₁×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
178	C₄²×C₁₁	C₂²×C₄	1	16	yes	—
179	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
180	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
181	C₄²×C₁₁	C₂⁴	1	4	yes	—
182	C₄²×C₁₁	C₂⁴	1	4	yes	—
183	#3428	C₂×C₁₁	1	1	yes	characteristic
184	#2925	C₂×C₁₁	1	8	yes	complemented
185	#2924	C₂×C₁₁	1	8	yes	complemented
186	#2923	C₂×C₁₁	1	4	yes	complemented
187	#2922	C₂×C₁₁	1	4	yes	complemented
188	#2905	C₂×C₁₁	1	1	yes	characteristic, complemented
189	C₂×#424	C₂×C₁₁	1	1	yes	characteristic, complemented
190	#2879	C₂×C₁₁	1	1	yes	characteristic
191	C₂×#408	C₂×C₁₁	1	1	yes	characteristic
192	#2873	C₂×C₁₁	1	1	yes	characteristic, complemented
193	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
194	C₂³×C₁₁	—	2	4	no	—
195	C₂³×C₁₁	—	4	2	no	—
196	C₂³×C₁₁	—	4	4	no	—
197	C₂³×C₁₁	#117	1	4	yes	—
198	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
199	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
200	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
201	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
202	Q₈×C₁₁	—	2	4	no	—
203	Q₈×C₁₁	—	2	4	no	—
204	D₄×C₁₁	—	2	8	no	—
205	D₄×C₁₁	—	2	8	no	—
206	D₄×C₁₁	—	2	4	no	—
207	D₄×C₁₁	—	2	4	no	—
208	C₂×C₄×C₁₁	—	2	4	no	—
209	C₂×C₄×C₁₁	—	2	8	no	—
210	C₂×C₄×C₁₁	—	2	4	no	—
211	C₂×C₄×C₁₁	—	2	4	no	—
212	C₂×C₄×C₁₁	—	4	4	no	—
213	C₂×C₄×C₁₁	—	4	4	no	—
214	C₂×C₄×C₁₁	—	4	16	no	—
215	C₂×C₄×C₁₁	#117	1	4	yes	—
216	C₂×C₄×C₁₁	#117	1	4	yes	—
217	C₂×C₄×C₁₁	#117	1	4	yes	—
218	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
219	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
220	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
221	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
226	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
227	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
228	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
229	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
230	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
231	C₈×C₁₁	—	2	2	no	—
232	C₈×C₁₁	—	2	2	no	—
233	C₈×C₁₁	—	2	4	no	—
234	C₈×C₁₁	—	2	4	no	—
235	C₈×C₁₁	—	2	4	no	—
236	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
238	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
239	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
240	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
241	#520	C₄×C₁₁	1	4	yes	—
242	#520	C₄×C₁₁	1	4	yes	—
243	#519	C₄×C₁₁	1	2	yes	—
244	#518	C₄×C₁₁	1	2	yes	—
245	#518	C₄×C₁₁	1	4	yes	—
246	C₄×#41	C₂²×C₁₁	1	4	yes	—
247	C₄×#41	C₂²×C₁₁	1	4	yes	—
248	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
249	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×#117	C₂²×C₁₁	1	4	yes	—
251	#433	C₂²×C₁₁	1	16	yes	complemented
252	#433	C₂²×C₁₁	1	16	yes	complemented
253	#432	C₂²×C₁₁	1	16	yes	complemented
254	#431	C₂²×C₁₁	1	16	yes	complemented
255	#424	C₂²×C₁₁	1	4	yes	—
256	#424	C₂²×C₁₁	1	4	yes	—
257	#424	C₂²×C₁₁	1	2	yes	complemented
258	#424	C₂²×C₁₁	1	2	yes	complemented
259	#424	C₂²×C₁₁	1	4	yes	complemented
260	#423	C₂²×C₁₁	1	4	yes	complemented
261	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	complemented
262	#408	C₂²×C₁₁	1	2	yes	—
263	#408	C₂²×C₁₁	1	2	yes	—
264	#408	C₂²×C₁₁	1	4	yes	—
265	#408	C₂²×C₁₁	1	4	yes	—
266	#408	C₂²×C₁₁	1	4	yes	—
267	#407	C₂²×C₁₁	1	4	yes	—
268	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
269	#405	C₂²×C₁₁	1	4	yes	—
270	#405	C₂²×C₁₁	1	4	yes	—
271	#405	C₂²×C₁₁	1	4	yes	complemented
272	#405	C₂²×C₁₁	1	4	yes	complemented
273	C₄×M₁₆	C₂²×C₁₁	1	4	yes	complemented
274	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
275	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
276	C₂²×C₁₁	—	2	2	no	—
277	C₂²×C₁₁	—	2	2	no	—
278	C₂²×C₁₁	—	2	2	no	—
279	C₂²×C₁₁	—	2	4	no	—
280	C₂²×C₁₁	—	2	8	no	—
281	C₂²×C₁₁	—	4	4	no	—
282	C₂²×C₁₁	—	8	4	no	—
283	C₂²×C₁₁	C₂×#117	1	2	yes	—
284	C₂²×C₁₁	C₂×#117	1	2	yes	—
285	C₂²×C₁₁	C₂×#117	1	2	yes	—
286	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
287	C₄×C₁₁	—	2	4	no	—
288	C₄×C₁₁	—	2	8	no	—
289	C₄×C₁₁	—	2	8	no	—
290	C₄×C₁₁	C₂×#117	1	2	yes	—
291	C₄×C₁₁	C₂×#117	1	2	yes	—
292	C₄×C₁₁	C₂×#117	1	2	yes	—
293	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
294	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
298	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
299	C₂×#41	C₂³×C₁₁	1	2	yes	—
300	C₂×#41	C₂³×C₁₁	1	2	yes	—
301	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
302	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
303	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
305	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
306	C₂×M₁₆	—	2	4	no	—
307	C₂×M₁₆	—	2	4	no	—
308	C₂×M₁₆	—	2	4	no	—
309	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
310	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
311	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
312	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
313	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
314	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
315	C₂²×C₈	—	2	4	no	—
316	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
319	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
320	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
321	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
322	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
323	C₄×Q₈	C₂×C₄×C₁₁	1	8	yes	—
324	C₄×Q₈	C₂×C₄×C₁₁	1	8	yes	—
325	C₄×D₄	C₂×C₄×C₁₁	1	16	yes	—
326	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
327	C₄×D₄	C₂×C₄×C₁₁	1	16	yes	—
328	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
329	#117	C₂×C₄×C₁₁	1	8	yes	—
330	#117	C₂×C₄×C₁₁	1	2	yes	—
331	#117	C₂×C₄×C₁₁	1	2	yes	—
332	#117	C₂×C₄×C₁₁	1	8	yes	—
333	#117	C₂×C₄×C₁₁	1	2	yes	—
334	#117	C₂×C₄×C₁₁	1	2	yes	—
335	#117	C₂³×C₁₁	1	2	yes	—
336	#117	C₂³×C₁₁	1	2	yes	—
337	#117	C₂³×C₁₁	1	2	yes	—
338	#117	C₂³×C₁₁	1	2	yes	—
339	#117	C₂³×C₁₁	1	8	yes	—
340	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
341	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
342	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
343	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
346	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
347	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
348	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
349	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
350	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
351	C₄⋊C₈	C₂³×C₁₁	1	16	yes	—
352	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
353	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
354	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	—
355	#97	C₂³×C₁₁	1	8	yes	—
356	#97	C₂³×C₁₁	1	8	yes	—
357	C₄×C₈	C₂³×C₁₁	1	8	yes	—
358	C₄×C₈	C₂³×C₁₁	1	8	yes	—
359	C₂×C₁₁	—	2	2	no	—
360	C₂×C₁₁	—	2	2	no	—
361	C₂×C₁₁	—	2	2	no	—
362	C₂×C₁₁	—	4	4	no	—
363	C₂×C₁₁	C₂²×#117	1	1	yes	characteristic
364	C₂×C₁₁	#3573	1	2	yes	—
365	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
366	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
367	#41	—	2	8	no	—
368	#41	—	2	8	no	—
369	#41	—	2	4	no	—
370	#41	—	2	4	no	—
371	#41	—	2	4	no	—
372	#41	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
375	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
379	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
380	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
381	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
385	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
386	C₂²×C₄	C₂²×C₄×C₁₁	1	16	yes	—
387	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
388	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
389	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
392	C₂²×C₄	C₁₁×#41	1	4	yes	—
393	C₂²×C₄	C₁₁×#41	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
395	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
398	M₁₆	—	2	4	no	—
399	M₁₆	—	2	4	no	—
400	M₁₆	—	2	4	no	—
401	M₁₆	—	2	4	no	—
402	M₁₆	—	2	4	no	—
403	M₁₆	—	2	4	no	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	4	no	—
409	C₂×C₈	—	2	4	no	—
410	C₂×C₈	—	2	4	no	—
411	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
412	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
413	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
414	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
415	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
416	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
417	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
418	C₄⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
419	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
420	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
421	C₂²⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
422	C₂²⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
423	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
424	C₂²⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
425	C₂²⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
426	C₄²	C₂²×C₄×C₁₁	1	16	yes	—
427	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
428	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
429	C₄²	C₂⁴×C₁₁	1	4	yes	—
430	C₄²	C₂⁴×C₁₁	1	4	yes	—
431	C₁₁	#60126	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	4	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	4	no	—
435	C₂³	C₁₁×#117	1	4	yes	—
436	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
437	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
438	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
439	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
440	Q₈	—	2	4	no	—
441	Q₈	—	2	4	no	—
442	D₄	—	2	8	no	—
443	D₄	—	2	8	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	16	no	—
453	C₂×C₄	C₁₁×#117	1	4	yes	—
454	C₂×C₄	C₁₁×#117	1	4	yes	—
455	C₂×C₄	C₁₁×#117	1	4	yes	—
456	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
457	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
458	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
459	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
460	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
461	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
462	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
463	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
464	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
465	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
466	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
467	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
468	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
469	C₈	—	2	2	no	—
470	C₈	—	2	2	no	—
471	C₈	—	2	4	no	—
472	C₈	—	2	4	no	—
473	C₈	—	2	4	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	8	4	no	—
481	C₂²	C₂×C₁₁×#117	1	2	yes	—
482	C₂²	C₂×C₁₁×#117	1	2	yes	—
483	C₂²	C₂×C₁₁×#117	1	2	yes	—
484	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
485	C₄	—	2	4	no	—
486	C₄	—	2	8	no	—
487	C₄	—	2	8	no	—
488	C₄	C₂×C₁₁×#117	1	2	yes	—
489	C₄	C₂×C₁₁×#117	1	2	yes	—
490	C₄	C₂×C₁₁×#117	1	2	yes	—
491	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
492	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	2	2	no	—
496	C₂	—	4	4	no	—
497	C₂	C₂²×C₁₁×#117	1	1	yes	characteristic
498	C₂	C₁₁×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂⁴×C₄
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2925	C₂	semidirect
3. C₁₁×#2924	C₂	semidirect
4. C₁₁×#2923	C₂	semidirect
5. C₁₁×#2922	C₂	semidirect
6. C₁₁×#2905	C₂	semidirect
7. C₂×C₁₁×#424	C₂	semidirect
10. C₁₁×#2873	C₂	semidirect
11. C₂×C₁₁×#405	C₂	semidirect
27. C₁₁×#433	C₂²	semidirect
28. C₁₁×#433	C₂²	semidirect
29. C₁₁×#432	C₂²	semidirect
30. C₁₁×#431	C₂²	semidirect
33. C₁₁×#424	C₂²	semidirect
34. C₁₁×#424	C₂²	semidirect
35. C₁₁×#424	C₂²	semidirect
36. C₁₁×#423	C₂²	semidirect
37. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
47. C₁₁×#405	C₂²	semidirect
48. C₁₁×#405	C₂²	semidirect
49. C₄×C₁₁×M₁₆	C₂²	semidirect
50. C₂×C₁₁×#97	C₂²	semidirect
51. C₂×C₄×C₈×C₁₁	C₂²	semidirect
116. #60126	C₁₁	direct (N × H)
184. #2925	C₂×C₁₁	semidirect
185. #2924	C₂×C₁₁	semidirect
186. #2923	C₂×C₁₁	semidirect
187. #2922	C₂×C₁₁	semidirect
188. #2905	C₂×C₁₁	semidirect
189. C₂×#424	C₂×C₁₁	semidirect
192. #2873	C₂×C₁₁	semidirect
193. C₂×#405	C₂×C₁₁	semidirect
251. #433	C₂²×C₁₁	semidirect
252. #433	C₂²×C₁₁	semidirect
253. #432	C₂²×C₁₁	semidirect
254. #431	C₂²×C₁₁	semidirect
257. #424	C₂²×C₁₁	semidirect
258. #424	C₂²×C₁₁	semidirect
259. #424	C₂²×C₁₁	semidirect
260. #423	C₂²×C₁₁	semidirect
261. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
271. #405	C₂²×C₁₁	semidirect
272. #405	C₂²×C₁₁	semidirect
273. C₄×M₁₆	C₂²×C₁₁	semidirect
274. C₂×#97	C₂²×C₁₁	semidirect
275. C₂×C₄×C₈	C₂²×C₁₁	semidirect
431. C₁₁	#60126	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×#3428	2
C₁₁×#2925	2
C₁₁×#2924	2
C₁₁×#2923	2
C₁₁×#2922	2
C₁₁×#2905	2
C₂×C₁₁×#424	2
C₁₁×#2879	2
C₂×C₁₁×#408	2
C₁₁×#2873	2
C₂×C₁₁×#405	2
#60126	11

Subgroups — C11×#60126 #14637319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60126 #14637319