Subgroups — C₁₁×#60093 #14637286

Order 2816.

4852 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2901	C₂	1	16	yes	maximal, complemented
5	C₂×C₁₁×#421	C₂	1	12	yes	maximal, complemented
6	C₁₁×#585	—	2	4	no	—
7	C₁₁×#585	—	2	4	no	—
8	C₁₁×#585	C₄	1	8	yes	complemented
9	C₁₁×#585	C₂²	1	8	yes	—
10	C₂×C₁₁×2₋¹⁺⁴	—	2	1	no	—
11	C₂×C₁₁×2₋¹⁺⁴	C₄	1	4	yes	complemented
12	C₂×C₁₁×H(5,𝔽₂)	—	2	3	no	—
13	C₂×C₁₁×H(5,𝔽₂)	C₄	1	4	yes	complemented
14	C₂²×C₁₁×#41	—	2	4	no	—
15	C₂²×C₁₁×#41	C₂²	1	6	yes	—
16	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
17	C₁₁×#568	—	2	4	no	—
18	C₁₁×#568	C₂²	1	8	yes	complemented
19	C₂×C₁₁×#131	—	2	4	no	—
20	C₂²×C₁₁×M₁₆	C₂²	1	6	yes	complemented
21	C₁₁×#520	—	2	4	no	—
22	C₁₁×#519	—	2	1	no	—
23	C₁₁×#518	—	2	3	no	—
24	C₄×C₁₁×#41	C₂²	1	8	yes	complemented
25	C₂×C₁₁×#117	C₂²	1	6	yes	complemented
26	C₁₁×#421	C₂²	1	16	yes	complemented
27	C₁₁×#421	C₂²	1	48	yes	complemented
28	C₂×C₁₁×#104	C₂²	1	48	yes	complemented
29	C₁₁×2₋¹⁺⁴	—	2	16	no	—
30	C₁₁×2₋¹⁺⁴	—	2	8	no	—
31	C₁₁×2₋¹⁺⁴	—	2	8	no	—
32	C₁₁×2₋¹⁺⁴	C₂×C₄	1	32	yes	complemented
33	C₁₁×H(5,𝔽₂)	—	2	16	no	—
34	C₁₁×H(5,𝔽₂)	—	2	24	no	—
35	C₁₁×H(5,𝔽₂)	—	2	24	no	—
36	C₁₁×H(5,𝔽₂)	C₂×C₄	1	32	yes	complemented
37	C₂×C₁₁×#41	—	2	32	no	—
38	C₂×C₁₁×#41	—	2	32	no	—
39	C₂×C₁₁×#41	—	2	4	no	—
40	C₂×C₁₁×#41	—	2	12	no	—
41	C₂×C₁₁×#41	—	2	6	no	—
42	C₂×C₁₁×#41	—	2	6	no	—
43	C₂×C₁₁×#41	—	2	12	no	—
44	C₂×C₁₁×#41	—	2	12	no	—
45	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
46	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
47	C₂×C₁₁×#41	C₂×C₄	1	12	yes	complemented
48	C₂×C₁₁×#41	C₂×C₄	1	24	yes	complemented
49	C₂×C₁₁×#41	D₄	1	4	yes	—
50	C₂×C₁₁×#41	D₄	1	4	yes	—
51	C₂×C₁₁×#41	D₄	1	4	yes	—
52	C₂×C₁₁×#41	C₂³	1	24	yes	—
53	C₂×C₁₁×#41	C₂³	1	4	yes	—
54	C₂×C₁₁×#41	C₂³	1	4	yes	—
55	C₂²×Q₈×C₁₁	—	2	4	no	—
56	C₂²×Q₈×C₁₁	C₂×C₄	1	6	yes	complemented
57	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₁₁	—	2	6	no	—
59	C₂²×D₄×C₁₁	—	2	12	no	—
60	C₂²×D₄×C₁₁	C₂×C₄	1	6	yes	complemented
61	C₂²×D₄×C₁₁	D₄	1	3	yes	—
62	C₂³×C₄×C₁₁	—	2	6	no	—
63	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
64	C₁₁×#131	—	2	32	no	—
65	C₂×C₁₁×M₁₆	—	2	6	no	—
66	C₂×C₁₁×M₁₆	—	2	12	no	—
67	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
68	C₂×C₁₁×M₁₆	C₂³	1	24	yes	complemented
69	C₂²×C₈×C₁₁	—	2	6	no	—
70	C₄×Q₈×C₁₁	—	2	8	no	—
71	C₄×D₄×C₁₁	—	2	24	no	—
72	C₁₁×#117	—	2	6	no	—
73	C₁₁×#117	—	2	6	no	—
74	C₁₁×#117	C₂³	1	4	yes	—
75	C₁₁×#117	C₂³	1	12	yes	complemented
76	C₂×C₁₁×C₄⋊C₄	—	2	6	no	—
77	C₂×C₁₁×C₂²⋊C₄	—	2	6	no	—
78	C₂×C₄²×C₁₁	C₂³	1	12	yes	complemented
79	C₁₁×#104	C₂³	1	64	yes	complemented
80	#60093	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₁	—	2	6	no	—
82	C₂⁴×C₁₁	C₂×D₄	1	3	yes	—
83	C₁₁×#41	—	2	32	no	—
84	C₁₁×#41	—	2	96	no	—
85	C₁₁×#41	—	2	24	no	—
86	C₁₁×#41	—	2	24	no	—
87	C₁₁×#41	—	2	24	no	—
88	C₁₁×#41	—	2	4	no	—
89	C₁₁×#41	—	2	4	no	—
90	C₁₁×#41	—	2	24	no	—
91	C₁₁×#41	—	2	24	no	—
92	C₁₁×#41	C₂²⋊C₄	1	16	yes	—
93	C₁₁×#41	C₂²⋊C₄	1	16	yes	—
94	C₁₁×#41	C₂²×C₄	1	8	yes	—
95	C₁₁×#41	C₂²×C₄	1	48	yes	—
96	C₁₁×#41	C₂²×C₄	1	16	yes	—
97	C₁₁×#41	C₂×D₄	1	16	yes	—
98	C₁₁×#41	C₂⁴	1	8	yes	—
99	C₂×Q₈×C₁₁	—	2	32	no	—
100	C₂×Q₈×C₁₁	—	2	6	no	—
101	C₂×Q₈×C₁₁	—	2	12	no	—
102	C₂×Q₈×C₁₁	C₂²⋊C₄	1	4	yes	—
103	C₂×Q₈×C₁₁	C₂²⋊C₄	1	4	yes	—
104	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
105	C₂×Q₈×C₁₁	C₂²×C₄	1	24	yes	—
106	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₁₁	—	2	12	no	—
108	C₂×D₄×C₁₁	—	2	24	no	—
109	C₂×D₄×C₁₁	—	2	4	no	—
110	C₂×D₄×C₁₁	—	2	24	no	—
111	C₂×D₄×C₁₁	—	2	96	no	—
112	C₂×D₄×C₁₁	—	2	6	no	—
113	C₂×D₄×C₁₁	—	2	12	no	—
114	C₂×D₄×C₁₁	C₂²⋊C₄	1	12	yes	—
115	C₂×D₄×C₁₁	C₂²⋊C₄	1	12	yes	—
116	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
117	C₂×D₄×C₁₁	C₂²×C₄	1	24	yes	—
118	C₂×D₄×C₁₁	C₂×D₄	1	12	yes	—
119	C₂²×C₄×C₁₁	—	2	6	no	—
120	C₂²×C₄×C₁₁	—	2	12	no	—
121	C₂²×C₄×C₁₁	—	2	24	no	—
122	C₂²×C₄×C₁₁	—	2	4	no	—
123	C₂²×C₄×C₁₁	—	2	24	no	—
124	C₂²×C₄×C₁₁	—	2	12	no	—
125	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
126	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
127	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
128	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
129	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
130	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
131	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
133	C₁₁×M₁₆	—	2	4	no	—
134	C₁₁×M₁₆	—	2	24	no	—
135	C₁₁×M₁₆	C₂⁴	1	8	yes	—
136	C₂×C₈×C₁₁	—	2	4	no	—
137	C₂×C₈×C₁₁	—	2	24	no	—
138	C₁₁×C₄⋊C₄	—	2	4	no	—
139	C₁₁×C₄⋊C₄	—	2	12	no	—
140	C₁₁×C₂²⋊C₄	—	2	4	no	—
141	C₁₁×C₂²⋊C₄	—	2	12	no	—
142	C₄²×C₁₁	—	2	12	no	—
143	C₄²×C₁₁	C₂⁴	1	8	yes	—
144	C₂×#585	C₂×C₁₁	1	1	yes	characteristic
145	C₂×#568	C₂×C₁₁	1	1	yes	characteristic, complemented
146	#3428	C₂×C₁₁	1	1	yes	characteristic, complemented
147	#2901	C₂×C₁₁	1	16	yes	complemented
148	C₂×#421	C₂×C₁₁	1	12	yes	complemented
149	C₂³×C₁₁	—	2	4	no	—
150	C₂³×C₁₁	—	2	24	no	—
151	C₂³×C₁₁	—	8	3	no	—
152	C₂³×C₁₁	—	8	12	no	—
153	C₂³×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
154	C₂³×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
155	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
156	C₂³×C₁₁	C₂²×D₄	1	6	yes	—
157	Q₈×C₁₁	—	2	24	no	—
158	Q₈×C₁₁	—	2	4	no	—
159	Q₈×C₁₁	C₂×C₂²⋊C₄	1	16	yes	—
160	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
161	D₄×C₁₁	—	2	48	no	—
162	D₄×C₁₁	—	2	8	no	—
163	D₄×C₁₁	—	2	8	no	—
164	D₄×C₁₁	—	2	24	no	—
165	D₄×C₁₁	—	2	4	no	—
166	D₄×C₁₁	C₂×C₂²⋊C₄	1	48	yes	—
167	D₄×C₁₁	C₂³×C₄	1	8	yes	—
168	C₂×C₄×C₁₁	—	2	4	no	—
169	C₂×C₄×C₁₁	—	2	24	no	—
170	C₂×C₄×C₁₁	—	2	8	no	—
171	C₂×C₄×C₁₁	—	2	48	no	—
172	C₂×C₄×C₁₁	—	2	8	no	—
173	C₂×C₄×C₁₁	—	2	8	no	—
174	C₂×C₄×C₁₁	—	8	12	no	—
175	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
176	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	12	yes	—
177	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	12	yes	—
178	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
179	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₁	C₂³×C₄	1	12	yes	—
182	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
183	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂²×D₄	1	12	yes	—
186	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
188	C₈×C₁₁	—	2	8	no	—
189	#585	—	2	4	no	—
190	#585	—	2	4	no	—
191	#585	C₄×C₁₁	1	8	yes	complemented
192	#585	C₂²×C₁₁	1	8	yes	—
193	C₂×2₋¹⁺⁴	—	2	1	no	—
194	C₂×2₋¹⁺⁴	C₄×C₁₁	1	4	yes	complemented
195	C₂×H(5,𝔽₂)	—	2	3	no	—
196	C₂×H(5,𝔽₂)	C₄×C₁₁	1	4	yes	complemented
197	C₂²×#41	—	2	4	no	—
198	C₂²×#41	C₂²×C₁₁	1	6	yes	—
199	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
200	#568	—	2	4	no	—
201	#568	C₂²×C₁₁	1	8	yes	complemented
202	C₂×#131	—	2	4	no	—
203	C₂²×M₁₆	C₂²×C₁₁	1	6	yes	complemented
204	#520	—	2	4	no	—
205	#519	—	2	1	no	—
206	#518	—	2	3	no	—
207	C₄×#41	C₂²×C₁₁	1	8	yes	complemented
208	C₂×#117	C₂²×C₁₁	1	6	yes	complemented
209	#421	C₂²×C₁₁	1	16	yes	complemented
210	#421	C₂²×C₁₁	1	48	yes	complemented
211	C₂×#104	C₂²×C₁₁	1	48	yes	complemented
212	C₂²×C₁₁	—	2	8	no	—
213	C₂²×C₁₁	—	4	6	no	—
214	C₂²×C₁₁	—	4	6	no	—
215	C₂²×C₁₁	—	4	1	no	—
216	C₂²×C₁₁	—	4	6	no	—
217	C₂²×C₁₁	—	4	8	no	—
218	C₂²×C₁₁	—	8	24	no	—
219	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	12	yes	—
221	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
222	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
223	C₄×C₁₁	—	2	8	no	—
224	C₄×C₁₁	—	4	8	no	—
225	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
226	C₄×C₁₁	C₂²×C₂²⋊C₄	1	12	yes	—
227	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
229	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
230	2₋¹⁺⁴	—	2	16	no	—
231	2₋¹⁺⁴	—	2	8	no	—
232	2₋¹⁺⁴	—	2	8	no	—
233	2₋¹⁺⁴	C₂×C₄×C₁₁	1	32	yes	complemented
234	H(5,𝔽₂)	—	2	16	no	—
235	H(5,𝔽₂)	—	2	24	no	—
236	H(5,𝔽₂)	—	2	24	no	—
237	H(5,𝔽₂)	C₂×C₄×C₁₁	1	32	yes	complemented
238	C₂×#41	—	2	32	no	—
239	C₂×#41	—	2	32	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	—	2	12	no	—
242	C₂×#41	—	2	6	no	—
243	C₂×#41	—	2	6	no	—
244	C₂×#41	—	2	12	no	—
245	C₂×#41	—	2	12	no	—
246	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
247	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
248	C₂×#41	C₂×C₄×C₁₁	1	12	yes	complemented
249	C₂×#41	C₂×C₄×C₁₁	1	24	yes	complemented
250	C₂×#41	D₄×C₁₁	1	4	yes	—
251	C₂×#41	D₄×C₁₁	1	4	yes	—
252	C₂×#41	D₄×C₁₁	1	4	yes	—
253	C₂×#41	C₂³×C₁₁	1	4	yes	—
254	C₂×#41	C₂³×C₁₁	1	24	yes	—
255	C₂×#41	C₂³×C₁₁	1	4	yes	—
256	C₂²×Q₈	—	2	4	no	—
257	C₂²×Q₈	C₂×C₄×C₁₁	1	6	yes	complemented
258	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
259	C₂²×D₄	—	2	6	no	—
260	C₂²×D₄	—	2	12	no	—
261	C₂²×D₄	C₂×C₄×C₁₁	1	6	yes	complemented
262	C₂²×D₄	D₄×C₁₁	1	3	yes	—
263	C₂³×C₄	—	2	6	no	—
264	C₂³×C₄	C₂³×C₁₁	1	3	yes	—
265	#131	—	2	32	no	—
266	C₂×M₁₆	—	2	6	no	—
267	C₂×M₁₆	—	2	12	no	—
268	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
269	C₂×M₁₆	C₂³×C₁₁	1	24	yes	complemented
270	C₂²×C₈	—	2	6	no	—
271	C₄×Q₈	—	2	8	no	—
272	C₄×D₄	—	2	24	no	—
273	#117	—	2	6	no	—
274	#117	—	2	6	no	—
275	#117	C₂³×C₁₁	1	4	yes	—
276	#117	C₂³×C₁₁	1	12	yes	complemented
277	C₂×C₄⋊C₄	—	2	6	no	—
278	C₂×C₂²⋊C₄	—	2	6	no	—
279	C₂×C₄²	C₂³×C₁₁	1	12	yes	complemented
280	#104	C₂³×C₁₁	1	64	yes	complemented
281	C₂×C₁₁	—	2	1	no	—
282	C₂×C₁₁	—	2	1	no	—
283	C₂×C₁₁	—	2	1	no	—
284	C₂×C₁₁	—	2	12	no	—
285	C₂×C₁₁	—	4	8	no	—
286	C₂×C₁₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
287	C₂⁴	—	2	6	no	—
288	C₂⁴	C₂×D₄×C₁₁	1	3	yes	—
289	#41	—	2	32	no	—
290	#41	—	2	96	no	—
291	#41	—	2	24	no	—
292	#41	—	2	24	no	—
293	#41	—	2	24	no	—
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	2	24	no	—
297	#41	—	2	24	no	—
298	#41	C₁₁×C₂²⋊C₄	1	16	yes	—
299	#41	C₁₁×C₂²⋊C₄	1	16	yes	—
300	#41	C₂²×C₄×C₁₁	1	8	yes	—
301	#41	C₂²×C₄×C₁₁	1	48	yes	—
302	#41	C₂²×C₄×C₁₁	1	16	yes	—
303	#41	C₂×D₄×C₁₁	1	16	yes	—
304	#41	C₂⁴×C₁₁	1	8	yes	—
305	C₂×Q₈	—	2	32	no	—
306	C₂×Q₈	—	2	6	no	—
307	C₂×Q₈	—	2	12	no	—
308	C₂×Q₈	C₁₁×C₂²⋊C₄	1	4	yes	—
309	C₂×Q₈	C₁₁×C₂²⋊C₄	1	4	yes	—
310	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
311	C₂×Q₈	C₂²×C₄×C₁₁	1	24	yes	—
312	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
313	C₂×D₄	—	2	12	no	—
314	C₂×D₄	—	2	24	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	24	no	—
317	C₂×D₄	—	2	96	no	—
318	C₂×D₄	—	2	6	no	—
319	C₂×D₄	—	2	12	no	—
320	C₂×D₄	C₁₁×C₂²⋊C₄	1	12	yes	—
321	C₂×D₄	C₁₁×C₂²⋊C₄	1	12	yes	—
322	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
323	C₂×D₄	C₂²×C₄×C₁₁	1	24	yes	—
324	C₂×D₄	C₂×D₄×C₁₁	1	12	yes	—
325	C₂²×C₄	—	2	6	no	—
326	C₂²×C₄	—	2	12	no	—
327	C₂²×C₄	—	2	24	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	24	no	—
330	C₂²×C₄	—	2	12	no	—
331	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
332	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
333	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
334	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
335	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
336	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
337	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
338	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
339	M₁₆	—	2	4	no	—
340	M₁₆	—	2	24	no	—
341	M₁₆	C₂⁴×C₁₁	1	8	yes	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	2	24	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	12	no	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₂²⋊C₄	—	2	12	no	—
348	C₄²	—	2	12	no	—
349	C₄²	C₂⁴×C₁₁	1	8	yes	—
350	C₁₁	#60093	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	—	2	4	no	—
352	C₂³	—	2	24	no	—
353	C₂³	—	8	3	no	—
354	C₂³	—	8	12	no	—
355	C₂³	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
356	C₂³	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
357	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
358	C₂³	C₂²×D₄×C₁₁	1	6	yes	—
359	Q₈	—	2	24	no	—
360	Q₈	—	2	4	no	—
361	Q₈	C₂×C₁₁×C₂²⋊C₄	1	16	yes	—
362	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
363	D₄	—	2	48	no	—
364	D₄	—	2	8	no	—
365	D₄	—	2	8	no	—
366	D₄	—	2	24	no	—
367	D₄	—	2	4	no	—
368	D₄	C₂×C₁₁×C₂²⋊C₄	1	48	yes	—
369	D₄	C₂³×C₄×C₁₁	1	8	yes	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	24	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	48	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	8	12	no	—
377	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
378	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	12	yes	—
379	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	12	yes	—
380	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
381	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
382	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
383	C₂×C₄	C₂³×C₄×C₁₁	1	12	yes	—
384	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
385	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₁₁	1	12	yes	—
388	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
389	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
390	C₈	—	2	8	no	—
391	C₂²	—	2	8	no	—
392	C₂²	—	4	6	no	—
393	C₂²	—	4	6	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	6	no	—
396	C₂²	—	4	8	no	—
397	C₂²	—	8	24	no	—
398	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
399	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	12	yes	—
400	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
401	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
402	C₄	—	2	8	no	—
403	C₄	—	4	8	no	—
404	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
405	C₄	C₂²×C₁₁×C₂²⋊C₄	1	12	yes	—
406	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
407	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
408	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	12	no	—
413	C₂	—	4	8	no	—
414	C₂	C₂³×C₁₁×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂×C₁₁	C₂³×C₂²⋊C₄
prime radical	C₂×C₁₁×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂²×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#568	C₂	semidirect
3. C₁₁×#3428	C₂	semidirect
4. C₁₁×#2901	C₂	semidirect
5. C₂×C₁₁×#421	C₂	semidirect
8. C₁₁×#585	C₄	semidirect
11. C₂×C₁₁×2₋¹⁺⁴	C₄	semidirect
13. C₂×C₁₁×H(5,𝔽₂)	C₄	semidirect
18. C₁₁×#568	C₂²	semidirect
20. C₂²×C₁₁×M₁₆	C₂²	semidirect
24. C₄×C₁₁×#41	C₂²	semidirect
25. C₂×C₁₁×#117	C₂²	semidirect
26. C₁₁×#421	C₂²	semidirect
27. C₁₁×#421	C₂²	semidirect
28. C₂×C₁₁×#104	C₂²	semidirect
32. C₁₁×2₋¹⁺⁴	C₂×C₄	semidirect
36. C₁₁×H(5,𝔽₂)	C₂×C₄	semidirect
47. C₂×C₁₁×#41	C₂×C₄	semidirect
48. C₂×C₁₁×#41	C₂×C₄	semidirect
56. C₂²×Q₈×C₁₁	C₂×C₄	semidirect
60. C₂²×D₄×C₁₁	C₂×C₄	semidirect
68. C₂×C₁₁×M₁₆	C₂³	semidirect
75. C₁₁×#117	C₂³	semidirect
78. C₂×C₄²×C₁₁	C₂³	semidirect
79. C₁₁×#104	C₂³	semidirect
80. #60093	C₁₁	direct (N × H)
145. C₂×#568	C₂×C₁₁	semidirect
146. #3428	C₂×C₁₁	semidirect
147. #2901	C₂×C₁₁	semidirect
148. C₂×#421	C₂×C₁₁	semidirect
191. #585	C₄×C₁₁	semidirect
194. C₂×2₋¹⁺⁴	C₄×C₁₁	semidirect
196. C₂×H(5,𝔽₂)	C₄×C₁₁	semidirect
201. #568	C₂²×C₁₁	semidirect
203. C₂²×M₁₆	C₂²×C₁₁	semidirect
207. C₄×#41	C₂²×C₁₁	semidirect
208. C₂×#117	C₂²×C₁₁	semidirect
209. #421	C₂²×C₁₁	semidirect
210. #421	C₂²×C₁₁	semidirect
211. C₂×#104	C₂²×C₁₁	semidirect
233. 2₋¹⁺⁴	C₂×C₄×C₁₁	semidirect
237. H(5,𝔽₂)	C₂×C₄×C₁₁	semidirect
248. C₂×#41	C₂×C₄×C₁₁	semidirect
249. C₂×#41	C₂×C₄×C₁₁	semidirect
257. C₂²×Q₈	C₂×C₄×C₁₁	semidirect
261. C₂²×D₄	C₂×C₄×C₁₁	semidirect
269. C₂×M₁₆	C₂³×C₁₁	semidirect
276. #117	C₂³×C₁₁	semidirect
279. C₂×C₄²	C₂³×C₁₁	semidirect
280. #104	C₂³×C₁₁	semidirect
350. C₁₁	#60093	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×#585	2
C₂×C₁₁×#568	2
C₁₁×#3428	2
C₁₁×#2901	2
C₂×C₁₁×#421	2
#60093	11

Subgroups — C11×#60093 #14637286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60093 #14637286