Subgroups — C₁₁×#34258 #14611451

Order 2816.

5682 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2341	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₁×C₂²⋊C₄	C₂	1	12	yes	maximal, complemented
6	C₁₁×#2311	C₂	1	3	yes	maximal, complemented
7	C₁₁×#2309	C₂	1	3	yes	maximal, complemented
8	C₁₁×#2297	C₂	1	3	yes	maximal, complemented
9	C₂×C₁₁×#390	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₁×H(5,𝔽₂)	—	2	8	no	—
11	C₂×C₁₁×H(5,𝔽₂)	—	2	8	no	—
12	C₂×C₁₁×H(5,𝔽₂)	C₄	1	16	yes	complemented
13	C₂²×C₁₁×#41	C₂²	1	3	yes	—
14	C₂²×C₁₁×#41	C₂²	1	2	yes	—
15	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₁	C₂²	1	3	yes	—
17	C₂³×D₄×C₁₁	C₂²	1	6	yes	—
18	C₁₁×#520	—	2	8	no	—
19	C₄×C₁₁×#41	—	2	8	no	—
20	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
21	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
22	C₂×C₄×D₄×C₁₁	C₂²	1	6	yes	complemented
23	C₂×C₄×D₄×C₁₁	C₂²	1	6	yes	complemented
24	C₂×C₁₁×#117	C₂²	1	3	yes	complemented
25	C₂×C₁₁×#117	C₂²	1	3	yes	complemented
26	C₂²×C₁₁×C₄⋊C₄	C₂²	1	3	yes	complemented
27	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	12	yes	complemented
28	C₂²×C₄²×C₁₁	C₂²	1	3	yes	complemented
29	C₁₁×#391	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#391	C₂²	1	3	yes	complemented
31	C₁₁×#390	C₂²	1	3	yes	complemented
32	C₁₁×#390	C₂²	1	6	yes	complemented
33	C₁₁×#390	C₂²	1	12	yes	complemented
34	C₁₁×#390	C₂²	1	3	yes	complemented
35	C₁₁×#390	C₂²	1	12	yes	complemented
36	C₁₁×#386	C₂²	1	12	yes	complemented
37	C₁₁×#386	C₂²	1	12	yes	complemented
38	C₁₁×#380	C₂²	1	12	yes	complemented
39	C₁₁×#379	C₂²	1	12	yes	complemented
40	C₄×C₁₁×C₂²⋊C₄	C₂²	1	12	yes	complemented
41	C₂⁵×C₁₁	C₂³	1	6	yes	—
42	C₁₁×H(5,𝔽₂)	—	2	128	no	—
43	C₂×C₁₁×#41	—	2	8	no	—
44	C₂×C₁₁×#41	—	2	8	no	—
45	C₂×C₁₁×#41	—	2	12	no	—
46	C₂×C₁₁×#41	—	2	12	no	—
47	C₂×C₁₁×#41	C₂×C₄	1	8	yes	—
48	C₂×C₁₁×#41	C₂×C₄	1	16	yes	complemented
49	C₂×C₁₁×#41	C₂×C₄	1	24	yes	complemented
50	C₂×C₁₁×#41	D₄	1	8	yes	—
51	C₂×C₁₁×#41	D₄	1	8	yes	—
52	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₁	—	2	24	no	—
55	C₂²×D₄×C₁₁	—	2	24	no	—
56	C₂²×D₄×C₁₁	—	2	12	no	—
57	C₂²×D₄×C₁₁	—	2	12	no	—
58	C₂²×D₄×C₁₁	C₂×C₄	1	48	yes	complemented
59	C₂²×D₄×C₁₁	C₂×C₄	1	24	yes	complemented
60	C₂²×D₄×C₁₁	C₂³	1	6	yes	—
61	C₂²×D₄×C₁₁	C₂³	1	3	yes	—
62	C₂²×D₄×C₁₁	C₂³	1	6	yes	—
63	C₂²×D₄×C₁₁	C₂³	1	3	yes	—
64	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
65	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
66	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
67	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
68	C₄×Q₈×C₁₁	—	2	8	no	—
69	C₄×Q₈×C₁₁	—	2	8	no	—
70	C₄×D₄×C₁₁	—	2	24	no	—
71	C₄×D₄×C₁₁	—	2	24	no	—
72	C₁₁×#117	—	2	12	no	—
73	C₁₁×#117	—	2	12	no	—
74	C₂×C₁₁×C₄⋊C₄	—	2	12	no	—
75	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
77	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
79	C₂×C₁₁×C₂²⋊C₄	—	4	24	no	—
80	C₂×C₁₁×C₂²⋊C₄	C₂³	1	12	yes	—
81	C₂×C₁₁×C₂²⋊C₄	C₂³	1	6	yes	—
82	C₂×C₁₁×C₂²⋊C₄	C₂³	1	6	yes	—
83	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
84	C₂×C₁₁×C₂²⋊C₄	C₂³	1	12	yes	—
85	C₂×C₄²×C₁₁	—	2	12	no	—
86	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
88	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
89	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
90	C₁₁×#95	C₂³	1	4	yes	—
91	C₁₁×#95	C₂³	1	12	yes	—
92	#34258	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₁	—	2	12	no	—
94	C₂⁴×C₁₁	—	2	12	no	—
95	C₂⁴×C₁₁	—	4	12	no	—
96	C₂⁴×C₁₁	—	4	12	no	—
97	C₂⁴×C₁₁	C₂²×C₄	1	24	yes	—
98	C₂⁴×C₁₁	C₂⁴	1	6	yes	—
99	C₂⁴×C₁₁	C₂⁴	1	3	yes	—
100	C₁₁×#41	—	2	64	no	—
101	C₁₁×#41	—	2	96	no	—
102	C₁₁×#41	C₂²⋊C₄	1	64	yes	complemented
103	C₂×Q₈×C₁₁	—	2	2	no	—
104	C₂×Q₈×C₁₁	—	2	2	no	—
105	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
106	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
107	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
108	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
109	C₂×D₄×C₁₁	—	2	12	no	—
110	C₂×D₄×C₁₁	—	2	12	no	—
111	C₂×D₄×C₁₁	—	2	192	no	—
112	C₂×D₄×C₁₁	—	2	96	no	—
113	C₂×D₄×C₁₁	—	2	6	no	—
114	C₂×D₄×C₁₁	—	2	12	no	—
115	C₂×D₄×C₁₁	—	2	12	no	—
116	C₂×D₄×C₁₁	—	2	6	no	—
117	C₂×D₄×C₁₁	C₂²×C₄	1	24	yes	—
118	C₂×D₄×C₁₁	C₂²×C₄	1	24	yes	—
119	C₂×D₄×C₁₁	C₂²×C₄	1	12	yes	—
120	C₂×D₄×C₁₁	C₂²×C₄	1	12	yes	—
121	C₂×D₄×C₁₁	C₂×D₄	1	12	yes	—
122	C₂×D₄×C₁₁	C₂×D₄	1	12	yes	—
123	C₂²×C₄×C₁₁	—	2	12	no	—
124	C₂²×C₄×C₁₁	—	2	12	no	—
125	C₂²×C₄×C₁₁	—	2	12	no	—
126	C₂²×C₄×C₁₁	—	2	12	no	—
127	C₂²×C₄×C₁₁	—	2	12	no	—
128	C₂²×C₄×C₁₁	—	4	6	no	—
129	C₂²×C₄×C₁₁	—	4	12	no	—
130	C₂²×C₄×C₁₁	C₂²×C₄	1	24	yes	—
131	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
132	C₂²×C₄×C₁₁	C₂×D₄	1	12	yes	—
133	C₂²×C₄×C₁₁	C₂×D₄	1	12	yes	—
134	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
136	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
137	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
141	C₁₁×C₄⋊C₄	—	2	6	no	—
142	C₁₁×C₄⋊C₄	—	2	12	no	—
143	C₁₁×C₄⋊C₄	—	2	2	no	—
144	C₁₁×C₄⋊C₄	—	2	12	no	—
145	C₁₁×C₂²⋊C₄	—	2	12	no	—
146	C₁₁×C₂²⋊C₄	—	2	12	no	—
147	C₁₁×C₂²⋊C₄	—	2	24	no	—
148	C₁₁×C₂²⋊C₄	—	4	24	no	—
149	C₁₁×C₂²⋊C₄	—	4	12	no	—
150	C₄²×C₁₁	—	2	2	no	—
151	C₄²×C₁₁	—	2	6	no	—
152	C₄²×C₁₁	—	2	12	no	—
153	C₄²×C₁₁	—	2	12	no	—
154	C₂²×H(5,𝔽₂)	C₂×C₁₁	1	1	yes	characteristic
155	C₂×#520	C₂×C₁₁	1	1	yes	characteristic, complemented
156	C₂×C₄×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
157	#2341	C₂×C₁₁	1	4	yes	complemented
158	D₄×C₂²⋊C₄	C₂×C₁₁	1	12	yes	complemented
159	#2311	C₂×C₁₁	1	3	yes	complemented
160	#2309	C₂×C₁₁	1	3	yes	complemented
161	#2297	C₂×C₁₁	1	3	yes	complemented
162	C₂×#390	C₂×C₁₁	1	3	yes	complemented
163	C₂³×C₁₁	—	2	6	no	—
164	C₂³×C₁₁	—	2	6	no	—
165	C₂³×C₁₁	—	2	6	no	—
166	C₂³×C₁₁	—	2	6	no	—
167	C₂³×C₁₁	—	2	12	no	—
168	C₂³×C₁₁	—	2	12	no	—
169	C₂³×C₁₁	—	2	48	no	—
170	C₂³×C₁₁	—	4	48	no	—
171	C₂³×C₁₁	—	8	24	no	—
172	C₂³×C₁₁	—	8	12	no	—
173	C₂³×C₁₁	—	8	12	no	—
174	C₂³×C₁₁	C₂³×C₄	1	12	yes	—
175	C₂³×C₁₁	C₂³×C₄	1	6	yes	—
176	C₂³×C₁₁	C₂²×D₄	1	6	yes	—
177	C₂³×C₁₁	C₂²×D₄	1	6	yes	—
178	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
179	Q₈×C₁₁	—	2	8	no	—
180	Q₈×C₁₁	C₂×C₂²⋊C₄	1	16	yes	complemented
181	D₄×C₁₁	—	2	48	no	—
182	D₄×C₁₁	—	2	48	no	—
183	D₄×C₁₁	—	2	24	no	—
184	D₄×C₁₁	C₂×C₂²⋊C₄	1	48	yes	complemented
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	2	no	—
189	C₂×C₄×C₁₁	—	2	48	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	6	no	—
192	C₂×C₄×C₁₁	—	2	6	no	—
193	C₂×C₄×C₁₁	—	2	12	no	—
194	C₂×C₄×C₁₁	—	2	6	no	—
195	C₂×C₄×C₁₁	—	2	4	no	—
196	C₂×C₄×C₁₁	—	2	6	no	—
197	C₂×C₄×C₁₁	—	4	24	no	—
198	C₂×C₄×C₁₁	—	8	12	no	—
199	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	48	yes	complemented
200	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
201	C₂×C₄×C₁₁	C₂³×C₄	1	6	yes	—
202	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
205	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
206	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	complemented
208	C₂×H(5,𝔽₂)	—	2	8	no	—
209	C₂×H(5,𝔽₂)	—	2	8	no	—
210	C₂×H(5,𝔽₂)	C₄×C₁₁	1	16	yes	complemented
211	C₂²×#41	C₂²×C₁₁	1	3	yes	—
212	C₂²×#41	C₂²×C₁₁	1	2	yes	—
213	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
214	C₂³×D₄	C₂²×C₁₁	1	3	yes	—
215	C₂³×D₄	C₂²×C₁₁	1	6	yes	—
216	#520	—	2	8	no	—
217	C₄×#41	—	2	8	no	—
218	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
219	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
220	C₂×C₄×D₄	C₂²×C₁₁	1	6	yes	complemented
221	C₂×C₄×D₄	C₂²×C₁₁	1	6	yes	complemented
222	C₂×#117	C₂²×C₁₁	1	3	yes	complemented
223	C₂×#117	C₂²×C₁₁	1	3	yes	complemented
224	C₂²×C₄⋊C₄	C₂²×C₁₁	1	3	yes	complemented
225	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	12	yes	complemented
226	C₂²×C₄²	C₂²×C₁₁	1	3	yes	complemented
227	#391	C₂²×C₁₁	1	3	yes	complemented
228	#391	C₂²×C₁₁	1	1	yes	characteristic, complemented
229	#390	C₂²×C₁₁	1	3	yes	complemented
230	#390	C₂²×C₁₁	1	6	yes	complemented
231	#390	C₂²×C₁₁	1	12	yes	complemented
232	#390	C₂²×C₁₁	1	12	yes	complemented
233	#390	C₂²×C₁₁	1	3	yes	complemented
234	#386	C₂²×C₁₁	1	12	yes	complemented
235	#386	C₂²×C₁₁	1	12	yes	complemented
236	#380	C₂²×C₁₁	1	12	yes	complemented
237	#379	C₂²×C₁₁	1	12	yes	complemented
238	C₄×C₂²⋊C₄	C₂²×C₁₁	1	12	yes	complemented
239	C₂²×C₁₁	—	2	12	no	—
240	C₂²×C₁₁	—	2	12	no	—
241	C₂²×C₁₁	—	2	6	no	—
242	C₂²×C₁₁	—	2	6	no	—
243	C₂²×C₁₁	—	2	12	no	—
244	C₂²×C₁₁	—	2	24	no	—
245	C₂²×C₁₁	—	4	12	no	—
246	C₂²×C₁₁	—	4	6	no	—
247	C₂²×C₁₁	—	4	6	no	—
248	C₂²×C₁₁	—	8	48	no	—
249	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	12	yes	—
250	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
251	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
252	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
253	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
254	C₂²×C₁₁	#585	1	2	yes	—
255	C₄×C₁₁	—	2	4	no	—
256	C₄×C₁₁	—	2	4	no	—
257	C₄×C₁₁	—	4	6	no	—
258	C₄×C₁₁	—	4	6	no	—
259	C₄×C₁₁	—	4	2	no	—
260	C₄×C₁₁	C₂²×C₂²⋊C₄	1	12	yes	—
261	C₄×C₁₁	C₂²×C₂²⋊C₄	1	4	yes	—
262	C₂⁵	C₂³×C₁₁	1	6	yes	—
263	H(5,𝔽₂)	—	2	128	no	—
264	C₂×#41	—	2	8	no	—
265	C₂×#41	—	2	8	no	—
266	C₂×#41	—	2	12	no	—
267	C₂×#41	—	2	12	no	—
268	C₂×#41	C₂×C₄×C₁₁	1	8	yes	—
269	C₂×#41	C₂×C₄×C₁₁	1	16	yes	complemented
270	C₂×#41	C₂×C₄×C₁₁	1	24	yes	complemented
271	C₂×#41	D₄×C₁₁	1	8	yes	—
272	C₂×#41	D₄×C₁₁	1	8	yes	—
273	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
274	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
275	C₂²×D₄	—	2	24	no	—
276	C₂²×D₄	—	2	24	no	—
277	C₂²×D₄	—	2	12	no	—
278	C₂²×D₄	—	2	12	no	—
279	C₂²×D₄	C₂×C₄×C₁₁	1	48	yes	complemented
280	C₂²×D₄	C₂×C₄×C₁₁	1	24	yes	complemented
281	C₂²×D₄	C₂³×C₁₁	1	6	yes	—
282	C₂²×D₄	C₂³×C₁₁	1	3	yes	—
283	C₂²×D₄	C₂³×C₁₁	1	6	yes	—
284	C₂²×D₄	C₂³×C₁₁	1	3	yes	—
285	C₂³×C₄	C₂³×C₁₁	1	6	yes	—
286	C₂³×C₄	C₂³×C₁₁	1	6	yes	—
287	C₂³×C₄	C₂³×C₁₁	1	6	yes	—
288	C₂³×C₄	C₂³×C₁₁	1	3	yes	—
289	C₄×Q₈	—	2	8	no	—
290	C₄×Q₈	—	2	8	no	—
291	C₄×D₄	—	2	24	no	—
292	C₄×D₄	—	2	24	no	—
293	#117	—	2	12	no	—
294	#117	—	2	12	no	—
295	C₂×C₄⋊C₄	—	2	12	no	—
296	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
300	C₂×C₂²⋊C₄	—	4	24	no	—
301	C₂×C₂²⋊C₄	C₂³×C₁₁	1	12	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₁₁	1	6	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₁	1	6	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₁	1	12	yes	—
306	C₂×C₄²	—	2	12	no	—
307	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
308	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
309	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
310	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
311	#95	C₂³×C₁₁	1	4	yes	—
312	#95	C₂³×C₁₁	1	12	yes	—
313	C₂×C₁₁	—	2	12	no	—
314	C₂×C₁₁	—	4	12	no	—
315	C₂×C₁₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₁₁	C₄×H(5,𝔽₂)	1	2	yes	—
317	C₂×C₁₁	#3488	1	2	yes	—
318	C₂×C₁₁	#3498	1	1	yes	characteristic
319	C₂×C₁₁	#3500	1	1	yes	characteristic
320	C₂⁴	—	2	12	no	—
321	C₂⁴	—	2	12	no	—
322	C₂⁴	—	4	12	no	—
323	C₂⁴	—	4	12	no	—
324	C₂⁴	C₂²×C₄×C₁₁	1	24	yes	—
325	C₂⁴	C₂⁴×C₁₁	1	6	yes	—
326	C₂⁴	C₂⁴×C₁₁	1	3	yes	—
327	#41	—	2	64	no	—
328	#41	—	2	96	no	—
329	#41	C₁₁×C₂²⋊C₄	1	64	yes	complemented
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
333	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
334	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
335	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
336	C₂×D₄	—	2	12	no	—
337	C₂×D₄	—	2	12	no	—
338	C₂×D₄	—	2	192	no	—
339	C₂×D₄	—	2	96	no	—
340	C₂×D₄	—	2	6	no	—
341	C₂×D₄	—	2	12	no	—
342	C₂×D₄	—	2	12	no	—
343	C₂×D₄	—	2	6	no	—
344	C₂×D₄	C₂²×C₄×C₁₁	1	24	yes	—
345	C₂×D₄	C₂²×C₄×C₁₁	1	24	yes	—
346	C₂×D₄	C₂²×C₄×C₁₁	1	12	yes	—
347	C₂×D₄	C₂²×C₄×C₁₁	1	12	yes	—
348	C₂×D₄	C₂×D₄×C₁₁	1	12	yes	—
349	C₂×D₄	C₂×D₄×C₁₁	1	12	yes	—
350	C₂²×C₄	—	2	12	no	—
351	C₂²×C₄	—	2	12	no	—
352	C₂²×C₄	—	2	12	no	—
353	C₂²×C₄	—	2	12	no	—
354	C₂²×C₄	—	2	12	no	—
355	C₂²×C₄	—	4	6	no	—
356	C₂²×C₄	—	4	12	no	—
357	C₂²×C₄	C₂²×C₄×C₁₁	1	24	yes	—
358	C₂²×C₄	C₂²×C₄×C₁₁	1	12	yes	—
359	C₂²×C₄	C₂×D₄×C₁₁	1	12	yes	—
360	C₂²×C₄	C₂×D₄×C₁₁	1	12	yes	—
361	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
363	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
364	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
368	C₄⋊C₄	—	2	6	no	—
369	C₄⋊C₄	—	2	12	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	12	no	—
372	C₂²⋊C₄	—	2	12	no	—
373	C₂²⋊C₄	—	2	12	no	—
374	C₂²⋊C₄	—	2	24	no	—
375	C₂²⋊C₄	—	4	24	no	—
376	C₂²⋊C₄	—	4	12	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	6	no	—
379	C₄²	—	2	12	no	—
380	C₄²	—	2	12	no	—
381	C₁₁	#34258	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	6	no	—
383	C₂³	—	2	6	no	—
384	C₂³	—	2	6	no	—
385	C₂³	—	2	6	no	—
386	C₂³	—	2	12	no	—
387	C₂³	—	2	12	no	—
388	C₂³	—	2	48	no	—
389	C₂³	—	4	48	no	—
390	C₂³	—	8	24	no	—
391	C₂³	—	8	12	no	—
392	C₂³	—	8	12	no	—
393	C₂³	C₂³×C₄×C₁₁	1	12	yes	—
394	C₂³	C₂³×C₄×C₁₁	1	6	yes	—
395	C₂³	C₂²×D₄×C₁₁	1	6	yes	—
396	C₂³	C₂²×D₄×C₁₁	1	6	yes	—
397	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
398	Q₈	—	2	8	no	—
399	Q₈	C₂×C₁₁×C₂²⋊C₄	1	16	yes	complemented
400	D₄	—	2	48	no	—
401	D₄	—	2	48	no	—
402	D₄	—	2	24	no	—
403	D₄	C₂×C₁₁×C₂²⋊C₄	1	48	yes	complemented
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	48	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	6	no	—
411	C₂×C₄	—	2	6	no	—
412	C₂×C₄	—	2	12	no	—
413	C₂×C₄	—	2	6	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	6	no	—
416	C₂×C₄	—	4	24	no	—
417	C₂×C₄	—	8	12	no	—
418	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	48	yes	complemented
419	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
420	C₂×C₄	C₂³×C₄×C₁₁	1	6	yes	—
421	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
424	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
425	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
426	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	complemented
427	C₂²	—	2	12	no	—
428	C₂²	—	2	12	no	—
429	C₂²	—	2	6	no	—
430	C₂²	—	2	6	no	—
431	C₂²	—	2	12	no	—
432	C₂²	—	2	24	no	—
433	C₂²	—	4	12	no	—
434	C₂²	—	4	6	no	—
435	C₂²	—	4	6	no	—
436	C₂²	—	8	48	no	—
437	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	12	yes	—
438	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
439	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
440	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
441	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
442	C₂²	C₁₁×#585	1	2	yes	—
443	C₄	—	2	4	no	—
444	C₄	—	2	4	no	—
445	C₄	—	4	6	no	—
446	C₄	—	4	6	no	—
447	C₄	—	4	2	no	—
448	C₄	C₂²×C₁₁×C₂²⋊C₄	1	12	yes	—
449	C₄	C₂²×C₁₁×C₂²⋊C₄	1	4	yes	—
450	C₂	—	2	12	no	—
451	C₂	—	4	12	no	—
452	C₂	C₂³×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
453	C₂	C₄×C₁₁×H(5,𝔽₂)	1	2	yes	—
454	C₂	C₁₁×#3488	1	2	yes	—
455	C₂	C₁₁×#3498	1	1	yes	characteristic
456	C₂	C₁₁×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂²×C₁₁×H(5,𝔽₂)	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#520	C₂	semidirect
3. C₂×C₄×C₁₁×#41	C₂	semidirect
4. C₁₁×#2341	C₂	semidirect
5. D₄×C₁₁×C₂²⋊C₄	C₂	semidirect
6. C₁₁×#2311	C₂	semidirect
7. C₁₁×#2309	C₂	semidirect
8. C₁₁×#2297	C₂	semidirect
9. C₂×C₁₁×#390	C₂	semidirect
12. C₂×C₁₁×H(5,𝔽₂)	C₄	semidirect
20. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
21. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
22. C₂×C₄×D₄×C₁₁	C₂²	semidirect
23. C₂×C₄×D₄×C₁₁	C₂²	semidirect
24. C₂×C₁₁×#117	C₂²	semidirect
25. C₂×C₁₁×#117	C₂²	semidirect
26. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
27. C₂²×C₁₁×C₂²⋊C₄	C₂²	semidirect
28. C₂²×C₄²×C₁₁	C₂²	semidirect
29. C₁₁×#391	C₂²	semidirect
30. C₁₁×#391	C₂²	semidirect
31. C₁₁×#390	C₂²	semidirect
32. C₁₁×#390	C₂²	semidirect
33. C₁₁×#390	C₂²	semidirect
34. C₁₁×#390	C₂²	semidirect
35. C₁₁×#390	C₂²	semidirect
36. C₁₁×#386	C₂²	semidirect
37. C₁₁×#386	C₂²	semidirect
38. C₁₁×#380	C₂²	semidirect
39. C₁₁×#379	C₂²	semidirect
40. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
48. C₂×C₁₁×#41	C₂×C₄	semidirect
49. C₂×C₁₁×#41	C₂×C₄	semidirect
58. C₂²×D₄×C₁₁	C₂×C₄	semidirect
59. C₂²×D₄×C₁₁	C₂×C₄	semidirect
92. #34258	C₁₁	direct (N × H)
102. C₁₁×#41	C₂²⋊C₄	semidirect
155. C₂×#520	C₂×C₁₁	semidirect
156. C₂×C₄×#41	C₂×C₁₁	semidirect
157. #2341	C₂×C₁₁	semidirect
158. D₄×C₂²⋊C₄	C₂×C₁₁	semidirect
159. #2311	C₂×C₁₁	semidirect
160. #2309	C₂×C₁₁	semidirect
161. #2297	C₂×C₁₁	semidirect
162. C₂×#390	C₂×C₁₁	semidirect
180. Q₈×C₁₁	C₂×C₂²⋊C₄	semidirect
184. D₄×C₁₁	C₂×C₂²⋊C₄	semidirect
199. C₂×C₄×C₁₁	C₂×C₂²⋊C₄	semidirect
207. C₂×C₄×C₁₁	H(5,𝔽₂)	semidirect
210. C₂×H(5,𝔽₂)	C₄×C₁₁	semidirect
218. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
219. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
220. C₂×C₄×D₄	C₂²×C₁₁	semidirect
221. C₂×C₄×D₄	C₂²×C₁₁	semidirect
222. C₂×#117	C₂²×C₁₁	semidirect
223. C₂×#117	C₂²×C₁₁	semidirect
224. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
225. C₂²×C₂²⋊C₄	C₂²×C₁₁	semidirect
226. C₂²×C₄²	C₂²×C₁₁	semidirect
227. #391	C₂²×C₁₁	semidirect
228. #391	C₂²×C₁₁	semidirect
229. #390	C₂²×C₁₁	semidirect
230. #390	C₂²×C₁₁	semidirect
231. #390	C₂²×C₁₁	semidirect
232. #390	C₂²×C₁₁	semidirect
233. #390	C₂²×C₁₁	semidirect
234. #386	C₂²×C₁₁	semidirect
235. #386	C₂²×C₁₁	semidirect
236. #380	C₂²×C₁₁	semidirect
237. #379	C₂²×C₁₁	semidirect
238. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
269. C₂×#41	C₂×C₄×C₁₁	semidirect
270. C₂×#41	C₂×C₄×C₁₁	semidirect
279. C₂²×D₄	C₂×C₄×C₁₁	semidirect
280. C₂²×D₄	C₂×C₄×C₁₁	semidirect
329. #41	C₁₁×C₂²⋊C₄	semidirect
381. C₁₁	#34258	direct (N × H)
399. Q₈	C₂×C₁₁×C₂²⋊C₄	semidirect
403. D₄	C₂×C₁₁×C₂²⋊C₄	semidirect
418. C₂×C₄	C₂×C₁₁×C₂²⋊C₄	semidirect
426. C₂×C₄	C₁₁×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×H(5,𝔽₂)	2
C₂×C₁₁×#520	2
C₂×C₄×C₁₁×#41	2
C₁₁×#2341	2
D₄×C₁₁×C₂²⋊C₄	2
C₁₁×#2311	2
C₁₁×#2309	2
C₁₁×#2297	2
C₂×C₁₁×#390	2
#34258	11

Subgroups — C11×#34258 #14611451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#34258 #14611451