Subgroups — C₁₁×#36594 #14613787

Order 2816.

2330 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×#556	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2868	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2858	C₂	1	2	yes	maximal
4	C₁₁×#2547	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2545	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2538	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2512	C₂	1	8	yes	maximal, complemented
8	C₁₁×#2354	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₁×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₁×#127	C₂	1	1	yes	maximal, characteristic
11	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#556	—	2	16	no	—
13	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#126	C₂²	1	8	yes	—
18	C₂×C₁₁×#124	C₂²	1	4	yes	—
19	C₂×C₁₁×#124	C₂²	1	4	yes	—
20	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₁₁	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
26	C₂×C₁₁×#117	C₂²	1	4	yes	—
27	C₁₁×#397	C₂²	1	8	yes	—
28	C₁₁×#396	C₂²	1	16	yes	—
29	C₁₁×#391	C₂²	1	4	yes	—
30	C₁₁×#390	C₂²	1	4	yes	—
31	C₁₁×#390	C₂²	1	8	yes	—
32	C₁₁×#390	C₂²	1	8	yes	—
33	C₁₁×#390	C₂²	1	2	yes	—
34	C₁₁×#389	C₂²	1	8	yes	—
35	C₁₁×#388	C₂²	1	16	yes	—
36	C₁₁×#384	C₂²	1	4	yes	—
37	C₁₁×#384	C₂²	1	4	yes	—
38	C₁₁×#384	C₂²	1	1	yes	characteristic
39	C₁₁×#380	C₂²	1	8	yes	—
40	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
41	C₄×C₁₁×C₄⋊C₄	C₂²	1	8	yes	—
42	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
43	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
45	C₄³×C₁₁	C₂²	1	1	yes	characteristic
46	C₄³×C₁₁	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
48	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
50	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
52	C₁₁×C₄⋊Q₈	—	2	8	no	—
53	C₁₁×C₄⋊Q₈	—	2	8	no	—
54	C₁₁×C₄⋊Q₈	—	4	4	no	—
55	C₁₁×#127	—	2	4	no	—
56	C₁₁×#126	—	2	32	no	—
57	C₁₁×#124	—	2	16	no	—
58	C₁₁×#124	—	4	8	no	—
59	C₁₁×C₂²⋊Q₈	—	2	16	no	—
60	C₄×Q₈×C₁₁	—	2	16	no	—
61	C₄×Q₈×C₁₁	—	2	8	no	—
62	C₄×Q₈×C₁₁	D₄	1	8	yes	complemented
63	C₄×D₄×C₁₁	—	2	8	no	—
64	C₄×D₄×C₁₁	—	2	16	no	—
65	C₁₁×#117	—	2	16	no	—
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
78	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₁×C₂²⋊C₄	C₂³	1	16	yes	—
82	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
88	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
92	C₁₁×#95	C₂³	1	4	yes	—
93	C₁₁×#95	C₂³	1	2	yes	—
94	C₁₁×#95	C₂³	1	16	yes	—
95	#36594	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
97	C₂×Q₈×C₁₁	—	2	8	no	—
98	C₂×Q₈×C₁₁	—	2	4	no	—
99	C₂×Q₈×C₁₁	—	2	8	no	—
100	C₂×Q₈×C₁₁	—	2	8	no	—
101	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
102	C₂×D₄×C₁₁	—	2	4	no	—
103	C₂×D₄×C₁₁	—	2	8	no	—
104	C₂×D₄×C₁₁	—	2	4	no	—
105	C₂×D₄×C₁₁	—	2	8	no	—
106	C₂×D₄×C₁₁	—	2	4	no	—
107	C₂×D₄×C₁₁	—	2	8	no	—
108	C₂²×C₄×C₁₁	—	2	8	no	—
109	C₂²×C₄×C₁₁	—	2	16	no	—
110	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
113	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
120	C₁₁×C₄⋊C₄	—	2	8	no	—
121	C₁₁×C₄⋊C₄	—	2	4	no	—
122	C₁₁×C₄⋊C₄	—	2	16	no	—
123	C₁₁×C₄⋊C₄	—	2	8	no	—
124	C₁₁×C₄⋊C₄	—	2	8	no	—
125	C₁₁×C₄⋊C₄	—	2	8	no	—
126	C₁₁×C₄⋊C₄	—	2	4	no	—
127	C₁₁×C₄⋊C₄	—	2	16	no	—
128	C₁₁×C₄⋊C₄	—	4	8	no	—
129	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
130	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
131	C₁₁×C₂²⋊C₄	—	2	16	no	—
132	C₁₁×C₂²⋊C₄	—	2	8	no	—
133	C₁₁×C₂²⋊C₄	—	2	16	no	—
134	C₁₁×C₂²⋊C₄	—	2	16	no	—
135	C₁₁×C₂²⋊C₄	—	4	16	no	—
136	C₄²×C₁₁	—	2	16	no	—
137	C₄²×C₁₁	—	2	8	no	—
138	C₄²×C₁₁	—	2	4	no	—
139	C₄²×C₁₁	—	2	2	no	—
140	C₄²×C₁₁	—	2	4	no	—
141	C₄²×C₁₁	—	2	8	no	—
142	C₄²×C₁₁	C₂×D₄	1	4	yes	—
143	C₄²×C₁₁	C₂×D₄	1	8	yes	—
144	C₄²×C₁₁	#41	1	8	yes	—
145	C₄²×C₁₁	#41	1	4	yes	—
146	C₂×#556	C₂×C₁₁	1	2	yes	complemented
147	#2868	C₂×C₁₁	1	1	yes	characteristic, complemented
148	#2858	C₂×C₁₁	1	2	yes	—
149	#2547	C₂×C₁₁	1	2	yes	complemented
150	#2545	C₂×C₁₁	1	4	yes	complemented
151	#2538	C₂×C₁₁	1	4	yes	complemented
152	#2512	C₂×C₁₁	1	8	yes	complemented
153	#2354	C₂×C₁₁	1	4	yes	complemented
154	C₄×C₄⋊Q₈	C₂×C₁₁	1	2	yes	complemented
155	C₄×#127	C₂×C₁₁	1	1	yes	characteristic
156	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
157	C₂³×C₁₁	—	2	4	no	—
158	C₂³×C₁₁	—	2	8	no	—
159	C₂³×C₁₁	—	2	4	no	—
160	C₂³×C₁₁	—	2	4	no	—
161	C₂³×C₁₁	—	2	8	no	—
162	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
163	Q₈×C₁₁	—	2	8	no	—
164	Q₈×C₁₁	—	4	16	no	—
165	D₄×C₁₁	—	4	8	no	—
166	D₄×C₁₁	—	4	16	no	—
167	C₂×C₄×C₁₁	—	2	4	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	—	2	4	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	4	no	—
173	C₂×C₄×C₁₁	—	2	8	no	—
174	C₂×C₄×C₁₁	—	2	4	no	—
175	C₂×C₄×C₁₁	—	2	8	no	—
176	C₂×C₄×C₁₁	—	2	8	no	—
177	C₂×C₄×C₁₁	—	2	4	no	—
178	C₂×C₄×C₁₁	—	2	8	no	—
179	C₂×C₄×C₁₁	—	2	4	no	—
180	C₂×C₄×C₁₁	—	4	16	no	—
181	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
184	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
187	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
188	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
190	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
191	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
192	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
193	#556	—	2	16	no	—
194	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
195	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
196	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
197	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×#126	C₂²×C₁₁	1	8	yes	—
199	C₂×#124	C₂²×C₁₁	1	4	yes	—
200	C₂×#124	C₂²×C₁₁	1	4	yes	—
201	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	—
202	C₂×C₄×Q₈	C₂²×C₁₁	1	4	yes	—
203	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
204	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
206	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
207	C₂×#117	C₂²×C₁₁	1	4	yes	—
208	#397	C₂²×C₁₁	1	8	yes	—
209	#396	C₂²×C₁₁	1	16	yes	—
210	#391	C₂²×C₁₁	1	4	yes	—
211	#390	C₂²×C₁₁	1	4	yes	—
212	#390	C₂²×C₁₁	1	2	yes	—
213	#390	C₂²×C₁₁	1	8	yes	—
214	#390	C₂²×C₁₁	1	8	yes	—
215	#389	C₂²×C₁₁	1	8	yes	—
216	#388	C₂²×C₁₁	1	16	yes	—
217	#384	C₂²×C₁₁	1	1	yes	characteristic
218	#384	C₂²×C₁₁	1	4	yes	—
219	#384	C₂²×C₁₁	1	4	yes	—
220	#380	C₂²×C₁₁	1	8	yes	—
221	C₄×C₄⋊C₄	C₂²×C₁₁	1	8	yes	—
222	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
223	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
225	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
226	C₄³	C₂²×C₁₁	1	1	yes	characteristic
227	C₄³	C₂²×C₁₁	1	2	yes	—
228	C₂²×C₁₁	—	4	4	no	—
229	C₂²×C₁₁	—	4	4	no	—
230	C₂²×C₁₁	—	4	8	no	—
231	C₂²×C₁₁	—	4	4	no	—
232	C₂²×C₁₁	—	4	8	no	—
233	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
234	C₂²×C₁₁	C₂²×#41	1	2	yes	—
235	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
236	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	2	yes	—
238	C₄×C₁₁	—	2	4	no	—
239	C₄×C₁₁	—	2	4	no	—
240	C₄×C₁₁	—	2	2	no	—
241	C₄×C₁₁	—	2	4	no	—
242	C₄×C₁₁	—	4	4	no	—
243	C₄×C₁₁	—	4	8	no	—
244	C₄×C₁₁	—	4	4	no	—
245	C₄×C₁₁	#532	1	4	yes	—
246	C₄×C₁₁	#550	1	4	yes	—
247	C₄×C₁₁	#556	1	8	yes	complemented
248	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
249	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
250	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
251	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
252	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
253	C₄⋊Q₈	—	2	8	no	—
254	C₄⋊Q₈	—	2	8	no	—
255	C₄⋊Q₈	—	4	4	no	—
256	#127	—	2	4	no	—
257	#126	—	2	32	no	—
258	#124	—	2	16	no	—
259	#124	—	4	8	no	—
260	C₂²⋊Q₈	—	2	16	no	—
261	C₄×Q₈	—	2	16	no	—
262	C₄×Q₈	—	2	8	no	—
263	C₄×Q₈	D₄×C₁₁	1	8	yes	complemented
264	C₄×D₄	—	2	8	no	—
265	C₄×D₄	—	2	16	no	—
266	#117	—	2	16	no	—
267	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₁	1	16	yes	—
283	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
284	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
285	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
288	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
289	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
292	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
293	#95	C₂³×C₁₁	1	4	yes	—
294	#95	C₂³×C₁₁	1	2	yes	—
295	#95	C₂³×C₁₁	1	16	yes	—
296	C₂×C₁₁	—	8	4	no	—
297	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
298	C₂×C₁₁	C₂×#550	1	1	yes	characteristic
299	C₂×C₁₁	C₂×#556	1	2	yes	—
300	C₂×C₁₁	#3499	1	1	yes	characteristic
301	C₂×C₁₁	#3511	1	2	yes	—
302	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
303	C₂×Q₈	—	2	8	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	—	2	8	no	—
307	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	16	no	—
316	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
317	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
318	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
319	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
322	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
325	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	16	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	16	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
336	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
337	C₂²⋊C₄	—	2	16	no	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	16	no	—
340	C₂²⋊C₄	—	2	16	no	—
341	C₂²⋊C₄	—	4	16	no	—
342	C₄²	—	2	16	no	—
343	C₄²	—	2	8	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	8	no	—
348	C₄²	C₂×D₄×C₁₁	1	4	yes	—
349	C₄²	C₂×D₄×C₁₁	1	8	yes	—
350	C₄²	C₁₁×#41	1	8	yes	—
351	C₄²	C₁₁×#41	1	4	yes	—
352	C₁₁	#36594	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	4	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	8	no	—
358	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
359	Q₈	—	2	8	no	—
360	Q₈	—	4	16	no	—
361	D₄	—	4	8	no	—
362	D₄	—	4	16	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	16	no	—
377	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
378	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
379	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
380	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
381	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
382	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
383	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
384	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
385	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
386	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
387	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
388	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	8	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	8	no	—
394	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
395	C₂²	C₂²×C₁₁×#41	1	2	yes	—
396	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
397	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	2	yes	—
399	C₄	—	2	4	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	8	no	—
405	C₄	—	4	4	no	—
406	C₄	C₁₁×#532	1	4	yes	—
407	C₄	C₁₁×#550	1	4	yes	—
408	C₄	C₁₁×#556	1	8	yes	complemented
409	C₂	—	8	4	no	—
410	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
411	C₂	C₂×C₁₁×#550	1	1	yes	characteristic
412	C₂	C₂×C₁₁×#556	1	2	yes	—
413	C₂	C₁₁×#3499	1	1	yes	characteristic
414	C₂	C₁₁×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#556	C₂	semidirect
2. C₁₁×#2868	C₂	semidirect
4. C₁₁×#2547	C₂	semidirect
5. C₁₁×#2545	C₂	semidirect
6. C₁₁×#2538	C₂	semidirect
7. C₁₁×#2512	C₂	semidirect
8. C₁₁×#2354	C₂	semidirect
9. C₄×C₁₁×C₄⋊Q₈	C₂	semidirect
11. C₄²×Q₈×C₁₁	C₂	semidirect
62. C₄×Q₈×C₁₁	D₄	semidirect
95. #36594	C₁₁	direct (N × H)
146. C₂×#556	C₂×C₁₁	semidirect
147. #2868	C₂×C₁₁	semidirect
149. #2547	C₂×C₁₁	semidirect
150. #2545	C₂×C₁₁	semidirect
151. #2538	C₂×C₁₁	semidirect
152. #2512	C₂×C₁₁	semidirect
153. #2354	C₂×C₁₁	semidirect
154. C₄×C₄⋊Q₈	C₂×C₁₁	semidirect
156. C₄²×Q₈	C₂×C₁₁	semidirect
247. C₄×C₁₁	#556	semidirect
263. C₄×Q₈	D₄×C₁₁	semidirect
352. C₁₁	#36594	direct (N × H)
408. C₄	C₁₁×#556	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#556	2
C₁₁×#2868	2
C₁₁×#2858	2
C₁₁×#2547	2
C₁₁×#2545	2
C₁₁×#2538	2
C₁₁×#2512	2
C₁₁×#2354	2
C₄×C₁₁×C₄⋊Q₈	2
C₄×C₁₁×#127	2
C₄²×Q₈×C₁₁	2
#36594	11

Subgroups — C11×#36594 #14613787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36594 #14613787