Subgroups — C₁₁×#36595 #14613788

Order 2816.

2706 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#559	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2867	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2858	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2548	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2548	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2544	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2445	C₂	1	8	yes	maximal, complemented
8	C₁₁×#2366	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₁×#127	C₂	1	2	yes	maximal, complemented
11	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#559	—	2	16	no	—
13	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#127	C₂²	1	2	yes	—
15	C₂×C₁₁×#127	C₂²	1	4	yes	—
16	C₂×C₁₁×#127	C₂²	1	2	yes	—
17	C₂×C₁₁×#127	C₂²	1	4	yes	—
18	C₂×C₁₁×#127	C₂²	1	2	yes	—
19	C₂×C₁₁×#124	C₂²	1	4	yes	—
20	C₂×C₁₁×#124	C₂²	1	4	yes	—
21	C₂×C₁₁×#124	C₂²	1	4	yes	—
22	C₂×C₁₁×#123	C₂²	1	8	yes	—
23	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₁	C₂²	1	8	yes	—
29	C₁₁×#394	C₂²	1	8	yes	—
30	C₁₁×#394	C₂²	1	16	yes	—
31	C₁₁×#391	C₂²	1	2	yes	—
32	C₁₁×#390	C₂²	1	8	yes	—
33	C₁₁×#390	C₂²	1	8	yes	—
34	C₁₁×#390	C₂²	1	8	yes	—
35	C₁₁×#390	C₂²	1	4	yes	—
36	C₁₁×#390	C₂²	1	8	yes	—
37	C₁₁×#389	C₂²	1	4	yes	—
38	C₁₁×#386	C₂²	1	16	yes	—
39	C₁₁×#384	C₂²	1	1	yes	characteristic
40	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
41	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
42	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
44	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
45	C₄³×C₁₁	C₂²	1	2	yes	—
46	C₄³×C₁₁	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
50	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₁	C₂³	1	8	yes	—
52	C₂²×D₄×C₁₁	C₂³	1	8	yes	—
53	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₁	C₂³	1	8	yes	—
55	C₁₁×C₄⋊Q₈	—	2	4	no	—
56	C₁₁×#127	—	2	8	no	—
57	C₁₁×#127	—	2	16	no	—
58	C₁₁×#127	—	2	8	no	—
59	C₁₁×#127	—	4	8	no	—
60	C₁₁×#127	—	4	4	no	—
61	C₁₁×#124	—	2	16	no	—
62	C₁₁×#124	—	2	16	no	—
63	C₁₁×#124	—	4	8	no	—
64	C₁₁×#123	—	2	32	no	—
65	C₄×Q₈×C₁₁	—	2	8	no	—
66	C₄×Q₈×C₁₁	—	2	8	no	—
67	C₄×Q₈×C₁₁	D₄	1	8	yes	complemented
68	C₄×D₄×C₁₁	—	2	16	no	—
69	C₄×D₄×C₁₁	—	2	16	no	—
70	C₄×D₄×C₁₁	—	4	16	no	—
71	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
77	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₂×C₁₁×C₂²⋊C₄	C₂³	1	16	yes	—
83	C₂×C₁₁×C₂²⋊C₄	C₂³	1	16	yes	—
84	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
89	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
90	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
94	C₁₁×#95	C₂³	1	4	yes	—
95	C₁₁×#95	C₂³	1	2	yes	—
96	C₁₁×#95	C₂³	1	8	yes	—
97	#36595	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₁	C₂⁴	1	8	yes	—
99	C₂×Q₈×C₁₁	—	2	4	no	—
100	C₂×Q₈×C₁₁	—	2	4	no	—
101	C₂×Q₈×C₁₁	—	2	4	no	—
102	C₂×Q₈×C₁₁	—	2	4	no	—
103	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
104	C₂×D₄×C₁₁	—	2	8	no	—
105	C₂×D₄×C₁₁	—	2	8	no	—
106	C₂×D₄×C₁₁	—	2	8	no	—
107	C₂×D₄×C₁₁	—	2	16	no	—
108	C₂×D₄×C₁₁	—	2	8	no	—
109	C₂×D₄×C₁₁	—	2	16	no	—
110	C₂×D₄×C₁₁	—	2	16	no	—
111	C₂×D₄×C₁₁	—	2	16	no	—
112	C₂×D₄×C₁₁	—	2	16	no	—
113	C₂×D₄×C₁₁	—	2	8	no	—
114	C₂×D₄×C₁₁	—	4	8	no	—
115	C₂×D₄×C₁₁	—	4	8	no	—
116	C₂×D₄×C₁₁	—	4	8	no	—
117	C₂²×C₄×C₁₁	—	2	16	no	—
118	C₂²×C₄×C₁₁	—	4	16	no	—
119	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
129	C₁₁×C₄⋊C₄	—	2	4	no	—
130	C₁₁×C₄⋊C₄	—	2	8	no	—
131	C₁₁×C₄⋊C₄	—	2	8	no	—
132	C₁₁×C₄⋊C₄	—	2	4	no	—
133	C₁₁×C₄⋊C₄	—	2	8	no	—
134	C₁₁×C₄⋊C₄	—	2	8	no	—
135	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
136	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
137	C₁₁×C₂²⋊C₄	—	2	16	no	—
138	C₁₁×C₂²⋊C₄	—	2	16	no	—
139	C₁₁×C₂²⋊C₄	—	2	16	no	—
140	C₁₁×C₂²⋊C₄	—	4	16	no	—
141	C₁₁×C₂²⋊C₄	—	4	16	no	—
142	C₄²×C₁₁	—	2	8	no	—
143	C₄²×C₁₁	—	2	8	no	—
144	C₄²×C₁₁	—	2	8	no	—
145	C₄²×C₁₁	—	2	4	no	—
146	C₄²×C₁₁	—	2	2	no	—
147	C₄²×C₁₁	—	2	4	no	—
148	C₄²×C₁₁	C₂×D₄	1	8	yes	—
149	C₄²×C₁₁	C₂×D₄	1	4	yes	—
150	C₄²×C₁₁	#41	1	8	yes	—
151	C₄²×C₁₁	#41	1	4	yes	—
152	C₂×#559	C₂×C₁₁	1	2	yes	complemented
153	#2867	C₂×C₁₁	1	1	yes	characteristic
154	#2858	C₂×C₁₁	1	2	yes	complemented
155	#2548	C₂×C₁₁	1	2	yes	complemented
156	#2548	C₂×C₁₁	1	4	yes	complemented
157	#2544	C₂×C₁₁	1	4	yes	complemented
158	#2445	C₂×C₁₁	1	8	yes	complemented
159	#2366	C₂×C₁₁	1	4	yes	complemented
160	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
161	C₄×#127	C₂×C₁₁	1	2	yes	complemented
162	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
163	C₂³×C₁₁	—	2	8	no	—
164	C₂³×C₁₁	—	2	16	no	—
165	C₂³×C₁₁	—	2	8	no	—
166	C₂³×C₁₁	—	2	8	no	—
167	C₂³×C₁₁	—	2	16	no	—
168	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
169	Q₈×C₁₁	—	2	8	no	—
170	Q₈×C₁₁	—	4	8	no	—
171	D₄×C₁₁	—	4	16	no	—
172	D₄×C₁₁	—	4	16	no	—
173	D₄×C₁₁	—	4	32	no	—
174	D₄×C₁₁	—	8	8	no	—
175	D₄×C₁₁	—	8	16	no	—
176	C₂×C₄×C₁₁	—	2	4	no	—
177	C₂×C₄×C₁₁	—	2	4	no	—
178	C₂×C₄×C₁₁	—	2	2	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	2	2	no	—
181	C₂×C₄×C₁₁	—	2	4	no	—
182	C₂×C₄×C₁₁	—	2	4	no	—
183	C₂×C₄×C₁₁	—	2	4	no	—
184	C₂×C₄×C₁₁	—	2	4	no	—
185	C₂×C₄×C₁₁	—	2	4	no	—
186	C₂×C₄×C₁₁	—	2	4	no	—
187	C₂×C₄×C₁₁	—	2	4	no	—
188	C₂×C₄×C₁₁	—	2	8	no	—
189	C₂×C₄×C₁₁	—	8	16	no	—
190	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
191	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
196	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
197	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
199	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
200	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
201	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
202	#559	—	2	16	no	—
203	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
204	C₂×#127	C₂²×C₁₁	1	2	yes	—
205	C₂×#127	C₂²×C₁₁	1	4	yes	—
206	C₂×#127	C₂²×C₁₁	1	2	yes	—
207	C₂×#127	C₂²×C₁₁	1	4	yes	—
208	C₂×#127	C₂²×C₁₁	1	2	yes	—
209	C₂×#124	C₂²×C₁₁	1	4	yes	—
210	C₂×#124	C₂²×C₁₁	1	4	yes	—
211	C₂×#124	C₂²×C₁₁	1	4	yes	—
212	C₂×#123	C₂²×C₁₁	1	8	yes	—
213	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
214	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
215	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
217	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
218	C₂×C₄×D₄	C₂²×C₁₁	1	8	yes	—
219	#394	C₂²×C₁₁	1	8	yes	—
220	#394	C₂²×C₁₁	1	16	yes	—
221	#391	C₂²×C₁₁	1	2	yes	—
222	#390	C₂²×C₁₁	1	8	yes	—
223	#390	C₂²×C₁₁	1	4	yes	—
224	#390	C₂²×C₁₁	1	8	yes	—
225	#390	C₂²×C₁₁	1	8	yes	—
226	#390	C₂²×C₁₁	1	8	yes	—
227	#389	C₂²×C₁₁	1	4	yes	—
228	#386	C₂²×C₁₁	1	16	yes	—
229	#384	C₂²×C₁₁	1	1	yes	characteristic
230	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
234	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
235	C₄³	C₂²×C₁₁	1	2	yes	—
236	C₄³	C₂²×C₁₁	1	1	yes	characteristic
237	C₂²×C₁₁	—	4	8	no	—
238	C₂²×C₁₁	—	4	8	no	—
239	C₂²×C₁₁	—	4	16	no	—
240	C₂²×C₁₁	—	4	8	no	—
241	C₂²×C₁₁	—	4	16	no	—
242	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
243	C₂²×C₁₁	C₂²×#41	1	2	yes	—
244	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
245	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
247	C₄×C₁₁	—	2	4	no	—
248	C₄×C₁₁	—	2	4	no	—
249	C₄×C₁₁	—	2	2	no	—
250	C₄×C₁₁	—	2	4	no	—
251	C₄×C₁₁	—	4	4	no	—
252	C₄×C₁₁	—	4	4	no	—
253	C₄×C₁₁	—	4	4	no	—
254	C₄×C₁₁	#532	1	4	yes	—
255	C₄×C₁₁	#550	1	4	yes	—
256	C₄×C₁₁	#559	1	8	yes	complemented
257	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
258	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
260	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
261	C₂²×D₄	C₂³×C₁₁	1	8	yes	—
262	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
263	C₂²×D₄	C₂³×C₁₁	1	8	yes	—
264	C₂³×C₄	C₂³×C₁₁	1	8	yes	—
265	C₄⋊Q₈	—	2	4	no	—
266	#127	—	2	8	no	—
267	#127	—	2	16	no	—
268	#127	—	2	8	no	—
269	#127	—	4	8	no	—
270	#127	—	4	4	no	—
271	#124	—	2	16	no	—
272	#124	—	2	16	no	—
273	#124	—	4	8	no	—
274	#123	—	2	32	no	—
275	C₄×Q₈	—	2	8	no	—
276	C₄×Q₈	—	2	8	no	—
277	C₄×Q₈	D₄×C₁₁	1	8	yes	complemented
278	C₄×D₄	—	2	16	no	—
279	C₄×D₄	—	2	16	no	—
280	C₄×D₄	—	4	16	no	—
281	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₁₁	1	16	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₁	1	16	yes	—
294	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
295	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
296	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
297	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
298	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
299	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
301	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
304	#95	C₂³×C₁₁	1	4	yes	—
305	#95	C₂³×C₁₁	1	2	yes	—
306	#95	C₂³×C₁₁	1	8	yes	—
307	C₂×C₁₁	—	8	8	no	—
308	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
309	C₂×C₁₁	C₂×#550	1	1	yes	characteristic
310	C₂×C₁₁	C₂×#559	1	2	yes	—
311	C₂×C₁₁	#3498	1	1	yes	characteristic
312	C₂×C₁₁	#3508	1	2	yes	—
313	C₂⁴	C₂⁴×C₁₁	1	8	yes	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	8	no	—
322	C₂×D₄	—	2	16	no	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	2	16	no	—
325	C₂×D₄	—	2	16	no	—
326	C₂×D₄	—	2	16	no	—
327	C₂×D₄	—	2	16	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	4	8	no	—
330	C₂×D₄	—	4	8	no	—
331	C₂×D₄	—	4	8	no	—
332	C₂²×C₄	—	2	16	no	—
333	C₂²×C₄	—	4	16	no	—
334	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
335	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
336	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
343	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
351	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
352	C₂²⋊C₄	—	2	16	no	—
353	C₂²⋊C₄	—	2	16	no	—
354	C₂²⋊C₄	—	2	16	no	—
355	C₂²⋊C₄	—	4	16	no	—
356	C₂²⋊C₄	—	4	16	no	—
357	C₄²	—	2	8	no	—
358	C₄²	—	2	8	no	—
359	C₄²	—	2	8	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	4	no	—
363	C₄²	C₂×D₄×C₁₁	1	8	yes	—
364	C₄²	C₂×D₄×C₁₁	1	4	yes	—
365	C₄²	C₁₁×#41	1	8	yes	—
366	C₄²	C₁₁×#41	1	4	yes	—
367	C₁₁	#36595	1	1	yes	characteristic, direct product factor, Sylow
368	C₂³	—	2	8	no	—
369	C₂³	—	2	16	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	8	no	—
372	C₂³	—	2	16	no	—
373	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
374	Q₈	—	2	8	no	—
375	Q₈	—	4	8	no	—
376	D₄	—	4	16	no	—
377	D₄	—	4	16	no	—
378	D₄	—	4	32	no	—
379	D₄	—	8	8	no	—
380	D₄	—	8	16	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	8	16	no	—
395	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
396	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
397	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
398	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
399	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
400	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
401	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
402	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
403	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
404	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
405	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
407	C₂²	—	4	8	no	—
408	C₂²	—	4	8	no	—
409	C₂²	—	4	16	no	—
410	C₂²	—	4	8	no	—
411	C₂²	—	4	16	no	—
412	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
413	C₂²	C₂²×C₁₁×#41	1	2	yes	—
414	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
415	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
417	C₄	—	2	4	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	4	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	4	no	—
423	C₄	—	4	4	no	—
424	C₄	C₁₁×#532	1	4	yes	—
425	C₄	C₁₁×#550	1	4	yes	—
426	C₄	C₁₁×#559	1	8	yes	complemented
427	C₂	—	8	8	no	—
428	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
429	C₂	C₂×C₁₁×#550	1	1	yes	characteristic
430	C₂	C₂×C₁₁×#559	1	2	yes	—
431	C₂	C₁₁×#3498	1	1	yes	characteristic
432	C₂	C₁₁×#3508	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₁₁×#2867	C₂
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×#559	C₂	semidirect
3. C₁₁×#2858	C₂	semidirect
4. C₁₁×#2548	C₂	semidirect
5. C₁₁×#2548	C₂	semidirect
6. C₁₁×#2544	C₂	semidirect
7. C₁₁×#2445	C₂	semidirect
8. C₁₁×#2366	C₂	semidirect
9. C₄×C₁₁×C₄⋊Q₈	C₂	semidirect
10. C₄×C₁₁×#127	C₂	semidirect
11. C₄²×Q₈×C₁₁	C₂	semidirect
67. C₄×Q₈×C₁₁	D₄	semidirect
97. #36595	C₁₁	direct (N × H)
152. C₂×#559	C₂×C₁₁	semidirect
154. #2858	C₂×C₁₁	semidirect
155. #2548	C₂×C₁₁	semidirect
156. #2548	C₂×C₁₁	semidirect
157. #2544	C₂×C₁₁	semidirect
158. #2445	C₂×C₁₁	semidirect
159. #2366	C₂×C₁₁	semidirect
160. C₄×C₄⋊Q₈	C₂×C₁₁	semidirect
161. C₄×#127	C₂×C₁₁	semidirect
162. C₄²×Q₈	C₂×C₁₁	semidirect
256. C₄×C₁₁	#559	semidirect
277. C₄×Q₈	D₄×C₁₁	semidirect
367. C₁₁	#36595	direct (N × H)
426. C₄	C₁₁×#559	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#559	2
C₁₁×#2867	2
C₁₁×#2858	2
C₁₁×#2548	2
C₁₁×#2544	2
C₁₁×#2445	2
C₁₁×#2366	2
C₄×C₁₁×C₄⋊Q₈	2
C₄×C₁₁×#127	2
C₄²×Q₈×C₁₁	2
#36595	11

Subgroups — C11×#36595 #14613788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36595 #14613788