Subgroups — #14907447

Order 2816.

526 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#4339	C₂	1	1	yes	maximal, characteristic
2	#13070523	C₂	1	2	yes	maximal, complemented
3	#13070446	C₂	1	2	yes	maximal, complemented
4	#13070440	C₂	1	2	yes	maximal, complemented
5	#13070439	C₂	1	2	yes	maximal, complemented
6	#13070419	C₂	1	1	yes	maximal, characteristic, complemented
7	#13070418	C₂	1	1	yes	maximal, characteristic, complemented
8	#13070414	C₂	1	1	yes	maximal, characteristic, complemented
9	#13070370	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2150	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4339	C₄	1	1	yes	characteristic
13	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
16	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
18	C₈×C₂²⋊D₁₁	C₂²	1	1	yes	characteristic
19	#10622538	C₄	1	1	yes	characteristic
20	C₂×#66862	C₂²	1	2	yes	—
21	C₂×C₁₆×D₁₁	C₂²	1	2	yes	—
22	C₈×D₄₄	C₄	1	1	yes	characteristic
23	C₈×D₄₄	C₂²	1	1	yes	characteristic
24	#10622298	C₄	1	1	yes	characteristic
25	#10622298	C₄	1	1	yes	characteristic
26	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
28	C₈×Dic₂₂	C₄	1	1	yes	characteristic
29	C₈×Dic₂₂	C₂²	1	1	yes	characteristic
30	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
31	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
32	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
33	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
34	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	—
35	(C₂×D₁₁)⋊C₁₆	C₂²	1	2	yes	—
36	#10622140	C₂²	1	2	yes	—
37	Dic₁₁⋊C₁₆	C₂²	1	2	yes	—
38	Dic₁₁⋊C₁₆	C₂²	1	2	yes	—
39	C₁₆×Dic₁₁	C₂²	1	2	yes	—
40	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
41	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	1	yes	characteristic
42	#10622099	C₂²	1	2	yes	—
43	C₂×#4339	C₈	1	1	yes	characteristic
44	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₁	C₈	1	1	yes	characteristic
49	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
51	#66979	C₈	1	1	yes	characteristic
52	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
56	C₄×D₄₄	C₈	1	1	yes	characteristic
57	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
58	#66925	C₈	1	1	yes	characteristic
59	#66925	C₈	1	1	yes	characteristic
60	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₂₂	C₈	1	1	yes	characteristic
63	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
64	C₁₁×M₃₂	—	4	2	no	—
65	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
66	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
67	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
70	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
71	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
72	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
73	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
74	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
75	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
76	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
77	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
78	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
79	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
80	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
84	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
85	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
86	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
87	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
88	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
89	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
91	#66862	—	4	2	no	—
92	C₁₆×D₁₁	—	4	2	no	—
93	#33503	—	11	1	no	maximal, Sylow
94	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₁	C₂×C₈	1	1	yes	characteristic
99	#4339	—	2	4	no	—
100	C₂×D₄₄	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₁	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×Dic₂₂	C₂×C₈	1	1	yes	characteristic
108	C₂×C₈×C₁₁	—	2	1	no	—
109	C₂×C₈×C₁₁	—	2	1	no	—
110	C₂×C₈×C₁₁	—	4	1	no	—
111	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
115	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
116	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
120	C₂²⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
121	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
122	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
123	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
124	(C₂×D₁₁)⋊C₄	C₂×C₈	1	1	yes	characteristic
125	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₁₁	C₂×C₈	1	1	yes	characteristic
127	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
128	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
129	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
130	Dic₁₁⋊C₄	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₁₁	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₈×D₁₁	—	2	1	no	—
142	C₈×D₁₁	—	2	1	no	—
143	C₈×D₁₁	—	2	1	no	—
144	C₈×D₁₁	—	2	1	no	—
145	C₈×D₁₁	—	4	1	no	—
146	C₈×D₁₁	—	4	1	no	—
147	C₁₁×C₁₆	—	2	2	no	—
148	C₁₁×C₁₆	—	2	2	no	—
149	C₁₁⋊C₁₆	—	2	2	no	—
150	C₁₁⋊C₁₆	—	2	2	no	—
151	C₈×#41	—	11	1	no	—
152	#2183	—	11	2	no	—
153	#2169	—	11	2	no	—
154	#2168	—	11	2	no	—
155	#2168	—	11	2	no	—
156	#2163	—	11	1	no	—
157	#2163	—	11	1	no	—
158	#2162	—	11	1	no	—
159	#2150	—	11	1	no	—
160	#2150	D₁₁	1	1	yes	characteristic, complemented
161	C₂×C₄⋊C₁₆	—	11	1	no	—
162	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
163	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
164	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	4	1	no	—
169	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
175	C₂²⋊D₁₁	—	2	2	no	—
176	C₂²⋊D₁₁	—	2	2	no	—
177	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
182	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
183	D₄₄	—	2	2	no	—
184	C₄×D₁₁	—	2	1	no	—
185	C₄×D₁₁	—	2	1	no	—
186	C₄×D₁₁	—	2	1	no	—
187	C₄×D₁₁	—	2	1	no	—
188	C₄×D₁₁	—	2	2	no	—
189	C₄×D₁₁	—	4	1	no	—
190	C₄×D₁₁	—	4	1	no	—
191	C₄×D₁₁	M₃₂	1	4	yes	complemented
192	Dic₂₂	—	2	2	no	—
193	C₈×C₁₁	—	2	1	no	—
194	C₈×C₁₁	—	2	1	no	—
195	C₈×C₁₁	—	2	1	no	—
196	C₈×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
197	C₈×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
198	C₁₁⋊C₈	—	2	1	no	—
199	C₁₁⋊C₈	—	2	1	no	—
200	C₁₁⋊C₈	—	2	1	no	—
201	C₁₁⋊C₈	—	2	1	no	—
202	C₄×#41	—	11	1	no	—
203	C₂×M₃₂	—	11	2	no	—
204	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
205	C₂²×C₁₆	—	11	2	no	—
206	C₈×Q₈	—	11	1	no	—
207	C₈×Q₈	—	11	1	no	—
208	C₈×D₄	—	11	1	no	—
209	C₈×D₄	—	11	1	no	—
210	C₈×D₄	—	11	1	no	—
211	C₈×D₄	—	11	1	no	—
212	C₈×D₄	—	11	1	no	—
213	C₈×D₄	—	11	1	no	—
214	#431	—	11	1	no	—
215	#431	—	11	1	no	—
216	#431	—	11	1	no	—
217	C₂×C₄×C₈	—	11	1	no	—
218	C₂×C₄×C₈	—	11	1	no	—
219	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
220	C₄⋊C₁₆	—	11	2	no	—
221	C₄⋊C₁₆	—	11	2	no	—
222	C₄⋊C₁₆	—	11	1	no	—
223	C₄⋊C₁₆	—	11	1	no	—
224	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
225	C₄⋊C₁₆	C₂×D₁₁	1	1	yes	characteristic
226	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
227	C₂²⋊C₁₆	—	11	2	no	—
228	C₂²⋊C₁₆	—	11	2	no	—
229	C₂²⋊C₁₆	—	11	2	no	—
230	#346	—	11	2	no	—
231	#346	—	11	2	no	—
232	C₄×C₁₆	—	11	2	no	—
233	C₂²×C₁₁	—	2	1	no	—
234	C₂²×C₁₁	—	2	1	no	—
235	C₂²×C₁₁	—	2	1	no	—
236	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
237	C₂×D₁₁	—	2	1	no	—
238	C₂×D₁₁	—	2	1	no	—
239	C₂×D₁₁	—	2	1	no	—
240	C₂×D₁₁	—	2	1	no	—
241	C₂×D₁₁	—	2	1	no	—
242	C₂×D₁₁	C₂×M₃₂	1	2	yes	—
243	C₄×C₁₁	—	2	1	no	—
244	C₄×C₁₁	—	2	1	no	—
245	C₄×C₁₁	—	2	1	no	—
246	C₄×C₁₁	—	2	1	no	—
247	C₄×C₁₁	C₂×M₃₂	1	2	yes	—
248	C₄×C₁₁	#520	1	1	yes	characteristic
249	C₄×C₁₁	#568	1	1	yes	characteristic
250	Dic₁₁	—	2	1	no	—
251	Dic₁₁	—	2	1	no	—
252	Dic₁₁	—	2	1	no	—
253	Dic₁₁	—	2	1	no	—
254	Dic₁₁	—	2	1	no	—
255	Dic₁₁	C₂×M₃₂	1	2	yes	—
256	C₂×#41	—	11	1	no	—
257	C₂²×C₈	—	11	1	no	—
258	C₂²×C₈	—	11	1	no	—
259	C₂²×C₈	—	11	1	no	—
260	C₂²×C₈	—	11	1	no	—
261	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
263	C₄×Q₈	—	11	1	no	—
264	C₄×Q₈	—	11	1	no	—
265	C₄×D₄	—	11	1	no	—
266	C₄×D₄	—	11	1	no	—
267	C₄×D₄	—	11	1	no	—
268	C₄×D₄	—	11	1	no	—
269	C₄×D₄	—	11	1	no	—
270	C₄×D₄	—	11	1	no	—
271	#117	—	11	1	no	—
272	#117	—	11	1	no	—
273	#117	—	11	1	no	—
274	C₂×C₄²	—	11	1	no	—
275	C₂×C₄²	—	11	1	no	—
276	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
277	M₃₂	—	4	2	no	—
278	M₃₂	—	44	2	no	—
279	C₂×C₁₆	—	11	2	no	—
280	C₂×C₁₆	—	11	2	no	—
281	C₂×C₁₆	—	44	2	no	—
282	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
283	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
284	C₄⋊C₈	—	11	1	no	—
285	C₄⋊C₈	—	11	1	no	—
286	C₄⋊C₈	—	11	1	no	—
287	C₄⋊C₈	—	11	1	no	—
288	C₄⋊C₈	—	11	1	no	—
289	C₄⋊C₈	—	11	1	no	—
290	C₂²⋊C₈	—	11	1	no	—
291	C₂²⋊C₈	—	11	1	no	—
292	C₂²⋊C₈	—	11	1	no	—
293	C₂²⋊C₈	—	11	1	no	—
294	C₂²⋊C₈	—	11	1	no	—
295	C₂²⋊C₈	—	11	1	no	—
296	C₄×C₈	—	11	1	no	—
297	C₄×C₈	—	11	1	no	—
298	C₄×C₈	—	11	1	no	—
299	C₄×C₈	—	11	1	no	—
300	C₄×C₈	—	11	1	no	—
301	C₄×C₈	—	11	1	no	—
302	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
303	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
305	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
306	C₂×C₁₁	—	4	1	no	—
307	C₂×C₁₁	#2988	1	1	yes	characteristic
308	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
309	C₂×C₁₁	#3407	1	1	yes	characteristic
310	D₁₁	—	2	2	no	—
311	D₁₁	—	4	1	no	—
312	#41	—	22	4	no	—
313	C₂×Q₈	—	11	1	no	—
314	C₂×D₄	—	11	1	no	—
315	C₂×D₄	—	11	1	no	—
316	C₂×D₄	—	11	1	no	—
317	C₂²×C₄	—	11	1	no	—
318	C₂²×C₄	—	11	1	no	—
319	C₂²×C₄	—	11	1	no	—
320	C₂²×C₄	—	11	1	no	—
321	C₂²×C₄	—	11	1	no	—
322	C₂²×C₄	—	11	1	no	—
323	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
324	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	11	1	no	—
330	C₂×C₈	—	11	1	no	—
331	C₂×C₈	—	11	1	no	—
332	C₂×C₈	—	11	1	no	—
333	C₂×C₈	—	22	1	no	—
334	C₂×C₈	—	22	1	no	—
335	C₂×C₈	—	22	1	no	—
336	C₂×C₈	—	22	1	no	—
337	C₂×C₈	—	44	1	no	—
338	C₂×C₈	—	44	1	no	—
339	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
341	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
342	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
343	C₄⋊C₄	—	11	1	no	—
344	C₄⋊C₄	—	11	1	no	—
345	C₄⋊C₄	—	11	1	no	—
346	C₄⋊C₄	—	11	1	no	—
347	C₄⋊C₄	—	11	1	no	—
348	C₄⋊C₄	—	11	1	no	—
349	C₂²⋊C₄	—	11	1	no	—
350	C₂²⋊C₄	—	11	1	no	—
351	C₂²⋊C₄	—	11	1	no	—
352	C₂²⋊C₄	—	11	1	no	—
353	C₂²⋊C₄	—	11	1	no	—
354	C₂²⋊C₄	—	11	1	no	—
355	C₄²	—	11	1	no	—
356	C₄²	—	11	1	no	—
357	C₄²	—	11	1	no	—
358	C₄²	—	11	1	no	—
359	C₄²	—	11	1	no	—
360	C₄²	—	11	1	no	—
361	C₄²	C₈×D₁₁	1	1	yes	characteristic
362	C₄²	C₈×D₁₁	1	1	yes	characteristic
363	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
364	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
365	C₁₆	—	2	2	no	—
366	C₁₆	—	2	2	no	—
367	C₁₆	—	22	2	no	—
368	C₁₆	—	22	2	no	—
369	C₁₁	#33503	1	1	yes	characteristic, complemented, Sylow
370	C₂³	—	11	1	no	—
371	C₂³	—	11	1	no	—
372	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
373	Q₈	—	22	2	no	—
374	D₄	—	22	2	no	—
375	D₄	—	22	2	no	—
376	D₄	—	22	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	11	1	no	—
382	C₂×C₄	—	11	4	no	—
383	C₂×C₄	—	11	1	no	—
384	C₂×C₄	—	11	1	no	—
385	C₂×C₄	—	11	1	no	—
386	C₂×C₄	—	11	1	no	—
387	C₂×C₄	—	11	1	no	—
388	C₂×C₄	—	22	1	no	—
389	C₂×C₄	—	22	1	no	—
390	C₂×C₄	—	22	2	no	—
391	C₂×C₄	—	22	1	no	—
392	C₂×C₄	—	22	1	no	—
393	C₂×C₄	—	44	1	no	—
394	C₂×C₄	—	44	1	no	—
395	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
396	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
397	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
398	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
399	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	22	1	no	—
405	C₈	—	22	1	no	—
406	C₈	—	22	1	no	—
407	C₈	—	22	1	no	—
408	C₈	#67037	1	1	yes	characteristic
409	C₈	#67040	1	1	yes	characteristic
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	11	2	no	—
414	C₂²	—	22	1	no	—
415	C₂²	—	22	1	no	—
416	C₂²	—	22	1	no	—
417	C₂²	—	22	1	no	—
418	C₂²	—	22	1	no	—
419	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	11	2	no	—
425	C₄	—	22	1	no	—
426	C₄	—	22	1	no	—
427	C₄	—	22	1	no	—
428	C₄	—	22	1	no	—
429	C₄	—	22	1	no	—
430	C₄	D₁₁×M₃₂	1	2	yes	—
431	C₄	#10623035	1	1	yes	characteristic
432	C₄	#10623276	1	1	yes	characteristic
433	C₂	—	4	1	no	—
434	C₂	—	22	2	no	—
435	C₂	—	44	1	no	—
436	C₂	#13077725	1	1	yes	characteristic
437	C₂	C₂×D₁₁×M₃₂	1	1	yes	characteristic
438	C₂	#13081718	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2150	C₂
prime radical	C₂×#4339	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2150	D₁₁
hypocenter	C₁₁	#33503
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2150

Complements

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

N	H ≅ G/N	type
2. #13070523	C₂	semidirect
3. #13070446	C₂	semidirect
4. #13070440	C₂	semidirect
5. #13070439	C₂	semidirect
6. #13070419	C₂	semidirect
7. #13070418	C₂	semidirect
8. #13070414	C₂	semidirect
9. #13070370	C₂	semidirect
10. D₁₁×C₄⋊C₁₆	C₂	semidirect
11. C₁₁×#2150	C₂	semidirect
160. #2150	D₁₁	semidirect
191. C₄×D₁₁	M₃₂	semidirect
369. C₁₁	#33503	semidirect

Maximal subgroups

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

subgroup	index
C₈×#4339	2
#13070523	2
#13070446	2
#13070440	2
#13070439	2
#13070419	2
#13070418	2
#13070414	2
#13070370	2
D₁₁×C₄⋊C₁₆	2
C₁₁×#2150	2
#33503	11