Subgroups — #14723005

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 470 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	#13077283	C₂	1	2	yes	maximal
3	#13067397	C₂	1	2	yes	maximal, complemented
4	#13067395	C₂	1	2	yes	maximal, complemented
5	#13067389	C₂	1	2	yes	maximal, complemented
6	#13067376	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067370	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067364	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067361	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4339	C₂²	1	1	yes	characteristic
13	C₁₁×#432	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	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₁₁	C₄	1	1	yes	characteristic
19	#10622538	C₂²	1	2	yes	—
20	#10622538	C₂²	1	1	yes	characteristic
21	#10622450	C₂²	1	2	yes	—
22	#10622448	C₂²	1	2	yes	—
23	#10622446	C₂²	1	2	yes	—
24	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
25	#10622340	—	2	2	no	—
26	#10622333	—	2	2	no	—
27	#10622322	—	2	2	no	—
28	#10622321	—	2	2	no	—
29	C₈×D₄₄	C₄	1	1	yes	characteristic
30	C₈×D₄₄	C₄	1	1	yes	characteristic
31	#10622298	C₂²	1	1	yes	characteristic
32	#10622298	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
35	C₈×Dic₂₂	C₄	1	1	yes	characteristic
36	C₈×Dic₂₂	C₄	1	1	yes	characteristic
37	C₁₁×#335	C₂²	1	2	yes	—
38	C₁₁×#334	C₂²	1	1	yes	characteristic
39	C₁₁×#334	C₂²	1	1	yes	characteristic
40	#10622118	C₂²	1	2	yes	—
41	#10622118	C₂²	1	2	yes	—
42	#10622117	C₂²	1	2	yes	—
43	#10622117	C₂²	1	2	yes	—
44	#10622096	C₂²	1	2	yes	—
45	#10622095	C₂²	1	1	yes	characteristic
46	#10622095	C₂²	1	1	yes	characteristic
47	C₂×#4339	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₁	Q₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₁₁	Q₈	1	1	yes	characteristic
55	#66979	D₄	1	1	yes	characteristic
56	C₂×#4313	—	2	2	no	—
57	C₂×C₈×D₁₁	—	2	2	no	—
58	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₁	C₂×C₄	1	1	yes	characteristic
62	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
63	C₄×D₄₄	Q₈	1	1	yes	characteristic
64	#66925	D₄	1	1	yes	characteristic
65	#66925	D₄	1	1	yes	characteristic
66	C₄²×D₁₁	C₂³	1	1	yes	characteristic
67	C₄²×D₁₁	C₂³	1	1	yes	characteristic
68	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₂₂	Q₈	1	1	yes	characteristic
70	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
71	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₁×C₂²⋊C₈	—	2	2	no	—
73	C₁₁×#97	—	2	2	no	—
74	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
78	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
79	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
81	(C₂×D₁₁)⋊C₈	—	2	2	no	—
82	(C₂×D₁₁)⋊C₈	—	2	2	no	—
83	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
84	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
85	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
86	(C₂×D₁₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
87	#66879	—	2	2	no	—
88	Dic₁₁⋊C₈	—	2	2	no	—
89	Dic₁₁⋊C₈	—	2	2	no	—
90	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
91	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
92	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
93	Dic₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₁	—	2	2	no	—
95	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₁	C₂×C₄	1	1	yes	characteristic
99	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
100	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
101	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
102	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
103	C₄×C₁₁⋊C₈	—	2	2	no	—
104	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
105	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
106	#17827	—	11	1	no	maximal, Sylow
107	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₁	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₁₁	C₄⋊C₄	1	1	yes	characteristic
112	#4339	—	2	4	no	—
113	C₂×D₄₄	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
120	C₂×Dic₂₂	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	4	1	no	—
125	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
132	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
134	C₂²⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
135	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
136	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
137	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
138	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
139	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
141	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
142	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
143	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
144	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
150	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
151	C₂×C₁₁⋊C₈	—	2	2	no	—
152	C₂×C₁₁⋊C₈	—	2	2	no	—
153	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
157	#4313	—	4	4	no	—
158	C₈×D₁₁	—	2	2	no	—
159	C₈×D₁₁	—	2	2	no	—
160	C₈×D₁₁	—	4	1	no	—
161	C₈×D₁₁	—	4	1	no	—
162	C₈×D₁₁	—	4	4	no	—
163	C₈×#41	—	11	1	no	—
164	#2925	—	11	2	no	—
165	#1572	—	11	2	no	—
166	#1572	—	11	2	no	—
167	#1571	—	11	2	no	—
168	#1568	—	11	1	no	—
169	#1568	D₁₁	1	1	yes	characteristic, complemented
170	#1566	—	11	1	no	—
171	#1564	—	11	1	no	—
172	#1564	—	11	1	no	—
173	C₂×#334	—	11	1	no	—
174	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	—	2	1	no	—
178	C₂×C₄×C₁₁	—	2	1	no	—
179	C₂×C₄×C₁₁	—	2	2	no	—
180	C₂×C₄×C₁₁	—	4	1	no	—
181	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
187	C₂²⋊D₁₁	—	2	2	no	—
188	C₂²⋊D₁₁	—	2	2	no	—
189	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
195	D₄₄	—	2	2	no	—
196	C₄×D₁₁	—	2	1	no	—
197	C₄×D₁₁	—	2	1	no	—
198	C₄×D₁₁	—	2	1	no	—
199	C₄×D₁₁	—	2	1	no	—
200	C₄×D₁₁	—	2	2	no	—
201	C₄×D₁₁	—	4	1	no	—
202	C₄×D₁₁	—	4	1	no	—
203	C₄×D₁₁	#135	1	4	yes	—
204	Dic₂₂	—	2	2	no	—
205	C₈×C₁₁	—	2	1	no	—
206	C₈×C₁₁	—	2	1	no	—
207	C₈×C₁₁	—	2	1	no	—
208	C₈×C₁₁	—	4	2	no	—
209	C₈×C₁₁	—	4	2	no	—
210	C₈×C₁₁	#131	1	2	yes	—
211	C₁₁⋊C₈	—	2	1	no	—
212	C₁₁⋊C₈	—	2	1	no	—
213	C₁₁⋊C₈	—	2	1	no	—
214	C₁₁⋊C₈	—	2	1	no	—
215	C₁₁⋊C₈	—	4	2	no	—
216	C₁₁⋊C₈	—	4	2	no	—
217	C₄×#41	—	11	1	no	—
218	C₈×Q₈	—	11	1	no	—
219	C₈×Q₈	—	11	1	no	—
220	C₈×D₄	—	11	1	no	—
221	C₈×D₄	—	11	1	no	—
222	C₈×D₄	—	11	1	no	—
223	C₈×D₄	—	11	1	no	—
224	C₈×D₄	—	11	1	no	—
225	C₈×D₄	—	11	1	no	—
226	#433	—	22	2	no	—
227	#433	—	22	2	no	—
228	#432	—	11	2	no	—
229	#432	C₂×D₁₁	1	2	yes	—
230	#431	—	11	1	no	—
231	#431	—	11	1	no	—
232	#431	—	11	1	no	—
233	#431	—	11	2	no	—
234	#431	—	11	2	no	—
235	#423	—	11	2	no	—
236	C₂×C₄⋊C₈	—	11	2	no	—
237	#408	—	22	2	no	—
238	#405	—	22	2	no	—
239	C₂×C₄×C₈	—	11	1	no	—
240	C₂×C₄×C₈	—	11	1	no	—
241	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
242	#335	—	11	2	no	—
243	#335	—	11	2	no	—
244	#335	—	11	2	no	—
245	#335	C₂×D₁₁	1	2	yes	—
246	#334	—	11	2	no	—
247	#334	—	11	2	no	—
248	#334	—	11	1	no	—
249	#334	—	11	1	no	—
250	#334	C₂×D₁₁	1	1	yes	characteristic
251	#334	C₂×D₁₁	1	1	yes	characteristic
252	C₂²×C₁₁	—	2	1	no	—
253	C₂²×C₁₁	—	2	1	no	—
254	C₂²×C₁₁	—	2	1	no	—
255	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
256	C₂×D₁₁	—	2	1	no	—
257	C₂×D₁₁	—	2	1	no	—
258	C₂×D₁₁	—	2	1	no	—
259	C₂×D₁₁	—	2	1	no	—
260	C₂×D₁₁	—	2	1	no	—
261	C₂×D₁₁	#427	1	2	yes	—
262	C₄×C₁₁	—	2	1	no	—
263	C₄×C₁₁	—	2	1	no	—
264	C₄×C₁₁	—	2	1	no	—
265	C₄×C₁₁	—	2	1	no	—
266	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
267	C₄×C₁₁	#568	1	1	yes	characteristic
268	C₄×C₁₁	C₂×#135	1	2	yes	—
269	Dic₁₁	—	2	1	no	—
270	Dic₁₁	—	2	1	no	—
271	Dic₁₁	—	2	1	no	—
272	Dic₁₁	—	2	1	no	—
273	Dic₁₁	—	2	1	no	—
274	Dic₁₁	#427	1	2	yes	—
275	C₂×#41	—	11	1	no	—
276	C₂×M₁₆	—	22	2	no	—
277	C₂²×C₈	—	11	1	no	—
278	C₂²×C₈	—	11	1	no	—
279	C₂²×C₈	—	11	1	no	—
280	C₂²×C₈	—	11	1	no	—
281	C₂²×C₈	—	22	2	no	—
282	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
283	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
284	C₄×Q₈	—	11	1	no	—
285	C₄×Q₈	—	11	1	no	—
286	C₄×D₄	—	11	1	no	—
287	C₄×D₄	—	11	1	no	—
288	C₄×D₄	—	11	1	no	—
289	C₄×D₄	—	11	1	no	—
290	C₄×D₄	—	11	1	no	—
291	C₄×D₄	—	11	1	no	—
292	#117	—	11	1	no	—
293	#117	—	11	1	no	—
294	#117	—	11	1	no	—
295	C₂×C₄²	—	11	1	no	—
296	C₂×C₄²	—	11	1	no	—
297	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
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	—	11	1	no	—
303	C₄⋊C₈	—	11	1	no	—
304	C₄⋊C₈	—	11	2	no	—
305	C₄⋊C₈	—	11	2	no	—
306	C₄⋊C₈	—	22	2	no	—
307	C₄⋊C₈	—	22	2	no	—
308	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
309	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	11	1	no	—
312	C₂²⋊C₈	—	11	1	no	—
313	C₂²⋊C₈	—	11	1	no	—
314	C₂²⋊C₈	—	11	1	no	—
315	C₂²⋊C₈	—	11	1	no	—
316	C₂²⋊C₈	—	11	1	no	—
317	C₂²⋊C₈	—	22	2	no	—
318	C₂²⋊C₈	—	22	2	no	—
319	C₂²⋊C₈	—	22	2	no	—
320	#97	—	2	2	no	—
321	#97	—	22	2	no	—
322	C₄×C₈	—	11	1	no	—
323	C₄×C₈	—	11	1	no	—
324	C₄×C₈	—	11	1	no	—
325	C₄×C₈	—	11	1	no	—
326	C₄×C₈	—	11	1	no	—
327	C₄×C₈	—	11	1	no	—
328	C₄×C₈	—	22	2	no	—
329	C₄×C₈	—	22	2	no	—
330	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
331	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
332	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
334	C₂×C₁₁	—	4	1	no	—
335	C₂×C₁₁	#2906	1	1	yes	characteristic
336	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
337	C₂×C₁₁	#2916	1	1	yes	characteristic
338	D₁₁	—	2	2	no	—
339	D₁₁	—	4	1	no	—
340	#41	—	22	4	no	—
341	C₂×Q₈	—	11	1	no	—
342	C₂×D₄	—	11	1	no	—
343	C₂×D₄	—	11	1	no	—
344	C₂×D₄	—	11	1	no	—
345	C₂²×C₄	—	11	1	no	—
346	C₂²×C₄	—	11	1	no	—
347	C₂²×C₄	—	11	1	no	—
348	C₂²×C₄	—	11	1	no	—
349	C₂²×C₄	—	11	1	no	—
350	C₂²×C₄	—	11	1	no	—
351	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
353	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
354	M₁₆	—	44	4	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	11	1	no	—
360	C₂×C₈	—	11	1	no	—
361	C₂×C₈	—	11	1	no	—
362	C₂×C₈	—	11	1	no	—
363	C₂×C₈	—	22	2	no	—
364	C₂×C₈	—	22	2	no	—
365	C₂×C₈	—	22	2	no	—
366	C₂×C₈	—	22	2	no	—
367	C₂×C₈	—	44	1	no	—
368	C₂×C₈	—	44	1	no	—
369	C₂×C₈	—	44	4	no	—
370	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
371	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
372	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
373	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
374	C₄⋊C₄	—	11	1	no	—
375	C₄⋊C₄	—	11	1	no	—
376	C₄⋊C₄	—	11	1	no	—
377	C₄⋊C₄	—	11	1	no	—
378	C₄⋊C₄	—	11	1	no	—
379	C₄⋊C₄	—	11	1	no	—
380	C₂²⋊C₄	—	11	1	no	—
381	C₂²⋊C₄	—	11	1	no	—
382	C₂²⋊C₄	—	11	1	no	—
383	C₂²⋊C₄	—	11	1	no	—
384	C₂²⋊C₄	—	11	1	no	—
385	C₂²⋊C₄	—	11	1	no	—
386	C₄²	—	11	1	no	—
387	C₄²	—	11	1	no	—
388	C₄²	—	11	1	no	—
389	C₄²	—	11	1	no	—
390	C₄²	—	11	1	no	—
391	C₄²	—	11	1	no	—
392	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
393	C₄²	D₄×D₁₁	1	1	yes	characteristic
394	C₄²	Q₈×D₁₁	1	1	yes	characteristic
395	C₄²	C₂³×D₁₁	1	1	yes	characteristic
396	C₁₁	#17827	1	1	yes	characteristic, complemented, Sylow
397	C₂³	—	11	1	no	—
398	C₂³	—	11	1	no	—
399	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
400	Q₈	—	22	2	no	—
401	D₄	—	22	2	no	—
402	D₄	—	22	2	no	—
403	D₄	—	22	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	11	1	no	—
409	C₂×C₄	—	11	4	no	—
410	C₂×C₄	—	11	1	no	—
411	C₂×C₄	—	11	1	no	—
412	C₂×C₄	—	11	1	no	—
413	C₂×C₄	—	11	1	no	—
414	C₂×C₄	—	11	1	no	—
415	C₂×C₄	—	22	1	no	—
416	C₂×C₄	—	22	1	no	—
417	C₂×C₄	—	22	1	no	—
418	C₂×C₄	—	22	1	no	—
419	C₂×C₄	—	22	2	no	—
420	C₂×C₄	—	44	1	no	—
421	C₂×C₄	—	44	1	no	—
422	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
423	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
424	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
426	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
427	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	4	2	no	—
432	C₈	—	4	2	no	—
433	C₈	—	22	1	no	—
434	C₈	—	22	1	no	—
435	C₈	—	22	1	no	—
436	C₈	—	22	1	no	—
437	C₈	—	44	2	no	—
438	C₈	—	44	2	no	—
439	C₈	#66960	1	2	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	11	2	no	—
444	C₂²	—	22	1	no	—
445	C₂²	—	22	1	no	—
446	C₂²	—	22	1	no	—
447	C₂²	—	22	1	no	—
448	C₂²	—	22	1	no	—
449	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	11	2	no	—
455	C₄	—	22	1	no	—
456	C₄	—	22	1	no	—
457	C₄	—	22	1	no	—
458	C₄	—	22	1	no	—
459	C₄	—	22	1	no	—
460	C₄	C₂×#66960	1	1	yes	characteristic
461	C₄	#10623276	1	1	yes	characteristic
462	C₄	D₁₁×#135	1	2	yes	—
463	C₂	—	4	1	no	—
464	C₂	—	22	2	no	—
465	C₂	—	44	1	no	—
466	C₂	#13077185	1	1	yes	characteristic
467	C₂	D₁₁×#427	1	1	yes	characteristic
468	C₂	#13077224	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1568	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×#4339	D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1568	D₁₁
hypocenter	C₁₁	#17827
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #13067397	C₂	semidirect
4. #13067395	C₂	semidirect
5. #13067389	C₂	semidirect
6. #13067376	C₂	semidirect
7. #13067370	C₂	semidirect
8. #13067364	C₂	semidirect
9. #13067361	C₂	semidirect
10. D₁₁×#334	C₂	semidirect
11. C₁₁×#1568	C₂	semidirect
169. #1568	D₁₁	semidirect
396. C₁₁	#17827	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
#13077283	2
#13067397	2
#13067395	2
#13067389	2
#13067376	2
#13067370	2
#13067364	2
#13067361	2
D₁₁×#334	2
C₁₁×#1568	2
#17827	11