Subgroups — #14723012

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 480 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	#13077277	C₂	1	2	yes	maximal
3	#13067394	C₂	1	2	yes	maximal, complemented
4	#13067393	C₂	1	2	yes	maximal, complemented
5	#13067385	C₂	1	2	yes	maximal, complemented
6	#13067379	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067378	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067373	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067363	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4339	C₂²	1	1	yes	characteristic
13	C₁₁×#431	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	#10622539	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	#10622303	—	2	2	no	—
28	#10622302	—	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	1	yes	characteristic
38	C₁₁×#335	C₂²	1	1	yes	characteristic
39	C₁₁×#334	C₂²	1	2	yes	—
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	1	yes	characteristic
45	#10622096	C₂²	1	1	yes	characteristic
46	#10622095	C₂²	1	2	yes	—
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	C₄×C₈×C₁₁	—	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	#66867	—	2	2	no	—
104	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
105	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
106	#17829	—	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	2	no	—
113	#4339	—	2	2	no	—
114	C₂×D₄₄	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
121	C₂×Dic₂₂	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	4	1	no	—
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	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
133	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
134	C₂²⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
135	C₂²⋊Dic₁₁	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	(C₂×D₁₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
141	C₄⋊Dic₁₁	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	Dic₁₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
151	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
152	C₂×C₁₁⋊C₈	—	2	2	no	—
153	C₂×C₁₁⋊C₈	—	2	2	no	—
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	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
158	#4313	—	4	4	no	—
159	C₈×D₁₁	—	2	2	no	—
160	C₈×D₁₁	—	2	2	no	—
161	C₈×D₁₁	—	4	1	no	—
162	C₈×D₁₁	—	4	1	no	—
163	C₈×D₁₁	—	4	4	no	—
164	C₈×#41	—	11	1	no	—
165	#2925	—	11	2	no	—
166	#1572	—	11	2	no	—
167	#1572	—	11	2	no	—
168	#1570	—	11	2	no	—
169	#1568	—	11	1	no	—
170	#1568	—	11	1	no	—
171	#1567	—	11	1	no	—
172	#1564	—	11	1	no	—
173	#1564	D₁₁	1	1	yes	characteristic, complemented
174	C₂×#335	—	11	1	no	—
175	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	—	2	1	no	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	1	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	4	1	no	—
183	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
189	C₂²⋊D₁₁	—	2	2	no	—
190	C₂²⋊D₁₁	—	2	2	no	—
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	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
197	D₄₄	—	2	2	no	—
198	C₄×D₁₁	—	2	1	no	—
199	C₄×D₁₁	—	2	1	no	—
200	C₄×D₁₁	—	2	1	no	—
201	C₄×D₁₁	—	2	1	no	—
202	C₄×D₁₁	—	2	1	no	—
203	C₄×D₁₁	—	2	1	no	—
204	C₄×D₁₁	—	4	1	no	—
205	C₄×D₁₁	—	4	1	no	—
206	C₄×D₁₁	#135	1	2	yes	—
207	C₄×D₁₁	#135	1	2	yes	—
208	Dic₂₂	—	2	2	no	—
209	C₈×C₁₁	—	2	1	no	—
210	C₈×C₁₁	—	2	1	no	—
211	C₈×C₁₁	—	2	1	no	—
212	C₈×C₁₁	—	4	2	no	—
213	C₈×C₁₁	—	4	2	no	—
214	C₈×C₁₁	#131	1	2	yes	—
215	C₁₁⋊C₈	—	2	1	no	—
216	C₁₁⋊C₈	—	2	1	no	—
217	C₁₁⋊C₈	—	2	1	no	—
218	C₁₁⋊C₈	—	2	1	no	—
219	C₁₁⋊C₈	—	4	2	no	—
220	C₁₁⋊C₈	—	4	2	no	—
221	C₄×#41	—	11	1	no	—
222	C₈×Q₈	—	11	1	no	—
223	C₈×Q₈	—	11	1	no	—
224	C₈×D₄	—	11	1	no	—
225	C₈×D₄	—	11	1	no	—
226	C₈×D₄	—	11	1	no	—
227	C₈×D₄	—	11	1	no	—
228	C₈×D₄	—	11	1	no	—
229	C₈×D₄	—	11	1	no	—
230	#433	—	22	2	no	—
231	#433	—	22	2	no	—
232	#432	—	11	2	no	—
233	#432	—	11	2	no	—
234	#431	—	11	1	no	—
235	#431	—	11	1	no	—
236	#431	—	11	1	no	—
237	#431	—	11	2	no	—
238	#431	C₂×D₁₁	1	2	yes	—
239	#423	—	11	2	no	—
240	C₂×C₄⋊C₈	—	11	2	no	—
241	#408	—	22	2	no	—
242	#405	—	22	2	no	—
243	C₂×C₄×C₈	—	11	1	no	—
244	C₂×C₄×C₈	—	11	1	no	—
245	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
246	#335	—	11	2	no	—
247	#335	—	11	2	no	—
248	#335	—	11	1	no	—
249	#335	—	11	1	no	—
250	#335	C₂×D₁₁	1	1	yes	characteristic
251	#335	C₂×D₁₁	1	1	yes	characteristic
252	#334	—	11	2	no	—
253	#334	—	11	2	no	—
254	#334	—	11	2	no	—
255	#334	C₂×D₁₁	1	2	yes	—
256	C₂²×C₁₁	—	2	1	no	—
257	C₂²×C₁₁	—	2	1	no	—
258	C₂²×C₁₁	—	2	1	no	—
259	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
260	C₂×D₁₁	—	2	1	no	—
261	C₂×D₁₁	—	2	1	no	—
262	C₂×D₁₁	—	2	1	no	—
263	C₂×D₁₁	—	2	1	no	—
264	C₂×D₁₁	—	2	1	no	—
265	C₂×D₁₁	#427	1	2	yes	—
266	C₄×C₁₁	—	2	1	no	—
267	C₄×C₁₁	—	2	1	no	—
268	C₄×C₁₁	—	2	1	no	—
269	C₄×C₁₁	—	2	1	no	—
270	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
271	C₄×C₁₁	#568	1	1	yes	characteristic
272	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
273	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
274	Dic₁₁	—	2	1	no	—
275	Dic₁₁	—	2	1	no	—
276	Dic₁₁	—	2	1	no	—
277	Dic₁₁	—	2	1	no	—
278	Dic₁₁	—	2	1	no	—
279	Dic₁₁	#427	1	2	yes	—
280	C₂×#41	—	11	1	no	—
281	C₂×M₁₆	—	22	2	no	—
282	C₂²×C₈	—	11	1	no	—
283	C₂²×C₈	—	11	1	no	—
284	C₂²×C₈	—	11	1	no	—
285	C₂²×C₈	—	11	1	no	—
286	C₂²×C₈	—	22	2	no	—
287	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
288	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
289	C₄×Q₈	—	11	1	no	—
290	C₄×Q₈	—	11	1	no	—
291	C₄×D₄	—	11	1	no	—
292	C₄×D₄	—	11	1	no	—
293	C₄×D₄	—	11	1	no	—
294	C₄×D₄	—	11	1	no	—
295	C₄×D₄	—	11	1	no	—
296	C₄×D₄	—	11	1	no	—
297	#117	—	11	1	no	—
298	#117	—	11	1	no	—
299	#117	—	11	1	no	—
300	C₂×C₄²	—	11	1	no	—
301	C₂×C₄²	—	11	1	no	—
302	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
303	C₄⋊C₈	—	11	1	no	—
304	C₄⋊C₈	—	11	1	no	—
305	C₄⋊C₈	—	11	1	no	—
306	C₄⋊C₈	—	11	1	no	—
307	C₄⋊C₈	—	11	1	no	—
308	C₄⋊C₈	—	11	1	no	—
309	C₄⋊C₈	—	11	2	no	—
310	C₄⋊C₈	—	11	2	no	—
311	C₄⋊C₈	—	22	2	no	—
312	C₄⋊C₈	—	22	2	no	—
313	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
314	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	11	1	no	—
317	C₂²⋊C₈	—	11	1	no	—
318	C₂²⋊C₈	—	11	1	no	—
319	C₂²⋊C₈	—	11	1	no	—
320	C₂²⋊C₈	—	11	1	no	—
321	C₂²⋊C₈	—	11	1	no	—
322	C₂²⋊C₈	—	22	2	no	—
323	C₂²⋊C₈	—	22	2	no	—
324	C₂²⋊C₈	—	22	2	no	—
325	#97	—	22	2	no	—
326	#97	—	22	2	no	—
327	C₄×C₈	—	2	2	no	—
328	C₄×C₈	—	11	1	no	—
329	C₄×C₈	—	11	1	no	—
330	C₄×C₈	—	11	1	no	—
331	C₄×C₈	—	11	1	no	—
332	C₄×C₈	—	11	1	no	—
333	C₄×C₈	—	11	1	no	—
334	C₄×C₈	—	22	2	no	—
335	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
336	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
338	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
339	C₂×C₁₁	—	4	1	no	—
340	C₂×C₁₁	#2906	1	1	yes	characteristic
341	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
342	C₂×C₁₁	#2916	1	1	yes	characteristic
343	D₁₁	—	2	2	no	—
344	D₁₁	—	4	1	no	—
345	#41	—	22	2	no	—
346	#41	—	22	2	no	—
347	C₂×Q₈	—	11	1	no	—
348	C₂×D₄	—	11	1	no	—
349	C₂×D₄	—	11	1	no	—
350	C₂×D₄	—	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	C₂²×C₄	—	11	1	no	—
356	C₂²×C₄	—	11	1	no	—
357	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
358	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
359	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
360	M₁₆	—	44	4	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	11	1	no	—
366	C₂×C₈	—	11	1	no	—
367	C₂×C₈	—	11	1	no	—
368	C₂×C₈	—	11	1	no	—
369	C₂×C₈	—	22	2	no	—
370	C₂×C₈	—	22	2	no	—
371	C₂×C₈	—	22	2	no	—
372	C₂×C₈	—	22	2	no	—
373	C₂×C₈	—	44	1	no	—
374	C₂×C₈	—	44	1	no	—
375	C₂×C₈	—	44	4	no	—
376	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
377	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
378	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
379	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
380	C₄⋊C₄	—	11	1	no	—
381	C₄⋊C₄	—	11	1	no	—
382	C₄⋊C₄	—	11	1	no	—
383	C₄⋊C₄	—	11	1	no	—
384	C₄⋊C₄	—	11	1	no	—
385	C₄⋊C₄	—	11	1	no	—
386	C₂²⋊C₄	—	11	1	no	—
387	C₂²⋊C₄	—	11	1	no	—
388	C₂²⋊C₄	—	11	1	no	—
389	C₂²⋊C₄	—	11	1	no	—
390	C₂²⋊C₄	—	11	1	no	—
391	C₂²⋊C₄	—	11	1	no	—
392	C₄²	—	11	1	no	—
393	C₄²	—	11	1	no	—
394	C₄²	—	11	1	no	—
395	C₄²	—	11	1	no	—
396	C₄²	—	11	1	no	—
397	C₄²	—	11	1	no	—
398	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
399	C₄²	D₄×D₁₁	1	1	yes	characteristic
400	C₄²	Q₈×D₁₁	1	1	yes	characteristic
401	C₄²	C₂³×D₁₁	1	1	yes	characteristic
402	C₁₁	#17829	1	1	yes	characteristic, complemented, Sylow
403	C₂³	—	11	1	no	—
404	C₂³	—	11	1	no	—
405	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
406	Q₈	—	22	2	no	—
407	D₄	—	22	2	no	—
408	D₄	—	22	2	no	—
409	D₄	—	22	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	11	1	no	—
416	C₂×C₄	—	11	2	no	—
417	C₂×C₄	—	11	2	no	—
418	C₂×C₄	—	11	1	no	—
419	C₂×C₄	—	11	1	no	—
420	C₂×C₄	—	11	1	no	—
421	C₂×C₄	—	11	1	no	—
422	C₂×C₄	—	11	1	no	—
423	C₂×C₄	—	22	1	no	—
424	C₂×C₄	—	22	1	no	—
425	C₂×C₄	—	22	1	no	—
426	C₂×C₄	—	22	1	no	—
427	C₂×C₄	—	22	1	no	—
428	C₂×C₄	—	22	1	no	—
429	C₂×C₄	—	44	1	no	—
430	C₂×C₄	—	44	1	no	—
431	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
432	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
433	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
436	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	22	1	no	—
443	C₈	—	22	1	no	—
444	C₈	—	22	1	no	—
445	C₈	—	22	1	no	—
446	C₈	—	44	2	no	—
447	C₈	—	44	2	no	—
448	C₈	#66954	1	2	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	11	2	no	—
453	C₂²	—	22	1	no	—
454	C₂²	—	22	1	no	—
455	C₂²	—	22	1	no	—
456	C₂²	—	22	1	no	—
457	C₂²	—	22	1	no	—
458	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	11	2	no	—
464	C₄	—	22	1	no	—
465	C₄	—	22	1	no	—
466	C₄	—	22	1	no	—
467	C₄	—	22	1	no	—
468	C₄	—	22	1	no	—
469	C₄	C₂×#66954	1	1	yes	characteristic
470	C₄	#10623276	1	1	yes	characteristic
471	C₄	D₁₁×#135	1	1	yes	characteristic
472	C₄	D₁₁×#135	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	22	2	no	—
475	C₂	—	44	1	no	—
476	C₂	#13077181	1	1	yes	characteristic
477	C₂	D₁₁×#427	1	1	yes	characteristic
478	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×#1564	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂×#4339	D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1564	D₁₁
hypocenter	C₁₁	#17829
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
3. #13067394	C₂	semidirect
4. #13067393	C₂	semidirect
5. #13067385	C₂	semidirect
6. #13067379	C₂	semidirect
7. #13067378	C₂	semidirect
8. #13067373	C₂	semidirect
9. #13067363	C₂	semidirect
10. D₁₁×#335	C₂	semidirect
11. C₁₁×#1564	C₂	semidirect
173. #1564	D₁₁	semidirect
402. C₁₁	#17829	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
#13077277	2
#13067394	2
#13067393	2
#13067385	2
#13067379	2
#13067378	2
#13067373	2
#13067363	2
D₁₁×#335	2
C₁₁×#1564	2
#17829	11