Subgroups — #14723494

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077733	C₂	1	1	yes	maximal, characteristic, complemented
2	#13077727	C₂	1	1	yes	maximal, characteristic, complemented
3	#13067488	C₂	1	2	yes	maximal, complemented
4	#13067481	C₂	1	2	yes	maximal, complemented
5	#13067460	C₂	1	2	yes	maximal, complemented
6	#13067453	C₂	1	2	yes	maximal, complemented
7	C₂×#10622095	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067003	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067003	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066908	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₁×#135	C₄	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
15	C₄×C₁₁×Q₁₆	C₄	1	1	yes	characteristic
16	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
17	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
18	C₄×C₁₁×SD₁₆	C₄	1	1	yes	characteristic
19	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
21	C₄×C₁₁×D₈	C₄	1	1	yes	characteristic
22	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic
23	C₁₁×#427	C₄	1	1	yes	characteristic
24	C₁₁×#416	C₄	1	1	yes	characteristic
25	C₁₁×#416	C₄	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
27	#10622637	C₂²	1	2	yes	—
28	Q₈×C₁₁⋊C₈	C₂²	1	2	yes	—
29	#10622625	C₂²	1	2	yes	—
30	#10622624	—	2	2	no	—
31	D₄×C₁₁⋊C₈	—	2	2	no	—
32	D₄×C₁₁⋊C₈	C₂²	1	2	yes	—
33	#10622539	—	2	1	no	—
34	#10622538	—	2	1	no	—
35	#10622538	C₂²	1	1	yes	characteristic
36	#10622538	C₂²	1	1	yes	characteristic
37	#10622537	—	2	1	no	—
38	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
39	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
42	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
43	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
44	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
45	#10622095	C₂²	1	2	yes	—
46	#10622095	C₂²	1	2	yes	—
47	#10622092	C₂²	1	2	yes	—
48	#10622092	C₂²	1	2	yes	—
49	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
51	C₁₁×#135	—	2	4	no	—
52	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₄×D₄×C₁₁	—	2	1	no	—
64	C₄×D₄×C₁₁	—	2	1	no	—
65	C₄×D₄×C₁₁	—	2	1	no	—
66	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×#117	—	2	1	no	—
71	C₁₁×#117	—	2	1	no	—
72	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
73	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₁	—	2	1	no	—
75	C₂×C₄²×C₁₁	—	2	1	no	—
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₂×#4318	—	2	2	no	—
78	C₂²×C₁₁⋊C₈	—	2	1	no	—
79	C₂²×C₁₁⋊C₈	—	2	1	no	—
80	C₂²×C₁₁⋊C₈	—	2	2	no	—
81	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
82	C₁₁×#107	C₂×C₄	1	1	yes	characteristic
83	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
84	C₁₁×#106	C₂×C₄	1	1	yes	characteristic
85	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
86	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
87	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#103	C₂×C₄	1	1	yes	characteristic
89	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
90	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
91	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
92	C₁₁×#102	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
97	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
98	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
99	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
100	C₂²⋊(C₁₁⋊C₈)	D₄	1	2	yes	—
101	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
102	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
103	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
104	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
105	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
106	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
107	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
108	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
109	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
110	#66867	—	2	2	no	—
111	C₄×C₁₁⋊C₈	—	2	2	no	—
112	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
113	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
114	#17882	—	11	1	no	maximal, Sylow
115	C₁₁×#41	—	2	2	no	—
116	C₁₁×#41	—	2	2	no	—
117	C₁₁×#41	—	2	2	no	—
118	C₁₁×#41	M₁₆	1	4	yes	complemented
119	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×D₄×C₁₁	—	2	1	no	—
122	C₂×D₄×C₁₁	—	2	1	no	—
123	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	—	2	1	no	—
126	C₂²×C₄×C₁₁	—	2	1	no	—
127	C₂²×C₄×C₁₁	—	2	1	no	—
128	C₂²×C₄×C₁₁	—	2	1	no	—
129	C₂²×C₄×C₁₁	—	2	1	no	—
130	C₂²×C₄×C₁₁	—	2	1	no	—
131	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
134	C₁₁×Q₁₆	—	2	2	no	—
135	C₁₁×SD₁₆	—	2	2	no	—
136	C₁₁×SD₁₆	—	2	2	no	—
137	C₁₁×D₈	—	2	2	no	—
138	C₂×C₈×C₁₁	—	2	2	no	—
139	C₂×C₈×C₁₁	—	2	2	no	—
140	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
144	C₁₁×C₄⋊C₄	—	2	1	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	—	2	1	no	—
147	C₁₁×C₄⋊C₄	—	2	1	no	—
148	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
149	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
150	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
151	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₁×C₂²⋊C₄	—	2	1	no	—
153	C₁₁×C₂²⋊C₄	—	2	1	no	—
154	C₁₁×C₂²⋊C₄	—	2	1	no	—
155	C₁₁×C₂²⋊C₄	—	2	1	no	—
156	C₁₁×C₂²⋊C₄	—	2	1	no	—
157	C₁₁×C₂²⋊C₄	—	2	1	no	—
158	C₄²×C₁₁	—	2	1	no	—
159	C₄²×C₁₁	—	2	1	no	—
160	C₄²×C₁₁	—	2	1	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	—	2	1	no	—
163	C₄²×C₁₁	—	2	1	no	—
164	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₁	#41	1	1	yes	characteristic
167	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
168	#4318	—	8	2	no	—
169	C₂×C₁₁⋊C₈	—	2	2	no	—
170	C₂×C₁₁⋊C₈	—	2	2	no	—
171	C₂×C₁₁⋊C₈	—	2	2	no	—
172	C₂×C₁₁⋊C₈	—	8	1	no	—
173	C₂×C₁₁⋊C₈	—	8	1	no	—
174	C₂×C₁₁⋊C₈	—	8	2	no	—
175	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
176	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
177	#2989	—	11	1	no	—
178	#2988	—	11	1	no	—
179	C₄×#135	D₁₁	1	1	yes	characteristic
180	#1587	—	11	2	no	—
181	#1586	—	11	2	no	—
182	#1583	—	11	2	no	—
183	#1582	—	11	2	no	—
184	C₂×#334	—	11	1	no	—
185	#1477	—	11	1	no	—
186	#1477	—	11	1	no	—
187	#1452	—	11	1	no	—
188	C₂³×C₁₁	—	2	1	no	—
189	C₂³×C₁₁	—	2	1	no	—
190	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
191	Q₈×C₁₁	—	2	1	no	—
192	Q₈×C₁₁	—	2	1	no	—
193	Q₈×C₁₁	—	2	1	no	—
194	Q₈×C₁₁	C₂×M₁₆	1	2	yes	—
195	D₄×C₁₁	—	2	4	no	—
196	D₄×C₁₁	—	2	1	no	—
197	D₄×C₁₁	—	2	1	no	—
198	D₄×C₁₁	—	2	1	no	—
199	D₄×C₁₁	—	4	2	no	—
200	D₄×C₁₁	C₂×M₁₆	1	2	yes	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	1	no	—
203	C₂×C₄×C₁₁	—	2	1	no	—
204	C₂×C₄×C₁₁	—	2	4	no	—
205	C₂×C₄×C₁₁	—	2	1	no	—
206	C₂×C₄×C₁₁	—	2	1	no	—
207	C₂×C₄×C₁₁	—	2	1	no	—
208	C₂×C₄×C₁₁	—	2	1	no	—
209	C₂×C₄×C₁₁	—	2	1	no	—
210	C₂×C₄×C₁₁	—	4	1	no	—
211	C₂×C₄×C₁₁	—	4	1	no	—
212	C₂×C₄×C₁₁	—	4	1	no	—
213	C₂×C₄×C₁₁	—	4	1	no	—
214	C₂×C₄×C₁₁	—	4	1	no	—
215	C₂×C₄×C₁₁	—	4	2	no	—
216	C₂×C₄×C₁₁	—	8	1	no	—
217	C₂×C₄×C₁₁	—	8	1	no	—
218	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
222	C₂×C₄×C₁₁	#131	1	2	yes	—
223	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
226	C₈×C₁₁	—	2	1	no	—
227	C₈×C₁₁	—	2	1	no	—
228	C₈×C₁₁	—	2	1	no	—
229	C₈×C₁₁	—	2	1	no	—
230	C₁₁⋊C₈	—	2	2	no	—
231	C₁₁⋊C₈	—	2	2	no	—
232	C₁₁⋊C₈	—	4	2	no	—
233	C₁₁⋊C₈	—	4	2	no	—
234	C₁₁⋊C₈	—	4	2	no	—
235	C₂×#135	Dic₁₁	1	1	yes	characteristic
236	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
237	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
238	#446	—	11	2	no	—
239	C₈×Q₈	—	11	2	no	—
240	C₄×Q₁₆	Dic₁₁	1	1	yes	characteristic
241	C₄×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
242	C₄×SD₁₆	Dic₁₁	1	1	yes	characteristic
243	C₄×SD₁₆	Dic₁₁	1	1	yes	characteristic
244	C₄×SD₁₆	C₂×D₁₁	1	1	yes	characteristic
245	C₄×SD₁₆	C₂×D₁₁	1	1	yes	characteristic
246	C₄×D₈	Dic₁₁	1	1	yes	characteristic
247	C₄×D₈	C₂×D₁₁	1	1	yes	characteristic
248	#436	—	11	2	no	—
249	#435	—	22	2	no	—
250	C₈×D₄	—	11	2	no	—
251	C₈×D₄	—	22	2	no	—
252	#432	—	22	1	no	—
253	#431	—	11	1	no	—
254	#431	—	11	1	no	—
255	#431	—	22	1	no	—
256	#427	Dic₁₁	1	1	yes	characteristic
257	#423	—	22	1	no	—
258	C₂×C₄⋊C₈	—	11	1	no	—
259	C₂×C₄⋊C₈	—	11	1	no	—
260	C₂×C₄⋊C₈	—	22	1	no	—
261	#416	Dic₁₁	1	1	yes	characteristic
262	#416	Dic₁₁	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
264	#334	—	11	2	no	—
265	#334	—	11	2	no	—
266	Q₈⋊C₈	—	11	2	no	—
267	Q₈⋊C₈	—	11	2	no	—
268	D₄⋊C₈	—	11	2	no	—
269	D₄⋊C₈	—	11	2	no	—
270	#322	—	11	2	no	—
271	#322	—	11	2	no	—
272	C₂²×C₁₁	—	2	1	no	—
273	C₂²×C₁₁	—	2	1	no	—
274	C₂²×C₁₁	—	2	2	no	—
275	C₂²×C₁₁	—	4	1	no	—
276	C₂²×C₁₁	—	4	1	no	—
277	C₂²×C₁₁	—	4	1	no	—
278	C₂²×C₁₁	—	4	1	no	—
279	C₂²×C₁₁	—	4	1	no	—
280	C₂²×C₁₁	#435	1	2	yes	—
281	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
282	C₄×C₁₁	—	2	2	no	—
283	C₄×C₁₁	—	2	1	no	—
284	C₄×C₁₁	—	2	1	no	—
285	C₄×C₁₁	—	2	1	no	—
286	C₄×C₁₁	—	4	1	no	—
287	C₄×C₁₁	—	4	1	no	—
288	C₄×C₁₁	—	4	1	no	—
289	C₄×C₁₁	—	4	1	no	—
290	C₄×C₁₁	—	4	1	no	—
291	C₄×C₁₁	#435	1	2	yes	—
292	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
293	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
294	C₄×C₁₁	#577	1	1	yes	characteristic
295	C₄×C₁₁	#577	1	1	yes	characteristic
296	C₂×#41	C₂×Dic₁₁	1	1	yes	characteristic
297	C₂×#41	C₂×Dic₁₁	1	1	yes	characteristic
298	#135	—	2	4	no	—
299	C₂×Q₁₆	C₂×Dic₁₁	1	1	yes	characteristic
300	C₂×SD₁₆	C₂×Dic₁₁	1	1	yes	characteristic
301	C₂×SD₁₆	C₂×Dic₁₁	1	1	yes	characteristic
302	C₂×D₈	C₂×Dic₁₁	1	1	yes	characteristic
303	C₂×M₁₆	—	22	2	no	—
304	C₂²×C₈	—	22	2	no	—
305	C₂²×C₈	—	22	1	no	—
306	C₂²×C₈	—	22	1	no	—
307	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
308	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
309	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
310	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
311	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
312	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
318	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
319	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
320	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
321	#117	—	2	1	no	—
322	#117	—	2	1	no	—
323	#117	C₂×Dic₁₁	1	1	yes	characteristic
324	#117	C₂×Dic₁₁	1	1	yes	characteristic
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
328	#107	C₂×Dic₁₁	1	1	yes	characteristic
329	#107	C₂×Dic₁₁	1	1	yes	characteristic
330	#106	C₂×Dic₁₁	1	1	yes	characteristic
331	#106	C₂×Dic₁₁	1	1	yes	characteristic
332	C₄⋊C₈	—	11	1	no	—
333	C₄⋊C₈	—	11	1	no	—
334	C₄⋊C₈	—	11	2	no	—
335	C₄⋊C₈	—	11	2	no	—
336	C₄⋊C₈	—	22	2	no	—
337	C₄⋊C₈	—	22	2	no	—
338	C₄⋊C₈	—	22	1	no	—
339	C₄⋊C₈	—	22	1	no	—
340	C₄⋊C₈	—	22	1	no	—
341	#103	C₂×Dic₁₁	1	1	yes	characteristic
342	#103	C₂×Dic₁₁	1	1	yes	characteristic
343	#103	C₂×Dic₁₁	1	1	yes	characteristic
344	#103	C₂×Dic₁₁	1	1	yes	characteristic
345	#102	C₂×Dic₁₁	1	1	yes	characteristic
346	#102	C₂×Dic₁₁	1	1	yes	characteristic
347	#102	C₂×Dic₁₁	1	1	yes	characteristic
348	#102	C₂×Dic₁₁	1	1	yes	characteristic
349	C₂²⋊C₈	—	11	2	no	—
350	C₂²⋊C₈	—	22	2	no	—
351	C₂²⋊C₈	—	22	2	no	—
352	C₂²⋊C₈	—	22	1	no	—
353	#97	—	22	2	no	—
354	C₄×C₈	—	11	2	no	—
355	C₄×C₈	—	11	2	no	—
356	C₄×C₈	—	22	2	no	—
357	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
358	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
360	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
361	C₂×C₁₁	—	2	2	no	—
362	C₂×C₁₁	—	4	2	no	—
363	C₂×C₁₁	—	8	1	no	—
364	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
365	C₂×C₁₁	#2952	1	1	yes	characteristic
366	C₂×C₁₁	#2957	1	1	yes	characteristic
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	2	2	no	—
370	#41	#4318	1	4	yes	complemented
371	C₂×Q₈	C₂²×Dic₁₁	1	1	yes	characteristic
372	C₂×Q₈	C₂²×Dic₁₁	1	1	yes	characteristic
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	C₂²×Dic₁₁	1	1	yes	characteristic
376	C₂×D₄	C₂²×Dic₁₁	1	1	yes	characteristic
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
384	C₂²×C₄	#4341	1	1	yes	characteristic
385	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
386	Q₁₆	—	2	2	no	—
387	SD₁₆	—	2	2	no	—
388	SD₁₆	—	2	2	no	—
389	D₈	—	2	2	no	—
390	M₁₆	—	88	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	11	2	no	—
394	C₂×C₈	—	11	2	no	—
395	C₂×C₈	—	22	2	no	—
396	C₂×C₈	—	22	2	no	—
397	C₂×C₈	—	22	2	no	—
398	C₂×C₈	—	88	2	no	—
399	C₂×C₈	—	88	1	no	—
400	C₂×C₈	—	88	1	no	—
401	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
402	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
403	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
404	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
410	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
411	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
412	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	D₄×D₁₁	1	1	yes	characteristic
426	C₄²	#4341	1	1	yes	characteristic
427	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
428	C₄²	C₂³×D₁₁	1	1	yes	characteristic
429	C₁₁	#17882	1	1	yes	characteristic, complemented, Sylow
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
433	Q₈	—	2	1	no	—
434	Q₈	—	2	1	no	—
435	Q₈	—	2	1	no	—
436	Q₈	C₂×#4318	1	2	yes	—
437	D₄	—	2	4	no	—
438	D₄	—	2	1	no	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	4	2	no	—
442	D₄	C₂×#4318	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	8	1	no	—
459	C₂×C₄	—	8	1	no	—
460	C₂×C₄	C₂×#4318	1	2	yes	—
461	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
462	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
463	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
464	C₂×C₄	#67001	1	2	yes	—
465	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#4341	1	1	yes	characteristic
467	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	22	2	no	—
473	C₈	—	22	2	no	—
474	C₈	—	44	2	no	—
475	C₈	—	44	2	no	—
476	C₈	—	44	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	#10622624	1	2	yes	—
486	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	#10622624	1	2	yes	—
497	C₄	#10623301	1	1	yes	characteristic
498	C₄	#10623301	1	1	yes	characteristic
499	C₄	C₂²×#4318	1	1	yes	characteristic
500	C₄	C₂×#67001	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	4	2	no	—
503	C₂	—	8	1	no	—
504	C₂	C₂×#10622624	1	1	yes	characteristic
505	C₂	#13077500	1	1	yes	characteristic
506	C₂	#13077533	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₄×C₁₁×#135	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#135	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₄×#135	D₁₁
hypocenter	C₁₁	#17882
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #13077733	C₂	semidirect
2. #13077727	C₂	semidirect
3. #13067488	C₂	semidirect
4. #13067481	C₂	semidirect
5. #13067460	C₂	semidirect
6. #13067453	C₂	semidirect
7. C₂×#10622095	C₂	semidirect
8. #13067003	C₂	semidirect
9. #13067003	C₂	semidirect
10. #13066908	C₂	semidirect
118. C₁₁×#41	M₁₆	semidirect
370. #41	#4318	semidirect
429. C₁₁	#17882	semidirect

Maximal subgroups

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

subgroup	index
#13077733	2
#13077727	2
#13067488	2
#13067481	2
#13067460	2
#13067453	2
C₂×#10622095	2
#13067003	2
#13066908	2
C₄×C₁₁×#135	2
#17882	11