Subgroups — #29587920

Order 15616.

958 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839660	C₂	1	1	yes	maximal, characteristic
2	C₂×#16839524	C₂	1	2	yes	maximal
3	C₂×#16839524	C₂	1	2	yes	maximal
4	C₂×#16839517	C₂	1	1	yes	maximal, characteristic
5	C₂×C₆₁×#384	C₂	1	1	yes	maximal, characteristic
6	C₂³×#92418	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
9	C₂²×#11758196	—	2	1	no	—
10	#16839660	—	2	2	no	—
11	#16839660	C₄	1	4	yes	complemented
12	C₂×#14519684	—	2	1	no	—
13	#16839524	—	2	4	no	—
14	#16839524	—	2	4	no	—
15	#16839517	—	2	2	no	—
16	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#384	—	2	4	no	—
21	C₂³×Dic₆₁	—	2	1	no	—
22	C₂³×Dic₆₁	—	2	1	no	—
23	C₂²×#92418	—	2	2	no	—
24	C₂²×#92418	—	2	2	no	—
25	C₂²×#92418	—	2	2	no	—
26	C₂²×#92418	—	2	2	no	—
27	C₂²×#92418	—	2	2	no	—
28	C₂²×#92418	—	2	2	no	—
29	C₂²×#92418	Q₈	1	4	yes	—
30	C₂×C₄⋊Dic₆₁	—	2	1	no	—
31	C₂×C₄⋊Dic₆₁	—	2	1	no	—
32	C₂×C₄⋊Dic₆₁	—	2	1	no	—
33	C₂×C₄⋊Dic₆₁	—	2	2	no	—
34	C₂×C₄⋊Dic₆₁	—	2	2	no	—
35	C₂×C₄⋊Dic₆₁	—	2	1	no	—
36	C₂×C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
37	C₂×C₄⋊Dic₆₁	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊Dic₆₁	D₄	1	2	yes	—
39	C₂×C₄⋊Dic₆₁	Q₈	1	2	yes	—
40	C₂×#11758196	—	2	4	no	—
41	C₂×#11758196	—	4	2	no	—
42	C₂×#11758196	—	4	2	no	—
43	#14519684	—	2	4	no	—
44	C₂³×C₄×C₆₁	—	2	2	no	—
45	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
56	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
57	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
58	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
59	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
60	C₂×C₄²×C₆₁	—	2	2	no	—
61	C₂×C₄²×C₆₁	—	2	2	no	—
62	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₆₁	D₄	1	2	yes	—
64	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₆₁	—	2	1	no	—
66	C₂²×C₄×C₆₁	—	2	1	no	—
67	C₂²×C₄×C₆₁	—	2	1	no	—
68	C₂²×C₄×C₆₁	—	2	1	no	—
69	C₂²×C₄×C₆₁	—	2	1	no	—
70	C₂²×C₄×C₆₁	—	2	1	no	—
71	C₂²×C₄×C₆₁	—	2	1	no	—
72	C₂²×C₄×C₆₁	—	2	1	no	—
73	C₂²×C₄×C₆₁	—	2	4	no	—
74	C₂²×C₄×C₆₁	—	4	2	no	—
75	C₂²×C₄×C₆₁	—	4	2	no	—
76	C₂²×C₄×C₆₁	—	4	2	no	—
77	C₂²×C₄×C₆₁	—	4	2	no	—
78	C₂²×C₄×C₆₁	—	4	2	no	—
79	C₂²×C₄×C₆₁	—	4	2	no	—
80	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
82	C₂²×C₄×C₆₁	D₈	1	2	yes	—
83	C₂²×C₄×C₆₁	SD₁₆	1	2	yes	—
84	C₂²×C₄×C₆₁	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₆₁	Q₁₆	1	2	yes	—
86	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	#41	1	2	yes	—
95	C₂²×C₄×C₆₁	#41	1	2	yes	—
96	C₂²×Dic₆₁	—	2	2	no	—
97	C₂²×Dic₆₁	—	2	2	no	—
98	C₂²×Dic₆₁	—	2	2	no	—
99	C₂²×Dic₆₁	—	2	2	no	—
100	C₂²×Dic₆₁	—	4	1	no	—
101	C₂²×Dic₆₁	—	4	1	no	—
102	C₂²×Dic₆₁	—	4	1	no	—
103	C₂²×Dic₆₁	—	4	1	no	—
104	C₂²×Dic₆₁	—	4	1	no	—
105	C₂²×Dic₆₁	—	4	1	no	—
106	C₂²×Dic₆₁	—	4	1	no	—
107	C₂²×Dic₆₁	—	4	1	no	—
108	C₂²×Dic₆₁	—	4	1	no	—
109	C₂²×Dic₆₁	—	4	1	no	—
110	C₄⋊C₄×C₆₁	—	2	4	no	—
111	C₄⋊C₄×C₆₁	—	2	4	no	—
112	C₄⋊C₄×C₆₁	—	4	8	no	—
113	C₄⋊C₄×C₆₁	—	4	8	no	—
114	C₄⋊C₄×C₆₁	—	4	2	no	—
115	C₄⋊C₄×C₆₁	—	4	2	no	—
116	C₄²×C₆₁	—	2	4	no	—
117	C₄²×C₆₁	—	2	4	no	—
118	C₄⋊Dic₆₁	—	2	2	no	—
119	C₄⋊Dic₆₁	—	2	2	no	—
120	C₄⋊Dic₆₁	—	2	2	no	—
121	C₄⋊Dic₆₁	—	2	4	no	—
122	C₄⋊Dic₆₁	—	4	2	no	—
123	C₄⋊Dic₆₁	C₄⋊C₄	1	4	yes	complemented
124	#11758196	—	4	8	no	—
125	C₂×#92418	—	2	4	no	—
126	C₂×#92418	—	2	4	no	—
127	C₂×#92418	—	2	4	no	—
128	C₂×#92418	—	4	2	no	—
129	C₂×#92418	—	4	2	no	—
130	C₂×#92418	—	4	2	no	—
131	C₂×#92418	—	4	2	no	—
132	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₆₁	#120	1	1	yes	characteristic
134	C₂³×C₆₁	#121	1	1	yes	characteristic
135	C₂³×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
136	C₂³×C₆₁	#123	1	1	yes	characteristic
137	C₂³×C₆₁	#124	1	1	yes	characteristic
138	C₂³×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
139	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
140	C₂³×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
141	C₂³×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
142	C₂³×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
143	C₂³×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂³×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂³×C₆₁	#137	1	1	yes	characteristic
146	C₂³×C₆₁	#137	1	1	yes	characteristic
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	2	no	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	2	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	2	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	4	4	no	—
160	C₂×C₄×C₆₁	—	4	4	no	—
161	C₂×C₄×C₆₁	—	4	4	no	—
162	C₂×C₄×C₆₁	—	8	2	no	—
163	C₂×C₄×C₆₁	—	8	2	no	—
164	C₂×C₄×C₆₁	—	8	2	no	—
165	C₂×C₄×C₆₁	—	8	2	no	—
166	C₂×C₄×C₆₁	#102	1	4	yes	—
167	C₂×C₄×C₆₁	#103	1	4	yes	—
168	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
170	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
172	C₂×C₄×C₆₁	#121	1	2	yes	—
173	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
174	C₂×C₄×C₆₁	#121	1	2	yes	—
175	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₆₁	#123	1	2	yes	—
180	C₂×C₄×C₆₁	#125	1	2	yes	—
181	C₂×C₄×C₆₁	#125	1	2	yes	—
182	C₂×C₄×C₆₁	#126	1	2	yes	—
183	C₂×C₄×C₆₁	C₄⋊Q₈	1	2	yes	—
184	C₂×Dic₆₁	—	2	4	no	—
185	C₂×Dic₆₁	—	4	2	no	—
186	C₂×Dic₆₁	—	4	2	no	—
187	C₂×Dic₆₁	—	4	2	no	—
188	C₂×Dic₆₁	—	4	2	no	—
189	C₂×Dic₆₁	—	4	2	no	—
190	C₂×Dic₆₁	—	4	2	no	—
191	C₂×Dic₆₁	—	4	2	no	—
192	C₂×Dic₆₁	—	4	2	no	—
193	C₂×Dic₆₁	—	4	2	no	—
194	C₂×Dic₆₁	—	8	1	no	—
195	C₂×Dic₆₁	—	8	1	no	—
196	C₂×Dic₆₁	—	8	1	no	—
197	C₂×Dic₆₁	—	8	1	no	—
198	#92418	—	4	4	no	—
199	#11207	—	61	1	no	maximal, Sylow
200	C₂²×C₆₁	#380	1	1	yes	characteristic
201	C₂²×C₆₁	#386	1	1	yes	characteristic
202	C₂²×C₆₁	#391	1	1	yes	characteristic
203	C₂²×C₆₁	#394	1	1	yes	characteristic
204	C₂²×C₆₁	#395	1	1	yes	characteristic
205	C₂²×C₆₁	#398	1	1	yes	characteristic
206	C₂²×C₆₁	#400	1	1	yes	characteristic
207	C₂²×C₆₁	C₂×#102	1	1	yes	characteristic
208	C₂²×C₆₁	C₂×#103	1	1	yes	characteristic
209	C₂²×C₆₁	#417	1	1	yes	characteristic
210	C₂²×C₆₁	#417	1	1	yes	characteristic
211	C₂²×C₆₁	#447	1	1	yes	characteristic
212	C₂²×C₆₁	#448	1	1	yes	characteristic
213	C₂²×C₆₁	#450	1	1	yes	characteristic
214	C₂²×C₆₁	#451	1	1	yes	characteristic
215	C₂²×C₆₁	#459	1	1	yes	characteristic
216	C₂²×C₆₁	#460	1	1	yes	characteristic
217	C₂²×C₆₁	#461	1	1	yes	characteristic
218	C₂²×C₆₁	#462	1	1	yes	characteristic
219	C₂²×C₆₁	#474	1	1	yes	characteristic
220	C₂²×C₆₁	#475	1	1	yes	characteristic
221	C₂²×C₆₁	#476	1	1	yes	characteristic
222	C₂²×C₆₁	#477	1	1	yes	characteristic
223	C₂²×C₆₁	#480	1	1	yes	characteristic
224	C₂²×C₆₁	#481	1	1	yes	characteristic
225	C₂²×C₆₁	#483	1	1	yes	characteristic
226	C₂²×C₆₁	#484	1	1	yes	characteristic
227	C₂²×C₆₁	#486	1	1	yes	characteristic
228	C₂²×C₆₁	#487	1	1	yes	characteristic
229	C₂²×C₆₁	#490	1	1	yes	characteristic
230	C₂²×C₆₁	#491	1	1	yes	characteristic
231	C₂²×C₆₁	#498	1	1	yes	characteristic
232	C₂²×C₆₁	#500	1	1	yes	characteristic
233	C₂²×C₆₁	#501	1	1	yes	characteristic
234	C₂²×C₆₁	#501	1	1	yes	characteristic
235	C₄×C₆₁	—	2	4	no	—
236	C₄×C₆₁	—	2	4	no	—
237	C₄×C₆₁	—	8	4	no	—
238	C₄×C₆₁	#387	1	2	yes	—
239	C₄×C₆₁	#389	1	2	yes	—
240	C₄×C₆₁	#396	1	2	yes	—
241	C₄×C₆₁	#398	1	2	yes	—
242	Dic₆₁	—	4	4	no	—
243	Dic₆₁	—	8	2	no	—
244	C₂×#389	—	61	1	no	—
245	C₂×#384	D₆₁	1	1	yes	characteristic
246	C₂×#340	—	61	2	no	—
247	C₂×#340	—	61	2	no	—
248	C₂×#336	—	61	1	no	—
249	C₂×C₆₁	#1441	1	1	yes	characteristic
250	C₂×C₆₁	#1802	1	1	yes	characteristic
251	C₂×C₆₁	#1803	1	1	yes	characteristic
252	C₂×C₆₁	#1872	1	1	yes	characteristic
253	C₂×C₆₁	#1874	1	1	yes	characteristic
254	C₂×C₆₁	#1990	1	1	yes	characteristic
255	C₂×C₆₁	#1992	1	1	yes	characteristic
256	C₂×C₆₁	#2041	1	1	yes	characteristic
257	C₂×C₆₁	#2043	1	1	yes	characteristic
258	C₂×C₆₁	#2057	1	1	yes	characteristic
259	C₂×C₆₁	#2058	1	1	yes	characteristic
260	C₂×C₆₁	#2083	1	1	yes	characteristic
261	C₂×C₆₁	#2084	1	1	yes	characteristic
262	C₂×C₆₁	#2099	1	1	yes	characteristic
263	C₂×C₆₁	#2100	1	1	yes	characteristic
264	C₂³×C₈	—	61	2	no	—
265	C₂²×C₄⋊C₄	—	2	1	no	—
266	C₂²×C₄⋊C₄	—	2	1	no	—
267	C₂²×C₄⋊C₄	—	61	1	no	—
268	C₂²×C₄⋊C₄	—	61	1	no	—
269	C₂²×C₄⋊C₄	—	122	1	no	—
270	C₂²×C₄⋊C₄	C₂×D₆₁	1	2	yes	—
271	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
272	#389	—	61	4	no	—
273	#389	—	122	2	no	—
274	#384	—	2	4	no	—
275	C₂×#95	—	122	1	no	—
276	#340	—	122	4	no	—
277	#340	—	122	4	no	—
278	#336	—	122	2	no	—
279	C₆₁	#11207	1	1	yes	characteristic, complemented, Sylow
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	—	122	1	no	—
282	C₂³×C₄	—	122	1	no	—
283	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
284	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
285	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
286	C₂²×C₈	—	61	4	no	—
287	C₂²×C₈	—	122	2	no	—
288	C₂²×C₈	—	122	2	no	—
289	C₂²×C₈	—	122	2	no	—
290	C₂²×C₈	—	122	2	no	—
291	C₂²×C₈	—	122	2	no	—
292	C₂²×C₈	—	122	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	4	2	no	—
301	C₂×C₄⋊C₄	—	4	2	no	—
302	C₂×C₄⋊C₄	—	4	2	no	—
303	C₂×C₄⋊C₄	—	4	2	no	—
304	C₂×C₄⋊C₄	—	61	2	no	—
305	C₂×C₄⋊C₄	—	61	2	no	—
306	C₂×C₄⋊C₄	—	61	2	no	—
307	C₂×C₄⋊C₄	—	61	2	no	—
308	C₂×C₄⋊C₄	—	122	1	no	—
309	C₂×C₄⋊C₄	—	122	1	no	—
310	C₂×C₄⋊C₄	—	122	1	no	—
311	C₂×C₄⋊C₄	—	122	2	no	—
312	C₂×C₄⋊C₄	—	122	2	no	—
313	C₂×C₄⋊C₄	—	122	4	no	—
314	C₂×C₄⋊C₄	—	122	1	no	—
315	C₂×C₄⋊C₄	—	244	2	no	—
316	C₂×C₄⋊C₄	—	244	2	no	—
317	C₂×C₄⋊C₄	C₂²⋊D₆₁	1	4	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	C₄×D₆₁	1	2	yes	—
321	C₂×C₄²	D₂₄₄	1	2	yes	—
322	#95	—	122	4	no	—
323	C₂⁴	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	122	2	no	—
340	C₂²×C₄	—	122	2	no	—
341	C₂²×C₄	—	122	2	no	—
342	C₂²×C₄	—	122	2	no	—
343	C₂²×C₄	—	244	1	no	—
344	C₂²×C₄	—	244	1	no	—
345	C₂²×C₄	—	244	1	no	—
346	C₂²×C₄	—	244	1	no	—
347	C₂²×C₄	—	244	1	no	—
348	C₂²×C₄	—	244	1	no	—
349	C₂²×C₄	—	244	1	no	—
350	C₂²×C₄	—	244	1	no	—
351	C₂²×C₄	—	244	1	no	—
352	C₂²×C₄	—	244	1	no	—
353	C₂²×C₄	#11758198	1	2	yes	—
354	C₂²×C₄	#11758198	1	2	yes	—
355	C₂²×C₄	#11758199	1	2	yes	—
356	C₂²×C₄	#11758200	1	2	yes	—
357	C₂²×C₄	#11758201	1	2	yes	—
358	C₂²×C₄	#11758202	1	2	yes	—
359	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
361	C₂²×C₄	#11758222	1	2	yes	—
362	C₂²×C₄	D₄×D₆₁	1	1	yes	characteristic
363	C₂²×C₄	#11758224	1	1	yes	characteristic
364	C₂²×C₄	#11758224	1	2	yes	—
365	C₂²×C₄	Q₈×D₆₁	1	1	yes	characteristic
366	C₂²×C₄	Q₈×D₆₁	1	2	yes	—
367	C₂²×C₄	#11758226	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₂²⋊D₆₁	1	2	yes	—
369	C₂×C₈	—	122	4	no	—
370	C₂×C₈	—	122	4	no	—
371	C₂×C₈	—	122	4	no	—
372	C₂×C₈	—	244	2	no	—
373	C₂×C₈	—	244	2	no	—
374	C₂×C₈	—	244	2	no	—
375	C₂×C₈	—	244	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	4	8	no	—
379	C₄⋊C₄	—	4	8	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	61	4	no	—
383	C₄⋊C₄	—	122	2	no	—
384	C₄⋊C₄	—	122	2	no	—
385	C₄⋊C₄	—	122	2	no	—
386	C₄⋊C₄	—	122	4	no	—
387	C₄⋊C₄	—	244	8	no	—
388	C₄⋊C₄	—	244	2	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	4	no	—
391	C₂³	C₂×#11758198	1	1	yes	characteristic
392	C₂³	#14519746	1	1	yes	characteristic
393	C₂³	#14519748	1	1	yes	characteristic
394	C₂³	#14519753	1	1	yes	characteristic
395	C₂³	#14519760	1	1	yes	characteristic
396	C₂³	#14519764	1	1	yes	characteristic
397	C₂³	#14519775	1	1	yes	characteristic
398	C₂³	C₂×#11758199	1	1	yes	characteristic
399	C₂³	C₂×#11758201	1	1	yes	characteristic
400	C₂³	C₂×#11758200	1	1	yes	characteristic
401	C₂³	C₂×#11758202	1	1	yes	characteristic
402	C₂³	#14519803	1	1	yes	characteristic
403	C₂³	#14519803	1	1	yes	characteristic
404	C₂³	#14519808	1	1	yes	characteristic
405	C₂³	#14519808	1	1	yes	characteristic
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	8	2	no	—
422	C₂×C₄	—	8	2	no	—
423	C₂×C₄	—	8	2	no	—
424	C₂×C₄	—	8	2	no	—
425	C₂×C₄	—	122	4	no	—
426	C₂×C₄	—	488	1	no	—
427	C₂×C₄	—	488	1	no	—
428	C₂×C₄	—	488	1	no	—
429	C₂×C₄	—	488	1	no	—
430	C₂×C₄	—	244	2	no	—
431	C₂×C₄	—	244	2	no	—
432	C₂×C₄	—	244	2	no	—
433	C₂×C₄	—	244	2	no	—
434	C₂×C₄	—	244	2	no	—
435	C₂×C₄	—	244	2	no	—
436	C₂×C₄	—	244	2	no	—
437	C₂×C₄	—	244	2	no	—
438	C₂×C₄	—	244	2	no	—
439	C₂×C₄	#14519697	1	4	yes	—
440	C₂×C₄	#14519700	1	4	yes	—
441	C₂×C₄	C₄⋊C₄×D₆₁	1	1	yes	characteristic
442	C₂×C₄	#14519735	1	1	yes	characteristic
443	C₂×C₄	C₄×C₂²⋊D₆₁	1	2	yes	—
444	C₂×C₄	#14519742	1	2	yes	—
445	C₂×C₄	#14519749	1	2	yes	—
446	C₂×C₄	#14519751	1	2	yes	—
447	C₂×C₄	#14519752	1	1	yes	characteristic
448	C₂×C₄	#14519753	1	2	yes	—
449	C₂×C₄	#14519755	1	2	yes	—
450	C₂×C₄	#14519757	1	2	yes	—
451	C₂×C₄	#14519757	1	1	yes	characteristic
452	C₂×C₄	#14519758	1	2	yes	—
453	C₂×C₄	#14519767	1	2	yes	—
454	C₂×C₄	#14519767	1	2	yes	—
455	C₂×C₄	#14519772	1	2	yes	—
456	C₂×C₄	#14519775	1	2	yes	—
457	C₈	—	244	4	no	—
458	C₂²	#16839619	1	1	yes	characteristic
459	C₂²	#16839641	1	1	yes	characteristic
460	C₂²	#16839667	1	1	yes	characteristic
461	C₂²	#16839676	1	1	yes	characteristic
462	C₂²	#16839681	1	1	yes	characteristic
463	C₂²	#16839693	1	1	yes	characteristic
464	C₂²	#16839700	1	1	yes	characteristic
465	C₂²	C₂×#14519697	1	1	yes	characteristic
466	C₂²	C₂×#14519700	1	1	yes	characteristic
467	C₂²	#16839761	1	1	yes	characteristic
468	C₂²	#16839761	1	1	yes	characteristic
469	C₂²	#16839896	1	1	yes	characteristic
470	C₂²	#16839901	1	1	yes	characteristic
471	C₂²	#16839913	1	1	yes	characteristic
472	C₂²	#16839918	1	1	yes	characteristic
473	C₂²	#16839954	1	1	yes	characteristic
474	C₂²	#16839959	1	1	yes	characteristic
475	C₂²	#16839964	1	1	yes	characteristic
476	C₂²	#16839969	1	1	yes	characteristic
477	C₂²	#16840039	1	1	yes	characteristic
478	C₂²	#16840044	1	1	yes	characteristic
479	C₂²	#16840049	1	1	yes	characteristic
480	C₂²	#16840054	1	1	yes	characteristic
481	C₂²	#16840075	1	1	yes	characteristic
482	C₂²	#16840080	1	1	yes	characteristic
483	C₂²	#16840092	1	1	yes	characteristic
484	C₂²	#16840097	1	1	yes	characteristic
485	C₂²	#16840108	1	1	yes	characteristic
486	C₂²	#16840112	1	1	yes	characteristic
487	C₂²	#16840126	1	1	yes	characteristic
488	C₂²	#16840130	1	1	yes	characteristic
489	C₂²	#16840158	1	1	yes	characteristic
490	C₂²	#16840165	1	1	yes	characteristic
491	C₂²	#16840168	1	1	yes	characteristic
492	C₂²	#16840168	1	1	yes	characteristic
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	8	4	no	—
496	C₄	—	488	2	no	—
497	C₄	—	244	4	no	—
498	C₄	#16839643	1	2	yes	—
499	C₄	#16839657	1	2	yes	—
500	C₄	#16839684	1	2	yes	—
501	C₄	#16839692	1	2	yes	—
502	C₂	#21444069	1	1	yes	characteristic
503	C₂	#21445816	1	1	yes	characteristic
504	C₂	#21445821	1	1	yes	characteristic
505	C₂	#21446126	1	1	yes	characteristic
506	C₂	#21446136	1	1	yes	characteristic
507	C₂	#21446779	1	1	yes	characteristic
508	C₂	#21446787	1	1	yes	characteristic
509	C₂	#21447050	1	1	yes	characteristic
510	C₂	#21447062	1	1	yes	characteristic
511	C₂	#21447144	1	1	yes	characteristic
512	C₂	#21447149	1	1	yes	characteristic
513	C₂	#21447291	1	1	yes	characteristic
514	C₂	#21447296	1	1	yes	characteristic
515	C₂	#21447376	1	1	yes	characteristic
516	C₂	#21447381	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₆₁
commutator	C₂²×C₄×C₆₁	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₆₁
Fitting	C₂×C₆₁×#384	C₂
socle, prime radical	C₂⁴×C₆₁	C₂×D₄
cosocle	C₂³×C₄×C₆₁	C₂³
hypercenter	C₂×#384	D₆₁
hypocenter	C₆₁	#11207
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
11. #16839660	C₄	semidirect
123. C₄⋊Dic₆₁	C₄⋊C₄	semidirect
279. C₆₁	#11207	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839660	2
C₂×#16839524	2
C₂×#16839517	2
C₂×C₆₁×#384	2
#11207	61