Subgroups — #29698785

Order 15616.

796 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#11758194	C₂	1	1	yes	maximal, characteristic
2	C₂×#16839834	C₂	1	1	yes	maximal, characteristic
3	#21446594	C₂	1	1	yes	maximal, characteristic, complemented
4	#21446592	C₂	1	1	yes	maximal, characteristic, complemented
5	#21446024	C₂	1	1	yes	maximal, characteristic, complemented
6	#21446024	C₂	1	1	yes	maximal, characteristic, complemented
7	#21446023	C₂	1	1	yes	maximal, characteristic, complemented
8	#21446023	C₂	1	1	yes	maximal, characteristic, complemented
9	#21445959	C₂	1	1	yes	maximal, characteristic, complemented
10	#21445859	C₂	1	1	yes	maximal, characteristic, complemented
11	#21445855	C₂	1	1	yes	maximal, characteristic, complemented
12	#21445726	C₂	1	1	yes	maximal, characteristic, complemented
13	#21445545	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16839526	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11758194	C₂²	1	1	yes	characteristic
17	C₂²×#11758194	C₂²	1	1	yes	characteristic
18	C₂²×#11758194	C₂²	1	1	yes	characteristic
19	C₂³×#92418	C₂²	1	1	yes	characteristic
20	#16839840	—	2	1	no	—
21	#16839834	—	2	1	no	—
22	#16839834	—	2	1	no	—
23	#16839834	C₄	1	2	yes	—
24	#16839834	C₄	1	2	yes	—
25	#16839834	C₄	1	2	yes	—
26	#16839834	C₄	1	2	yes	—
27	D₄×#92418	—	2	1	no	—
28	C₂×#14519712	C₂²	1	1	yes	characteristic
29	C₂×#14519712	C₂²	1	1	yes	characteristic
30	C₂×#14519712	C₂²	1	1	yes	characteristic
31	C₂×#14519712	C₂²	1	1	yes	characteristic
32	C₂×#14519712	C₂²	1	1	yes	characteristic
33	C₂×#14519712	C₂²	1	1	yes	characteristic
34	#16839786	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
36	#16839726	C₂²	1	1	yes	characteristic
37	#16839726	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊#92418	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊#92418	C₂²	1	1	yes	characteristic
40	C₄×#11758194	C₂²	1	1	yes	characteristic
41	C₂×#14519688	C₂²	1	1	yes	characteristic
42	#16839526	C₂²	1	1	yes	characteristic
43	#16839526	C₂²	1	1	yes	characteristic
44	#16839526	C₂²	1	1	yes	characteristic
45	#16839526	C₂²	1	1	yes	characteristic
46	#16839526	C₂²	1	1	yes	characteristic
47	#16839526	C₂²	1	1	yes	characteristic
48	#16839526	C₂²	1	1	yes	characteristic
49	#16839526	C₂²	1	1	yes	characteristic
50	#16839526	C₂²	1	1	yes	characteristic
51	#16839526	C₂²	1	1	yes	characteristic
52	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
53	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#436	—	2	1	no	—
56	C₆₁×#435	—	2	1	no	—
57	C₆₁×#435	—	2	1	no	—
58	C₈×D₄×C₆₁	—	2	1	no	—
59	C₆₁×#423	C₂²	1	1	yes	characteristic
60	C₆₁×#407	C₂²	1	1	yes	characteristic
61	C₆₁×#407	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
63	C₂×#11758194	—	2	1	no	—
64	C₂×#11758194	—	2	1	no	—
65	C₂×#11758194	—	2	2	no	—
66	C₂×#11758194	—	2	2	no	—
67	C₂×#11758194	—	4	1	no	—
68	C₂×#11758194	—	4	1	no	—
69	C₂×#11758194	—	4	1	no	—
70	C₂×#11758194	—	4	1	no	—
71	C₂×#11758194	C₂×C₄	1	2	yes	—
72	C₂×#11758194	C₂×C₄	1	2	yes	—
73	C₂×#11758194	C₂³	1	1	yes	characteristic
74	C₂×#11758194	C₂³	1	1	yes	characteristic
75	C₂×#11758194	C₂³	1	1	yes	characteristic
76	C₂×#11758194	C₂³	1	1	yes	characteristic
77	C₂²×#92418	—	2	1	no	—
78	C₂²×#92418	—	2	1	no	—
79	C₂²×#92418	—	4	1	no	—
80	C₂²×#92418	—	4	1	no	—
81	C₂²×#92418	C₂×C₄	1	2	yes	—
82	C₂²×#92418	C₂×C₄	1	2	yes	—
83	C₂²×#92418	C₂³	1	1	yes	characteristic
84	C₂²×#92418	C₂³	1	1	yes	characteristic
85	C₂²×#92418	C₂³	1	1	yes	characteristic
86	C₂²×#92418	C₂³	1	1	yes	characteristic
87	#14519712	—	2	2	no	—
88	#14519712	—	2	2	no	—
89	#14519712	—	4	1	no	—
90	#14519712	—	4	1	no	—
91	#14519712	—	4	1	no	—
92	#14519712	—	4	1	no	—
93	C₄⋊#92418	—	2	1	no	—
94	C₄⋊#92418	—	2	1	no	—
95	C₄⋊#92418	C₂×C₄	1	2	yes	—
96	C₄⋊#92418	C₂×C₄	1	2	yes	—
97	C₂²⋊#92418	—	2	1	no	—
98	C₂²⋊#92418	—	2	1	no	—
99	C₂²⋊#92418	—	2	1	no	—
100	C₂²⋊#92418	—	2	1	no	—
101	C₂²⋊#92418	C₂×C₄	1	2	yes	—
102	C₂²⋊#92418	C₂×C₄	1	2	yes	—
103	C₂²⋊#92418	C₂×C₄	1	2	yes	—
104	C₂²⋊#92418	C₂×C₄	1	2	yes	—
105	#14519688	—	2	1	no	—
106	#14519688	C₂×C₄	1	2	yes	—
107	#14519688	C₂×C₄	1	2	yes	—
108	C₄×#92418	—	2	1	no	—
109	C₂²×D₄×C₆₁	Q₈	1	1	yes	characteristic
110	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₆₁	—	2	1	no	—
113	C₂×M₁₆×C₆₁	—	2	1	no	—
114	C₂×M₁₆×C₆₁	—	2	2	no	—
115	C₂×M₁₆×C₆₁	—	2	2	no	—
116	C₂×M₁₆×C₆₁	—	4	1	no	—
117	C₂×M₁₆×C₆₁	—	4	1	no	—
118	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₆₁	—	2	1	no	—
123	C₂²×C₈×C₆₁	—	2	1	no	—
124	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
126	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
127	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
128	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
129	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
130	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
131	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₆₁	Q₈	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₆₁	Q₈	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₆₁	Q₈	1	1	yes	characteristic
135	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₆₁	—	2	1	no	—
137	C₄⋊C₈×C₆₁	—	2	1	no	—
138	C₂²⋊C₈×C₆₁	—	2	1	no	—
139	C₂²⋊C₈×C₆₁	—	2	1	no	—
140	C₂²⋊C₈×C₆₁	—	2	1	no	—
141	C₂²⋊C₈×C₆₁	—	2	1	no	—
142	#97×C₆₁	—	2	1	no	—
143	C₄×C₈×C₆₁	—	2	1	no	—
144	C₂⁴×C₆₁	C₂×Q₈	1	1	yes	characteristic
145	C₂⁴×C₆₁	C₂×Q₈	1	1	yes	characteristic
146	C₂×D₄×C₆₁	—	4	2	no	—
147	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
148	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
149	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
150	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	—	2	1	no	—
152	C₂²×C₄×C₆₁	—	2	1	no	—
153	C₂²×C₄×C₆₁	—	2	1	no	—
154	C₂²×C₄×C₆₁	—	2	1	no	—
155	C₂²×C₄×C₆₁	—	2	1	no	—
156	C₂²×C₄×C₆₁	—	2	1	no	—
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
168	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
169	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
170	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
171	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₆₁	—	2	1	no	—
173	M₁₆×C₆₁	—	2	1	no	—
174	M₁₆×C₆₁	—	2	1	no	—
175	M₁₆×C₆₁	—	2	1	no	—
176	M₁₆×C₆₁	—	2	1	no	—
177	M₁₆×C₆₁	—	2	1	no	—
178	M₁₆×C₆₁	—	2	1	no	—
179	M₁₆×C₆₁	—	4	2	no	—
180	M₁₆×C₆₁	—	4	2	no	—
181	M₁₆×C₆₁	#41	1	2	yes	—
182	C₂×C₈×C₆₁	—	2	1	no	—
183	C₂×C₈×C₆₁	—	2	1	no	—
184	C₂×C₈×C₆₁	—	2	1	no	—
185	C₂×C₈×C₆₁	—	2	1	no	—
186	C₂×C₈×C₆₁	—	4	2	no	—
187	C₂×C₈×C₆₁	—	4	2	no	—
188	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
190	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
196	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
198	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
200	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
202	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
204	#11758194	—	2	1	no	—
205	#11758194	—	2	1	no	—
206	#11758194	—	2	1	no	—
207	#11758194	—	2	1	no	—
208	#11758194	—	2	1	no	—
209	#11758194	—	2	1	no	—
210	#11758194	—	2	1	no	—
211	#11758194	—	4	2	no	—
212	#11758194	—	4	2	no	—
213	#11758194	—	4	2	no	—
214	#11758194	—	4	2	no	—
215	#11758194	#41	1	2	yes	—
216	C₂×#92418	—	2	1	no	—
217	C₂×#92418	—	2	1	no	—
218	C₂×#92418	—	2	1	no	—
219	C₂×#92418	—	2	1	no	—
220	C₂×#92418	—	2	1	no	—
221	C₂×#92418	—	2	1	no	—
222	C₂×#92418	—	2	1	no	—
223	C₂×#92418	—	2	1	no	—
224	C₂×#92418	—	2	1	no	—
225	C₂×#92418	—	2	1	no	—
226	C₂×#92418	—	2	1	no	—
227	C₂×#92418	—	2	1	no	—
228	C₂×#92418	—	4	2	no	—
229	C₂×#92418	—	4	2	no	—
230	C₂×#92418	—	4	2	no	—
231	C₂×#92418	—	4	2	no	—
232	C₂×#92418	C₂²×C₄	1	2	yes	—
233	C₂×#92418	C₂²×C₄	1	2	yes	—
234	C₂×#92418	C₂²×C₄	1	2	yes	—
235	C₂×#92418	C₂²×C₄	1	2	yes	—
236	C₂³×C₆₁	—	2	1	no	—
237	C₂³×C₆₁	—	2	1	no	—
238	C₂³×C₆₁	—	2	2	no	—
239	C₂³×C₆₁	—	2	1	no	—
240	C₂³×C₆₁	—	2	1	no	—
241	C₂³×C₆₁	—	4	1	no	—
242	C₂³×C₆₁	—	4	1	no	—
243	C₂³×C₆₁	—	4	1	no	—
244	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂³×C₆₁	C₂²×Q₈	1	1	yes	characteristic
249	D₄×C₆₁	—	2	2	no	—
250	D₄×C₆₁	—	2	2	no	—
251	D₄×C₆₁	—	4	1	no	—
252	D₄×C₆₁	—	4	1	no	—
253	C₂×C₄×C₆₁	—	2	1	no	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	1	no	—
258	C₂×C₄×C₆₁	—	2	1	no	—
259	C₂×C₄×C₆₁	—	2	1	no	—
260	C₂×C₄×C₆₁	—	2	1	no	—
261	C₂×C₄×C₆₁	—	2	1	no	—
262	C₂×C₄×C₆₁	—	2	1	no	—
263	C₂×C₄×C₆₁	—	2	1	no	—
264	C₂×C₄×C₆₁	—	2	1	no	—
265	C₂×C₄×C₆₁	—	2	1	no	—
266	C₂×C₄×C₆₁	—	2	1	no	—
267	C₂×C₄×C₆₁	—	2	1	no	—
268	C₂×C₄×C₆₁	—	2	1	no	—
269	C₂×C₄×C₆₁	—	2	1	no	—
270	C₂×C₄×C₆₁	—	2	1	no	—
271	C₂×C₄×C₆₁	—	2	1	no	—
272	C₂×C₄×C₆₁	—	2	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	—	4	1	no	—
275	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
289	C₈×C₆₁	—	2	2	no	—
290	C₈×C₆₁	—	4	1	no	—
291	C₈×C₆₁	—	4	1	no	—
292	C₈×C₆₁	—	4	1	no	—
293	#92418	—	2	2	no	—
294	#92418	—	2	2	no	—
295	#92418	—	2	2	no	—
296	#92418	—	2	2	no	—
297	#92418	—	2	2	no	—
298	#92418	—	4	1	no	—
299	#92418	—	4	1	no	—
300	#92418	—	4	1	no	—
301	#22718	—	61	1	no	maximal, Sylow
302	C₂²×C₆₁	—	2	1	no	—
303	C₂²×C₆₁	—	2	1	no	—
304	C₂²×C₆₁	—	2	1	no	—
305	C₂²×C₆₁	—	2	1	no	—
306	C₂²×C₆₁	—	2	1	no	—
307	C₂²×C₆₁	—	2	1	no	—
308	C₂²×C₆₁	—	2	1	no	—
309	C₂²×C₆₁	—	2	1	no	—
310	C₂²×C₆₁	—	2	1	no	—
311	C₂²×C₆₁	—	2	1	no	—
312	C₂²×C₆₁	—	2	1	no	—
313	C₂²×C₆₁	—	2	1	no	—
314	C₂²×C₆₁	—	2	1	no	—
315	C₂²×C₆₁	—	4	2	no	—
316	C₂²×C₆₁	—	4	2	no	—
317	C₂²×C₆₁	—	8	1	no	—
318	C₂²×C₆₁	—	8	1	no	—
319	C₂²×C₆₁	#430	1	2	yes	—
320	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
321	C₂²×C₆₁	#554	1	1	yes	characteristic
322	C₂²×C₆₁	#554	1	1	yes	characteristic
323	C₄×C₆₁	—	2	1	no	—
324	C₄×C₆₁	—	2	1	no	—
325	C₄×C₆₁	—	2	1	no	—
326	C₄×C₆₁	—	2	1	no	—
327	C₄×C₆₁	—	2	1	no	—
328	C₄×C₆₁	—	2	1	no	—
329	C₄×C₆₁	—	2	1	no	—
330	C₄×C₆₁	—	2	1	no	—
331	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
332	C₄×C₆₁	#518	1	1	yes	characteristic
333	C₄×C₆₁	#546	1	1	yes	characteristic
334	C₄×C₆₁	#546	1	1	yes	characteristic
335	D₄×M₁₆	—	61	1	no	—
336	D₄×M₁₆	D₆₁	1	1	yes	characteristic
337	C₂×#435	—	61	1	no	—
338	#1950	—	61	1	no	—
339	#1950	—	61	1	no	—
340	#1855	—	61	1	no	—
341	#1855	—	61	1	no	—
342	#1855	—	61	1	no	—
343	#1855	—	61	1	no	—
344	#1838	—	61	1	no	—
345	#1811	—	61	1	no	—
346	#1810	—	61	1	no	—
347	#1778	—	61	1	no	—
348	#1738	—	61	1	no	—
349	C₂×#341	—	61	1	no	—
350	C₂×C₆₁	—	2	1	no	—
351	C₂×C₆₁	—	2	1	no	—
352	C₂×C₆₁	—	2	2	no	—
353	C₂×C₆₁	—	4	1	no	—
354	C₂×C₆₁	—	4	1	no	—
355	C₂×C₆₁	—	4	1	no	—
356	C₂×C₆₁	#2349	1	1	yes	characteristic
357	C₂×C₆₁	C₂×#430	1	1	yes	characteristic
358	C₂×C₆₁	#2916	1	1	yes	characteristic
359	C₂²×M₁₆	—	61	1	no	—
360	C₂²×M₁₆	—	61	1	no	—
361	C₂²×M₁₆	—	61	1	no	—
362	C₂²×M₁₆	C₂×D₆₁	1	1	yes	characteristic
363	C₂²×M₁₆	C₂×D₆₁	1	1	yes	characteristic
364	C₂³×C₈	—	61	1	no	—
365	C₂×C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
366	#436	—	2	1	no	—
367	#436	—	122	1	no	—
368	#435	—	2	1	no	—
369	#435	—	2	1	no	—
370	#435	—	61	2	no	—
371	#435	—	61	2	no	—
372	#435	—	61	2	no	—
373	#435	—	61	2	no	—
374	#435	—	122	1	no	—
375	#435	—	122	1	no	—
376	C₈×D₄	—	2	1	no	—
377	C₈×D₄	—	122	1	no	—
378	C₂×#108	—	61	1	no	—
379	C₂×#108	—	61	1	no	—
380	C₂×#108	—	61	1	no	—
381	C₂×#108	—	61	1	no	—
382	C₂×#108	—	61	1	no	—
383	C₂×#108	—	61	1	no	—
384	#423	—	61	1	no	—
385	#423	C₂×D₆₁	1	1	yes	characteristic
386	C₂×C₄⋊C₈	—	61	1	no	—
387	#407	—	61	1	no	—
388	#407	—	61	1	no	—
389	#407	C₂×D₆₁	1	1	yes	characteristic
390	#407	C₂×D₆₁	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	—	61	1	no	—
392	C₂×C₂²⋊C₈	—	61	1	no	—
393	C₄×M₁₆	—	61	1	no	—
394	C₄×M₁₆	C₂×D₆₁	1	1	yes	characteristic
395	C₂×#97	—	61	1	no	—
396	#341	—	61	1	no	—
397	#341	—	61	1	no	—
398	#341	—	61	1	no	—
399	#341	—	61	1	no	—
400	#341	—	61	1	no	—
401	#341	—	61	1	no	—
402	#341	—	61	1	no	—
403	#341	—	61	1	no	—
404	#341	—	61	1	no	—
405	#341	—	61	1	no	—
406	C₆₁	#22718	1	1	yes	characteristic, complemented, Sylow
407	C₂²×D₄	Dic₁₂₂	1	1	yes	characteristic
408	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
409	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	2	no	—
413	C₂×M₁₆	—	2	2	no	—
414	C₂×M₁₆	—	4	1	no	—
415	C₂×M₁₆	—	4	1	no	—
416	C₂×M₁₆	—	61	2	no	—
417	C₂×M₁₆	—	61	2	no	—
418	C₂×M₁₆	—	61	1	no	—
419	C₂×M₁₆	—	61	1	no	—
420	C₂×M₁₆	—	61	1	no	—
421	C₂×M₁₆	—	61	1	no	—
422	C₂×M₁₆	—	122	1	no	—
423	C₂×M₁₆	—	122	1	no	—
424	C₂×M₁₆	—	122	2	no	—
425	C₂×M₁₆	—	122	2	no	—
426	C₂×M₁₆	—	244	1	no	—
427	C₂×M₁₆	—	244	1	no	—
428	C₂×M₁₆	—	244	1	no	—
429	C₂×M₁₆	—	244	1	no	—
430	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
431	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
432	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
433	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
434	C₂²×C₈	—	2	1	no	—
435	C₂²×C₈	—	2	1	no	—
436	C₂²×C₈	—	61	1	no	—
437	C₂²×C₈	—	61	1	no	—
438	C₂²×C₈	—	61	1	no	—
439	C₂²×C₈	—	61	1	no	—
440	C₂²×C₈	—	61	2	no	—
441	C₂²×C₈	—	61	2	no	—
442	C₂²×C₈	—	122	1	no	—
443	C₂²×C₈	—	122	1	no	—
444	C₂²×C₈	—	244	1	no	—
445	C₂²×C₈	—	244	1	no	—
446	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
447	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
448	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
449	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
450	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
451	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
452	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
453	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	Dic₁₂₂	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	Dic₁₂₂	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	Dic₁₂₂	1	1	yes	characteristic
457	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
458	#108	—	122	2	no	—
459	#108	—	122	2	no	—
460	#108	—	244	1	no	—
461	#108	—	244	1	no	—
462	#108	—	244	1	no	—
463	#108	—	244	1	no	—
464	C₄⋊C₈	—	2	1	no	—
465	C₄⋊C₈	—	2	1	no	—
466	C₄⋊C₈	—	61	2	no	—
467	C₄⋊C₈	—	61	2	no	—
468	C₄⋊C₈	—	122	1	no	—
469	C₄⋊C₈	—	122	1	no	—
470	C₂²⋊C₈	—	2	1	no	—
471	C₂²⋊C₈	—	2	1	no	—
472	C₂²⋊C₈	—	2	1	no	—
473	C₂²⋊C₈	—	2	1	no	—
474	C₂²⋊C₈	—	61	2	no	—
475	C₂²⋊C₈	—	61	2	no	—
476	C₂²⋊C₈	—	61	2	no	—
477	C₂²⋊C₈	—	61	2	no	—
478	C₂²⋊C₈	—	122	1	no	—
479	C₂²⋊C₈	—	122	1	no	—
480	C₂²⋊C₈	—	122	1	no	—
481	C₂²⋊C₈	—	122	1	no	—
482	#97	—	2	1	no	—
483	#97	—	61	2	no	—
484	#97	—	61	2	no	—
485	#97	—	122	1	no	—
486	C₄×C₈	—	2	1	no	—
487	C₄×C₈	—	122	1	no	—
488	C₂⁴	C₂×Dic₁₂₂	1	1	yes	characteristic
489	C₂⁴	C₂×Dic₁₂₂	1	1	yes	characteristic
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	#11758196	1	1	yes	characteristic
492	C₂×D₄	#11758196	1	1	yes	characteristic
493	C₂×D₄	#11758196	1	1	yes	characteristic
494	C₂×D₄	#11758196	1	1	yes	characteristic
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
504	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
505	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
506	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
508	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
509	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
510	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
512	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
513	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
515	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	4	2	no	—
524	M₁₆	—	4	2	no	—
525	M₁₆	—	61	2	no	—
526	M₁₆	—	122	1	no	—
527	M₁₆	—	122	1	no	—
528	M₁₆	—	122	1	no	—
529	M₁₆	—	122	1	no	—
530	M₁₆	—	122	1	no	—
531	M₁₆	—	122	1	no	—
532	M₁₆	—	122	1	no	—
533	M₁₆	—	244	2	no	—
534	M₁₆	—	244	2	no	—
535	M₁₆	—	244	2	no	—
536	M₁₆	—	244	2	no	—
537	M₁₆	#11758224	1	2	yes	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	4	2	no	—
543	C₂×C₈	—	4	2	no	—
544	C₂×C₈	—	61	2	no	—
545	C₂×C₈	—	61	2	no	—
546	C₂×C₈	—	61	2	no	—
547	C₂×C₈	—	61	2	no	—
548	C₂×C₈	—	122	1	no	—
549	C₂×C₈	—	122	1	no	—
550	C₂×C₈	—	122	1	no	—
551	C₂×C₈	—	122	1	no	—
552	C₂×C₈	—	122	1	no	—
553	C₂×C₈	—	122	1	no	—
554	C₂×C₈	—	122	1	no	—
555	C₂×C₈	—	122	1	no	—
556	C₂×C₈	—	122	1	no	—
557	C₂×C₈	—	122	1	no	—
558	C₂×C₈	—	122	1	no	—
559	C₂×C₈	—	122	1	no	—
560	C₂×C₈	—	244	2	no	—
561	C₂×C₈	—	244	2	no	—
562	C₂×C₈	—	244	2	no	—
563	C₂×C₈	—	244	2	no	—
564	C₄⋊C₄	#11758196	1	1	yes	characteristic
565	C₄⋊C₄	#11758196	1	1	yes	characteristic
566	C₄⋊C₄	#11758196	1	1	yes	characteristic
567	C₄⋊C₄	#11758196	1	1	yes	characteristic
568	C₂²⋊C₄	#11758196	1	1	yes	characteristic
569	C₂²⋊C₄	#11758196	1	1	yes	characteristic
570	C₂²⋊C₄	#11758196	1	1	yes	characteristic
571	C₂²⋊C₄	#11758196	1	1	yes	characteristic
572	C₂²⋊C₄	#11758196	1	1	yes	characteristic
573	C₂²⋊C₄	#11758196	1	1	yes	characteristic
574	C₂²⋊C₄	#11758196	1	1	yes	characteristic
575	C₂²⋊C₄	#11758196	1	1	yes	characteristic
576	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
577	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
578	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
579	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	C₂×#11758196	1	1	yes	characteristic
589	C₂³	C₂×#11758196	1	1	yes	characteristic
590	C₂³	C₂×#11758196	1	1	yes	characteristic
591	C₂³	C₂×#11758196	1	1	yes	characteristic
592	C₂³	C₂²×Dic₁₂₂	1	1	yes	characteristic
593	D₄	—	2	2	no	—
594	D₄	—	2	2	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
620	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
621	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
622	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
623	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
624	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
625	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
626	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
627	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
628	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
629	C₂×C₄	#41×D₆₁	1	1	yes	characteristic
630	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
631	C₂×C₄	#14519822	1	1	yes	characteristic
632	C₂×C₄	#14519823	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	4	1	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₈	—	122	2	no	—
638	C₈	—	122	2	no	—
639	C₈	—	122	2	no	—
640	C₈	—	122	2	no	—
641	C₈	—	122	2	no	—
642	C₈	—	244	1	no	—
643	C₈	—	244	1	no	—
644	C₈	—	244	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	8	1	no	—
661	C₂²	—	8	1	no	—
662	C₂²	#16839810	1	2	yes	—
663	C₂²	C₂²×#11758196	1	1	yes	characteristic
664	C₂²	#16840469	1	1	yes	characteristic
665	C₂²	#16840471	1	1	yes	characteristic
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	C₄×#11758224	1	1	yes	characteristic
675	C₄	#16840234	1	1	yes	characteristic
676	C₄	#16840400	1	1	yes	characteristic
677	C₄	#16840406	1	1	yes	characteristic
678	C₂	—	2	1	no	—
679	C₂	—	2	1	no	—
680	C₂	—	2	2	no	—
681	C₂	—	4	1	no	—
682	C₂	—	4	1	no	—
683	C₂	—	4	1	no	—
684	C₂	#21448724	1	1	yes	characteristic
685	C₂	C₂×#16839810	1	1	yes	characteristic
686	C₂	#21454428	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting	D₄×M₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₆₁	Q₈
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	D₄×M₁₆	D₆₁
hypocenter	C₆₁	#22718
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #21446594	C₂	semidirect
4. #21446592	C₂	semidirect
5. #21446024	C₂	semidirect
6. #21446024	C₂	semidirect
7. #21446023	C₂	semidirect
8. #21446023	C₂	semidirect
9. #21445959	C₂	semidirect
10. #21445859	C₂	semidirect
11. #21445855	C₂	semidirect
12. #21445726	C₂	semidirect
13. #21445545	C₂	semidirect
14. C₂×#16839526	C₂	semidirect
406. C₆₁	#22718	semidirect

Maximal subgroups

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

subgroup	index
D₄×#11758194	2
C₂×#16839834	2
#21446594	2
#21446592	2
#21446024	2
#21446023	2
#21445959	2
#21445859	2
#21445855	2
#21445726	2
#21445545	2
C₂×#16839526	2
D₄×M₁₆×C₆₁	2
#22718	61