Subgroups — #29698269

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 700 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	C₂×#16839810	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#14519712	C₂	1	1	yes	maximal, characteristic, complemented
5	#21446594	C₂	1	1	yes	maximal, characteristic, complemented
6	#21446592	C₂	1	1	yes	maximal, characteristic, complemented
7	#21446024	C₂	1	1	yes	maximal, characteristic, complemented
8	#21446024	C₂	1	1	yes	maximal, characteristic, complemented
9	#21446023	C₂	1	1	yes	maximal, characteristic, complemented
10	#21446023	C₂	1	1	yes	maximal, characteristic, complemented
11	#21445993	C₂	1	1	yes	maximal, characteristic, complemented
12	#21445859	C₂	1	1	yes	maximal, characteristic, complemented
13	#21445855	C₂	1	1	yes	maximal, characteristic, complemented
14	#21445726	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	#16839810	—	2	4	no	—
29	C₂×#14519712	—	2	4	no	—
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	C₂×#14519712	C₂²	1	1	yes	characteristic
35	C₂×#14519712	C₂²	1	1	yes	characteristic
36	C₂×#14519712	C₂²	1	1	yes	characteristic
37	C₂×#14519712	C₂²	1	1	yes	characteristic
38	C₂×#14519712	C₂²	1	1	yes	characteristic
39	C₂×#14519712	C₂²	1	1	yes	characteristic
40	#16839786	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
42	#16839726	C₂²	1	1	yes	characteristic
43	#16839726	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊#92418	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊#92418	C₂²	1	1	yes	characteristic
46	C₄×#11758194	C₂²	1	1	yes	characteristic
47	C₂×#14519688	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	#16839526	C₂²	1	1	yes	characteristic
53	#16839526	C₂²	1	1	yes	characteristic
54	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
55	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#436	—	2	1	no	—
58	C₆₁×#435	—	2	1	no	—
59	C₆₁×#435	—	2	1	no	—
60	C₈×D₄×C₆₁	—	2	1	no	—
61	C₆₁×#423	C₂²	1	1	yes	characteristic
62	C₆₁×#407	C₂²	1	1	yes	characteristic
63	C₆₁×#407	C₂²	1	1	yes	characteristic
64	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
65	C₂×#11758194	—	2	1	no	—
66	C₂×#11758194	—	2	1	no	—
67	C₂×#11758194	—	2	2	no	—
68	C₂×#11758194	—	2	2	no	—
69	C₂×#11758194	—	2	2	no	—
70	C₂×#11758194	—	2	2	no	—
71	C₂×#11758194	—	4	1	no	—
72	C₂×#11758194	—	4	1	no	—
73	C₂×#11758194	C₂×C₄	1	2	yes	—
74	C₂×#11758194	C₂×C₄	1	2	yes	—
75	C₂×#11758194	C₂³	1	1	yes	characteristic
76	C₂×#11758194	C₂³	1	1	yes	characteristic
77	C₂×#11758194	C₂³	1	1	yes	characteristic
78	C₂×#11758194	C₂³	1	1	yes	characteristic
79	C₂²×#92418	—	2	2	no	—
80	C₂²×#92418	—	2	2	no	—
81	C₂²×#92418	—	2	1	no	—
82	C₂²×#92418	—	2	1	no	—
83	C₂²×#92418	C₂×C₄	1	2	yes	—
84	C₂²×#92418	C₂×C₄	1	2	yes	—
85	C₂²×#92418	C₂³	1	1	yes	characteristic
86	C₂²×#92418	C₂³	1	1	yes	characteristic
87	C₂²×#92418	C₂³	1	1	yes	characteristic
88	C₂²×#92418	C₂³	1	1	yes	characteristic
89	#14519712	—	2	2	no	—
90	#14519712	—	2	2	no	—
91	#14519712	—	2	2	no	—
92	#14519712	—	2	2	no	—
93	#14519712	—	2	2	no	—
94	#14519712	—	2	2	no	—
95	#14519712	—	2	2	no	—
96	#14519712	—	4	1	no	—
97	#14519712	—	4	1	no	—
98	#14519712	D₄	1	4	yes	complemented
99	C₄⋊#92418	—	2	1	no	—
100	C₄⋊#92418	—	2	1	no	—
101	C₄⋊#92418	C₂×C₄	1	2	yes	—
102	C₄⋊#92418	C₂×C₄	1	2	yes	—
103	C₂²⋊#92418	—	2	1	no	—
104	C₂²⋊#92418	—	2	1	no	—
105	C₂²⋊#92418	—	2	1	no	—
106	C₂²⋊#92418	—	2	1	no	—
107	C₂²⋊#92418	C₂×C₄	1	2	yes	—
108	C₂²⋊#92418	C₂×C₄	1	2	yes	—
109	C₂²⋊#92418	C₂×C₄	1	2	yes	—
110	C₂²⋊#92418	C₂×C₄	1	2	yes	—
111	#14519688	—	2	1	no	—
112	#14519688	C₂×C₄	1	2	yes	—
113	#14519688	C₂×C₄	1	2	yes	—
114	C₄×#92418	—	2	1	no	—
115	C₂²×D₄×C₆₁	Q₈	1	1	yes	characteristic
116	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₆₁	—	2	1	no	—
119	C₂×M₁₆×C₆₁	—	2	1	no	—
120	C₂×M₁₆×C₆₁	—	2	2	no	—
121	C₂×M₁₆×C₆₁	—	2	2	no	—
122	C₂×M₁₆×C₆₁	—	4	1	no	—
123	C₂×M₁₆×C₆₁	—	4	1	no	—
124	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
125	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₆₁	—	2	1	no	—
129	C₂²×C₈×C₆₁	—	2	1	no	—
130	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
131	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
132	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
133	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
134	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
135	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
136	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
137	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₁	Q₈	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₆₁	Q₈	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₆₁	Q₈	1	1	yes	characteristic
141	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
142	C₄⋊C₈×C₆₁	—	2	1	no	—
143	C₄⋊C₈×C₆₁	—	2	1	no	—
144	C₂²⋊C₈×C₆₁	—	2	1	no	—
145	C₂²⋊C₈×C₆₁	—	2	1	no	—
146	C₂²⋊C₈×C₆₁	—	2	1	no	—
147	C₂²⋊C₈×C₆₁	—	2	1	no	—
148	#97×C₆₁	—	2	1	no	—
149	C₄×C₈×C₆₁	—	2	1	no	—
150	C₂⁴×C₆₁	C₂×Q₈	1	1	yes	characteristic
151	C₂⁴×C₆₁	C₂×Q₈	1	1	yes	characteristic
152	C₂×D₄×C₆₁	—	4	2	no	—
153	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
154	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
155	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
156	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	—	2	1	no	—
160	C₂²×C₄×C₆₁	—	2	1	no	—
161	C₂²×C₄×C₆₁	—	2	1	no	—
162	C₂²×C₄×C₆₁	—	2	1	no	—
163	C₂²×C₄×C₆₁	—	2	1	no	—
164	C₂²×C₄×C₆₁	—	2	1	no	—
165	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
174	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
175	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
176	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
177	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
178	M₁₆×C₆₁	—	2	1	no	—
179	M₁₆×C₆₁	—	2	1	no	—
180	M₁₆×C₆₁	—	2	1	no	—
181	M₁₆×C₆₁	—	2	1	no	—
182	M₁₆×C₆₁	—	2	1	no	—
183	M₁₆×C₆₁	—	2	1	no	—
184	M₁₆×C₆₁	—	2	1	no	—
185	M₁₆×C₆₁	—	4	2	no	—
186	M₁₆×C₆₁	—	4	2	no	—
187	M₁₆×C₆₁	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₆₁	—	2	1	no	—
189	C₂×C₈×C₆₁	—	2	1	no	—
190	C₂×C₈×C₆₁	—	2	1	no	—
191	C₂×C₈×C₆₁	—	2	1	no	—
192	C₂×C₈×C₆₁	—	4	2	no	—
193	C₂×C₈×C₆₁	—	4	2	no	—
194	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
197	C₄⋊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	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
201	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
202	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
203	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
204	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
206	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
210	#11758194	—	2	1	no	—
211	#11758194	—	2	4	no	—
212	#11758194	—	2	4	no	—
213	#11758194	—	2	1	no	—
214	#11758194	—	2	1	no	—
215	#11758194	—	2	1	no	—
216	#11758194	—	2	1	no	—
217	#11758194	—	2	1	no	—
218	#11758194	—	2	1	no	—
219	#11758194	—	4	2	no	—
220	#11758194	—	4	2	no	—
221	#11758194	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
229	C₂×#92418	—	2	4	no	—
230	C₂×#92418	—	2	4	no	—
231	C₂×#92418	—	2	1	no	—
232	C₂×#92418	—	2	1	no	—
233	C₂×#92418	—	2	1	no	—
234	C₂×#92418	—	4	2	no	—
235	C₂×#92418	—	4	2	no	—
236	C₂×#92418	C₂²×C₄	1	2	yes	—
237	C₂×#92418	C₂²×C₄	1	2	yes	—
238	C₂×#92418	C₂²×C₄	1	2	yes	—
239	C₂×#92418	C₂²×C₄	1	2	yes	—
240	C₂×#92418	C₂×D₄	1	2	yes	—
241	C₂×#92418	#41	1	2	yes	—
242	C₂³×C₆₁	—	2	1	no	—
243	C₂³×C₆₁	—	2	1	no	—
244	C₂³×C₆₁	—	2	2	no	—
245	C₂³×C₆₁	—	2	1	no	—
246	C₂³×C₆₁	—	2	1	no	—
247	C₂³×C₆₁	—	4	1	no	—
248	C₂³×C₆₁	—	4	1	no	—
249	C₂³×C₆₁	—	4	1	no	—
250	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
252	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
253	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₂³×C₆₁	C₂²×Q₈	1	1	yes	characteristic
255	D₄×C₆₁	—	2	2	no	—
256	D₄×C₆₁	—	2	2	no	—
257	D₄×C₆₁	—	4	1	no	—
258	D₄×C₆₁	—	4	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	—	2	1	no	—
274	C₂×C₄×C₆₁	—	2	1	no	—
275	C₂×C₄×C₆₁	—	2	1	no	—
276	C₂×C₄×C₆₁	—	2	1	no	—
277	C₂×C₄×C₆₁	—	2	1	no	—
278	C₂×C₄×C₆₁	—	2	1	no	—
279	C₂×C₄×C₆₁	—	4	1	no	—
280	C₂×C₄×C₆₁	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
289	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
290	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
295	C₈×C₆₁	—	2	2	no	—
296	C₈×C₆₁	—	4	1	no	—
297	C₈×C₆₁	—	4	1	no	—
298	C₈×C₆₁	—	4	1	no	—
299	#92418	—	2	2	no	—
300	#92418	—	2	2	no	—
301	#92418	—	2	2	no	—
302	#92418	—	2	2	no	—
303	#92418	—	4	1	no	—
304	#92418	—	4	1	no	—
305	#92418	—	4	1	no	—
306	#92418	C₄×D₄	1	4	yes	—
307	#22668	—	61	1	no	maximal, Sylow
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	—	2	1	no	—
316	C₂²×C₆₁	—	2	1	no	—
317	C₂²×C₆₁	—	2	1	no	—
318	C₂²×C₆₁	—	2	1	no	—
319	C₂²×C₆₁	—	2	1	no	—
320	C₂²×C₆₁	—	2	1	no	—
321	C₂²×C₆₁	—	4	2	no	—
322	C₂²×C₆₁	—	4	2	no	—
323	C₂²×C₆₁	—	8	1	no	—
324	C₂²×C₆₁	—	8	1	no	—
325	C₂²×C₆₁	#430	1	2	yes	complemented
326	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
327	C₂²×C₆₁	D₄×Q₈	1	1	yes	characteristic
328	C₂²×C₆₁	#554	1	1	yes	characteristic
329	C₄×C₆₁	—	2	1	no	—
330	C₄×C₆₁	—	2	1	no	—
331	C₄×C₆₁	—	2	1	no	—
332	C₄×C₆₁	—	2	1	no	—
333	C₄×C₆₁	—	2	1	no	—
334	C₄×C₆₁	—	2	1	no	—
335	C₄×C₆₁	—	2	1	no	—
336	C₄×C₆₁	—	2	1	no	—
337	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
338	C₄×C₆₁	#520	1	1	yes	characteristic
339	C₄×C₆₁	D₄²	1	1	yes	characteristic
340	C₄×C₆₁	#547	1	1	yes	characteristic
341	D₄×M₁₆	—	61	1	no	—
342	D₄×M₁₆	D₆₁	1	1	yes	characteristic
343	C₂×#435	—	61	1	no	—
344	C₂×#430	—	61	1	no	—
345	C₂²×#108	—	61	1	no	—
346	#1950	—	61	1	no	—
347	#1950	—	61	1	no	—
348	#1855	—	61	1	no	—
349	#1855	—	61	1	no	—
350	#1855	—	61	1	no	—
351	#1855	—	61	1	no	—
352	#1849	—	61	1	no	—
353	#1811	—	61	1	no	—
354	#1810	—	61	1	no	—
355	#1778	—	61	1	no	—
356	C₂×C₆₁	—	2	1	no	—
357	C₂×C₆₁	—	2	1	no	—
358	C₂×C₆₁	—	2	2	no	—
359	C₂×C₆₁	—	4	1	no	—
360	C₂×C₆₁	—	4	1	no	—
361	C₂×C₆₁	—	4	1	no	—
362	C₂×C₆₁	D₄×C₄⋊C₄	1	1	yes	characteristic
363	C₂×C₆₁	C₂×#430	1	1	yes	characteristic
364	C₂×C₆₁	#2916	1	1	yes	characteristic
365	C₂²×M₁₆	—	61	1	no	—
366	C₂²×M₁₆	—	61	1	no	—
367	C₂²×M₁₆	—	61	1	no	—
368	C₂²×M₁₆	C₂×D₆₁	1	1	yes	characteristic
369	C₂²×M₁₆	C₂×D₆₁	1	1	yes	characteristic
370	C₂³×C₈	—	61	1	no	—
371	C₂×C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
372	#436	—	2	1	no	—
373	#436	—	122	1	no	—
374	#435	—	2	1	no	—
375	#435	—	2	1	no	—
376	#435	—	61	2	no	—
377	#435	—	61	2	no	—
378	#435	—	61	2	no	—
379	#435	—	61	2	no	—
380	#435	—	122	1	no	—
381	#435	—	122	1	no	—
382	C₈×D₄	—	2	1	no	—
383	C₈×D₄	—	122	1	no	—
384	#430	—	122	4	no	—
385	C₂×#108	—	61	1	no	—
386	C₂×#108	—	61	1	no	—
387	C₂×#108	—	61	1	no	—
388	C₂×#108	—	61	1	no	—
389	C₂×#108	—	61	1	no	—
390	C₂×#108	—	61	1	no	—
391	C₂×#108	—	61	1	no	—
392	C₂×#108	—	61	1	no	—
393	C₂×#108	—	61	1	no	—
394	C₂×#108	—	61	1	no	—
395	C₂×#108	—	122	4	no	—
396	#423	—	61	1	no	—
397	#423	C₂×D₆₁	1	1	yes	characteristic
398	C₂×C₄⋊C₈	—	61	1	no	—
399	#407	—	61	1	no	—
400	#407	—	61	1	no	—
401	#407	C₂×D₆₁	1	1	yes	characteristic
402	#407	C₂×D₆₁	1	1	yes	characteristic
403	C₂×C₂²⋊C₈	—	61	1	no	—
404	C₂×C₂²⋊C₈	—	61	1	no	—
405	C₄×M₁₆	—	61	1	no	—
406	C₄×M₁₆	C₂×D₆₁	1	1	yes	characteristic
407	C₂×#97	—	61	1	no	—
408	#341	—	61	1	no	—
409	#341	—	61	1	no	—
410	#341	—	61	1	no	—
411	#341	—	61	1	no	—
412	#341	—	61	1	no	—
413	#341	—	61	1	no	—
414	C₆₁	#22668	1	1	yes	characteristic, complemented, Sylow
415	C₂²×D₄	Dic₁₂₂	1	1	yes	characteristic
416	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
417	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
418	C₂×M₁₆	—	2	1	no	—
419	C₂×M₁₆	—	2	1	no	—
420	C₂×M₁₆	—	2	2	no	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂×M₁₆	—	4	1	no	—
423	C₂×M₁₆	—	4	1	no	—
424	C₂×M₁₆	—	61	2	no	—
425	C₂×M₁₆	—	61	2	no	—
426	C₂×M₁₆	—	61	1	no	—
427	C₂×M₁₆	—	61	1	no	—
428	C₂×M₁₆	—	61	1	no	—
429	C₂×M₁₆	—	61	1	no	—
430	C₂×M₁₆	—	122	2	no	—
431	C₂×M₁₆	—	122	2	no	—
432	C₂×M₁₆	—	122	1	no	—
433	C₂×M₁₆	—	122	1	no	—
434	C₂×M₁₆	—	122	2	no	—
435	C₂×M₁₆	—	122	2	no	—
436	C₂×M₁₆	—	244	1	no	—
437	C₂×M₁₆	—	244	1	no	—
438	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
439	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
440	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
441	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
442	C₂²×C₈	—	2	1	no	—
443	C₂²×C₈	—	2	1	no	—
444	C₂²×C₈	—	61	1	no	—
445	C₂²×C₈	—	61	2	no	—
446	C₂²×C₈	—	61	2	no	—
447	C₂²×C₈	—	61	1	no	—
448	C₂²×C₈	—	61	1	no	—
449	C₂²×C₈	—	61	1	no	—
450	C₂²×C₈	—	122	2	no	—
451	C₂²×C₈	—	122	2	no	—
452	C₂²×C₈	—	122	1	no	—
453	C₂²×C₈	—	122	1	no	—
454	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
455	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
456	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
457	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
458	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
459	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
460	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
461	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
462	C₂×C₄⋊C₄	Dic₁₂₂	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	Dic₁₂₂	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	Dic₁₂₂	1	1	yes	characteristic
465	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
466	#108	—	61	4	no	—
467	#108	—	122	2	no	—
468	#108	—	122	2	no	—
469	#108	—	122	2	no	—
470	#108	—	122	2	no	—
471	#108	—	122	2	no	—
472	#108	—	122	2	no	—
473	#108	—	122	2	no	—
474	#108	—	244	1	no	—
475	#108	—	244	1	no	—
476	C₄⋊C₈	—	2	1	no	—
477	C₄⋊C₈	—	2	1	no	—
478	C₄⋊C₈	—	61	2	no	—
479	C₄⋊C₈	—	61	2	no	—
480	C₄⋊C₈	—	122	1	no	—
481	C₄⋊C₈	—	122	1	no	—
482	C₂²⋊C₈	—	2	1	no	—
483	C₂²⋊C₈	—	2	1	no	—
484	C₂²⋊C₈	—	2	1	no	—
485	C₂²⋊C₈	—	2	1	no	—
486	C₂²⋊C₈	—	61	2	no	—
487	C₂²⋊C₈	—	61	2	no	—
488	C₂²⋊C₈	—	61	2	no	—
489	C₂²⋊C₈	—	61	2	no	—
490	C₂²⋊C₈	—	122	1	no	—
491	C₂²⋊C₈	—	122	1	no	—
492	C₂²⋊C₈	—	122	1	no	—
493	C₂²⋊C₈	—	122	1	no	—
494	#97	—	2	1	no	—
495	#97	—	61	2	no	—
496	#97	—	61	2	no	—
497	#97	—	122	1	no	—
498	C₄×C₈	—	2	1	no	—
499	C₄×C₈	—	122	1	no	—
500	C₂⁴	C₂×Dic₁₂₂	1	1	yes	characteristic
501	C₂⁴	C₂×Dic₁₂₂	1	1	yes	characteristic
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	#11758196	1	1	yes	characteristic
504	C₂×D₄	#11758196	1	1	yes	characteristic
505	C₂×D₄	#11758196	1	1	yes	characteristic
506	C₂×D₄	#11758196	1	1	yes	characteristic
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
516	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
517	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
518	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
522	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
526	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
527	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
528	M₁₆	—	2	1	no	—
529	M₁₆	—	2	1	no	—
530	M₁₆	—	2	1	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	4	2	no	—
536	M₁₆	—	4	2	no	—
537	M₁₆	—	61	2	no	—
538	M₁₆	—	122	4	no	—
539	M₁₆	—	122	4	no	—
540	M₁₆	—	122	1	no	—
541	M₁₆	—	122	1	no	—
542	M₁₆	—	122	1	no	—
543	M₁₆	—	122	1	no	—
544	M₁₆	—	122	1	no	—
545	M₁₆	—	122	1	no	—
546	M₁₆	—	122	1	no	—
547	M₁₆	—	244	2	no	—
548	M₁₆	—	244	2	no	—
549	M₁₆	D₄×D₆₁	1	2	yes	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	4	2	no	—
555	C₂×C₈	—	4	2	no	—
556	C₂×C₈	—	61	2	no	—
557	C₂×C₈	—	61	2	no	—
558	C₂×C₈	—	61	2	no	—
559	C₂×C₈	—	61	2	no	—
560	C₂×C₈	—	61	2	no	—
561	C₂×C₈	—	61	2	no	—
562	C₂×C₈	—	122	4	no	—
563	C₂×C₈	—	122	4	no	—
564	C₂×C₈	—	122	1	no	—
565	C₂×C₈	—	122	1	no	—
566	C₂×C₈	—	122	1	no	—
567	C₂×C₈	—	122	1	no	—
568	C₂×C₈	—	122	1	no	—
569	C₂×C₈	—	122	1	no	—
570	C₂×C₈	—	122	1	no	—
571	C₂×C₈	—	122	1	no	—
572	C₂×C₈	—	122	1	no	—
573	C₂×C₈	—	122	1	no	—
574	C₂×C₈	—	244	2	no	—
575	C₂×C₈	—	244	2	no	—
576	C₄⋊C₄	#11758196	1	1	yes	characteristic
577	C₄⋊C₄	#11758196	1	1	yes	characteristic
578	C₄⋊C₄	#11758196	1	1	yes	characteristic
579	C₄⋊C₄	#11758196	1	1	yes	characteristic
580	C₂²⋊C₄	#11758196	1	1	yes	characteristic
581	C₂²⋊C₄	#11758196	1	1	yes	characteristic
582	C₂²⋊C₄	#11758196	1	1	yes	characteristic
583	C₂²⋊C₄	#11758196	1	1	yes	characteristic
584	C₂²⋊C₄	#11758196	1	1	yes	characteristic
585	C₂²⋊C₄	#11758196	1	1	yes	characteristic
586	C₂²⋊C₄	#11758196	1	1	yes	characteristic
587	C₂²⋊C₄	#11758196	1	1	yes	characteristic
588	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
589	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
590	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
591	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
592	C₂³	—	2	1	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	C₂×#11758196	1	1	yes	characteristic
601	C₂³	C₂×#11758196	1	1	yes	characteristic
602	C₂³	C₂×#11758196	1	1	yes	characteristic
603	C₂³	C₂×#11758196	1	1	yes	characteristic
604	C₂³	C₂²×Dic₁₂₂	1	1	yes	characteristic
605	D₄	—	2	2	no	—
606	D₄	—	2	2	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	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	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
632	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
633	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
634	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
635	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
636	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
637	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
638	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
639	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
640	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
641	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
642	C₂×C₄	#41×D₆₁	1	1	yes	characteristic
643	C₂×C₄	#14519822	1	1	yes	characteristic
644	C₂×C₄	#14519824	1	1	yes	characteristic
645	C₈	—	2	2	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	61	4	no	—
650	C₈	—	122	2	no	—
651	C₈	—	122	2	no	—
652	C₈	—	122	2	no	—
653	C₈	—	122	2	no	—
654	C₈	—	244	1	no	—
655	C₈	—	244	1	no	—
656	C₈	—	244	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	#16839810	1	2	yes	complemented
675	C₂²	C₂²×#11758196	1	1	yes	characteristic
676	C₂²	D₄×Dic₁₂₂	1	1	yes	characteristic
677	C₂²	#16840471	1	1	yes	characteristic
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	C₄×D₄×D₆₁	1	1	yes	characteristic
687	C₄	#16840241	1	1	yes	characteristic
688	C₄	D₄×C₂²⋊D₆₁	1	1	yes	characteristic
689	C₄	#16840411	1	1	yes	characteristic
690	C₂	—	2	1	no	—
691	C₂	—	2	1	no	—
692	C₂	—	2	2	no	—
693	C₂	—	4	1	no	—
694	C₂	—	4	1	no	—
695	C₂	—	4	1	no	—
696	C₂	D₄×#11758196	1	1	yes	characteristic
697	C₂	C₂×#16839810	1	1	yes	characteristic
698	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	#22668
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. C₂×#16839810	C₂	semidirect
4. C₂²×#14519712	C₂	semidirect
5. #21446594	C₂	semidirect
6. #21446592	C₂	semidirect
7. #21446024	C₂	semidirect
8. #21446024	C₂	semidirect
9. #21446023	C₂	semidirect
10. #21446023	C₂	semidirect
11. #21445993	C₂	semidirect
12. #21445859	C₂	semidirect
13. #21445855	C₂	semidirect
14. #21445726	C₂	semidirect
98. #14519712	D₄	semidirect
325. C₂²×C₆₁	#430	semidirect
414. C₆₁	#22668	semidirect
674. C₂²	#16839810	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
C₂×#16839810	2
C₂²×#14519712	2
#21446594	2
#21446592	2
#21446024	2
#21446023	2
#21445993	2
#21445859	2
#21445855	2
#21445726	2
D₄×M₁₆×C₆₁	2
#22668	61