Subgroups — Q₁₆×#41×C₆₁ #29564862

Order 15616.

1826 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₆₁	C₂	1	2	yes	maximal
2	C₆₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3363	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3338	C₂	1	3	yes	maximal, complemented
6	C₆₁×#3299	C₂	1	6	yes	maximal, complemented
7	D₄×Q₁₆×C₆₁	C₂	1	3	yes	maximal, complemented
8	C₆₁×#3170	C₂	1	3	yes	maximal, complemented
9	C₆₁×#3104	C₂	1	6	yes	maximal, complemented
10	C₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×Q₁₆×C₆₁	C₂	1	3	yes	maximal, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	3	yes	—
13	Q₈²×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#557	—	2	2	no	—
15	C₆₁×#557	C₂²	1	2	yes	—
16	C₆₁×#554	—	2	6	no	—
17	C₆₁×#554	C₂²	1	6	yes	—
18	D₄×Q₈×C₆₁	C₂²	1	6	yes	—
19	C₆₁×#533	—	2	6	no	—
20	C₆₁×#533	C₂²	1	6	yes	—
21	C₄×#41×C₆₁	—	2	2	no	—
22	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₁	C₂²	1	6	yes	—
24	C₆₁×#500	C₂²	1	3	yes	—
25	C₆₁×#494	C₂²	1	3	yes	—
26	C₆₁×#487	C₂²	1	6	yes	—
27	C₆₁×#484	C₂²	1	12	yes	—
28	C₆₁×#477	C₂²	1	6	yes	—
29	C₆₁×#477	C₂²	1	6	yes	—
30	C₆₁×#467	C₂²	1	6	yes	—
31	C₆₁×#467	C₂²	1	6	yes	—
32	C₆₁×#462	C₂²	1	6	yes	—
33	C₆₁×#462	C₂²	1	6	yes	—
34	C₆₁×#451	C₂²	1	12	yes	—
35	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₄×Q₁₆×C₆₁	C₂²	1	6	yes	—
38	C₄×Q₁₆×C₆₁	C₂²	1	3	yes	—
39	C₄×Q₁₆×C₆₁	C₂²	1	6	yes	—
40	C₄×Q₁₆×C₆₁	C₂²	1	6	yes	—
41	C₄×Q₁₆×C₆₁	C₂²	1	3	yes	—
42	C₄×Q₁₆×C₆₁	C₂²	1	3	yes	—
43	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
44	C₈×D₄×C₆₁	C₂²	1	3	yes	—
45	C₈×D₄×C₆₁	C₂²	1	3	yes	—
46	C₆₁×#431	C₂²	1	3	yes	—
47	C₂×#107×C₆₁	C₂²	1	3	yes	—
48	C₂×#103×C₆₁	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₆₁	C₂²	1	3	yes	—
50	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₆₁	C₂³	1	6	yes	—
52	C₂×Q₁₆×C₆₁	—	2	12	no	—
53	C₂×Q₁₆×C₆₁	C₂³	1	6	yes	—
54	C₂×Q₁₆×C₆₁	C₂³	1	3	yes	—
55	C₂×Q₁₆×C₆₁	C₂³	1	6	yes	—
56	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂³	1	3	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	3	yes	—
59	C₄⋊Q₈×C₆₁	—	2	6	no	—
60	C₄⋊Q₈×C₆₁	—	2	6	no	—
61	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
62	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
63	#125×C₆₁	—	2	6	no	—
64	#125×C₆₁	—	2	6	no	—
65	#125×C₆₁	—	2	6	no	—
66	C₂²⋊Q₈×C₆₁	—	2	6	no	—
67	C₂²⋊Q₈×C₆₁	—	2	12	no	—
68	C₂²⋊Q₈×C₆₁	—	2	12	no	—
69	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
70	C₄×Q₈×C₆₁	—	2	2	no	—
71	C₄×Q₈×C₆₁	—	2	2	no	—
72	C₄×Q₈×C₆₁	—	2	6	no	—
73	C₄×Q₈×C₆₁	—	2	6	no	—
74	C₄×Q₈×C₆₁	—	2	6	no	—
75	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
76	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
77	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
78	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
79	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
80	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₆₁	—	2	6	no	—
82	C₄×D₄×C₆₁	—	2	6	no	—
83	C₄×D₄×C₆₁	D₄	1	3	yes	—
84	C₄×D₄×C₆₁	C₂³	1	3	yes	—
85	#117×C₆₁	—	2	6	no	—
86	#117×C₆₁	D₄	1	3	yes	—
87	C₂×C₄⋊C₄×C₆₁	—	2	6	no	—
88	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
89	C₂×C₄²×C₆₁	—	2	6	no	—
90	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
91	#107×C₆₁	C₂³	1	1	yes	characteristic
92	#107×C₆₁	C₂³	1	3	yes	—
93	#107×C₆₁	C₂³	1	6	yes	—
94	#107×C₆₁	C₂³	1	6	yes	—
95	C₄⋊C₈×C₆₁	C₂³	1	3	yes	—
96	C₄⋊C₈×C₆₁	C₂³	1	3	yes	—
97	#103×C₆₁	C₂³	1	2	yes	—
98	#103×C₆₁	C₂³	1	6	yes	—
99	#103×C₆₁	C₂³	1	6	yes	—
100	#103×C₆₁	C₂³	1	6	yes	—
101	#103×C₆₁	C₂³	1	12	yes	—
102	C₂²⋊C₈×C₆₁	C₂³	1	6	yes	—
103	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₄×C₈×C₆₁	C₂³	1	3	yes	—
105	C₄×C₈×C₆₁	C₂³	1	3	yes	—
106	C₄×C₈×C₆₁	C₂³	1	3	yes	—
107	#41×C₆₁	Q₁₆	1	8	yes	direct product factor
108	C₂×Q₈×C₆₁	—	2	6	no	—
109	C₂×Q₈×C₆₁	—	2	6	no	—
110	C₂×Q₈×C₆₁	—	2	12	no	—
111	C₂×Q₈×C₆₁	—	4	6	no	—
112	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
114	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
115	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
116	C₂²×C₄×C₆₁	—	2	6	no	—
117	C₂²×C₄×C₆₁	—	2	6	no	—
118	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
119	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
120	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
121	Q₁₆×C₆₁	—	2	12	no	—
122	Q₁₆×C₆₁	—	2	6	no	—
123	Q₁₆×C₆₁	—	4	6	no	—
124	Q₁₆×C₆₁	#41	1	4	yes	direct product factor
125	C₂×C₈×C₆₁	—	2	6	no	—
126	C₂×C₈×C₆₁	—	4	3	no	—
127	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
129	C₂×C₈×C₆₁	C₂⁴	1	3	yes	—
130	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	2	6	no	—
133	C₄⋊C₄×C₆₁	—	2	6	no	—
134	C₄⋊C₄×C₆₁	—	2	6	no	—
135	C₄⋊C₄×C₆₁	—	2	6	no	—
136	C₄⋊C₄×C₆₁	—	2	6	no	—
137	C₄⋊C₄×C₆₁	—	2	6	no	—
138	C₄⋊C₄×C₆₁	—	2	6	no	—
139	C₄⋊C₄×C₆₁	—	2	12	no	—
140	C₄⋊C₄×C₆₁	C₂×D₄	1	3	yes	—
141	C₄⋊C₄×C₆₁	C₂×D₄	1	3	yes	—
142	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
143	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
144	C₂²⋊C₄×C₆₁	—	2	12	no	—
145	C₂²⋊C₄×C₆₁	C₂×D₄	1	6	yes	—
146	C₄²×C₆₁	—	2	6	no	—
147	C₄²×C₆₁	—	2	6	no	—
148	C₄²×C₆₁	—	2	2	no	—
149	C₄²×C₆₁	—	2	6	no	—
150	C₄²×C₆₁	C₂×D₄	1	3	yes	—
151	C₄²×C₆₁	C₂×D₄	1	3	yes	—
152	C₄²×C₆₁	C₂⁴	1	3	yes	—
153	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
154	C₂³×C₆₁	C₂²×D₄	1	3	yes	—
155	Q₈×C₆₁	—	2	2	no	—
156	Q₈×C₆₁	—	2	6	no	—
157	Q₈×C₆₁	—	2	6	no	—
158	Q₈×C₆₁	—	4	12	no	—
159	Q₈×C₆₁	—	8	6	no	—
160	Q₈×C₆₁	C₂×Q₁₆	1	4	yes	complemented
161	Q₈×C₆₁	C₂×#41	1	4	yes	—
162	D₄×C₆₁	C₂×Q₁₆	1	12	yes	complemented
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	3	no	—
165	C₂×C₄×C₆₁	—	2	3	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	6	no	—
168	C₂×C₄×C₆₁	—	2	6	no	—
169	C₂×C₄×C₆₁	—	4	3	no	—
170	C₂×C₄×C₆₁	—	4	12	no	—
171	C₂×C₄×C₆₁	—	8	6	no	—
172	C₂×C₄×C₆₁	C₂×Q₁₆	1	12	yes	complemented
173	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
175	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
176	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
177	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
179	C₈×C₆₁	—	2	3	no	—
180	C₈×C₆₁	—	2	1	no	—
181	C₈×C₆₁	—	2	3	no	—
182	C₈×C₆₁	C₂×#41	1	2	yes	—
183	Q₁₆×#41	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₆₁	—	2	3	no	—
185	C₂²×C₆₁	—	2	3	no	—
186	C₂²×C₆₁	C₂²×Q₁₆	1	6	yes	—
187	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
188	C₄×C₆₁	—	2	1	no	—
189	C₄×C₆₁	—	2	3	no	—
190	C₄×C₆₁	—	2	3	no	—
191	C₄×C₆₁	—	2	4	no	—
192	C₄×C₆₁	—	4	2	no	—
193	C₄×C₆₁	—	4	6	no	—
194	C₄×C₆₁	—	4	6	no	—
195	C₄×C₆₁	C₂²×Q₁₆	1	2	yes	—
196	C₄×C₆₁	C₂²×Q₁₆	1	6	yes	—
197	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
198	C₄×C₆₁	#585	1	1	yes	characteristic
199	Q₈×#41	C₂×C₆₁	1	2	yes	—
200	#3395	C₂×C₆₁	1	1	yes	characteristic, complemented
201	Q₈×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#3363	C₂×C₆₁	1	2	yes	complemented
203	#3338	C₂×C₆₁	1	3	yes	complemented
204	#3299	C₂×C₆₁	1	6	yes	complemented
205	D₄×Q₁₆	C₂×C₆₁	1	3	yes	complemented
206	#3170	C₂×C₆₁	1	3	yes	complemented
207	#3104	C₂×C₆₁	1	6	yes	complemented
208	C₈×#41	C₂×C₆₁	1	1	yes	characteristic
209	C₂×C₄×Q₁₆	C₂×C₆₁	1	3	yes	complemented
210	C₂×C₆₁	—	2	6	no	—
211	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
212	C₂×C₆₁	C₂³×Q₁₆	1	1	yes	characteristic
213	C₂×C₆₁	#3584	1	1	yes	characteristic
214	C₂²×Q₁₆	C₂²×C₆₁	1	3	yes	—
215	Q₈²	C₂²×C₆₁	1	2	yes	—
216	#557	—	2	2	no	—
217	#557	C₂²×C₆₁	1	2	yes	—
218	#554	—	2	6	no	—
219	#554	C₂²×C₆₁	1	6	yes	—
220	D₄×Q₈	C₂²×C₆₁	1	6	yes	—
221	#533	—	2	6	no	—
222	#533	C₂²×C₆₁	1	6	yes	—
223	C₄×#41	—	2	2	no	—
224	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂²×C₆₁	1	6	yes	—
226	#500	C₂²×C₆₁	1	3	yes	—
227	#494	C₂²×C₆₁	1	3	yes	—
228	#487	C₂²×C₆₁	1	6	yes	—
229	#484	C₂²×C₆₁	1	12	yes	—
230	#477	C₂²×C₆₁	1	6	yes	—
231	#477	C₂²×C₆₁	1	6	yes	—
232	#467	C₂²×C₆₁	1	6	yes	—
233	#467	C₂²×C₆₁	1	6	yes	—
234	#462	C₂²×C₆₁	1	6	yes	—
235	#462	C₂²×C₆₁	1	6	yes	—
236	#451	C₂²×C₆₁	1	12	yes	—
237	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
238	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
239	C₄×Q₁₆	C₂²×C₆₁	1	3	yes	—
240	C₄×Q₁₆	C₂²×C₆₁	1	6	yes	—
241	C₄×Q₁₆	C₂²×C₆₁	1	6	yes	—
242	C₄×Q₁₆	C₂²×C₆₁	1	6	yes	—
243	C₄×Q₁₆	C₂²×C₆₁	1	3	yes	—
244	C₄×Q₁₆	C₂²×C₆₁	1	3	yes	—
245	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
246	C₈×D₄	C₂²×C₆₁	1	3	yes	—
247	C₈×D₄	C₂²×C₆₁	1	3	yes	—
248	#431	C₂²×C₆₁	1	3	yes	—
249	C₂×#107	C₂²×C₆₁	1	3	yes	—
250	C₂×#103	C₂²×C₆₁	1	6	yes	—
251	C₂×C₄×C₈	C₂²×C₆₁	1	3	yes	—
252	C₆₁	Q₁₆×#41	1	1	yes	characteristic, direct product factor, Sylow
253	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
254	C₂²×Q₈	C₂³×C₆₁	1	6	yes	—
255	C₂×Q₁₆	—	2	12	no	—
256	C₂×Q₁₆	C₂³×C₆₁	1	6	yes	—
257	C₂×Q₁₆	C₂³×C₆₁	1	3	yes	—
258	C₂×Q₁₆	C₂³×C₆₁	1	6	yes	—
259	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₆₁	1	3	yes	—
261	C₂²×C₈	C₂³×C₆₁	1	3	yes	—
262	C₄⋊Q₈	—	2	6	no	—
263	C₄⋊Q₈	—	2	6	no	—
264	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
265	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
266	#125	—	2	6	no	—
267	#125	—	2	6	no	—
268	#125	—	2	6	no	—
269	C₂²⋊Q₈	—	2	6	no	—
270	C₂²⋊Q₈	—	2	12	no	—
271	C₂²⋊Q₈	—	2	12	no	—
272	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	6	no	—
276	C₄×Q₈	—	2	6	no	—
277	C₄×Q₈	—	2	6	no	—
278	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
279	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
280	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
281	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
282	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
283	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₄×D₄	—	2	6	no	—
285	C₄×D₄	—	2	6	no	—
286	C₄×D₄	D₄×C₆₁	1	3	yes	—
287	C₄×D₄	C₂³×C₆₁	1	3	yes	—
288	#117	—	2	6	no	—
289	#117	D₄×C₆₁	1	3	yes	—
290	C₂×C₄⋊C₄	—	2	6	no	—
291	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
292	C₂×C₄²	—	2	6	no	—
293	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
294	#107	C₂³×C₆₁	1	1	yes	characteristic
295	#107	C₂³×C₆₁	1	3	yes	—
296	#107	C₂³×C₆₁	1	6	yes	—
297	#107	C₂³×C₆₁	1	6	yes	—
298	C₄⋊C₈	C₂³×C₆₁	1	3	yes	—
299	C₄⋊C₈	C₂³×C₆₁	1	3	yes	—
300	#103	C₂³×C₆₁	1	2	yes	—
301	#103	C₂³×C₆₁	1	6	yes	—
302	#103	C₂³×C₆₁	1	6	yes	—
303	#103	C₂³×C₆₁	1	6	yes	—
304	#103	C₂³×C₆₁	1	12	yes	—
305	C₂²⋊C₈	C₂³×C₆₁	1	6	yes	—
306	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
307	C₄×C₈	C₂³×C₆₁	1	3	yes	—
308	C₄×C₈	C₂³×C₆₁	1	3	yes	—
309	C₄×C₈	C₂³×C₆₁	1	3	yes	—
310	#41	Q₁₆×C₆₁	1	8	yes	direct product factor
311	C₂×Q₈	—	2	6	no	—
312	C₂×Q₈	—	2	6	no	—
313	C₂×Q₈	—	2	12	no	—
314	C₂×Q₈	—	4	6	no	—
315	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
316	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
317	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
318	C₂×D₄	C₂×D₄×C₆₁	1	3	yes	—
319	C₂²×C₄	—	2	6	no	—
320	C₂²×C₄	—	2	6	no	—
321	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
322	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
323	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
324	Q₁₆	—	2	12	no	—
325	Q₁₆	—	2	6	no	—
326	Q₁₆	—	4	6	no	—
327	Q₁₆	#41×C₆₁	1	4	yes	direct product factor
328	C₂×C₈	—	2	6	no	—
329	C₂×C₈	—	4	3	no	—
330	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
331	C₂×C₈	C₂⁴×C₆₁	1	3	yes	—
332	C₂×C₈	C₂⁴×C₆₁	1	3	yes	—
333	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	6	no	—
336	C₄⋊C₄	—	2	6	no	—
337	C₄⋊C₄	—	2	6	no	—
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	—	2	6	no	—
340	C₄⋊C₄	—	2	6	no	—
341	C₄⋊C₄	—	2	6	no	—
342	C₄⋊C₄	—	2	12	no	—
343	C₄⋊C₄	C₂×D₄×C₆₁	1	3	yes	—
344	C₄⋊C₄	C₂×D₄×C₆₁	1	3	yes	—
345	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
346	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
347	C₂²⋊C₄	—	2	12	no	—
348	C₂²⋊C₄	C₂×D₄×C₆₁	1	6	yes	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	6	no	—
351	C₄²	—	2	6	no	—
352	C₄²	—	2	6	no	—
353	C₄²	C₂×D₄×C₆₁	1	3	yes	—
354	C₄²	C₂×D₄×C₆₁	1	3	yes	—
355	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
356	C₄²	C₂⁴×C₆₁	1	3	yes	—
357	C₂³	C₂²×D₄×C₆₁	1	3	yes	—
358	Q₈	—	2	2	no	—
359	Q₈	—	2	6	no	—
360	Q₈	—	2	6	no	—
361	Q₈	—	4	12	no	—
362	Q₈	—	8	6	no	—
363	Q₈	C₂×Q₁₆×C₆₁	1	4	yes	complemented
364	Q₈	C₂×#41×C₆₁	1	4	yes	—
365	D₄	C₂×Q₁₆×C₆₁	1	12	yes	complemented
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	3	no	—
368	C₂×C₄	—	2	3	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	4	3	no	—
373	C₂×C₄	—	4	12	no	—
374	C₂×C₄	—	8	6	no	—
375	C₂×C₄	C₂×Q₁₆×C₆₁	1	12	yes	complemented
376	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
378	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
379	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
380	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
381	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
382	C₈	—	2	3	no	—
383	C₈	—	2	1	no	—
384	C₈	—	2	3	no	—
385	C₈	C₂×#41×C₆₁	1	2	yes	—
386	C₂²	—	2	3	no	—
387	C₂²	—	2	3	no	—
388	C₂²	C₂²×Q₁₆×C₆₁	1	6	yes	—
389	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	3	no	—
392	C₄	—	2	3	no	—
393	C₄	—	2	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	6	no	—
396	C₄	—	4	6	no	—
397	C₄	C₂²×Q₁₆×C₆₁	1	2	yes	—
398	C₄	C₂²×Q₁₆×C₆₁	1	6	yes	—
399	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
400	C₄	C₆₁×#585	1	1	yes	characteristic
401	C₂	—	2	6	no	—
402	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
403	C₂	C₂³×Q₁₆×C₆₁	1	1	yes	characteristic
404	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂²×C₆₁	C₂³×D₄
prime radical	C₂×#41×C₆₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3395	C₂	semidirect
3. Q₈×Q₁₆×C₆₁	C₂	semidirect
4. C₆₁×#3363	C₂	semidirect
5. C₆₁×#3338	C₂	semidirect
6. C₆₁×#3299	C₂	semidirect
7. D₄×Q₁₆×C₆₁	C₂	semidirect
8. C₆₁×#3170	C₂	semidirect
9. C₆₁×#3104	C₂	semidirect
11. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
107. #41×C₆₁	Q₁₆	direct (N × H)
124. Q₁₆×C₆₁	#41	direct (N × H)
160. Q₈×C₆₁	C₂×Q₁₆	semidirect
162. D₄×C₆₁	C₂×Q₁₆	semidirect
172. C₂×C₄×C₆₁	C₂×Q₁₆	semidirect
183. Q₁₆×#41	C₆₁	direct (N × H)
200. #3395	C₂×C₆₁	semidirect
201. Q₈×Q₁₆	C₂×C₆₁	semidirect
202. #3363	C₂×C₆₁	semidirect
203. #3338	C₂×C₆₁	semidirect
204. #3299	C₂×C₆₁	semidirect
205. D₄×Q₁₆	C₂×C₆₁	semidirect
206. #3170	C₂×C₆₁	semidirect
207. #3104	C₂×C₆₁	semidirect
209. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
252. C₆₁	Q₁₆×#41	direct (N × H)
310. #41	Q₁₆×C₆₁	direct (N × H)
327. Q₁₆	#41×C₆₁	direct (N × H)
363. Q₈	C₂×Q₁₆×C₆₁	semidirect
365. D₄	C₂×Q₁₆×C₆₁	semidirect
375. C₂×C₄	C₂×Q₁₆×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#41×C₆₁	2
C₆₁×#3395	2
Q₈×Q₁₆×C₆₁	2
C₆₁×#3363	2
C₆₁×#3338	2
C₆₁×#3299	2
D₄×Q₁₆×C₆₁	2
C₆₁×#3170	2
C₆₁×#3104	2
C₈×#41×C₆₁	2
C₂×C₄×Q₁₆×C₆₁	2
Q₁₆×#41	61

Subgroups — Q16×#41×C61 #29564862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#41×C₆₁ #29564862