Subgroups — C₂×D₄×SD₁₆×C₆₁ #29564474

Order 15616.

3226 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₆₁	C₂	1	1	yes	maximal, characteristic
4	D₄×SD₁₆×C₆₁	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#465	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#448	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#450	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₈×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₆₁	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₆₁	—	2	1	no	—
15	C₂³×D₄×C₆₁	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₆₁	—	2	16	no	—
17	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
21	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
22	C₂²×SD₁₆×C₆₁	C₂²	1	16	yes	complemented
23	C₂³×C₈×C₆₁	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₆₁	—	2	4	no	—
25	D₄×Q₈×C₆₁	C₂²	1	8	yes	complemented
26	D₄²×C₆₁	—	2	4	no	—
27	D₄²×C₆₁	C₂²	1	8	yes	—
28	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
32	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
33	C₂×#121×C₆₁	—	2	1	no	—
34	C₂×#121×C₆₁	C₂²	1	2	yes	—
35	C₂×#120×C₆₁	—	2	2	no	—
36	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₆₁	—	2	1	no	—
38	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#492	C₂²	1	8	yes	complemented
41	C₆₁×#465	C₂²	1	16	yes	complemented
42	C₆₁×#461	C₂²	1	8	yes	complemented
43	C₆₁×#460	C₂²	1	8	yes	complemented
44	C₆₁×#450	C₂²	1	16	yes	complemented
45	C₆₁×#448	C₂²	1	16	yes	complemented
46	C₄×SD₁₆×C₆₁	C₂²	1	8	yes	complemented
47	C₈×D₄×C₆₁	C₂²	1	8	yes	complemented
48	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
50	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
51	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
52	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
53	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
54	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
56	C₂⁵×C₆₁	—	2	2	no	—
57	C₂²×Q₈×C₆₁	—	2	2	no	—
58	C₂²×Q₈×C₆₁	—	2	4	no	—
59	C₂²×Q₈×C₆₁	—	2	8	no	—
60	C₂²×Q₈×C₆₁	—	4	4	no	—
61	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
62	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₆₁	C₂³	1	8	yes	complemented
64	C₂²×D₄×C₆₁	—	2	8	no	—
65	C₂²×D₄×C₆₁	—	2	2	no	—
66	C₂²×D₄×C₆₁	—	2	8	no	—
67	C₂²×D₄×C₆₁	—	2	1	no	—
68	C₂²×D₄×C₆₁	—	2	4	no	—
69	C₂²×D₄×C₆₁	—	2	2	no	—
70	C₂²×D₄×C₆₁	—	2	1	no	—
71	C₂²×D₄×C₆₁	—	4	4	no	—
72	C₂²×D₄×C₆₁	—	4	8	no	—
73	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
74	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
75	C₂²×D₄×C₆₁	C₂³	1	8	yes	—
76	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₁	—	2	2	no	—
78	C₂³×C₄×C₆₁	—	2	1	no	—
79	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
80	C₂×SD₁₆×C₆₁	—	2	8	no	—
81	C₂×SD₁₆×C₆₁	—	2	8	no	—
82	C₂×SD₁₆×C₆₁	—	2	64	no	—
83	C₂×SD₁₆×C₆₁	—	2	8	no	—
84	C₂×SD₁₆×C₆₁	—	4	4	no	—
85	C₂×SD₁₆×C₆₁	D₄	1	8	yes	direct product factor
86	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
87	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
88	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	complemented
89	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	complemented
90	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	complemented
91	C₂²×C₈×C₆₁	—	2	8	no	—
92	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
93	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₆₁	C₂³	1	8	yes	complemented
96	C₄⋊Q₈×C₆₁	—	2	8	no	—
97	C₄⋊Q₈×C₆₁	—	2	2	no	—
98	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	complemented
99	#127×C₆₁	—	2	2	no	—
100	#127×C₆₁	C₂³	1	4	yes	—
101	C₂²⋊Q₈×C₆₁	—	2	4	no	—
102	C₂²⋊Q₈×C₆₁	—	2	16	no	—
103	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	complemented
104	#121×C₆₁	—	2	4	no	—
105	#121×C₆₁	—	2	8	no	—
106	#121×C₆₁	C₂³	1	8	yes	—
107	#120×C₆₁	—	2	16	no	—
108	C₄×Q₈×C₆₁	—	2	2	no	—
109	C₄×Q₈×C₆₁	C₂³	1	4	yes	complemented
110	C₄×D₄×C₆₁	—	2	8	no	—
111	C₄×D₄×C₆₁	—	2	2	no	—
112	C₄×D₄×C₆₁	D₄	1	4	yes	—
113	C₄×D₄×C₆₁	C₂³	1	4	yes	—
114	C₄×D₄×C₆₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
116	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
118	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
119	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
126	C₂×C₄²×C₆₁	—	2	1	no	—
127	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
128	#106×C₆₁	C₂³	1	4	yes	complemented
129	C₄⋊C₈×C₆₁	C₂³	1	4	yes	complemented
130	#103×C₆₁	C₂³	1	4	yes	complemented
131	#103×C₆₁	C₂³	1	8	yes	complemented
132	#102×C₆₁	C₂³	1	4	yes	—
133	#102×C₆₁	C₂³	1	8	yes	complemented
134	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	complemented
135	C₄×C₈×C₆₁	C₂³	1	4	yes	complemented
136	C₂⁴×C₆₁	—	2	1	no	—
137	C₂⁴×C₆₁	—	2	2	no	—
138	C₂⁴×C₆₁	—	2	8	no	—
139	C₂⁴×C₆₁	—	4	8	no	—
140	C₂⁴×C₆₁	—	4	8	no	—
141	C₂⁴×C₆₁	—	8	4	no	—
142	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₆₁	—	2	1	no	—
144	C₂×Q₈×C₆₁	—	2	2	no	—
145	C₂×Q₈×C₆₁	—	2	8	no	—
146	C₂×Q₈×C₆₁	—	2	2	no	—
147	C₂×Q₈×C₆₁	—	2	16	no	—
148	C₂×Q₈×C₆₁	—	2	4	no	—
149	C₂×Q₈×C₆₁	—	2	4	no	—
150	C₂×Q₈×C₆₁	—	4	8	no	—
151	C₂×Q₈×C₆₁	—	4	8	no	—
152	C₂×Q₈×C₆₁	—	4	16	no	—
153	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	complemented
154	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
155	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
156	C₂×D₄×C₆₁	—	2	16	no	—
157	C₂×D₄×C₆₁	—	2	8	no	—
158	C₂×D₄×C₆₁	—	2	1	no	—
159	C₂×D₄×C₆₁	—	2	4	no	—
160	C₂×D₄×C₆₁	—	2	8	no	—
161	C₂×D₄×C₆₁	—	2	2	no	—
162	C₂×D₄×C₆₁	—	2	4	no	—
163	C₂×D₄×C₆₁	—	2	4	no	—
164	C₂×D₄×C₆₁	—	2	2	no	—
165	C₂×D₄×C₆₁	—	2	4	no	—
166	C₂×D₄×C₆₁	—	4	8	no	—
167	C₂×D₄×C₆₁	—	4	16	no	—
168	C₂×D₄×C₆₁	—	4	8	no	—
169	C₂×D₄×C₆₁	—	4	8	no	—
170	C₂×D₄×C₆₁	—	4	32	no	—
171	C₂×D₄×C₆₁	—	4	4	no	—
172	C₂×D₄×C₆₁	—	8	2	no	—
173	C₂×D₄×C₆₁	SD₁₆	1	8	yes	direct product factor
174	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
175	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
177	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₆₁	—	2	1	no	—
179	C₂²×C₄×C₆₁	—	2	4	no	—
180	C₂²×C₄×C₆₁	—	2	4	no	—
181	C₂²×C₄×C₆₁	—	2	8	no	—
182	C₂²×C₄×C₆₁	—	2	1	no	—
183	C₂²×C₄×C₆₁	—	2	1	no	—
184	C₂²×C₄×C₆₁	—	2	2	no	—
185	C₂²×C₄×C₆₁	—	2	4	no	—
186	C₂²×C₄×C₆₁	—	4	8	no	—
187	C₂²×C₄×C₆₁	—	4	4	no	—
188	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
194	SD₁₆×C₆₁	—	2	16	no	—
195	SD₁₆×C₆₁	—	2	16	no	—
196	SD₁₆×C₆₁	—	2	16	no	—
197	SD₁₆×C₆₁	—	4	8	no	—
198	SD₁₆×C₆₁	C₂×D₄	1	16	yes	direct product factor
199	C₂×C₈×C₆₁	—	2	4	no	—
200	C₂×C₈×C₆₁	—	2	2	no	—
201	C₂×C₈×C₆₁	—	2	16	no	—
202	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	complemented
203	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
204	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
205	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
206	C₄⋊C₄×C₆₁	—	2	4	no	—
207	C₄⋊C₄×C₆₁	—	2	4	no	—
208	C₄⋊C₄×C₆₁	—	2	4	no	—
209	C₄⋊C₄×C₆₁	—	2	8	no	—
210	C₄⋊C₄×C₆₁	—	2	1	no	—
211	C₄⋊C₄×C₆₁	—	2	1	no	—
212	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
213	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
214	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
215	C₂²⋊C₄×C₆₁	—	2	8	no	—
216	C₂²⋊C₄×C₆₁	—	2	4	no	—
217	C₂²⋊C₄×C₆₁	—	2	8	no	—
218	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
219	C₄²×C₆₁	—	2	4	no	—
220	C₄²×C₆₁	C₂×D₄	1	2	yes	—
221	C₄²×C₆₁	C₂⁴	1	2	yes	—
222	C₂³×C₆₁	—	2	4	no	—
223	C₂³×C₆₁	—	2	4	no	—
224	C₂³×C₆₁	—	2	4	no	—
225	C₂³×C₆₁	—	2	2	no	—
226	C₂³×C₆₁	—	2	4	no	—
227	C₂³×C₆₁	—	4	16	no	—
228	C₂³×C₆₁	—	4	2	no	—
229	C₂³×C₆₁	—	4	2	no	—
230	C₂³×C₆₁	—	4	4	no	—
231	C₂³×C₆₁	—	4	4	no	—
232	C₂³×C₆₁	—	4	16	no	—
233	C₂³×C₆₁	—	4	4	no	—
234	C₂³×C₆₁	—	8	8	no	—
235	C₂³×C₆₁	—	8	32	no	—
236	C₂³×C₆₁	C₂×SD₁₆	1	8	yes	complemented
237	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
238	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₆₁	—	2	4	no	—
240	Q₈×C₆₁	—	2	2	no	—
241	Q₈×C₆₁	—	2	4	no	—
242	Q₈×C₆₁	—	2	4	no	—
243	Q₈×C₆₁	—	4	16	no	—
244	Q₈×C₆₁	—	4	4	no	—
245	Q₈×C₆₁	C₂²×D₄	1	4	yes	complemented
246	D₄×C₆₁	—	2	4	no	—
247	D₄×C₆₁	—	2	4	no	—
248	D₄×C₆₁	—	2	2	no	—
249	D₄×C₆₁	—	2	4	no	—
250	D₄×C₆₁	—	4	16	no	—
251	D₄×C₆₁	—	4	16	no	—
252	D₄×C₆₁	—	4	4	no	—
253	D₄×C₆₁	—	4	8	no	—
254	D₄×C₆₁	—	8	4	no	—
255	D₄×C₆₁	C₂×SD₁₆	1	16	yes	direct product factor
256	D₄×C₆₁	C₂²×D₄	1	4	yes	—
257	C₂×C₄×C₆₁	—	2	4	no	—
258	C₂×C₄×C₆₁	—	2	4	no	—
259	C₂×C₄×C₆₁	—	2	2	no	—
260	C₂×C₄×C₆₁	—	2	2	no	—
261	C₂×C₄×C₆₁	—	2	8	no	—
262	C₂×C₄×C₆₁	—	2	4	no	—
263	C₂×C₄×C₆₁	—	2	4	no	—
264	C₂×C₄×C₆₁	—	2	2	no	—
265	C₂×C₄×C₆₁	—	2	2	no	—
266	C₂×C₄×C₆₁	—	2	4	no	—
267	C₂×C₄×C₆₁	—	4	16	no	—
268	C₂×C₄×C₆₁	—	4	4	no	—
269	C₂×C₄×C₆₁	—	4	2	no	—
270	C₂×C₄×C₆₁	—	4	2	no	—
271	C₂×C₄×C₆₁	—	4	8	no	—
272	C₂×C₄×C₆₁	C₂×SD₁₆	1	4	yes	complemented
273	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
275	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
279	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
280	C₈×C₆₁	—	2	4	no	—
281	C₈×C₆₁	—	2	2	no	—
282	C₈×C₆₁	C₂²×D₄	1	4	yes	complemented
283	C₂×D₄×SD₁₆	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂²×C₆₁	—	2	4	no	—
285	C₂²×C₆₁	—	2	16	no	—
286	C₂²×C₆₁	—	2	4	no	—
287	C₂²×C₆₁	—	2	4	no	—
288	C₂²×C₆₁	—	4	8	no	—
289	C₂²×C₆₁	—	4	2	no	—
290	C₂²×C₆₁	—	4	2	no	—
291	C₂²×C₆₁	—	4	4	no	—
292	C₂²×C₆₁	—	4	4	no	—
293	C₂²×C₆₁	—	4	4	no	—
294	C₂²×C₆₁	—	8	32	no	—
295	C₂²×C₆₁	—	8	8	no	—
296	C₂²×C₆₁	D₄²	1	2	yes	—
297	C₂²×C₆₁	C₂²×SD₁₆	1	2	yes	—
298	C₂²×C₆₁	C₂²×SD₁₆	1	8	yes	complemented
299	C₂²×C₆₁	#577	1	2	yes	—
300	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
301	C₄×C₆₁	—	2	4	no	—
302	C₄×C₆₁	—	2	4	no	—
303	C₄×C₆₁	—	2	2	no	—
304	C₄×C₆₁	—	4	4	no	—
305	C₄×C₆₁	—	4	2	no	—
306	C₄×C₆₁	—	4	2	no	—
307	C₄×C₆₁	D₄²	1	2	yes	—
308	C₄×C₆₁	C₂²×SD₁₆	1	4	yes	complemented
309	C₄×C₆₁	C₂³×D₄	1	1	yes	characteristic
310	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
311	C₂³×SD₁₆	C₂×C₆₁	1	2	yes	complemented
312	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
313	C₂×D₄²	C₂×C₆₁	1	1	yes	characteristic
314	D₄×SD₁₆	C₂×C₆₁	1	16	yes	direct product factor
315	C₂×#492	C₂×C₆₁	1	1	yes	characteristic, complemented
316	C₂×#465	C₂×C₆₁	1	2	yes	complemented
317	C₂×#460	C₂×C₆₁	1	1	yes	characteristic, complemented
318	C₂×#461	C₂×C₆₁	1	1	yes	characteristic, complemented
319	C₂×#448	C₂×C₆₁	1	2	yes	complemented
320	C₂×#450	C₂×C₆₁	1	2	yes	complemented
321	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
322	C₂×C₈×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
323	C₂×C₆₁	—	2	8	no	—
324	C₂×C₆₁	—	4	4	no	—
325	C₂×C₆₁	—	8	4	no	—
326	C₂×C₆₁	D₄×SD₁₆	1	4	yes	direct product factor
327	C₂×C₆₁	C₂×D₄²	1	1	yes	characteristic
328	C₂×C₆₁	C₂³×SD₁₆	1	1	yes	characteristic
329	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
330	C₂³×Q₈	C₂²×C₆₁	1	2	yes	complemented
331	C₂³×D₄	—	2	1	no	—
332	C₂³×D₄	C₂²×C₆₁	1	2	yes	—
333	C₂²×SD₁₆	—	2	16	no	—
334	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
335	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
336	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
337	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
338	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
339	C₂²×SD₁₆	C₂²×C₆₁	1	16	yes	complemented
340	C₂³×C₈	C₂²×C₆₁	1	2	yes	complemented
341	D₄×Q₈	—	2	4	no	—
342	D₄×Q₈	C₂²×C₆₁	1	8	yes	complemented
343	D₄²	—	2	4	no	—
344	D₄²	C₂²×C₆₁	1	8	yes	—
345	C₂×C₄⋊Q₈	—	2	1	no	—
346	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
347	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×C₂²⋊Q₈	—	2	2	no	—
349	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
350	C₂×#121	—	2	1	no	—
351	C₂×#121	C₂²×C₆₁	1	2	yes	—
352	C₂×#120	—	2	2	no	—
353	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
354	C₂×C₄×D₄	—	2	1	no	—
355	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
357	#492	C₂²×C₆₁	1	8	yes	complemented
358	#465	C₂²×C₆₁	1	16	yes	complemented
359	#461	C₂²×C₆₁	1	8	yes	complemented
360	#460	C₂²×C₆₁	1	8	yes	complemented
361	#450	C₂²×C₆₁	1	16	yes	complemented
362	#448	C₂²×C₆₁	1	16	yes	complemented
363	C₄×SD₁₆	C₂²×C₆₁	1	8	yes	complemented
364	C₈×D₄	C₂²×C₆₁	1	8	yes	complemented
365	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
366	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
367	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
368	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
369	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
371	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	complemented
372	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
373	C₆₁	C₂×D₄×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
374	C₂⁵	—	2	2	no	—
375	C₂²×Q₈	—	2	2	no	—
376	C₂²×Q₈	—	2	4	no	—
377	C₂²×Q₈	—	2	8	no	—
378	C₂²×Q₈	—	4	4	no	—
379	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
380	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₆₁	1	8	yes	complemented
382	C₂²×D₄	—	2	8	no	—
383	C₂²×D₄	—	2	2	no	—
384	C₂²×D₄	—	2	8	no	—
385	C₂²×D₄	—	2	2	no	—
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	—	2	4	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	—	4	4	no	—
390	C₂²×D₄	—	4	8	no	—
391	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
392	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
393	C₂²×D₄	C₂³×C₆₁	1	8	yes	—
394	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
395	C₂³×C₄	—	2	2	no	—
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
398	C₂×SD₁₆	—	2	8	no	—
399	C₂×SD₁₆	—	2	8	no	—
400	C₂×SD₁₆	—	2	64	no	—
401	C₂×SD₁₆	—	2	8	no	—
402	C₂×SD₁₆	—	4	4	no	—
403	C₂×SD₁₆	D₄×C₆₁	1	8	yes	direct product factor
404	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
405	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
406	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	complemented
407	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	complemented
408	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	complemented
409	C₂²×C₈	—	2	8	no	—
410	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
411	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₆₁	1	8	yes	complemented
414	C₄⋊Q₈	—	2	8	no	—
415	C₄⋊Q₈	—	2	2	no	—
416	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	complemented
417	#127	—	2	2	no	—
418	#127	C₂³×C₆₁	1	4	yes	—
419	C₂²⋊Q₈	—	2	4	no	—
420	C₂²⋊Q₈	—	2	16	no	—
421	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	complemented
422	#121	—	2	4	no	—
423	#121	—	2	8	no	—
424	#121	C₂³×C₆₁	1	8	yes	—
425	#120	—	2	16	no	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	C₂³×C₆₁	1	4	yes	complemented
428	C₄×D₄	—	2	8	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	D₄×C₆₁	1	4	yes	—
431	C₄×D₄	C₂³×C₆₁	1	4	yes	—
432	C₄×D₄	C₂³×C₆₁	1	4	yes	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	2	no	—
437	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	2	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	2	no	—
443	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
446	#106	C₂³×C₆₁	1	4	yes	complemented
447	C₄⋊C₈	C₂³×C₆₁	1	4	yes	complemented
448	#103	C₂³×C₆₁	1	4	yes	complemented
449	#103	C₂³×C₆₁	1	8	yes	complemented
450	#102	C₂³×C₆₁	1	4	yes	—
451	#102	C₂³×C₆₁	1	8	yes	complemented
452	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	complemented
453	C₄×C₈	C₂³×C₆₁	1	4	yes	complemented
454	C₂⁴	—	2	1	no	—
455	C₂⁴	—	2	2	no	—
456	C₂⁴	—	2	8	no	—
457	C₂⁴	—	4	8	no	—
458	C₂⁴	—	4	8	no	—
459	C₂⁴	—	8	4	no	—
460	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	2	8	no	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	16	no	—
466	C₂×Q₈	—	2	4	no	—
467	C₂×Q₈	—	2	4	no	—
468	C₂×Q₈	—	4	8	no	—
469	C₂×Q₈	—	4	8	no	—
470	C₂×Q₈	—	4	16	no	—
471	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	complemented
472	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
473	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
474	C₂×D₄	—	2	16	no	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	8	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	4	8	no	—
485	C₂×D₄	—	4	16	no	—
486	C₂×D₄	—	4	8	no	—
487	C₂×D₄	—	4	8	no	—
488	C₂×D₄	—	4	32	no	—
489	C₂×D₄	—	4	4	no	—
490	C₂×D₄	—	8	2	no	—
491	C₂×D₄	SD₁₆×C₆₁	1	8	yes	direct product factor
492	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
493	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
494	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
495	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	8	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	4	8	no	—
505	C₂²×C₄	—	4	4	no	—
506	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
508	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
509	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
510	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
511	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
512	SD₁₆	—	2	16	no	—
513	SD₁₆	—	2	16	no	—
514	SD₁₆	—	2	16	no	—
515	SD₁₆	—	4	8	no	—
516	SD₁₆	C₂×D₄×C₆₁	1	16	yes	direct product factor
517	C₂×C₈	—	2	4	no	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	2	16	no	—
520	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	complemented
521	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
522	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
523	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	8	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
531	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
532	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
533	C₂²⋊C₄	—	2	8	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
537	C₄²	—	2	4	no	—
538	C₄²	C₂×D₄×C₆₁	1	2	yes	—
539	C₄²	C₂⁴×C₆₁	1	2	yes	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	4	16	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	16	no	—
551	C₂³	—	4	4	no	—
552	C₂³	—	8	8	no	—
553	C₂³	—	8	32	no	—
554	C₂³	C₂×SD₁₆×C₆₁	1	8	yes	complemented
555	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
556	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
557	Q₈	—	2	4	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	2	4	no	—
560	Q₈	—	2	4	no	—
561	Q₈	—	4	16	no	—
562	Q₈	—	4	4	no	—
563	Q₈	C₂²×D₄×C₆₁	1	4	yes	complemented
564	D₄	—	2	4	no	—
565	D₄	—	2	4	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	4	no	—
568	D₄	—	4	16	no	—
569	D₄	—	4	16	no	—
570	D₄	—	4	4	no	—
571	D₄	—	4	8	no	—
572	D₄	—	8	4	no	—
573	D₄	C₂×SD₁₆×C₆₁	1	16	yes	direct product factor
574	D₄	C₂²×D₄×C₆₁	1	4	yes	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	4	16	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	8	no	—
590	C₂×C₄	C₂×SD₁₆×C₆₁	1	4	yes	complemented
591	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
596	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
597	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
598	C₈	—	2	4	no	—
599	C₈	—	2	2	no	—
600	C₈	C₂²×D₄×C₆₁	1	4	yes	complemented
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	16	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	8	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	8	32	no	—
612	C₂²	—	8	8	no	—
613	C₂²	D₄²×C₆₁	1	2	yes	—
614	C₂²	C₂²×SD₁₆×C₆₁	1	2	yes	—
615	C₂²	C₂²×SD₁₆×C₆₁	1	8	yes	complemented
616	C₂²	C₆₁×#577	1	2	yes	—
617	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	4	no	—
620	C₄	—	2	4	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	4	no	—
624	C₄	D₄²×C₆₁	1	2	yes	—
625	C₄	C₂²×SD₁₆×C₆₁	1	4	yes	complemented
626	C₄	C₂³×D₄×C₆₁	1	1	yes	characteristic
627	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
628	C₂	—	2	8	no	—
629	C₂	—	4	4	no	—
630	C₂	—	8	4	no	—
631	C₂	D₄×SD₁₆×C₆₁	1	4	yes	direct product factor
632	C₂	C₂×D₄²×C₆₁	1	1	yes	characteristic
633	C₂	C₂³×SD₁₆×C₆₁	1	1	yes	characteristic
634	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×D₄²×C₆₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×SD₁₆×C₆₁	C₂	semidirect
2. C₂×D₄×Q₈×C₆₁	C₂	semidirect
4. D₄×SD₁₆×C₆₁	C₂	direct (N × H)
5. C₂×C₆₁×#492	C₂	semidirect
6. C₂×C₆₁×#465	C₂	semidirect
7. C₂×C₆₁×#460	C₂	semidirect
8. C₂×C₆₁×#461	C₂	semidirect
9. C₂×C₆₁×#448	C₂	semidirect
10. C₂×C₆₁×#450	C₂	semidirect
11. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
12. C₂×C₈×D₄×C₆₁	C₂	semidirect
13. C₂³×Q₈×C₆₁	C₂²	semidirect
19. C₂²×SD₁₆×C₆₁	C₂²	semidirect
20. C₂²×SD₁₆×C₆₁	C₂²	semidirect
21. C₂²×SD₁₆×C₆₁	C₂²	semidirect
22. C₂²×SD₁₆×C₆₁	C₂²	semidirect
23. C₂³×C₈×C₆₁	C₂²	semidirect
25. D₄×Q₈×C₆₁	C₂²	semidirect
29. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
36. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
40. C₆₁×#492	C₂²	semidirect
41. C₆₁×#465	C₂²	semidirect
42. C₆₁×#461	C₂²	semidirect
43. C₆₁×#460	C₂²	semidirect
44. C₆₁×#450	C₂²	semidirect
45. C₆₁×#448	C₂²	semidirect
46. C₄×SD₁₆×C₆₁	C₂²	semidirect
47. C₈×D₄×C₆₁	C₂²	semidirect
48. C₂×#106×C₆₁	C₂²	semidirect
49. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
50. C₂×#103×C₆₁	C₂²	semidirect
51. C₂×#103×C₆₁	C₂²	semidirect
53. C₂×#102×C₆₁	C₂²	semidirect
54. C₂×C₂²⋊C₈×C₆₁	C₂²	semidirect
55. C₂×C₄×C₈×C₆₁	C₂²	semidirect
63. C₂²×Q₈×C₆₁	C₂³	semidirect
85. C₂×SD₁₆×C₆₁	D₄	direct (N × H)
88. C₂×SD₁₆×C₆₁	C₂³	semidirect
89. C₂×SD₁₆×C₆₁	C₂³	semidirect
90. C₂×SD₁₆×C₆₁	C₂³	semidirect
95. C₂²×C₈×C₆₁	C₂³	semidirect
98. C₄⋊Q₈×C₆₁	C₂³	semidirect
103. C₂²⋊Q₈×C₆₁	C₂³	semidirect
109. C₄×Q₈×C₆₁	C₂³	semidirect
128. #106×C₆₁	C₂³	semidirect
129. C₄⋊C₈×C₆₁	C₂³	semidirect
130. #103×C₆₁	C₂³	semidirect
131. #103×C₆₁	C₂³	semidirect
133. #102×C₆₁	C₂³	semidirect
134. C₂²⋊C₈×C₆₁	C₂³	semidirect
135. C₄×C₈×C₆₁	C₂³	semidirect
153. C₂×Q₈×C₆₁	C₂×D₄	semidirect
173. C₂×D₄×C₆₁	SD₁₆	direct (N × H)
198. SD₁₆×C₆₁	C₂×D₄	direct (N × H)
202. C₂×C₈×C₆₁	C₂×D₄	semidirect
236. C₂³×C₆₁	C₂×SD₁₆	semidirect
245. Q₈×C₆₁	C₂²×D₄	semidirect
255. D₄×C₆₁	C₂×SD₁₆	direct (N × H)
272. C₂×C₄×C₆₁	C₂×SD₁₆	semidirect
282. C₈×C₆₁	C₂²×D₄	semidirect
283. C₂×D₄×SD₁₆	C₆₁	direct (N × H)
298. C₂²×C₆₁	C₂²×SD₁₆	semidirect
308. C₄×C₆₁	C₂²×SD₁₆	semidirect
311. C₂³×SD₁₆	C₂×C₆₁	semidirect
312. C₂×D₄×Q₈	C₂×C₆₁	semidirect
314. D₄×SD₁₆	C₂×C₆₁	direct (N × H)
315. C₂×#492	C₂×C₆₁	semidirect
316. C₂×#465	C₂×C₆₁	semidirect
317. C₂×#460	C₂×C₆₁	semidirect
318. C₂×#461	C₂×C₆₁	semidirect
319. C₂×#448	C₂×C₆₁	semidirect
320. C₂×#450	C₂×C₆₁	semidirect
321. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
322. C₂×C₈×D₄	C₂×C₆₁	semidirect
326. C₂×C₆₁	D₄×SD₁₆	direct (N × H)
330. C₂³×Q₈	C₂²×C₆₁	semidirect
336. C₂²×SD₁₆	C₂²×C₆₁	semidirect
337. C₂²×SD₁₆	C₂²×C₆₁	semidirect
338. C₂²×SD₁₆	C₂²×C₆₁	semidirect
339. C₂²×SD₁₆	C₂²×C₆₁	semidirect
340. C₂³×C₈	C₂²×C₆₁	semidirect
342. D₄×Q₈	C₂²×C₆₁	semidirect
346. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
349. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
353. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
357. #492	C₂²×C₆₁	semidirect
358. #465	C₂²×C₆₁	semidirect
359. #461	C₂²×C₆₁	semidirect
360. #460	C₂²×C₆₁	semidirect
361. #450	C₂²×C₆₁	semidirect
362. #448	C₂²×C₆₁	semidirect
363. C₄×SD₁₆	C₂²×C₆₁	semidirect
364. C₈×D₄	C₂²×C₆₁	semidirect
365. C₂×#106	C₂²×C₆₁	semidirect
366. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
367. C₂×#103	C₂²×C₆₁	semidirect
368. C₂×#103	C₂²×C₆₁	semidirect
370. C₂×#102	C₂²×C₆₁	semidirect
371. C₂×C₂²⋊C₈	C₂²×C₆₁	semidirect
372. C₂×C₄×C₈	C₂²×C₆₁	semidirect
373. C₆₁	C₂×D₄×SD₁₆	direct (N × H)
381. C₂²×Q₈	C₂³×C₆₁	semidirect
403. C₂×SD₁₆	D₄×C₆₁	direct (N × H)
406. C₂×SD₁₆	C₂³×C₆₁	semidirect
407. C₂×SD₁₆	C₂³×C₆₁	semidirect
408. C₂×SD₁₆	C₂³×C₆₁	semidirect
413. C₂²×C₈	C₂³×C₆₁	semidirect
416. C₄⋊Q₈	C₂³×C₆₁	semidirect
421. C₂²⋊Q₈	C₂³×C₆₁	semidirect
427. C₄×Q₈	C₂³×C₆₁	semidirect
446. #106	C₂³×C₆₁	semidirect
447. C₄⋊C₈	C₂³×C₆₁	semidirect
448. #103	C₂³×C₆₁	semidirect
449. #103	C₂³×C₆₁	semidirect
451. #102	C₂³×C₆₁	semidirect
452. C₂²⋊C₈	C₂³×C₆₁	semidirect
453. C₄×C₈	C₂³×C₆₁	semidirect
471. C₂×Q₈	C₂×D₄×C₆₁	semidirect
491. C₂×D₄	SD₁₆×C₆₁	direct (N × H)
516. SD₁₆	C₂×D₄×C₆₁	direct (N × H)
520. C₂×C₈	C₂×D₄×C₆₁	semidirect
554. C₂³	C₂×SD₁₆×C₆₁	semidirect
563. Q₈	C₂²×D₄×C₆₁	semidirect
573. D₄	C₂×SD₁₆×C₆₁	direct (N × H)
590. C₂×C₄	C₂×SD₁₆×C₆₁	semidirect
600. C₈	C₂²×D₄×C₆₁	semidirect
615. C₂²	C₂²×SD₁₆×C₆₁	semidirect
625. C₄	C₂²×SD₁₆×C₆₁	semidirect
631. C₂	D₄×SD₁₆×C₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₆₁	2
C₂×D₄×Q₈×C₆₁	2
C₂×D₄²×C₆₁	2
D₄×SD₁₆×C₆₁	2
C₂×C₆₁×#492	2
C₂×C₆₁×#465	2
C₂×C₆₁×#460	2
C₂×C₆₁×#461	2
C₂×C₆₁×#448	2
C₂×C₆₁×#450	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₈×D₄×C₆₁	2
C₂×D₄×SD₁₆	61

Subgroups — C2×D4×SD16×C61 #29564474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×SD₁₆×C₆₁ #29564474