Subgroups — C₆₁×#33844 #29537277

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#510	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3287	C₂	1	1	yes	maximal, characteristic
3	D₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2220	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2189	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2185	C₂	1	2	yes	maximal, complemented
10	C₄×Q₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#550	—	2	1	no	—
15	D₄×Q₈×C₆₁	—	2	1	no	—
16	C₆₁×#510	—	2	8	no	—
17	C₂×Q₃₂×C₆₁	C₂²	1	2	yes	—
18	C₂×Q₃₂×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	—
20	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	—
21	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	—
22	C₂×M₃₂×C₆₁	C₂²	1	2	yes	—
23	C₆₁×#494	C₂²	1	1	yes	characteristic
24	C₆₁×#493	C₂²	1	1	yes	characteristic
25	C₆₁×#467	C₂²	1	2	yes	—
26	C₆₁×#466	C₂²	1	2	yes	—
27	C₆₁×#462	—	2	1	no	—
28	C₆₁×#460	—	2	1	no	—
29	C₆₁×#451	—	2	2	no	—
30	C₆₁×#449	—	2	2	no	—
31	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
32	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#366	C₂²	1	1	yes	characteristic
35	C₆₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₆₁×#358	C₂²	1	1	yes	characteristic
37	C₆₁×#358	C₂²	1	1	yes	characteristic
38	C₆₁×#358	C₂²	1	2	yes	—
39	C₆₁×#357	C₂²	1	2	yes	—
40	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#41×C₆₁	—	2	2	no	—
43	C₂²×Q₈×C₆₁	—	2	2	no	—
44	#135×C₆₁	—	2	4	no	—
45	#135×C₆₁	—	4	2	no	—
46	C₂×Q₁₆×C₆₁	—	2	4	no	—
47	C₂×Q₁₆×C₆₁	—	2	2	no	—
48	C₂×Q₁₆×C₆₁	—	2	1	no	—
49	C₂×Q₁₆×C₆₁	—	4	2	no	—
50	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
51	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×D₈×C₆₁	—	2	1	no	—
55	C₂×D₈×C₆₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₆₁	—	2	1	no	—
58	C₄⋊Q₈×C₆₁	—	4	1	no	—
59	#127×C₆₁	—	2	1	no	—
60	#127×C₆₁	—	4	1	no	—
61	C₂²⋊Q₈×C₆₁	—	2	2	no	—
62	C₂²⋊Q₈×C₆₁	—	4	2	no	—
63	#121×C₆₁	—	2	2	no	—
64	#121×C₆₁	—	4	2	no	—
65	C₄×Q₈×C₆₁	—	2	1	no	—
66	C₄×Q₈×C₆₁	—	2	1	no	—
67	C₄×D₄×C₆₁	—	4	1	no	—
68	C₄×D₄×C₆₁	—	4	1	no	—
69	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
70	Q₃₂×C₆₁	—	2	4	no	—
71	Q₃₂×C₆₁	D₄	1	4	yes	complemented
72	SD₃₂×C₆₁	—	2	4	no	—
73	SD₃₂×C₆₁	—	2	4	no	—
74	SD₃₂×C₆₁	—	4	2	no	—
75	M₃₂×C₆₁	—	2	4	no	—
76	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
78	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
79	#107×C₆₁	C₂³	1	1	yes	characteristic
80	#107×C₆₁	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₆₁	D₄	1	1	yes	characteristic
82	#103×C₆₁	—	2	1	no	—
83	#103×C₆₁	—	2	1	no	—
84	#103×C₆₁	—	2	2	no	—
85	#102×C₆₁	—	2	2	no	—
86	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
87	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	#41×C₆₁	—	4	4	no	—
89	#41×C₆₁	—	8	2	no	—
90	C₂×Q₈×C₆₁	—	2	1	no	—
91	C₂×Q₈×C₆₁	—	2	1	no	—
92	C₂×Q₈×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	—	4	4	no	—
94	C₂×Q₈×C₆₁	—	4	2	no	—
95	C₂×Q₈×C₆₁	—	8	2	no	—
96	C₂×D₄×C₆₁	—	2	2	no	—
97	C₂×D₄×C₆₁	—	4	2	no	—
98	C₂×D₄×C₆₁	—	4	2	no	—
99	C₂×D₄×C₆₁	—	4	1	no	—
100	C₂×D₄×C₆₁	—	4	1	no	—
101	C₂×D₄×C₆₁	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₆₁	—	4	2	no	—
103	C₂²×C₄×C₆₁	—	4	2	no	—
104	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
105	Q₁₆×C₆₁	—	2	2	no	—
106	Q₁₆×C₆₁	—	2	1	no	—
107	Q₁₆×C₆₁	—	2	1	no	—
108	Q₁₆×C₆₁	—	2	2	no	—
109	Q₁₆×C₆₁	—	4	4	no	—
110	Q₁₆×C₆₁	—	8	1	no	—
111	Q₁₆×C₆₁	C₂×D₄	1	2	yes	—
112	Q₁₆×C₆₁	C₂×D₄	1	2	yes	—
113	SD₁₆×C₆₁	—	4	4	no	—
114	D₈×C₆₁	—	2	2	no	—
115	D₈×C₆₁	—	2	2	no	—
116	D₈×C₆₁	—	8	1	no	—
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₂×C₈×C₆₁	—	2	2	no	—
119	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
122	C₄⋊C₄×C₆₁	—	2	1	no	—
123	C₄⋊C₄×C₆₁	—	2	1	no	—
124	C₄⋊C₄×C₆₁	—	4	1	no	—
125	C₄⋊C₄×C₆₁	—	4	1	no	—
126	C₄⋊C₄×C₆₁	—	4	1	no	—
127	C₄⋊C₄×C₆₁	—	4	2	no	—
128	C₄⋊C₄×C₆₁	—	4	1	no	—
129	C₄⋊C₄×C₆₁	D₈	1	1	yes	characteristic
130	C₂²⋊C₄×C₆₁	—	4	2	no	—
131	C₂²⋊C₄×C₆₁	—	4	2	no	—
132	C₂²⋊C₄×C₆₁	D₈	1	2	yes	—
133	C₄²×C₆₁	—	4	1	no	—
134	C₄²×C₆₁	—	4	1	no	—
135	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₁₆×C₆₁	—	2	2	no	—
137	C₁₆×C₆₁	—	2	1	no	—
138	C₁₆×C₆₁	C₂×D₄	1	2	yes	—
139	C₂³×C₆₁	—	4	2	no	—
140	C₂³×C₆₁	C₂×D₈	1	2	yes	—
141	Q₈×C₆₁	—	2	2	no	—
142	Q₈×C₆₁	—	2	2	no	—
143	Q₈×C₆₁	—	4	1	no	—
144	Q₈×C₆₁	—	4	1	no	—
145	Q₈×C₆₁	—	4	2	no	—
146	Q₈×C₆₁	—	4	2	no	—
147	Q₈×C₆₁	—	8	4	no	—
148	D₄×C₆₁	—	2	2	no	—
149	D₄×C₆₁	—	4	2	no	—
150	D₄×C₆₁	—	4	2	no	—
151	D₄×C₆₁	—	8	4	no	—
152	D₄×C₆₁	—	8	2	no	—
153	D₄×C₆₁	—	16	1	no	—
154	D₄×C₆₁	—	16	2	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	4	1	no	—
158	C₂×C₄×C₆₁	—	4	1	no	—
159	C₂×C₄×C₆₁	—	4	1	no	—
160	C₂×C₄×C₆₁	—	4	1	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	8	4	no	—
163	C₂×C₄×C₆₁	—	8	4	no	—
164	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
166	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
168	C₈×C₆₁	—	2	2	no	—
169	C₈×C₆₁	—	2	1	no	—
170	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
172	#33844	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₆₁	—	2	2	no	—
174	C₂²×C₆₁	—	2	2	no	—
175	C₂²×C₆₁	—	2	2	no	—
176	C₂²×C₆₁	—	8	2	no	—
177	C₂²×C₆₁	—	8	2	no	—
178	C₂²×C₆₁	—	8	2	no	—
179	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
180	C₄×C₆₁	—	2	1	no	—
181	C₄×C₆₁	—	2	2	no	—
182	C₄×C₆₁	—	4	2	no	—
183	C₄×C₆₁	—	4	2	no	—
184	C₄×C₆₁	—	8	1	no	—
185	C₄×C₆₁	—	8	1	no	—
186	C₄×C₆₁	—	8	2	no	—
187	C₄×C₆₁	#510	1	2	yes	complemented
188	C₄×C₆₁	D₄²	1	1	yes	characteristic
189	C₄×C₆₁	#576	1	1	yes	characteristic
190	C₂×#510	C₂×C₆₁	1	2	yes	complemented
191	#3287	C₂×C₆₁	1	1	yes	characteristic
192	D₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
193	#2248	C₂×C₆₁	1	1	yes	characteristic, complemented
194	#2220	C₂×C₆₁	1	2	yes	complemented
195	#2209	C₂×C₆₁	1	1	yes	characteristic, complemented
196	#2207	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#2189	C₂×C₆₁	1	2	yes	complemented
198	#2185	C₂×C₆₁	1	2	yes	complemented
199	C₄×Q₃₂	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#2169	C₂×C₆₁	1	1	yes	characteristic, complemented
201	C₂×C₆₁	—	4	2	no	—
202	C₂×C₆₁	—	16	2	no	—
203	C₂×C₆₁	D₄×D₈	1	1	yes	characteristic
204	C₂×C₆₁	C₂×#510	1	1	yes	characteristic
205	C₂×C₆₁	#3416	1	1	yes	characteristic
206	C₂×#135	C₂²×C₆₁	1	2	yes	—
207	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
208	#550	—	2	1	no	—
209	D₄×Q₈	—	2	1	no	—
210	#510	—	2	8	no	—
211	C₂×Q₃₂	C₂²×C₆₁	1	2	yes	—
212	C₂×Q₃₂	C₂²×C₆₁	1	1	yes	characteristic
213	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	—
214	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	—
215	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	—
216	C₂×M₃₂	C₂²×C₆₁	1	2	yes	—
217	#494	C₂²×C₆₁	1	1	yes	characteristic
218	#493	C₂²×C₆₁	1	1	yes	characteristic
219	#467	C₂²×C₆₁	1	2	yes	—
220	#466	C₂²×C₆₁	1	2	yes	—
221	#462	—	2	1	no	—
222	#460	—	2	1	no	—
223	#451	—	2	2	no	—
224	#449	—	2	2	no	—
225	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
226	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
227	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
228	#366	C₂²×C₆₁	1	1	yes	characteristic
229	C₄⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
230	#358	C₂²×C₆₁	1	1	yes	characteristic
231	#358	C₂²×C₆₁	1	1	yes	characteristic
232	#358	C₂²×C₆₁	1	2	yes	—
233	#357	C₂²×C₆₁	1	2	yes	—
234	C₂²⋊C₁₆	C₂²×C₆₁	1	2	yes	—
235	C₄×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
236	C₆₁	#33844	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×#41	—	2	2	no	—
238	C₂²×Q₈	—	2	2	no	—
239	#135	—	2	4	no	—
240	#135	—	4	2	no	—
241	C₂×Q₁₆	—	2	4	no	—
242	C₂×Q₁₆	—	2	2	no	—
243	C₂×Q₁₆	—	2	1	no	—
244	C₂×Q₁₆	—	4	2	no	—
245	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
246	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
247	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	C₂³×C₆₁	1	2	yes	—
251	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	4	1	no	—
254	#127	—	2	1	no	—
255	#127	—	4	1	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	C₂²⋊Q₈	—	4	2	no	—
258	#121	—	2	2	no	—
259	#121	—	4	2	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×D₄	—	4	1	no	—
263	C₄×D₄	—	4	1	no	—
264	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
265	Q₃₂	—	2	4	no	—
266	Q₃₂	D₄×C₆₁	1	4	yes	complemented
267	SD₃₂	—	2	4	no	—
268	SD₃₂	—	2	4	no	—
269	SD₃₂	—	4	2	no	—
270	M₃₂	—	2	4	no	—
271	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
272	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
273	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
274	#107	C₂³×C₆₁	1	1	yes	characteristic
275	#107	C₂³×C₆₁	1	1	yes	characteristic
276	C₄⋊C₈	D₄×C₆₁	1	1	yes	characteristic
277	#103	—	2	1	no	—
278	#103	—	2	1	no	—
279	#103	—	2	2	no	—
280	#102	—	2	2	no	—
281	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
282	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
283	#41	—	4	4	no	—
284	#41	—	8	2	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	8	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	D₈×C₆₁	1	1	yes	characteristic
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
300	Q₁₆	—	2	2	no	—
301	Q₁₆	—	2	1	no	—
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	4	4	no	—
305	Q₁₆	—	8	1	no	—
306	Q₁₆	C₂×D₄×C₆₁	1	2	yes	—
307	Q₁₆	C₂×D₄×C₆₁	1	2	yes	—
308	SD₁₆	—	4	4	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	8	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
316	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	D₈×C₆₁	1	1	yes	characteristic
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	D₈×C₆₁	1	2	yes	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
331	C₁₆	—	2	2	no	—
332	C₁₆	—	2	1	no	—
333	C₁₆	C₂×D₄×C₆₁	1	2	yes	—
334	C₂³	—	4	2	no	—
335	C₂³	C₂×D₈×C₆₁	1	2	yes	—
336	Q₈	—	2	2	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	8	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	D₄	—	8	4	no	—
347	D₄	—	8	2	no	—
348	D₄	—	16	1	no	—
349	D₄	—	16	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	4	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
360	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
361	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	1	no	—
365	C₈	C₂²×D₄×C₆₁	1	1	yes	characteristic
366	C₈	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	2	no	—
381	C₄	C₆₁×#510	1	2	yes	complemented
382	C₄	D₄²×C₆₁	1	1	yes	characteristic
383	C₄	C₆₁×#576	1	1	yes	characteristic
384	C₂	—	4	2	no	—
385	C₂	—	16	2	no	—
386	C₂	D₄×D₈×C₆₁	1	1	yes	characteristic
387	C₂	C₂×C₆₁×#510	1	1	yes	characteristic
388	C₂	C₆₁×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₁
prime radical	C₆₁×#3287	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×D₄×C₆₁ ◁ C₈×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#510	C₂	semidirect
3. D₄×Q₁₆×C₆₁	C₂	semidirect
4. C₆₁×#2248	C₂	semidirect
5. C₆₁×#2220	C₂	semidirect
6. C₆₁×#2209	C₂	semidirect
7. C₆₁×#2207	C₂	semidirect
8. C₆₁×#2189	C₂	semidirect
9. C₆₁×#2185	C₂	semidirect
10. C₄×Q₃₂×C₆₁	C₂	semidirect
11. C₆₁×#2169	C₂	semidirect
71. Q₃₂×C₆₁	D₄	semidirect
172. #33844	C₆₁	direct (N × H)
187. C₄×C₆₁	#510	semidirect
190. C₂×#510	C₂×C₆₁	semidirect
192. D₄×Q₁₆	C₂×C₆₁	semidirect
193. #2248	C₂×C₆₁	semidirect
194. #2220	C₂×C₆₁	semidirect
195. #2209	C₂×C₆₁	semidirect
196. #2207	C₂×C₆₁	semidirect
197. #2189	C₂×C₆₁	semidirect
198. #2185	C₂×C₆₁	semidirect
199. C₄×Q₃₂	C₂×C₆₁	semidirect
200. #2169	C₂×C₆₁	semidirect
236. C₆₁	#33844	direct (N × H)
266. Q₃₂	D₄×C₆₁	semidirect
381. C₄	C₆₁×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#510	2
C₆₁×#3287	2
D₄×Q₁₆×C₆₁	2
C₆₁×#2248	2
C₆₁×#2220	2
C₆₁×#2209	2
C₆₁×#2207	2
C₆₁×#2189	2
C₆₁×#2185	2
C₄×Q₃₂×C₆₁	2
C₆₁×#2169	2
#33844	61

Subgroups — C61×#33844 #29537277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#33844 #29537277