Subgroups — C₆₁×#24319 #29527752

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3078	C₂	1	2	yes	maximal
3	C₆₁×#2327	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2061	C₂	1	2	yes	maximal
5	C₆₁×#2028	C₂	1	2	yes	maximal
6	C₆₁×#1995	C₂	1	2	yes	maximal
7	C₆₁×#1886	C₂	1	2	yes	maximal
8	C₆₁×#1857	C₂	1	2	yes	maximal
9	C₆₁×#1801	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₆₁	—	2	2	no	—
11	C₆₁×#557	—	2	2	no	—
12	C₆₁×#557	—	2	4	no	—
13	C₆₁×#544	—	2	2	no	—
14	C₆₁×#544	C₂²	1	2	yes	—
15	C₆₁×#533	—	2	2	no	—
16	C₆₁×#533	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#519	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#479	—	2	4	no	—
22	C₆₁×#477	—	2	2	no	—
23	C₆₁×#475	—	2	2	no	—
24	C₆₁×#428	C₂²	1	4	yes	—
25	C₆₁×#423	C₂²	1	2	yes	—
26	C₆₁×#419	C₂²	1	4	yes	—
27	C₂×#101×C₆₁	C₂²	1	2	yes	—
28	C₆₁×#391	C₂²	1	1	yes	characteristic
29	C₆₁×#391	C₂²	1	1	yes	characteristic
30	C₆₁×#387	—	2	2	no	—
31	C₆₁×#387	—	2	2	no	—
32	C₆₁×#382	C₂²	1	1	yes	characteristic
33	C₆₁×#376	C₂²	1	1	yes	characteristic
34	C₆₁×#343	C₂²	1	2	yes	—
35	C₆₁×#339	C₂²	1	4	yes	—
36	C₆₁×#339	C₂²	1	4	yes	—
37	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₆₁	—	2	2	no	—
41	C₄⋊Q₈×C₆₁	—	2	2	no	—
42	C₄⋊Q₈×C₆₁	—	2	8	no	—
43	C₄⋊Q₈×C₆₁	—	2	2	no	—
44	C₄⋊Q₈×C₆₁	—	2	4	no	—
45	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
46	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
47	C₄⋊Q₈×C₆₁	Q₈	1	4	yes	complemented
48	#125×C₆₁	—	2	4	no	—
49	#125×C₆₁	—	2	8	no	—
50	#125×C₆₁	—	2	4	no	—
51	#125×C₆₁	D₄	1	4	yes	—
52	C₂²⋊Q₈×C₆₁	—	2	2	no	—
53	C₂²⋊Q₈×C₆₁	—	2	4	no	—
54	C₂²⋊Q₈×C₆₁	—	2	2	no	—
55	C₄×Q₈×C₆₁	—	2	4	no	—
56	C₄×Q₈×C₆₁	—	2	4	no	—
57	C₄×Q₈×C₆₁	—	2	4	no	—
58	C₄×Q₈×C₆₁	—	2	4	no	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×Q₈×C₆₁	—	2	2	no	—
61	C₄×Q₈×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×Q₈×C₆₁	—	2	2	no	—
64	C₄×Q₈×C₆₁	—	2	2	no	—
65	#117×C₆₁	—	2	4	no	—
66	#117×C₆₁	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	—	2	1	no	—
73	C₂×C₄²×C₆₁	D₄	1	2	yes	—
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
77	#107×C₆₁	—	2	4	no	—
78	#106×C₆₁	—	2	4	no	—
79	C₄⋊C₈×C₆₁	—	2	2	no	—
80	C₄⋊C₈×C₆₁	—	2	2	no	—
81	#103×C₆₁	—	2	4	no	—
82	#103×C₆₁	—	2	4	no	—
83	#101×C₆₁	—	2	4	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	1	no	—
86	#95×C₆₁	—	2	2	no	—
87	#95×C₆₁	—	2	2	no	—
88	#95×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	2	4	no	—
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	—	2	2	no	—
92	C₂×Q₈×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	—	2	1	no	—
94	C₂×Q₈×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	C₂×Q₈	1	2	yes	—
98	C₂×Q₈×C₆₁	C₂×Q₈	1	2	yes	—
99	C₂×Q₈×C₆₁	#41	1	2	yes	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	1	no	—
103	C₂²×C₄×C₆₁	—	2	1	no	—
104	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
109	M₁₆×C₆₁	—	2	4	no	—
110	M₁₆×C₆₁	—	2	4	no	—
111	C₂×C₈×C₆₁	—	2	4	no	—
112	C₄⋊C₄×C₆₁	—	2	4	no	—
113	C₄⋊C₄×C₆₁	—	2	4	no	—
114	C₄⋊C₄×C₆₁	—	2	4	no	—
115	C₄⋊C₄×C₆₁	—	2	8	no	—
116	C₄⋊C₄×C₆₁	—	2	4	no	—
117	C₄⋊C₄×C₆₁	—	2	4	no	—
118	C₄⋊C₄×C₆₁	—	2	2	no	—
119	C₄⋊C₄×C₆₁	—	2	2	no	—
120	C₄⋊C₄×C₆₁	—	2	4	no	—
121	C₄⋊C₄×C₆₁	—	2	8	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	4	1	no	—
125	C₄⋊C₄×C₆₁	—	4	1	no	—
126	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
127	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
128	C₂²⋊C₄×C₆₁	—	2	4	no	—
129	C₄²×C₆₁	—	2	8	no	—
130	C₄²×C₆₁	—	2	2	no	—
131	C₄²×C₆₁	—	2	2	no	—
132	C₄²×C₆₁	—	2	4	no	—
133	C₄²×C₆₁	—	2	1	no	—
134	C₄²×C₆₁	—	2	2	no	—
135	C₄²×C₆₁	—	4	2	no	—
136	C₄²×C₆₁	C₂×D₄	1	2	yes	—
137	C₄²×C₆₁	C₂×D₄	1	2	yes	—
138	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
139	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₆₁	—	2	4	no	—
141	Q₈×C₆₁	—	2	4	no	—
142	Q₈×C₆₁	—	2	4	no	—
143	Q₈×C₆₁	—	4	4	no	—
144	Q₈×C₆₁	—	4	2	no	—
145	Q₈×C₆₁	—	8	2	no	—
146	Q₈×C₆₁	—	8	4	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	4	no	—
150	C₂×C₄×C₆₁	—	2	4	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	4	1	no	—
155	C₂×C₄×C₆₁	—	4	1	no	—
156	C₂×C₄×C₆₁	—	4	1	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	2	no	—
161	C₂×C₄×C₆₁	—	4	1	no	—
162	C₂×C₄×C₆₁	—	4	1	no	—
163	C₂×C₄×C₆₁	—	4	2	no	—
164	C₂×C₄×C₆₁	—	4	1	no	—
165	C₂×C₄×C₆₁	—	4	1	no	—
166	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
167	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
168	C₂×C₄×C₆₁	#120	1	2	yes	—
169	C₂×C₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
170	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₆₁	—	4	4	no	—
175	#24319	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₆₁	—	2	1	no	—
177	C₂²×C₆₁	—	2	1	no	—
178	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
179	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
180	C₂²×C₆₁	#536	1	1	yes	characteristic
181	C₄×C₆₁	—	2	4	no	—
182	C₄×C₆₁	—	2	1	no	—
183	C₄×C₆₁	—	2	1	no	—
184	C₄×C₆₁	—	2	2	no	—
185	C₄×C₆₁	—	4	2	no	—
186	C₄×C₆₁	—	4	2	no	—
187	C₄×C₆₁	—	4	4	no	—
188	C₄×C₆₁	—	4	2	no	—
189	C₄×C₆₁	—	4	4	no	—
190	C₄×C₆₁	—	8	1	no	—
191	C₄×C₆₁	—	8	1	no	—
192	C₄×C₆₁	#548	1	2	yes	—
193	C₄×C₆₁	D₄×Q₈	1	2	yes	—
194	#3502	C₂×C₆₁	1	1	yes	characteristic
195	#3078	C₂×C₆₁	1	2	yes	—
196	#2327	C₂×C₆₁	1	1	yes	characteristic
197	#2061	C₂×C₆₁	1	2	yes	—
198	#2028	C₂×C₆₁	1	2	yes	—
199	#1995	C₂×C₆₁	1	2	yes	—
200	#1886	C₂×C₆₁	1	2	yes	—
201	#1857	C₂×C₆₁	1	2	yes	—
202	#1801	C₂×C₆₁	1	1	yes	characteristic
203	C₂×C₆₁	—	2	1	no	—
204	C₂×C₆₁	—	2	1	no	—
205	C₂×C₆₁	#2409	1	1	yes	characteristic
206	C₂×C₆₁	#3020	1	1	yes	characteristic
207	C₂×C₆₁	#3022	1	1	yes	characteristic
208	Q₈²	—	2	2	no	—
209	#557	—	2	2	no	—
210	#557	—	2	4	no	—
211	#544	—	2	2	no	—
212	#544	C₂²×C₆₁	1	2	yes	—
213	#533	—	2	2	no	—
214	#533	C₂²×C₆₁	1	2	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
216	#519	C₂²×C₆₁	1	2	yes	—
217	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
219	#479	—	2	4	no	—
220	#477	—	2	2	no	—
221	#475	—	2	2	no	—
222	#428	C₂²×C₆₁	1	4	yes	—
223	#423	C₂²×C₆₁	1	2	yes	—
224	#419	C₂²×C₆₁	1	4	yes	—
225	C₂×#101	C₂²×C₆₁	1	2	yes	—
226	#391	C₂²×C₆₁	1	1	yes	characteristic
227	#391	C₂²×C₆₁	1	1	yes	characteristic
228	#387	—	2	2	no	—
229	#387	—	2	2	no	—
230	#382	C₂²×C₆₁	1	1	yes	characteristic
231	#376	C₂²×C₆₁	1	1	yes	characteristic
232	#343	C₂²×C₆₁	1	2	yes	—
233	#339	C₂²×C₆₁	1	4	yes	—
234	#339	C₂²×C₆₁	1	4	yes	—
235	C₆₁	#24319	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
238	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	8	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	4	no	—
244	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
245	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
246	C₄⋊Q₈	Q₈×C₆₁	1	4	yes	complemented
247	#125	—	2	4	no	—
248	#125	—	2	8	no	—
249	#125	—	2	4	no	—
250	#125	D₄×C₆₁	1	4	yes	—
251	C₂²⋊Q₈	—	2	2	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	4	no	—
255	C₄×Q₈	—	2	4	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	—	2	4	no	—
258	C₄×Q₈	—	2	2	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	—	2	2	no	—
264	#117	—	2	4	no	—
265	#117	C₂³×C₆₁	1	4	yes	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	D₄×C₆₁	1	2	yes	—
273	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
276	#107	—	2	4	no	—
277	#106	—	2	4	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	#103	—	2	4	no	—
281	#103	—	2	4	no	—
282	#101	—	2	4	no	—
283	#95	—	2	1	no	—
284	#95	—	2	1	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	C₂×Q₈×C₆₁	1	2	yes	—
297	C₂×Q₈	C₂×Q₈×C₆₁	1	2	yes	—
298	C₂×Q₈	#41×C₆₁	1	2	yes	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
308	M₁₆	—	2	4	no	—
309	M₁₆	—	2	4	no	—
310	C₂×C₈	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
326	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₄²	—	2	8	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	4	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	2	no	—
335	C₄²	C₂×D₄×C₆₁	1	2	yes	—
336	C₄²	C₂×D₄×C₆₁	1	2	yes	—
337	C₄²	C₂×Q₈×C₆₁	1	2	yes	—
338	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
339	Q₈	—	2	4	no	—
340	Q₈	—	2	4	no	—
341	Q₈	—	2	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	2	no	—
345	Q₈	—	8	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
366	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
367	C₂×C₄	#120×C₆₁	1	2	yes	—
368	C₂×C₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
369	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
370	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
372	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
377	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
378	C₂²	C₆₁×#536	1	1	yes	characteristic
379	C₄	—	2	4	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	4	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₄	C₆₁×#548	1	2	yes	—
391	C₄	D₄×Q₈×C₆₁	1	2	yes	—
392	C₂	—	2	1	no	—
393	C₂	—	2	1	no	—
394	C₂	C₆₁×#2409	1	1	yes	characteristic
395	C₂	C₆₁×#3020	1	1	yes	characteristic
396	C₂	C₆₁×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂³×C₆₁	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
47. C₄⋊Q₈×C₆₁	Q₈	semidirect
175. #24319	C₆₁	direct (N × H)
235. C₆₁	#24319	direct (N × H)
246. C₄⋊Q₈	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3502	2
C₆₁×#3078	2
C₆₁×#2327	2
C₆₁×#2061	2
C₆₁×#2028	2
C₆₁×#1995	2
C₆₁×#1886	2
C₆₁×#1857	2
C₆₁×#1801	2
#24319	61

Subgroups — C61×#24319 #29527752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24319 #29527752