Subgroups — C₂×C₆₁×#1772 #29523875

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#427	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#405	C₂	1	2	yes	maximal
4	C₂²×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1772	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₆₁×#339	C₂	1	2	yes	maximal
7	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×#117×C₆₁	C₂²	1	2	yes	—
11	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×#108×C₆₁	C₄	1	8	yes	complemented
13	C₂×#108×C₆₁	C₂²	1	4	yes	—
14	C₆₁×#427	C₄	1	4	yes	complemented
15	C₆₁×#427	C₂²	1	4	yes	—
16	C₂×#107×C₆₁	C₄	1	2	yes	complemented
17	C₂×#106×C₆₁	C₄	1	2	yes	complemented
18	C₆₁×#405	—	2	4	no	—
19	C₆₁×#405	C₂²	1	8	yes	—
20	C₂×#97×C₆₁	—	2	2	no	—
21	C₂×C₄×C₈×C₆₁	—	2	2	no	—
22	C₂×C₄×C₈×C₆₁	C₄	1	8	yes	complemented
23	C₂×C₄×C₈×C₆₁	C₂²	1	4	yes	—
24	C₆₁×#339	C₂²	1	8	yes	—
25	C₂³×C₄×C₆₁	—	2	1	no	—
26	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
27	C₂×M₁₆×C₆₁	—	2	2	no	—
28	C₂×M₁₆×C₆₁	—	2	4	no	—
29	C₂×M₁₆×C₆₁	C₂×C₄	1	8	yes	—
30	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
31	C₂²×C₈×C₆₁	—	2	2	no	—
32	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
37	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
38	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₆₁	D₄	1	2	yes	—
40	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₆₁	Q₈	1	4	yes	—
42	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
44	#117×C₆₁	—	2	2	no	—
45	#117×C₆₁	—	2	2	no	—
46	#117×C₆₁	C₂×C₄	1	4	yes	—
47	#117×C₆₁	C₂³	1	4	yes	—
48	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
50	C₂×C₄²×C₆₁	—	2	2	no	—
51	C₂×C₄²×C₆₁	—	2	1	no	—
52	C₂×C₄²×C₆₁	—	2	2	no	—
53	C₂×C₄²×C₆₁	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
55	#108×C₆₁	C₂×C₄	1	16	yes	complemented
56	#107×C₆₁	C₂×C₄	1	8	yes	complemented
57	#106×C₆₁	C₂×C₄	1	8	yes	complemented
58	#97×C₆₁	—	2	8	no	—
59	C₄×C₈×C₆₁	—	2	8	no	—
60	C₄×C₈×C₆₁	C₂×C₄	1	16	yes	complemented
61	C₂⁴×C₆₁	#41	1	1	yes	characteristic
62	C₂²×C₄×C₆₁	—	2	8	no	—
63	C₂²×C₄×C₆₁	—	2	4	no	—
64	C₂²×C₄×C₆₁	—	2	2	no	—
65	C₂²×C₄×C₆₁	—	2	4	no	—
66	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
68	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
73	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	#41	1	2	yes	—
75	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
76	M₁₆×C₆₁	—	2	8	no	—
77	M₁₆×C₆₁	—	2	4	no	—
78	M₁₆×C₆₁	C₂²×C₄	1	8	yes	—
79	C₂×C₈×C₆₁	—	2	8	no	—
80	C₂×C₈×C₆₁	—	2	4	no	—
81	C₂×C₈×C₆₁	C₄²	1	4	yes	—
82	C₂×C₈×C₆₁	C₄²	1	4	yes	—
83	C₂×C₈×C₆₁	C₄²	1	8	yes	—
84	C₂×C₈×C₆₁	C₄⋊C₄	1	4	yes	—
85	C₂×C₈×C₆₁	C₄⋊C₄	1	8	yes	—
86	C₂×C₈×C₆₁	C₄⋊C₄	1	4	yes	—
87	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
88	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
91	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
92	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
93	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
94	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
95	C₄⋊C₄×C₆₁	—	2	4	no	—
96	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
97	C₂²⋊C₄×C₆₁	—	2	4	no	—
98	C₂²⋊C₄×C₆₁	—	2	4	no	—
99	C₄²×C₆₁	—	2	4	no	—
100	C₄²×C₆₁	—	2	4	no	—
101	C₄²×C₆₁	—	2	4	no	—
102	C₄²×C₆₁	—	2	2	no	—
103	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
104	C₂³×C₆₁	—	2	4	no	—
105	C₂³×C₆₁	#117	1	2	yes	—
106	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
107	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
108	C₂³×C₆₁	C₄×Q₈	1	2	yes	—
109	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
110	C₂×C₄×C₆₁	—	2	8	no	—
111	C₂×C₄×C₆₁	—	2	16	no	—
112	C₂×C₄×C₆₁	—	2	4	no	—
113	C₂×C₄×C₆₁	—	2	8	no	—
114	C₂×C₄×C₆₁	—	4	8	no	—
115	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
116	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
117	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
118	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
119	C₂×C₄×C₆₁	#117	1	2	yes	—
120	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
121	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
122	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
123	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
124	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
125	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
126	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
127	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
128	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
129	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
132	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
133	C₈×C₆₁	—	2	8	no	—
134	C₈×C₆₁	C₂×C₄²	1	4	yes	—
135	C₈×C₆₁	C₂×C₄²	1	4	yes	—
136	C₈×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
137	C₈×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
138	C₂×#1772	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂²×C₆₁	—	2	2	no	—
140	C₂²×C₆₁	—	2	2	no	—
141	C₂²×C₆₁	—	2	4	no	—
142	C₂²×C₆₁	—	2	4	no	—
143	C₂²×C₆₁	C₄×C₄⋊C₄	1	2	yes	—
144	C₂²×C₆₁	C₄×C₄⋊C₄	1	2	yes	—
145	C₂²×C₆₁	#443	1	4	yes	—
146	C₂²×C₆₁	C₂×#117	1	1	yes	characteristic
147	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
148	C₂²×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
149	C₄×C₆₁	—	2	8	no	—
150	C₄×C₆₁	—	4	8	no	—
151	C₄×C₆₁	C₄×C₄⋊C₄	1	2	yes	—
152	C₄×C₆₁	C₄×C₄⋊C₄	1	2	yes	—
153	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
154	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
155	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
156	C₄×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
157	C₂²×#108	C₂×C₆₁	1	1	yes	characteristic
158	C₂×#427	C₂×C₆₁	1	1	yes	characteristic
159	C₂×#405	C₂×C₆₁	1	2	yes	—
160	C₂²×C₄×C₈	C₂×C₆₁	1	1	yes	characteristic
161	#1772	C₂×C₆₁	1	8	yes	direct product factor
162	C₂×#339	C₂×C₆₁	1	2	yes	—
163	C₂×C₆₁	—	2	1	no	—
164	C₂×C₆₁	—	2	1	no	—
165	C₂×C₆₁	—	2	2	no	—
166	C₂×C₆₁	#1772	1	4	yes	direct product factor
167	C₂×C₆₁	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₆₁	C₂×#443	1	2	yes	—
169	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
170	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
172	C₂×#117	C₂²×C₆₁	1	2	yes	—
173	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
174	C₂×#108	C₄×C₆₁	1	8	yes	complemented
175	C₂×#108	C₂²×C₆₁	1	4	yes	—
176	#427	C₄×C₆₁	1	4	yes	complemented
177	#427	C₂²×C₆₁	1	4	yes	—
178	C₂×#107	C₄×C₆₁	1	2	yes	complemented
179	C₂×#106	C₄×C₆₁	1	2	yes	complemented
180	#405	—	2	4	no	—
181	#405	C₂²×C₆₁	1	8	yes	—
182	C₂×#97	—	2	2	no	—
183	C₂×C₄×C₈	—	2	2	no	—
184	C₂×C₄×C₈	C₄×C₆₁	1	8	yes	complemented
185	C₂×C₄×C₈	C₂²×C₆₁	1	4	yes	—
186	#339	C₂²×C₆₁	1	8	yes	—
187	C₆₁	C₂×#1772	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³×C₄	—	2	1	no	—
189	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
190	C₂×M₁₆	—	2	2	no	—
191	C₂×M₁₆	—	2	4	no	—
192	C₂×M₁₆	C₂×C₄×C₆₁	1	8	yes	—
193	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
194	C₂²×C₈	—	2	2	no	—
195	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
196	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
197	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
198	C₂²×C₈	C₂×C₄×C₆₁	1	2	yes	—
199	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
200	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
201	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
202	C₂²×C₈	D₄×C₆₁	1	2	yes	—
203	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
204	C₂²×C₈	Q₈×C₆₁	1	4	yes	—
205	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
206	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
207	#117	—	2	2	no	—
208	#117	—	2	2	no	—
209	#117	C₂×C₄×C₆₁	1	4	yes	—
210	#117	C₂³×C₆₁	1	4	yes	—
211	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
212	C₂×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₄²	—	2	2	no	—
214	C₂×C₄²	—	2	1	no	—
215	C₂×C₄²	—	2	2	no	—
216	C₂×C₄²	C₂×C₄×C₆₁	1	4	yes	—
217	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
218	#108	C₂×C₄×C₆₁	1	16	yes	complemented
219	#107	C₂×C₄×C₆₁	1	8	yes	complemented
220	#106	C₂×C₄×C₆₁	1	8	yes	complemented
221	#97	—	2	8	no	—
222	C₄×C₈	—	2	8	no	—
223	C₄×C₈	C₂×C₄×C₆₁	1	16	yes	complemented
224	C₂⁴	#41×C₆₁	1	1	yes	characteristic
225	C₂²×C₄	—	2	8	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
230	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
231	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
232	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
233	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
234	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
235	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
236	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
237	C₂²×C₄	#41×C₆₁	1	2	yes	—
238	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
239	M₁₆	—	2	8	no	—
240	M₁₆	—	2	4	no	—
241	M₁₆	C₂²×C₄×C₆₁	1	8	yes	—
242	C₂×C₈	—	2	8	no	—
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	C₄²×C₆₁	1	4	yes	—
245	C₂×C₈	C₄²×C₆₁	1	4	yes	—
246	C₂×C₈	C₄²×C₆₁	1	8	yes	—
247	C₂×C₈	C₄⋊C₄×C₆₁	1	4	yes	—
248	C₂×C₈	C₄⋊C₄×C₆₁	1	8	yes	—
249	C₂×C₈	C₄⋊C₄×C₆₁	1	4	yes	—
250	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
251	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
252	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
253	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
254	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
255	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
256	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
257	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
260	C₂²⋊C₄	—	2	4	no	—
261	C₂²⋊C₄	—	2	4	no	—
262	C₄²	—	2	4	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	2	4	no	—
265	C₄²	—	2	2	no	—
266	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
267	C₂³	—	2	4	no	—
268	C₂³	#117×C₆₁	1	2	yes	—
269	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
270	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
271	C₂³	C₄×Q₈×C₆₁	1	2	yes	—
272	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
273	C₂×C₄	—	2	16	no	—
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	8	no	—
277	C₂×C₄	—	4	8	no	—
278	C₂×C₄	C₂×C₄²×C₆₁	1	2	yes	—
279	C₂×C₄	C₂×C₄²×C₆₁	1	2	yes	—
280	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
281	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
282	C₂×C₄	#117×C₆₁	1	2	yes	—
283	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
284	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
285	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
286	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
287	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
288	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
289	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
290	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
291	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
292	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
293	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
294	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
295	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
296	C₈	—	2	8	no	—
297	C₈	C₂×C₄²×C₆₁	1	4	yes	—
298	C₈	C₂×C₄²×C₆₁	1	4	yes	—
299	C₈	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
300	C₈	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
301	C₂²	—	2	4	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	2	2	no	—
304	C₂²	—	2	2	no	—
305	C₂²	C₄×C₄⋊C₄×C₆₁	1	2	yes	—
306	C₂²	C₄×C₄⋊C₄×C₆₁	1	2	yes	—
307	C₂²	C₆₁×#443	1	4	yes	—
308	C₂²	C₂×#117×C₆₁	1	1	yes	characteristic
309	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
310	C₂²	C₂×C₄×Q₈×C₆₁	1	1	yes	characteristic
311	C₄	—	2	8	no	—
312	C₄	—	4	8	no	—
313	C₄	C₄×C₄⋊C₄×C₆₁	1	2	yes	—
314	C₄	C₄×C₄⋊C₄×C₆₁	1	2	yes	—
315	C₄	C₂²×C₄²×C₆₁	1	1	yes	characteristic
316	C₄	C₂²×C₄⋊C₄×C₆₁	1	1	yes	characteristic
317	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
318	C₄	C₂×C₄×Q₈×C₆₁	1	1	yes	characteristic
319	C₂	—	2	1	no	—
320	C₂	—	2	2	no	—
321	C₂	—	2	1	no	—
322	C₂	C₆₁×#1772	1	4	yes	direct product factor
323	C₂	C₂×C₄×C₄⋊C₄×C₆₁	1	1	yes	characteristic
324	C₂	C₂×C₆₁×#443	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₆₁	D₄
commutator	C₄	C₂²×C₄²×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₄×D₄
prime radical	C₂⁴×C₆₁	#41
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₆₁ ◁ C₂³×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₁×#1772	C₂	direct (N × H)
12. C₂×#108×C₆₁	C₄	semidirect
14. C₆₁×#427	C₄	semidirect
16. C₂×#107×C₆₁	C₄	semidirect
17. C₂×#106×C₆₁	C₄	semidirect
22. C₂×C₄×C₈×C₆₁	C₄	semidirect
55. #108×C₆₁	C₂×C₄	semidirect
56. #107×C₆₁	C₂×C₄	semidirect
57. #106×C₆₁	C₂×C₄	semidirect
60. C₄×C₈×C₆₁	C₂×C₄	semidirect
138. C₂×#1772	C₆₁	direct (N × H)
161. #1772	C₂×C₆₁	direct (N × H)
166. C₂×C₆₁	#1772	direct (N × H)
174. C₂×#108	C₄×C₆₁	semidirect
176. #427	C₄×C₆₁	semidirect
178. C₂×#107	C₄×C₆₁	semidirect
179. C₂×#106	C₄×C₆₁	semidirect
184. C₂×C₄×C₈	C₄×C₆₁	semidirect
187. C₆₁	C₂×#1772	direct (N × H)
218. #108	C₂×C₄×C₆₁	semidirect
219. #107	C₂×C₄×C₆₁	semidirect
220. #106	C₂×C₄×C₆₁	semidirect
223. C₄×C₈	C₂×C₄×C₆₁	semidirect
322. C₂	C₆₁×#1772	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#108×C₆₁	2
C₂×C₆₁×#427	2
C₂×C₆₁×#405	2
C₂²×C₄×C₈×C₆₁	2
C₆₁×#1772	2
C₂×C₆₁×#339	2
C₂×#1772	61

Subgroups — C2×C61×#1772 #29523875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1772 #29523875