Subgroups — C₂×C₆₁×#3027 #29563829

Order 15616.

5110 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#535	C₂	1	3	yes	maximal, complemented
3	C₆₁×#3027	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₆₁×B(4,𝔽₂)	C₂	1	8	yes	maximal, complemented
5	C₂×C₆₁×#410	C₂	1	3	yes	maximal, complemented
6	C₆₁×#585	—	2	12	no	—
7	C₆₁×#585	C₂²	1	8	yes	complemented
8	C₂×2₋¹⁺⁴×C₆₁	—	2	3	no	—
9	C₂×H(5,𝔽₂)×C₆₁	—	2	3	no	—
10	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	4	yes	—
11	C₂²×#41×C₆₁	—	2	6	no	—
12	C₂²×#41×C₆₁	C₂²	1	3	yes	—
13	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
14	C₆₁×#535	—	2	12	no	—
15	C₆₁×#535	C₂²	1	24	yes	complemented
16	C₂×#127×C₆₁	—	2	3	no	—
17	C₂×#124×C₆₁	—	2	3	no	—
18	C₂×#121×C₆₁	—	2	6	no	—
19	C₂×#120×C₆₁	C₂²	1	12	yes	complemented
20	C₂×#117×C₆₁	C₂²	1	3	yes	complemented
21	C₆₁×B(4,𝔽₂)	C₂²	1	64	yes	complemented
22	C₆₁×#410	C₂²	1	24	yes	complemented
23	C₂×#99×C₆₁	C₂²	1	12	yes	complemented
24	C₂⁵×C₆₁	C₂³	1	2	yes	—
25	2₋¹⁺⁴×C₆₁	—	2	24	no	—
26	2₋¹⁺⁴×C₆₁	—	2	24	no	—
27	H(5,𝔽₂)×C₆₁	—	2	24	no	—
28	H(5,𝔽₂)×C₆₁	—	2	24	no	—
29	H(5,𝔽₂)×C₆₁	—	2	24	no	—
30	H(5,𝔽₂)×C₆₁	C₂³	1	16	yes	—
31	C₂×#41×C₆₁	—	2	4	no	—
32	C₂×#41×C₆₁	—	2	12	no	—
33	C₂×#41×C₆₁	—	2	48	no	—
34	C₂×#41×C₆₁	—	2	6	no	—
35	C₂×#41×C₆₁	—	2	12	no	—
36	C₂×#41×C₆₁	—	2	6	no	—
37	C₂×#41×C₆₁	—	2	12	no	—
38	C₂×#41×C₆₁	—	2	48	no	—
39	C₂×#41×C₆₁	D₄	1	12	yes	complemented
40	C₂×#41×C₆₁	C₂³	1	12	yes	—
41	C₂²×Q₈×C₆₁	—	2	6	no	—
42	C₂²×Q₈×C₆₁	D₄	1	3	yes	complemented
43	C₂²×D₄×C₆₁	—	2	6	no	—
44	C₂²×D₄×C₆₁	—	2	12	no	—
45	C₂²×D₄×C₆₁	—	2	12	no	—
46	C₂²×D₄×C₆₁	—	2	3	no	—
47	C₂²×D₄×C₆₁	—	2	6	no	—
48	C₂²×D₄×C₆₁	—	2	3	no	—
49	C₂²×D₄×C₆₁	D₄	1	3	yes	complemented
50	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
51	C₂²×D₄×C₆₁	C₂³	1	4	yes	complemented
52	C₂³×C₄×C₆₁	—	2	4	no	—
53	C₂³×C₄×C₆₁	D₄	1	6	yes	complemented
54	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
55	#127×C₆₁	—	2	24	no	—
56	#124×C₆₁	—	2	24	no	—
57	#121×C₆₁	—	2	48	no	—
58	#120×C₆₁	—	2	24	no	—
59	#120×C₆₁	C₂³	1	48	yes	complemented
60	#117×C₆₁	—	2	6	no	—
61	#117×C₆₁	C₂³	1	12	yes	complemented
62	C₂×C₄⋊C₄×C₆₁	—	2	3	no	—
63	C₂×C₂²⋊C₄×C₆₁	—	2	12	no	—
64	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
65	C₂×C₄²×C₆₁	—	2	3	no	—
66	#99×C₆₁	C₂³	1	48	yes	complemented
67	C₂⁴×C₆₁	—	2	4	no	—
68	C₂⁴×C₆₁	—	2	6	no	—
69	C₂⁴×C₆₁	—	2	6	no	—
70	C₂⁴×C₆₁	—	8	4	no	—
71	C₂⁴×C₆₁	C₂×D₄	1	6	yes	—
72	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
73	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
74	#41×C₆₁	—	2	32	no	—
75	#41×C₆₁	—	2	48	no	—
76	#41×C₆₁	—	2	96	no	—
77	#41×C₆₁	—	2	24	no	—
78	#41×C₆₁	—	2	24	no	—
79	#41×C₆₁	—	2	24	no	—
80	#41×C₆₁	—	2	48	no	—
81	#41×C₆₁	—	2	24	no	—
82	C₂×Q₈×C₆₁	—	2	4	no	—
83	C₂×Q₈×C₆₁	—	2	48	no	—
84	C₂×Q₈×C₆₁	—	2	6	no	—
85	C₂×Q₈×C₆₁	—	2	6	no	—
86	C₂×Q₈×C₆₁	C₂×D₄	1	12	yes	complemented
87	C₂×D₄×C₆₁	—	2	12	no	—
88	C₂×D₄×C₆₁	—	2	48	no	—
89	C₂×D₄×C₆₁	—	2	48	no	—
90	C₂×D₄×C₆₁	—	2	12	no	—
91	C₂×D₄×C₆₁	—	2	48	no	—
92	C₂×D₄×C₆₁	—	2	12	no	—
93	C₂×D₄×C₆₁	—	2	48	no	—
94	C₂×D₄×C₆₁	—	2	6	no	—
95	C₂×D₄×C₆₁	—	2	6	no	—
96	C₂×D₄×C₆₁	—	2	12	no	—
97	C₂×D₄×C₆₁	—	2	12	no	—
98	C₂×D₄×C₆₁	—	4	6	no	—
99	C₂×D₄×C₆₁	—	4	6	no	—
100	C₂×D₄×C₆₁	—	4	1	no	—
101	C₂×D₄×C₆₁	—	4	3	no	—
102	C₂×D₄×C₆₁	—	8	24	no	—
103	C₂×D₄×C₆₁	C₂×D₄	1	12	yes	—
104	C₂×D₄×C₆₁	C₂×D₄	1	12	yes	complemented
105	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
106	C₂²×C₄×C₆₁	—	2	12	no	—
107	C₂²×C₄×C₆₁	—	2	32	no	—
108	C₂²×C₄×C₆₁	—	2	6	no	—
109	C₂²×C₄×C₆₁	—	2	6	no	—
110	C₂²×C₄×C₆₁	—	2	12	no	—
111	C₂²×C₄×C₆₁	—	2	6	no	—
112	C₂²×C₄×C₆₁	C₂×D₄	1	6	yes	—
113	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
114	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
115	C₂²×C₄×C₆₁	C₂×D₄	1	6	yes	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	24	yes	complemented
117	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
118	C₄⋊C₄×C₆₁	—	2	12	no	—
119	C₂²⋊C₄×C₆₁	—	2	6	no	—
120	C₂²⋊C₄×C₆₁	—	2	48	no	—
121	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
122	C₄²×C₆₁	—	2	12	no	—
123	C₂³×C₆₁	—	2	16	no	—
124	C₂³×C₆₁	—	2	6	no	—
125	C₂³×C₆₁	—	2	6	no	—
126	C₂³×C₆₁	—	2	12	no	—
127	C₂³×C₆₁	—	4	2	no	—
128	C₂³×C₆₁	—	4	12	no	—
129	C₂³×C₆₁	—	4	24	no	—
130	C₂³×C₆₁	—	4	6	no	—
131	C₂³×C₆₁	—	4	2	no	—
132	C₂³×C₆₁	—	8	4	no	—
133	C₂³×C₆₁	—	8	8	no	—
134	C₂³×C₆₁	—	8	12	no	—
135	C₂³×C₆₁	C₂²×D₄	1	3	yes	—
136	C₂³×C₆₁	C₂²×D₄	1	12	yes	—
137	C₂³×C₆₁	C₂²×D₄	1	3	yes	—
138	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
139	Q₈×C₆₁	—	2	16	no	—
140	Q₈×C₆₁	—	2	24	no	—
141	D₄×C₆₁	—	2	48	no	—
142	D₄×C₆₁	—	2	24	no	—
143	D₄×C₆₁	—	2	24	no	—
144	D₄×C₆₁	—	2	24	no	—
145	D₄×C₆₁	—	4	4	no	—
146	D₄×C₆₁	—	4	12	no	—
147	D₄×C₆₁	—	8	48	no	—
148	C₂×C₄×C₆₁	—	2	48	no	—
149	C₂×C₄×C₆₁	—	2	6	no	—
150	C₂×C₄×C₆₁	—	2	6	no	—
151	C₂×C₄×C₆₁	—	2	24	no	—
152	C₂×C₄×C₆₁	—	2	24	no	—
153	C₂×C₄×C₆₁	—	2	12	no	—
154	C₂×C₄×C₆₁	—	4	12	no	—
155	C₂×C₄×C₆₁	#120	1	6	yes	—
156	C₂×C₄×C₆₁	#120	1	6	yes	—
157	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
158	C₂×C₄×C₆₁	#120	1	3	yes	—
159	C₂×C₄×C₆₁	C₂²×D₄	1	12	yes	—
160	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
161	C₂×C₄×C₆₁	C₂²×D₄	1	6	yes	—
162	C₂×#3027	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₆₁	—	2	6	no	—
164	C₂²×C₆₁	—	2	12	no	—
165	C₂²×C₆₁	—	4	3	no	—
166	C₂²×C₆₁	—	4	1	no	—
167	C₂²×C₆₁	—	4	12	no	—
168	C₂²×C₆₁	—	4	24	no	—
169	C₂²×C₆₁	—	4	12	no	—
170	C₂²×C₆₁	—	4	4	no	—
171	C₂²×C₆₁	—	8	6	no	—
172	C₂²×C₆₁	—	8	12	no	—
173	C₂²×C₆₁	—	8	16	no	—
174	C₂²×C₆₁	—	8	4	no	—
175	C₂²×C₆₁	C₂×#120	1	3	yes	—
176	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
177	C₂²×C₆₁	C₂³×D₄	1	3	yes	—
178	C₄×C₆₁	—	2	12	no	—
179	C₄×C₆₁	—	4	12	no	—
180	C₄×C₆₁	C₂×#120	1	2	yes	—
181	C₄×C₆₁	C₂×#120	1	6	yes	—
182	C₂×#585	C₂×C₆₁	1	1	yes	characteristic, complemented
183	C₂×#535	C₂×C₆₁	1	3	yes	complemented
184	#3027	C₂×C₆₁	1	16	yes	direct product factor
185	C₂×B(4,𝔽₂)	C₂×C₆₁	1	8	yes	complemented
186	C₂×#410	C₂×C₆₁	1	3	yes	complemented
187	C₂×C₆₁	—	2	3	no	—
188	C₂×C₆₁	—	2	3	no	—
189	C₂×C₆₁	—	4	12	no	—
190	C₂×C₆₁	—	8	4	no	—
191	C₂×C₆₁	#3027	1	2	yes	direct product factor
192	C₂×C₆₁	C₂²×#120	1	1	yes	characteristic
193	#585	—	2	12	no	—
194	#585	C₂²×C₆₁	1	8	yes	complemented
195	C₂×2₋¹⁺⁴	—	2	3	no	—
196	C₂×H(5,𝔽₂)	—	2	3	no	—
197	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	4	yes	—
198	C₂²×#41	—	2	6	no	—
199	C₂²×#41	C₂²×C₆₁	1	3	yes	—
200	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
201	#535	—	2	12	no	—
202	#535	C₂²×C₆₁	1	24	yes	complemented
203	C₂×#127	—	2	3	no	—
204	C₂×#124	—	2	3	no	—
205	C₂×#121	—	2	6	no	—
206	C₂×#120	C₂²×C₆₁	1	12	yes	complemented
207	C₂×#117	C₂²×C₆₁	1	3	yes	complemented
208	B(4,𝔽₂)	C₂²×C₆₁	1	64	yes	complemented
209	#410	C₂²×C₆₁	1	24	yes	complemented
210	C₂×#99	C₂²×C₆₁	1	12	yes	complemented
211	C₆₁	C₂×#3027	1	1	yes	characteristic, direct product factor, Sylow
212	C₂⁵	C₂³×C₆₁	1	2	yes	—
213	2₋¹⁺⁴	—	2	24	no	—
214	2₋¹⁺⁴	—	2	24	no	—
215	H(5,𝔽₂)	—	2	24	no	—
216	H(5,𝔽₂)	—	2	24	no	—
217	H(5,𝔽₂)	—	2	24	no	—
218	H(5,𝔽₂)	C₂³×C₆₁	1	16	yes	—
219	C₂×#41	—	2	4	no	—
220	C₂×#41	—	2	12	no	—
221	C₂×#41	—	2	48	no	—
222	C₂×#41	—	2	6	no	—
223	C₂×#41	—	2	12	no	—
224	C₂×#41	—	2	6	no	—
225	C₂×#41	—	2	12	no	—
226	C₂×#41	—	2	48	no	—
227	C₂×#41	D₄×C₆₁	1	12	yes	complemented
228	C₂×#41	C₂³×C₆₁	1	12	yes	—
229	C₂²×Q₈	—	2	6	no	—
230	C₂²×Q₈	D₄×C₆₁	1	3	yes	complemented
231	C₂²×D₄	—	2	6	no	—
232	C₂²×D₄	—	2	12	no	—
233	C₂²×D₄	—	2	12	no	—
234	C₂²×D₄	—	2	3	no	—
235	C₂²×D₄	—	2	3	no	—
236	C₂²×D₄	—	2	6	no	—
237	C₂²×D₄	D₄×C₆₁	1	3	yes	complemented
238	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
239	C₂²×D₄	C₂³×C₆₁	1	4	yes	complemented
240	C₂³×C₄	—	2	4	no	—
241	C₂³×C₄	D₄×C₆₁	1	6	yes	complemented
242	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
243	#127	—	2	24	no	—
244	#124	—	2	24	no	—
245	#121	—	2	48	no	—
246	#120	—	2	24	no	—
247	#120	C₂³×C₆₁	1	48	yes	complemented
248	#117	—	2	6	no	—
249	#117	C₂³×C₆₁	1	12	yes	complemented
250	C₂×C₄⋊C₄	—	2	3	no	—
251	C₂×C₂²⋊C₄	—	2	12	no	—
252	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
253	C₂×C₄²	—	2	3	no	—
254	#99	C₂³×C₆₁	1	48	yes	complemented
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	6	no	—
257	C₂⁴	—	2	6	no	—
258	C₂⁴	—	8	4	no	—
259	C₂⁴	C₂×D₄×C₆₁	1	6	yes	—
260	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
261	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
262	#41	—	2	32	no	—
263	#41	—	2	48	no	—
264	#41	—	2	96	no	—
265	#41	—	2	24	no	—
266	#41	—	2	24	no	—
267	#41	—	2	24	no	—
268	#41	—	2	48	no	—
269	#41	—	2	24	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	48	no	—
272	C₂×Q₈	—	2	6	no	—
273	C₂×Q₈	—	2	6	no	—
274	C₂×Q₈	C₂×D₄×C₆₁	1	12	yes	complemented
275	C₂×D₄	—	2	12	no	—
276	C₂×D₄	—	2	48	no	—
277	C₂×D₄	—	2	48	no	—
278	C₂×D₄	—	2	12	no	—
279	C₂×D₄	—	2	48	no	—
280	C₂×D₄	—	2	12	no	—
281	C₂×D₄	—	2	48	no	—
282	C₂×D₄	—	2	6	no	—
283	C₂×D₄	—	2	6	no	—
284	C₂×D₄	—	2	12	no	—
285	C₂×D₄	—	2	12	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	3	no	—
288	C₂×D₄	—	4	6	no	—
289	C₂×D₄	—	4	6	no	—
290	C₂×D₄	—	8	24	no	—
291	C₂×D₄	C₂×D₄×C₆₁	1	12	yes	—
292	C₂×D₄	C₂×D₄×C₆₁	1	12	yes	complemented
293	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
294	C₂²×C₄	—	2	12	no	—
295	C₂²×C₄	—	2	32	no	—
296	C₂²×C₄	—	2	6	no	—
297	C₂²×C₄	—	2	6	no	—
298	C₂²×C₄	—	2	12	no	—
299	C₂²×C₄	—	2	6	no	—
300	C₂²×C₄	C₂×D₄×C₆₁	1	6	yes	—
301	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
302	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
303	C₂²×C₄	C₂×D₄×C₆₁	1	6	yes	—
304	C₂²×C₄	C₂×D₄×C₆₁	1	24	yes	complemented
305	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
306	C₄⋊C₄	—	2	12	no	—
307	C₂²⋊C₄	—	2	6	no	—
308	C₂²⋊C₄	—	2	48	no	—
309	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
310	C₄²	—	2	12	no	—
311	C₂³	—	2	16	no	—
312	C₂³	—	2	6	no	—
313	C₂³	—	2	6	no	—
314	C₂³	—	2	12	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	12	no	—
317	C₂³	—	4	24	no	—
318	C₂³	—	4	6	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	8	4	no	—
321	C₂³	—	8	8	no	—
322	C₂³	—	8	12	no	—
323	C₂³	C₂²×D₄×C₆₁	1	3	yes	—
324	C₂³	C₂²×D₄×C₆₁	1	12	yes	—
325	C₂³	C₂²×D₄×C₆₁	1	3	yes	—
326	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
327	Q₈	—	2	16	no	—
328	Q₈	—	2	24	no	—
329	D₄	—	2	48	no	—
330	D₄	—	2	24	no	—
331	D₄	—	2	24	no	—
332	D₄	—	2	24	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	12	no	—
335	D₄	—	8	48	no	—
336	C₂×C₄	—	2	48	no	—
337	C₂×C₄	—	2	6	no	—
338	C₂×C₄	—	2	6	no	—
339	C₂×C₄	—	2	24	no	—
340	C₂×C₄	—	2	24	no	—
341	C₂×C₄	—	2	12	no	—
342	C₂×C₄	—	4	12	no	—
343	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
344	C₂×C₄	#120×C₆₁	1	3	yes	—
345	C₂×C₄	#120×C₆₁	1	6	yes	—
346	C₂×C₄	#120×C₆₁	1	6	yes	—
347	C₂×C₄	C₂²×D₄×C₆₁	1	12	yes	—
348	C₂×C₄	C₂²×D₄×C₆₁	1	6	yes	—
349	C₂×C₄	C₂²×D₄×C₆₁	1	6	yes	—
350	C₂²	—	2	6	no	—
351	C₂²	—	2	12	no	—
352	C₂²	—	4	3	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	12	no	—
355	C₂²	—	4	24	no	—
356	C₂²	—	4	12	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	8	6	no	—
359	C₂²	—	8	12	no	—
360	C₂²	—	8	16	no	—
361	C₂²	—	8	4	no	—
362	C₂²	C₂×#120×C₆₁	1	3	yes	—
363	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
364	C₂²	C₂³×D₄×C₆₁	1	3	yes	—
365	C₄	—	2	12	no	—
366	C₄	—	4	12	no	—
367	C₄	C₂×#120×C₆₁	1	2	yes	—
368	C₄	C₂×#120×C₆₁	1	6	yes	—
369	C₂	—	2	3	no	—
370	C₂	—	2	3	no	—
371	C₂	—	4	12	no	—
372	C₂	—	8	4	no	—
373	C₂	C₆₁×#3027	1	2	yes	direct product factor
374	C₂	C₂²×#120×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂³×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#585	C₂	semidirect
2. C₂×C₆₁×#535	C₂	semidirect
3. C₆₁×#3027	C₂	direct (N × H)
4. C₂×C₆₁×B(4,𝔽₂)	C₂	semidirect
5. C₂×C₆₁×#410	C₂	semidirect
7. C₆₁×#585	C₂²	semidirect
13. C₂³×D₄×C₆₁	C₂²	semidirect
15. C₆₁×#535	C₂²	semidirect
19. C₂×#120×C₆₁	C₂²	semidirect
20. C₂×#117×C₆₁	C₂²	semidirect
21. C₆₁×B(4,𝔽₂)	C₂²	semidirect
22. C₆₁×#410	C₂²	semidirect
23. C₂×#99×C₆₁	C₂²	semidirect
39. C₂×#41×C₆₁	D₄	semidirect
42. C₂²×Q₈×C₆₁	D₄	semidirect
49. C₂²×D₄×C₆₁	D₄	semidirect
51. C₂²×D₄×C₆₁	C₂³	semidirect
53. C₂³×C₄×C₆₁	D₄	semidirect
59. #120×C₆₁	C₂³	semidirect
61. #117×C₆₁	C₂³	semidirect
66. #99×C₆₁	C₂³	semidirect
86. C₂×Q₈×C₆₁	C₂×D₄	semidirect
104. C₂×D₄×C₆₁	C₂×D₄	semidirect
116. C₂²×C₄×C₆₁	C₂×D₄	semidirect
162. C₂×#3027	C₆₁	direct (N × H)
182. C₂×#585	C₂×C₆₁	semidirect
183. C₂×#535	C₂×C₆₁	semidirect
184. #3027	C₂×C₆₁	direct (N × H)
185. C₂×B(4,𝔽₂)	C₂×C₆₁	semidirect
186. C₂×#410	C₂×C₆₁	semidirect
191. C₂×C₆₁	#3027	direct (N × H)
194. #585	C₂²×C₆₁	semidirect
200. C₂³×D₄	C₂²×C₆₁	semidirect
202. #535	C₂²×C₆₁	semidirect
206. C₂×#120	C₂²×C₆₁	semidirect
207. C₂×#117	C₂²×C₆₁	semidirect
208. B(4,𝔽₂)	C₂²×C₆₁	semidirect
209. #410	C₂²×C₆₁	semidirect
210. C₂×#99	C₂²×C₆₁	semidirect
211. C₆₁	C₂×#3027	direct (N × H)
227. C₂×#41	D₄×C₆₁	semidirect
230. C₂²×Q₈	D₄×C₆₁	semidirect
237. C₂²×D₄	D₄×C₆₁	semidirect
239. C₂²×D₄	C₂³×C₆₁	semidirect
241. C₂³×C₄	D₄×C₆₁	semidirect
247. #120	C₂³×C₆₁	semidirect
249. #117	C₂³×C₆₁	semidirect
254. #99	C₂³×C₆₁	semidirect
274. C₂×Q₈	C₂×D₄×C₆₁	semidirect
292. C₂×D₄	C₂×D₄×C₆₁	semidirect
304. C₂²×C₄	C₂×D₄×C₆₁	semidirect
373. C₂	C₆₁×#3027	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#585	2
C₂×C₆₁×#535	2
C₆₁×#3027	2
C₂×C₆₁×B(4,𝔽₂)	2
C₂×C₆₁×#410	2
C₂×#3027	61

Subgroups — C2×C61×#3027 #29563829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3027 #29563829