Subgroups — #29569451

Order 15616.

714 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839815	C₂	1	1	yes	maximal, characteristic
2	C₄×#14519736	C₂	1	1	yes	maximal, characteristic
3	#21443651	C₂	1	4	yes	maximal, complemented
4	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic
5	C₂×#14519736	C₄	1	2	yes	—
6	#16839815	—	2	1	no	—
7	#16839815	—	2	1	no	—
8	#16839815	C₄	1	2	yes	complemented
9	#16839815	C₂²	1	2	yes	—
10	C₂×C₄⋊#92418	C₄	1	2	yes	complemented
11	C₂×C₂²⋊#92418	—	2	1	no	—
12	C₂×C₄×#92418	—	2	1	no	—
13	C₄×C₄⋊Dic₆₁	—	2	1	no	—
14	C₄×C₄⋊Dic₆₁	—	2	1	no	—
15	C₄×C₂²⋊Dic₆₁	—	2	1	no	—
16	C₄×C₂²⋊Dic₆₁	—	2	1	no	—
17	#16839608	C₄	1	2	yes	—
18	C₄²×Dic₆₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#431	—	2	1	no	—
21	C₆₁×#431	—	2	1	no	—
22	C₆₁×#431	C₄	1	2	yes	complemented
23	C₆₁×#431	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₆₁	C₄	1	2	yes	complemented
25	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
26	C₂×C₄×C₈×C₆₁	—	2	1	no	—
27	C₂²×#92418	—	2	2	no	—
28	#14519736	—	2	4	no	—
29	#14519736	C₈	1	8	yes	complemented
30	C₂×C₄⋊Dic₆₁	—	2	2	no	—
31	C₂×C₂²⋊Dic₆₁	—	2	2	no	—
32	C₂×C₄×Dic₆₁	—	2	2	no	—
33	C₂×C₄×Dic₆₁	—	2	2	no	—
34	C₂×C₄×Dic₆₁	C₂×C₄	1	4	yes	—
35	C₄⋊#92418	—	2	2	no	—
36	C₄⋊#92418	C₂×C₄	1	4	yes	—
37	C₂²⋊#92418	—	2	2	no	—
38	C₂²⋊#92418	—	2	2	no	—
39	C₄×#92418	—	2	2	no	—
40	C₄×#92418	—	2	2	no	—
41	#14519684	—	2	2	no	—
42	#14519684	—	2	2	no	—
43	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₆₁	—	2	2	no	—
47	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
57	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
58	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₆₁	—	2	2	no	—
60	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
61	C₂²⋊C₈×C₆₁	—	2	2	no	—
62	C₂²⋊C₈×C₆₁	—	2	2	no	—
63	C₄×C₈×C₆₁	—	2	2	no	—
64	C₄×C₈×C₆₁	—	2	2	no	—
65	C₂⁴×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₆₁	—	4	2	no	—
67	C₂²×C₄×C₆₁	—	4	2	no	—
68	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
69	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₁	C₂×C₈	1	4	yes	—
84	C₂²×C₄×C₆₁	M₁₆	1	4	yes	—
85	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₆₁	—	2	4	no	—
89	C₂×C₈×C₆₁	—	2	4	no	—
90	C₂×C₈×C₆₁	—	4	4	no	—
91	C₄²×C₆₁	C₄²	1	1	yes	characteristic
92	C₄²×C₆₁	C₄²	1	1	yes	characteristic
93	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
107	C₂²⋊Dic₆₁	—	2	8	no	—
108	C₄⋊Dic₆₁	—	2	8	no	—
109	C₄×Dic₆₁	—	2	4	no	—
110	C₄×Dic₆₁	—	4	4	no	—
111	C₄×Dic₆₁	—	4	4	no	—
112	C₄×Dic₆₁	C₂×C₈	1	8	yes	complemented
113	C₂×#92418	—	2	4	no	—
114	C₂×#92418	—	4	4	no	—
115	C₂³×C₆₁	—	4	1	no	—
116	C₂³×C₆₁	—	4	1	no	—
117	C₂³×C₆₁	#95	1	1	yes	characteristic
118	C₂³×C₆₁	#95	1	1	yes	characteristic
119	C₂³×C₆₁	C₂²⋊C₈	1	4	yes	—
120	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₆₁	—	2	2	no	—
122	C₂×C₄×C₆₁	—	2	2	no	—
123	C₂×C₄×C₆₁	—	2	2	no	—
124	C₂×C₄×C₆₁	—	2	2	no	—
125	C₂×C₄×C₆₁	—	2	2	no	—
126	C₂×C₄×C₆₁	—	2	2	no	—
127	C₂×C₄×C₆₁	—	4	1	no	—
128	C₂×C₄×C₆₁	—	4	1	no	—
129	C₂×C₄×C₆₁	—	4	1	no	—
130	C₂×C₄×C₆₁	—	4	1	no	—
131	C₂×C₄×C₆₁	—	4	1	no	—
132	C₂×C₄×C₆₁	—	4	1	no	—
133	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
134	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
135	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
136	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
137	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
138	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
139	C₂×C₄×C₆₁	C₄×C₈	1	2	yes	—
140	C₂×C₄×C₆₁	C₄×C₈	1	2	yes	—
141	C₂×C₄×C₆₁	#97	1	2	yes	—
142	C₂×C₄×C₆₁	#97	1	2	yes	—
143	C₂×C₄×C₆₁	C₂²⋊C₈	1	4	yes	—
144	C₂×C₄×C₆₁	C₄⋊C₈	1	4	yes	—
145	C₂×C₄×C₆₁	C₄⋊C₈	1	4	yes	—
146	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
153	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
154	C₂×Dic₆₁	—	2	8	no	—
155	C₂×Dic₆₁	—	4	4	no	—
156	C₂×Dic₆₁	—	4	4	no	—
157	C₈×C₆₁	—	4	4	no	—
158	#92418	—	4	4	no	—
159	#7866	—	61	1	no	maximal, Sylow
160	C₂²×C₆₁	—	2	1	no	—
161	C₂²×C₆₁	—	2	1	no	—
162	C₂²×C₆₁	—	2	1	no	—
163	C₂²×C₆₁	—	2	1	no	—
164	C₂²×C₆₁	—	2	1	no	—
165	C₂²×C₆₁	—	2	1	no	—
166	C₂²×C₆₁	—	4	4	no	—
167	C₂²×C₆₁	#336	1	2	yes	—
168	C₂²×C₆₁	#336	1	2	yes	—
169	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
170	C₂²×C₆₁	C₂×C₂²⋊C₈	1	2	yes	—
171	C₄×C₆₁	—	2	1	no	—
172	C₄×C₆₁	—	2	1	no	—
173	C₄×C₆₁	—	2	1	no	—
174	C₄×C₆₁	—	2	1	no	—
175	C₄×C₆₁	—	2	1	no	—
176	C₄×C₆₁	—	2	1	no	—
177	C₄×C₆₁	#336	1	2	yes	—
178	C₄×C₆₁	#336	1	2	yes	—
179	C₄×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
180	C₄×C₆₁	C₂×#97	1	1	yes	characteristic
181	C₄×C₆₁	#421	1	2	yes	—
182	C₄×C₆₁	#421	1	2	yes	—
183	C₄×C₆₁	C₂×C₄⋊C₈	1	2	yes	—
184	Dic₆₁	—	4	8	no	—
185	C₂×#431	—	61	1	no	—
186	C₂×#431	D₆₁	1	1	yes	characteristic
187	C₄×#117	—	61	1	no	—
188	#1276	—	61	4	no	—
189	C₂×C₆₁	—	2	2	no	—
190	C₂×C₆₁	—	2	2	no	—
191	C₂×C₆₁	—	2	2	no	—
192	C₂×C₆₁	C₂×#336	1	1	yes	characteristic
193	C₂×C₆₁	#1733	1	1	yes	characteristic
194	C₂×C₆₁	#1733	1	1	yes	characteristic
195	C₂×#117	—	61	2	no	—
196	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
197	#431	—	2	1	no	—
198	#431	—	2	1	no	—
199	#431	—	61	2	no	—
200	#431	—	61	2	no	—
201	#431	—	122	1	no	—
202	#431	—	122	1	no	—
203	#431	Dic₆₁	1	2	yes	complemented
204	#431	C₂×D₆₁	1	2	yes	—
205	C₂×C₄⋊C₈	—	61	2	no	—
206	C₂×C₄⋊C₈	Dic₆₁	1	2	yes	complemented
207	C₂×C₂²⋊C₈	—	2	1	no	—
208	C₂×C₂²⋊C₈	—	122	1	no	—
209	C₂×C₄×C₈	—	2	1	no	—
210	C₂×C₄×C₈	—	122	1	no	—
211	C₄×C₄⋊C₄	—	122	1	no	—
212	C₄×C₄⋊C₄	—	122	1	no	—
213	C₄×C₂²⋊C₄	—	122	1	no	—
214	C₄×C₂²⋊C₄	—	122	1	no	—
215	#376	—	61	2	no	—
216	C₄³	—	61	2	no	—
217	C₆₁	#7866	1	1	yes	characteristic, complemented, Sylow
218	C₂³×C₄	C₄×D₆₁	1	1	yes	characteristic
219	C₂³×C₄	D₂₄₄	1	1	yes	characteristic
220	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	122	2	no	—
223	#117	—	61	8	no	—
224	#117	—	122	4	no	—
225	C₂×C₄⋊C₄	—	122	2	no	—
226	C₂×C₂²⋊C₄	—	122	2	no	—
227	C₂×C₄²	—	61	4	no	—
228	C₂×C₄²	—	122	2	no	—
229	C₂×C₄²	—	122	2	no	—
230	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
231	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
233	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
234	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
235	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
237	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	61	4	no	—
244	C₄⋊C₈	—	122	2	no	—
245	C₄⋊C₈	C₂×Dic₆₁	1	4	yes	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	122	2	no	—
249	C₂²⋊C₈	—	122	2	no	—
250	C₄×C₈	—	2	2	no	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	—	122	2	no	—
253	C₄×C₈	—	122	2	no	—
254	#95	—	122	2	no	—
255	#95	—	122	2	no	—
256	C₂⁴	#11758198	1	1	yes	characteristic
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	122	4	no	—
260	C₂²×C₄	C₈×D₆₁	1	4	yes	—
261	C₂²×C₄	#11758189	1	4	yes	—
262	C₂²×C₄	C₄×Dic₆₁	1	1	yes	characteristic
263	C₂²×C₄	C₄×Dic₆₁	1	1	yes	characteristic
264	C₂²×C₄	#11758196	1	1	yes	characteristic
265	C₂²×C₄	#11758196	1	1	yes	characteristic
266	C₂²×C₄	#11758196	1	1	yes	characteristic
267	C₂²×C₄	#11758196	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
270	C₂²×C₄	#11758198	1	1	yes	characteristic
271	C₂²×C₄	#11758198	1	1	yes	characteristic
272	C₂²×C₄	#11758198	1	1	yes	characteristic
273	C₂²×C₄	#11758198	1	1	yes	characteristic
274	C₂²×C₄	#11758198	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	4	no	—
282	C₂×C₈	—	122	4	no	—
283	C₂×C₈	—	244	4	no	—
284	C₄⋊C₄	—	122	8	no	—
285	C₂²⋊C₄	—	122	8	no	—
286	C₄²	—	61	8	no	—
287	C₄²	—	122	4	no	—
288	C₄²	—	244	4	no	—
289	C₄²	—	244	4	no	—
290	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
291	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
292	C₄²	#11758196	1	1	yes	characteristic
293	C₄²	#11758196	1	1	yes	characteristic
294	C₄²	#11758196	1	1	yes	characteristic
295	C₄²	#11758196	1	1	yes	characteristic
296	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
297	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
298	C₄²	#11758198	1	1	yes	characteristic
299	C₄²	#11758198	1	1	yes	characteristic
300	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
301	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
302	C₄²	C₂×Dic₁₂₂	1	1	yes	characteristic
303	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
304	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
305	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	#14519684	1	1	yes	characteristic
309	C₂³	#14519684	1	1	yes	characteristic
310	C₂³	#14519689	1	4	yes	—
311	C₂³	C₂×#11758198	1	1	yes	characteristic
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	122	8	no	—
325	C₂×C₄	—	244	4	no	—
326	C₂×C₄	—	244	4	no	—
327	C₂×C₄	#14519684	1	1	yes	characteristic
328	C₂×C₄	#14519684	1	1	yes	characteristic
329	C₂×C₄	#14519684	1	1	yes	characteristic
330	C₂×C₄	#14519684	1	1	yes	characteristic
331	C₂×C₄	#14519684	1	1	yes	characteristic
332	C₂×C₄	#14519684	1	1	yes	characteristic
333	C₂×C₄	C₈×Dic₆₁	1	2	yes	—
334	C₂×C₄	C₈×Dic₆₁	1	2	yes	—
335	C₂×C₄	#14519687	1	2	yes	—
336	C₂×C₄	#14519687	1	2	yes	—
337	C₂×C₄	#14519689	1	4	yes	—
338	C₂×C₄	#14519706	1	4	yes	—
339	C₂×C₄	#14519706	1	4	yes	—
340	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
341	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
343	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
344	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
346	C₂×C₄	C₂×C₈×D₆₁	1	2	yes	—
347	C₂×C₄	C₂×#11758189	1	2	yes	—
348	C₈	—	4	4	no	—
349	C₈	—	244	4	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	4	no	—
357	C₂²	#16839516	1	2	yes	—
358	C₂²	#16839516	1	2	yes	—
359	C₂²	C₂×#14519684	1	1	yes	characteristic
360	C₂²	C₂×#14519689	1	2	yes	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	244	8	no	—
368	C₄	#16839516	1	2	yes	—
369	C₄	#16839516	1	2	yes	—
370	C₄	C₂×C₈×Dic₆₁	1	1	yes	characteristic
371	C₄	C₂×#14519687	1	1	yes	characteristic
372	C₄	#16839778	1	2	yes	—
373	C₄	#16839779	1	2	yes	—
374	C₄	C₂×#14519706	1	2	yes	—
375	C₂	—	2	2	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	2	no	—
378	C₂	C₂×#16839516	1	1	yes	characteristic
379	C₂	#21445528	1	1	yes	characteristic
380	C₂	#21445530	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₂×C₆₁×#431	C₂
socle	C₂²×C₆₁	C₂×#95
prime radical	C₂⁴×C₆₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	C₂×#431	D₆₁
hypocenter	C₆₁	#7866
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #21443651	C₂	semidirect
8. #16839815	C₄	semidirect
10. C₂×C₄⋊#92418	C₄	semidirect
22. C₆₁×#431	C₄	semidirect
24. C₂×C₄⋊C₈×C₆₁	C₄	semidirect
29. #14519736	C₈	semidirect
112. C₄×Dic₆₁	C₂×C₈	semidirect
203. #431	Dic₆₁	semidirect
206. C₂×C₄⋊C₈	Dic₆₁	semidirect
217. C₆₁	#7866	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839815	2
C₄×#14519736	2
#21443651	2
C₂×C₆₁×#431	2
#7866	61