Subgroups — #29569902

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839819	C₂	1	1	yes	maximal, characteristic
2	#21448217	C₂	1	1	yes	maximal, characteristic
3	#21443686	C₂	1	4	yes	maximal
4	C₆₁×#2285	C₂	1	1	yes	maximal, characteristic
5	#16839819	—	2	1	no	—
6	#16839819	—	2	1	no	—
7	#16839819	—	2	1	no	—
8	#16839819	—	2	1	no	—
9	C₂×C₄⋊#92418	C₄	1	2	yes	complemented
10	C₂×C₂²⋊#92418	C₂²	1	2	yes	—
11	C₂×#14519688	C₄	1	2	yes	complemented
12	#16839630	C₄	1	2	yes	complemented
13	#16839628	—	2	1	no	—
14	#16839625	—	2	1	no	—
15	#16839622	C₂²	1	2	yes	—
16	C₄×C₄⋊Dic₆₁	—	2	1	no	—
17	C₄×C₂²⋊Dic₆₁	—	2	1	no	—
18	#16839608	C₄	1	2	yes	complemented
19	C₂×#117×C₆₁	—	2	1	no	—
20	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#384	—	2	1	no	—
22	C₆₁×#382	C₄	1	2	yes	complemented
23	C₆₁×#380	—	2	1	no	—
24	C₆₁×#380	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
26	C₄×C₄⋊C₄×C₆₁	C₄	1	2	yes	complemented
27	C₂²×#92418	C₂×C₄	1	4	yes	—
28	C₂×C₄⋊Dic₆₁	—	2	2	no	—
29	C₂×C₂²⋊Dic₆₁	—	2	2	no	—
30	C₂×C₄×Dic₆₁	—	2	2	no	—
31	C₄⋊#92418	—	2	2	no	—
32	C₄⋊#92418	—	2	2	no	—
33	C₂²⋊#92418	—	2	2	no	—
34	C₂²⋊#92418	—	2	2	no	—
35	#14519688	—	2	2	no	—
36	#14519688	—	2	2	no	—
37	#14519684	—	2	2	no	—
38	#14519684	—	2	2	no	—
39	#14519684	—	2	2	no	—
40	#14519684	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
44	#117×C₆₁	—	4	4	no	—
45	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
46	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
49	C₂×C₄²×C₆₁	—	2	2	no	—
50	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
62	#95×C₆₁	—	2	2	no	—
63	#95×C₆₁	C₂×C₄	1	4	yes	—
64	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₆₁	—	2	2	no	—
66	C₂²×C₄×C₆₁	—	2	2	no	—
67	C₂²×C₄×C₆₁	—	2	4	no	—
68	C₂²×C₄×C₆₁	—	4	2	no	—
69	C₂²×C₄×C₆₁	—	4	2	no	—
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	C₂²⋊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	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
88	C₂²×Dic₆₁	—	2	4	no	—
89	C₄⋊C₄×C₆₁	—	4	4	no	—
90	C₄⋊C₄×C₆₁	—	4	4	no	—
91	C₄⋊C₄×C₆₁	—	4	4	no	—
92	C₂²⋊C₄×C₆₁	—	4	4	no	—
93	C₄²×C₆₁	—	4	4	no	—
94	C₄²×C₆₁	C₄²	1	1	yes	characteristic
95	C₄²×C₆₁	C₄²	1	1	yes	characteristic
96	C₄²×C₆₁	C₄²	1	1	yes	characteristic
97	C₄²×C₆₁	C₄²	1	1	yes	characteristic
98	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂²⋊Dic₆₁	—	4	2	no	—
111	C₂²⋊Dic₆₁	—	4	2	no	—
112	C₄⋊Dic₆₁	—	4	4	no	—
113	C₄×Dic₆₁	—	4	4	no	—
114	C₂×#92418	—	2	4	no	—
115	C₂×#92418	—	4	4	no	—
116	C₂³×C₆₁	—	4	1	no	—
117	C₂³×C₆₁	—	4	1	no	—
118	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
122	C₂³×C₆₁	#137	1	2	yes	—
123	C₂×C₄×C₆₁	—	2	2	no	—
124	C₂×C₄×C₆₁	—	2	2	no	—
125	C₂×C₄×C₆₁	—	2	1	no	—
126	C₂×C₄×C₆₁	—	2	1	no	—
127	C₂×C₄×C₆₁	—	2	1	no	—
128	C₂×C₄×C₆₁	—	2	1	no	—
129	C₂×C₄×C₆₁	—	2	2	no	—
130	C₂×C₄×C₆₁	—	2	2	no	—
131	C₂×C₄×C₆₁	—	2	2	no	—
132	C₂×C₄×C₆₁	—	2	2	no	—
133	C₂×C₄×C₆₁	—	2	2	no	—
134	C₂×C₄×C₆₁	—	2	2	no	—
135	C₂×C₄×C₆₁	—	2	2	no	—
136	C₂×C₄×C₆₁	—	2	2	no	—
137	C₂×C₄×C₆₁	—	4	1	no	—
138	C₂×C₄×C₆₁	—	4	1	no	—
139	C₂×C₄×C₆₁	—	4	1	no	—
140	C₂×C₄×C₆₁	—	4	1	no	—
141	C₂×C₄×C₆₁	—	4	1	no	—
142	C₂×C₄×C₆₁	—	4	1	no	—
143	C₂×C₄×C₆₁	—	4	4	no	—
144	C₂×C₄×C₆₁	—	4	4	no	—
145	C₂×C₄×C₆₁	—	4	4	no	—
146	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
148	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
149	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
150	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
151	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
152	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
153	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₆₁	—	4	4	no	—
159	C₂×Dic₆₁	—	4	4	no	—
160	C₂×Dic₆₁	—	4	4	no	—
161	#92418	—	4	4	no	—
162	#7984	—	61	1	no	maximal, Sylow
163	C₂²×C₆₁	—	2	1	no	—
164	C₂²×C₆₁	—	2	1	no	—
165	C₂²×C₆₁	—	2	1	no	—
166	C₂²×C₆₁	—	2	1	no	—
167	C₂²×C₆₁	—	2	1	no	—
168	C₂²×C₆₁	—	2	1	no	—
169	C₂²×C₆₁	—	4	2	no	—
170	C₂²×C₆₁	—	4	2	no	—
171	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
172	C₂²×C₆₁	#417	1	2	yes	—
173	C₂²×C₆₁	#418	1	1	yes	characteristic
174	C₂²×C₆₁	#419	1	1	yes	characteristic
175	C₂²×C₆₁	#428	1	2	yes	—
176	C₄×C₆₁	—	2	1	no	—
177	C₄×C₆₁	—	2	1	no	—
178	C₄×C₆₁	—	2	1	no	—
179	C₄×C₆₁	—	2	1	no	—
180	C₄×C₆₁	—	2	1	no	—
181	C₄×C₆₁	—	2	1	no	—
182	C₄×C₆₁	—	2	1	no	—
183	C₄×C₆₁	—	2	1	no	—
184	C₄×C₆₁	—	2	1	no	—
185	C₄×C₆₁	—	2	1	no	—
186	C₄×C₆₁	—	8	4	no	—
187	C₄×C₆₁	H(3,ℤ/4)	1	2	yes	—
188	C₄×C₆₁	#410	1	2	yes	—
189	Dic₆₁	—	8	4	no	—
190	C₂×#432	—	61	1	no	—
191	#2285	D₆₁	1	1	yes	characteristic
192	#2283	—	61	1	no	—
193	#1289	—	61	4	no	—
194	C₂×C₆₁	—	2	2	no	—
195	C₂×C₆₁	—	2	1	no	—
196	C₂×C₆₁	—	2	1	no	—
197	C₂×C₆₁	—	2	2	no	—
198	C₂×C₆₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
199	C₂×C₆₁	#1736	1	1	yes	characteristic
200	C₂×C₆₁	#1740	1	1	yes	characteristic
201	C₂×#117	—	2	1	no	—
202	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
203	#432	—	122	1	no	—
204	#432	—	122	1	no	—
205	#432	—	122	1	no	—
206	#432	—	122	1	no	—
207	C₂×C₄⋊C₈	—	61	2	no	—
208	C₂×C₂²⋊C₈	—	61	2	no	—
209	C₂×#97	—	61	2	no	—
210	#384	—	2	1	no	—
211	#383	—	61	2	no	—
212	#382	—	122	1	no	—
213	#382	Dic₆₁	1	2	yes	complemented
214	#381	—	122	1	no	—
215	#380	—	2	1	no	—
216	#380	—	61	2	no	—
217	#380	C₂×D₆₁	1	2	yes	—
218	C₄×C₄⋊C₄	—	2	1	no	—
219	C₄×C₄⋊C₄	—	122	1	no	—
220	C₄×C₄⋊C₄	Dic₆₁	1	2	yes	complemented
221	C₄×C₂²⋊C₄	—	122	1	no	—
222	#376	—	61	2	no	—
223	C₆₁	#7984	1	1	yes	characteristic, complemented, Sylow
224	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
226	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
227	C₂²×C₈	—	61	4	no	—
228	#117	—	4	4	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	122	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	122	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	122	2	no	—
237	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
238	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
239	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
240	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
243	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
244	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
247	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
248	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
249	C₄⋊C₈	—	122	2	no	—
250	C₄⋊C₈	—	122	2	no	—
251	C₂²⋊C₈	—	122	2	no	—
252	C₂²⋊C₈	—	122	2	no	—
253	#97	—	122	2	no	—
254	#97	—	122	2	no	—
255	#95	—	2	2	no	—
256	#95	—	61	4	no	—
257	#95	—	122	2	no	—
258	#95	—	122	2	no	—
259	#95	—	122	2	no	—
260	#95	C₂×Dic₆₁	1	4	yes	—
261	C₂⁴	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	122	4	no	—
268	C₂²×C₄	#11758196	1	1	yes	characteristic
269	C₂²×C₄	#11758196	1	1	yes	characteristic
270	C₂²×C₄	#11758196	1	1	yes	characteristic
271	C₂²×C₄	#11758196	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	#11758198	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
280	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
286	C₂×C₈	—	122	4	no	—
287	C₂×C₈	—	244	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	244	4	no	—
292	C₂²⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	244	2	no	—
294	C₂²⋊C₄	—	244	2	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	244	4	no	—
297	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
298	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
299	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
300	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
301	C₄²	#11758196	1	1	yes	characteristic
302	C₄²	#11758196	1	1	yes	characteristic
303	C₄²	#11758196	1	1	yes	characteristic
304	C₄²	#11758196	1	1	yes	characteristic
305	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
306	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
307	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
308	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
309	C₄²	#11758198	1	1	yes	characteristic
310	C₄²	#11758198	1	1	yes	characteristic
311	C₄²	#11758198	1	1	yes	characteristic
312	C₄²	#11758198	1	1	yes	characteristic
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	C₂×#11758198	1	1	yes	characteristic
316	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
317	C₂³	C₂×#11758196	1	1	yes	characteristic
318	C₂³	#14519803	1	2	yes	—
319	C₂³	#14519808	1	2	yes	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	244	4	no	—
344	C₂×C₄	—	244	4	no	—
345	C₂×C₄	—	244	4	no	—
346	C₂×C₄	#14519684	1	1	yes	characteristic
347	C₂×C₄	#14519684	1	1	yes	characteristic
348	C₂×C₄	#14519684	1	1	yes	characteristic
349	C₂×C₄	#14519684	1	1	yes	characteristic
350	C₂×C₄	#14519684	1	1	yes	characteristic
351	C₂×C₄	#14519684	1	1	yes	characteristic
352	C₂×C₄	#14519684	1	1	yes	characteristic
353	C₂×C₄	#14519684	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
355	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
356	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
358	C₈	—	244	4	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×#14519684	1	1	yes	characteristic
368	C₂²	#16839761	1	2	yes	—
369	C₂²	#16839767	1	1	yes	characteristic
370	C₂²	#16839771	1	1	yes	characteristic
371	C₂²	#16839802	1	2	yes	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	4	no	—
383	C₄	—	488	4	no	—
384	C₄	#16839518	1	2	yes	—
385	C₄	#16839735	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	2	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	2	no	—
390	C₂	C₂×#16839518	1	1	yes	characteristic
391	C₂	#21445538	1	1	yes	characteristic
392	C₂	#21445551	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14519684
commutator	C₂×C₄×C₆₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₁
Fitting	C₆₁×#2285	C₂
socle	C₂²×C₆₁	C₂×#95
prime radical	C₂⁴×C₆₁	C₂×D₄
cosocle	C₂³×C₄×C₆₁	C₂³
hypercenter	#2285	D₆₁
hypocenter	C₆₁	#7984
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
9. C₂×C₄⋊#92418	C₄	semidirect
11. C₂×#14519688	C₄	semidirect
12. #16839630	C₄	semidirect
18. #16839608	C₄	semidirect
22. C₆₁×#382	C₄	semidirect
26. C₄×C₄⋊C₄×C₆₁	C₄	semidirect
213. #382	Dic₆₁	semidirect
220. C₄×C₄⋊C₄	Dic₆₁	semidirect
223. C₆₁	#7984	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839819	2
#21448217	2
#21443686	2
C₆₁×#2285	2
#7984	61