Subgroups — #29585917

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14519711	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14519709	C₂	1	1	yes	maximal, characteristic
3	C₂×#16839525	C₂	1	2	yes	maximal
4	#21444049	C₂	1	2	yes	maximal
5	C₂²×#97×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₆₁	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₆₁	C₂²	1	2	yes	—
8	C₂×#14519711	—	2	2	no	—
9	C₂×#14519711	—	2	2	no	—
10	C₂×#14519711	C₄	1	4	yes	complemented
11	C₂×#14519709	—	2	2	no	—
12	C₂×#14519709	—	2	2	no	—
13	C₂×#14519709	C₄	1	4	yes	complemented
14	C₂×#14519684	—	2	4	no	—
15	#16839525	—	2	4	no	—
16	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#97×C₆₁	—	2	2	no	—
20	C₂×#97×C₆₁	—	2	2	no	—
21	C₂×#97×C₆₁	C₄	1	4	yes	complemented
22	C₂³×Dic₆₁	—	2	2	no	—
23	C₂³×Dic₆₁	—	2	2	no	—
24	C₂×C₄⋊Dic₆₁	—	2	2	no	—
25	C₂×C₄⋊Dic₆₁	—	2	2	no	—
26	C₂×C₄⋊Dic₆₁	—	2	2	no	—
27	C₂×C₄⋊Dic₆₁	—	2	2	no	—
28	C₂×C₄⋊Dic₆₁	—	2	2	no	—
29	C₂×C₄⋊Dic₆₁	—	2	2	no	—
30	C₂×C₄⋊Dic₆₁	—	2	2	no	—
31	C₂×C₄⋊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	C₂×C₄⋊Dic₆₁	C₂×C₄	1	4	yes	—
36	#14519711	—	2	8	no	—
37	#14519709	—	2	8	no	—
38	#14519684	—	4	8	no	—
39	C₂³×C₄×C₆₁	D₄	1	2	yes	—
40	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₆₁	—	2	1	no	—
42	C₂²×C₈×C₆₁	—	2	1	no	—
43	C₂²×C₈×C₆₁	—	2	1	no	—
44	C₂²×C₈×C₆₁	—	2	1	no	—
45	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
46	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
47	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₆₁	D₄	1	2	yes	—
50	C₂²×C₈×C₆₁	D₄	1	2	yes	—
51	C₂²×C₈×C₆₁	D₄	1	2	yes	—
52	C₂²×C₈×C₆₁	D₄	1	2	yes	—
53	C₂²×C₈×C₆₁	Q₈	1	2	yes	—
54	C₂²×C₈×C₆₁	Q₈	1	2	yes	—
55	C₂×C₄²×C₆₁	—	2	1	no	—
56	C₂×C₄²×C₆₁	—	2	1	no	—
57	C₂×C₄²×C₆₁	—	2	1	no	—
58	C₂×C₄²×C₆₁	—	2	1	no	—
59	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₆₁	Q₈	1	2	yes	—
61	#97×C₆₁	—	2	8	no	—
62	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₆₁	—	2	2	no	—
64	C₂²×C₄×C₆₁	—	2	2	no	—
65	C₂²×C₄×C₆₁	—	2	4	no	—
66	C₂²×C₄×C₆₁	—	2	4	no	—
67	C₂²×C₄×C₆₁	C₄⋊C₄	1	4	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	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
80	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
82	C₂²×Dic₆₁	—	2	4	no	—
83	C₂²×Dic₆₁	—	2	4	no	—
84	C₂²×Dic₆₁	—	4	2	no	—
85	C₂²×Dic₆₁	—	4	2	no	—
86	C₂²×Dic₆₁	—	4	2	no	—
87	C₂²×Dic₆₁	—	4	2	no	—
88	C₂²×Dic₆₁	—	4	4	no	—
89	C₂²×Dic₆₁	—	4	4	no	—
90	C₂²×Dic₆₁	—	4	4	no	—
91	C₂²×Dic₆₁	—	4	4	no	—
92	C₂×C₈×C₆₁	—	2	2	no	—
93	C₂×C₈×C₆₁	—	2	2	no	—
94	C₂×C₈×C₆₁	—	2	2	no	—
95	C₂×C₈×C₆₁	—	2	2	no	—
96	C₂×C₈×C₆₁	—	2	2	no	—
97	C₂×C₈×C₆₁	—	2	2	no	—
98	C₂×C₈×C₆₁	C₄²	1	4	yes	—
99	C₂×C₈×C₆₁	C₂²⋊C₄	1	4	yes	—
100	C₂×C₈×C₆₁	C₂²⋊C₄	1	4	yes	—
101	C₂×C₈×C₆₁	C₂²⋊C₄	1	4	yes	—
102	C₂×C₈×C₆₁	C₄⋊C₄	1	4	yes	—
103	C₂×C₈×C₆₁	C₄⋊C₄	1	4	yes	—
104	C₂×C₈×C₆₁	C₄⋊C₄	1	4	yes	—
105	C₂×C₈×C₆₁	C₄⋊C₄	1	4	yes	—
106	C₄²×C₆₁	—	2	2	no	—
107	C₄²×C₆₁	—	2	2	no	—
108	C₄²×C₆₁	—	2	2	no	—
109	C₄²×C₆₁	—	2	2	no	—
110	C₄⋊Dic₆₁	—	2	4	no	—
111	C₄⋊Dic₆₁	—	2	4	no	—
112	C₄⋊Dic₆₁	—	2	4	no	—
113	C₄⋊Dic₆₁	—	2	4	no	—
114	C₄⋊Dic₆₁	—	4	2	no	—
115	C₄⋊Dic₆₁	—	4	2	no	—
116	C₄⋊Dic₆₁	—	4	2	no	—
117	C₄⋊Dic₆₁	—	4	2	no	—
118	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
120	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
121	C₂³×C₆₁	#121	1	1	yes	characteristic
122	C₂³×C₆₁	#121	1	1	yes	characteristic
123	C₂³×C₆₁	#127	1	1	yes	characteristic
124	C₂³×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
125	C₂³×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
126	C₂³×C₆₁	#137	1	4	yes	—
127	C₂×C₄×C₆₁	—	2	4	no	—
128	C₂×C₄×C₆₁	—	2	8	no	—
129	C₂×C₄×C₆₁	—	4	4	no	—
130	C₂×C₄×C₆₁	—	4	2	no	—
131	C₂×C₄×C₆₁	—	4	2	no	—
132	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
133	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
141	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
142	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
149	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
155	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
156	C₂×C₄×C₆₁	#125	1	1	yes	characteristic
157	C₂×C₄×C₆₁	#125	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×Dic₆₁	—	4	4	no	—
161	C₂×Dic₆₁	—	4	4	no	—
162	C₂×Dic₆₁	—	4	8	no	—
163	C₂×Dic₆₁	—	4	8	no	—
164	C₂×Dic₆₁	—	8	4	no	—
165	C₂×Dic₆₁	—	8	4	no	—
166	C₂×Dic₆₁	—	8	2	no	—
167	C₂×Dic₆₁	—	8	2	no	—
168	C₂×Dic₆₁	—	8	2	no	—
169	C₂×Dic₆₁	—	8	2	no	—
170	C₈×C₆₁	—	2	4	no	—
171	C₈×C₆₁	#95	1	8	yes	complemented
172	#10863	—	61	1	no	maximal, Sylow
173	C₂²×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×C₆₁	#380	1	1	yes	characteristic
175	C₂²×C₆₁	#384	1	1	yes	characteristic
176	C₂²×C₆₁	#389	1	1	yes	characteristic
177	C₂²×C₆₁	#389	1	1	yes	characteristic
178	C₂²×C₆₁	#390	1	1	yes	characteristic
179	C₂²×C₆₁	#390	1	1	yes	characteristic
180	C₂²×C₆₁	#428	1	4	yes	—
181	C₂²×C₆₁	#440	1	4	yes	—
182	C₂²×C₆₁	#441	1	2	yes	—
183	C₂²×C₆₁	#442	1	2	yes	—
184	C₂²×C₆₁	#468	1	4	yes	—
185	C₂²×C₆₁	#469	1	2	yes	—
186	C₂²×C₆₁	#470	1	2	yes	—
187	C₂²×C₆₁	#496	1	2	yes	—
188	C₂²×C₆₁	#497	1	2	yes	—
189	C₂²×C₆₁	#501	1	4	yes	—
190	C₄×C₆₁	—	4	4	no	—
191	C₄×C₆₁	C₂×#95	1	1	yes	characteristic
192	C₄×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
193	C₄×C₆₁	#380	1	1	yes	characteristic
194	C₄×C₆₁	#382	1	1	yes	characteristic
195	C₄×C₆₁	#389	1	1	yes	characteristic
196	C₄×C₆₁	#389	1	1	yes	characteristic
197	C₄×C₆₁	#391	1	1	yes	characteristic
198	C₄×C₆₁	#391	1	1	yes	characteristic
199	Dic₆₁	—	8	4	no	—
200	Dic₆₁	—	8	4	no	—
201	C₂²×#107	—	61	1	no	—
202	C₂²×#106	—	61	1	no	—
203	C₂²×#97	D₆₁	1	1	yes	characteristic
204	C₂×#340	—	61	2	no	—
205	C₄⋊#95	—	61	2	no	—
206	C₂×C₆₁	C₄⋊#95	1	1	yes	characteristic
207	C₂×C₆₁	#1776	1	2	yes	—
208	C₂×C₆₁	#1809	1	2	yes	—
209	C₂×C₆₁	#1847	1	2	yes	—
210	C₂×C₆₁	#1943	1	2	yes	—
211	C₂×C₆₁	#1944	1	2	yes	—
212	C₂×C₆₁	#1971	1	1	yes	characteristic
213	C₂×C₆₁	#1972	1	1	yes	characteristic
214	C₂×C₆₁	#1973	1	2	yes	—
215	C₂³×C₈	C₂×D₆₁	1	1	yes	characteristic
216	C₂³×C₈	C₂×D₆₁	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	—	61	2	no	—
218	C₂²×C₄⋊C₄	—	61	2	no	—
219	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
220	C₂×#107	—	61	4	no	—
221	C₂×#107	—	122	2	no	—
222	C₂×#107	—	122	2	no	—
223	C₂×#106	—	61	4	no	—
224	C₂×#106	—	122	2	no	—
225	C₂×#106	—	122	2	no	—
226	C₂×#97	—	2	2	no	—
227	C₂×#97	—	2	2	no	—
228	C₂×#97	Dic₆₁	1	4	yes	complemented
229	C₂×#95	—	122	4	no	—
230	#340	—	122	4	no	—
231	C₆₁	#10863	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₄	—	122	2	no	—
233	C₂³×C₄	—	122	2	no	—
234	C₂³×C₄	D₂₄₄	1	2	yes	—
235	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	Dic₁₂₂	1	2	yes	—
241	C₂²×C₈	Dic₁₂₂	1	2	yes	—
242	C₂²×C₈	C₄×D₆₁	1	2	yes	—
243	C₂²×C₈	C₄×D₆₁	1	2	yes	—
244	C₂²×C₈	D₂₄₄	1	2	yes	—
245	C₂²×C₈	D₂₄₄	1	2	yes	—
246	C₂²×C₈	C₂×Dic₆₁	1	2	yes	—
247	C₂²×C₈	C₂×Dic₆₁	1	2	yes	—
248	C₂²×C₈	C₂²⋊D₆₁	1	2	yes	—
249	C₂²×C₈	C₂²⋊D₆₁	1	2	yes	—
250	C₂×C₄⋊C₄	—	61	4	no	—
251	C₂×C₄⋊C₄	—	61	4	no	—
252	C₂×C₄⋊C₄	—	122	2	no	—
253	C₂×C₄⋊C₄	—	122	2	no	—
254	C₂×C₄⋊C₄	—	122	2	no	—
255	C₂×C₄⋊C₄	—	122	2	no	—
256	C₂×C₄⋊C₄	—	122	2	no	—
257	C₂×C₄⋊C₄	—	122	2	no	—
258	C₂×C₄⋊C₄	—	122	2	no	—
259	C₂×C₄⋊C₄	—	122	2	no	—
260	C₂×C₄⋊C₄	—	122	2	no	—
261	C₂×C₄⋊C₄	—	122	2	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	Dic₁₂₂	1	2	yes	—
267	C₂×C₄²	C₂×Dic₆₁	1	2	yes	—
268	#107	—	122	8	no	—
269	#106	—	122	8	no	—
270	#97	—	2	8	no	—
271	#95	—	244	8	no	—
272	C₂⁴	C₂×D₂₄₄	1	1	yes	characteristic
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	122	4	no	—
278	C₂²×C₄	—	122	4	no	—
279	C₂²×C₄	—	244	4	no	—
280	C₂²×C₄	—	244	2	no	—
281	C₂²×C₄	—	244	2	no	—
282	C₂²×C₄	—	244	2	no	—
283	C₂²×C₄	—	244	2	no	—
284	C₂²×C₄	—	244	4	no	—
285	C₂²×C₄	—	244	4	no	—
286	C₂²×C₄	—	244	4	no	—
287	C₂²×C₄	C₄⋊Dic₆₁	1	4	yes	—
288	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
289	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
290	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
295	C₂²×C₄	#11758222	1	1	yes	characteristic
296	C₂²×C₄	#11758222	1	1	yes	characteristic
297	C₂²×C₄	#11758222	1	1	yes	characteristic
298	C₂²×C₄	#11758222	1	1	yes	characteristic
299	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	C₄×Dic₆₁	1	4	yes	—
309	C₂×C₈	#11758196	1	4	yes	—
310	C₂×C₈	#11758196	1	4	yes	—
311	C₂×C₈	C₄⋊Dic₆₁	1	4	yes	—
312	C₂×C₈	C₄⋊Dic₆₁	1	4	yes	—
313	C₂×C₈	#11758198	1	4	yes	—
314	C₂×C₈	#11758198	1	4	yes	—
315	C₂×C₈	C₂²⋊Dic₆₁	1	4	yes	—
316	C₄⋊C₄	—	122	4	no	—
317	C₄⋊C₄	—	122	4	no	—
318	C₄⋊C₄	—	122	4	no	—
319	C₄⋊C₄	—	122	4	no	—
320	C₄⋊C₄	—	244	2	no	—
321	C₄⋊C₄	—	244	2	no	—
322	C₄⋊C₄	—	244	2	no	—
323	C₄⋊C₄	—	244	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₂³	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
329	C₂³	C₄×D₂₄₄	1	1	yes	characteristic
330	C₂³	C₄×D₂₄₄	1	1	yes	characteristic
331	C₂³	#14519751	1	1	yes	characteristic
332	C₂³	#14519751	1	1	yes	characteristic
333	C₂³	#14519774	1	1	yes	characteristic
334	C₂³	#14519777	1	1	yes	characteristic
335	C₂³	#14519805	1	4	yes	—
336	C₂³	#14519810	1	4	yes	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	488	4	no	—
343	C₂×C₄	—	488	4	no	—
344	C₂×C₄	—	488	2	no	—
345	C₂×C₄	—	488	2	no	—
346	C₂×C₄	—	488	2	no	—
347	C₂×C₄	—	488	2	no	—
348	C₂×C₄	—	244	8	no	—
349	C₂×C₄	—	244	8	no	—
350	C₂×C₄	—	244	4	no	—
351	C₂×C₄	—	244	4	no	—
352	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
353	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
354	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
356	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
357	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
360	C₂×C₄	#14519736	1	1	yes	characteristic
361	C₂×C₄	#14519736	1	1	yes	characteristic
362	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
363	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
364	C₂×C₄	C₄×Dic₁₂₂	1	1	yes	characteristic
365	C₂×C₄	C₄×Dic₁₂₂	1	1	yes	characteristic
366	C₂×C₄	C₄×Dic₁₂₂	1	1	yes	characteristic
367	C₂×C₄	C₄×Dic₁₂₂	1	1	yes	characteristic
368	C₂×C₄	#14519751	1	1	yes	characteristic
369	C₂×C₄	#14519751	1	1	yes	characteristic
370	C₂×C₄	#14519756	1	1	yes	characteristic
371	C₂×C₄	#14519756	1	1	yes	characteristic
372	C₂×C₄	#14519756	1	1	yes	characteristic
373	C₂×C₄	#14519756	1	1	yes	characteristic
374	C₂×C₄	#14519765	1	1	yes	characteristic
375	C₂×C₄	#14519765	1	1	yes	characteristic
376	C₂×C₄	#14519769	1	1	yes	characteristic
377	C₂×C₄	#14519769	1	1	yes	characteristic
378	C₂×C₄	#14519777	1	1	yes	characteristic
379	C₂×C₄	#14519777	1	1	yes	characteristic
380	C₈	—	2	4	no	—
381	C₈	#14519684	1	8	yes	complemented
382	C₂²	C₄×C₄⋊Dic₆₁	1	1	yes	characteristic
383	C₂²	#16839622	1	1	yes	characteristic
384	C₂²	#16839632	1	1	yes	characteristic
385	C₂²	#16839660	1	1	yes	characteristic
386	C₂²	#16839660	1	1	yes	characteristic
387	C₂²	#16839664	1	1	yes	characteristic
388	C₂²	#16839664	1	1	yes	characteristic
389	C₂²	#16839804	1	4	yes	—
390	C₂²	#16839864	1	4	yes	—
391	C₂²	#16839870	1	2	yes	—
392	C₂²	#16839875	1	2	yes	—
393	C₂²	#16840008	1	4	yes	—
394	C₂²	#16840015	1	2	yes	—
395	C₂²	#16840020	1	2	yes	—
396	C₂²	#16840151	1	2	yes	—
397	C₂²	#16840156	1	2	yes	—
398	C₂²	#16840171	1	4	yes	—
399	C₄	—	4	4	no	—
400	C₄	—	488	4	no	—
401	C₄	—	488	4	no	—
402	C₄	C₂×#14519684	1	1	yes	characteristic
403	C₄	C₄×C₄⋊Dic₆₁	1	1	yes	characteristic
404	C₄	#16839622	1	1	yes	characteristic
405	C₄	#16839628	1	1	yes	characteristic
406	C₄	#16839660	1	1	yes	characteristic
407	C₄	#16839660	1	1	yes	characteristic
408	C₄	#16839668	1	1	yes	characteristic
409	C₄	#16839668	1	1	yes	characteristic
410	C₂	#21444049	1	1	yes	characteristic
411	C₂	#21445716	1	2	yes	—
412	C₂	#21445852	1	2	yes	—
413	C₂	#21445987	1	2	yes	—
414	C₂	#21446557	1	2	yes	—
415	C₂	#21446562	1	2	yes	—
416	C₂	#21446690	1	1	yes	characteristic
417	C₂	#21446695	1	1	yes	characteristic
418	C₂	#21446700	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₁
Fitting	C₂²×#97×C₆₁	C₂
socle, prime radical	C₂⁴×C₆₁	C₂×D₄
cosocle	C₂³×C₄×C₆₁	C₂³
hypercenter	C₂²×#97	D₆₁
hypocenter	C₆₁	#10863
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
10. C₂×#14519711	C₄	semidirect
13. C₂×#14519709	C₄	semidirect
21. C₂×#97×C₆₁	C₄	semidirect
171. C₈×C₆₁	#95	semidirect
228. C₂×#97	Dic₆₁	semidirect
231. C₆₁	#10863	semidirect
381. C₈	#14519684	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14519711	2
C₂²×#14519709	2
C₂×#16839525	2
#21444049	2
C₂²×#97×C₆₁	2
#10863	61