Subgroups — #29833535

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11758222	C₂	1	1	yes	maximal, characteristic
2	#21447725	C₂	1	2	yes	maximal, complemented
3	#21447649	C₂	1	2	yes	maximal, complemented
4	#21447646	C₂	1	2	yes	maximal, complemented
5	#21447642	C₂	1	2	yes	maximal, complemented
6	#21447618	C₂	1	1	yes	maximal, characteristic, complemented
7	#21447616	C₂	1	1	yes	maximal, characteristic, complemented
8	#21447616	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14519716	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11758222	C₄	1	1	yes	characteristic
13	C₂×#14519716	C₂²	1	2	yes	—
14	C₂×C₁₆×D₆₁	C₂²	1	2	yes	—
15	C₈×Dic₁₂₂	C₄	1	1	yes	characteristic
16	C₈×Dic₁₂₂	C₂²	1	1	yes	characteristic
17	C₈×D₂₄₄	C₄	1	1	yes	characteristic
18	C₈×D₂₄₄	C₂²	1	1	yes	characteristic
19	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
23	#16839815	C₄	1	1	yes	characteristic
24	#16839813	C₄	1	1	yes	characteristic
25	#16839813	C₄	1	1	yes	characteristic
26	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
28	C₄⋊#11758185	C₂²	1	2	yes	—
29	#16839580	C₂²	1	2	yes	—
30	#16839580	C₂²	1	2	yes	—
31	C₂²⋊#11758185	C₂²	1	2	yes	—
32	#16839541	C₂²	1	2	yes	—
33	#16839541	C₂²	1	2	yes	—
34	#16839537	C₂²	1	2	yes	—
35	C₄×#11758185	C₂²	1	1	yes	characteristic
36	C₄×#11758185	C₂²	1	1	yes	characteristic
37	C₁₆×Dic₆₁	C₂²	1	2	yes	—
38	C₂×M₃₂×C₆₁	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#346	C₂²	1	2	yes	—
41	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#11758222	C₈	1	1	yes	characteristic
44	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
48	C₄×Dic₁₂₂	C₈	1	1	yes	characteristic
49	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
50	C₄×D₂₄₄	C₈	1	1	yes	characteristic
51	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
52	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₆₁	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
55	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
56	#14519736	C₈	1	1	yes	characteristic
57	#14519734	C₈	1	1	yes	characteristic
58	#14519734	C₈	1	1	yes	characteristic
59	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
61	#14519716	—	2	4	no	—
62	C₂×#11758185	C₂³	1	2	yes	—
63	C₂×#11758185	C₂³	1	2	yes	—
64	C₁₆×D₆₁	—	2	4	no	—
65	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
66	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
67	#14519706	C₂×C₄	1	1	yes	characteristic
68	#14519706	C₂×C₄	1	1	yes	characteristic
69	#14519706	C₂×C₄	1	1	yes	characteristic
70	#14519706	C₂×C₄	1	1	yes	characteristic
71	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
72	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
73	#14519689	C₂×C₄	1	1	yes	characteristic
74	#14519689	C₂×C₄	1	1	yes	characteristic
75	#14519689	C₂×C₄	1	1	yes	characteristic
76	#14519689	C₂×C₄	1	1	yes	characteristic
77	C₄×#92418	C₂×C₄	1	1	yes	characteristic
78	C₄×#92418	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
82	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
86	M₃₂×C₆₁	—	2	4	no	—
87	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
88	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
89	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
97	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
98	#11758222	—	2	4	no	—
99	C₂×D₂₄₄	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×Dic₁₂₂	C₂×C₈	1	1	yes	characteristic
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
113	C₄²×C₆₁	C₂×C₈	1	1	yes	characteristic
114	C₄²×C₆₁	C₂×C₈	1	1	yes	characteristic
115	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
118	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
119	#11758198	C₂×C₈	1	1	yes	characteristic
120	#11758198	C₂×C₈	1	1	yes	characteristic
121	#11758198	C₂×C₈	1	1	yes	characteristic
122	#11758198	C₂×C₈	1	1	yes	characteristic
123	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
124	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
125	#11758196	C₂×C₈	1	1	yes	characteristic
126	#11758196	C₂×C₈	1	1	yes	characteristic
127	#11758196	C₂×C₈	1	1	yes	characteristic
128	#11758196	C₂×C₈	1	1	yes	characteristic
129	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
136	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
137	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
138	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
139	C₈×D₆₁	—	2	2	no	—
140	C₈×D₆₁	—	2	2	no	—
141	C₈×D₆₁	—	2	2	no	—
142	C₈×D₆₁	—	2	2	no	—
143	C₁₆×C₆₁	—	2	2	no	—
144	C₁₆×C₆₁	#41	1	4	yes	complemented
145	#11758185	—	2	2	no	—
146	#11758185	—	2	2	no	—
147	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
148	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₆₁	—	2	1	no	—
151	C₂×C₄×C₆₁	—	2	1	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
160	C₂²⋊D₆₁	—	2	2	no	—
161	C₂²⋊D₆₁	—	2	2	no	—
162	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
163	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
168	D₂₄₄	—	2	2	no	—
169	C₄×D₆₁	—	2	1	no	—
170	C₄×D₆₁	—	2	1	no	—
171	C₄×D₆₁	—	2	1	no	—
172	C₄×D₆₁	—	2	1	no	—
173	C₄×D₆₁	—	2	2	no	—
174	C₄×D₆₁	—	2	2	no	—
175	C₄×D₆₁	—	2	2	no	—
176	C₄×D₆₁	M₃₂	1	4	yes	complemented
177	Dic₁₂₂	—	2	2	no	—
178	C₈×C₆₁	—	2	1	no	—
179	C₈×C₆₁	—	2	1	no	—
180	C₈×C₆₁	#131	1	2	yes	—
181	C₈×C₆₁	C₂×#41	1	2	yes	—
182	#92418	—	2	1	no	—
183	#92418	—	2	1	no	—
184	#92418	—	2	1	no	—
185	#92418	—	2	1	no	—
186	#33479	—	61	1	no	maximal, Sylow
187	C₂²×C₆₁	—	2	1	no	—
188	C₂²×C₆₁	—	2	1	no	—
189	C₂²×C₆₁	—	2	1	no	—
190	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
191	C₂×D₆₁	—	2	1	no	—
192	C₂×D₆₁	—	2	1	no	—
193	C₂×D₆₁	—	2	1	no	—
194	C₂×D₆₁	—	2	1	no	—
195	C₂×D₆₁	—	2	1	no	—
196	C₂×D₆₁	C₂×M₃₂	1	2	yes	—
197	C₄×C₆₁	—	2	1	no	—
198	C₄×C₆₁	—	2	1	no	—
199	C₄×C₆₁	—	2	1	no	—
200	C₄×C₆₁	C₂×M₃₂	1	2	yes	—
201	C₄×C₆₁	#504	1	2	yes	—
202	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
203	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
204	Dic₆₁	—	2	1	no	—
205	Dic₆₁	—	2	1	no	—
206	Dic₆₁	—	2	1	no	—
207	Dic₆₁	—	2	1	no	—
208	Dic₆₁	—	2	1	no	—
209	Dic₆₁	C₂×M₃₂	1	2	yes	—
210	C₈×#41	—	61	1	no	—
211	#2183	—	61	2	no	—
212	#2169	—	61	2	no	—
213	#2168	—	61	2	no	—
214	#2168	—	61	2	no	—
215	#2162	—	61	1	no	—
216	#2162	—	61	1	no	—
217	#2162	—	61	1	no	—
218	C₄×M₃₂	—	61	1	no	—
219	C₄×M₃₂	D₆₁	1	1	yes	characteristic, complemented
220	C₂×C₄×C₁₆	—	61	1	no	—
221	C₂×C₆₁	—	4	1	no	—
222	C₂×C₆₁	C₈×#41	1	1	yes	characteristic
223	C₂×C₆₁	C₂²×M₃₂	1	1	yes	characteristic
224	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
225	D₆₁	—	2	2	no	—
226	D₆₁	—	4	1	no	—
227	C₄×#41	—	61	1	no	—
228	C₂×M₃₂	—	61	2	no	—
229	C₂×M₃₂	C₂×D₆₁	1	2	yes	—
230	C₂²×C₁₆	—	61	2	no	—
231	C₈×Q₈	—	61	1	no	—
232	C₈×Q₈	—	61	1	no	—
233	C₈×D₄	—	61	1	no	—
234	C₈×D₄	—	61	1	no	—
235	C₈×D₄	—	61	1	no	—
236	C₈×D₄	—	61	1	no	—
237	C₈×D₄	—	61	1	no	—
238	C₈×D₄	—	61	1	no	—
239	#431	—	61	1	no	—
240	#431	—	61	1	no	—
241	#431	—	61	1	no	—
242	C₂×C₄×C₈	—	61	1	no	—
243	C₂×C₄×C₈	—	61	1	no	—
244	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
245	C₄⋊C₁₆	—	61	2	no	—
246	C₄⋊C₁₆	—	61	2	no	—
247	C₄⋊C₁₆	—	61	2	no	—
248	C₂²⋊C₁₆	—	61	2	no	—
249	C₂²⋊C₁₆	—	61	2	no	—
250	C₂²⋊C₁₆	—	61	2	no	—
251	#346	—	61	2	no	—
252	#346	C₂×D₆₁	1	2	yes	—
253	C₄×C₁₆	—	61	2	no	—
254	C₄×C₁₆	—	61	1	no	—
255	C₄×C₁₆	—	61	1	no	—
256	C₄×C₁₆	C₂×D₆₁	1	1	yes	characteristic
257	C₄×C₁₆	C₂×D₆₁	1	1	yes	characteristic
258	C₆₁	#33479	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	61	1	no	—
260	C₂²×C₈	—	61	1	no	—
261	C₂²×C₈	—	61	1	no	—
262	C₂²×C₈	—	61	1	no	—
263	C₂²×C₈	—	61	1	no	—
264	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
266	C₄×Q₈	—	61	1	no	—
267	C₄×Q₈	—	61	1	no	—
268	C₄×D₄	—	61	1	no	—
269	C₄×D₄	—	61	1	no	—
270	C₄×D₄	—	61	1	no	—
271	C₄×D₄	—	61	1	no	—
272	C₄×D₄	—	61	1	no	—
273	C₄×D₄	—	61	1	no	—
274	#117	—	61	1	no	—
275	#117	—	61	1	no	—
276	#117	—	61	1	no	—
277	C₂×C₄²	—	61	1	no	—
278	C₂×C₄²	—	61	1	no	—
279	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
280	M₃₂	—	2	4	no	—
281	M₃₂	—	122	4	no	—
282	C₂×C₁₆	—	61	2	no	—
283	C₂×C₁₆	—	61	2	no	—
284	C₂×C₁₆	—	122	4	no	—
285	C₂×C₁₆	C₂²×D₆₁	1	2	yes	—
286	C₂×C₁₆	C₂²×D₆₁	1	2	yes	—
287	C₄⋊C₈	—	61	1	no	—
288	C₄⋊C₈	—	61	1	no	—
289	C₄⋊C₈	—	61	1	no	—
290	C₄⋊C₈	—	61	1	no	—
291	C₄⋊C₈	—	61	1	no	—
292	C₄⋊C₈	—	61	1	no	—
293	C₂²⋊C₈	—	61	1	no	—
294	C₂²⋊C₈	—	61	1	no	—
295	C₂²⋊C₈	—	61	1	no	—
296	C₂²⋊C₈	—	61	1	no	—
297	C₂²⋊C₈	—	61	1	no	—
298	C₂²⋊C₈	—	61	1	no	—
299	C₄×C₈	—	61	1	no	—
300	C₄×C₈	—	61	1	no	—
301	C₄×C₈	—	61	1	no	—
302	C₄×C₈	—	61	1	no	—
303	C₄×C₈	—	61	1	no	—
304	C₄×C₈	—	61	1	no	—
305	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
306	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
309	#41	—	122	4	no	—
310	C₂×Q₈	—	61	1	no	—
311	C₂×D₄	—	61	1	no	—
312	C₂×D₄	—	61	1	no	—
313	C₂×D₄	—	61	1	no	—
314	C₂²×C₄	—	61	1	no	—
315	C₂²×C₄	—	61	1	no	—
316	C₂²×C₄	—	61	1	no	—
317	C₂²×C₄	—	61	1	no	—
318	C₂²×C₄	—	61	1	no	—
319	C₂²×C₄	—	61	1	no	—
320	C₂²×C₄	C₈×D₆₁	1	1	yes	characteristic
321	C₂²×C₄	C₈×D₆₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	61	1	no	—
326	C₂×C₈	—	61	1	no	—
327	C₂×C₈	—	61	1	no	—
328	C₂×C₈	—	61	1	no	—
329	C₂×C₈	—	122	2	no	—
330	C₂×C₈	—	122	2	no	—
331	C₂×C₈	—	122	2	no	—
332	C₂×C₈	—	122	2	no	—
333	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
336	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
337	C₄⋊C₄	—	61	1	no	—
338	C₄⋊C₄	—	61	1	no	—
339	C₄⋊C₄	—	61	1	no	—
340	C₄⋊C₄	—	61	1	no	—
341	C₄⋊C₄	—	61	1	no	—
342	C₄⋊C₄	—	61	1	no	—
343	C₂²⋊C₄	—	61	1	no	—
344	C₂²⋊C₄	—	61	1	no	—
345	C₂²⋊C₄	—	61	1	no	—
346	C₂²⋊C₄	—	61	1	no	—
347	C₂²⋊C₄	—	61	1	no	—
348	C₂²⋊C₄	—	61	1	no	—
349	C₄²	—	61	1	no	—
350	C₄²	—	61	1	no	—
351	C₄²	—	61	1	no	—
352	C₄²	—	61	1	no	—
353	C₄²	—	61	1	no	—
354	C₄²	—	61	1	no	—
355	C₄²	C₈×D₆₁	1	1	yes	characteristic
356	C₄²	C₈×D₆₁	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
358	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
359	C₁₆	—	2	2	no	—
360	C₁₆	—	122	2	no	—
361	C₁₆	—	122	2	no	—
362	C₁₆	#11758222	1	4	yes	complemented
363	C₂³	—	61	1	no	—
364	C₂³	—	61	1	no	—
365	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
366	Q₈	—	122	2	no	—
367	D₄	—	122	2	no	—
368	D₄	—	122	2	no	—
369	D₄	—	122	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	61	1	no	—
375	C₂×C₄	—	61	4	no	—
376	C₂×C₄	—	61	1	no	—
377	C₂×C₄	—	61	1	no	—
378	C₂×C₄	—	61	1	no	—
379	C₂×C₄	—	61	1	no	—
380	C₂×C₄	—	61	1	no	—
381	C₂×C₄	—	122	1	no	—
382	C₂×C₄	—	122	1	no	—
383	C₂×C₄	—	122	1	no	—
384	C₂×C₄	—	122	1	no	—
385	C₂×C₄	—	122	2	no	—
386	C₂×C₄	—	122	2	no	—
387	C₂×C₄	—	122	2	no	—
388	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
389	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
390	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
391	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
392	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	122	1	no	—
397	C₈	—	122	1	no	—
398	C₈	—	122	1	no	—
399	C₈	—	122	1	no	—
400	C₈	#14519783	1	2	yes	—
401	C₈	C₂×#11758222	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	61	2	no	—
406	C₂²	—	122	1	no	—
407	C₂²	—	122	1	no	—
408	C₂²	—	122	1	no	—
409	C₂²	—	122	1	no	—
410	C₂²	—	122	1	no	—
411	C₂²	C₂²×C₈×D₆₁	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	61	2	no	—
416	C₄	—	122	1	no	—
417	C₄	—	122	1	no	—
418	C₄	—	122	1	no	—
419	C₄	—	122	1	no	—
420	C₄	—	122	1	no	—
421	C₄	M₃₂×D₆₁	1	2	yes	—
422	C₄	#16840180	1	2	yes	—
423	C₄	C₄×#11758222	1	1	yes	characteristic
424	C₄	C₂×#14519783	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	122	2	no	—
427	C₂	—	244	1	no	—
428	C₂	C₈×#11758222	1	1	yes	characteristic
429	C₂	C₂×M₃₂×D₆₁	1	1	yes	characteristic
430	C₂	C₂×#16840180	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₆₁
Fitting	C₄×M₃₂×C₆₁	C₂
prime radical	C₂×#11758222	C₈
cosocle	C₂×C₈×C₆₁	C₂⁴
hypercenter	C₄×M₃₂	D₆₁
hypocenter	C₆₁	#33479
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
2. #21447725	C₂	semidirect
3. #21447649	C₂	semidirect
4. #21447646	C₂	semidirect
5. #21447642	C₂	semidirect
6. #21447618	C₂	semidirect
7. #21447616	C₂	semidirect
8. #21447616	C₂	semidirect
9. C₄×#14519716	C₂	semidirect
10. C₄×C₁₆×D₆₁	C₂	semidirect
11. C₄×M₃₂×C₆₁	C₂	semidirect
144. C₁₆×C₆₁	#41	semidirect
176. C₄×D₆₁	M₃₂	semidirect
219. C₄×M₃₂	D₆₁	semidirect
258. C₆₁	#33479	semidirect
362. C₁₆	#11758222	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11758222	2
#21447725	2
#21447649	2
#21447646	2
#21447642	2
#21447618	2
#21447616	2
C₄×#14519716	2
C₄×C₁₆×D₆₁	2
C₄×M₃₂×C₆₁	2
#33479	61