Subgroups — #30612184

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462514	C₂	1	2	yes	maximal
2	#21461391	C₂	1	2	yes	maximal, complemented
3	#21461390	C₂	1	2	yes	maximal, complemented
4	#21461388	C₂	1	2	yes	maximal, complemented
5	#21461382	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461381	C₂	1	1	yes	maximal, characteristic, complemented
7	#21461373	C₂	1	1	yes	maximal, characteristic, complemented
8	#21461369	C₂	1	1	yes	maximal, characteristic, complemented
9	#21461368	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16840624	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11758224	C₂	1	1	yes	maximal, characteristic
12	#16840787	—	2	2	no	—
13	#16840786	—	2	2	no	—
14	#16840784	C₂²	1	2	yes	—
15	#16840783	C₂²	1	2	yes	—
16	#16840781	C₂²	1	2	yes	—
17	#16840778	C₂²	1	2	yes	—
18	#16840765	C₂²	1	2	yes	—
19	C₂×C₄⋊#92420	C₂²	1	2	yes	—
20	#16840735	—	2	2	no	—
21	#16840726	—	2	2	no	—
22	#16840626	C₂²	1	2	yes	—
23	#16840626	C₂²	1	2	yes	—
24	#16840625	C₂²	1	2	yes	—
25	#16840625	C₂²	1	2	yes	—
26	#16840624	C₂²	1	1	yes	characteristic
27	#16840624	C₂²	1	1	yes	characteristic
28	#16840624	C₂²	1	2	yes	—
29	#16840624	C₂²	1	1	yes	characteristic
30	#16840624	C₂²	1	1	yes	characteristic
31	#16840623	C₂²	1	2	yes	—
32	C₄×#11758224	C₂²	1	1	yes	characteristic
33	C₈×Dic₁₂₂	C₄	1	1	yes	characteristic
34	#16839886	C₄	1	1	yes	characteristic
35	D₄×#92418	C₄	1	1	yes	characteristic
36	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
37	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
38	#16839825	C₄	1	1	yes	characteristic
39	#16839825	C₄	1	1	yes	characteristic
40	#16839814	C₂²	1	1	yes	characteristic
41	#16839812	C₂²	1	1	yes	characteristic
42	#16839812	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
46	C₈×D₄×C₆₁	C₄	1	1	yes	characteristic
47	C₂×#11758217	—	2	2	no	—
48	C₂²×#92420	—	2	2	no	—
49	#14519844	—	2	2	no	—
50	C₄⋊#92420	—	2	2	no	—
51	C₄⋊#92420	C₂³	1	2	yes	—
52	C₄⋊#92420	C₂³	1	2	yes	—
53	C₄⋊#92420	C₂³	1	2	yes	—
54	C₄⋊#92420	C₂³	1	2	yes	—
55	#14519834	—	2	2	no	—
56	#14519834	—	2	2	no	—
57	C₂²⋊#92420	—	2	2	no	—
58	C₂²⋊#92420	—	2	2	no	—
59	#14519832	—	2	2	no	—
60	#14519832	—	2	2	no	—
61	C₄×#92420	—	2	2	no	—
62	C₄×#92420	—	2	2	no	—
63	C₂×#11758224	D₄	1	1	yes	characteristic
64	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
65	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
68	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
69	#14519742	Q₈	1	1	yes	characteristic
70	D₄×Dic₆₁	Q₈	1	1	yes	characteristic
71	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
73	#14519737	Q₈	1	1	yes	characteristic
74	#14519737	Q₈	1	1	yes	characteristic
75	#14519735	D₄	1	1	yes	characteristic
76	#14519733	D₄	1	1	yes	characteristic
77	#14519733	D₄	1	1	yes	characteristic
78	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
80	C₄²×D₆₁	C₂³	1	1	yes	characteristic
81	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
82	#14519706	C₂×C₄	1	1	yes	characteristic
83	#14519706	C₂×C₄	1	1	yes	characteristic
84	#14519706	C₂×C₄	1	1	yes	characteristic
85	#14519706	C₂×C₄	1	1	yes	characteristic
86	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
88	#14519689	C₂×C₄	1	1	yes	characteristic
89	#14519689	C₂×C₄	1	1	yes	characteristic
90	C₄×#92418	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
96	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
97	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
98	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
101	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
103	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
106	C₂×D₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊D₆₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₆₁	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
114	C₂²×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
115	#11758224	—	2	4	no	—
116	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
119	C₂×Dic₁₂₂	C₄⋊C₄	1	1	yes	characteristic
120	#11758217	—	4	4	no	—
121	C₂×#92420	—	2	2	no	—
122	C₂×#92420	—	2	2	no	—
123	C₂×#92420	—	2	2	no	—
124	C₂×#92420	—	2	2	no	—
125	C₂×#92420	—	4	4	no	—
126	C₂×C₈×C₆₁	—	4	1	no	—
127	C₂×C₈×C₆₁	—	4	1	no	—
128	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
135	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²⋊Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
137	C₂²⋊Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
138	#11758198	C₄⋊C₄	1	1	yes	characteristic
139	#11758198	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
141	#11758196	C₄⋊C₄	1	1	yes	characteristic
142	#11758196	C₄⋊C₄	1	1	yes	characteristic
143	#11758196	C₄⋊C₄	1	1	yes	characteristic
144	#11758196	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
151	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
152	C₄×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
153	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
154	C₂×#92418	—	2	2	no	—
155	C₂×#92418	—	2	2	no	—
156	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
157	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
158	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
159	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
160	C₈×D₆₁	—	2	2	no	—
161	C₈×D₆₁	—	4	1	no	—
162	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	D₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
175	C₂²⋊D₆₁	—	2	2	no	—
176	C₂²⋊D₆₁	—	2	2	no	—
177	C₂×Dic₆₁	—	2	2	no	—
178	C₂×Dic₆₁	—	4	1	no	—
179	C₂×Dic₆₁	—	4	1	no	—
180	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₆₁	#135	1	4	yes	—
186	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×Dic₆₁	C₂²×Q₈	1	1	yes	characteristic
188	C₄×D₆₁	—	2	1	no	—
189	C₄×D₆₁	—	2	1	no	—
190	C₄×D₆₁	—	2	2	no	—
191	C₄×D₆₁	—	4	1	no	—
192	Dic₁₂₂	—	2	2	no	—
193	#92420	—	4	2	no	—
194	#92420	—	4	2	no	—
195	#92420	—	4	2	no	—
196	#92420	—	4	2	no	—
197	C₈×C₆₁	—	2	1	no	—
198	C₈×C₆₁	—	2	1	no	—
199	C₈×C₆₁	—	2	1	no	—
200	C₈×C₆₁	—	2	1	no	—
201	#92418	—	2	1	no	—
202	#92418	—	2	1	no	—
203	#92418	—	2	1	no	—
204	#92418	#131	1	2	yes	—
205	#17827	—	61	1	no	maximal, Sylow
206	C₂²×C₆₁	—	2	1	no	—
207	C₂²×C₆₁	—	2	1	no	—
208	C₂²×C₆₁	—	2	1	no	—
209	C₂²×C₆₁	—	2	1	no	—
210	C₂²×C₆₁	—	2	1	no	—
211	C₂²×C₆₁	#427	1	2	yes	—
212	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
213	C₂×D₆₁	—	2	1	no	—
214	C₂×D₆₁	—	2	1	no	—
215	C₂×D₆₁	—	2	1	no	—
216	C₄×C₆₁	—	2	1	no	—
217	C₄×C₆₁	—	2	1	no	—
218	C₄×C₆₁	—	2	1	no	—
219	C₄×C₆₁	—	2	1	no	—
220	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
221	C₄×C₆₁	#568	1	1	yes	characteristic
222	Dic₆₁	—	2	1	no	—
223	Dic₆₁	—	2	1	no	—
224	Dic₆₁	—	2	1	no	—
225	Dic₆₁	—	2	1	no	—
226	Dic₆₁	—	2	1	no	—
227	Dic₆₁	#427	1	2	yes	—
228	Dic₆₁	C₂×#135	1	2	yes	—
229	C₈×#41	—	61	1	no	—
230	#2925	—	61	2	no	—
231	#1572	—	61	2	no	—
232	#1572	—	61	2	no	—
233	#1571	—	61	2	no	—
234	#1568	—	61	1	no	—
235	#1568	—	61	1	no	—
236	#1566	—	61	1	no	—
237	#1564	—	61	1	no	—
238	#1564	—	61	1	no	—
239	C₂×#334	—	61	1	no	—
240	C₂×C₆₁	—	2	2	no	—
241	C₂×C₆₁	—	4	1	no	—
242	C₂×C₆₁	#2906	1	1	yes	characteristic
243	C₂×C₆₁	C₂×#427	1	1	yes	characteristic
244	C₂×C₆₁	#2916	1	1	yes	characteristic
245	D₆₁	—	4	1	no	—
246	C₄×#41	—	61	1	no	—
247	C₈×Q₈	—	61	1	no	—
248	C₈×Q₈	—	61	1	no	—
249	C₈×D₄	—	61	1	no	—
250	C₈×D₄	—	61	1	no	—
251	C₈×D₄	—	61	1	no	—
252	C₈×D₄	—	61	1	no	—
253	C₈×D₄	—	61	1	no	—
254	C₈×D₄	#6923	1	1	yes	characteristic
255	#433	—	122	2	no	—
256	#433	—	122	2	no	—
257	#432	—	61	2	no	—
258	#432	—	61	2	no	—
259	#431	—	61	1	no	—
260	#431	—	61	1	no	—
261	#431	—	61	1	no	—
262	#431	—	61	2	no	—
263	#431	—	61	2	no	—
264	#423	—	61	2	no	—
265	C₂×C₄⋊C₈	—	61	2	no	—
266	#408	—	122	2	no	—
267	#405	—	122	2	no	—
268	C₂×C₄×C₈	—	61	1	no	—
269	C₂×C₄×C₈	—	61	1	no	—
270	C₂×C₄×C₈	—	61	1	no	—
271	#335	—	61	2	no	—
272	#335	—	61	2	no	—
273	#335	—	61	2	no	—
274	#335	—	61	2	no	—
275	#334	—	61	1	no	—
276	#334	—	61	1	no	—
277	#334	—	61	2	no	—
278	#334	—	61	1	no	—
279	#334	—	61	1	no	—
280	#334	—	61	2	no	—
281	C₆₁	#17827	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	—	61	1	no	—
283	C₂×M₁₆	—	122	2	no	—
284	C₂²×C₈	—	61	1	no	—
285	C₂²×C₈	—	61	1	no	—
286	C₂²×C₈	—	61	1	no	—
287	C₂²×C₈	—	61	1	no	—
288	C₂²×C₈	—	122	2	no	—
289	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
290	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
291	C₄×Q₈	—	61	1	no	—
292	C₄×Q₈	—	61	1	no	—
293	C₄×D₄	—	61	1	no	—
294	C₄×D₄	—	61	1	no	—
295	C₄×D₄	—	61	1	no	—
296	C₄×D₄	—	61	1	no	—
297	C₄×D₄	—	61	1	no	—
298	C₄×D₄	C₂×#6923	1	1	yes	characteristic
299	#117	—	61	1	no	—
300	#117	—	61	1	no	—
301	#117	—	61	1	no	—
302	C₂×C₄²	—	61	1	no	—
303	C₂×C₄²	—	61	1	no	—
304	C₂×C₄²	—	61	1	no	—
305	C₄⋊C₈	—	61	1	no	—
306	C₄⋊C₈	—	61	1	no	—
307	C₄⋊C₈	—	61	1	no	—
308	C₄⋊C₈	—	61	1	no	—
309	C₄⋊C₈	—	61	2	no	—
310	C₄⋊C₈	—	61	2	no	—
311	C₄⋊C₈	—	61	2	no	—
312	C₄⋊C₈	—	61	2	no	—
313	C₄⋊C₈	—	61	1	no	—
314	C₄⋊C₈	—	122	2	no	—
315	C₄⋊C₈	—	122	2	no	—
316	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic
317	C₂²⋊C₈	—	61	1	no	—
318	C₂²⋊C₈	—	61	1	no	—
319	C₂²⋊C₈	—	61	1	no	—
320	C₂²⋊C₈	—	61	1	no	—
321	C₂²⋊C₈	—	122	2	no	—
322	C₂²⋊C₈	—	122	2	no	—
323	C₂²⋊C₈	—	122	2	no	—
324	C₂²⋊C₈	—	122	2	no	—
325	C₂²⋊C₈	C₂×#6923	1	1	yes	characteristic
326	C₂²⋊C₈	C₂×#6923	1	1	yes	characteristic
327	#97	—	122	2	no	—
328	#97	—	122	2	no	—
329	C₄×C₈	—	61	1	no	—
330	C₄×C₈	—	61	1	no	—
331	C₄×C₈	—	61	1	no	—
332	C₄×C₈	—	61	1	no	—
333	C₄×C₈	—	61	1	no	—
334	C₄×C₈	—	61	1	no	—
335	C₄×C₈	—	61	1	no	—
336	C₄×C₈	—	61	1	no	—
337	C₄×C₈	—	61	1	no	—
338	C₄×C₈	—	122	2	no	—
339	C₄×C₈	—	122	2	no	—
340	C₄×C₈	C₂×#6923	1	1	yes	characteristic
341	#41	—	122	4	no	—
342	C₂×Q₈	—	61	1	no	—
343	C₂×D₄	—	61	1	no	—
344	C₂×D₄	—	61	1	no	—
345	C₂×D₄	C₄⋊#6923	1	1	yes	characteristic
346	C₂²×C₄	—	61	1	no	—
347	C₂²×C₄	—	61	1	no	—
348	C₂²×C₄	—	61	1	no	—
349	C₂²×C₄	—	61	1	no	—
350	C₂²×C₄	—	61	1	no	—
351	C₂²×C₄	—	61	1	no	—
352	C₂²×C₄	—	61	1	no	—
353	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
354	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
355	M₁₆	—	244	4	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	61	1	no	—
359	C₂×C₈	—	61	1	no	—
360	C₂×C₈	—	61	1	no	—
361	C₂×C₈	—	61	1	no	—
362	C₂×C₈	—	122	2	no	—
363	C₂×C₈	—	122	2	no	—
364	C₂×C₈	—	122	2	no	—
365	C₂×C₈	—	122	2	no	—
366	C₂×C₈	—	122	2	no	—
367	C₂×C₈	—	122	2	no	—
368	C₂×C₈	—	122	2	no	—
369	C₂×C₈	—	244	1	no	—
370	C₂×C₈	—	244	4	no	—
371	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
372	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
373	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
374	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
375	C₄⋊C₄	—	61	1	no	—
376	C₄⋊C₄	—	61	1	no	—
377	C₄⋊C₄	—	61	1	no	—
378	C₄⋊C₄	—	61	1	no	—
379	C₄⋊C₄	—	61	1	no	—
380	C₄⋊C₄	C₄⋊#6923	1	1	yes	characteristic
381	C₂²⋊C₄	—	61	1	no	—
382	C₂²⋊C₄	—	61	1	no	—
383	C₂²⋊C₄	—	61	1	no	—
384	C₂²⋊C₄	—	61	1	no	—
385	C₂²⋊C₄	C₄⋊#6923	1	1	yes	characteristic
386	C₂²⋊C₄	C₄⋊#6923	1	1	yes	characteristic
387	C₄²	—	61	1	no	—
388	C₄²	—	61	1	no	—
389	C₄²	—	61	1	no	—
390	C₄²	—	61	1	no	—
391	C₄²	—	61	1	no	—
392	C₄²	—	61	1	no	—
393	C₄²	—	61	1	no	—
394	C₄²	—	61	1	no	—
395	C₄²	—	61	1	no	—
396	C₄²	C₂²×#6923	1	1	yes	characteristic
397	C₂³	—	61	1	no	—
398	C₂³	C₂×C₄⋊#6923	1	1	yes	characteristic
399	C₂³	C₂×C₄⋊#6923	1	1	yes	characteristic
400	Q₈	—	122	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	122	2	no	—
403	D₄	—	122	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	61	4	no	—
409	C₂×C₄	—	61	1	no	—
410	C₂×C₄	—	61	1	no	—
411	C₂×C₄	—	61	1	no	—
412	C₂×C₄	—	61	1	no	—
413	C₂×C₄	—	61	1	no	—
414	C₂×C₄	—	61	1	no	—
415	C₂×C₄	—	61	1	no	—
416	C₂×C₄	—	122	2	no	—
417	C₂×C₄	—	122	2	no	—
418	C₂×C₄	—	122	1	no	—
419	C₂×C₄	—	122	1	no	—
420	C₂×C₄	—	244	1	no	—
421	C₂×C₄	—	244	1	no	—
422	C₂×C₄	—	244	1	no	—
423	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
427	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	61	2	no	—
433	C₈	—	122	1	no	—
434	C₈	—	122	1	no	—
435	C₈	—	122	1	no	—
436	C₈	—	244	2	no	—
437	C₈	—	244	2	no	—
438	C₈	—	244	2	no	—
439	C₈	—	244	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	122	1	no	—
446	C₂²	—	122	1	no	—
447	C₂²	—	122	1	no	—
448	C₂²	#16840772	1	2	yes	—
449	C₂²	C₂²×C₄⋊#6923	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	61	2	no	—
455	C₄	—	61	2	no	—
456	C₄	—	122	1	no	—
457	C₄	—	122	1	no	—
458	C₄	—	122	1	no	—
459	C₄	—	122	1	no	—
460	C₄	—	122	1	no	—
461	C₄	D₆₁⋊#131	1	1	yes	characteristic
462	C₄	#16840840	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	1	no	—
465	C₂	—	244	1	no	—
466	C₂	#21462466	1	1	yes	characteristic
467	C₂	C₂×#16840772	1	1	yes	characteristic
468	C₂	#21462481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₈×D₄×C₆₁	C₄
socle	C₂²×C₆₁	C₂²×C₄⋊C₄
prime radical	C₂×#11758224	D₄
cosocle	C₄×Dic₆₁	C₂⁴
hypercenter	C₈×D₄	#6923
hypocenter	C₆₁	#17827
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
2. #21461391	C₂	semidirect
3. #21461390	C₂	semidirect
4. #21461388	C₂	semidirect
5. #21461382	C₂	semidirect
6. #21461381	C₂	semidirect
7. #21461373	C₂	semidirect
8. #21461369	C₂	semidirect
9. #21461368	C₂	semidirect
10. C₂×#16840624	C₂	semidirect
281. C₆₁	#17827	semidirect

Maximal subgroups

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

subgroup	index
#21462514	2
#21461391	2
#21461390	2
#21461388	2
#21461382	2
#21461381	2
#21461373	2
#21461369	2
#21461368	2
C₂×#16840624	2
C₈×#11758224	2
#17827	61