Subgroups — #30614533

Order 15616.

998 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁⋊#444	C₂	1	1	yes	maximal, characteristic
2	#135×#6923	C₂	1	1	yes	maximal, characteristic
3	#21462389	C₂	1	2	yes	maximal, complemented
4	#108×#6923	C₂	1	1	yes	maximal, characteristic, complemented
5	#21461628	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461625	C₂	1	1	yes	maximal, characteristic, complemented
7	#21461595	C₂	1	2	yes	maximal, complemented
8	#21461593	C₂	1	2	yes	maximal, complemented
9	#21461584	C₂	1	2	yes	maximal, complemented
10	#21461477	C₂	1	1	yes	maximal, characteristic, complemented
11	#444×D₆₁	C₂	1	1	yes	maximal, characteristic
12	D₆₁⋊#131	C₂²	1	2	yes	—
13	#41×#6923	C₂²	1	2	yes	—
14	#16840809	C₄	1	2	yes	complemented
15	#16840808	C₄	1	2	yes	complemented
16	#16840807	C₄	1	4	yes	complemented
17	Q₁₆×#6923	C₄	1	2	yes	complemented
18	SD₁₆×#6923	C₄	1	4	yes	complemented
19	D₈×#6923	C₄	1	2	yes	complemented
20	D₆₁⋊#108	C₂²	1	1	yes	characteristic
21	#16840772	C₂²	1	1	yes	characteristic
22	D₆₁⋊#104	C₂²	1	2	yes	—
23	#16840752	C₂²	1	2	yes	—
24	#16840728	—	2	2	no	—
25	#16840728	C₂²	1	2	yes	—
26	#16840725	—	2	2	no	—
27	#16840725	C₂²	1	2	yes	—
28	M₁₆×#6923	—	2	2	no	—
29	M₁₆×#6923	C₂²	1	2	yes	—
30	C₂×#14519831	—	2	2	no	—
31	C₂×#14519831	C₂²	1	1	yes	characteristic
32	C₂×#14519831	C₂²	1	1	yes	characteristic
33	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
35	C₂×C₈×#6923	C₂²	1	1	yes	characteristic
36	#16840698	C₂²	1	1	yes	characteristic
37	#16840637	C₂²	1	2	yes	—
38	#16840634	C₂²	1	2	yes	—
39	#16840633	C₂²	1	2	yes	—
40	#135×D₆₁	C₂²	1	1	yes	characteristic
41	#131×D₆₁	C₂²	1	2	yes	—
42	#16839885	C₄	1	1	yes	characteristic, complemented
43	#16839884	C₄	1	1	yes	characteristic, complemented
44	#16839883	C₄	1	1	yes	characteristic, complemented
45	#16839882	C₄	1	2	yes	complemented
46	#16839881	C₄	1	2	yes	complemented
47	#108×D₆₁	C₂²	1	1	yes	characteristic
48	#104×D₆₁	C₂²	1	2	yes	—
49	#97×D₆₁	C₂²	1	1	yes	characteristic
50	C₆₁×#444	C₄	1	1	yes	characteristic, complemented
51	#14519865	C₂×C₄	1	4	yes	complemented
52	#14519864	—	2	4	no	—
53	#14519864	C₂×C₄	1	4	yes	complemented
54	D₆₁⋊M₁₆	—	2	2	no	—
55	D₆₁⋊M₁₆	C₂³	1	2	yes	—
56	C₂×D₆₁⋊C₈	—	2	2	no	—
57	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×D₆₁⋊C₈	C₂³	1	1	yes	characteristic
59	Q₈×#6923	C₂×C₄	1	4	yes	—
60	D₄×#6923	—	2	4	no	—
61	D₄×#6923	C₂×C₄	1	4	yes	—
62	#14519856	—	2	2	no	—
63	#14519856	C₂³	1	2	yes	—
64	C₂×C₄×#6923	—	2	2	no	—
65	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
66	C₂×C₄×#6923	C₂³	1	1	yes	characteristic
67	#14519848	C₂×C₄	1	2	yes	complemented
68	#14519847	C₂×C₄	1	2	yes	complemented
69	#14519846	C₂×C₄	1	2	yes	—
70	#14519845	C₂×C₄	1	2	yes	—
71	#14519842	C₂×C₄	1	4	yes	complemented
72	#14519841	C₂×C₄	1	4	yes	complemented
73	#14519840	C₂×C₄	1	4	yes	—
74	#14519839	C₂×C₄	1	4	yes	—
75	#14519831	—	2	2	no	—
76	#14519831	—	2	2	no	—
77	#14519831	—	2	2	no	—
78	#14519831	C₂×C₄	1	2	yes	complemented
79	#14519831	C₂×C₄	1	2	yes	complemented
80	#14519831	D₄	1	2	yes	—
81	#14519831	D₄	1	2	yes	—
82	C₄×#92420	—	2	2	no	—
83	C₈×#6923	—	2	2	no	—
84	C₈×#6923	—	2	2	no	—
85	C₈×#6923	—	2	2	no	—
86	C₈×#6923	—	2	2	no	—
87	C₈×#6923	C₂×C₄	1	2	yes	—
88	C₈×#6923	C₂×C₄	1	2	yes	—
89	(C₂×#6923)⋊C₄	—	2	2	no	—
90	#41×D₆₁	C₂³	1	2	yes	—
91	#14519800	C₂×C₄	1	1	yes	characteristic
92	#14519799	C₂×C₄	1	1	yes	characteristic
93	#14519798	C₂×C₄	1	2	yes	—
94	#14519797	C₂×C₄	1	2	yes	—
95	#14519796	C₂×C₄	1	1	yes	characteristic
96	Q₁₆×D₆₁	C₂×C₄	1	1	yes	characteristic
97	SD₁₆×D₆₁	C₂×C₄	1	2	yes	—
98	D₈×D₆₁	C₂×C₄	1	1	yes	characteristic
99	#14519785	—	2	2	no	—
100	#14519785	C₂×C₄	1	2	yes	complemented
101	#14519784	C₂×C₄	1	2	yes	complemented
102	#14519783	—	2	2	no	—
103	#14519783	C₂×C₄	1	2	yes	complemented
104	M₁₆×D₆₁	—	2	2	no	—
105	M₁₆×D₆₁	C₂³	1	2	yes	—
106	C₂×C₈×D₆₁	—	2	2	no	—
107	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
108	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
109	C₄²×D₆₁	C₂³	1	1	yes	characteristic
110	#14519713	C₂×C₄	1	1	yes	characteristic, complemented
111	#14519712	C₂×C₄	1	2	yes	complemented
112	#14519705	C₂×C₄	1	2	yes	complemented
113	#14519704	C₂×C₄	1	2	yes	complemented
114	#14519703	C₂×C₄	1	2	yes	complemented
115	#14519688	C₂×C₄	1	1	yes	characteristic, complemented
116	#14519687	C₂×C₄	1	1	yes	characteristic, complemented
117	#14519687	C₂×C₄	1	1	yes	characteristic, complemented
118	#135×C₆₁	C₂×C₄	1	1	yes	characteristic
119	#131×C₆₁	C₂×C₄	1	2	yes	complemented
120	#108×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
121	#104×C₆₁	C₂×C₄	1	2	yes	complemented
122	#97×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
123	C₂²×#6923	—	2	1	no	—
124	C₂²×#6923	—	2	4	no	—
125	C₂²×#6923	#41	1	2	yes	—
126	#41×C₆₁	C₂²×C₄	1	2	yes	—
127	#11758226	C₂²×C₄	1	2	yes	—
128	Q₈×D₆₁	C₂²×C₄	1	2	yes	—
129	#11758224	—	2	2	no	—
130	#11758224	C₂²×C₄	1	2	yes	—
131	D₄×D₆₁	—	2	2	no	—
132	D₄×D₆₁	C₂²×C₄	1	2	yes	—
133	#11758222	—	2	2	no	—
134	#11758222	C₂²×C₄	1	2	yes	—
135	C₂×C₄×D₆₁	—	2	2	no	—
136	C₂×C₄×D₆₁	—	2	1	no	—
137	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
138	C₂²⋊#6923	—	2	2	no	—
139	C₂²⋊#6923	—	2	4	no	—
140	#11758217	—	2	2	no	—
141	#11758217	—	2	4	no	—
142	C₂×#92420	—	2	1	no	—
143	C₂×#92420	—	2	4	no	—
144	C₂×#92420	#41	1	2	yes	—
145	C₄⋊#6923	—	2	4	no	—
146	C₄⋊#6923	C₂²×C₄	1	4	yes	—
147	C₄×#6923	—	2	4	no	—
148	C₄×#6923	—	2	2	no	—
149	C₄×#6923	—	2	1	no	—
150	C₄×#6923	C₂²×C₄	1	2	yes	—
151	C₄×#6923	C₂²×C₄	1	2	yes	—
152	C₄×#6923	C₂×D₄	1	1	yes	characteristic
153	C₄×#6923	C₂×D₄	1	1	yes	characteristic
154	#11758213	—	2	4	no	—
155	#11758213	C₂²×C₄	1	4	yes	—
156	D₆₁⋊C₈	—	2	2	no	—
157	D₆₁⋊C₈	—	2	1	no	—
158	D₆₁⋊C₈	—	2	4	no	—
159	D₆₁⋊C₈	C₂²×C₄	1	2	yes	—
160	D₆₁⋊C₈	C₂²×C₄	1	2	yes	—
161	D₆₁⋊C₈	C₂×D₄	1	2	yes	—
162	Q₁₆×C₆₁	C₄²	1	1	yes	characteristic
163	SD₁₆×C₆₁	C₄²	1	2	yes	—
164	D₈×C₆₁	C₄²	1	1	yes	characteristic
165	M₁₆×C₆₁	—	2	2	no	—
166	M₁₆×C₆₁	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₆₁	—	2	2	no	—
168	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
171	#11758202	C₄²	1	2	yes	—
172	#11758201	C₄²	1	2	yes	—
173	#11758200	C₄²	1	2	yes	—
174	#11758199	C₄²	1	2	yes	—
175	C₄×Dic₆₁	—	2	1	no	—
176	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
177	#11758194	—	2	2	no	—
178	#11758194	C₂²×C₄	1	2	yes	—
179	C₂×#92418	—	2	2	no	—
180	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
181	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
182	Dic₂₄₄	C₄²	1	1	yes	characteristic
183	D₄₈₈	C₄²	1	1	yes	characteristic
184	#11758190	C₄²	1	2	yes	—
185	#11758189	—	2	2	no	—
186	#11758189	—	2	2	no	—
187	#11758189	—	2	2	no	—
188	C₈×D₆₁	—	2	2	no	—
189	C₈×D₆₁	—	2	2	no	—
190	C₈×D₆₁	—	2	2	no	—
191	C₈×D₆₁	C₂²×C₄	1	1	yes	characteristic
192	C₈×D₆₁	C₂²×C₄	1	1	yes	characteristic
193	C₈×D₆₁	C₂²×C₄	1	1	yes	characteristic
194	C₈×D₆₁	C₂²×C₄	1	1	yes	characteristic
195	C₈×D₆₁	C₂×D₄	1	2	yes	—
196	C₈×D₆₁	#41	1	2	yes	—
197	C₂²×D₆₁	—	2	2	no	—
198	C₂²×D₆₁	C₂×#41	1	1	yes	characteristic
199	C₂×#6923	—	2	4	no	—
200	C₂×#6923	—	2	2	no	—
201	C₂×#6923	—	4	2	no	—
202	C₂×#6923	—	4	2	no	—
203	C₂×#6923	—	8	4	no	—
204	C₂×#6923	C₄×D₄	1	2	yes	—
205	C₂×#6923	C₄×D₄	1	2	yes	—
206	Q₈×C₆₁	C₂×C₄²	1	2	yes	—
207	D₄×C₆₁	—	2	2	no	—
208	D₄×C₆₁	C₂×C₄²	1	2	yes	—
209	C₂×C₄×C₆₁	—	2	2	no	—
210	C₂×C₄×C₆₁	—	2	1	no	—
211	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
212	C₂²⋊D₆₁	—	2	2	no	—
213	C₂²⋊D₆₁	—	2	2	no	—
214	C₂²⋊D₆₁	—	2	2	no	—
215	C₂×Dic₆₁	—	2	2	no	—
216	C₂×Dic₆₁	—	2	1	no	—
217	C₂×Dic₆₁	C₂×#41	1	1	yes	characteristic
218	D₂₄₄	—	2	2	no	—
219	D₂₄₄	C₂×C₄²	1	2	yes	—
220	C₄×D₆₁	—	2	2	no	—
221	C₄×D₆₁	—	2	2	no	—
222	C₄×D₆₁	—	2	2	no	—
223	C₄×D₆₁	—	4	2	no	—
224	C₄×D₆₁	C₂³×C₄	1	1	yes	characteristic
225	C₄×D₆₁	C₂³×C₄	1	1	yes	characteristic
226	C₄×D₆₁	C₂²×D₄	1	1	yes	characteristic
227	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
228	Dic₁₂₂	—	2	2	no	—
229	Dic₁₂₂	C₂×C₄²	1	2	yes	—
230	#92420	—	2	4	no	—
231	#92420	—	2	2	no	—
232	#92420	C₄×D₄	1	4	yes	—
233	C₈×C₆₁	—	2	2	no	—
234	C₈×C₆₁	C₂×C₄²	1	1	yes	characteristic
235	C₈×C₆₁	C₂×C₄²	1	1	yes	characteristic
236	C₈×C₆₁	C₄×D₄	1	2	yes	—
237	#92418	—	2	2	no	—
238	#92418	C₂×C₄²	1	1	yes	characteristic
239	#92418	C₂×C₄²	1	1	yes	characteristic
240	#92418	C₄×D₄	1	2	yes	—
241	#20513	—	61	1	no	maximal, Sylow
242	C₂²×C₆₁	—	2	2	no	—
243	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
244	C₂×D₆₁	—	2	2	no	—
245	C₂×D₆₁	—	2	2	no	—
246	C₂×D₆₁	—	4	4	no	—
247	C₂×D₆₁	C₂×C₄×D₄	1	1	yes	characteristic
248	C₂×D₆₁	C₄×#41	1	1	yes	characteristic
249	#6923	—	2	2	no	—
250	#6923	—	2	2	no	—
251	#6923	—	4	2	no	—
252	#6923	—	4	4	no	—
253	C₄×C₆₁	—	2	2	no	—
254	C₄×C₆₁	—	4	1	no	—
255	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
256	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
257	Dic₆₁	—	2	2	no	—
258	Dic₆₁	—	4	1	no	—
259	Dic₆₁	C₂×C₄×D₄	1	1	yes	characteristic
260	Dic₆₁	C₄×#41	1	1	yes	characteristic
261	C₂×#444	—	61	1	no	—
262	C₂×#444	—	61	1	no	—
263	C₄×#135	—	61	1	no	—
264	#2875	—	61	2	no	—
265	C₄×#108	—	61	1	no	—
266	#1773	—	61	1	no	—
267	#1773	—	61	1	no	—
268	#1764	—	61	2	no	—
269	#1764	—	61	2	no	—
270	#1759	—	61	2	no	—
271	#1726	—	61	1	no	—
272	C₂×C₆₁	—	2	1	no	—
273	C₂×C₆₁	—	4	2	no	—
274	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
275	D₆₁	—	2	1	no	—
276	D₆₁	—	4	2	no	—
277	D₆₁	#2957	1	2	yes	—
278	C₂×#135	—	61	1	no	—
279	C₂×#131	—	61	2	no	—
280	C₂×#131	—	61	2	no	—
281	C₄×#41	—	61	2	no	—
282	#444	—	61	4	no	—
283	#444	—	61	2	no	—
284	#444	—	61	2	no	—
285	#444	—	61	1	no	—
286	#444	—	61	2	no	—
287	#444	—	61	1	no	—
288	#444	—	61	2	no	—
289	#444	—	61	1	no	—
290	#444	#6923	1	1	yes	characteristic, complemented
291	C₄×Q₁₆	—	61	2	no	—
292	C₄×SD₁₆	—	61	4	no	—
293	C₄×D₈	—	61	2	no	—
294	C₂×#108	—	61	1	no	—
295	C₂×#108	—	61	1	no	—
296	#427	—	61	1	no	—
297	C₂×#104	—	61	2	no	—
298	C₂×#104	—	61	2	no	—
299	#416	—	61	2	no	—
300	#405	—	61	2	no	—
301	#405	—	61	2	no	—
302	#405	—	122	2	no	—
303	#405	—	122	2	no	—
304	C₄×M₁₆	—	61	2	no	—
305	C₄×M₁₆	—	122	2	no	—
306	C₂×#97	—	61	1	no	—
307	C₂×#97	—	61	1	no	—
308	C₂×#97	—	61	1	no	—
309	C₂×#97	—	122	2	no	—
310	C₂×C₄×C₈	—	61	1	no	—
311	C₂×C₄×C₈	—	61	1	no	—
312	C₂×C₄×C₈	—	61	1	no	—
313	#376	—	61	1	no	—
314	#341	—	61	2	no	—
315	#339	—	61	2	no	—
316	#339	—	61	2	no	—
317	C₆₁	#20513	1	1	yes	characteristic, complemented, Sylow
318	C₂×#41	—	61	2	no	—
319	#135	—	61	2	no	—
320	#135	—	61	1	no	—
321	#135	—	61	2	no	—
322	#135	—	61	1	no	—
323	#135	—	61	1	no	—
324	#135	C₂×#6923	1	1	yes	characteristic
325	C₂×Q₁₆	—	61	1	no	—
326	C₂×SD₁₆	—	61	2	no	—
327	C₂×D₈	—	61	1	no	—
328	#131	—	61	4	no	—
329	#131	—	61	4	no	—
330	#131	—	61	2	no	—
331	#131	—	61	2	no	—
332	#131	—	61	2	no	—
333	#131	—	122	2	no	—
334	#131	—	122	2	no	—
335	#131	—	122	4	no	—
336	#131	C₂×#6923	1	2	yes	complemented
337	C₂×M₁₆	—	61	2	no	—
338	C₂×M₁₆	—	61	2	no	—
339	C₂×M₁₆	—	122	2	no	—
340	C₂×M₁₆	—	122	2	no	—
341	C₂²×C₈	—	61	1	no	—
342	C₂²×C₈	—	61	1	no	—
343	C₂²×C₈	—	61	1	no	—
344	C₂²×C₈	—	61	1	no	—
345	C₂²×C₈	—	122	2	no	—
346	C₂²×C₈	—	122	2	no	—
347	C₄×Q₈	—	61	4	no	—
348	C₄×D₄	—	61	4	no	—
349	C₄×D₄	—	122	4	no	—
350	#117	—	61	2	no	—
351	#117	—	122	2	no	—
352	C₂×C₄²	—	61	1	no	—
353	C₂×C₄²	—	61	1	no	—
354	C₂×C₄²	—	61	1	no	—
355	C₂×C₄²	—	122	2	no	—
356	#108	—	61	2	no	—
357	#108	—	61	2	no	—
358	#108	—	61	2	no	—
359	#108	—	61	1	no	—
360	#108	C₂×#6923	1	1	yes	characteristic, complemented
361	#107	—	61	2	no	—
362	#106	—	61	2	no	—
363	#104	—	61	4	no	—
364	#104	—	61	4	no	—
365	#104	—	61	2	no	—
366	#104	—	61	2	no	—
367	#104	—	61	2	no	—
368	#104	C₂×#6923	1	2	yes	complemented
369	#103	—	61	4	no	—
370	#102	—	61	4	no	—
371	#97	—	61	2	no	—
372	#97	—	61	2	no	—
373	#97	—	61	2	no	—
374	#97	—	61	2	no	—
375	#97	—	61	1	no	—
376	#97	—	61	1	no	—
377	#97	—	61	1	no	—
378	#97	—	122	2	no	—
379	#97	—	122	2	no	—
380	#97	—	122	2	no	—
381	#97	C₂×#6923	1	1	yes	characteristic, complemented
382	C₄×C₈	—	61	2	no	—
383	C₄×C₈	—	61	2	no	—
384	C₄×C₈	—	122	2	no	—
385	C₄×C₈	—	122	2	no	—
386	C₄×C₈	—	122	2	no	—
387	C₄×C₈	—	122	2	no	—
388	C₄×C₈	—	122	2	no	—
389	#95	—	122	2	no	—
390	#41	—	61	2	no	—
391	#41	—	61	2	no	—
392	#41	—	61	2	no	—
393	#41	—	122	2	no	—
394	#41	—	122	2	no	—
395	#41	C₂²×#6923	1	2	yes	—
396	C₂×Q₈	—	61	2	no	—
397	C₂×D₄	—	61	2	no	—
398	C₂×D₄	—	122	2	no	—
399	C₂²×C₄	—	61	1	no	—
400	C₂²×C₄	—	61	2	no	—
401	C₂²×C₄	—	122	2	no	—
402	C₂²×C₄	—	122	1	no	—
403	C₂²×C₄	—	122	4	no	—
404	C₂²×C₄	—	122	1	no	—
405	Q₁₆	—	61	2	no	—
406	Q₁₆	—	61	1	no	—
407	Q₁₆	C₄×#6923	1	1	yes	characteristic
408	SD₁₆	—	61	2	no	—
409	SD₁₆	—	61	2	no	—
410	SD₁₆	—	61	2	no	—
411	SD₁₆	C₄×#6923	1	2	yes	—
412	D₈	—	61	2	no	—
413	D₈	—	61	1	no	—
414	D₈	C₄×#6923	1	1	yes	characteristic
415	M₁₆	—	2	2	no	—
416	M₁₆	—	61	4	no	—
417	M₁₆	—	61	2	no	—
418	M₁₆	—	122	2	no	—
419	M₁₆	—	122	2	no	—
420	M₁₆	—	122	2	no	—
421	M₁₆	—	122	4	no	—
422	M₁₆	—	122	4	no	—
423	M₁₆	—	122	2	no	—
424	M₁₆	—	122	2	no	—
425	M₁₆	C₂²×#6923	1	2	yes	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	61	2	no	—
428	C₂×C₈	—	61	2	no	—
429	C₂×C₈	—	61	2	no	—
430	C₂×C₈	—	61	1	no	—
431	C₂×C₈	—	61	1	no	—
432	C₂×C₈	—	61	1	no	—
433	C₂×C₈	—	61	1	no	—
434	C₂×C₈	—	61	1	no	—
435	C₂×C₈	—	61	1	no	—
436	C₂×C₈	—	61	2	no	—
437	C₂×C₈	—	61	2	no	—
438	C₂×C₈	—	61	2	no	—
439	C₂×C₈	—	122	2	no	—
440	C₂×C₈	—	122	2	no	—
441	C₂×C₈	—	122	2	no	—
442	C₂×C₈	—	122	4	no	—
443	C₂×C₈	—	122	4	no	—
444	C₂×C₈	—	122	2	no	—
445	C₂×C₈	—	122	1	no	—
446	C₂×C₈	—	122	1	no	—
447	C₂×C₈	—	122	2	no	—
448	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
449	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
450	C₄⋊C₄	—	61	4	no	—
451	C₄⋊C₄	—	122	4	no	—
452	C₂²⋊C₄	—	122	4	no	—
453	C₂²⋊C₄	—	122	2	no	—
454	C₄²	—	61	2	no	—
455	C₄²	—	61	1	no	—
456	C₄²	—	61	1	no	—
457	C₄²	—	61	2	no	—
458	C₄²	—	61	1	no	—
459	C₄²	—	122	1	no	—
460	C₄²	—	122	2	no	—
461	C₄²	—	122	1	no	—
462	C₄²	—	122	4	no	—
463	C₄²	C₂²×#6923	1	1	yes	characteristic
464	C₂³	—	61	1	no	—
465	C₂³	—	122	2	no	—
466	Q₈	—	61	2	no	—
467	Q₈	—	122	2	no	—
468	Q₈	C₂×C₄×#6923	1	2	yes	—
469	D₄	—	2	2	no	—
470	D₄	—	61	2	no	—
471	D₄	—	122	2	no	—
472	D₄	—	122	2	no	—
473	D₄	—	122	2	no	—
474	D₄	—	122	2	no	—
475	D₄	C₂×C₄×#6923	1	2	yes	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	61	1	no	—
479	C₂×C₄	—	61	1	no	—
480	C₂×C₄	—	61	1	no	—
481	C₂×C₄	—	61	1	no	—
482	C₂×C₄	—	61	1	no	—
483	C₂×C₄	—	61	2	no	—
484	C₂×C₄	—	61	2	no	—
485	C₂×C₄	—	122	2	no	—
486	C₂×C₄	—	122	2	no	—
487	C₂×C₄	—	122	2	no	—
488	C₂×C₄	—	122	2	no	—
489	C₂×C₄	—	122	2	no	—
490	C₂×C₄	—	122	4	no	—
491	C₂×C₄	—	122	1	no	—
492	C₂×C₄	—	488	4	no	—
493	C₂×C₄	—	244	2	no	—
494	C₂×C₄	—	244	2	no	—
495	C₂×C₄	—	244	2	no	—
496	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	61	4	no	—
499	C₈	—	61	1	no	—
500	C₈	—	61	1	no	—
501	C₈	—	61	2	no	—
502	C₈	—	122	2	no	—
503	C₈	—	122	4	no	—
504	C₈	—	122	2	no	—
505	C₈	C₂×C₄×#6923	1	1	yes	characteristic
506	C₈	C₂×C₄×#6923	1	1	yes	characteristic
507	C₈	D₄×#6923	1	2	yes	—
508	C₂²	—	2	2	no	—
509	C₂²	—	61	1	no	—
510	C₂²	—	61	1	no	—
511	C₂²	—	122	2	no	—
512	C₂²	—	122	2	no	—
513	C₂²	—	244	4	no	—
514	C₂²	#41×#6923	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	4	1	no	—
517	C₄	—	61	1	no	—
518	C₄	—	61	1	no	—
519	C₄	—	122	2	no	—
520	C₄	—	122	2	no	—
521	C₄	—	122	2	no	—
522	C₄	—	244	1	no	—
523	C₄	—	244	4	no	—
524	C₄	—	244	2	no	—
525	C₄	C₂²×C₄×#6923	1	1	yes	characteristic
526	C₄	C₂×D₄×#6923	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	4	2	no	—
529	C₂	—	61	2	no	—
530	C₂	—	122	1	no	—
531	C₂	—	244	2	no	—
532	C₂	C₄×D₄×#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#6923
commutator	C₄×C₆₁	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₆₁×#444	C₄
socle	C₂×C₆₁	C₄²×D₄
prime radical	#135×D₆₁	C₂²
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	#444	#6923
hypocenter	C₆₁	#20513
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #444

Complements

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

N	H ≅ G/N	type
3. #21462389	C₂	semidirect
4. #108×#6923	C₂	semidirect
5. #21461628	C₂	semidirect
6. #21461625	C₂	semidirect
7. #21461595	C₂	semidirect
8. #21461593	C₂	semidirect
9. #21461584	C₂	semidirect
10. #21461477	C₂	semidirect
14. #16840809	C₄	semidirect
15. #16840808	C₄	semidirect
16. #16840807	C₄	semidirect
17. Q₁₆×#6923	C₄	semidirect
18. SD₁₆×#6923	C₄	semidirect
19. D₈×#6923	C₄	semidirect
42. #16839885	C₄	semidirect
43. #16839884	C₄	semidirect
44. #16839883	C₄	semidirect
45. #16839882	C₄	semidirect
46. #16839881	C₄	semidirect
50. C₆₁×#444	C₄	semidirect
51. #14519865	C₂×C₄	semidirect
53. #14519864	C₂×C₄	semidirect
67. #14519848	C₂×C₄	semidirect
68. #14519847	C₂×C₄	semidirect
71. #14519842	C₂×C₄	semidirect
72. #14519841	C₂×C₄	semidirect
78. #14519831	C₂×C₄	semidirect
79. #14519831	C₂×C₄	semidirect
100. #14519785	C₂×C₄	semidirect
101. #14519784	C₂×C₄	semidirect
103. #14519783	C₂×C₄	semidirect
110. #14519713	C₂×C₄	semidirect
111. #14519712	C₂×C₄	semidirect
112. #14519705	C₂×C₄	semidirect
113. #14519704	C₂×C₄	semidirect
114. #14519703	C₂×C₄	semidirect
115. #14519688	C₂×C₄	semidirect
116. #14519687	C₂×C₄	semidirect
117. #14519687	C₂×C₄	semidirect
119. #131×C₆₁	C₂×C₄	semidirect
120. #108×C₆₁	C₂×C₄	semidirect
121. #104×C₆₁	C₂×C₄	semidirect
122. #97×C₆₁	C₂×C₄	semidirect
290. #444	#6923	semidirect
317. C₆₁	#20513	semidirect
336. #131	C₂×#6923	semidirect
360. #108	C₂×#6923	semidirect
368. #104	C₂×#6923	semidirect
381. #97	C₂×#6923	semidirect

Maximal subgroups

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

subgroup	index
D₆₁⋊#444	2
#135×#6923	2
#21462389	2
#108×#6923	2
#21461628	2
#21461625	2
#21461595	2
#21461593	2
#21461584	2
#21461477	2
#444×D₆₁	2
#20513	61