Subgroups — #24991358

Order 11008.

764 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583094	C₂	1	1	yes	maximal, characteristic
2	#19135522	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132478	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621882	—	2	1	no	—
9	C₂×#13063322	C₂²	1	1	yes	characteristic
10	#14583094	—	2	2	no	—
11	#14583094	C₄	1	4	yes	complemented
12	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13063245	—	2	1	no	—
15	C₂×#13063245	—	2	1	no	—
16	C₂×#13063245	—	2	1	no	—
17	C₂×#13063245	—	2	2	no	—
18	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	D₄⋊(C₄₃⋊C₈)	—	2	2	no	—
20	C₂×C₄×D₄×C₄₃	—	2	1	no	—
21	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
23	C₄₃×#389	—	2	1	no	—
24	C₄₃×#385	—	2	2	no	—
25	C₄₃×#384	C₂²	1	1	yes	characteristic
26	C₄₃×#380	—	2	1	no	—
27	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×D₁₇₂	—	2	1	no	—
29	C₂²×D₁₇₂	—	2	1	no	—
30	C₂²×D₁₇₂	—	2	1	no	—
31	C₂×#10621882	—	2	4	no	—
32	C₂×#10621882	—	4	2	no	—
33	C₂×#10621882	—	4	2	no	—
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	#13063322	—	2	1	no	—
38	#13063322	—	2	1	no	—
39	#13063322	—	2	1	no	—
40	#13063322	C₂×C₄	1	2	yes	complemented
41	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
42	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
43	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
44	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	complemented
45	#13063245	—	2	4	no	—
46	#13063245	—	4	4	no	—
47	#13063245	—	4	2	no	—
48	#13063245	—	4	2	no	—
49	C₄×C₄₃⋊C₈	—	2	1	no	—
50	C₄×C₄₃⋊C₈	—	2	1	no	—
51	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	—	2	1	no	—
53	C₂³×C₄×C₄₃	—	2	2	no	—
54	C₄×D₄×C₄₃	—	2	1	no	—
55	C₄×D₄×C₄₃	—	2	1	no	—
56	C₄×D₄×C₄₃	—	4	2	no	—
57	C₄×D₄×C₄₃	—	4	2	no	—
58	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
59	C₄×D₄×C₄₃	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
65	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	—	2	1	no	—
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	#95×C₄₃	—	2	2	no	—
74	#95×C₄₃	—	2	1	no	—
75	C₂⁴×C₄₃	—	2	1	no	—
76	C₂³×D₄₃	—	4	1	no	—
77	C₂×D₄×C₄₃	—	2	1	no	—
78	C₂×D₄×C₄₃	—	2	1	no	—
79	C₂×D₄×C₄₃	—	2	1	no	—
80	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
81	C₂×D₄×C₄₃	D₈	1	2	yes	—
82	C₂×D₄×C₄₃	SD₁₆	1	2	yes	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	—	2	1	no	—
87	C₂²×C₄×C₄₃	—	2	1	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	4	4	no	—
90	C₂²×C₄×C₄₃	—	4	4	no	—
91	C₂²×C₄×C₄₃	—	4	1	no	—
92	C₂²×C₄×C₄₃	—	4	1	no	—
93	C₂²×C₄×C₄₃	—	4	1	no	—
94	C₂²×C₄×C₄₃	—	4	1	no	—
95	C₂²×C₄×C₄₃	—	8	2	no	—
96	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂×D₁₇₂	—	2	2	no	—
100	C₂×D₁₇₂	—	2	2	no	—
101	C₂×D₁₇₂	—	2	2	no	—
102	C₂×D₁₇₂	—	4	1	no	—
103	C₂×D₁₇₂	—	4	1	no	—
104	C₂×D₁₇₂	—	4	1	no	—
105	C₂×D₁₇₂	—	4	2	no	—
106	C₂×D₁₇₂	—	4	2	no	—
107	C₂×D₁₇₂	—	4	1	no	—
108	C₂×D₁₇₂	—	4	1	no	—
109	C₂×D₁₇₂	—	4	1	no	—
110	C₂×D₁₇₂	—	4	1	no	—
111	C₂×D₁₇₂	—	4	1	no	—
112	C₂×D₁₇₂	—	4	1	no	—
113	C₂×D₁₇₂	—	4	1	no	—
114	C₂×D₁₇₂	—	4	1	no	—
115	C₄⋊C₄×C₄₃	—	2	1	no	—
116	C₄⋊C₄×C₄₃	—	2	1	no	—
117	C₄⋊C₄×C₄₃	—	2	1	no	—
118	C₄⋊C₄×C₄₃	—	2	1	no	—
119	C₄⋊C₄×C₄₃	—	4	2	no	—
120	C₄⋊C₄×C₄₃	—	4	4	no	—
121	C₄⋊C₄×C₄₃	—	4	1	no	—
122	C₄⋊C₄×C₄₃	—	4	1	no	—
123	C₄⋊C₄×C₄₃	—	4	1	no	—
124	C₄⋊C₄×C₄₃	—	4	1	no	—
125	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
126	C₄⋊C₄×C₄₃	D₈	1	2	yes	complemented
127	C₂²⋊C₄×C₄₃	—	2	2	no	—
128	C₂²⋊C₄×C₄₃	—	2	2	no	—
129	C₂²⋊C₄×C₄₃	—	4	4	no	—
130	C₄²×C₄₃	—	4	1	no	—
131	C₄²×C₄₃	—	4	1	no	—
132	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₃	#41	1	1	yes	characteristic
135	C₄²×C₄₃	#41	1	1	yes	characteristic
136	#10621882	—	4	8	no	—
137	C₂×C₄₃⋊C₈	—	2	2	no	—
138	C₂×C₄₃⋊C₈	—	2	2	no	—
139	C₂×C₄₃⋊C₈	—	4	1	no	—
140	C₂×C₄₃⋊C₈	—	4	1	no	—
141	C₂×C₄₃⋊C₈	—	4	1	no	—
142	C₂×C₄₃⋊C₈	—	4	1	no	—
143	C₂×C₄₃⋊C₈	—	4	1	no	—
144	C₂×C₄₃⋊C₈	—	4	1	no	—
145	C₂×C₄₃⋊C₈	—	4	1	no	—
146	C₂³×C₄₃	—	2	2	no	—
147	C₂³×C₄₃	—	2	2	no	—
148	C₂³×C₄₃	—	2	2	no	—
149	C₂³×C₄₃	—	4	1	no	—
150	C₂³×C₄₃	—	4	1	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	—	4	1	no	—
153	C₂³×C₄₃	#120	1	1	yes	characteristic
154	C₂²×D₄₃	—	4	2	no	—
155	C₂²×D₄₃	—	8	1	no	—
156	C₂²×D₄₃	—	8	1	no	—
157	C₂²×D₄₃	—	8	1	no	—
158	C₂²×D₄₃	—	8	1	no	—
159	C₂²×D₄₃	—	8	1	no	—
160	C₂²×D₄₃	—	8	1	no	—
161	D₄×C₄₃	—	2	2	no	—
162	D₄×C₄₃	—	2	2	no	—
163	D₄×C₄₃	—	2	2	no	—
164	D₄×C₄₃	#102	1	4	yes	complemented
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	1	no	—
183	C₂×C₄×C₄₃	—	8	8	no	—
184	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
193	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
194	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
198	D₁₇₂	—	4	4	no	—
199	D₁₇₂	—	4	2	no	—
200	D₁₇₂	—	4	2	no	—
201	D₁₇₂	—	4	2	no	—
202	D₁₇₂	—	4	2	no	—
203	D₁₇₂	—	8	2	no	—
204	D₁₇₂	—	8	1	no	—
205	D₁₇₂	—	8	1	no	—
206	D₁₇₂	—	8	1	no	—
207	D₁₇₂	—	8	1	no	—
208	C₄₃⋊C₈	—	4	2	no	—
209	C₄₃⋊C₈	—	4	2	no	—
210	C₄₃⋊C₈	—	8	1	no	—
211	#8977	—	43	1	no	maximal, Sylow
212	C₂²×C₄₃	—	2	4	no	—
213	C₂²×C₄₃	—	4	2	no	—
214	C₂²×C₄₃	—	4	2	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	—	4	2	no	—
219	C₂²×C₄₃	#386	1	1	yes	characteristic
220	C₂²×C₄₃	#447	1	1	yes	characteristic
221	C₂²×C₄₃	#447	1	1	yes	characteristic
222	C₂²×C₄₃	#448	1	1	yes	characteristic
223	C₂²×C₄₃	#449	1	1	yes	characteristic
224	C₂²×C₄₃	#453	1	1	yes	characteristic
225	C₂²×C₄₃	#454	1	1	yes	characteristic
226	C₂×D₄₃	—	8	2	no	—
227	C₂×D₄₃	—	8	2	no	—
228	C₂×D₄₃	—	8	2	no	—
229	C₂×D₄₃	—	16	1	no	—
230	C₂×D₄₃	—	16	1	no	—
231	C₂×D₄₃	—	16	1	no	—
232	C₂×D₄₃	—	16	1	no	—
233	C₄×C₄₃	—	2	1	no	—
234	C₄×C₄₃	—	2	1	no	—
235	C₄×C₄₃	—	4	2	no	—
236	C₄×C₄₃	—	4	2	no	—
237	C₄×C₄₃	—	8	2	no	—
238	C₄×C₄₃	—	8	1	no	—
239	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
240	C₄×C₄₃	#417	1	1	yes	characteristic
241	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
242	C₄×C₄₃	#442	1	1	yes	characteristic
243	C₄×C₄₃	#459	1	1	yes	characteristic
244	C₄×C₄₃	#463	1	1	yes	characteristic
245	C₄×C₄₃	#480	1	1	yes	characteristic
246	C₄×C₄₃	#481	1	1	yes	characteristic
247	C₂×#459	—	43	1	no	—
248	D₄×C₄⋊C₄	D₄₃	1	1	yes	characteristic, complemented
249	#1982	—	43	1	no	—
250	#1957	—	43	1	no	—
251	C₂×D₄⋊C₈	—	43	1	no	—
252	#1296	—	43	1	no	—
253	#1279	—	43	1	no	—
254	C₂×C₄₃	—	4	4	no	—
255	C₂×C₄₃	#1619	1	1	yes	characteristic
256	C₂×C₄₃	#1622	1	1	yes	characteristic
257	C₂×C₄₃	#1625	1	1	yes	characteristic
258	C₂×C₄₃	#1627	1	1	yes	characteristic
259	C₂×C₄₃	#1874	1	1	yes	characteristic
260	C₂×C₄₃	#1879	1	1	yes	characteristic
261	C₂×C₄₃	#1883	1	1	yes	characteristic
262	D₄₃	—	16	2	no	—
263	C₂²×D₈	—	86	1	no	—
264	C₂×#127	—	43	1	no	—
265	C₂×C₄×D₄	—	2	1	no	—
266	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	—	2	1	no	—
268	#459	—	43	4	no	—
269	#459	—	86	2	no	—
270	C₂×C₄⋊C₈	—	43	1	no	—
271	C₂×C₄⋊C₈	—	43	1	no	—
272	C₂×#102	—	86	1	no	—
273	C₂×#102	—	86	2	no	—
274	C₂×#102	—	86	1	no	—
275	C₂×#102	—	86	1	no	—
276	C₂×C₄×C₈	—	43	1	no	—
277	#389	—	2	1	no	—
278	#385	—	2	2	no	—
279	#384	C₂×D₄₃	1	1	yes	characteristic
280	#380	—	2	1	no	—
281	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
282	D₄⋊C₈	—	86	2	no	—
283	C₄₃	#8977	1	1	yes	characteristic, complemented, Sylow
284	C₂²×D₄	—	86	1	no	—
285	C₂²×D₄	—	86	1	no	—
286	C₂²×D₄	—	86	1	no	—
287	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂×D₈	—	86	4	no	—
291	C₂×D₈	—	172	2	no	—
292	C₂×D₈	—	172	2	no	—
293	C₂²×C₈	—	86	1	no	—
294	C₂²×C₈	—	86	1	no	—
295	C₂²×C₈	—	86	1	no	—
296	#127	—	43	2	no	—
297	#127	—	86	1	no	—
298	#127	—	86	1	no	—
299	#127	—	86	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	4	2	no	—
303	C₄×D₄	—	4	2	no	—
304	C₄×D₄	C₄×D₄₃	1	2	yes	—
305	C₄×D₄	D₁₇₂	1	2	yes	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	4	2	no	—
310	C₂×C₄⋊C₄	—	4	2	no	—
311	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
319	C₄⋊C₈	—	43	2	no	—
320	C₄⋊C₈	—	86	1	no	—
321	C₄⋊C₈	—	86	1	no	—
322	C₄⋊C₈	—	86	1	no	—
323	#102	—	86	4	no	—
324	#102	—	172	2	no	—
325	#102	—	172	4	no	—
326	#102	—	172	2	no	—
327	C₄×C₈	—	86	1	no	—
328	C₄×C₈	—	86	1	no	—
329	#95	—	2	2	no	—
330	#95	—	2	1	no	—
331	C₂⁴	—	2	1	no	—
332	C₂⁴	—	172	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	86	2	no	—
337	C₂×D₄	—	86	2	no	—
338	C₂×D₄	—	86	2	no	—
339	C₂×D₄	—	172	2	no	—
340	C₂×D₄	—	172	2	no	—
341	C₂×D₄	—	172	1	no	—
342	C₂×D₄	—	172	1	no	—
343	C₂×D₄	—	172	1	no	—
344	C₂×D₄	—	172	1	no	—
345	C₂×D₄	—	172	1	no	—
346	C₂×D₄	—	172	1	no	—
347	C₂×D₄	—	172	1	no	—
348	C₂×D₄	—	172	1	no	—
349	C₂×D₄	—	172	1	no	—
350	C₂×D₄	—	172	1	no	—
351	C₂×D₄	—	172	1	no	—
352	C₂×D₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
353	C₂×D₄	#10621882	1	2	yes	—
354	C₂×D₄	#10621884	1	2	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	4	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	4	no	—
367	C₂²×C₄	—	8	2	no	—
368	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
371	D₈	—	172	8	no	—
372	C₂×C₈	—	86	2	no	—
373	C₂×C₈	—	86	2	no	—
374	C₂×C₈	—	172	1	no	—
375	C₂×C₈	—	172	1	no	—
376	C₂×C₈	—	172	1	no	—
377	C₂×C₈	—	172	1	no	—
378	C₂×C₈	—	172	1	no	—
379	C₂×C₈	—	172	1	no	—
380	C₂×C₈	—	172	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
392	C₄⋊C₄	#10621882	1	2	yes	complemented
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	4	1	no	—
398	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
399	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
400	C₄²	#10621898	1	1	yes	characteristic
401	C₄²	#10621898	1	1	yes	characteristic
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	344	1	no	—
410	C₂³	—	344	1	no	—
411	C₂³	—	344	1	no	—
412	C₂³	—	344	1	no	—
413	C₂³	—	344	1	no	—
414	C₂³	—	344	1	no	—
415	C₂³	—	172	2	no	—
416	C₂³	#13063294	1	1	yes	characteristic
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	344	2	no	—
421	D₄	—	344	1	no	—
422	D₄	—	344	1	no	—
423	D₄	—	344	1	no	—
424	D₄	—	344	1	no	—
425	D₄	—	172	4	no	—
426	D₄	—	172	2	no	—
427	D₄	—	172	2	no	—
428	D₄	—	172	2	no	—
429	D₄	—	172	2	no	—
430	D₄	#13063245	1	4	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	8	8	no	—
450	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
451	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
452	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
453	C₂×C₄	#13063299	1	1	yes	characteristic
454	C₂×C₄	#13063299	1	1	yes	characteristic
455	C₂×C₄	#13063308	1	1	yes	characteristic
456	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
457	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
458	C₂×C₄	C₂×#10621884	1	1	yes	characteristic
459	C₂×C₄	#13063345	1	1	yes	characteristic
460	C₂×C₄	#13063350	1	1	yes	characteristic
461	C₂×C₄	#13063351	1	1	yes	characteristic
462	C₂×C₄	#13063351	1	1	yes	characteristic
463	C₂×C₄	#13063356	1	1	yes	characteristic
464	C₈	—	344	1	no	—
465	C₈	—	172	2	no	—
466	C₈	—	172	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	344	2	no	—
475	C₂²	—	344	2	no	—
476	C₂²	—	344	2	no	—
477	C₂²	—	688	1	no	—
478	C₂²	—	688	1	no	—
479	C₂²	—	688	1	no	—
480	C₂²	—	688	1	no	—
481	C₂²	#14582778	1	1	yes	characteristic
482	C₂²	#14583033	1	1	yes	characteristic
483	C₂²	#14583033	1	1	yes	characteristic
484	C₂²	#14583038	1	1	yes	characteristic
485	C₂²	#14583044	1	1	yes	characteristic
486	C₂²	#14583067	1	1	yes	characteristic
487	C₂²	#14583072	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	2	no	—
493	C₄	—	8	1	no	—
494	C₄	C₂×#13063245	1	1	yes	characteristic
495	C₄	#14582898	1	1	yes	characteristic
496	C₄	C₄×#10621882	1	1	yes	characteristic
497	C₄	#14583009	1	1	yes	characteristic
498	C₄	#14583094	1	1	yes	characteristic
499	C₄	#14583114	1	1	yes	characteristic
500	C₄	#14583212	1	1	yes	characteristic
501	C₄	#14583217	1	1	yes	characteristic
502	C₂	—	4	4	no	—
503	C₂	—	688	2	no	—
504	C₂	#19133649	1	1	yes	characteristic
505	C₂	#19133667	1	1	yes	characteristic
506	C₂	#19133684	1	1	yes	characteristic
507	C₂	#19133698	1	1	yes	characteristic
508	C₂	#19134912	1	1	yes	characteristic
509	C₂	#19134943	1	1	yes	characteristic
510	C₂	#19134971	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063294
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	D₄×C₄⋊C₄×C₄₃	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂×#14583094	C₂
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	D₄×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#8977
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ D₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #19135522	C₂	semidirect
3. #19135400	C₂	semidirect
4. C₂×D₄⋊(C₄₃⋊C₈)	C₂	semidirect
5. #19132478	C₂	semidirect
6. #19132436	C₂	semidirect
7. D₄×C₄⋊C₄×C₄₃	C₂	semidirect
11. #14583094	C₄	semidirect
40. #13063322	C₂×C₄	semidirect
44. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
126. C₄⋊C₄×C₄₃	D₈	semidirect
164. D₄×C₄₃	#102	semidirect
248. D₄×C₄⋊C₄	D₄₃	semidirect
283. C₄₃	#8977	semidirect
392. C₄⋊C₄	#10621882	semidirect
430. D₄	#13063245	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583094	2
#19135522	2
#19135400	2
C₂×D₄⋊(C₄₃⋊C₈)	2
#19132478	2
#19132436	2
D₄×C₄⋊C₄×C₄₃	2
#8977	43