Subgroups — #25147604

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145052	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583171	C₂	1	2	yes	maximal, complemented
3	#19144067	C₂	1	1	yes	maximal, characteristic
4	#19143338	C₂	1	1	yes	maximal, characteristic
5	#19135895	C₂	1	2	yes	maximal, complemented
6	#19135714	C₂	1	2	yes	maximal, complemented
7	#19135440	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135371	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135113	C₂	1	2	yes	maximal, complemented
10	C₄×#13063244	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	C₂²	1	2	yes	—
13	C₂×#13063356	C₂²	1	2	yes	—
14	C₂×#13063356	C₂²	1	2	yes	—
15	C₂×#13063331	C₂²	1	2	yes	—
16	#14583449	C₂²	1	1	yes	characteristic
17	#14583291	—	2	2	no	—
18	#14583278	—	2	1	no	—
19	#14583273	—	2	1	no	—
20	#14583171	—	2	8	no	—
21	#14583121	—	2	2	no	—
22	#14583109	—	2	1	no	—
23	#14583099	—	2	1	no	—
24	#14582976	—	2	1	no	—
25	#14582969	—	2	2	no	—
26	#14582964	—	2	1	no	—
27	C₂×#13063261	C₂²	1	2	yes	—
28	#14582923	C₂²	1	1	yes	characteristic
29	#14582898	C₂²	1	2	yes	—
30	C₂×#13063244	C₂²	1	2	yes	—
31	C₂×#13063244	C₂²	1	1	yes	characteristic
32	C₂×#13063244	C₂²	1	2	yes	—
33	C₂×#13063244	C₂²	1	1	yes	characteristic
34	#14582865	C₂²	1	2	yes	—
35	C₄×#10621877	C₂²	1	1	yes	characteristic
36	C₄×#10621877	C₂²	1	1	yes	characteristic
37	#14582668	C₂²	1	1	yes	characteristic
38	#14582668	C₂²	1	1	yes	characteristic
39	#14582664	C₂²	1	2	yes	—
40	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
41	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#462	—	2	1	no	—
44	C₄₃×#462	—	2	2	no	—
45	C₄₃×#462	—	2	1	no	—
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#103×C₄₃	C₂²	1	2	yes	—
48	C₂×#10621898	C₂³	1	2	yes	—
49	#13063356	—	2	4	no	—
50	#13063356	—	2	4	no	—
51	#13063356	—	2	4	no	—
52	#13063356	—	4	2	no	—
53	#13063356	—	4	2	no	—
54	#13063356	—	4	2	no	—
55	C₂×#10621885	—	2	2	no	—
56	C₂×#10621885	—	2	2	no	—
57	C₂×#10621885	—	2	2	no	—
58	C₂×#10621884	—	2	2	no	—
59	C₂×#10621884	—	2	2	no	—
60	C₂×#10621884	—	2	2	no	—
61	#13063331	—	2	4	no	—
62	#13063331	—	4	2	no	—
63	C₂×#10621877	C₂³	1	1	yes	characteristic
64	C₂×#10621877	C₂³	1	2	yes	—
65	C₂×#10621877	C₂³	1	1	yes	characteristic
66	C₂×#10621877	C₂³	1	1	yes	characteristic
67	C₂×#10621877	C₂³	1	1	yes	characteristic
68	C₂×#10621872	—	2	2	no	—
69	C₂×C₈×D₄₃	—	2	2	no	—
70	#13063325	D₄	1	1	yes	characteristic
71	#13063322	D₄	1	1	yes	characteristic
72	#13063313	D₄	1	2	yes	—
73	#13063299	—	2	1	no	—
74	#13063299	—	2	1	no	—
75	C₄×D₁₇₂	—	2	1	no	—
76	C₄×D₁₇₂	—	2	1	no	—
77	#13063261	—	2	4	no	—
78	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
79	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
80	#13063248	—	2	2	no	—
81	#13063245	—	2	2	no	—
82	#13063244	—	2	4	no	—
83	#13063244	—	2	2	no	—
84	#13063244	—	4	2	no	—
85	#13063244	D₄	1	4	yes	complemented
86	(C₂×D₄₃)⋊C₈	—	2	2	no	—
87	(C₂×D₄₃)⋊C₈	—	2	2	no	—
88	#13063236	—	2	1	no	—
89	#13063236	—	2	1	no	—
90	C₄×C₄₃⋊C₈	—	2	1	no	—
91	C₄×C₄₃⋊C₈	—	2	1	no	—
92	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
93	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×Q₁₆×C₄₃	—	2	4	no	—
95	C₂×Q₁₆×C₄₃	—	2	2	no	—
96	C₂×Q₁₆×C₄₃	—	2	2	no	—
97	C₂×Q₁₆×C₄₃	—	4	2	no	—
98	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₄₃	—	2	1	no	—
100	C₄⋊Q₈×C₄₃	—	2	1	no	—
101	C₄⋊Q₈×C₄₃	—	2	1	no	—
102	C₄⋊Q₈×C₄₃	—	2	1	no	—
103	C₄×Q₈×C₄₃	—	2	1	no	—
104	C₄×Q₈×C₄₃	—	2	1	no	—
105	C₄×Q₈×C₄₃	—	2	1	no	—
106	C₄×Q₈×C₄₃	—	2	1	no	—
107	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
108	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
109	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₄₃	—	2	1	no	—
112	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
114	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
115	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
116	#103×C₄₃	—	2	2	no	—
117	#103×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	—	2	1	no	—
120	C₂×Q₈×C₄₃	—	2	1	no	—
121	C₂×Q₈×C₄₃	—	2	2	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	1	no	—
126	C₂×Q₈×C₄₃	—	2	1	no	—
127	C₂×Q₈×C₄₃	—	2	2	no	—
128	C₂×Q₈×C₄₃	—	2	2	no	—
129	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₂²⋊D₄₃	—	2	2	no	—
137	#10621898	—	2	2	no	—
138	#10621898	—	2	2	no	—
139	#10621898	—	2	2	no	—
140	#10621898	—	2	2	no	—
141	C₂×D₁₇₂	—	2	1	no	—
142	C₂×D₁₇₂	—	2	1	no	—
143	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
144	C₂×C₄×D₄₃	—	2	2	no	—
145	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
146	Q₁₆×C₄₃	—	4	4	no	—
147	Q₁₆×C₄₃	—	4	4	no	—
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₄₃	—	2	1	no	—
153	C₄⋊C₄×C₄₃	—	2	1	no	—
154	C₄⋊C₄×C₄₃	—	4	1	no	—
155	C₄⋊C₄×C₄₃	—	4	1	no	—
156	C₄⋊C₄×C₄₃	—	4	1	no	—
157	C₄⋊C₄×C₄₃	—	4	1	no	—
158	C₄⋊C₄×C₄₃	—	4	1	no	—
159	C₄⋊C₄×C₄₃	—	4	1	no	—
160	C₄²×C₄₃	—	4	1	no	—
161	C₄²×C₄₃	—	4	1	no	—
162	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
166	#10621885	—	4	4	no	—
167	#10621885	—	4	4	no	—
168	#10621885	—	4	4	no	—
169	#10621884	—	4	4	no	—
170	#10621884	—	4	4	no	—
171	#10621884	—	4	4	no	—
172	(C₂×D₄₃)⋊C₄	—	2	2	no	—
173	(C₂×D₄₃)⋊C₄	—	2	2	no	—
174	C₄⋊Dic₄₃	—	2	1	no	—
175	C₄⋊Dic₄₃	—	2	1	no	—
176	#10621877	—	2	1	no	—
177	#10621877	—	2	1	no	—
178	#10621877	—	2	1	no	—
179	#10621877	—	2	2	no	—
180	#10621877	—	2	1	no	—
181	#10621877	—	2	1	no	—
182	#10621877	—	2	2	no	—
183	#10621877	C₂×D₄	1	2	yes	—
184	#10621877	C₂×D₄	1	2	yes	—
185	#10621877	#41	1	2	yes	—
186	C₂×C₄₃⋊C₈	—	2	1	no	—
187	C₂×C₄₃⋊C₈	—	2	1	no	—
188	C₂×C₄₃⋊C₈	—	2	1	no	—
189	C₂×C₄₃⋊C₈	—	2	1	no	—
190	C₂×C₄₃⋊C₈	—	2	2	no	—
191	#10621872	—	4	4	no	—
192	C₈×D₄₃	—	4	4	no	—
193	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂²×D₄₃	—	2	2	no	—
195	Q₈×C₄₃	—	2	2	no	—
196	Q₈×C₄₃	—	2	2	no	—
197	Q₈×C₄₃	—	4	1	no	—
198	Q₈×C₄₃	—	4	1	no	—
199	Q₈×C₄₃	—	4	2	no	—
200	Q₈×C₄₃	—	4	2	no	—
201	Q₈×C₄₃	—	4	2	no	—
202	Q₈×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	4	1	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	8	1	no	—
213	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
214	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
215	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
216	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂²⋊D₄₃	—	4	2	no	—
224	C₂²⋊D₄₃	—	4	2	no	—
225	C₂×Dic₄₃	—	2	2	no	—
226	D₁₇₂	—	2	2	no	—
227	D₁₇₂	—	2	2	no	—
228	D₁₇₂	—	4	2	no	—
229	D₁₇₂	—	8	1	no	—
230	C₄×D₄₃	—	4	2	no	—
231	C₄×D₄₃	—	4	2	no	—
232	Dic₈₆	—	2	2	no	—
233	Dic₈₆	—	2	2	no	—
234	C₈×C₄₃	—	2	2	no	—
235	C₈×C₄₃	—	2	2	no	—
236	C₄₃⋊C₈	—	2	2	no	—
237	C₄₃⋊C₈	—	2	2	no	—
238	C₄₃⋊C₈	—	2	2	no	—
239	C₄₃⋊C₈	—	4	2	no	—
240	C₄₃⋊C₈	—	4	1	no	—
241	#25406	—	43	1	no	maximal, Sylow
242	C₂²×C₄₃	—	2	1	no	—
243	C₂²×C₄₃	—	2	1	no	—
244	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
245	C₂²×C₄₃	#532	1	1	yes	characteristic
246	C₂²×C₄₃	#540	1	1	yes	characteristic
247	C₂×D₄₃	—	4	2	no	—
248	C₂×D₄₃	—	4	2	no	—
249	C₂×D₄₃	—	4	2	no	—
250	C₄×C₄₃	—	2	1	no	—
251	C₄×C₄₃	—	2	1	no	—
252	C₄×C₄₃	—	2	1	no	—
253	C₄×C₄₃	—	4	2	no	—
254	C₄×C₄₃	—	8	2	no	—
255	C₄×C₄₃	—	8	1	no	—
256	C₄×C₄₃	#473	1	2	yes	complemented
257	C₄×C₄₃	D₄²	1	1	yes	characteristic
258	C₄×C₄₃	D₄²	1	1	yes	characteristic
259	C₄×C₄₃	#546	1	1	yes	characteristic
260	C₄×C₄₃	#550	1	1	yes	characteristic
261	Dic₄₃	—	4	2	no	—
262	#3152	—	43	1	no	—
263	C₂×#473	—	43	2	no	—
264	#3037	—	43	1	no	—
265	C₂×#462	D₄₃	1	1	yes	characteristic, complemented
266	#2935	—	43	1	no	—
267	#2052	—	43	2	no	—
268	#2020	—	43	2	no	—
269	#1966	—	43	1	no	—
270	#1950	—	43	1	no	—
271	#1908	—	43	2	no	—
272	C₄×#101	—	43	1	no	—
273	C₂×C₄₃	—	2	1	no	—
274	C₂×C₄₃	—	2	1	no	—
275	C₂×C₄₃	#2428	1	1	yes	characteristic
276	C₂×C₄₃	C₂×#473	1	1	yes	characteristic
277	C₂×C₄₃	#3069	1	1	yes	characteristic
278	D₄₃	—	8	2	no	—
279	C₂×#137	—	43	2	no	—
280	C₂×#137	—	43	2	no	—
281	C₂×#137	—	43	2	no	—
282	C₂²×Q₁₆	C₂×D₄₃	1	2	yes	—
283	C₂×#131	—	43	2	no	—
284	#532	—	43	1	no	—
285	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
286	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
287	#497	—	86	2	no	—
288	#494	—	86	1	no	—
289	#492	—	86	1	no	—
290	#473	—	86	8	no	—
291	#464	—	86	2	no	—
292	#462	—	2	1	no	—
293	#462	—	2	2	no	—
294	#462	—	2	1	no	—
295	#462	—	86	1	no	—
296	#460	—	86	1	no	—
297	#436	—	86	1	no	—
298	#435	—	86	2	no	—
299	C₈×D₄	—	86	1	no	—
300	C₂×#108	—	43	2	no	—
301	#423	—	43	1	no	—
302	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
303	#417	—	43	2	no	—
304	C₂×#103	C₂×D₄₃	1	2	yes	—
305	C₂×#101	—	43	1	no	—
306	C₂×#101	—	43	2	no	—
307	C₂×#101	—	43	1	no	—
308	C₂×#101	—	43	2	no	—
309	#408	—	43	2	no	—
310	C₄×M₁₆	—	43	1	no	—
311	C₄×M₁₆	—	43	1	no	—
312	#343	—	43	1	no	—
313	#343	—	43	1	no	—
314	#341	—	43	2	no	—
315	C₄₃	#25406	1	1	yes	characteristic, complemented, Sylow
316	C₂×#41	—	43	2	no	—
317	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
318	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
319	#137	—	86	4	no	—
320	#137	—	86	4	no	—
321	#137	—	86	4	no	—
322	#137	—	172	2	no	—
323	#137	—	172	2	no	—
324	#137	—	172	2	no	—
325	C₂×Q₁₆	—	2	4	no	—
326	C₂×Q₁₆	—	2	2	no	—
327	C₂×Q₁₆	—	2	2	no	—
328	C₂×Q₁₆	—	4	2	no	—
329	C₂×Q₁₆	—	86	2	no	—
330	C₂×Q₁₆	—	86	2	no	—
331	C₂×Q₁₆	—	86	2	no	—
332	C₂×SD₁₆	—	86	2	no	—
333	C₂×SD₁₆	—	86	2	no	—
334	C₂×SD₁₆	—	86	2	no	—
335	#131	—	86	4	no	—
336	#131	—	172	2	no	—
337	C₂×M₁₆	—	43	1	no	—
338	C₂×M₁₆	—	43	1	no	—
339	C₂×M₁₆	—	43	1	no	—
340	C₂×M₁₆	—	43	2	no	—
341	C₂×M₁₆	—	43	1	no	—
342	C₂×M₁₆	—	86	2	no	—
343	C₂²×C₈	—	86	2	no	—
344	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	—	43	1	no	—
350	#127	—	43	1	no	—
351	#124	—	43	2	no	—
352	#121	—	86	1	no	—
353	#121	—	86	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×D₄	—	86	1	no	—
359	C₄×D₄	—	86	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
366	#108	—	86	4	no	—
367	C₄⋊C₈	—	86	1	no	—
368	C₄⋊C₈	—	86	1	no	—
369	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
370	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
371	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	86	2	no	—
375	#102	—	86	2	no	—
376	#101	—	43	4	no	—
377	#101	—	86	2	no	—
378	#101	—	86	4	no	—
379	#101	—	172	2	no	—
380	C₂²⋊C₈	—	86	2	no	—
381	C₂²⋊C₈	—	86	2	no	—
382	#97	—	86	1	no	—
383	#97	—	86	1	no	—
384	C₄×C₈	—	86	1	no	—
385	C₄×C₈	—	86	1	no	—
386	#41	—	86	2	no	—
387	#41	—	86	2	no	—
388	#41	—	86	2	no	—
389	#41	—	86	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	43	2	no	—
402	C₂×Q₈	D₄×D₄₃	1	2	yes	—
403	C₂×D₄	—	43	2	no	—
404	C₂×D₄	—	86	2	no	—
405	C₂×D₄	—	86	1	no	—
406	C₂×D₄	—	86	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	86	2	no	—
411	C₂²×C₄	#10621900	1	1	yes	characteristic
412	C₂²×C₄	#10621900	1	1	yes	characteristic
413	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
414	Q₁₆	—	4	4	no	—
415	Q₁₆	—	4	4	no	—
416	Q₁₆	—	172	4	no	—
417	Q₁₆	—	172	4	no	—
418	Q₁₆	—	172	4	no	—
419	SD₁₆	—	172	4	no	—
420	SD₁₆	—	172	4	no	—
421	SD₁₆	—	172	4	no	—
422	M₁₆	—	43	2	no	—
423	M₁₆	—	43	2	no	—
424	M₁₆	—	43	2	no	—
425	M₁₆	—	86	1	no	—
426	M₁₆	—	86	1	no	—
427	M₁₆	—	86	1	no	—
428	M₁₆	—	86	2	no	—
429	M₁₆	—	86	1	no	—
430	M₁₆	—	86	1	no	—
431	M₁₆	—	86	2	no	—
432	M₁₆	—	172	4	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	86	1	no	—
436	C₂×C₈	—	86	1	no	—
437	C₂×C₈	—	86	1	no	—
438	C₂×C₈	—	86	2	no	—
439	C₂×C₈	—	86	1	no	—
440	C₂×C₈	—	172	4	no	—
441	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
442	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	86	1	no	—
452	C₄⋊C₄	—	86	1	no	—
453	C₂²⋊C₄	—	86	2	no	—
454	C₂²⋊C₄	—	86	2	no	—
455	C₄²	—	4	1	no	—
456	C₄²	—	4	1	no	—
457	C₄²	D₄×D₄₃	1	1	yes	characteristic
458	C₄²	D₄×D₄₃	1	1	yes	characteristic
459	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
460	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
461	C₂³	—	86	2	no	—
462	C₂³	C₂×#10621900	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	86	2	no	—
472	Q₈	—	86	2	no	—
473	D₄	—	86	2	no	—
474	D₄	—	86	2	no	—
475	D₄	—	344	1	no	—
476	D₄	—	172	2	no	—
477	D₄	—	172	2	no	—
478	D₄	—	172	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	1	no	—
489	C₂×C₄	—	86	2	no	—
490	C₂×C₄	—	172	2	no	—
491	C₂×C₄	—	172	2	no	—
492	C₂×C₄	#13063296	1	1	yes	characteristic
493	C₂×C₄	#13063296	1	1	yes	characteristic
494	C₂×C₄	#13063296	1	1	yes	characteristic
495	C₂×C₄	#13063296	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
497	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
498	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
499	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
500	C₂×C₄	#13063370	1	1	yes	characteristic
501	C₂×C₄	#13063371	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	86	2	no	—
505	C₈	—	86	2	no	—
506	C₈	—	86	2	no	—
507	C₈	—	172	1	no	—
508	C₈	—	172	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	172	2	no	—
512	C₂²	—	172	2	no	—
513	C₂²	—	172	2	no	—
514	C₂²	C₂×#13063296	1	1	yes	characteristic
515	C₂²	#14583444	1	1	yes	characteristic
516	C₂²	#14583502	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	2	no	—
522	C₄	—	8	1	no	—
523	C₄	—	172	2	no	—
524	C₄	#14583171	1	2	yes	complemented
525	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
526	C₄	#14583533	1	1	yes	characteristic
527	C₄	#14583546	1	1	yes	characteristic
528	C₄	#14583568	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	344	2	no	—
532	C₂	#19138179	1	1	yes	characteristic
533	C₂	C₂×#14583171	1	1	yes	characteristic
534	C₂	#19144328	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#462	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	C₂×#462	D₄₃
hypocenter	C₄₃	#25406
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#462

Complements

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

N	H ≅ G/N	type
2. C₂×#14583171	C₂	semidirect
5. #19135895	C₂	semidirect
6. #19135714	C₂	semidirect
7. #19135440	C₂	semidirect
8. #19135371	C₂	semidirect
9. #19135113	C₂	semidirect
10. C₄×#13063244	C₂	semidirect
11. C₂×C₄₃×#462	C₂	semidirect
85. #13063244	D₄	semidirect
256. C₄×C₄₃	#473	semidirect
265. C₂×#462	D₄₃	semidirect
315. C₄₃	#25406	semidirect
524. C₄	#14583171	semidirect

Maximal subgroups

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

subgroup	index
#19145052	2
C₂×#14583171	2
#19144067	2
#19143338	2
#19135895	2
#19135714	2
#19135440	2
#19135371	2
#19135113	2
C₄×#13063244	2
C₂×C₄₃×#462	2
#25406	43