Subgroups — #25960941

Order 11008.

2604 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149368	C₂	1	1	yes	maximal, characteristic
2	#19149306	C₂	1	2	yes	maximal, complemented
3	#19143508	C₂	1	2	yes	maximal, complemented
4	#19143507	C₂	1	4	yes	maximal, complemented
5	#19143505	C₂	1	1	yes	maximal, characteristic, complemented
6	#19143504	C₂	1	1	yes	maximal, characteristic, complemented
7	#19143500	C₂	1	4	yes	maximal, complemented
8	#19143499	C₂	1	1	yes	maximal, characteristic, complemented
9	#19143495	C₂	1	4	yes	maximal, complemented
10	C₂×#14583019	C₂	1	2	yes	maximal, complemented
11	#444×D₄₃	C₂	1	4	yes	maximal, complemented
12	#19143205	C₂	1	1	yes	maximal, characteristic, complemented
13	#19143141	C₂	1	2	yes	maximal, complemented
14	#19143022	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583735	C₂²	1	2	yes	—
17	#14583715	C₄	1	4	yes	complemented
18	#14583709	C₄	1	4	yes	complemented
19	#14583708	C₄	1	4	yes	complemented
20	#14583703	C₄	1	4	yes	complemented
21	#14583699	C₂²	1	1	yes	characteristic
22	#14583696	C₂²	1	4	yes	—
23	C₂×#13063345	C₂²	1	2	yes	—
24	#135×D₄₃	C₂²	1	4	yes	—
25	#14583666	C₂²	1	2	yes	complemented
26	#14583665	—	2	4	no	—
27	#14583665	C₂²	1	2	yes	—
28	#14583665	C₂²	1	2	yes	complemented
29	#14583664	—	2	4	no	—
30	#14583664	C₂²	1	8	yes	complemented
31	C₂×#13063333	C₂²	1	1	yes	characteristic
32	C₂×#13063331	—	2	4	no	—
33	C₂×#13063331	C₂²	1	1	yes	characteristic
34	C₂×#13063331	C₂²	1	2	yes	complemented
35	#131×D₄₃	—	2	4	no	—
36	#131×D₄₃	C₂²	1	8	yes	complemented
37	#14583367	C₂²	1	1	yes	characteristic
38	#14583022	C₂²	1	4	yes	complemented
39	#14583021	C₂²	1	4	yes	complemented
40	#14583020	C₂²	1	4	yes	complemented
41	#14583019	C₂²	1	4	yes	complemented
42	#14583019	C₂²	1	4	yes	complemented
43	#14583019	C₂²	1	4	yes	complemented
44	#14583019	C₂²	1	4	yes	complemented
45	#14583018	C₂²	1	8	yes	complemented
46	#14583017	C₂²	1	4	yes	complemented
47	#14583016	C₂²	1	4	yes	complemented
48	#14583015	C₂²	1	4	yes	complemented
49	#14583013	C₂²	1	8	yes	complemented
50	#14582948	C₂²	1	1	yes	characteristic, complemented
51	#14582946	C₂²	1	4	yes	complemented
52	C₂×#13063260	C₂²	1	2	yes	complemented
53	#108×D₄₃	C₂²	1	4	yes	complemented
54	#14582917	C₂²	1	2	yes	complemented
55	#14582914	C₂²	1	8	yes	complemented
56	C₂×#13063252	C₂²	1	2	yes	complemented
57	C₂×#13063251	C₂²	1	2	yes	complemented
58	#104×D₄₃	C₂²	1	8	yes	complemented
59	#14582856	C₂²	1	2	yes	complemented
60	#14582855	C₂²	1	1	yes	characteristic, complemented
61	#14582853	C₂²	1	2	yes	complemented
62	M₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
63	C₄×#10621872	C₂²	1	2	yes	complemented
64	C₂×#13063235	C₂²	1	1	yes	characteristic, complemented
65	#97×D₄₃	C₂²	1	2	yes	complemented
66	C₄₃×#575	C₂²	1	1	yes	characteristic
67	C₂×#131×C₄₃	C₂²	1	2	yes	complemented
68	C₄₃×#444	C₂²	1	4	yes	complemented
69	C₄₃×#443	C₂²	1	4	yes	complemented
70	C₄₃×#430	C₂²	1	1	yes	characteristic, complemented
71	C₄₃×#421	C₂²	1	2	yes	complemented
72	C₄₃×#405	C₂²	1	1	yes	characteristic, complemented
73	#13063373	C₂×C₄	1	4	yes	—
74	#13063372	—	2	2	no	—
75	#13063372	C₂×C₄	1	4	yes	—
76	#13063371	—	2	2	no	—
77	#13063371	C₂×C₄	1	4	yes	—
78	#13063370	—	2	4	no	—
79	#13063370	C₂×C₄	1	4	yes	—
80	C₂×#10621898	—	2	4	no	—
81	C₂×#10621898	C₂³	1	2	yes	—
82	C₂×#10621898	C₂³	1	1	yes	characteristic
83	#41×D₄₃	—	2	4	no	—
84	#41×D₄₃	C₂³	1	8	yes	—
85	#13063358	C₂×C₄	1	4	yes	complemented
86	#13063357	C₂×C₄	1	8	yes	complemented
87	#13063354	C₂×C₄	1	8	yes	complemented
88	#13063353	C₂×C₄	1	4	yes	complemented
89	#13063352	C₂×C₄	1	8	yes	complemented
90	#13063349	C₂×C₄	1	8	yes	complemented
91	#13063348	C₂×C₄	1	4	yes	complemented
92	#13063347	C₂³	1	4	yes	—
93	#13063346	C₂×C₄	1	8	yes	complemented
94	#13063345	C₂×C₄	1	4	yes	complemented
95	#13063345	C₂×C₄	1	4	yes	complemented
96	#13063345	C₂³	1	4	yes	—
97	#13063345	C₂³	1	4	yes	—
98	#13063344	C₂×C₄	1	4	yes	complemented
99	C₂×#10621885	C₂×C₄	1	2	yes	complemented
100	Q₁₆×D₄₃	C₂×C₄	1	4	yes	complemented
101	C₂×#10621883	C₂×C₄	1	2	yes	complemented
102	C₂×#10621884	C₂×C₄	1	2	yes	complemented
103	SD₁₆×D₄₃	C₂×C₄	1	8	yes	complemented
104	C₂×#10621882	C₂×C₄	1	2	yes	complemented
105	D₈×D₄₃	C₂×C₄	1	4	yes	complemented
106	#13063333	—	2	4	no	—
107	#13063333	—	2	8	no	—
108	#13063333	—	2	8	no	—
109	#13063333	C₂×C₄	1	4	yes	—
110	#13063333	C₂×C₄	1	4	yes	—
111	#13063333	C₂³	1	8	yes	—
112	#13063332	—	2	4	no	—
113	#13063332	C₂³	1	8	yes	—
114	#13063331	—	2	4	no	—
115	#13063331	—	2	2	no	—
116	#13063331	—	2	2	no	—
117	#13063331	—	2	4	no	—
118	#13063331	—	2	8	no	—
119	#13063331	—	2	8	no	—
120	#13063331	D₄	1	4	yes	—
121	#13063331	D₄	1	4	yes	—
122	#13063331	C₂³	1	4	yes	—
123	#13063331	C₂³	1	4	yes	—
124	C₂×#10621877	—	2	4	no	—
125	C₂×#10621877	C₂³	1	2	yes	—
126	C₂×#10621877	C₂³	1	1	yes	characteristic
127	C₂×#10621872	—	2	2	no	—
128	C₂×#10621872	—	2	8	no	—
129	C₂×#10621872	C₂³	1	2	yes	—
130	C₂×#10621872	C₂³	1	2	yes	—
131	M₁₆×D₄₃	—	2	4	no	—
132	M₁₆×D₄₃	—	2	8	no	—
133	M₁₆×D₄₃	—	2	8	no	—
134	M₁₆×D₄₃	C₂³	1	8	yes	—
135	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
136	C₂×C₈×D₄₃	—	2	2	no	—
137	C₂×C₈×D₄₃	—	2	8	no	—
138	C₂×C₈×D₄₃	C₂³	1	2	yes	—
139	C₂×C₈×D₄₃	C₂³	1	2	yes	—
140	#13063290	—	2	1	no	—
141	#13063287	—	2	1	no	—
142	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
143	#13063282	C₂³	1	2	yes	—
144	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
145	C₄²×D₄₃	C₂³	1	2	yes	—
146	#13063261	C₂³	1	4	yes	—
147	#13063260	C₂³	1	4	yes	—
148	#13063260	C₂³	1	4	yes	—
149	#13063253	C₂³	1	8	yes	—
150	#13063252	C₂³	1	4	yes	—
151	#13063252	C₂³	1	4	yes	—
152	#13063251	C₂³	1	4	yes	—
153	#13063251	C₂³	1	4	yes	—
154	#13063236	C₂³	1	2	yes	—
155	#13063235	C₂³	1	1	yes	characteristic
156	#13063235	C₂³	1	2	yes	—
157	#13063235	C₂³	1	1	yes	characteristic
158	#13063235	C₂³	1	1	yes	characteristic
159	#13063235	C₂³	1	1	yes	characteristic
160	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
161	C₈×Dic₄₃	C₂³	1	2	yes	—
162	C₂×#41×C₄₃	C₂³	1	2	yes	—
163	#137×C₄₃	C₂×C₄	1	4	yes	complemented
164	AGL(1,ℤ/8)×C₄₃	C₂×C₄	1	4	yes	complemented
165	#135×C₄₃	C₂³	1	4	yes	—
166	#131×C₄₃	—	2	2	no	—
167	#131×C₄₃	—	2	2	no	—
168	#131×C₄₃	C₂³	1	4	yes	—
169	#131×C₄₃	C₂³	1	4	yes	—
170	C₂×M₁₆×C₄₃	—	2	2	no	—
171	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₄₃	—	2	2	no	—
174	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
175	#117×C₄₃	C₂³	1	1	yes	characteristic
176	#108×C₄₃	C₂³	1	4	yes	—
177	#104×C₄₃	C₂³	1	8	yes	—
178	#97×C₄₃	C₂³	1	2	yes	—
179	C₄×C₈×C₄₃	C₂³	1	2	yes	—
180	#41×C₄₃	—	2	2	no	—
181	#41×C₄₃	—	2	2	no	—
182	#41×C₄₃	C₂²×C₄	1	4	yes	—
183	#41×C₄₃	C₂⁴	1	4	yes	—
184	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
185	C₂×D₄×C₄₃	—	2	2	no	—
186	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₄₃	—	2	2	no	—
188	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₂²⋊D₄₃	—	2	8	no	—
190	C₂×C₂²⋊D₄₃	—	2	2	no	—
191	C₂×C₂²⋊D₄₃	#41	1	2	yes	—
192	C₂²×Dic₄₃	—	2	1	no	—
193	#10621902	—	2	4	no	—
194	#10621902	C₂²×C₄	1	8	yes	—
195	Q₈×D₄₃	—	2	4	no	—
196	Q₈×D₄₃	C₂²×C₄	1	8	yes	—
197	#10621900	—	2	8	no	—
198	#10621900	—	2	8	no	—
199	#10621900	—	2	4	no	—
200	#10621900	C₂²×C₄	1	8	yes	—
201	D₄×D₄₃	—	2	8	no	—
202	D₄×D₄₃	—	2	4	no	—
203	D₄×D₄₃	—	2	8	no	—
204	D₄×D₄₃	C₂²×C₄	1	8	yes	—
205	#10621898	—	2	2	no	—
206	#10621898	—	2	2	no	—
207	#10621898	—	2	8	no	—
208	#10621898	—	2	4	no	—
209	#10621898	—	2	8	no	—
210	#10621898	—	2	4	no	—
211	#10621898	C₂²×C₄	1	4	yes	—
212	#10621898	C₂²×C₄	1	4	yes	—
213	#10621898	C₂×D₄	1	4	yes	—
214	#10621898	C₂⁴	1	4	yes	—
215	C₂×D₁₇₂	—	2	4	no	—
216	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
217	C₂×D₁₇₂	#41	1	1	yes	characteristic
218	C₂×C₄×D₄₃	—	2	2	no	—
219	C₂×C₄×D₄₃	—	2	8	no	—
220	C₂×C₄×D₄₃	—	2	2	no	—
221	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
222	C₂×Dic₈₆	—	2	4	no	—
223	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
224	C₂×Dic₈₆	#41	1	1	yes	characteristic
225	Q₁₆×C₄₃	C₂²×C₄	1	4	yes	—
226	SD₁₆×C₄₃	C₂²×C₄	1	8	yes	—
227	D₈×C₄₃	C₂²×C₄	1	4	yes	—
228	M₁₆×C₄₃	—	2	2	no	—
229	M₁₆×C₄₃	—	2	4	no	—
230	M₁₆×C₄₃	—	2	4	no	—
231	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
232	M₁₆×C₄₃	C₂⁴	1	4	yes	—
233	C₂×C₈×C₄₃	—	2	2	no	—
234	C₂×C₈×C₄₃	—	2	4	no	—
235	C₂×C₈×C₄₃	—	2	4	no	—
236	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
237	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
238	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₄⋊C₄×C₄₃	—	2	1	no	—
242	C₂²⋊C₄×C₄₃	—	2	1	no	—
243	C₄²×C₄₃	C₂⁴	1	2	yes	—
244	#10621885	C₂²×C₄	1	4	yes	—
245	#10621885	C₂²×C₄	1	4	yes	—
246	#10621884	C₂²×C₄	1	4	yes	—
247	#10621884	C₂²×C₄	1	4	yes	—
248	#10621883	C₂²×C₄	1	4	yes	—
249	#10621883	C₂²×C₄	1	4	yes	—
250	#10621882	C₂²×C₄	1	4	yes	—
251	#10621882	C₂²×C₄	1	4	yes	—
252	(C₂×D₄₃)⋊C₄	—	2	2	no	—
253	Dic₄₃⋊C₄	—	2	2	no	—
254	C₄×Dic₄₃	—	2	1	no	—
255	C₄×Dic₄₃	—	2	2	no	—
256	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
257	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
258	#10621877	—	2	2	no	—
259	#10621877	—	2	8	no	—
260	#10621877	C₂×D₄	1	4	yes	—
261	#10621877	C₂⁴	1	4	yes	—
262	C₂×C₄₃⋊C₈	—	2	2	no	—
263	C₂×C₄₃⋊C₈	—	2	8	no	—
264	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
265	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
266	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
268	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
269	Dic₁₇₂	C₂²×C₄	1	4	yes	—
270	D₃₄₄	C₂²×C₄	1	4	yes	—
271	#10621873	C₂²×C₄	1	8	yes	—
272	#10621872	—	2	8	no	—
273	#10621872	—	2	4	no	—
274	#10621872	—	2	4	no	—
275	#10621872	—	2	8	no	—
276	#10621872	C₂²×C₄	1	8	yes	—
277	#10621872	C₂×D₄	1	4	yes	—
278	#10621872	C₂×D₄	1	4	yes	—
279	C₈×D₄₃	—	2	8	no	—
280	C₈×D₄₃	—	2	4	no	—
281	C₈×D₄₃	—	2	4	no	—
282	C₈×D₄₃	—	2	8	no	—
283	C₈×D₄₃	C₂²×C₄	1	4	yes	—
284	C₈×D₄₃	C₂²×C₄	1	4	yes	—
285	C₈×D₄₃	C₂×D₄	1	8	yes	—
286	C₂³×C₄₃	—	2	2	no	—
287	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
288	C₂²×D₄₃	—	2	2	no	—
289	C₂²×D₄₃	—	2	8	no	—
290	C₂²×D₄₃	C₂×#41	1	2	yes	—
291	Q₈×C₄₃	—	2	2	no	—
292	Q₈×C₄₃	C₂³×C₄	1	4	yes	—
293	D₄×C₄₃	—	2	4	no	—
294	D₄×C₄₃	—	2	4	no	—
295	D₄×C₄₃	—	2	2	no	—
296	D₄×C₄₃	C₂³×C₄	1	4	yes	—
297	C₂×C₄×C₄₃	—	2	2	no	—
298	C₂×C₄×C₄₃	—	2	4	no	—
299	C₂×C₄×C₄₃	—	2	4	no	—
300	C₂×C₄×C₄₃	—	2	2	no	—
301	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
302	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
305	C₂²⋊D₄₃	—	2	4	no	—
306	C₂²⋊D₄₃	—	2	4	no	—
307	C₂²⋊D₄₃	—	2	8	no	—
308	C₂²⋊D₄₃	—	2	8	no	—
309	C₂²⋊D₄₃	C₄×D₄	1	8	yes	—
310	C₂×Dic₄₃	—	2	2	no	—
311	C₂×Dic₄₃	—	2	8	no	—
312	C₂×Dic₄₃	—	2	1	no	—
313	C₂×Dic₄₃	—	2	1	no	—
314	C₂×Dic₄₃	—	8	1	no	—
315	C₂×Dic₄₃	C₂×#41	1	2	yes	—
316	D₁₇₂	—	2	8	no	—
317	D₁₇₂	—	2	2	no	—
318	D₁₇₂	C₄×D₄	1	4	yes	—
319	D₁₇₂	C₂³×C₄	1	4	yes	—
320	C₄×D₄₃	—	2	8	no	—
321	C₄×D₄₃	—	2	4	no	—
322	C₄×D₄₃	—	2	4	no	—
323	C₄×D₄₃	—	2	8	no	—
324	C₄×D₄₃	—	8	2	no	—
325	C₄×D₄₃	C₂³×C₄	1	4	yes	—
326	C₄×D₄₃	C₂²×D₄	1	4	yes	—
327	Dic₈₆	—	2	2	no	—
328	Dic₈₆	—	2	8	no	—
329	Dic₈₆	C₄×D₄	1	4	yes	—
330	Dic₈₆	C₂³×C₄	1	4	yes	—
331	C₈×C₄₃	—	2	4	no	—
332	C₈×C₄₃	C₂³×C₄	1	4	yes	—
333	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
334	C₈×C₄₃	C₂²×D₄	1	2	yes	—
335	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
336	C₄₃⋊C₈	—	2	4	no	—
337	C₄₃⋊C₈	C₂³×C₄	1	1	yes	characteristic
338	C₄₃⋊C₈	C₂³×C₄	1	1	yes	characteristic
339	C₄₃⋊C₈	C₂³×C₄	1	2	yes	—
340	C₄₃⋊C₈	C₂²×D₄	1	4	yes	—
341	#60184	—	43	1	no	maximal, Sylow
342	C₂²×C₄₃	—	2	4	no	—
343	C₂²×C₄₃	—	4	1	no	—
344	C₂²×C₄₃	—	8	2	no	—
345	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
346	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
347	C₂×D₄₃	—	2	4	no	—
348	C₂×D₄₃	—	4	2	no	—
349	C₂×D₄₃	—	8	8	no	—
350	C₂×D₄₃	—	8	2	no	—
351	C₂×D₄₃	C₂×C₄×D₄	1	4	yes	—
352	C₄×C₄₃	—	2	4	no	—
353	C₄×C₄₃	—	4	2	no	—
354	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
355	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
356	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
357	Dic₄₃	—	2	4	no	—
358	Dic₄₃	—	4	1	no	—
359	Dic₄₃	—	4	1	no	—
360	Dic₄₃	C₂×C₄×D₄	1	4	yes	—
361	#3584	—	43	1	no	—
362	#3573	—	43	2	no	—
363	#2957	—	43	4	no	—
364	#2957	—	43	2	no	—
365	#2956	—	43	4	no	—
366	#2956	—	43	1	no	—
367	#2956	—	43	1	no	—
368	#2955	—	43	4	no	—
369	#2955	—	43	1	no	—
370	#2955	D₄₃	1	1	yes	characteristic, complemented
371	C₂×#444	—	43	4	no	—
372	C₂×#444	—	43	2	no	—
373	#2916	—	43	1	no	—
374	#2901	—	43	2	no	—
375	#2875	—	43	1	no	—
376	C₂×C₄₃	—	2	1	no	—
377	C₂×C₄₃	—	2	2	no	—
378	C₂×C₄₃	—	4	4	no	—
379	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
380	D₄₃	—	2	4	no	—
381	D₄₃	—	4	4	no	—
382	#585	—	43	2	no	—
383	#578	—	43	4	no	—
384	#577	—	43	4	no	—
385	#577	—	43	4	no	—
386	#576	—	43	4	no	—
387	#575	—	43	4	no	—
388	#575	—	43	1	no	—
389	#575	C₂×D₄₃	1	1	yes	characteristic
390	C₂×#135	—	43	2	no	—
391	C₂×#135	—	43	4	no	—
392	#568	—	43	2	no	—
393	#568	—	43	2	no	—
394	#568	—	43	8	no	—
395	#568	—	43	2	no	—
396	#568	—	86	4	no	—
397	#568	—	86	4	no	—
398	C₂×#131	—	43	1	no	—
399	C₂×#131	—	43	1	no	—
400	C₂×#131	—	43	8	no	—
401	C₂×#131	—	43	2	no	—
402	C₂×#131	—	86	4	no	—
403	C₂×#131	—	86	4	no	—
404	C₂×#131	C₂×D₄₃	1	2	yes	complemented
405	C₄×#41	—	43	1	no	—
406	#444	—	43	4	no	—
407	#444	—	43	4	no	—
408	#444	—	43	4	no	—
409	#444	—	43	4	no	—
410	#444	—	43	4	no	—
411	#444	—	43	4	no	—
412	#444	—	43	8	no	—
413	#444	—	43	4	no	—
414	#444	C₂×D₄₃	1	4	yes	complemented
415	#443	—	43	4	no	—
416	#443	—	43	4	no	—
417	#443	—	43	8	no	—
418	#443	—	43	4	no	—
419	#443	C₂×D₄₃	1	4	yes	complemented
420	#430	—	43	1	no	—
421	#430	—	43	4	no	—
422	#430	C₂×D₄₃	1	1	yes	characteristic, complemented
423	C₂×#108	—	43	2	no	—
424	C₂×#108	—	43	4	no	—
425	#421	—	43	2	no	—
426	#421	—	43	8	no	—
427	#421	C₂×D₄₃	1	2	yes	complemented
428	C₂×#104	—	43	2	no	—
429	C₂×#104	—	43	2	no	—
430	C₂×#104	—	43	8	no	—
431	#405	—	43	1	no	—
432	#405	—	43	2	no	—
433	#405	—	43	2	no	—
434	#405	C₂×D₄₃	1	1	yes	characteristic, complemented
435	C₄×M₁₆	—	43	1	no	—
436	C₄×M₁₆	—	43	2	no	—
437	C₂×#97	—	43	1	no	—
438	C₂×#97	—	43	2	no	—
439	C₄₃	#60184	1	1	yes	characteristic, complemented, Sylow
440	2₋¹⁺⁴	—	43	4	no	—
441	2₋¹⁺⁴	—	43	4	no	—
442	2₋¹⁺⁴	—	86	2	no	—
443	H(5,𝔽₂)	—	43	4	no	—
444	H(5,𝔽₂)	—	43	4	no	—
445	H(5,𝔽₂)	—	86	4	no	—
446	H(5,𝔽₂)	—	86	2	no	—
447	C₂×#41	—	43	1	no	—
448	C₂×#41	—	43	8	no	—
449	C₂×#41	—	43	2	no	—
450	C₂×#41	—	86	4	no	—
451	C₂×#41	—	86	4	no	—
452	C₂×#41	C₂²×D₄₃	1	2	yes	—
453	#137	—	43	8	no	—
454	#137	—	43	8	no	—
455	#137	—	43	4	no	—
456	#137	C₄×D₄₃	1	4	yes	complemented
457	AGL(1,ℤ/8)	—	43	8	no	—
458	AGL(1,ℤ/8)	—	43	8	no	—
459	AGL(1,ℤ/8)	—	43	4	no	—
460	AGL(1,ℤ/8)	C₄×D₄₃	1	4	yes	complemented
461	#135	—	43	4	no	—
462	#135	—	43	4	no	—
463	#135	—	43	4	no	—
464	#135	—	43	4	no	—
465	#135	—	43	4	no	—
466	#135	—	43	8	no	—
467	#135	—	43	4	no	—
468	#135	—	43	4	no	—
469	#135	C₂²×D₄₃	1	4	yes	—
470	C₂×Q₁₆	—	43	2	no	—
471	C₂×Q₁₆	—	43	4	no	—
472	C₂×SD₁₆	—	43	2	no	—
473	C₂×SD₁₆	—	43	2	no	—
474	C₂×SD₁₆	—	43	8	no	—
475	C₂×D₈	—	43	2	no	—
476	C₂×D₈	—	43	4	no	—
477	#131	—	2	2	no	—
478	#131	—	2	2	no	—
479	#131	—	43	4	no	—
480	#131	—	43	4	no	—
481	#131	—	43	4	no	—
482	#131	—	43	4	no	—
483	#131	—	43	8	no	—
484	#131	—	43	8	no	—
485	#131	—	43	4	no	—
486	#131	—	43	4	no	—
487	#131	—	86	8	no	—
488	#131	—	86	4	no	—
489	#131	—	86	8	no	—
490	#131	—	86	4	no	—
491	#131	—	86	8	no	—
492	#131	—	86	8	no	—
493	#131	—	86	4	no	—
494	#131	—	86	4	no	—
495	#131	—	86	2	no	—
496	#131	—	86	2	no	—
497	#131	C₂²×D₄₃	1	4	yes	—
498	#131	C₂²×D₄₃	1	4	yes	—
499	C₂×M₁₆	—	2	2	no	—
500	C₂×M₁₆	—	43	1	no	—
501	C₂×M₁₆	—	43	2	no	—
502	C₂×M₁₆	—	43	2	no	—
503	C₂×M₁₆	—	43	2	no	—
504	C₂×M₁₆	—	43	8	no	—
505	C₂×M₁₆	—	86	8	no	—
506	C₂×M₁₆	—	86	8	no	—
507	C₂×M₁₆	—	86	4	no	—
508	C₂×M₁₆	—	86	8	no	—
509	C₂×M₁₆	—	86	4	no	—
510	C₂×M₁₆	—	86	2	no	—
511	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
512	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
513	C₂²×C₈	—	2	2	no	—
514	C₂²×C₈	—	43	1	no	—
515	C₂²×C₈	—	43	2	no	—
516	C₂²×C₈	—	43	2	no	—
517	C₂²×C₈	—	86	8	no	—
518	C₂²×C₈	—	86	2	no	—
519	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
520	C₄×Q₈	—	86	1	no	—
521	C₄×D₄	—	86	2	no	—
522	C₄×D₄	—	86	1	no	—
523	#117	—	43	2	no	—
524	#117	C₂²×D₄₃	1	1	yes	characteristic
525	C₂×C₄²	—	43	1	no	—
526	C₂×C₄²	—	43	2	no	—
527	#108	—	43	4	no	—
528	#108	—	43	4	no	—
529	#108	—	43	4	no	—
530	#108	C₂²×D₄₃	1	4	yes	—
531	#104	—	43	4	no	—
532	#104	—	43	4	no	—
533	#104	—	43	4	no	—
534	#104	—	43	4	no	—
535	#104	—	43	8	no	—
536	#104	C₂²×D₄₃	1	8	yes	—
537	#97	—	43	1	no	—
538	#97	—	43	1	no	—
539	#97	—	43	2	no	—
540	#97	—	43	1	no	—
541	#97	—	43	1	no	—
542	#97	—	43	2	no	—
543	#97	C₂²×D₄₃	1	2	yes	—
544	C₄×C₈	—	43	2	no	—
545	C₄×C₈	—	43	2	no	—
546	C₄×C₈	C₂²×D₄₃	1	2	yes	—
547	#41	—	2	2	no	—
548	#41	—	2	2	no	—
549	#41	—	43	4	no	—
550	#41	—	43	4	no	—
551	#41	—	43	8	no	—
552	#41	—	43	8	no	—
553	#41	—	43	4	no	—
554	#41	—	43	4	no	—
555	#41	—	86	8	no	—
556	#41	—	86	8	no	—
557	#41	—	86	4	no	—
558	#41	—	86	4	no	—
559	#41	—	86	8	no	—
560	#41	—	86	8	no	—
561	#41	—	86	4	no	—
562	#41	—	86	4	no	—
563	#41	—	86	2	no	—
564	#41	—	86	2	no	—
565	#41	C₂×C₄×D₄₃	1	4	yes	—
566	#41	C₂³×D₄₃	1	4	yes	—
567	C₂×Q₈	—	43	1	no	—
568	C₂×Q₈	—	43	8	no	—
569	C₂×Q₈	—	43	2	no	—
570	C₂×Q₈	—	86	4	no	—
571	C₂×Q₈	—	86	4	no	—
572	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	43	2	no	—
575	C₂×D₄	—	43	8	no	—
576	C₂×D₄	—	43	2	no	—
577	C₂×D₄	—	43	1	no	—
578	C₂×D₄	—	86	4	no	—
579	C₂×D₄	—	86	8	no	—
580	C₂×D₄	—	86	4	no	—
581	C₂×D₄	—	86	8	no	—
582	C₂×D₄	—	86	8	no	—
583	C₂×D₄	—	86	2	no	—
584	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	43	2	no	—
587	C₂²×C₄	—	86	8	no	—
588	C₂²×C₄	—	86	2	no	—
589	C₂²×C₄	—	86	2	no	—
590	C₂²×C₄	—	86	1	no	—
591	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
592	Q₁₆	—	43	4	no	—
593	Q₁₆	—	43	4	no	—
594	Q₁₆	—	43	4	no	—
595	Q₁₆	C₂×C₄×D₄₃	1	4	yes	—
596	SD₁₆	—	43	4	no	—
597	SD₁₆	—	43	4	no	—
598	SD₁₆	—	43	4	no	—
599	SD₁₆	—	43	4	no	—
600	SD₁₆	—	43	8	no	—
601	SD₁₆	C₂×C₄×D₄₃	1	8	yes	—
602	D₈	—	43	4	no	—
603	D₈	—	43	4	no	—
604	D₈	—	43	4	no	—
605	D₈	C₂×C₄×D₄₃	1	4	yes	—
606	M₁₆	—	2	2	no	—
607	M₁₆	—	2	4	no	—
608	M₁₆	—	2	4	no	—
609	M₁₆	—	43	4	no	—
610	M₁₆	—	43	8	no	—
611	M₁₆	—	43	4	no	—
612	M₁₆	—	43	4	no	—
613	M₁₆	—	43	4	no	—
614	M₁₆	—	86	8	no	—
615	M₁₆	—	86	8	no	—
616	M₁₆	—	86	8	no	—
617	M₁₆	—	86	2	no	—
618	M₁₆	—	86	4	no	—
619	M₁₆	—	86	4	no	—
620	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
621	M₁₆	C₂³×D₄₃	1	4	yes	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	4	no	—
624	C₂×C₈	—	2	4	no	—
625	C₂×C₈	—	43	2	no	—
626	C₂×C₈	—	43	2	no	—
627	C₂×C₈	—	43	1	no	—
628	C₂×C₈	—	43	2	no	—
629	C₂×C₈	—	43	1	no	—
630	C₂×C₈	—	43	4	no	—
631	C₂×C₈	—	43	4	no	—
632	C₂×C₈	—	43	8	no	—
633	C₂×C₈	—	86	8	no	—
634	C₂×C₈	—	86	8	no	—
635	C₂×C₈	—	86	8	no	—
636	C₂×C₈	—	86	2	no	—
637	C₂×C₈	—	86	4	no	—
638	C₂×C₈	—	86	4	no	—
639	C₂×C₈	D₄×D₄₃	1	2	yes	—
640	C₂×C₈	D₄×D₄₃	1	2	yes	—
641	C₂×C₈	C₂³×D₄₃	1	2	yes	—
642	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
643	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	86	2	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	86	2	no	—
648	C₄²	—	43	1	no	—
649	C₄²	—	43	1	no	—
650	C₄²	—	86	2	no	—
651	C₄²	—	86	1	no	—
652	C₄²	C₂³×D₄₃	1	2	yes	—
653	C₂³	—	2	2	no	—
654	C₂³	—	43	2	no	—
655	C₂³	—	86	8	no	—
656	C₂³	—	86	2	no	—
657	C₂³	#41×D₄₃	1	1	yes	characteristic
658	Q₈	—	2	2	no	—
659	Q₈	—	43	4	no	—
660	Q₈	—	43	4	no	—
661	Q₈	—	86	8	no	—
662	Q₈	—	86	2	no	—
663	Q₈	C₂²×C₄×D₄₃	1	4	yes	—
664	D₄	—	2	4	no	—
665	D₄	—	2	4	no	—
666	D₄	—	2	2	no	—
667	D₄	—	43	8	no	—
668	D₄	—	43	4	no	—
669	D₄	—	43	4	no	—
670	D₄	—	86	8	no	—
671	D₄	—	86	8	no	—
672	D₄	—	86	8	no	—
673	D₄	—	86	4	no	—
674	D₄	—	86	4	no	—
675	D₄	—	86	2	no	—
676	D₄	C₂²×C₄×D₄₃	1	4	yes	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	43	2	no	—
682	C₂×C₄	—	43	4	no	—
683	C₂×C₄	—	43	4	no	—
684	C₂×C₄	—	86	8	no	—
685	C₂×C₄	—	86	8	no	—
686	C₂×C₄	—	86	8	no	—
687	C₂×C₄	—	86	2	no	—
688	C₂×C₄	—	86	4	no	—
689	C₂×C₄	—	86	4	no	—
690	C₂×C₄	—	86	1	no	—
691	C₂×C₄	—	86	1	no	—
692	C₂×C₄	—	344	2	no	—
693	C₂×C₄	—	344	1	no	—
694	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
695	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
696	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
697	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
698	C₈	—	2	4	no	—
699	C₈	—	43	1	no	—
700	C₈	—	43	1	no	—
701	C₈	—	43	2	no	—
702	C₈	—	43	4	no	—
703	C₈	—	86	4	no	—
704	C₈	C₂²×C₄×D₄₃	1	4	yes	—
705	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
706	C₈	C₂×D₄×D₄₃	1	2	yes	—
707	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
708	C₂²	—	2	4	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	8	2	no	—
711	C₂²	—	43	4	no	—
712	C₂²	—	86	4	no	—
713	C₂²	—	344	2	no	—
714	C₂²	—	344	8	no	—
715	C₂²	—	172	2	no	—
716	C₂²	C₄×D₄×D₄₃	1	2	yes	—
717	C₂²	C₂×#41×D₄₃	1	1	yes	characteristic
718	C₄	—	2	4	no	—
719	C₄	—	4	2	no	—
720	C₄	—	43	4	no	—
721	C₄	—	86	4	no	—
722	C₄	—	172	1	no	—
723	C₄	—	172	1	no	—
724	C₄	C₄×D₄×D₄₃	1	2	yes	—
725	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
726	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
727	C₂	—	2	1	no	—
728	C₂	—	2	2	no	—
729	C₂	—	4	4	no	—
730	C₂	—	86	4	no	—
731	C₂	—	172	4	no	—
732	C₂	C₂×C₄×D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#2955	C₂
socle	C₂×C₄₃	C₂²×C₄×D₄
prime radical	#19149368	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2955	D₄₃
hypocenter	C₄₃	#60184
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₈ ◁ #2955

Complements

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

N	H ≅ G/N	type
2. #19149306	C₂	semidirect
3. #19143508	C₂	semidirect
4. #19143507	C₂	semidirect
5. #19143505	C₂	semidirect
6. #19143504	C₂	semidirect
7. #19143500	C₂	semidirect
8. #19143499	C₂	semidirect
9. #19143495	C₂	semidirect
10. C₂×#14583019	C₂	semidirect
11. #444×D₄₃	C₂	semidirect
12. #19143205	C₂	semidirect
13. #19143141	C₂	semidirect
14. #19143022	C₂	semidirect
15. C₄₃×#2955	C₂	semidirect
17. #14583715	C₄	semidirect
18. #14583709	C₄	semidirect
19. #14583708	C₄	semidirect
20. #14583703	C₄	semidirect
25. #14583666	C₂²	semidirect
28. #14583665	C₂²	semidirect
30. #14583664	C₂²	semidirect
34. C₂×#13063331	C₂²	semidirect
36. #131×D₄₃	C₂²	semidirect
38. #14583022	C₂²	semidirect
39. #14583021	C₂²	semidirect
40. #14583020	C₂²	semidirect
41. #14583019	C₂²	semidirect
42. #14583019	C₂²	semidirect
43. #14583019	C₂²	semidirect
44. #14583019	C₂²	semidirect
45. #14583018	C₂²	semidirect
46. #14583017	C₂²	semidirect
47. #14583016	C₂²	semidirect
48. #14583015	C₂²	semidirect
49. #14583013	C₂²	semidirect
50. #14582948	C₂²	semidirect
51. #14582946	C₂²	semidirect
52. C₂×#13063260	C₂²	semidirect
53. #108×D₄₃	C₂²	semidirect
54. #14582917	C₂²	semidirect
55. #14582914	C₂²	semidirect
56. C₂×#13063252	C₂²	semidirect
57. C₂×#13063251	C₂²	semidirect
58. #104×D₄₃	C₂²	semidirect
59. #14582856	C₂²	semidirect
60. #14582855	C₂²	semidirect
61. #14582853	C₂²	semidirect
62. M₁₆×Dic₄₃	C₂²	semidirect
63. C₄×#10621872	C₂²	semidirect
64. C₂×#13063235	C₂²	semidirect
65. #97×D₄₃	C₂²	semidirect
67. C₂×#131×C₄₃	C₂²	semidirect
68. C₄₃×#444	C₂²	semidirect
69. C₄₃×#443	C₂²	semidirect
70. C₄₃×#430	C₂²	semidirect
71. C₄₃×#421	C₂²	semidirect
72. C₄₃×#405	C₂²	semidirect
85. #13063358	C₂×C₄	semidirect
86. #13063357	C₂×C₄	semidirect
87. #13063354	C₂×C₄	semidirect
88. #13063353	C₂×C₄	semidirect
89. #13063352	C₂×C₄	semidirect
90. #13063349	C₂×C₄	semidirect
91. #13063348	C₂×C₄	semidirect
93. #13063346	C₂×C₄	semidirect
94. #13063345	C₂×C₄	semidirect
95. #13063345	C₂×C₄	semidirect
98. #13063344	C₂×C₄	semidirect
99. C₂×#10621885	C₂×C₄	semidirect
100. Q₁₆×D₄₃	C₂×C₄	semidirect
101. C₂×#10621883	C₂×C₄	semidirect
102. C₂×#10621884	C₂×C₄	semidirect
103. SD₁₆×D₄₃	C₂×C₄	semidirect
104. C₂×#10621882	C₂×C₄	semidirect
105. D₈×D₄₃	C₂×C₄	semidirect
163. #137×C₄₃	C₂×C₄	semidirect
164. AGL(1,ℤ/8)×C₄₃	C₂×C₄	semidirect
370. #2955	D₄₃	semidirect
404. C₂×#131	C₂×D₄₃	semidirect
414. #444	C₂×D₄₃	semidirect
419. #443	C₂×D₄₃	semidirect
422. #430	C₂×D₄₃	semidirect
427. #421	C₂×D₄₃	semidirect
434. #405	C₂×D₄₃	semidirect
439. C₄₃	#60184	semidirect
456. #137	C₄×D₄₃	semidirect
460. AGL(1,ℤ/8)	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19149368	2
#19149306	2
#19143508	2
#19143507	2
#19143505	2
#19143504	2
#19143500	2
#19143499	2
#19143495	2
C₂×#14583019	2
#444×D₄₃	2
#19143205	2
#19143141	2
#19143022	2
C₄₃×#2955	2
#60184	43