Subgroups — #25068343

Order 11008.

652 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143721	C₂	1	1	yes	maximal, characteristic, complemented
2	#19143720	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13063345	C₂	1	1	yes	maximal, characteristic
4	#19133501	C₂	1	2	yes	maximal, complemented
5	#19133434	C₂	1	2	yes	maximal, complemented
6	#19133428	C₂	1	2	yes	maximal, complemented
7	#19133416	C₂	1	2	yes	maximal, complemented
8	#19133350	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133035	C₂	1	1	yes	maximal, characteristic, complemented
10	#19132882	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063345	C₄	1	1	yes	characteristic
13	C₄×#10621898	C₂²	1	1	yes	characteristic
14	#14583030	C₂²	1	2	yes	—
15	#14583026	C₂²	1	2	yes	—
16	C₄×#10621885	C₄	1	1	yes	characteristic
17	C₄×#10621885	C₂²	1	1	yes	characteristic
18	C₄×#10621884	C₄	1	1	yes	characteristic
19	C₄×#10621884	C₂²	1	1	yes	characteristic
20	C₄×#10621883	C₄	1	1	yes	characteristic
21	C₄×#10621883	C₂²	1	1	yes	characteristic
22	C₄×#10621882	C₄	1	1	yes	characteristic
23	C₄×#10621882	C₂²	1	1	yes	characteristic
24	#14582971	—	2	2	no	—
25	#14582968	—	2	2	no	—
26	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
27	#14582964	C₂²	1	2	yes	—
28	#14582956	—	2	1	no	—
29	#14582955	—	2	1	no	—
30	#14582952	C₂²	1	1	yes	characteristic
31	#14582935	C₄	1	1	yes	characteristic
32	#14582923	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
34	C₄⋊C₈×D₄₃	—	2	1	no	—
35	#14582895	C₄	1	1	yes	characteristic
36	#14582893	C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	#14582649	C₂²	1	2	yes	—
39	#14582649	C₂²	1	2	yes	—
40	#14582631	C₂²	1	2	yes	—
41	#14582628	C₂²	1	2	yes	—
42	#14582621	C₂²	1	2	yes	—
43	#14582621	C₂²	1	2	yes	—
44	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
49	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
50	#13063345	—	2	4	no	—
51	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
52	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
53	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
54	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
55	C₂×#10621877	—	2	1	no	—
56	C₂²×C₄₃⋊C₈	—	2	2	no	—
57	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₄₃	—	2	2	no	—
60	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
62	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
63	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₄₃	—	2	1	no	—
65	C₄×C₂²⋊D₄₃	—	2	1	no	—
66	#13063284	C₂×C₄	1	1	yes	characteristic
67	#13063282	—	2	1	no	—
68	C₄²×D₄₃	—	2	1	no	—
69	#13063258	C₂×C₄	1	1	yes	characteristic
70	#13063258	C₂×C₄	1	1	yes	characteristic
71	#13063256	C₂×C₄	1	1	yes	characteristic
72	#13063256	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
74	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
75	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
76	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
77	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
78	Dic₄₃⋊C₈	—	2	2	no	—
79	#13063249	C₂×C₄	1	1	yes	characteristic
80	#13063249	C₂×C₄	1	1	yes	characteristic
81	#13063248	C₂×C₄	1	1	yes	characteristic
82	#13063248	C₂×C₄	1	1	yes	characteristic
83	#13063246	C₂×C₄	1	1	yes	characteristic
84	#13063246	C₂×C₄	1	1	yes	characteristic
85	#13063245	C₂×C₄	1	1	yes	characteristic
86	#13063245	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
88	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
89	(C₂×D₄₃)⋊C₈	—	2	2	no	—
90	#13063236	—	2	2	no	—
91	#13063235	—	2	2	no	—
92	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
97	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₂×M₁₆×C₄₃	—	2	1	no	—
99	C₂×M₁₆×C₄₃	—	2	1	no	—
100	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₄₃	—	2	1	no	—
103	C₄×D₄×C₄₃	—	2	1	no	—
104	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
106	#117×C₄₃	—	2	1	no	—
107	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₄₃	—	2	1	no	—
109	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₄₃	—	2	1	no	—
111	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
112	#97×C₄₃	—	2	1	no	—
113	C₄×C₈×C₄₃	C₂³	1	2	yes	—
114	#41×C₄₃	—	2	2	no	—
115	#41×C₄₃	—	4	1	no	—
116	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₄₃	—	2	1	no	—
118	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	1	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₃	—	2	1	no	—
126	#10621898	—	2	2	no	—
127	#10621898	—	4	1	no	—
128	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₄₃	—	2	1	no	—
130	C₂×C₄×D₄₃	—	2	1	no	—
131	C₂×C₄×D₄₃	—	2	1	no	—
132	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
133	M₁₆×C₄₃	—	4	2	no	—
134	M₁₆×C₄₃	—	8	1	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₄₃	—	2	1	no	—
142	C₂²⋊C₄×C₄₃	—	2	1	no	—
143	C₂²⋊C₄×C₄₃	—	2	1	no	—
144	C₄²×C₄₃	—	2	1	no	—
145	C₄²×C₄₃	—	2	1	no	—
146	C₄²×C₄₃	—	2	1	no	—
147	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₃	#41	1	1	yes	characteristic
150	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂²⋊Dic₄₃	—	2	1	no	—
152	#10621885	—	2	2	no	—
153	#10621884	—	2	2	no	—
154	#10621883	—	2	2	no	—
155	#10621882	M₁₆	1	4	yes	complemented
156	(C₂×D₄₃)⋊C₄	—	2	1	no	—
157	(C₂×D₄₃)⋊C₄	—	2	1	no	—
158	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
160	Dic₄₃⋊C₄	—	2	1	no	—
161	Dic₄₃⋊C₄	—	2	1	no	—
162	C₄×Dic₄₃	—	2	1	no	—
163	C₄×Dic₄₃	—	2	1	no	—
164	C₄×Dic₄₃	—	2	1	no	—
165	#10621877	—	8	1	no	—
166	C₂×C₄₃⋊C₈	—	2	2	no	—
167	C₂×C₄₃⋊C₈	—	2	2	no	—
168	C₂×C₄₃⋊C₈	—	4	1	no	—
169	C₂×C₄₃⋊C₈	—	8	2	no	—
170	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
175	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
176	C₈×D₄₃	—	8	2	no	—
177	C₂³×C₄₃	—	2	1	no	—
178	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
179	C₂²×D₄₃	—	2	1	no	—
180	Q₈×C₄₃	—	2	1	no	—
181	Q₈×C₄₃	—	2	1	no	—
182	D₄×C₄₃	—	2	1	no	—
183	D₄×C₄₃	—	4	2	no	—
184	D₄×C₄₃	C₂×M₁₆	1	2	yes	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	1	no	—
195	C₂×C₄×C₄₃	—	4	1	no	—
196	C₂×C₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
203	C₂²⋊D₄₃	—	4	2	no	—
204	C₂×Dic₄₃	—	2	1	no	—
205	C₂×Dic₄₃	—	2	1	no	—
206	C₂×Dic₄₃	—	2	1	no	—
207	D₁₇₂	—	2	1	no	—
208	D₁₇₂	C₂×M₁₆	1	2	yes	—
209	C₄×D₄₃	—	4	2	no	—
210	C₄×D₄₃	—	4	1	no	—
211	C₄×D₄₃	—	4	1	no	—
212	C₄×D₄₃	—	4	2	no	—
213	Dic₈₆	—	2	1	no	—
214	Dic₈₆	—	2	1	no	—
215	C₈×C₄₃	—	4	2	no	—
216	C₈×C₄₃	—	4	2	no	—
217	C₄₃⋊C₈	—	2	1	no	—
218	C₄₃⋊C₈	—	2	1	no	—
219	C₄₃⋊C₈	—	2	1	no	—
220	C₄₃⋊C₈	—	2	2	no	—
221	C₄₃⋊C₈	—	2	2	no	—
222	C₄₃⋊C₈	—	4	2	no	—
223	C₄₃⋊C₈	C₂×M₁₆	1	2	yes	—
224	#18065	—	43	1	no	maximal, Sylow
225	C₂²×C₄₃	—	2	2	no	—
226	C₂²×C₄₃	—	2	1	no	—
227	C₂²×C₄₃	—	2	1	no	—
228	C₂²×C₄₃	—	2	1	no	—
229	C₂²×C₄₃	—	4	1	no	—
230	C₂²×C₄₃	—	4	1	no	—
231	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂×D₄₃	—	2	2	no	—
233	C₂×D₄₃	—	4	1	no	—
234	C₂×D₄₃	—	4	1	no	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	2	1	no	—
237	C₄×C₄₃	—	2	1	no	—
238	C₄×C₄₃	—	4	1	no	—
239	C₄×C₄₃	—	4	1	no	—
240	C₄×C₄₃	—	4	1	no	—
241	C₄×C₄₃	#444	1	2	yes	—
242	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
243	C₄×C₄₃	#568	1	1	yes	characteristic
244	C₄×C₄₃	#577	1	1	yes	characteristic
245	C₄×C₄₃	#577	1	1	yes	characteristic
246	Dic₄₃	—	4	1	no	—
247	Dic₄₃	—	4	1	no	—
248	Dic₄₃	—	4	1	no	—
249	#2990	—	43	1	no	—
250	#2990	—	43	1	no	—
251	C₄×#135	—	43	1	no	—
252	#1593	—	43	2	no	—
253	#1582	—	43	2	no	—
254	#1582	—	43	2	no	—
255	#1580	—	43	2	no	—
256	#1566	—	43	1	no	—
257	#1489	—	43	1	no	—
258	#1489	D₄₃	1	1	yes	characteristic, complemented
259	#1451	—	43	1	no	—
260	C₂×C₄₃	—	4	1	no	—
261	C₂×C₄₃	—	4	2	no	—
262	C₂×C₄₃	D₄×M₁₆	1	1	yes	characteristic
263	C₂×C₄₃	#2952	1	1	yes	characteristic
264	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
265	D₄₃	—	4	2	no	—
266	C₂×#135	—	43	1	no	—
267	C₄×#41	—	43	1	no	—
268	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
269	#446	—	43	2	no	—
270	#446	—	43	2	no	—
271	C₄×Q₁₆	—	43	1	no	—
272	C₄×Q₁₆	—	43	1	no	—
273	C₄×SD₁₆	—	43	1	no	—
274	C₄×SD₁₆	—	43	1	no	—
275	C₄×SD₁₆	—	43	1	no	—
276	C₄×SD₁₆	—	43	1	no	—
277	C₄×D₈	—	43	1	no	—
278	C₄×D₈	—	43	1	no	—
279	#435	—	86	2	no	—
280	#435	—	86	2	no	—
281	C₈×D₄	—	43	2	no	—
282	C₈×D₄	—	43	2	no	—
283	#432	—	86	1	no	—
284	#432	—	86	1	no	—
285	#431	—	43	1	no	—
286	#427	—	43	1	no	—
287	#423	—	43	1	no	—
288	#423	C₂×D₄₃	1	1	yes	characteristic
289	C₂×C₄⋊C₈	—	86	1	no	—
290	C₂×C₄⋊C₈	—	86	1	no	—
291	#416	—	43	1	no	—
292	#416	—	43	1	no	—
293	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
294	C₂×C₄×C₈	—	43	1	no	—
295	#334	—	43	2	no	—
296	#334	—	43	2	no	—
297	Q₈⋊C₈	—	43	2	no	—
298	Q₈⋊C₈	C₂×D₄₃	1	2	yes	—
299	D₄⋊C₈	—	43	2	no	—
300	D₄⋊C₈	C₂×D₄₃	1	2	yes	—
301	#322	—	43	2	no	—
302	#322	—	43	2	no	—
303	C₄₃	#18065	1	1	yes	characteristic, complemented, Sylow
304	C₂×#41	—	43	1	no	—
305	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
306	#135	—	86	4	no	—
307	C₂×Q₁₆	—	43	1	no	—
308	C₂×SD₁₆	—	43	1	no	—
309	C₂×SD₁₆	—	43	1	no	—
310	C₂×D₈	—	43	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	86	1	no	—
314	C₂²×C₈	—	43	1	no	—
315	C₂²×C₈	—	43	1	no	—
316	C₂²×C₈	—	86	2	no	—
317	C₂²×C₈	—	86	2	no	—
318	C₄×Q₈	—	43	1	no	—
319	C₄×Q₈	—	43	1	no	—
320	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
321	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	43	1	no	—
325	C₄×D₄	—	43	1	no	—
326	C₄×D₄	—	86	1	no	—
327	C₄×D₄	—	86	1	no	—
328	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
329	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
330	#117	—	2	1	no	—
331	#117	—	43	1	no	—
332	#117	—	86	1	no	—
333	#117	C₄×D₄₃	1	1	yes	characteristic
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	86	1	no	—
336	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
337	#107	—	43	1	no	—
338	#107	—	43	1	no	—
339	#106	—	43	1	no	—
340	#106	—	43	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	43	1	no	—
343	C₄⋊C₈	—	43	1	no	—
344	C₄⋊C₈	—	43	2	no	—
345	C₄⋊C₈	—	86	2	no	—
346	C₄⋊C₈	—	86	2	no	—
347	C₄⋊C₈	—	86	1	no	—
348	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
349	#103	—	43	1	no	—
350	#103	—	43	1	no	—
351	#103	—	43	1	no	—
352	#103	—	43	1	no	—
353	#102	—	43	1	no	—
354	#102	—	43	1	no	—
355	#102	—	43	1	no	—
356	#102	—	43	1	no	—
357	C₂²⋊C₈	—	43	2	no	—
358	C₂²⋊C₈	—	86	2	no	—
359	C₂²⋊C₈	—	86	2	no	—
360	#97	—	2	1	no	—
361	#97	—	86	2	no	—
362	#97	—	86	2	no	—
363	C₄×C₈	—	43	1	no	—
364	C₄×C₈	—	43	1	no	—
365	C₄×C₈	—	43	1	no	—
366	C₄×C₈	—	43	1	no	—
367	C₄×C₈	—	43	2	no	—
368	C₄×C₈	C₂²×D₄₃	1	2	yes	—
369	#41	—	2	2	no	—
370	#41	—	4	1	no	—
371	#41	—	86	2	no	—
372	#41	—	172	1	no	—
373	C₂×Q₈	—	43	1	no	—
374	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	43	1	no	—
377	C₂×D₄	—	86	1	no	—
378	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	86	1	no	—
383	C₂²×C₄	—	86	1	no	—
384	C₂²×C₄	—	86	1	no	—
385	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
386	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
387	C₂²×C₄	#10621900	1	1	yes	characteristic
388	Q₁₆	—	86	2	no	—
389	SD₁₆	—	86	2	no	—
390	SD₁₆	—	86	2	no	—
391	D₈	—	43	4	no	—
392	M₁₆	—	4	2	no	—
393	M₁₆	—	8	1	no	—
394	M₁₆	—	344	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	43	1	no	—
398	C₂×C₈	—	43	1	no	—
399	C₂×C₈	—	43	1	no	—
400	C₂×C₈	—	43	1	no	—
401	C₂×C₈	—	43	2	no	—
402	C₂×C₈	—	43	2	no	—
403	C₂×C₈	—	86	2	no	—
404	C₂×C₈	—	86	2	no	—
405	C₂×C₈	—	344	2	no	—
406	C₂×C₈	—	344	2	no	—
407	C₂×C₈	—	172	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	43	1	no	—
411	C₄⋊C₄	—	43	1	no	—
412	C₄⋊C₄	—	86	1	no	—
413	C₄⋊C₄	—	86	1	no	—
414	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
415	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	86	1	no	—
420	C₂²⋊C₄	—	86	1	no	—
421	C₂²⋊C₄	—	86	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	86	1	no	—
426	C₄²	—	86	1	no	—
427	C₄²	—	86	1	no	—
428	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
429	C₄²	D₄×D₄₃	1	1	yes	characteristic
430	C₄²	#10621900	1	1	yes	characteristic
431	C₄²	C₂³×D₄₃	1	1	yes	characteristic
432	C₂³	—	2	1	no	—
433	C₂³	—	86	1	no	—
434	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	86	1	no	—
438	Q₈	—	86	1	no	—
439	D₄	—	2	1	no	—
440	D₄	—	4	2	no	—
441	D₄	—	43	2	no	—
442	D₄	—	86	1	no	—
443	D₄	—	172	2	no	—
444	D₄	M₁₆×D₄₃	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	86	1	no	—
458	C₂×C₄	—	86	1	no	—
459	C₂×C₄	—	86	1	no	—
460	C₂×C₄	—	172	2	no	—
461	C₂×C₄	—	172	1	no	—
462	C₂×C₄	—	172	1	no	—
463	C₂×C₄	—	172	2	no	—
464	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
465	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
466	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
468	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
469	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
470	C₈	—	4	2	no	—
471	C₈	—	4	2	no	—
472	C₈	—	43	2	no	—
473	C₈	—	86	1	no	—
474	C₈	—	86	1	no	—
475	C₈	—	86	1	no	—
476	C₈	—	86	2	no	—
477	C₈	—	86	2	no	—
478	C₈	—	172	2	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	86	2	no	—
486	C₂²	—	172	1	no	—
487	C₂²	—	172	1	no	—
488	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	172	1	no	—
496	C₄	—	172	1	no	—
497	C₄	—	172	1	no	—
498	C₄	#14583018	1	2	yes	—
499	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
500	C₄	#14583665	1	1	yes	characteristic
501	C₄	#14583708	1	1	yes	characteristic
502	C₄	#14583709	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	4	2	no	—
505	C₂	—	172	2	no	—
506	C₂	#19143327	1	1	yes	characteristic
507	C₂	#19143474	1	1	yes	characteristic
508	C₂	C₂×#14583018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1489	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063345	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1489	D₄₃
hypocenter	C₄₃	#18065
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1489

Complements

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

N	H ≅ G/N	type
1. #19143721	C₂	semidirect
2. #19143720	C₂	semidirect
4. #19133501	C₂	semidirect
5. #19133434	C₂	semidirect
6. #19133428	C₂	semidirect
7. #19133416	C₂	semidirect
8. #19133350	C₂	semidirect
9. #19133035	C₂	semidirect
10. #19132882	C₂	semidirect
11. C₄₃×#1489	C₂	semidirect
155. #10621882	M₁₆	semidirect
258. #1489	D₄₃	semidirect
303. C₄₃	#18065	semidirect

Maximal subgroups

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

subgroup	index
#19143721	2
#19143720	2
C₄×#13063345	2
#19133501	2
#19133434	2
#19133428	2
#19133416	2
#19133350	2
#19133035	2
#19132882	2
C₄₃×#1489	2
#18065	43