Subgroups — #25066381

Order 11008.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13063353	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582976	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133508	C₂	1	2	yes	maximal, complemented
5	#19133496	C₂	1	2	yes	maximal, complemented
6	#19133484	C₂	1	2	yes	maximal, complemented
7	#19133479	C₂	1	2	yes	maximal, complemented
8	#19132985	C₂	1	1	yes	maximal, characteristic, complemented
9	#19132980	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063353	C₄	1	1	yes	characteristic
13	C₂²×#10621872	—	2	1	no	—
14	C₄×#10621898	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
16	#14583026	C₂²	1	1	yes	characteristic, complemented
17	#14583026	C₂²	1	1	yes	characteristic, complemented
18	#14583012	C₄	1	2	yes	—
19	#14583001	C₄	1	2	yes	—
20	C₄×#10621873	C₂²	1	2	yes	—
21	C₄×D₃₄₄	C₂²	1	2	yes	—
22	#14582976	—	2	1	no	—
23	#14582976	—	2	1	no	—
24	#14582976	C₂²	1	2	yes	—
25	#14582976	C₂²	1	2	yes	—
26	#14582976	C₂²	1	1	yes	characteristic, complemented
27	#14582976	C₂²	1	1	yes	characteristic, complemented
28	#14582967	—	2	1	no	—
29	#14582967	—	2	1	no	—
30	#14582952	C₂²	1	1	yes	characteristic
31	#14582950	—	2	1	no	—
32	#14582941	C₄	1	1	yes	characteristic
33	#14582905	C₄	1	1	yes	characteristic
34	#14582901	C₄	1	1	yes	characteristic
35	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
36	C₄×#10621872	—	2	1	no	—
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	#14582629	C₂²	1	2	yes	complemented
39	#14582626	C₂²	1	2	yes	—
40	#14582626	C₂²	1	2	yes	—
41	#14582626	C₂²	1	2	yes	complemented
42	#14582620	C₂²	1	2	yes	complemented
43	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#335	C₂²	1	2	yes	complemented
48	C₄₃×#334	C₂²	1	2	yes	complemented
49	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₄₃	—	2	1	no	—
52	#13063353	—	2	4	no	—
53	C₂×#10621873	C₂×C₄	1	2	yes	—
54	C₂×D₃₄₄	C₂×C₄	1	2	yes	—
55	C₂×#10621872	—	2	1	no	—
56	C₂×#10621872	—	2	1	no	—
57	C₂×#10621872	—	2	2	no	—
58	C₂×#10621872	—	2	2	no	—
59	C₂×#10621872	—	4	4	no	—
60	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
62	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
64	C₄×D₁₇₂	—	2	1	no	—
65	C₄×D₁₇₂	—	2	1	no	—
66	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
67	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
68	C₄×D₁₇₂	C₂³	1	2	yes	—
69	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
70	C₄×C₂²⋊D₄₃	—	2	1	no	—
71	C₄×C₂²⋊D₄₃	—	2	1	no	—
72	#13063284	C₂×C₄	1	1	yes	characteristic
73	#13063282	—	2	1	no	—
74	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
75	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
76	C₄²×D₄₃	—	2	1	no	—
77	#13063259	C₂×C₄	1	2	yes	—
78	#13063257	C₂×C₄	1	2	yes	—
79	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
80	Dic₄₃⋊C₈	—	2	1	no	—
81	Dic₄₃⋊C₈	—	2	1	no	—
82	#13063250	C₂×C₄	1	2	yes	—
83	#13063247	C₂×C₄	1	2	yes	—
84	#13063247	C₂×C₄	1	2	yes	—
85	#13063247	C₂×C₄	1	2	yes	—
86	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
87	(C₂×D₄₃)⋊C₈	—	2	2	no	—
88	(C₂×D₄₃)⋊C₈	—	2	2	no	—
89	(C₂×D₄₃)⋊C₈	—	2	1	no	—
90	(C₂×D₄₃)⋊C₈	—	2	1	no	—
91	#13063235	—	2	1	no	—
92	#13063235	—	2	1	no	—
93	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
94	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
95	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
96	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
97	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₃	—	2	1	no	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₃	—	2	1	no	—
103	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
105	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
106	C₂²⋊C₈×C₄₃	—	2	1	no	—
107	#97×C₄₃	C₂×C₄	1	2	yes	—
108	C₄×C₈×C₄₃	—	2	1	no	—
109	C₄×C₈×C₄₃	C₂³	1	2	yes	—
110	C₂³×D₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₃	—	2	1	no	—
115	C₂²×Dic₄₃	—	2	1	no	—
116	#10621898	—	2	2	no	—
117	#10621898	—	2	2	no	—
118	C₂×D₁₇₂	—	2	1	no	—
119	C₂×D₁₇₂	—	2	2	no	—
120	C₂×D₁₇₂	—	2	2	no	—
121	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
122	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
123	C₂×C₄×D₄₃	—	2	1	no	—
124	C₂×C₄×D₄₃	—	2	1	no	—
125	C₂×C₄×D₄₃	—	2	2	no	—
126	C₂×C₄×D₄₃	—	2	1	no	—
127	C₂×C₄×D₄₃	—	2	2	no	—
128	C₂×C₄×D₄₃	—	4	2	no	—
129	C₂×C₄×D₄₃	—	4	2	no	—
130	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
131	M₁₆×C₄₃	—	2	2	no	—
132	M₁₆×C₄₃	M₁₆	1	4	yes	complemented
133	C₂×C₈×C₄₃	—	2	1	no	—
134	C₂×C₈×C₄₃	—	2	1	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	4	2	no	—
137	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₃	#41	1	1	yes	characteristic
142	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₄₃	—	2	1	no	—
144	(C₂×D₄₃)⋊C₄	—	2	2	no	—
145	(C₂×D₄₃)⋊C₄	—	2	1	no	—
146	(C₂×D₄₃)⋊C₄	—	2	2	no	—
147	(C₂×D₄₃)⋊C₄	—	2	1	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
152	Dic₄₃⋊C₄	—	2	1	no	—
153	Dic₄₃⋊C₄	—	2	1	no	—
154	C₄×Dic₄₃	—	2	1	no	—
155	C₄×Dic₄₃	—	2	1	no	—
156	C₄×Dic₄₃	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	4	1	no	—
160	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
164	D₃₄₄	—	2	4	no	—
165	#10621873	—	2	4	no	—
166	#10621872	—	4	2	no	—
167	#10621872	—	4	4	no	—
168	#10621872	—	4	2	no	—
169	#10621872	—	4	4	no	—
170	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
171	C₂²×D₄₃	—	2	1	no	—
172	C₂²×D₄₃	—	2	2	no	—
173	C₂²×D₄₃	—	4	2	no	—
174	C₂²×D₄₃	—	4	2	no	—
175	C₂²×D₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₄₃	#131	1	2	yes	—
184	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₄₃	—	4	2	no	—
188	C₂×Dic₄₃	—	2	1	no	—
189	C₂×Dic₄₃	—	2	1	no	—
190	C₂×Dic₄₃	—	2	1	no	—
191	C₂×Dic₄₃	—	2	2	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	D₁₇₂	—	2	2	no	—
194	D₁₇₂	—	2	1	no	—
195	D₁₇₂	—	2	2	no	—
196	D₁₇₂	—	2	1	no	—
197	D₁₇₂	—	4	2	no	—
198	C₄×D₄₃	—	4	2	no	—
199	C₄×D₄₃	—	4	4	no	—
200	C₄×D₄₃	—	4	2	no	—
201	C₄×D₄₃	—	4	1	no	—
202	C₄×D₄₃	—	4	1	no	—
203	C₄×D₄₃	—	4	2	no	—
204	C₄×D₄₃	—	4	2	no	—
205	Dic₈₆	—	2	1	no	—
206	Dic₈₆	—	2	1	no	—
207	C₈×C₄₃	—	2	2	no	—
208	C₈×C₄₃	—	4	2	no	—
209	C₈×C₄₃	—	4	1	no	—
210	C₈×C₄₃	—	4	1	no	—
211	C₈×C₄₃	C₂×M₁₆	1	4	yes	complemented
212	C₄₃⋊C₈	—	2	1	no	—
213	C₄₃⋊C₈	—	2	1	no	—
214	C₄₃⋊C₈	—	2	1	no	—
215	C₄₃⋊C₈	—	4	2	no	—
216	C₄₃⋊C₈	AGL(1,ℤ/8)	1	2	yes	complemented
217	#17891	—	43	1	no	maximal, Sylow
218	C₂²×C₄₃	—	2	1	no	—
219	C₂²×C₄₃	—	2	1	no	—
220	C₂²×C₄₃	#436	1	2	yes	—
221	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂×D₄₃	—	4	2	no	—
223	C₂×D₄₃	—	4	1	no	—
224	C₂×D₄₃	—	4	2	no	—
225	C₂×D₄₃	—	4	1	no	—
226	C₂×D₄₃	—	4	2	no	—
227	C₂×D₄₃	—	4	1	no	—
228	C₂×D₄₃	—	8	4	no	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	#436	1	2	yes	—
233	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
234	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
235	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₄×C₄₃	#575	1	1	yes	characteristic
237	Dic₄₃	—	4	1	no	—
238	Dic₄₃	—	4	2	no	—
239	Dic₄₃	—	4	1	no	—
240	Dic₄₃	—	4	1	no	—
241	#2965	—	43	1	no	—
242	C₄×AGL(1,ℤ/8)	—	43	1	no	—
243	C₂×#436	—	43	1	no	—
244	#1594	—	43	2	no	—
245	#1592	—	43	2	no	—
246	#1590	—	43	2	no	—
247	#1589	—	43	2	no	—
248	#1565	D₄₃	1	1	yes	characteristic, complemented
249	#1478	—	43	1	no	—
250	#1477	—	43	1	no	—
251	C₈×M₁₆	—	43	1	no	—
252	C₂×C₄₃	—	2	2	no	—
253	C₂×C₄₃	C₂×#436	1	1	yes	characteristic
254	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂×C₄₃	#2955	1	1	yes	characteristic
256	D₄₃	—	8	1	no	—
257	D₄₃	—	8	2	no	—
258	C₂×AGL(1,ℤ/8)	—	43	1	no	—
259	C₂²×M₁₆	—	86	1	no	—
260	C₄×#41	—	43	1	no	—
261	C₂×C₄×D₄	—	43	1	no	—
262	#446	—	43	1	no	—
263	#446	—	43	1	no	—
264	#442	—	43	2	no	—
265	#440	—	43	2	no	—
266	C₄×SD₁₆	—	43	2	no	—
267	C₄×D₈	—	43	2	no	—
268	#436	—	43	1	no	—
269	#436	—	43	2	no	—
270	#436	—	43	2	no	—
271	#436	—	43	1	no	—
272	#436	—	86	1	no	—
273	#436	—	86	1	no	—
274	#435	—	86	1	no	—
275	#435	—	86	1	no	—
276	#431	—	43	1	no	—
277	#431	—	86	1	no	—
278	#431	C₂×D₄₃	1	1	yes	characteristic
279	#428	—	43	1	no	—
280	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
281	#418	—	43	1	no	—
282	#417	—	43	1	no	—
283	C₂×C₂²⋊C₈	—	86	1	no	—
284	C₄×M₁₆	—	86	1	no	—
285	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
286	C₂×C₄×C₈	—	43	1	no	—
287	#335	C₂×D₄₃	1	2	yes	complemented
288	#334	C₂×D₄₃	1	2	yes	complemented
289	Q₈⋊C₈	—	43	2	no	—
290	D₄⋊C₈	—	43	2	no	—
291	D₄⋊C₈	—	43	2	no	—
292	D₄⋊C₈	—	43	2	no	—
293	#322	—	43	2	no	—
294	C₈²	—	43	2	no	—
295	C₄₃	#17891	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	—	43	1	no	—
297	C₂²×D₄	—	43	1	no	—
298	C₂³×C₄	—	86	1	no	—
299	AGL(1,ℤ/8)	—	86	4	no	—
300	C₂×SD₁₆	—	43	2	no	—
301	C₂×D₈	—	43	2	no	—
302	C₂×M₁₆	—	86	2	no	—
303	C₂×M₁₆	—	86	2	no	—
304	C₂×M₁₆	—	86	1	no	—
305	C₂×M₁₆	—	86	1	no	—
306	C₂×M₁₆	—	172	4	no	—
307	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
308	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	43	1	no	—
311	C₂²×C₈	—	43	1	no	—
312	C₄×Q₈	—	43	1	no	—
313	C₄×Q₈	—	43	1	no	—
314	C₄×D₄	—	43	2	no	—
315	C₄×D₄	—	43	1	no	—
316	C₄×D₄	—	43	2	no	—
317	C₄×D₄	—	43	1	no	—
318	C₄×D₄	—	86	1	no	—
319	C₄×D₄	—	86	1	no	—
320	C₄×D₄	—	86	1	no	—
321	C₄×D₄	—	86	1	no	—
322	#117	—	43	1	no	—
323	#117	—	86	1	no	—
324	C₂×C₄⋊C₄	—	43	1	no	—
325	C₂×C₂²⋊C₄	—	86	1	no	—
326	C₂×C₄²	—	86	1	no	—
327	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
328	#107	—	43	2	no	—
329	#106	—	43	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	86	1	no	—
332	C₄⋊C₈	—	86	1	no	—
333	C₄⋊C₈	—	86	1	no	—
334	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
335	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
336	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
337	#103	—	43	2	no	—
338	#102	—	43	2	no	—
339	#102	—	43	2	no	—
340	#102	—	43	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	86	2	no	—
343	C₂²⋊C₈	—	86	2	no	—
344	C₂²⋊C₈	—	86	1	no	—
345	C₂²⋊C₈	—	86	1	no	—
346	C₂²⋊C₈	—	86	1	no	—
347	#97	—	86	1	no	—
348	#97	—	86	1	no	—
349	#97	C₄×D₄₃	1	2	yes	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	—	43	1	no	—
352	C₄×C₈	—	43	1	no	—
353	C₄×C₈	—	43	1	no	—
354	C₄×C₈	—	43	1	no	—
355	C₄×C₈	—	43	2	no	—
356	C₄×C₈	C₂²×D₄₃	1	2	yes	—
357	C₂⁴	—	86	1	no	—
358	#41	—	86	2	no	—
359	#41	—	86	2	no	—
360	C₂×Q₈	—	43	1	no	—
361	C₂×D₄	—	43	1	no	—
362	C₂×D₄	—	43	2	no	—
363	C₂×D₄	—	86	1	no	—
364	C₂×D₄	—	86	1	no	—
365	C₂×D₄	—	86	2	no	—
366	C₂×D₄	—	86	2	no	—
367	C₂²×C₄	—	86	1	no	—
368	C₂²×C₄	—	86	1	no	—
369	C₂²×C₄	—	86	1	no	—
370	C₂²×C₄	—	86	2	no	—
371	C₂²×C₄	—	86	1	no	—
372	C₂²×C₄	—	86	2	no	—
373	C₂²×C₄	—	172	2	no	—
374	C₂²×C₄	—	172	2	no	—
375	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
377	C₂²×C₄	#10621902	1	1	yes	characteristic
378	SD₁₆	—	86	4	no	—
379	D₈	—	86	4	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	172	4	no	—
382	M₁₆	—	172	2	no	—
383	M₁₆	—	172	4	no	—
384	M₁₆	—	172	2	no	—
385	M₁₆	#10621872	1	4	yes	complemented
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	—	43	1	no	—
391	C₂×C₈	—	43	1	no	—
392	C₂×C₈	—	43	1	no	—
393	C₂×C₈	—	43	1	no	—
394	C₂×C₈	—	86	2	no	—
395	C₂×C₈	—	86	2	no	—
396	C₂×C₈	—	172	1	no	—
397	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
398	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
399	C₄⋊C₄	—	43	1	no	—
400	C₄⋊C₄	—	43	1	no	—
401	C₄⋊C₄	—	43	2	no	—
402	C₄⋊C₄	—	86	1	no	—
403	C₄⋊C₄	—	86	1	no	—
404	C₄⋊C₄	—	86	1	no	—
405	C₂²⋊C₄	—	86	1	no	—
406	C₂²⋊C₄	—	86	2	no	—
407	C₂²⋊C₄	—	86	1	no	—
408	C₂²⋊C₄	—	86	2	no	—
409	C₂²⋊C₄	—	86	1	no	—
410	C₄²	—	86	1	no	—
411	C₄²	—	86	1	no	—
412	C₄²	—	86	1	no	—
413	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
414	C₄²	D₄×D₄₃	1	1	yes	characteristic
415	C₄²	#10621902	1	1	yes	characteristic
416	C₄²	C₂³×D₄₃	1	1	yes	characteristic
417	C₂³	—	86	1	no	—
418	C₂³	—	86	2	no	—
419	C₂³	—	172	2	no	—
420	C₂³	—	172	2	no	—
421	C₂³	—	172	2	no	—
422	C₂³	#13063287	1	1	yes	characteristic
423	Q₈	—	86	1	no	—
424	Q₈	—	86	1	no	—
425	D₄	—	86	1	no	—
426	D₄	—	86	2	no	—
427	D₄	—	86	2	no	—
428	D₄	—	86	1	no	—
429	D₄	—	172	2	no	—
430	D₄	—	172	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	86	1	no	—
435	C₂×C₄	—	86	1	no	—
436	C₂×C₄	—	86	1	no	—
437	C₂×C₄	—	86	2	no	—
438	C₂×C₄	—	172	4	no	—
439	C₂×C₄	—	172	2	no	—
440	C₂×C₄	—	172	2	no	—
441	C₂×C₄	—	172	2	no	—
442	C₂×C₄	—	172	1	no	—
443	C₂×C₄	—	172	1	no	—
444	C₂×C₄	—	172	2	no	—
445	C₂×C₄	—	172	2	no	—
446	C₂×C₄	#13063287	1	1	yes	characteristic
447	C₂×C₄	#13063287	1	1	yes	characteristic
448	C₂×C₄	#13063287	1	1	yes	characteristic
449	C₂×C₄	C₂×#10621872	1	2	yes	—
450	C₂×C₄	#13063333	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
452	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	43	2	no	—
459	C₈	—	86	1	no	—
460	C₈	—	86	1	no	—
461	C₈	—	86	1	no	—
462	C₈	—	172	2	no	—
463	C₈	C₂×#10621872	1	4	yes	complemented
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	344	4	no	—
467	C₂²	—	172	1	no	—
468	C₂²	—	172	2	no	—
469	C₂²	—	172	1	no	—
470	C₂²	—	172	2	no	—
471	C₂²	—	172	2	no	—
472	C₂²	—	172	1	no	—
473	C₂²	#14582976	1	2	yes	—
474	C₂²	C₂×#13063287	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	172	1	no	—
479	C₄	—	172	1	no	—
480	C₄	—	172	2	no	—
481	C₄	—	172	1	no	—
482	C₄	#14582976	1	2	yes	—
483	C₄	C₂²×#10621872	1	1	yes	characteristic
484	C₄	C₂×#13063333	1	1	yes	characteristic
485	C₄	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
486	C₄	#14583698	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	344	2	no	—
489	C₂	—	344	1	no	—
490	C₂	C₂×#14582976	1	1	yes	characteristic
491	C₂	#19143402	1	1	yes	characteristic
492	C₂	#19143497	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×#1565	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063353	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1565	D₄₃
hypocenter	C₄₃	#17891
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
1. #19143556	C₂	semidirect
3. C₂×#14582976	C₂	semidirect
4. #19133508	C₂	semidirect
5. #19133496	C₂	semidirect
6. #19133484	C₂	semidirect
7. #19133479	C₂	semidirect
8. #19132985	C₂	semidirect
9. #19132980	C₂	semidirect
10. M₁₆×C₄₃⋊C₈	C₂	semidirect
11. C₄₃×#1565	C₂	semidirect
16. #14583026	C₂²	semidirect
17. #14583026	C₂²	semidirect
26. #14582976	C₂²	semidirect
27. #14582976	C₂²	semidirect
38. #14582629	C₂²	semidirect
41. #14582626	C₂²	semidirect
42. #14582620	C₂²	semidirect
43. C₈×C₄₃⋊C₈	C₂²	semidirect
47. C₄₃×#335	C₂²	semidirect
48. C₄₃×#334	C₂²	semidirect
132. M₁₆×C₄₃	M₁₆	semidirect
211. C₈×C₄₃	C₂×M₁₆	semidirect
216. C₄₃⋊C₈	AGL(1,ℤ/8)	semidirect
248. #1565	D₄₃	semidirect
287. #335	C₂×D₄₃	semidirect
288. #334	C₂×D₄₃	semidirect
295. C₄₃	#17891	semidirect
385. M₁₆	#10621872	semidirect
463. C₈	C₂×#10621872	semidirect

Maximal subgroups

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

subgroup	index
#19143556	2
C₄×#13063353	2
C₂×#14582976	2
#19133508	2
#19133496	2
#19133484	2
#19133479	2
#19132985	2
#19132980	2
M₁₆×C₄₃⋊C₈	2
C₄₃×#1565	2
#17891	43