Subgroups — #25080378

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145155	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144059	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134016	C₂	1	2	yes	maximal, complemented
5	#19134006	C₂	1	2	yes	maximal, complemented
6	#19133972	C₂	1	2	yes	maximal, complemented
7	#19133938	C₂	1	2	yes	maximal, complemented
8	#19133350	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133285	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063351	—	2	1	no	—
13	C₂³×C₄₃⋊C₈	—	2	1	no	—
14	#14583449	C₂²	1	1	yes	characteristic
15	#14583295	C₂²	1	1	yes	characteristic, complemented
16	#14583273	C₂²	1	1	yes	characteristic, complemented
17	#14583249	C₂²	1	1	yes	characteristic, complemented
18	#14583247	C₂²	1	1	yes	characteristic, complemented
19	#14583130	—	2	1	no	—
20	#14583130	—	2	1	no	—
21	#14583114	—	2	2	no	—
22	#14583104	C₂²	1	2	yes	—
23	#14583094	C₂²	1	2	yes	—
24	C₄×#10621884	—	2	1	no	—
25	C₄×#10621884	—	2	1	no	—
26	D₄×C₄₃⋊C₈	—	2	1	no	—
27	D₄×C₄₃⋊C₈	—	2	1	no	—
28	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
29	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
30	#14582923	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	#14582898	—	2	1	no	—
33	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
34	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	#14582649	C₂²	1	2	yes	complemented
36	#14582649	C₂²	1	2	yes	complemented
37	#14582648	C₂²	1	2	yes	complemented
38	#14582646	C₂²	1	2	yes	complemented
39	#14582645	C₂²	1	2	yes	complemented
40	#14582642	C₂²	1	2	yes	complemented
41	C₄₃×#533	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#478	—	2	2	no	—
44	C₄₃×#476	C₂²	1	2	yes	—
45	C₄₃×#474	C₂²	1	2	yes	—
46	C₄₃×#428	—	2	1	no	—
47	C₄₃×#423	C₂²	1	1	yes	characteristic
48	C₄₃×#418	—	2	1	no	—
49	C₂×#10621898	—	2	1	no	—
50	#13063351	—	4	4	no	—
51	C₂×#10621883	—	2	2	no	—
52	C₂×#10621884	—	2	1	no	—
53	C₂×#10621884	—	2	1	no	—
54	C₂×#10621882	—	2	2	no	—
55	C₂×#10621877	—	2	1	no	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	C₂²×C₄₃⋊C₈	—	2	2	no	—
58	C₂²×C₄₃⋊C₈	—	2	2	no	—
59	C₂²×C₄₃⋊C₈	—	4	4	no	—
60	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
62	#13063325	C₂³	1	1	yes	characteristic
63	#13063322	C₂³	1	1	yes	characteristic
64	#13063313	—	2	1	no	—
65	#13063299	—	2	1	no	—
66	#13063299	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	C₄×D₁₇₂	—	2	1	no	—
69	#13063256	—	2	1	no	—
70	#13063256	—	2	1	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
72	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
75	#13063249	—	2	1	no	—
76	#13063249	—	2	1	no	—
77	#13063248	—	2	2	no	—
78	#13063245	—	2	2	no	—
79	#13063245	—	2	1	no	—
80	#13063245	—	2	1	no	—
81	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
82	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
83	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
85	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂³×C₄×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
92	#125×C₄₃	—	2	1	no	—
93	C₂²⋊Q₈×C₄₃	—	2	1	no	—
94	C₂²⋊Q₈×C₄₃	—	2	1	no	—
95	C₄×Q₈×C₄₃	—	2	1	no	—
96	C₄×Q₈×C₄₃	—	2	1	no	—
97	C₄×D₄×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	—	2	1	no	—
99	C₄×D₄×C₄₃	D₄	1	2	yes	—
100	C₄×D₄×C₄₃	C₂³	1	2	yes	—
101	#117×C₄₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	#107×C₄₃	—	2	2	no	—
106	#106×C₄₃	—	2	2	no	—
107	C₄⋊C₈×C₄₃	—	2	1	no	—
108	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
109	#102×C₄₃	—	2	2	no	—
110	#102×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂×Q₈×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	SD₁₆	1	4	yes	complemented
117	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	1	no	—
121	C₂²×C₄×C₄₃	—	4	2	no	—
122	C₂²×C₄×C₄₃	—	4	2	no	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
126	C₂×C₂²⋊D₄₃	—	4	1	no	—
127	#10621898	—	4	2	no	—
128	#10621898	—	4	2	no	—
129	C₂×D₁₇₂	—	2	1	no	—
130	C₂×D₁₇₂	—	2	1	no	—
131	C₂×D₁₇₂	—	2	1	no	—
132	C₂×C₄×D₄₃	—	4	1	no	—
133	C₂×Dic₈₆	—	2	1	no	—
134	M₁₆×C₄₃	—	4	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	—	2	1	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	4	1	no	—
142	C₄⋊C₄×C₄₃	—	4	1	no	—
143	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₂²⋊C₄×C₄₃	—	2	2	no	—
146	C₂²⋊C₄×C₄₃	—	4	1	no	—
147	C₄²×C₄₃	—	4	1	no	—
148	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₄₃	#41	1	1	yes	characteristic
151	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
152	#10621884	—	4	2	no	—
153	#10621884	—	4	2	no	—
154	#10621883	—	4	4	no	—
155	#10621882	—	4	4	no	—
156	(C₂×D₄₃)⋊C₄	—	4	1	no	—
157	(C₂×D₄₃)⋊C₄	—	4	1	no	—
158	C₄⋊Dic₄₃	—	2	1	no	—
159	C₄⋊Dic₄₃	—	2	1	no	—
160	#10621877	—	4	2	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	2	2	no	—
163	C₂×C₄₃⋊C₈	—	2	2	no	—
164	C₂×C₄₃⋊C₈	—	4	1	no	—
165	C₂×C₄₃⋊C₈	—	4	4	no	—
166	C₂×C₄₃⋊C₈	—	4	2	no	—
167	C₂×C₄₃⋊C₈	—	4	4	no	—
168	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	—	2	4	no	—
174	C₂³×C₄₃	—	4	2	no	—
175	C₂³×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	#121	1	1	yes	characteristic
177	C₂²×D₄₃	—	4	1	no	—
178	Q₈×C₄₃	—	4	1	no	—
179	Q₈×C₄₃	—	4	1	no	—
180	Q₈×C₄₃	—	8	1	no	—
181	D₄×C₄₃	—	2	2	no	—
182	D₄×C₄₃	—	2	4	no	—
183	D₄×C₄₃	C₂×SD₁₆	1	4	yes	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	—	4	4	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
195	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
196	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
198	C₂×C₄×C₄₃	#135	1	2	yes	—
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
202	C₂²⋊D₄₃	—	8	2	no	—
203	C₂×Dic₄₃	—	4	1	no	—
204	D₁₇₂	—	4	1	no	—
205	D₁₇₂	—	4	1	no	—
206	D₁₇₂	—	4	1	no	—
207	D₁₇₂	—	4	1	no	—
208	D₁₇₂	—	8	1	no	—
209	C₄×D₄₃	—	8	2	no	—
210	Dic₈₆	—	4	1	no	—
211	Dic₈₆	—	4	1	no	—
212	C₈×C₄₃	—	4	2	no	—
213	C₄₃⋊C₈	—	2	1	no	—
214	C₄₃⋊C₈	—	2	1	no	—
215	C₄₃⋊C₈	—	2	1	no	—
216	C₄₃⋊C₈	—	4	2	no	—
217	C₄₃⋊C₈	—	4	2	no	—
218	C₄₃⋊C₈	AGL(1,ℤ/8)	1	2	yes	complemented
219	#19254	—	43	1	no	maximal, Sylow
220	C₂²×C₄₃	—	2	1	no	—
221	C₂²×C₄₃	—	2	1	no	—
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	4	8	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	4	2	no	—
226	C₂²×C₄₃	#465	1	2	yes	—
227	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
228	C₂×D₄₃	—	8	1	no	—
229	C₂×D₄₃	—	8	1	no	—
230	C₂×D₄₃	—	8	1	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	—	2	1	no	—
234	C₄×C₄₃	—	4	2	no	—
235	C₄×C₄₃	—	8	1	no	—
236	C₄×C₄₃	—	8	1	no	—
237	C₄×C₄₃	#465	1	2	yes	—
238	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
239	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
240	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₄×C₄₃	#575	1	1	yes	characteristic
242	Dic₄₃	—	8	1	no	—
243	#3167	—	43	1	no	—
244	#3077	D₄₃	1	1	yes	characteristic, complemented
245	#3036	—	43	1	no	—
246	C₂×C₈×D₄	—	43	1	no	—
247	#1679	—	43	2	no	—
248	#1677	—	43	2	no	—
249	#1671	—	43	2	no	—
250	#1665	—	43	2	no	—
251	#1566	—	43	1	no	—
252	#1550	—	43	1	no	—
253	#1547	—	43	1	no	—
254	C₂×C₄₃	—	2	2	no	—
255	C₂×C₄₃	—	4	4	no	—
256	C₂×C₄₃	#3036	1	1	yes	characteristic
257	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
258	C₂×C₄₃	#3067	1	1	yes	characteristic
259	D₄₃	—	16	1	no	—
260	C₂×AGL(1,ℤ/8)	—	86	1	no	—
261	C₂³×C₈	—	86	1	no	—
262	#533	C₂×D₄₃	1	1	yes	characteristic
263	#532	—	43	1	no	—
264	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
265	#498	—	43	1	no	—
266	#492	—	43	1	no	—
267	#487	—	43	1	no	—
268	#486	—	43	1	no	—
269	#478	—	2	2	no	—
270	#476	C₂×D₄₃	1	2	yes	—
271	#474	C₂×D₄₃	1	2	yes	—
272	#465	—	86	1	no	—
273	#465	—	86	1	no	—
274	#463	—	86	2	no	—
275	#461	—	43	2	no	—
276	#459	—	43	2	no	—
277	C₄×SD₁₆	—	86	1	no	—
278	C₄×SD₁₆	—	86	1	no	—
279	C₈×D₄	—	43	2	no	—
280	C₈×D₄	—	43	2	no	—
281	C₈×D₄	—	86	1	no	—
282	C₈×D₄	—	86	1	no	—
283	#428	—	2	1	no	—
284	#423	—	43	1	no	—
285	#423	C₂×D₄₃	1	1	yes	characteristic
286	C₂×C₄⋊C₈	—	43	1	no	—
287	#418	—	2	1	no	—
288	#417	—	86	1	no	—
289	C₂×C₂²⋊C₈	—	86	1	no	—
290	C₂×C₄×C₈	—	43	1	no	—
291	#334	—	43	2	no	—
292	#334	—	43	2	no	—
293	#333	—	43	2	no	—
294	#332	—	43	2	no	—
295	#332	—	43	2	no	—
296	#331	—	43	2	no	—
297	C₄₃	#19254	1	1	yes	characteristic, complemented, Sylow
298	C₂×#41	—	86	1	no	—
299	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
300	C₂³×C₄	—	2	1	no	—
301	AGL(1,ℤ/8)	—	172	4	no	—
302	C₂×SD₁₆	—	86	1	no	—
303	C₂×SD₁₆	—	86	1	no	—
304	C₂×SD₁₆	—	86	2	no	—
305	C₂×D₈	—	86	2	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	86	1	no	—
308	C₂²×C₈	—	43	1	no	—
309	C₂²×C₈	—	43	1	no	—
310	C₂²×C₈	—	86	2	no	—
311	C₂²×C₈	—	86	2	no	—
312	C₂²×C₈	—	86	1	no	—
313	C₂²×C₈	—	172	4	no	—
314	C₄⋊Q₈	—	43	1	no	—
315	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
316	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
317	#127	—	43	1	no	—
318	#125	—	2	1	no	—
319	#124	—	86	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	#121	—	86	1	no	—
323	#121	—	86	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	86	1	no	—
329	C₄×D₄	—	86	1	no	—
330	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
331	C₄×D₄	C₂²×D₄₃	1	2	yes	—
332	#117	—	2	1	no	—
333	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
336	#107	—	2	2	no	—
337	#106	—	2	2	no	—
338	#106	—	86	1	no	—
339	#106	—	86	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	43	2	no	—
342	C₄⋊C₈	—	43	2	no	—
343	C₄⋊C₈	—	86	1	no	—
344	C₄⋊C₈	—	86	1	no	—
345	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
346	#103	—	86	1	no	—
347	#103	—	86	1	no	—
348	#103	—	86	2	no	—
349	#102	—	2	2	no	—
350	#102	—	2	2	no	—
351	#102	—	86	1	no	—
352	#102	—	86	1	no	—
353	#102	—	86	2	no	—
354	C₂²⋊C₈	—	86	2	no	—
355	C₂²⋊C₈	—	86	2	no	—
356	C₄×C₈	—	43	1	no	—
357	C₄×C₈	—	43	1	no	—
358	C₄×C₈	—	43	1	no	—
359	C₄×C₈	—	43	1	no	—
360	C₂⁴	—	2	1	no	—
361	#41	—	172	2	no	—
362	#41	—	172	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	86	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	86	1	no	—
369	C₂×D₄	—	86	1	no	—
370	C₂×D₄	—	86	1	no	—
371	C₂×D₄	—	172	1	no	—
372	C₂×D₄	#10621884	1	4	yes	complemented
373	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	172	1	no	—
380	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
381	C₂²×C₄	#10621900	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
383	SD₁₆	—	172	2	no	—
384	SD₁₆	—	172	2	no	—
385	SD₁₆	—	172	4	no	—
386	D₈	—	172	4	no	—
387	M₁₆	—	4	2	no	—
388	M₁₆	—	172	2	no	—
389	C₂×C₈	—	2	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	—	86	2	no	—
397	C₂×C₈	—	172	4	no	—
398	C₂×C₈	—	172	1	no	—
399	C₂×C₈	—	172	4	no	—
400	C₂×C₈	—	172	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	86	1	no	—
409	C₄⋊C₄	—	86	1	no	—
410	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	172	1	no	—
415	C₂²⋊C₄	—	172	1	no	—
416	C₄²	—	4	1	no	—
417	C₄²	D₄×D₄₃	1	1	yes	characteristic
418	C₄²	#10621900	1	1	yes	characteristic
419	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
420	C₄²	C₂³×D₄₃	1	1	yes	characteristic
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	172	1	no	—
426	C₂³	#13063297	1	1	yes	characteristic
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	8	1	no	—
430	Q₈	—	172	1	no	—
431	Q₈	—	172	1	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	2	no	—
434	D₄	—	344	1	no	—
435	D₄	—	344	2	no	—
436	D₄	—	172	1	no	—
437	D₄	—	172	1	no	—
438	D₄	—	172	1	no	—
439	D₄	—	172	1	no	—
440	D₄	C₂×#10621884	1	4	yes	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	344	2	no	—
452	C₂×C₄	—	172	1	no	—
453	C₂×C₄	#13063297	1	1	yes	characteristic
454	C₂×C₄	#13063297	1	1	yes	characteristic
455	C₂×C₄	#13063297	1	1	yes	characteristic
456	C₂×C₄	C₂×#10621884	1	2	yes	—
457	C₂×C₄	#13063345	1	2	yes	—
458	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
460	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
461	C₈	—	4	2	no	—
462	C₈	—	43	2	no	—
463	C₈	—	86	1	no	—
464	C₈	—	86	1	no	—
465	C₈	—	86	1	no	—
466	C₈	—	172	2	no	—
467	C₈	—	172	2	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	4	8	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	344	1	no	—
475	C₂²	—	344	1	no	—
476	C₂²	—	344	1	no	—
477	C₂²	#14583130	1	2	yes	—
478	C₂²	C₂×#13063297	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	344	1	no	—
486	C₄	#14583130	1	2	yes	—
487	C₄	C₂²×#10621884	1	1	yes	characteristic
488	C₄	C₂×#13063345	1	1	yes	characteristic
489	C₄	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
490	C₄	#14583695	1	1	yes	characteristic
491	C₂	—	2	2	no	—
492	C₂	—	4	4	no	—
493	C₂	—	688	1	no	—
494	C₂	#19144056	1	1	yes	characteristic
495	C₂	C₂×#14583130	1	1	yes	characteristic
496	C₂	#19144312	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3077	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19144059	C₂
hypercenter	#3077	D₄₃
hypocenter	C₄₃	#19254
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3077

Complements

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

N	H ≅ G/N	type
1. #19145155	C₂	semidirect
3. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
4. #19134016	C₂	semidirect
5. #19134006	C₂	semidirect
6. #19133972	C₂	semidirect
7. #19133938	C₂	semidirect
8. #19133350	C₂	semidirect
9. #19133285	C₂	semidirect
10. #19133273	C₂	semidirect
11. C₄₃×#3077	C₂	semidirect
15. #14583295	C₂²	semidirect
16. #14583273	C₂²	semidirect
17. #14583249	C₂²	semidirect
18. #14583247	C₂²	semidirect
35. #14582649	C₂²	semidirect
36. #14582649	C₂²	semidirect
37. #14582648	C₂²	semidirect
38. #14582646	C₂²	semidirect
39. #14582645	C₂²	semidirect
40. #14582642	C₂²	semidirect
116. C₂×D₄×C₄₃	SD₁₆	semidirect
218. C₄₃⋊C₈	AGL(1,ℤ/8)	semidirect
244. #3077	D₄₃	semidirect
297. C₄₃	#19254	semidirect
372. C₂×D₄	#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145155	2
#19144059	2
C₂×D₄×C₄₃⋊C₈	2
#19134016	2
#19134006	2
#19133972	2
#19133938	2
#19133350	2
#19133285	2
#19133273	2
C₄₃×#3077	2
#19254	43