Subgroups — #25066596

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144666	C₂	1	1	yes	maximal, characteristic
2	#41×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#19143525	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133463	C₂	1	2	yes	maximal, complemented
5	#19133449	C₂	1	2	yes	maximal, complemented
6	#19133399	C₂	1	2	yes	maximal, complemented
7	#19133398	C₂	1	2	yes	maximal, complemented
8	#19133386	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133017	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1489	C₂	1	1	yes	maximal, characteristic
12	#14583456	C₂²	1	1	yes	characteristic
13	#14583240	C₄	1	2	yes	—
14	#14583184	C₄	1	1	yes	characteristic
15	#14583179	C₄	1	1	yes	characteristic
16	#14583109	C₄	1	1	yes	characteristic
17	#14583104	C₄	1	1	yes	characteristic
18	#14583061	C₄	1	2	yes	—
19	#14583026	—	2	1	no	—
20	#14583026	C₂²	1	2	yes	—
21	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	#14583023	—	2	1	no	—
24	#14583023	C₂²	1	2	yes	—
25	C₄×#10621885	C₂²	1	2	yes	—
26	C₄×#10621883	C₂²	1	2	yes	—
27	D₄×C₄₃⋊C₈	—	2	1	no	—
28	D₄×C₄₃⋊C₈	—	2	1	no	—
29	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
30	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
31	#14582952	—	2	1	no	—
32	#14582952	C₂²	1	1	yes	characteristic
33	#14582952	C₂²	1	1	yes	characteristic
34	#14582927	—	2	1	no	—
35	#14582857	—	2	1	no	—
36	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	#14582651	C₂²	1	2	yes	—
39	#14582649	C₂²	1	2	yes	—
40	#14582631	C₂²	1	2	yes	—
41	#14582631	C₂²	1	2	yes	—
42	#14582620	C₂²	1	2	yes	—
43	C₈×C₄₃⋊C₈	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×#10621885	C₂×C₄	1	2	yes	—
50	C₂×#10621883	C₂×C₄	1	2	yes	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
54	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
55	#13063325	C₂×C₄	1	1	yes	characteristic
56	#13063325	C₂×C₄	1	1	yes	characteristic
57	#13063317	—	2	1	no	—
58	#13063304	—	2	1	no	—
59	#13063304	C₂×C₄	1	2	yes	—
60	C₄×Dic₈₆	—	2	1	no	—
61	C₄×Dic₈₆	C₂³	1	2	yes	—
62	#13063284	—	2	1	no	—
63	#13063258	C₂×C₄	1	2	yes	—
64	#13063256	C₂×C₄	1	2	yes	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
67	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
71	Dic₄₃⋊C₈	—	2	2	no	—
72	Dic₄₃⋊C₈	—	2	2	no	—
73	#13063249	C₂×C₄	1	2	yes	—
74	#13063248	C₂×C₄	1	2	yes	—
75	#13063248	C₂×C₄	1	2	yes	—
76	#13063246	C₂×C₄	1	2	yes	—
77	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
78	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
79	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
81	#13063235	—	2	2	no	—
82	C₄×C₄₃⋊C₈	—	2	1	no	—
83	C₄×C₄₃⋊C₈	—	2	1	no	—
84	C₄×C₄₃⋊C₈	—	2	1	no	—
85	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
86	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
87	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
88	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₈×Dic₄₃	—	2	2	no	—
91	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₂×M₁₆×C₄₃	—	2	1	no	—
93	C₂×M₁₆×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₄₃	—	2	1	no	—
97	C₄×D₄×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
100	#117×C₄₃	—	2	1	no	—
101	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	—	2	1	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₃	—	2	1	no	—
105	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
106	#97×C₄₃	—	2	1	no	—
107	C₄×C₈×C₄₃	C₂³	1	2	yes	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₄×C₄₃	—	2	1	no	—
112	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	2	1	no	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
119	C₂×Dic₈₆	—	2	1	no	—
120	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
121	M₁₆×C₄₃	—	2	4	no	—
122	M₁₆×C₄₃	—	4	2	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂²⋊C₄×C₄₃	—	2	1	no	—
131	C₂²⋊C₄×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₄²×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₃	#41	1	1	yes	characteristic
138	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₄₃	—	2	2	no	—
140	#10621885	—	2	4	no	—
141	#10621883	—	2	4	no	—
142	C₄⋊Dic₄₃	—	2	1	no	—
143	C₄⋊Dic₄₃	—	2	1	no	—
144	C₄⋊Dic₄₃	—	2	1	no	—
145	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
146	Dic₄₃⋊C₄	—	2	2	no	—
147	Dic₄₃⋊C₄	—	2	2	no	—
148	C₄×Dic₄₃	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	1	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	4	1	no	—
153	C₂×C₄₃⋊C₈	—	4	2	no	—
154	C₂×C₄₃⋊C₈	—	4	2	no	—
155	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
157	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂³×C₄₃	—	2	1	no	—
162	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
163	Q₈×C₄₃	—	2	1	no	—
164	Q₈×C₄₃	#131	1	2	yes	—
165	D₄×C₄₃	—	2	4	no	—
166	D₄×C₄₃	—	2	1	no	—
167	D₄×C₄₃	#131	1	2	yes	—
168	C₂×C₄×C₄₃	—	2	4	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
186	C₂×Dic₄₃	—	2	2	no	—
187	C₂×Dic₄₃	—	2	2	no	—
188	Dic₈₆	—	2	2	no	—
189	Dic₈₆	—	2	2	no	—
190	Dic₈₆	—	4	2	no	—
191	C₈×C₄₃	—	2	4	no	—
192	C₈×C₄₃	—	4	2	no	—
193	C₄₃⋊C₈	—	2	2	no	—
194	C₄₃⋊C₈	—	2	2	no	—
195	C₄₃⋊C₈	—	2	1	no	—
196	C₄₃⋊C₈	—	2	1	no	—
197	C₄₃⋊C₈	—	2	1	no	—
198	C₄₃⋊C₈	—	4	1	no	—
199	C₄₃⋊C₈	—	4	1	no	—
200	C₄₃⋊C₈	#137	1	2	yes	—
201	#17913	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	1	no	—
205	C₂²×C₄₃	—	2	1	no	—
206	C₂²×C₄₃	—	4	1	no	—
207	C₂²×C₄₃	—	4	1	no	—
208	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	2	2	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	4	1	no	—
214	C₄×C₄₃	—	4	1	no	—
215	C₄×C₄₃	#443	1	2	yes	—
216	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
217	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
218	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
219	C₄×C₄₃	#575	1	1	yes	characteristic
220	Dic₄₃	—	4	2	no	—
221	Dic₄₃	—	4	2	no	—
222	#3107	—	43	1	no	—
223	C₈×#41	—	43	1	no	—
224	#2960	—	43	1	no	—
225	#1587	—	43	2	no	—
226	#1585	—	43	2	no	—
227	C₈×Q₁₆	—	43	2	no	—
228	C₈×SD₁₆	—	43	2	no	—
229	#1574	—	43	1	no	—
230	#1489	D₄₃	1	1	yes	characteristic
231	#1485	—	43	1	no	—
232	C₈×M₁₆	—	43	1	no	—
233	C₂×C₄₃	—	4	1	no	—
234	C₂×C₄₃	—	4	2	no	—
235	C₂×C₄₃	#2929	1	1	yes	characteristic
236	C₂×C₄₃	C₄×#137	1	1	yes	characteristic
237	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
238	#533	—	43	1	no	—
239	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
240	#485	—	43	2	no	—
241	#475	—	43	1	no	—
242	#474	—	43	1	no	—
243	#462	—	43	1	no	—
244	#461	—	43	1	no	—
245	#452	—	43	2	no	—
246	#446	—	43	2	no	—
247	#446	—	86	1	no	—
248	C₈×Q₈	—	43	1	no	—
249	C₈×Q₈	—	43	1	no	—
250	C₈×Q₈	—	43	2	no	—
251	C₈×Q₈	—	86	1	no	—
252	C₄×Q₁₆	—	43	2	no	—
253	C₄×SD₁₆	—	43	2	no	—
254	C₈×D₄	—	43	1	no	—
255	C₈×D₄	—	43	1	no	—
256	C₈×D₄	—	86	1	no	—
257	C₈×D₄	—	86	1	no	—
258	#431	—	43	1	no	—
259	#431	—	43	1	no	—
260	#431	—	86	1	no	—
261	#424	—	86	1	no	—
262	#423	C₂×D₄₃	1	1	yes	characteristic
263	#405	—	86	1	no	—
264	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
265	C₂×C₄×C₈	—	43	1	no	—
266	C₂×C₄×C₈	—	86	1	no	—
267	#335	—	43	2	no	—
268	#334	—	43	2	no	—
269	Q₈⋊C₈	—	43	2	no	—
270	Q₈⋊C₈	—	43	2	no	—
271	Q₈⋊C₈	C₂×D₄₃	1	2	yes	—
272	D₄⋊C₈	C₂×D₄₃	1	2	yes	—
273	#322	—	43	2	no	—
274	C₈²	—	43	2	no	—
275	C₄₃	#17913	1	1	yes	characteristic, complemented, Sylow
276	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
277	C₂×Q₁₆	—	43	2	no	—
278	C₂×SD₁₆	—	43	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂²×C₈	—	43	1	no	—
282	C₂²×C₈	—	43	1	no	—
283	C₂²×C₈	—	86	1	no	—
284	C₂²×C₈	—	86	1	no	—
285	C₄⋊Q₈	—	43	1	no	—
286	C₄⋊Q₈	—	43	1	no	—
287	#125	—	86	1	no	—
288	C₂²⋊Q₈	—	43	2	no	—
289	C₂²⋊Q₈	—	86	1	no	—
290	C₄×Q₈	—	43	2	no	—
291	C₄×Q₈	—	86	1	no	—
292	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	—	86	1	no	—
300	#117	C₄×D₄₃	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
303	#107	—	43	2	no	—
304	#106	—	43	2	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	43	1	no	—
307	C₄⋊C₈	—	43	1	no	—
308	C₄⋊C₈	—	43	1	no	—
309	C₄⋊C₈	—	43	1	no	—
310	C₄⋊C₈	—	86	1	no	—
311	C₄⋊C₈	—	86	1	no	—
312	C₄⋊C₈	—	86	2	no	—
313	C₄⋊C₈	—	86	2	no	—
314	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
315	#103	—	43	2	no	—
316	#103	—	43	2	no	—
317	#103	—	43	2	no	—
318	#102	—	43	2	no	—
319	C₂²⋊C₈	—	43	2	no	—
320	C₂²⋊C₈	—	86	1	no	—
321	C₂²⋊C₈	—	86	1	no	—
322	C₂²⋊C₈	—	86	1	no	—
323	#97	—	2	1	no	—
324	#97	—	86	2	no	—
325	C₄×C₈	—	43	1	no	—
326	C₄×C₈	—	43	1	no	—
327	C₄×C₈	—	43	1	no	—
328	C₄×C₈	—	43	2	no	—
329	C₄×C₈	—	43	1	no	—
330	C₄×C₈	—	86	1	no	—
331	C₄×C₈	—	86	1	no	—
332	C₄×C₈	—	86	2	no	—
333	C₄×C₈	—	86	1	no	—
334	C₄×C₈	C₂²×D₄₃	1	2	yes	—
335	#41	—	2	2	no	—
336	#41	—	2	2	no	—
337	C₂×Q₈	—	43	2	no	—
338	C₂×Q₈	—	86	1	no	—
339	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
347	C₂²×C₄	#10621900	1	1	yes	characteristic
348	Q₁₆	—	86	4	no	—
349	SD₁₆	—	86	4	no	—
350	M₁₆	—	2	4	no	—
351	M₁₆	—	4	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	43	1	no	—
355	C₂×C₈	—	43	2	no	—
356	C₂×C₈	—	43	2	no	—
357	C₂×C₈	—	43	1	no	—
358	C₂×C₈	—	43	1	no	—
359	C₂×C₈	—	43	1	no	—
360	C₂×C₈	—	86	2	no	—
361	C₂×C₈	—	86	1	no	—
362	C₂×C₈	—	86	1	no	—
363	C₂×C₈	—	172	2	no	—
364	C₂×C₈	—	172	1	no	—
365	C₂×C₈	—	172	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	43	2	no	—
369	C₄⋊C₄	—	86	1	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	86	2	no	—
372	C₄⋊C₄	—	86	1	no	—
373	C₄⋊C₄	—	86	2	no	—
374	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
375	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
376	C₂²⋊C₄	—	2	1	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	86	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	86	2	no	—
384	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
385	C₄²	D₄×D₄₃	1	1	yes	characteristic
386	C₄²	#10621900	1	1	yes	characteristic
387	C₄²	C₂³×D₄₃	1	1	yes	characteristic
388	C₂³	—	2	1	no	—
389	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
390	Q₈	—	2	1	no	—
391	Q₈	—	86	2	no	—
392	Q₈	—	86	2	no	—
393	Q₈	—	172	2	no	—
394	Q₈	#13063333	1	2	yes	—
395	D₄	—	2	4	no	—
396	D₄	—	2	1	no	—
397	D₄	#13063333	1	2	yes	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	86	2	no	—
411	C₂×C₄	—	86	2	no	—
412	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
413	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
414	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	4	2	no	—
420	C₈	—	43	2	no	—
421	C₈	—	86	2	no	—
422	C₈	—	86	2	no	—
423	C₈	—	86	1	no	—
424	C₈	—	86	1	no	—
425	C₈	—	86	1	no	—
426	C₈	—	172	1	no	—
427	C₈	—	172	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	172	2	no	—
442	C₄	—	172	2	no	—
443	C₄	#14583013	1	2	yes	—
444	C₄	C₂×#13063333	1	1	yes	characteristic
445	C₄	C₂×#13063333	1	1	yes	characteristic
446	C₄	#137×D₄₃	1	1	yes	characteristic
447	C₄	#14583695	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	4	2	no	—
450	C₂	#19143285	1	1	yes	characteristic
451	C₂	#19143419	1	1	yes	characteristic
452	C₂	C₂×#14583013	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×#41×C₄₃	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1489	D₄₃
hypocenter	C₄₃	#17913
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
3. #19143525	C₂	semidirect
4. #19133463	C₂	semidirect
5. #19133449	C₂	semidirect
6. #19133399	C₂	semidirect
7. #19133398	C₂	semidirect
8. #19133386	C₂	semidirect
9. #19133017	C₂	semidirect
10. M₁₆×C₄₃⋊C₈	C₂	semidirect
275. C₄₃	#17913	semidirect

Maximal subgroups

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

subgroup	index
#19144666	2
#41×C₄₃⋊C₈	2
#19143525	2
#19133463	2
#19133449	2
#19133399	2
#19133398	2
#19133386	2
#19133017	2
M₁₆×C₄₃⋊C₈	2
C₄₃×#1489	2
#17913	43