Subgroups — D₄₃×#1952 #25100139

Order 11008.

918 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#428×D₄₃	C₂	1	2	yes	maximal
3	C₂×#107×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#405×D₄₃	C₂	1	1	yes	maximal, characteristic
5	#19135381	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135380	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135379	C₂	1	2	yes	maximal, complemented
8	#19135378	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135377	C₂	1	2	yes	maximal, complemented
10	#343×D₄₃	C₂	1	2	yes	maximal
11	C₄₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₄₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
15	#117×D₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
17	C₂×#13063261	C₂²	1	1	yes	characteristic
18	C₂×#13063260	C₂²	1	2	yes	—
19	#108×D₄₃	C₄	1	8	yes	complemented
20	#14582942	C₂²	1	2	yes	—
21	#14582941	C₂²	1	2	yes	—
22	#14582940	—	2	2	no	—
23	#14582939	C₂²	1	2	yes	—
24	#14582938	—	2	2	no	—
25	C₂×#13063259	C₂²	1	1	yes	characteristic
26	C₂×#13063258	C₂²	1	2	yes	—
27	#107×D₄₃	—	2	1	no	—
28	#107×D₄₃	—	2	1	no	—
29	#107×D₄₃	—	2	1	no	—
30	#107×D₄₃	—	2	1	no	—
31	#107×D₄₃	—	2	2	no	—
32	#106×D₄₃	—	2	2	no	—
33	#14582857	C₂²	1	1	yes	characteristic
34	#14582856	—	2	1	no	—
35	#14582855	C₂²	1	1	yes	characteristic
36	#14582854	C₂²	1	1	yes	characteristic
37	#14582853	—	2	1	no	—
38	#97×D₄₃	—	2	1	no	—
39	C₄×C₈×D₄₃	—	2	1	no	—
40	#14582668	C₂²	1	2	yes	—
41	#14582667	C₂²	1	2	yes	—
42	#14582667	C₂²	1	2	yes	—
43	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#428	C₂²	1	2	yes	—
45	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
46	C₄₃×#405	C₂²	1	1	yes	characteristic
47	C₄₃×#343	C₂²	1	2	yes	—
48	C₂²×C₄×D₄₃	—	2	2	no	—
49	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
50	C₂×#10621877	C₂³	1	2	yes	—
51	C₂×#10621877	C₂³	1	1	yes	characteristic
52	C₂×#10621872	—	2	1	no	—
53	C₂×#10621872	—	2	2	no	—
54	M₁₆×D₄₃	—	2	4	no	—
55	M₁₆×D₄₃	—	2	2	no	—
56	M₁₆×D₄₃	C₂×C₄	1	8	yes	—
57	M₁₆×D₄₃	Q₈	1	4	yes	—
58	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₄₃	—	2	1	no	—
60	C₂×C₈×D₄₃	—	2	2	no	—
61	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
62	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
66	C₂×C₈×D₄₃	Q₈	1	4	yes	—
67	#13063284	C₂³	1	1	yes	characteristic
68	#13063283	D₄	1	1	yes	characteristic
69	#13063283	D₄	1	1	yes	characteristic
70	#13063282	—	2	1	no	—
71	#13063281	—	2	1	no	—
72	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
73	C₂×Dic₄₃⋊C₄	—	2	2	no	—
74	C₄⋊C₄×D₄₃	—	2	2	no	—
75	C₄⋊C₄×D₄₃	—	2	2	no	—
76	C₄⋊C₄×D₄₃	—	2	2	no	—
77	C₄⋊C₄×D₄₃	—	2	2	no	—
78	C₄⋊C₄×D₄₃	D₄	1	1	yes	characteristic
79	C₄⋊C₄×D₄₃	D₄	1	1	yes	characteristic
80	C₂²⋊C₄×D₄₃	—	2	1	no	—
81	C₄²×D₄₃	—	2	1	no	—
82	#13063261	C₂×C₄	1	4	yes	complemented
83	#13063260	C₂×C₄	1	8	yes	complemented
84	#13063259	—	2	1	no	—
85	#13063259	—	2	1	no	—
86	#13063259	—	2	2	no	—
87	#13063258	—	2	2	no	—
88	#13063258	—	2	2	no	—
89	#13063258	—	2	2	no	—
90	#13063258	—	2	2	no	—
91	#13063257	—	2	2	no	—
92	#13063256	—	2	2	no	—
93	#13063256	—	2	2	no	—
94	#13063236	—	2	1	no	—
95	#13063235	—	2	1	no	—
96	#13063235	—	2	1	no	—
97	C₄×C₄₃⋊C₈	—	2	1	no	—
98	C₈×Dic₄₃	—	2	1	no	—
99	C₈×Dic₄₃	—	2	1	no	—
100	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
101	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	#117×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
105	#108×C₄₃	C₂×C₄	1	4	yes	complemented
106	#107×C₄₃	—	2	1	no	—
107	#107×C₄₃	—	2	1	no	—
108	#107×C₄₃	—	2	2	no	—
109	#106×C₄₃	—	2	2	no	—
110	#97×C₄₃	—	2	1	no	—
111	C₄×C₈×C₄₃	—	2	1	no	—
112	C₂³×D₄₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₄₃	—	2	2	no	—
116	C₂²×Dic₄₃	#41	1	1	yes	characteristic
117	C₂×C₄×D₄₃	—	2	1	no	—
118	C₂×C₄×D₄₃	—	2	1	no	—
119	C₂×C₄×D₄₃	—	4	2	no	—
120	C₂×C₄×D₄₃	—	4	2	no	—
121	C₂×C₄×D₄₃	—	8	4	no	—
122	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
123	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
128	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
129	C₂×C₄×D₄₃	#41	1	2	yes	—
130	M₁₆×C₄₃	—	2	2	no	—
131	M₁₆×C₄₃	—	2	1	no	—
132	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
133	M₁₆×C₄₃	C₂×Q₈	1	2	yes	—
134	C₂×C₈×C₄₃	—	2	1	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
140	C₄⋊C₄×C₄₃	—	2	2	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂²⋊C₄×C₄₃	—	2	1	no	—
145	C₄²×C₄₃	—	2	1	no	—
146	C₂²⋊Dic₄₃	—	2	1	no	—
147	(C₂×D₄₃)⋊C₄	—	2	1	no	—
148	(C₂×D₄₃)⋊C₄	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	2	no	—
150	C₄⋊Dic₄₃	—	2	2	no	—
151	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
152	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
153	Dic₄₃⋊C₄	—	2	1	no	—
154	Dic₄₃⋊C₄	—	2	1	no	—
155	Dic₄₃⋊C₄	—	4	2	no	—
156	Dic₄₃⋊C₄	—	4	2	no	—
157	C₄×Dic₄₃	—	2	1	no	—
158	C₄×Dic₄₃	—	2	1	no	—
159	C₄×Dic₄₃	—	2	1	no	—
160	#10621877	—	2	2	no	—
161	#10621877	—	2	1	no	—
162	#10621877	C₂²×C₄	1	4	yes	—
163	#10621877	C₂×Q₈	1	2	yes	—
164	C₂×C₄₃⋊C₈	—	2	1	no	—
165	C₂×C₄₃⋊C₈	—	2	2	no	—
166	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
167	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
170	#10621872	—	2	8	no	—
171	#10621872	—	2	4	no	—
172	C₈×D₄₃	—	2	8	no	—
173	C₈×D₄₃	—	2	4	no	—
174	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
175	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
176	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
177	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
178	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂²×D₄₃	—	2	2	no	—
180	C₂²×D₄₃	—	2	2	no	—
181	C₂²×D₄₃	C₄×Q₈	1	2	yes	—
182	C₂²×D₄₃	#121	1	1	yes	characteristic
183	C₂²×D₄₃	#121	1	1	yes	characteristic
184	C₂²×D₄₃	#125	1	2	yes	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	8	2	no	—
189	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
195	C₂×Dic₄₃	—	2	1	no	—
196	C₂×Dic₄₃	—	2	1	no	—
197	C₂×Dic₄₃	—	4	2	no	—
198	C₂×Dic₄₃	—	8	2	no	—
199	C₂×Dic₄₃	C₄×Q₈	1	2	yes	—
200	C₂×Dic₄₃	#121	1	1	yes	characteristic
201	C₂×Dic₄₃	#121	1	1	yes	characteristic
202	C₂×Dic₄₃	#125	1	2	yes	—
203	C₄×D₄₃	—	4	2	no	—
204	C₄×D₄₃	—	4	2	no	—
205	C₄×D₄₃	—	8	4	no	—
206	C₄×D₄₃	—	8	4	no	—
207	C₄×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
208	C₄×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
209	C₄×D₄₃	C₄×D₄	1	2	yes	—
210	C₄×D₄₃	C₄×D₄	1	2	yes	—
211	C₄×D₄₃	C₂²⋊Q₈	1	2	yes	—
212	C₄×D₄₃	C₂²⋊Q₈	1	2	yes	—
213	C₄×D₄₃	C₄⋊Q₈	1	2	yes	—
214	C₄×D₄₃	C₄⋊Q₈	1	2	yes	—
215	C₈×C₄₃	—	2	4	no	—
216	C₈×C₄₃	—	2	2	no	—
217	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
218	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
219	C₄₃⋊C₈	—	2	4	no	—
220	C₄₃⋊C₈	—	2	2	no	—
221	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
222	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
223	C₂×#1952	—	43	1	no	maximal, Sylow
224	C₂²×C₄₃	—	2	1	no	—
225	C₂²×C₄₃	—	2	1	no	—
226	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
227	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
228	C₂²×C₄₃	C₂×#125	1	1	yes	characteristic
229	C₂×D₄₃	—	2	1	no	—
230	C₂×D₄₃	—	2	1	no	—
231	C₂×D₄₃	—	2	4	no	—
232	C₂×D₄₃	—	2	4	no	—
233	C₂×D₄₃	#389	1	2	yes	—
234	C₂×D₄₃	#389	1	2	yes	—
235	C₂×D₄₃	#472	1	2	yes	—
236	C₂×D₄₃	#473	1	2	yes	—
237	C₄×C₄₃	—	4	1	no	—
238	C₄×C₄₃	—	4	1	no	—
239	C₄×C₄₃	—	8	2	no	—
240	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
241	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
242	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₄×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
244	Dic₄₃	—	4	1	no	—
245	Dic₄₃	—	4	1	no	—
246	Dic₄₃	—	8	2	no	—
247	Dic₄₃	#389	1	2	yes	—
248	Dic₄₃	#389	1	2	yes	—
249	C₂²×#108	—	43	1	no	—
250	C₂×#428	—	43	2	no	—
251	C₂²×#107	—	43	1	no	—
252	C₂×#405	—	43	1	no	—
253	#1952	—	43	1	no	—
254	#1952	—	43	2	no	—
255	#1952	—	43	1	no	—
256	#1952	—	43	1	no	—
257	#1952	—	43	2	no	—
258	#1952	D₄₃	1	1	yes	characteristic, direct product factor
259	C₂×#343	—	43	2	no	—
260	C₂×C₄₃	—	2	1	no	—
261	C₂×C₄₃	—	2	1	no	—
262	C₂×C₄₃	C₂×#389	1	1	yes	characteristic
263	C₂×C₄₃	C₂×#472	1	1	yes	characteristic
264	C₂×C₄₃	C₂×#473	1	1	yes	characteristic
265	D₄₃	—	2	2	no	—
266	D₄₃	#1952	1	4	yes	direct product factor
267	C₂²×M₁₆	—	43	1	no	—
268	C₂²×M₁₆	—	43	2	no	—
269	C₂³×C₈	—	43	1	no	—
270	C₂×#117	—	43	1	no	—
271	C₂²×C₄⋊C₄	—	43	2	no	—
272	C₂×#108	—	43	2	no	—
273	C₂×#108	—	43	1	no	—
274	C₂×#108	—	43	8	no	—
275	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
276	#428	—	43	2	no	—
277	#428	—	43	2	no	—
278	#428	—	43	2	no	—
279	#428	—	86	2	no	—
280	#428	—	86	2	no	—
281	#428	C₂×D₄₃	1	2	yes	—
282	C₂×#107	—	43	1	no	—
283	C₂×#107	—	43	2	no	—
284	C₂×#107	—	86	2	no	—
285	C₂×#107	—	86	1	no	—
286	C₂×#107	—	86	1	no	—
287	C₂×#107	—	86	1	no	—
288	C₂×#107	—	86	1	no	—
289	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
290	C₂×#106	—	86	2	no	—
291	#405	—	43	1	no	—
292	#405	—	43	1	no	—
293	#405	—	43	1	no	—
294	#405	—	86	1	no	—
295	#405	—	86	1	no	—
296	#405	C₂×D₄₃	1	1	yes	characteristic
297	C₂×#97	—	86	1	no	—
298	C₂×C₄×C₈	—	86	1	no	—
299	#343	—	43	2	no	—
300	#343	—	43	2	no	—
301	#343	—	43	2	no	—
302	#343	C₂×D₄₃	1	2	yes	—
303	C₄₃	C₂×#1952	1	1	yes	characteristic, complemented, Sylow
304	C₂³×C₄	—	43	1	no	—
305	C₂³×C₄	—	86	2	no	—
306	C₂×M₁₆	—	43	1	no	—
307	C₂×M₁₆	—	43	2	no	—
308	C₂×M₁₆	—	43	8	no	—
309	C₂×M₁₆	—	43	4	no	—
310	C₂×M₁₆	—	86	1	no	—
311	C₂×M₁₆	—	86	2	no	—
312	C₂×M₁₆	—	86	2	no	—
313	C₂×M₁₆	—	86	4	no	—
314	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
315	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
316	C₂²×C₈	—	43	1	no	—
317	C₂²×C₈	—	43	4	no	—
318	C₂²×C₈	—	43	1	no	—
319	C₂²×C₈	—	43	1	no	—
320	C₂²×C₈	—	43	1	no	—
321	C₂²×C₈	—	43	1	no	—
322	C₂²×C₈	—	43	4	no	—
323	C₂²×C₈	—	86	1	no	—
324	C₂²×C₈	—	86	2	no	—
325	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
326	#117	—	43	1	no	—
327	#117	—	43	1	no	—
328	#117	—	43	1	no	—
329	#117	—	86	1	no	—
330	#117	—	86	1	no	—
331	#117	C₂²×D₄₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	—	43	1	no	—
333	C₂×C₄⋊C₄	—	43	1	no	—
334	C₂×C₄⋊C₄	—	43	2	no	—
335	C₂×C₄⋊C₄	—	86	2	no	—
336	C₂×C₄⋊C₄	—	86	2	no	—
337	C₂×C₄⋊C₄	—	86	2	no	—
338	C₂×C₄⋊C₄	—	86	2	no	—
339	C₂×C₄⋊C₄	—	86	2	no	—
340	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
341	C₂×C₂²⋊C₄	—	86	1	no	—
342	C₂×C₄²	—	86	1	no	—
343	#108	—	43	8	no	—
344	#108	—	43	4	no	—
345	#108	C₄×D₄₃	1	4	yes	complemented
346	#107	—	2	1	no	—
347	#107	—	2	1	no	—
348	#107	—	2	2	no	—
349	#107	—	86	2	no	—
350	#107	—	86	2	no	—
351	#107	—	86	2	no	—
352	#107	—	86	2	no	—
353	#107	—	86	1	no	—
354	#107	—	86	1	no	—
355	#107	—	86	2	no	—
356	#106	—	2	2	no	—
357	#106	—	86	2	no	—
358	#106	—	86	2	no	—
359	#106	—	86	2	no	—
360	#97	—	2	1	no	—
361	#97	—	86	1	no	—
362	#97	—	86	1	no	—
363	#97	—	86	1	no	—
364	C₄×C₈	—	2	1	no	—
365	C₄×C₈	—	86	1	no	—
366	C₄×C₈	—	86	1	no	—
367	C₄×C₈	—	86	1	no	—
368	C₂⁴	—	43	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	43	1	no	—
371	C₂²×C₄	—	43	2	no	—
372	C₂²×C₄	—	43	1	no	—
373	C₂²×C₄	—	43	1	no	—
374	C₂²×C₄	—	43	1	no	—
375	C₂²×C₄	—	43	1	no	—
376	C₂²×C₄	—	43	2	no	—
377	C₂²×C₄	—	43	2	no	—
378	C₂²×C₄	—	43	2	no	—
379	C₂²×C₄	—	86	1	no	—
380	C₂²×C₄	—	86	1	no	—
381	C₂²×C₄	—	86	2	no	—
382	C₂²×C₄	—	344	4	no	—
383	C₂²×C₄	—	172	2	no	—
384	C₂²×C₄	—	172	2	no	—
385	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	43	4	no	—
389	M₁₆	—	43	2	no	—
390	M₁₆	—	86	8	no	—
391	M₁₆	—	86	4	no	—
392	M₁₆	—	86	2	no	—
393	M₁₆	—	86	1	no	—
394	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
395	M₁₆	Q₈×D₄₃	1	2	yes	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	43	2	no	—
399	C₂×C₈	—	43	1	no	—
400	C₂×C₈	—	43	1	no	—
401	C₂×C₈	—	43	2	no	—
402	C₂×C₈	—	43	4	no	—
403	C₂×C₈	—	43	4	no	—
404	C₂×C₈	—	43	4	no	—
405	C₂×C₈	—	43	4	no	—
406	C₂×C₈	—	86	8	no	—
407	C₂×C₈	—	86	4	no	—
408	C₂×C₈	—	86	1	no	—
409	C₂×C₈	—	86	2	no	—
410	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
411	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
412	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
413	C₂×C₈	Q₈×D₄₃	1	2	yes	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	43	1	no	—
417	C₄⋊C₄	—	43	1	no	—
418	C₄⋊C₄	—	86	1	no	—
419	C₄⋊C₄	—	86	1	no	—
420	C₄⋊C₄	—	86	2	no	—
421	C₄⋊C₄	—	86	2	no	—
422	C₄⋊C₄	—	172	2	no	—
423	C₄⋊C₄	—	172	2	no	—
424	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
425	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	86	1	no	—
428	C₂²⋊C₄	—	86	1	no	—
429	C₂²⋊C₄	—	86	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	86	1	no	—
432	C₄²	—	86	1	no	—
433	C₄²	—	86	1	no	—
434	C₂³	—	43	1	no	—
435	C₂³	—	43	2	no	—
436	C₂³	—	43	1	no	—
437	C₂³	—	43	2	no	—
438	C₂³	—	86	2	no	—
439	C₂³	—	86	2	no	—
440	C₂³	#41×D₄₃	1	1	yes	characteristic
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	—	43	2	no	—
446	C₂×C₄	—	43	1	no	—
447	C₂×C₄	—	43	1	no	—
448	C₂×C₄	—	43	2	no	—
449	C₂×C₄	—	43	2	no	—
450	C₂×C₄	—	43	2	no	—
451	C₂×C₄	—	43	2	no	—
452	C₂×C₄	—	43	2	no	—
453	C₂×C₄	—	43	2	no	—
454	C₂×C₄	—	43	2	no	—
455	C₂×C₄	—	43	2	no	—
456	C₂×C₄	—	43	2	no	—
457	C₂×C₄	—	86	1	no	—
458	C₂×C₄	—	86	1	no	—
459	C₂×C₄	—	344	4	no	—
460	C₂×C₄	—	344	4	no	—
461	C₂×C₄	—	344	2	no	—
462	C₂×C₄	—	172	2	no	—
463	C₂×C₄	—	172	2	no	—
464	C₂×C₄	—	172	2	no	—
465	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
467	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
468	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
469	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
470	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
471	C₈	—	2	4	no	—
472	C₈	—	2	2	no	—
473	C₈	—	43	2	no	—
474	C₈	—	43	2	no	—
475	C₈	—	86	4	no	—
476	C₈	—	86	2	no	—
477	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
478	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	43	2	no	—
482	C₂²	—	43	2	no	—
483	C₂²	—	43	2	no	—
484	C₂²	—	43	2	no	—
485	C₂²	—	86	4	no	—
486	C₂²	—	86	4	no	—
487	C₂²	—	86	1	no	—
488	C₂²	—	86	1	no	—
489	C₂²	C₄×Q₈×D₄₃	1	1	yes	characteristic
490	C₂²	#121×D₄₃	1	1	yes	characteristic
491	C₂²	#125×D₄₃	1	1	yes	characteristic
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	8	2	no	—
495	C₄	—	43	2	no	—
496	C₄	—	43	2	no	—
497	C₄	—	344	2	no	—
498	C₄	—	172	1	no	—
499	C₄	—	172	1	no	—
500	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
501	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
502	C₄	C₂²⋊Q₈×D₄₃	1	1	yes	characteristic
503	C₄	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
504	C₂	—	2	1	no	—
505	C₂	—	2	1	no	—
506	C₂	—	43	4	no	—
507	C₂	—	86	2	no	—
508	C₂	#389×D₄₃	1	1	yes	characteristic
509	C₂	#472×D₄₃	1	1	yes	characteristic
510	C₂	#473×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1952	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂³×D₄₃	#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1952	D₄₃
hypocenter	C₄₃	C₂×#1952
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1952

Complements

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

N	H ≅ G/N	type
5. #19135381	C₂	semidirect
6. #19135380	C₂	semidirect
7. #19135379	C₂	semidirect
8. #19135378	C₂	semidirect
9. #19135377	C₂	semidirect
11. C₄₃×#1952	C₂	semidirect
19. #108×D₄₃	C₄	semidirect
82. #13063261	C₂×C₄	semidirect
83. #13063260	C₂×C₄	semidirect
105. #108×C₄₃	C₂×C₄	semidirect
258. #1952	D₄₃	direct (N × H)
266. D₄₃	#1952	direct (N × H)
303. C₄₃	C₂×#1952	semidirect
345. #108	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#108×D₄₃	2
#428×D₄₃	2
C₂×#107×D₄₃	2
#405×D₄₃	2
#19135381	2
#19135380	2
#19135379	2
#19135378	2
#19135377	2
#343×D₄₃	2
C₄₃×#1952	2
C₂×#1952	43

Subgroups — D43×#1952 #25100139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1952 #25100139