Subgroups — D₄₃×#1951 #25100133

Order 11008.

918 conjugacy classes of subgroups.

The subgroup lattice has 476 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×#106×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#405×D₄₃	C₂	1	1	yes	maximal, characteristic
5	#19135376	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135375	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135374	C₂	1	2	yes	maximal, complemented
8	#19135373	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135372	C₂	1	2	yes	maximal, complemented
10	#343×D₄₃	C₂	1	2	yes	maximal
11	C₄₃×#1951	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	#107×D₄₃	—	2	2	no	—
26	C₂×#13063257	C₂²	1	1	yes	characteristic
27	C₂×#13063256	C₂²	1	2	yes	—
28	#106×D₄₃	—	2	1	no	—
29	#106×D₄₃	—	2	1	no	—
30	#106×D₄₃	—	2	1	no	—
31	#106×D₄₃	—	2	1	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×#106×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	2	yes	—
69	#13063282	—	2	1	no	—
70	#13063281	—	2	1	no	—
71	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
72	C₂×Dic₄₃⋊C₄	—	2	2	no	—
73	C₄⋊C₄×D₄₃	—	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	D₄	1	2	yes	—
78	C₂²⋊C₄×D₄₃	—	2	1	no	—
79	C₄²×D₄₃	—	2	1	no	—
80	#13063261	C₂×C₄	1	4	yes	complemented
81	#13063260	C₂×C₄	1	8	yes	complemented
82	#13063259	—	2	2	no	—
83	#13063258	—	2	2	no	—
84	#13063258	—	2	2	no	—
85	#13063257	—	2	1	no	—
86	#13063257	—	2	1	no	—
87	#13063257	—	2	2	no	—
88	#13063256	—	2	2	no	—
89	#13063256	—	2	2	no	—
90	#13063256	—	2	2	no	—
91	#13063256	—	2	2	no	—
92	#13063236	—	2	1	no	—
93	#13063235	—	2	1	no	—
94	#13063235	—	2	1	no	—
95	C₄×C₄₃⋊C₈	—	2	1	no	—
96	C₈×Dic₄₃	—	2	1	no	—
97	C₈×Dic₄₃	—	2	1	no	—
98	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
99	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	#117×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
103	#108×C₄₃	C₂×C₄	1	4	yes	complemented
104	#107×C₄₃	—	2	2	no	—
105	#106×C₄₃	—	2	1	no	—
106	#106×C₄₃	—	2	1	no	—
107	#106×C₄₃	—	2	2	no	—
108	#97×C₄₃	—	2	1	no	—
109	C₄×C₈×C₄₃	—	2	1	no	—
110	C₂³×D₄₃	#41	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₃	—	2	2	no	—
114	C₂²×Dic₄₃	#41	1	1	yes	characteristic
115	C₂×C₄×D₄₃	—	2	2	no	—
116	C₂×C₄×D₄₃	—	4	2	no	—
117	C₂×C₄×D₄₃	—	4	2	no	—
118	C₂×C₄×D₄₃	—	8	4	no	—
119	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
125	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
126	C₂×C₄×D₄₃	#41	1	2	yes	—
127	M₁₆×C₄₃	—	2	2	no	—
128	M₁₆×C₄₃	—	2	1	no	—
129	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
130	M₁₆×C₄₃	C₂×Q₈	1	2	yes	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₄₃	—	2	1	no	—
141	C₄²×C₄₃	—	2	1	no	—
142	C₂²⋊Dic₄₃	—	2	1	no	—
143	(C₂×D₄₃)⋊C₄	—	2	2	no	—
144	C₄⋊Dic₄₃	—	2	2	no	—
145	C₄⋊Dic₄₃	—	2	2	no	—
146	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
147	Dic₄₃⋊C₄	—	2	2	no	—
148	Dic₄₃⋊C₄	—	4	2	no	—
149	Dic₄₃⋊C₄	—	4	2	no	—
150	C₄×Dic₄₃	—	2	1	no	—
151	C₄×Dic₄₃	—	2	2	no	—
152	#10621877	—	2	2	no	—
153	#10621877	—	2	1	no	—
154	#10621877	C₂²×C₄	1	4	yes	—
155	#10621877	C₂×Q₈	1	2	yes	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
162	#10621872	—	2	8	no	—
163	#10621872	—	2	4	no	—
164	C₈×D₄₃	—	2	8	no	—
165	C₈×D₄₃	—	2	4	no	—
166	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
167	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
168	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
169	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
170	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₂²×D₄₃	—	2	4	no	—
172	C₂²×D₄₃	C₄×Q₈	1	2	yes	—
173	C₂²×D₄₃	#121	1	1	yes	characteristic
174	C₂²×D₄₃	#121	1	1	yes	characteristic
175	C₂²×D₄₃	#125	1	2	yes	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	8	2	no	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
185	C₂×Dic₄₃	—	2	2	no	—
186	C₂×Dic₄₃	—	4	2	no	—
187	C₂×Dic₄₃	—	8	2	no	—
188	C₂×Dic₄₃	C₄×Q₈	1	2	yes	—
189	C₂×Dic₄₃	#121	1	1	yes	characteristic
190	C₂×Dic₄₃	#121	1	1	yes	characteristic
191	C₂×Dic₄₃	#125	1	2	yes	—
192	C₄×D₄₃	—	4	4	no	—
193	C₄×D₄₃	—	8	4	no	—
194	C₄×D₄₃	—	8	4	no	—
195	C₄×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
196	C₄×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
197	C₄×D₄₃	C₄×D₄	1	2	yes	—
198	C₄×D₄₃	C₄×D₄	1	2	yes	—
199	C₄×D₄₃	C₂²⋊Q₈	1	2	yes	—
200	C₄×D₄₃	C₂²⋊Q₈	1	2	yes	—
201	C₄×D₄₃	C₄⋊Q₈	1	2	yes	—
202	C₄×D₄₃	C₄⋊Q₈	1	2	yes	—
203	C₈×C₄₃	—	2	4	no	—
204	C₈×C₄₃	—	2	2	no	—
205	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
206	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
207	C₄₃⋊C₈	—	2	4	no	—
208	C₄₃⋊C₈	—	2	2	no	—
209	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
210	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×#1951	—	43	1	no	maximal, Sylow
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
214	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
215	C₂²×C₄₃	C₂×#125	1	1	yes	characteristic
216	C₂×D₄₃	—	2	2	no	—
217	C₂×D₄₃	—	2	4	no	—
218	C₂×D₄₃	—	2	4	no	—
219	C₂×D₄₃	#389	1	2	yes	—
220	C₂×D₄₃	#389	1	2	yes	—
221	C₂×D₄₃	#471	1	4	yes	—
222	C₄×C₄₃	—	4	2	no	—
223	C₄×C₄₃	—	8	2	no	—
224	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
225	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₄×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
228	Dic₄₃	—	4	2	no	—
229	Dic₄₃	—	8	2	no	—
230	Dic₄₃	#389	1	2	yes	—
231	Dic₄₃	#389	1	2	yes	—
232	C₂²×#108	—	43	1	no	—
233	C₂×#428	—	43	2	no	—
234	C₂²×#106	—	43	1	no	—
235	C₂×#405	—	43	1	no	—
236	#1951	—	43	1	no	—
237	#1951	—	43	2	no	—
238	#1951	—	43	1	no	—
239	#1951	—	43	1	no	—
240	#1951	—	43	2	no	—
241	#1951	D₄₃	1	1	yes	characteristic, direct product factor
242	C₂×#343	—	43	2	no	—
243	C₂×C₄₃	—	2	1	no	—
244	C₂×C₄₃	—	2	1	no	—
245	C₂×C₄₃	C₂×#389	1	1	yes	characteristic
246	C₂×C₄₃	C₂×#471	1	2	yes	—
247	D₄₃	—	2	2	no	—
248	D₄₃	#1951	1	4	yes	direct product factor
249	C₂²×M₁₆	—	43	1	no	—
250	C₂²×M₁₆	—	43	2	no	—
251	C₂³×C₈	—	43	1	no	—
252	C₂×#117	—	43	1	no	—
253	C₂²×C₄⋊C₄	—	43	2	no	—
254	C₂×#108	—	43	2	no	—
255	C₂×#108	—	43	1	no	—
256	C₂×#108	—	43	8	no	—
257	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
258	#428	—	43	2	no	—
259	#428	—	43	2	no	—
260	#428	—	43	2	no	—
261	#428	—	86	2	no	—
262	#428	—	86	2	no	—
263	#428	C₂×D₄₃	1	2	yes	—
264	C₂×#107	—	86	2	no	—
265	C₂×#106	—	43	1	no	—
266	C₂×#106	—	43	2	no	—
267	C₂×#106	—	86	2	no	—
268	C₂×#106	—	86	1	no	—
269	C₂×#106	—	86	1	no	—
270	C₂×#106	—	86	1	no	—
271	C₂×#106	—	86	1	no	—
272	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
273	#405	—	43	1	no	—
274	#405	—	43	1	no	—
275	#405	—	43	1	no	—
276	#405	—	86	1	no	—
277	#405	—	86	1	no	—
278	#405	C₂×D₄₃	1	1	yes	characteristic
279	C₂×#97	—	86	1	no	—
280	C₂×C₄×C₈	—	86	1	no	—
281	#343	—	43	2	no	—
282	#343	—	43	2	no	—
283	#343	—	43	2	no	—
284	#343	C₂×D₄₃	1	2	yes	—
285	C₄₃	C₂×#1951	1	1	yes	characteristic, complemented, Sylow
286	C₂³×C₄	—	43	1	no	—
287	C₂³×C₄	—	86	2	no	—
288	C₂×M₁₆	—	43	1	no	—
289	C₂×M₁₆	—	43	2	no	—
290	C₂×M₁₆	—	43	8	no	—
291	C₂×M₁₆	—	43	4	no	—
292	C₂×M₁₆	—	86	1	no	—
293	C₂×M₁₆	—	86	2	no	—
294	C₂×M₁₆	—	86	2	no	—
295	C₂×M₁₆	—	86	4	no	—
296	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
297	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
298	C₂²×C₈	—	43	1	no	—
299	C₂²×C₈	—	43	4	no	—
300	C₂²×C₈	—	43	1	no	—
301	C₂²×C₈	—	43	1	no	—
302	C₂²×C₈	—	43	1	no	—
303	C₂²×C₈	—	43	1	no	—
304	C₂²×C₈	—	43	4	no	—
305	C₂²×C₈	—	86	1	no	—
306	C₂²×C₈	—	86	2	no	—
307	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
308	#117	—	43	1	no	—
309	#117	—	43	2	no	—
310	#117	—	86	1	no	—
311	#117	—	86	1	no	—
312	#117	C₂²×D₄₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	—	43	2	no	—
314	C₂×C₄⋊C₄	—	43	2	no	—
315	C₂×C₄⋊C₄	—	86	2	no	—
316	C₂×C₄⋊C₄	—	86	2	no	—
317	C₂×C₄⋊C₄	—	86	2	no	—
318	C₂×C₄⋊C₄	—	86	2	no	—
319	C₂×C₄⋊C₄	—	86	2	no	—
320	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
321	C₂×C₂²⋊C₄	—	86	1	no	—
322	C₂×C₄²	—	86	1	no	—
323	#108	—	43	8	no	—
324	#108	—	43	4	no	—
325	#108	C₄×D₄₃	1	4	yes	complemented
326	#107	—	2	2	no	—
327	#107	—	86	2	no	—
328	#107	—	86	2	no	—
329	#107	—	86	2	no	—
330	#106	—	2	1	no	—
331	#106	—	2	1	no	—
332	#106	—	2	2	no	—
333	#106	—	86	2	no	—
334	#106	—	86	2	no	—
335	#106	—	86	2	no	—
336	#106	—	86	2	no	—
337	#106	—	86	1	no	—
338	#106	—	86	1	no	—
339	#106	—	86	2	no	—
340	#97	—	2	1	no	—
341	#97	—	86	1	no	—
342	#97	—	86	1	no	—
343	#97	—	86	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	—	86	1	no	—
346	C₄×C₈	—	86	1	no	—
347	C₄×C₈	—	86	1	no	—
348	C₂⁴	—	43	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	43	1	no	—
351	C₂²×C₄	—	43	2	no	—
352	C₂²×C₄	—	43	1	no	—
353	C₂²×C₄	—	43	1	no	—
354	C₂²×C₄	—	43	1	no	—
355	C₂²×C₄	—	43	1	no	—
356	C₂²×C₄	—	43	2	no	—
357	C₂²×C₄	—	43	2	no	—
358	C₂²×C₄	—	43	2	no	—
359	C₂²×C₄	—	86	2	no	—
360	C₂²×C₄	—	86	2	no	—
361	C₂²×C₄	—	344	4	no	—
362	C₂²×C₄	—	172	2	no	—
363	C₂²×C₄	—	172	2	no	—
364	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	43	4	no	—
368	M₁₆	—	43	2	no	—
369	M₁₆	—	86	8	no	—
370	M₁₆	—	86	4	no	—
371	M₁₆	—	86	2	no	—
372	M₁₆	—	86	1	no	—
373	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
374	M₁₆	Q₈×D₄₃	1	2	yes	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	43	2	no	—
378	C₂×C₈	—	43	1	no	—
379	C₂×C₈	—	43	1	no	—
380	C₂×C₈	—	43	2	no	—
381	C₂×C₈	—	43	4	no	—
382	C₂×C₈	—	43	4	no	—
383	C₂×C₈	—	43	4	no	—
384	C₂×C₈	—	43	4	no	—
385	C₂×C₈	—	86	8	no	—
386	C₂×C₈	—	86	4	no	—
387	C₂×C₈	—	86	1	no	—
388	C₂×C₈	—	86	2	no	—
389	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
390	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
391	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
392	C₂×C₈	Q₈×D₄₃	1	2	yes	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	43	2	no	—
396	C₄⋊C₄	—	86	2	no	—
397	C₄⋊C₄	—	86	2	no	—
398	C₄⋊C₄	—	86	2	no	—
399	C₄⋊C₄	—	172	2	no	—
400	C₄⋊C₄	—	172	2	no	—
401	C₄⋊C₄	D₄×D₄₃	1	2	yes	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	86	2	no	—
404	C₂²⋊C₄	—	86	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	86	2	no	—
407	C₄²	—	86	1	no	—
408	C₂³	—	43	1	no	—
409	C₂³	—	43	2	no	—
410	C₂³	—	43	1	no	—
411	C₂³	—	43	2	no	—
412	C₂³	—	86	4	no	—
413	C₂³	#41×D₄₃	1	1	yes	characteristic
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	—	43	2	no	—
418	C₂×C₄	—	43	1	no	—
419	C₂×C₄	—	43	1	no	—
420	C₂×C₄	—	43	2	no	—
421	C₂×C₄	—	43	2	no	—
422	C₂×C₄	—	43	2	no	—
423	C₂×C₄	—	43	2	no	—
424	C₂×C₄	—	43	2	no	—
425	C₂×C₄	—	43	2	no	—
426	C₂×C₄	—	43	2	no	—
427	C₂×C₄	—	43	2	no	—
428	C₂×C₄	—	43	2	no	—
429	C₂×C₄	—	86	2	no	—
430	C₂×C₄	—	344	4	no	—
431	C₂×C₄	—	344	4	no	—
432	C₂×C₄	—	344	2	no	—
433	C₂×C₄	—	172	4	no	—
434	C₂×C₄	—	172	2	no	—
435	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
437	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
438	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
440	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
441	C₈	—	2	4	no	—
442	C₈	—	2	2	no	—
443	C₈	—	43	2	no	—
444	C₈	—	43	2	no	—
445	C₈	—	86	4	no	—
446	C₈	—	86	2	no	—
447	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
448	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
449	C₂²	—	2	2	no	—
450	C₂²	—	43	2	no	—
451	C₂²	—	43	4	no	—
452	C₂²	—	43	2	no	—
453	C₂²	—	86	4	no	—
454	C₂²	—	86	4	no	—
455	C₂²	—	86	2	no	—
456	C₂²	C₄×Q₈×D₄₃	1	1	yes	characteristic
457	C₂²	#121×D₄₃	1	1	yes	characteristic
458	C₂²	#125×D₄₃	1	1	yes	characteristic
459	C₄	—	4	2	no	—
460	C₄	—	8	2	no	—
461	C₄	—	43	2	no	—
462	C₄	—	43	2	no	—
463	C₄	—	344	2	no	—
464	C₄	—	172	2	no	—
465	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
466	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
467	C₄	C₂²⋊Q₈×D₄₃	1	1	yes	characteristic
468	C₄	C₄⋊Q₈×D₄₃	1	1	yes	characteristic
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	43	4	no	—
472	C₂	—	86	2	no	—
473	C₂	#389×D₄₃	1	1	yes	characteristic
474	C₂	#471×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂²	#121×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1951	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂³×D₄₃	#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1951	D₄₃
hypocenter	C₄₃	C₂×#1951
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1951

Complements

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

N	H ≅ G/N	type
5. #19135376	C₂	semidirect
6. #19135375	C₂	semidirect
7. #19135374	C₂	semidirect
8. #19135373	C₂	semidirect
9. #19135372	C₂	semidirect
11. C₄₃×#1951	C₂	semidirect
19. #108×D₄₃	C₄	semidirect
80. #13063261	C₂×C₄	semidirect
81. #13063260	C₂×C₄	semidirect
103. #108×C₄₃	C₂×C₄	semidirect
241. #1951	D₄₃	direct (N × H)
248. D₄₃	#1951	direct (N × H)
285. C₄₃	C₂×#1951	semidirect
325. #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×#106×D₄₃	2
#405×D₄₃	2
#19135376	2
#19135375	2
#19135374	2
#19135373	2
#19135372	2
#343×D₄₃	2
C₄₃×#1951	2
C₂×#1951	43

Subgroups — D43×#1951 #25100133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1951 #25100133