Subgroups — #25960986

Order 11008.

1810 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147998	C₂	1	1	yes	maximal, characteristic
2	#19143536	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143534	C₂	1	2	yes	maximal, complemented
4	#19143532	C₂	1	1	yes	maximal, characteristic, complemented
5	#19143531	C₂	1	8	yes	maximal, complemented
6	#19143529	C₂	1	1	yes	maximal, characteristic, complemented
7	#19143527	C₂	1	2	yes	maximal, complemented
8	#19143524	C₂	1	8	yes	maximal, complemented
9	#19143157	C₂	1	1	yes	maximal, characteristic
10	#19143156	C₂	1	2	yes	maximal
11	C₂×#14582853	C₂	1	1	yes	maximal, characteristic
12	#405×D₄₃	C₂	1	2	yes	maximal
13	C₄₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#10621872	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×D₄₃	C₂²	1	2	yes	—
16	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
17	#14583529	C₄	1	4	yes	—
18	#14583528	C₄	1	4	yes	—
19	#14583526	C₄	1	4	yes	—
20	#14583524	C₄	1	4	yes	—
21	#14583456	C₂²	1	1	yes	characteristic
22	#14583453	C₂²	1	8	yes	—
23	#14583452	C₂²	1	2	yes	—
24	C₂×#13063282	C₂²	1	1	yes	characteristic
25	#117×D₄₃	C₂²	1	2	yes	—
26	#14583030	C₂²	1	8	yes	complemented
27	#14583029	C₂²	1	4	yes	complemented
28	#14583028	C₂²	1	8	yes	complemented
29	#14583028	C₂²	1	8	yes	complemented
30	#14583027	C₂²	1	8	yes	complemented
31	#14583026	C₂²	1	8	yes	complemented
32	C₈×Dic₈₆	C₂²	1	8	yes	complemented
33	C₈×Dic₈₆	C₂²	1	4	yes	complemented
34	#14582927	C₂²	1	2	yes	—
35	#14582926	C₂²	1	2	yes	—
36	#14582925	C₂²	1	2	yes	—
37	#14582924	C₂²	1	8	yes	—
38	#14582924	C₂²	1	8	yes	—
39	#14582923	C₂²	1	1	yes	characteristic
40	#14582922	C₂²	1	2	yes	—
41	#14582921	C₂²	1	8	yes	—
42	#14582857	C₂²	1	2	yes	—
43	#14582856	C₂²	1	4	yes	—
44	#14582855	C₂²	1	2	yes	—
45	#14582854	C₂²	1	2	yes	—
46	#14582853	C₂²	1	4	yes	—
47	#14582853	C₂²	1	4	yes	—
48	#14582853	C₂²	1	4	yes	—
49	C₂×#13063236	C₂²	1	1	yes	characteristic
50	C₂×#13063235	C₂²	1	1	yes	characteristic
51	#97×D₄₃	C₂²	1	4	yes	—
52	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
53	C₄×C₈×D₄₃	C₂²	1	4	yes	—
54	C₄₃×#533	C₂²	1	1	yes	characteristic
55	C₄₃×#446	C₂²	1	4	yes	complemented
56	C₈×Q₈×C₄₃	C₂²	1	4	yes	complemented
57	C₄₃×#424	C₂²	1	2	yes	—
58	C₄₃×#423	C₂²	1	1	yes	characteristic
59	C₄₃×#405	C₂²	1	2	yes	—
60	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
61	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
62	C₂×#10621877	C₂³	1	2	yes	—
63	C₂×#10621872	—	2	4	no	—
64	C₂×#10621872	C₂³	1	4	yes	—
65	C₂×#10621872	C₂³	1	4	yes	—
66	M₁₆×D₄₃	—	2	8	no	—
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×C₈×D₄₃	Q₈	1	8	yes	complemented
70	C₂×C₈×D₄₃	C₂³	1	4	yes	—
71	C₂×C₈×D₄₃	C₂³	1	2	yes	—
72	C₂×C₈×D₄₃	C₂³	1	2	yes	—
73	#13063325	C₂×C₄	1	2	yes	—
74	#13063324	C₂×C₄	1	4	yes	—
75	#13063324	C₂×C₄	1	8	yes	—
76	#13063323	C₂×C₄	1	8	yes	—
77	#13063317	C₂×C₄	1	2	yes	—
78	#13063316	C₂×C₄	1	4	yes	—
79	#13063315	C₂×C₄	1	8	yes	—
80	#13063315	C₂×C₄	1	8	yes	—
81	#13063305	C₂×C₄	1	8	yes	—
82	#13063304	C₂×C₄	1	4	yes	—
83	#13063303	C₂×C₄	1	8	yes	—
84	#13063303	C₂×C₄	1	8	yes	—
85	#13063302	C₂×C₄	1	8	yes	—
86	#13063301	C₂×C₄	1	8	yes	—
87	C₄×Dic₈₆	C₂³	1	8	yes	—
88	C₄×Dic₈₆	C₂³	1	4	yes	—
89	#13063284	C₂³	1	2	yes	—
90	#13063283	C₂×C₄	1	4	yes	—
91	#13063282	C₂×C₄	1	2	yes	—
92	#13063282	C₂×C₄	1	2	yes	—
93	#13063282	C₂³	1	4	yes	—
94	#13063282	C₂³	1	4	yes	—
95	#13063281	C₂×C₄	1	4	yes	—
96	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
97	C₄⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
98	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
99	C₂²⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
100	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
101	C₄²×D₄₃	C₂³	1	4	yes	—
102	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
103	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
104	Dic₄₃⋊C₈	C₂³	1	8	yes	—
105	Dic₄₃⋊C₈	C₂³	1	8	yes	—
106	Dic₄₃⋊C₈	C₂³	1	8	yes	—
107	#13063236	C₂³	1	4	yes	—
108	#13063236	C₂³	1	4	yes	—
109	#13063235	C₂³	1	4	yes	—
110	#13063235	C₂³	1	4	yes	—
111	#13063235	C₂³	1	4	yes	—
112	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
113	C₈×Dic₄₃	C₂³	1	4	yes	—
114	C₈×Dic₄₃	C₂³	1	4	yes	—
115	C₈×Dic₄₃	C₂³	1	2	yes	—
116	C₈×Dic₄₃	C₂³	1	2	yes	—
117	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
118	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
121	#125×C₄₃	C₂×C₄	1	2	yes	—
122	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
123	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
124	#117×C₄₃	C₂³	1	2	yes	—
125	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
126	C₄⋊C₈×C₄₃	C₂³	1	8	yes	—
127	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
128	#97×C₄₃	C₂³	1	4	yes	—
129	C₄×C₈×C₄₃	C₂³	1	4	yes	—
130	C₄×C₈×C₄₃	C₂³	1	2	yes	—
131	C₄×C₈×C₄₃	C₂³	1	2	yes	—
132	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
134	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
136	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
137	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
139	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
140	C₂×C₄×D₄₃	C₂×Q₈	1	4	yes	—
141	C₂×C₄×D₄₃	#41	1	4	yes	—
142	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
143	C₂×Dic₈₆	C₂²×C₄	1	8	yes	—
144	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
145	M₁₆×C₄₃	—	2	4	no	—
146	C₂×C₈×C₄₃	—	2	2	no	—
147	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
148	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
149	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
150	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
153	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
154	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
155	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
156	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₄₃	C₂⁴	1	2	yes	—
159	C₄²×C₄₃	C₂⁴	1	4	yes	—
160	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
161	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	8	yes	—
162	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
163	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
164	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
165	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
166	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
167	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
168	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
169	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
170	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
171	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
172	Dic₄₃⋊C₄	C₂²×C₄	1	8	yes	—
173	C₄×Dic₄₃	C₂²×C₄	1	8	yes	—
174	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
175	C₄×Dic₄₃	C₂⁴	1	4	yes	—
176	C₄×Dic₄₃	C₂⁴	1	2	yes	—
177	#10621877	—	2	4	no	—
178	C₂×C₄₃⋊C₈	—	2	2	no	—
179	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
180	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
181	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
182	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
183	#10621872	—	2	8	no	—
184	#10621872	—	2	8	no	—
185	C₈×D₄₃	—	2	8	no	—
186	C₈×D₄₃	C₂×Q₈	1	8	yes	—
187	C₈×D₄₃	C₂×Q₈	1	8	yes	—
188	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
189	C₂²×D₄₃	—	4	2	no	—
190	C₂²×D₄₃	C₄×Q₈	1	4	yes	—
191	C₂²×D₄₃	C₂³×C₄	1	2	yes	—
192	Q₈×C₄₃	—	4	4	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
195	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
196	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
199	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
200	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
201	C₂×Dic₄₃	—	4	2	no	—
202	C₂×Dic₄₃	C₄×Q₈	1	4	yes	—
203	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
204	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
205	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
206	C₄×D₄₃	—	4	8	no	—
207	C₄×D₄₃	C₄×Q₈	1	8	yes	—
208	C₄×D₄₃	C₂²×Q₈	1	4	yes	—
209	C₄×D₄₃	C₂×#41	1	4	yes	—
210	Dic₈₆	—	4	4	no	—
211	Dic₈₆	—	4	8	no	—
212	C₈×C₄₃	—	2	4	no	—
213	C₈×C₄₃	—	2	2	no	—
214	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
215	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
216	C₄₃⋊C₈	—	2	4	no	—
217	C₄₃⋊C₈	—	2	2	no	—
218	C₄₃⋊C₈	C₂²×Q₈	1	4	yes	—
219	#60191	—	43	1	no	maximal, Sylow
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
222	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
223	C₂×D₄₃	—	2	4	no	—
224	C₂×D₄₃	—	4	4	no	—
225	C₂×D₄₃	C₂×C₄×Q₈	1	4	yes	—
226	C₄×C₄₃	—	2	2	no	—
227	C₄×C₄₃	—	2	8	no	—
228	C₄×C₄₃	—	2	2	no	—
229	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
230	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
231	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
232	Dic₄₃	—	2	8	no	—
233	Dic₄₃	—	2	4	no	—
234	Dic₄₃	C₂×C₄×Q₈	1	4	yes	—
235	#3458	—	43	1	no	—
236	#2961	—	43	8	no	—
237	#2961	—	43	2	no	—
238	#2961	—	43	1	no	—
239	#2961	—	43	1	no	—
240	#2960	—	43	8	no	—
241	#2960	—	43	2	no	—
242	#2960	—	43	1	no	—
243	#2960	D₄₃	1	1	yes	characteristic, complemented
244	#2905	—	43	2	no	—
245	#2905	—	43	1	no	—
246	C₂×#405	—	43	2	no	—
247	C₂×#405	—	43	1	no	—
248	C₂×C₄₃	—	2	2	no	—
249	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
250	C₂×C₄₃	#3573	1	2	yes	—
251	D₄₃	—	2	4	no	—
252	C₂²×M₁₆	—	43	2	no	—
253	C₂²×M₁₆	—	43	1	no	—
254	C₂³×C₈	—	43	1	no	—
255	#544	—	43	4	no	—
256	#544	—	43	4	no	—
257	#544	—	43	4	no	—
258	#543	—	43	4	no	—
259	#533	—	43	8	no	—
260	#533	—	43	2	no	—
261	#533	—	43	1	no	—
262	#533	C₂×D₄₃	1	1	yes	characteristic
263	C₂×#117	—	43	2	no	—
264	C₂×#117	—	43	1	no	—
265	#446	—	43	8	no	—
266	#446	—	43	8	no	—
267	#446	—	43	8	no	—
268	#446	—	43	8	no	—
269	#446	—	43	8	no	—
270	#446	—	43	4	no	—
271	#446	C₂×D₄₃	1	4	yes	complemented
272	C₈×Q₈	—	43	8	no	—
273	C₈×Q₈	—	43	4	no	—
274	C₈×Q₈	C₂×D₄₃	1	4	yes	complemented
275	#424	—	43	2	no	—
276	#424	—	43	2	no	—
277	#424	—	43	2	no	—
278	#424	—	43	8	no	—
279	#424	—	43	8	no	—
280	#424	C₂×D₄₃	1	2	yes	—
281	#423	—	43	2	no	—
282	#423	—	43	1	no	—
283	#423	—	43	8	no	—
284	#423	C₂×D₄₃	1	1	yes	characteristic
285	#405	—	43	2	no	—
286	#405	—	43	2	no	—
287	#405	—	43	2	no	—
288	#405	—	43	4	no	—
289	#405	—	43	4	no	—
290	#405	—	43	4	no	—
291	#405	—	43	4	no	—
292	#405	C₂×D₄₃	1	2	yes	—
293	C₂×#97	—	43	1	no	—
294	C₂×#97	—	43	1	no	—
295	C₂×#97	—	43	4	no	—
296	C₂×C₄×C₈	—	43	1	no	—
297	C₂×C₄×C₈	—	43	4	no	—
298	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
299	C₄₃	#60191	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₄	—	43	1	no	—
301	C₂×M₁₆	—	43	2	no	—
302	C₂×M₁₆	—	43	4	no	—
303	C₂×M₁₆	—	43	4	no	—
304	C₂×M₁₆	—	86	4	no	—
305	C₂×M₁₆	—	86	8	no	—
306	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
307	C₂²×C₈	—	43	1	no	—
308	C₂²×C₈	—	43	8	no	—
309	C₂²×C₈	—	43	2	no	—
310	C₂²×C₈	—	43	2	no	—
311	C₂²×C₈	—	43	1	no	—
312	C₂²×C₈	—	43	4	no	—
313	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
314	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
315	C₄⋊Q₈	—	43	8	no	—
316	C₄⋊Q₈	—	43	8	no	—
317	C₄⋊Q₈	—	43	4	no	—
318	C₄⋊Q₈	—	43	2	no	—
319	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
320	#125	—	43	8	no	—
321	#125	—	43	8	no	—
322	#125	—	43	4	no	—
323	#125	—	43	2	no	—
324	#125	C₄×D₄₃	1	2	yes	—
325	C₂²⋊Q₈	—	43	8	no	—
326	C₂²⋊Q₈	—	43	4	no	—
327	C₂²⋊Q₈	—	43	8	no	—
328	C₂²⋊Q₈	—	43	8	no	—
329	C₂²⋊Q₈	—	43	8	no	—
330	C₂²⋊Q₈	—	43	8	no	—
331	C₂²⋊Q₈	C₄×D₄₃	1	4	yes	—
332	C₄×Q₈	—	43	8	no	—
333	C₄×Q₈	—	43	4	no	—
334	C₄×Q₈	C₂²×D₄₃	1	4	yes	—
335	#117	—	43	2	no	—
336	#117	—	43	4	no	—
337	#117	—	43	4	no	—
338	#117	—	43	2	no	—
339	#117	—	43	2	no	—
340	#117	—	43	4	no	—
341	#117	—	43	4	no	—
342	#117	C₂²×D₄₃	1	2	yes	—
343	C₂×C₄⋊C₄	—	43	2	no	—
344	C₂×C₄⋊C₄	—	43	4	no	—
345	C₂×C₂²⋊C₄	—	43	2	no	—
346	C₂×C₂²⋊C₄	—	43	4	no	—
347	C₂×C₄²	—	43	1	no	—
348	C₂×C₄²	—	43	4	no	—
349	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
350	C₄⋊C₈	—	43	8	no	—
351	C₄⋊C₈	—	43	8	no	—
352	C₄⋊C₈	—	43	8	no	—
353	C₄⋊C₈	—	43	8	no	—
354	C₄⋊C₈	—	43	4	no	—
355	C₄⋊C₈	C₂²×D₄₃	1	8	yes	—
356	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
357	#97	—	43	4	no	—
358	#97	—	43	4	no	—
359	#97	—	43	4	no	—
360	#97	—	43	4	no	—
361	#97	—	43	4	no	—
362	#97	C₂²×D₄₃	1	4	yes	—
363	C₄×C₈	—	43	4	no	—
364	C₄×C₈	—	43	2	no	—
365	C₄×C₈	—	43	4	no	—
366	C₄×C₈	—	43	2	no	—
367	C₄×C₈	—	43	4	no	—
368	C₄×C₈	C₂²×D₄₃	1	2	yes	—
369	C₄×C₈	C₂²×D₄₃	1	4	yes	—
370	C₄×C₈	C₂²×D₄₃	1	2	yes	—
371	C₂⁴	—	43	1	no	—
372	C₂×Q₈	—	43	8	no	—
373	C₂×Q₈	—	43	4	no	—
374	C₂×Q₈	C₂×C₄×D₄₃	1	4	yes	—
375	C₂²×C₄	—	43	1	no	—
376	C₂²×C₄	—	43	2	no	—
377	C₂²×C₄	—	43	4	no	—
378	C₂²×C₄	—	43	4	no	—
379	C₂²×C₄	—	43	2	no	—
380	C₂²×C₄	—	43	2	no	—
381	C₂²×C₄	—	43	8	no	—
382	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
383	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
384	M₁₆	—	2	4	no	—
385	M₁₆	—	86	8	no	—
386	M₁₆	—	86	8	no	—
387	M₁₆	—	86	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	43	4	no	—
390	C₂×C₈	—	43	2	no	—
391	C₂×C₈	—	43	8	no	—
392	C₂×C₈	—	43	8	no	—
393	C₂×C₈	—	43	2	no	—
394	C₂×C₈	—	43	4	no	—
395	C₂×C₈	—	86	8	no	—
396	C₂×C₈	—	86	2	no	—
397	C₂×C₈	Q₈×D₄₃	1	4	yes	—
398	C₂×C₈	C₂³×D₄₃	1	4	yes	—
399	C₂×C₈	C₂³×D₄₃	1	2	yes	—
400	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
401	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
402	C₄⋊C₄	—	43	8	no	—
403	C₄⋊C₄	—	43	4	no	—
404	C₄⋊C₄	—	43	4	no	—
405	C₄⋊C₄	—	43	4	no	—
406	C₄⋊C₄	—	43	8	no	—
407	C₄⋊C₄	—	43	8	no	—
408	C₄⋊C₄	—	43	8	no	—
409	C₄⋊C₄	—	43	8	no	—
410	C₄⋊C₄	—	43	4	no	—
411	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
412	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
413	C₄⋊C₄	C₂×C₄×D₄₃	1	8	yes	—
414	C₂²⋊C₄	—	43	4	no	—
415	C₂²⋊C₄	—	43	8	no	—
416	C₂²⋊C₄	—	43	4	no	—
417	C₂²⋊C₄	—	43	4	no	—
418	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
419	C₄²	—	43	8	no	—
420	C₄²	—	43	2	no	—
421	C₄²	—	43	2	no	—
422	C₄²	—	43	4	no	—
423	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
424	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
425	C₄²	C₂³×D₄₃	1	4	yes	—
426	C₄²	C₂³×D₄₃	1	2	yes	—
427	C₂³	—	43	2	no	—
428	C₂³	—	43	4	no	—
429	C₂³	—	172	2	no	—
430	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
431	Q₈	—	4	4	no	—
432	Q₈	—	172	4	no	—
433	Q₈	—	172	8	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	43	4	no	—
436	C₂×C₄	—	43	2	no	—
437	C₂×C₄	—	43	8	no	—
438	C₂×C₄	—	43	4	no	—
439	C₂×C₄	—	43	4	no	—
440	C₂×C₄	—	43	8	no	—
441	C₂×C₄	—	43	4	no	—
442	C₂×C₄	—	172	8	no	—
443	C₂×C₄	—	172	2	no	—
444	C₂×C₄	C₂²×C₄×D₄₃	1	8	yes	—
445	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
446	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
447	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
448	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
449	C₂×C₄	#41×D₄₃	1	2	yes	—
450	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	4	no	—
453	C₈	—	43	4	no	—
454	C₈	—	86	4	no	—
455	C₈	—	86	2	no	—
456	C₈	C₂×Q₈×D₄₃	1	2	yes	—
457	C₈	C₂×Q₈×D₄₃	1	2	yes	—
458	C₂²	—	2	2	no	—
459	C₂²	—	43	4	no	—
460	C₂²	—	86	4	no	—
461	C₂²	—	172	4	no	—
462	C₂²	C₄×Q₈×D₄₃	1	2	yes	—
463	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	8	no	—
467	C₄	—	43	4	no	—
468	C₄	—	86	8	no	—
469	C₄	—	86	4	no	—
470	C₄	C₄×Q₈×D₄₃	1	2	yes	—
471	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
472	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	86	4	no	—
475	C₂	C₂×C₄×Q₈×D₄₃	1	1	yes	characteristic
476	C₂	#19149306	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#2960	C₂
prime radical	C₂³×D₄₃	C₂²×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2960	D₄₃
hypocenter	C₄₃	#60191
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
2. #19143536	C₂	semidirect
3. #19143534	C₂	semidirect
4. #19143532	C₂	semidirect
5. #19143531	C₂	semidirect
6. #19143529	C₂	semidirect
7. #19143527	C₂	semidirect
8. #19143524	C₂	semidirect
13. C₄₃×#2960	C₂	semidirect
26. #14583030	C₂²	semidirect
27. #14583029	C₂²	semidirect
28. #14583028	C₂²	semidirect
29. #14583028	C₂²	semidirect
30. #14583027	C₂²	semidirect
31. #14583026	C₂²	semidirect
32. C₈×Dic₈₆	C₂²	semidirect
33. C₈×Dic₈₆	C₂²	semidirect
55. C₄₃×#446	C₂²	semidirect
56. C₈×Q₈×C₄₃	C₂²	semidirect
69. C₂×C₈×D₄₃	Q₈	semidirect
243. #2960	D₄₃	semidirect
271. #446	C₂×D₄₃	semidirect
274. C₈×Q₈	C₂×D₄₃	semidirect
299. C₄₃	#60191	semidirect

Maximal subgroups

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

subgroup	index
#19147998	2
#19143536	2
#19143534	2
#19143532	2
#19143531	2
#19143529	2
#19143527	2
#19143524	2
#19143157	2
#19143156	2
C₂×#14582853	2
#405×D₄₃	2
C₄₃×#2960	2
#60191	43