Subgroups — #25966288

Order 11008.

1834 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148407	C₂	1	2	yes	maximal
2	#19145142	C₂	1	2	yes	maximal, complemented
3	#19145136	C₂	1	4	yes	maximal, complemented
4	#19145135	C₂	1	4	yes	maximal, complemented
5	#19145132	C₂	1	8	yes	maximal, complemented
6	#19145106	C₂	1	2	yes	maximal, complemented
7	C₂×#14583304	C₂	1	1	yes	maximal, characteristic, complemented
8	#500×D₄₃	C₂	1	2	yes	maximal, complemented
9	#19143192	C₂	1	4	yes	maximal
10	C₄×#13063331	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063331	C₂²	1	2	yes	—
13	Q₈×Dic₈₆	—	2	2	no	—
14	#14583627	—	2	2	no	—
15	#14583609	—	2	2	no	—
16	#14583607	—	2	4	no	—
17	Q₈×D₁₇₂	—	2	2	no	—
18	#14583562	—	2	4	no	—
19	#14583529	C₂²	1	8	yes	—
20	#14583527	C₂²	1	4	yes	—
21	#14583454	C₂²	1	4	yes	—
22	C₂×#13063325	C₂²	1	2	yes	—
23	C₄⋊Q₈×D₄₃	C₂²	1	4	yes	—
24	#14583379	C₂²	1	4	yes	—
25	C₄×#10621898	C₂²	1	1	yes	characteristic
26	#14583309	C₂²	1	8	yes	—
27	#14583306	C₂²	1	16	yes	—
28	#14583304	C₂²	1	2	yes	—
29	#14583304	C₂²	1	4	yes	—
30	#14583304	C₂²	1	2	yes	—
31	#14583303	C₂²	1	8	yes	—
32	#14583302	C₂²	1	4	yes	—
33	#14583300	C₂²	1	8	yes	—
34	#14583295	C₂²	1	4	yes	—
35	#14582942	C₂²	1	8	yes	—
36	#14582938	C₂²	1	16	yes	—
37	#14582936	C₂²	1	8	yes	—
38	C₂×#13063259	C₂²	1	4	yes	—
39	#107×D₄₃	C₂²	1	8	yes	—
40	#14582854	C₂²	1	2	yes	—
41	#14582853	C₂²	1	4	yes	—
42	C₄×#10621877	C₂²	1	1	yes	characteristic
43	C₄×#10621872	C₂²	1	2	yes	—
44	C₄×C₈×D₄₃	C₂²	1	2	yes	—
45	C₄₃×#533	C₂²	1	2	yes	—
46	C₄₃×#500	C₂²	1	1	yes	characteristic
47	C₄₃×#500	C₂²	1	1	yes	characteristic
48	C₄₃×#499	C₂²	1	4	yes	—
49	C₄₃×#498	C₂²	1	2	yes	—
50	C₄₃×#427	C₂²	1	4	yes	—
51	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×#10621898	C₂³	1	1	yes	characteristic
53	C₂²×Dic₈₆	—	2	2	no	—
54	C₂×Q₈×D₄₃	—	2	4	no	—
55	#13063331	Q₈	1	16	yes	complemented
56	C₂×#10621877	C₂³	1	2	yes	—
57	C₂×#10621872	C₂³	1	4	yes	—
58	C₂×C₈×D₄₃	C₂³	1	4	yes	—
59	#13063325	—	2	2	no	—
60	#13063325	—	2	2	no	—
61	#13063325	—	2	4	no	—
62	#13063325	C₂³	1	4	yes	—
63	#13063325	C₂³	1	4	yes	—
64	#13063324	—	2	8	no	—
65	#13063324	—	2	4	no	—
66	#13063324	C₂³	1	8	yes	—
67	#13063323	—	2	4	no	—
68	#13063317	—	2	4	no	—
69	#13063316	C₂³	1	8	yes	—
70	#13063315	—	2	8	no	—
71	#13063305	—	2	4	no	—
72	#13063305	—	2	8	no	—
73	#13063303	—	2	8	no	—
74	#13063302	—	2	8	no	—
75	#13063301	—	2	4	no	—
76	Q₈×Dic₄₃	—	2	4	no	—
77	C₄×Dic₈₆	—	2	4	no	—
78	C₄×Dic₈₆	D₄	1	1	yes	characteristic
79	C₄×Dic₈₆	D₄	1	1	yes	characteristic
80	#13063290	—	2	4	no	—
81	C₄×D₁₇₂	—	2	4	no	—
82	C₄×D₁₇₂	D₄	1	1	yes	characteristic
83	C₄×D₁₇₂	D₄	1	1	yes	characteristic
84	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
85	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
86	(C₂²⋊D₄₃)⋊C₄	—	2	8	no	—
87	#13063284	C₂³	1	1	yes	characteristic
88	#13063283	C₂³	1	8	yes	—
89	#13063282	C₂³	1	2	yes	—
90	C₂×C₄⋊Dic₄₃	—	2	2	no	—
91	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
92	C₄⋊C₄×D₄₃	—	2	4	no	—
93	C₄⋊C₄×D₄₃	C₂³	1	8	yes	—
94	C₄²×D₄₃	C₂³	1	2	yes	—
95	#13063259	C₂³	1	8	yes	—
96	#13063259	C₂³	1	8	yes	—
97	#13063258	C₂³	1	16	yes	—
98	#13063256	C₂³	1	16	yes	—
99	#13063236	C₂³	1	2	yes	—
100	#13063235	C₂³	1	4	yes	—
101	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
102	C₈×Dic₄₃	C₂³	1	4	yes	—
103	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
106	#125×C₄₃	C₂³	1	4	yes	—
107	C₂²⋊Q₈×C₄₃	—	2	2	no	—
108	C₂²⋊Q₈×C₄₃	—	2	2	no	—
109	C₄×Q₈×C₄₃	—	2	2	no	—
110	C₄×Q₈×C₄₃	—	2	2	no	—
111	#117×C₄₃	C₂³	1	4	yes	—
112	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
113	#107×C₄₃	C₂³	1	4	yes	—
114	#107×C₄₃	C₂³	1	4	yes	—
115	#106×C₄₃	C₂³	1	8	yes	—
116	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
117	C₄×C₈×C₄₃	C₂³	1	2	yes	—
118	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
119	C₂×Q₈×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
125	C₂²×Dic₄₃	—	2	4	no	—
126	Q₈×D₄₃	—	8	8	no	—
127	#10621898	C₂×Q₈	1	8	yes	—
128	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₄₃	—	2	8	no	—
130	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
131	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
132	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
133	C₂×Dic₈₆	—	2	4	no	—
134	C₂×Dic₈₆	—	2	4	no	—
135	C₂×Dic₈₆	—	2	8	no	—
136	C₂×Dic₈₆	—	8	4	no	—
137	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₃	C₂×Q₈	1	8	yes	complemented
139	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
140	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
141	C₄⋊C₄×C₄₃	—	2	4	no	—
142	C₄⋊C₄×C₄₃	—	2	4	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
146	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
147	C₂²⋊C₄×C₄₃	—	2	4	no	—
148	C₄²×C₄₃	—	2	4	no	—
149	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
153	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
154	(C₂×D₄₃)⋊C₄	—	2	8	no	—
155	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
156	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
157	C₄⋊Dic₄₃	—	2	4	no	—
158	C₄⋊Dic₄₃	—	2	4	no	—
159	C₄⋊Dic₄₃	—	2	4	no	—
160	C₄⋊Dic₄₃	—	2	8	no	—
161	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
162	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
163	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
164	Dic₄₃⋊C₄	—	2	8	no	—
165	Dic₄₃⋊C₄	—	2	8	no	—
166	Dic₄₃⋊C₄	—	2	8	no	—
167	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
168	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
169	C₄×Dic₄₃	—	2	8	no	—
170	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
171	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
172	C₄×Dic₄₃	C₂⁴	1	2	yes	—
173	#10621877	C₂×Q₈	1	8	yes	complemented
174	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
175	#10621872	C₂×Q₈	1	16	yes	complemented
176	C₈×D₄₃	C₂×Q₈	1	16	yes	complemented
177	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
179	Q₈×C₄₃	—	4	4	no	—
180	Q₈×C₄₃	—	4	4	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
191	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
192	C₂²⋊D₄₃	C₄⋊Q₈	1	8	yes	—
193	C₂×Dic₄₃	—	2	8	no	—
194	C₂×Dic₄₃	—	8	4	no	—
195	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
196	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
197	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
198	D₁₇₂	C₄⋊Q₈	1	4	yes	—
199	C₄×D₄₃	—	2	4	no	—
200	C₄×D₄₃	—	2	4	no	—
201	C₄×D₄₃	—	8	8	no	—
202	C₄×D₄₃	C₂²×Q₈	1	8	yes	—
203	Dic₈₆	—	4	8	no	—
204	Dic₈₆	—	8	8	no	—
205	Dic₈₆	—	8	4	no	—
206	Dic₈₆	C₄⋊Q₈	1	4	yes	—
207	C₈×C₄₃	C₂²×Q₈	1	4	yes	—
208	C₈×C₄₃	C₂²×Q₈	1	4	yes	—
209	C₄₃⋊C₈	C₂²×Q₈	1	8	yes	—
210	#60667	—	43	1	no	maximal, Sylow
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	—	2	1	no	—
213	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
214	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
215	C₂×D₄₃	—	2	2	no	—
216	C₂×D₄₃	—	2	2	no	—
217	C₂×D₄₃	C₂×C₄⋊Q₈	1	4	yes	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	4	4	no	—
221	C₄×C₄₃	—	4	4	no	—
222	C₄×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
223	C₄×C₄₃	#576	1	2	yes	—
224	C₄×C₄₃	#578	1	2	yes	—
225	C₄×C₄₃	C₂³×Q₈	1	2	yes	—
226	Dic₄₃	—	2	2	no	—
227	Dic₄₃	—	2	2	no	—
228	Dic₄₃	—	4	8	no	—
229	Dic₄₃	C₂×C₄⋊Q₈	1	4	yes	—
230	#3503	—	43	2	no	—
231	#3165	—	43	4	no	—
232	#3165	—	43	2	no	—
233	#3164	—	43	8	no	—
234	#3164	—	43	4	no	—
235	#3160	—	43	2	no	—
236	#3160	D₄₃	1	1	yes	characteristic, complemented
237	C₂×#500	—	43	2	no	—
238	C₂×#500	—	43	1	no	—
239	#2913	—	43	4	no	—
240	C₄×#131	—	43	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
244	C₂×C₄₃	C₂×#578	1	1	yes	characteristic
245	D₄₃	—	2	4	no	—
246	C₂×#131	—	43	2	no	—
247	Q₈²	—	86	2	no	—
248	#557	—	86	2	no	—
249	#554	—	86	2	no	—
250	#554	—	86	4	no	—
251	D₄×Q₈	—	86	2	no	—
252	D₄×Q₈	—	86	4	no	—
253	#544	—	43	8	no	—
254	#544	—	43	4	no	—
255	#533	—	43	4	no	—
256	#533	C₂×D₄₃	1	2	yes	—
257	C₂×C₄⋊Q₈	—	43	4	no	—
258	C₂×C₄⋊Q₈	—	43	2	no	—
259	#520	—	43	4	no	—
260	C₄×#41	—	43	1	no	—
261	#501	—	43	8	no	—
262	#501	—	43	16	no	—
263	#500	—	43	4	no	—
264	#500	—	43	8	no	—
265	#500	—	43	2	no	—
266	#500	—	43	4	no	—
267	#500	—	43	2	no	—
268	#500	C₂×D₄₃	1	1	yes	characteristic
269	#500	C₂×D₄₃	1	1	yes	characteristic
270	#499	—	43	8	no	—
271	#499	C₂×D₄₃	1	4	yes	—
272	#498	—	43	4	no	—
273	#498	C₂×D₄₃	1	2	yes	—
274	#428	—	43	8	no	—
275	#428	—	43	16	no	—
276	#427	—	43	8	no	—
277	#427	C₂×D₄₃	1	4	yes	—
278	C₂×#107	—	43	4	no	—
279	C₂×#107	—	43	8	no	—
280	#405	—	43	2	no	—
281	#405	—	43	4	no	—
282	C₄×M₁₆	—	43	1	no	—
283	C₄×M₁₆	—	43	2	no	—
284	C₂×C₄×C₈	—	43	2	no	—
285	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
286	C₄₃	#60667	1	1	yes	characteristic, complemented, Sylow
287	C₂×#41	—	43	1	no	—
288	C₂²×Q₈	—	86	4	no	—
289	C₂²×Q₈	—	86	2	no	—
290	#131	—	43	16	no	—
291	C₂×M₁₆	—	43	2	no	—
292	C₂×M₁₆	—	43	4	no	—
293	C₂²×C₈	—	43	4	no	—
294	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
295	C₄⋊Q₈	—	43	8	no	—
296	C₄⋊Q₈	—	43	4	no	—
297	C₄⋊Q₈	—	43	4	no	—
298	C₄⋊Q₈	—	86	4	no	—
299	C₄⋊Q₈	—	86	4	no	—
300	C₄⋊Q₈	—	86	4	no	—
301	C₄⋊Q₈	—	86	8	no	—
302	C₄⋊Q₈	—	86	2	no	—
303	C₄⋊Q₈	—	86	2	no	—
304	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
305	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
306	#125	—	43	8	no	—
307	#125	—	86	4	no	—
308	#125	—	86	8	no	—
309	#125	C₂²×D₄₃	1	4	yes	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	2	no	—
312	C₂²⋊Q₈	—	86	8	no	—
313	C₂²⋊Q₈	—	86	8	no	—
314	C₂²⋊Q₈	—	86	8	no	—
315	C₂²⋊Q₈	—	86	4	no	—
316	C₂²⋊Q₈	—	86	4	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	43	1	no	—
320	C₄×Q₈	—	43	1	no	—
321	C₄×Q₈	—	86	4	no	—
322	C₄×Q₈	—	86	4	no	—
323	C₄×Q₈	—	86	4	no	—
324	C₄×D₄	—	43	2	no	—
325	C₄×D₄	—	43	2	no	—
326	C₄×D₄	—	43	1	no	—
327	C₄×D₄	—	43	1	no	—
328	C₄×D₄	—	86	4	no	—
329	C₄×D₄	—	86	8	no	—
330	#117	—	43	1	no	—
331	#117	—	43	2	no	—
332	#117	—	43	8	no	—
333	#117	C₂²×D₄₃	1	4	yes	—
334	C₂×C₄⋊C₄	—	43	4	no	—
335	C₂×C₄⋊C₄	—	43	8	no	—
336	C₂×C₄⋊C₄	—	86	4	no	—
337	C₂×C₄⋊C₄	—	86	2	no	—
338	C₂×C₄²	—	43	2	no	—
339	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
340	#107	—	43	8	no	—
341	#107	—	43	8	no	—
342	#107	—	43	16	no	—
343	#107	C₂²×D₄₃	1	4	yes	—
344	#107	C₂²×D₄₃	1	4	yes	—
345	#106	—	43	16	no	—
346	#106	C₂²×D₄₃	1	8	yes	—
347	#97	—	43	4	no	—
348	#97	—	43	2	no	—
349	C₄×C₈	—	43	4	no	—
350	C₄×C₈	—	43	2	no	—
351	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
352	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
353	C₄×C₈	C₂²×D₄₃	1	2	yes	—
354	#41	—	43	8	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	43	1	no	—
358	C₂×Q₈	—	86	8	no	—
359	C₂×Q₈	—	86	4	no	—
360	C₂×Q₈	—	86	4	no	—
361	C₂×Q₈	—	344	4	no	—
362	C₂×Q₈	—	344	8	no	—
363	C₂×D₄	—	43	2	no	—
364	C₂×D₄	—	43	1	no	—
365	C₂²×C₄	—	43	2	no	—
366	C₂²×C₄	—	43	2	no	—
367	C₂²×C₄	—	43	2	no	—
368	C₂²×C₄	—	86	8	no	—
369	C₂²×C₄	—	86	4	no	—
370	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
371	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
372	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
373	M₁₆	—	43	8	no	—
374	M₁₆	—	43	16	no	—
375	C₂×C₈	—	43	4	no	—
376	C₂×C₈	—	43	16	no	—
377	C₂×C₈	Q₈×D₄₃	1	8	yes	complemented
378	C₂×C₈	C₂³×D₄₃	1	2	yes	—
379	C₂×C₈	C₂³×D₄₃	1	2	yes	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	43	2	no	—
385	C₄⋊C₄	—	43	1	no	—
386	C₄⋊C₄	—	43	2	no	—
387	C₄⋊C₄	—	43	1	no	—
388	C₄⋊C₄	—	43	8	no	—
389	C₄⋊C₄	—	86	8	no	—
390	C₄⋊C₄	—	86	8	no	—
391	C₄⋊C₄	—	86	8	no	—
392	C₄⋊C₄	—	86	8	no	—
393	C₄⋊C₄	—	86	4	no	—
394	C₄⋊C₄	—	86	4	no	—
395	C₄⋊C₄	—	86	4	no	—
396	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
397	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	43	2	no	—
400	C₂²⋊C₄	—	43	2	no	—
401	C₂²⋊C₄	—	43	2	no	—
402	C₂²⋊C₄	—	86	8	no	—
403	C₄²	—	2	4	no	—
404	C₄²	—	43	2	no	—
405	C₄²	—	43	2	no	—
406	C₄²	—	43	2	no	—
407	C₄²	—	86	8	no	—
408	C₄²	D₄×D₄₃	1	1	yes	characteristic
409	C₄²	D₄×D₄₃	1	1	yes	characteristic
410	C₄²	C₂³×D₄₃	1	1	yes	characteristic
411	C₄²	C₂³×D₄₃	1	1	yes	characteristic
412	C₂³	—	43	2	no	—
413	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
414	Q₈	—	4	4	no	—
415	Q₈	—	4	4	no	—
416	Q₈	—	43	4	no	—
417	Q₈	—	344	4	no	—
418	Q₈	—	344	8	no	—
419	Q₈	—	172	8	no	—
420	D₄	—	43	8	no	—
421	D₄	—	43	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	43	2	no	—
427	C₂×C₄	—	43	8	no	—
428	C₂×C₄	—	43	2	no	—
429	C₂×C₄	—	43	2	no	—
430	C₂×C₄	—	86	4	no	—
431	C₂×C₄	—	86	4	no	—
432	C₂×C₄	—	86	8	no	—
433	C₂×C₄	—	344	8	no	—
434	C₂×C₄	—	344	4	no	—
435	C₂×C₄	C₂×D₄×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×D₄×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂×Q₈×D₄₃	1	4	yes	—
441	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
442	C₈	—	43	8	no	—
443	C₈	C₂×Q₈×D₄₃	1	4	yes	—
444	C₈	C₂×Q₈×D₄₃	1	4	yes	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	43	4	no	—
448	C₂²	—	86	2	no	—
449	C₂²	—	86	2	no	—
450	C₂²	C₄⋊Q₈×D₄₃	1	2	yes	—
451	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	—	43	4	no	—
457	C₄	—	86	2	no	—
458	C₄	—	86	2	no	—
459	C₄	—	172	8	no	—
460	C₄	C₄⋊Q₈×D₄₃	1	2	yes	—
461	C₄	#14583701	1	2	yes	—
462	C₄	#14583713	1	2	yes	—
463	C₄	C₂²×Q₈×D₄₃	1	2	yes	—
464	C₂	—	2	2	no	—
465	C₂	—	86	4	no	—
466	C₂	C₂×C₄⋊Q₈×D₄₃	1	1	yes	characteristic
467	C₂	C₂×#14583701	1	1	yes	characteristic
468	C₂	C₂×#14583713	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3160	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×#10621898	C₂³
hypercenter	#3160	D₄₃
hypocenter	C₄₃	#60667
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
2. #19145142	C₂	semidirect
3. #19145136	C₂	semidirect
4. #19145135	C₂	semidirect
5. #19145132	C₂	semidirect
6. #19145106	C₂	semidirect
7. C₂×#14583304	C₂	semidirect
8. #500×D₄₃	C₂	semidirect
11. C₄₃×#3160	C₂	semidirect
55. #13063331	Q₈	semidirect
138. C₂×C₈×C₄₃	C₂×Q₈	semidirect
173. #10621877	C₂×Q₈	semidirect
175. #10621872	C₂×Q₈	semidirect
176. C₈×D₄₃	C₂×Q₈	semidirect
236. #3160	D₄₃	semidirect
286. C₄₃	#60667	semidirect
377. C₂×C₈	Q₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19148407	2
#19145142	2
#19145136	2
#19145135	2
#19145132	2
#19145106	2
C₂×#14583304	2
#500×D₄₃	2
#19143192	2
C₄×#13063331	2
C₄₃×#3160	2
#60667	43