Subgroups — #25976040

Order 11008.

1754 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148460	C₂	1	2	yes	maximal
2	#19147212	C₂	1	4	yes	maximal, complemented
3	#19147171	C₂	1	4	yes	maximal, complemented
4	#19147027	C₂	1	2	yes	maximal, complemented
5	#19146989	C₂	1	2	yes	maximal, complemented
6	#19146965	C₂	1	4	yes	maximal, complemented
7	#19145109	C₂	1	1	yes	maximal, characteristic, complemented
8	#19144560	C₂	1	4	yes	maximal, complemented
9	#19144400	C₂	1	2	yes	maximal, complemented
10	#19144246	C₂	1	2	yes	maximal, complemented
11	#19143308	C₂	1	1	yes	maximal, characteristic
12	#19143191	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13063331	C₂²	1	2	yes	—
15	#14583634	—	2	2	no	—
16	#14583627	—	2	2	no	—
17	#14583622	C₂²	1	4	yes	—
18	#14583621	—	2	4	no	—
19	#14583609	C₂²	1	4	yes	—
20	#14583590	C₂²	1	8	yes	—
21	#14583496	—	2	4	no	—
22	#14583473	C₂²	1	4	yes	—
23	#14583456	C₂²	1	2	yes	—
24	#14583449	C₂²	1	1	yes	characteristic
25	#14583433	—	2	4	no	—
26	#14583380	C₂²	1	4	yes	—
27	#14583304	C₂²	1	1	yes	characteristic
28	#14583304	C₂²	1	1	yes	characteristic
29	#14583301	C₂²	1	2	yes	—
30	#14583301	C₂²	1	2	yes	—
31	#14583297	C₂²	1	2	yes	—
32	#14583239	C₂²	1	8	yes	—
33	#14583238	C₂²	1	8	yes	—
34	#14583233	C₂²	1	8	yes	—
35	#14583228	C₂²	1	8	yes	—
36	#14583206	C₂²	1	8	yes	—
37	#14583194	C₂²	1	4	yes	—
38	#14583184	C₂²	1	4	yes	—
39	#14583154	C₂²	1	8	yes	—
40	#14583137	C₂²	1	4	yes	—
41	#14583137	C₂²	1	4	yes	—
42	#14582978	C₂²	1	2	yes	—
43	#14582978	C₂²	1	2	yes	—
44	C₈×D₁₇₂	C₂²	1	2	yes	—
45	C₈×D₁₇₂	C₂²	1	2	yes	—
46	#14582940	C₂²	1	8	yes	—
47	#14582939	C₂²	1	4	yes	—
48	#14582937	C₂²	1	2	yes	—
49	#14582937	C₂²	1	2	yes	—
50	#14582936	C₂²	1	4	yes	—
51	#107×D₄₃	C₂²	1	4	yes	—
52	#14582923	C₂²	1	1	yes	characteristic
53	#14582908	C₂²	1	4	yes	—
54	#14582865	C₂²	1	2	yes	—
55	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
57	C₄×Q₁₆×C₄₃	C₂²	1	2	yes	—
58	C₄×Q₁₆×C₄₃	C₂²	1	2	yes	—
59	C₄×Q₁₆×C₄₃	C₂²	1	2	yes	—
60	C₄×Q₁₆×C₄₃	C₂²	1	2	yes	—
61	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
62	C₂×#103×C₄₃	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
64	C₂×#10621898	C₂³	1	2	yes	—
65	#13063331	—	2	8	no	—
66	C₂×#10621877	C₂³	1	2	yes	—
67	C₂×#10621872	C₂³	1	4	yes	—
68	C₂×C₈×D₄₃	C₂³	1	4	yes	—
69	#13063325	D₄	1	1	yes	characteristic
70	#13063325	C₂³	1	2	yes	—
71	#13063325	C₂³	1	2	yes	—
72	#13063323	—	2	4	no	—
73	#13063322	D₄	1	1	yes	characteristic
74	#13063320	—	2	8	no	—
75	#13063319	—	2	8	no	—
76	#13063317	—	2	4	no	—
77	#13063317	C₂³	1	4	yes	—
78	#13063315	—	2	8	no	—
79	#13063314	—	2	4	no	—
80	#13063313	—	2	4	no	—
81	#13063313	D₄	1	2	yes	—
82	#13063310	—	2	8	no	—
83	#13063308	—	2	8	no	—
84	#13063304	—	2	2	no	—
85	#13063304	—	2	2	no	—
86	#13063303	—	2	8	no	—
87	#13063301	C₂³	1	8	yes	—
88	#13063301	C₂³	1	8	yes	—
89	#13063299	D₄	1	2	yes	—
90	#13063299	D₄	1	2	yes	—
91	C₄×Dic₈₆	—	2	2	no	—
92	C₄×Dic₈₆	—	2	2	no	—
93	C₄×Dic₈₆	—	2	4	no	—
94	#13063290	—	2	4	no	—
95	C₄×D₁₇₂	—	2	4	no	—
96	C₄×D₁₇₂	C₂³	1	2	yes	—
97	C₄×D₁₇₂	C₂³	1	2	yes	—
98	#13063287	—	2	4	no	—
99	C₄×C₂²⋊D₄₃	—	2	8	no	—
100	#13063284	C₂³	1	4	yes	—
101	#13063283	C₂³	1	8	yes	—
102	#13063282	—	2	8	no	—
103	C₄⋊C₄×D₄₃	C₂³	1	8	yes	—
104	#13063259	C₂³	1	2	yes	—
105	#13063259	C₂³	1	2	yes	—
106	#13063259	C₂³	1	2	yes	—
107	#13063259	C₂³	1	2	yes	—
108	#13063258	C₂³	1	8	yes	—
109	#13063257	C₂³	1	4	yes	—
110	#13063257	C₂³	1	4	yes	—
111	#13063256	C₂³	1	8	yes	—
112	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
113	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
114	#13063249	C₂³	1	8	yes	—
115	#13063249	C₂³	1	8	yes	—
116	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
117	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
118	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
119	C₂×Q₁₆×C₄₃	—	2	4	no	—
120	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
121	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
122	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₄×Q₈×C₄₃	—	2	2	no	—
125	C₄×Q₈×C₄₃	—	2	2	no	—
126	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
127	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
130	C₂×C₄²×C₄₃	—	2	2	no	—
131	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
132	#107×C₄₃	C₂³	1	2	yes	—
133	#107×C₄₃	C₂³	1	2	yes	—
134	#103×C₄₃	C₂³	1	4	yes	—
135	#103×C₄₃	C₂³	1	4	yes	—
136	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
140	C₂×Q₈×C₄₃	—	2	2	no	—
141	C₂×Q₈×C₄₃	—	2	4	no	—
142	C₂×Q₈×C₄₃	—	2	4	no	—
143	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
149	C₂×C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
150	#10621898	—	2	4	no	—
151	#10621898	—	2	4	no	—
152	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
153	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
154	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
155	C₂×C₄×D₄₃	—	2	8	no	—
156	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
157	C₂×Dic₈₆	—	2	2	no	—
158	C₂×Dic₈₆	—	2	2	no	—
159	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
160	Q₁₆×C₄₃	—	2	4	no	—
161	Q₁₆×C₄₃	—	2	4	no	—
162	C₂×C₈×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	#41	1	4	yes	—
164	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
168	C₄⋊C₄×C₄₃	—	2	4	no	—
169	C₄⋊C₄×C₄₃	—	2	4	no	—
170	C₄⋊C₄×C₄₃	—	2	2	no	—
171	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
172	C₄²×C₄₃	—	2	4	no	—
173	C₄²×C₄₃	—	2	4	no	—
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
177	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊Dic₄₃	—	2	4	no	—
179	(C₂×D₄₃)⋊C₄	—	2	8	no	—
180	(C₂×D₄₃)⋊C₄	—	2	8	no	—
181	(C₂×D₄₃)⋊C₄	—	2	8	no	—
182	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
183	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
184	C₄⋊Dic₄₃	—	2	2	no	—
185	C₄⋊Dic₄₃	—	2	2	no	—
186	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
187	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
188	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
189	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
190	Dic₄₃⋊C₄	—	2	4	no	—
191	Dic₄₃⋊C₄	—	2	4	no	—
192	Dic₄₃⋊C₄	—	2	8	no	—
193	Dic₄₃⋊C₄	—	2	8	no	—
194	Dic₄₃⋊C₄	—	2	8	no	—
195	C₄×Dic₄₃	—	2	4	no	—
196	C₄×Dic₄₃	—	2	8	no	—
197	#10621877	—	2	4	no	—
198	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
199	#10621872	—	2	8	no	—
200	C₈×D₄₃	—	2	8	no	—
201	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂²×D₄₃	C₂²×D₄	1	4	yes	—
203	Q₈×C₄₃	—	2	4	no	—
204	Q₈×C₄₃	—	2	4	no	—
205	Q₈×C₄₃	—	4	4	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	4	no	—
211	C₂×C₄×C₄₃	—	8	2	no	—
212	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
218	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
219	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
220	C₂²⋊D₄₃	—	2	8	no	—
221	C₂×Dic₄₃	—	2	4	no	—
222	C₂×Dic₄₃	—	2	4	no	—
223	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
224	D₁₇₂	—	2	4	no	—
225	D₁₇₂	—	2	4	no	—
226	D₁₇₂	—	4	2	no	—
227	C₄×D₄₃	—	2	4	no	—
228	C₄×D₄₃	—	2	4	no	—
229	C₄×D₄₃	—	8	8	no	—
230	Dic₈₆	—	2	4	no	—
231	Dic₈₆	—	4	4	no	—
232	Dic₈₆	—	8	2	no	—
233	C₈×C₄₃	—	2	1	no	—
234	C₈×C₄₃	—	2	1	no	—
235	C₈×C₄₃	C₂×#41	1	2	yes	—
236	C₈×C₄₃	C₂×#41	1	2	yes	—
237	C₄₃⋊C₈	—	2	4	no	—
238	#61286	—	43	1	no	maximal, Sylow
239	C₂²×C₄₃	—	2	1	no	—
240	C₂²×C₄₃	—	2	1	no	—
241	C₂²×C₄₃	#547	1	2	yes	—
242	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
243	C₂×D₄₃	—	2	4	no	—
244	C₂×D₄₃	—	2	4	no	—
245	C₂×D₄₃	—	2	4	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	2	1	no	—
248	C₄×C₄₃	—	2	1	no	—
249	C₄×C₄₃	—	4	4	no	—
250	C₄×C₄₃	—	4	4	no	—
251	C₄×C₄₃	#547	1	2	yes	—
252	C₄×C₄₃	#578	1	2	yes	—
253	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
254	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
255	Dic₄₃	—	2	4	no	—
256	Dic₄₃	—	4	4	no	—
257	Dic₄₃	—	4	4	no	—
258	#3507	—	43	2	no	—
259	#3356	—	43	4	no	—
260	#3352	—	43	4	no	—
261	#3342	—	43	2	no	—
262	#3338	—	43	2	no	—
263	#3336	—	43	4	no	—
264	#3160	—	43	1	no	—
265	#3097	—	43	4	no	—
266	#3078	—	43	2	no	—
267	#3059	—	43	2	no	—
268	C₂×C₄×Q₁₆	D₄₃	1	1	yes	characteristic, complemented
269	#2931	—	43	1	no	—
270	#2913	—	43	2	no	—
271	C₂×C₄₃	—	2	2	no	—
272	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
273	C₂×C₄₃	C₂×#578	1	1	yes	characteristic
274	C₂×C₄₃	#3584	1	1	yes	characteristic
275	D₄₃	—	4	4	no	—
276	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
277	C₂×#131	—	43	2	no	—
278	#559	—	86	2	no	—
279	#557	—	86	2	no	—
280	#556	—	43	4	no	—
281	#556	—	86	4	no	—
282	#554	—	43	4	no	—
283	#552	—	43	8	no	—
284	#539	—	86	4	no	—
285	#536	—	43	4	no	—
286	#533	—	43	2	no	—
287	#532	—	43	1	no	—
288	#529	—	86	4	no	—
289	#520	—	43	4	no	—
290	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
291	#500	—	43	1	no	—
292	#500	—	43	1	no	—
293	#499	—	43	2	no	—
294	#499	—	43	2	no	—
295	#498	—	43	2	no	—
296	#485	—	43	8	no	—
297	#485	—	43	8	no	—
298	#484	—	43	8	no	—
299	#483	—	43	8	no	—
300	#479	—	43	8	no	—
301	#477	—	43	4	no	—
302	#475	—	43	4	no	—
303	#470	—	43	8	no	—
304	#467	—	43	4	no	—
305	#467	—	43	4	no	—
306	C₄×Q₁₆	C₂×D₄₃	1	2	yes	—
307	C₄×Q₁₆	C₂×D₄₃	1	2	yes	—
308	C₄×Q₁₆	C₂×D₄₃	1	2	yes	—
309	C₄×Q₁₆	C₂×D₄₃	1	2	yes	—
310	#436	—	43	2	no	—
311	#436	—	43	2	no	—
312	C₈×D₄	—	43	2	no	—
313	C₈×D₄	—	43	2	no	—
314	#428	—	43	4	no	—
315	#428	—	43	8	no	—
316	#427	—	43	2	no	—
317	#427	—	43	2	no	—
318	#427	—	43	4	no	—
319	C₂×#107	—	43	4	no	—
320	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
321	#423	—	43	1	no	—
322	#419	—	43	4	no	—
323	C₂×#103	C₂×D₄₃	1	2	yes	—
324	#408	—	43	2	no	—
325	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
326	C₄₃	#61286	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	43	2	no	—
328	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
329	C₂×Q₁₆	—	2	4	no	—
330	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
331	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
332	#131	—	86	8	no	—
333	C₂×M₁₆	—	43	2	no	—
334	C₂×M₁₆	—	43	4	no	—
335	C₂²×C₈	—	43	4	no	—
336	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
337	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
338	C₄⋊Q₈	—	43	1	no	—
339	C₄⋊Q₈	—	43	2	no	—
340	C₄⋊Q₈	—	43	2	no	—
341	C₄⋊Q₈	—	86	4	no	—
342	#127	—	43	1	no	—
343	#126	—	86	8	no	—
344	#126	—	86	8	no	—
345	#125	—	43	4	no	—
346	#125	—	86	4	no	—
347	#125	—	86	8	no	—
348	#124	—	43	2	no	—
349	#124	—	86	4	no	—
350	#124	—	86	4	no	—
351	#123	—	86	8	no	—
352	#123	—	86	8	no	—
353	C₂²⋊Q₈	—	43	8	no	—
354	C₂²⋊Q₈	—	43	8	no	—
355	C₂²⋊Q₈	—	86	8	no	—
356	C₂²⋊Q₈	—	86	2	no	—
357	C₂²⋊Q₈	—	86	2	no	—
358	#121	—	43	2	no	—
359	#121	—	43	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	86	4	no	—
363	C₄×Q₈	—	86	4	no	—
364	C₄×Q₈	—	86	2	no	—
365	C₄×Q₈	—	86	2	no	—
366	C₄×Q₈	C₂²×D₄₃	1	4	yes	—
367	C₄×Q₈	C₂²×D₄₃	1	4	yes	—
368	C₄×D₄	—	43	2	no	—
369	C₄×D₄	—	43	2	no	—
370	C₄×D₄	—	86	4	no	—
371	C₄×D₄	—	86	4	no	—
372	C₄×D₄	—	86	8	no	—
373	#117	—	43	4	no	—
374	#117	—	43	8	no	—
375	#117	—	86	8	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	43	8	no	—
378	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
379	C₂×C₄²	—	2	2	no	—
380	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
381	#107	—	43	2	no	—
382	#107	—	43	2	no	—
383	#107	—	43	2	no	—
384	#107	—	43	2	no	—
385	#107	—	43	8	no	—
386	#107	C₂²×D₄₃	1	2	yes	—
387	#107	C₂²×D₄₃	1	2	yes	—
388	#106	—	43	4	no	—
389	#106	—	43	4	no	—
390	#106	—	43	8	no	—
391	C₄⋊C₈	—	43	2	no	—
392	C₄⋊C₈	—	43	2	no	—
393	#103	—	43	8	no	—
394	#103	—	43	8	no	—
395	#103	C₂²×D₄₃	1	4	yes	—
396	#103	C₂²×D₄₃	1	4	yes	—
397	C₂²⋊C₈	—	43	4	no	—
398	C₂²⋊C₈	—	43	4	no	—
399	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
400	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
401	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
402	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
403	#41	—	86	4	no	—
404	#41	—	86	4	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	43	2	no	—
409	C₂×Q₈	—	86	2	no	—
410	C₂×Q₈	—	86	2	no	—
411	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
412	C₂×D₄	—	43	4	no	—
413	C₂×D₄	—	43	2	no	—
414	C₂×D₄	—	43	2	no	—
415	C₂×D₄	—	43	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	43	4	no	—
419	C₂²×C₄	—	86	8	no	—
420	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
421	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
422	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
423	Q₁₆	—	2	4	no	—
424	Q₁₆	—	2	4	no	—
425	M₁₆	—	86	4	no	—
426	M₁₆	—	86	8	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	43	4	no	—
429	C₂×C₈	—	86	8	no	—
430	C₂×C₈	#10621898	1	4	yes	—
431	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
432	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
433	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
434	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	43	2	no	—
439	C₄⋊C₄	—	43	2	no	—
440	C₄⋊C₄	—	43	4	no	—
441	C₄⋊C₄	—	43	4	no	—
442	C₄⋊C₄	—	86	8	no	—
443	C₄⋊C₄	—	86	8	no	—
444	C₄⋊C₄	—	86	8	no	—
445	C₄⋊C₄	—	86	4	no	—
446	C₄⋊C₄	—	86	2	no	—
447	C₄⋊C₄	—	86	4	no	—
448	C₄⋊C₄	—	86	2	no	—
449	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
450	C₂²⋊C₄	—	43	4	no	—
451	C₂²⋊C₄	—	43	4	no	—
452	C₂²⋊C₄	—	86	8	no	—
453	C₂²⋊C₄	—	86	8	no	—
454	C₂²⋊C₄	—	86	8	no	—
455	C₂²⋊C₄	—	86	4	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	86	8	no	—
459	C₄²	—	86	4	no	—
460	C₄²	D₄×D₄₃	1	1	yes	characteristic
461	C₄²	D₄×D₄₃	1	1	yes	characteristic
462	C₄²	C₂³×D₄₃	1	1	yes	characteristic
463	C₄²	C₂³×D₄₃	1	1	yes	characteristic
464	C₂³	—	43	4	no	—
465	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
466	Q₈	—	2	4	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	4	4	no	—
469	Q₈	—	86	4	no	—
470	Q₈	—	344	2	no	—
471	Q₈	—	172	4	no	—
472	D₄	—	86	8	no	—
473	D₄	—	86	4	no	—
474	D₄	—	86	4	no	—
475	D₄	—	172	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	8	2	no	—
482	C₂×C₄	—	43	4	no	—
483	C₂×C₄	—	86	4	no	—
484	C₂×C₄	—	86	4	no	—
485	C₂×C₄	—	86	4	no	—
486	C₂×C₄	—	86	4	no	—
487	C₂×C₄	—	344	8	no	—
488	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
489	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
491	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
493	C₂×C₄	C₂×#10621898	1	2	yes	—
494	C₂×C₄	#13063372	1	2	yes	—
495	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
496	C₈	—	2	1	no	—
497	C₈	—	2	1	no	—
498	C₈	—	86	4	no	—
499	C₈	C₂×#10621898	1	2	yes	—
500	C₈	C₂×#10621898	1	2	yes	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	86	4	no	—
504	C₂²	—	86	4	no	—
505	C₂²	—	86	4	no	—
506	C₂²	#14583554	1	2	yes	—
507	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	2	1	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	—	86	4	no	—
514	C₄	—	172	4	no	—
515	C₄	—	172	4	no	—
516	C₄	#14583554	1	2	yes	—
517	C₄	#14583712	1	2	yes	—
518	C₄	C₂²×#10621898	1	1	yes	characteristic
519	C₄	C₂×#13063372	1	1	yes	characteristic
520	C₂	—	2	2	no	—
521	C₂	—	172	4	no	—
522	C₂	C₂×#14583554	1	1	yes	characteristic
523	C₂	C₂×#14583712	1	1	yes	characteristic
524	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#14583449	C₂²
hypercenter	C₂×C₄×Q₁₆	D₄₃
hypocenter	C₄₃	#61286
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #19147212	C₂	semidirect
3. #19147171	C₂	semidirect
4. #19147027	C₂	semidirect
5. #19146989	C₂	semidirect
6. #19146965	C₂	semidirect
7. #19145109	C₂	semidirect
8. #19144560	C₂	semidirect
9. #19144400	C₂	semidirect
10. #19144246	C₂	semidirect
12. #19143191	C₂	semidirect
13. C₂×C₄×Q₁₆×C₄₃	C₂	semidirect
268. C₂×C₄×Q₁₆	D₄₃	semidirect
326. C₄₃	#61286	semidirect

Maximal subgroups

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

subgroup	index
#19148460	2
#19147212	2
#19147171	2
#19147027	2
#19146989	2
#19146965	2
#19145109	2
#19144560	2
#19144400	2
#19144246	2
#19143308	2
#19143191	2
C₂×C₄×Q₁₆×C₄₃	2
#61286	43