Subgroups — #25101029

Order 11008.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143393	C₂	1	1	yes	maximal, characteristic
2	#19143247	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143246	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135485	C₂	1	1	yes	maximal, characteristic
5	#19135480	C₂	1	1	yes	maximal, characteristic
6	#19135347	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135342	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135307	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135303	C₂	1	1	yes	maximal, characteristic, complemented
10	#19135300	C₂	1	1	yes	maximal, characteristic, complemented
11	#19135296	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134502	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#13063253	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#13063236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#104×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063345	C₂²	1	1	yes	characteristic
17	C₄×#10621898	C₂²	1	1	yes	characteristic
18	#14583009	C₄	1	2	yes	complemented
19	#14583004	C₄	1	2	yes	complemented
20	#14582999	C₄	1	2	yes	complemented
21	#14582997	C₄	1	2	yes	complemented
22	#14582960	—	2	2	no	—
23	#14582958	—	2	2	no	—
24	#14582956	—	2	2	no	—
25	#14582954	—	2	2	no	—
26	C₂×#13063260	C₂²	1	1	yes	characteristic
27	C₂×#13063260	C₂²	1	1	yes	characteristic
28	#14582935	C₂²	1	1	yes	characteristic
29	#14582927	C₂²	1	1	yes	characteristic
30	#14582927	C₂²	1	1	yes	characteristic
31	#14582926	C₂²	1	1	yes	characteristic
32	#14582926	C₂²	1	1	yes	characteristic
33	C₂×#13063253	C₂²	1	1	yes	characteristic
34	C₂×#13063253	C₂²	1	1	yes	characteristic
35	#14582895	C₂²	1	1	yes	characteristic
36	#14582893	C₂²	1	1	yes	characteristic
37	#14582867	C₂²	1	1	yes	characteristic
38	#14582867	C₂²	1	1	yes	characteristic
39	#14582866	C₂²	1	1	yes	characteristic
40	#14582866	C₂²	1	1	yes	characteristic
41	C₄×#10621877	C₂²	1	1	yes	characteristic
42	C₂×#13063236	C₂²	1	1	yes	characteristic
43	C₂×#13063236	C₂²	1	1	yes	characteristic
44	C₂×#13063236	C₂²	1	1	yes	characteristic
45	C₂×#13063236	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
48	#14582663	C₂²	1	1	yes	characteristic
49	#14582663	C₂²	1	1	yes	characteristic
50	#14582659	C₂²	1	1	yes	characteristic
51	#14582659	C₂²	1	1	yes	characteristic
52	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×#104×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×#104×C₄₃	C₂²	1	1	yes	characteristic
55	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
56	C₄³×C₄₃	C₂²	1	1	yes	characteristic
57	C₄₃×#339	C₂²	1	1	yes	characteristic
58	C₄₃×#339	C₂²	1	1	yes	characteristic
59	C₂×#10621898	C₂³	1	1	yes	characteristic
60	#13063345	—	2	2	no	—
61	#13063345	—	2	2	no	—
62	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
63	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
64	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
65	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
66	C₂×#10621877	C₂³	1	1	yes	characteristic
67	C₂×#10621877	C₂³	1	1	yes	characteristic
68	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
73	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
74	C₄×C₂²⋊D₄₃	—	2	2	no	—
75	#13063284	C₂³	1	1	yes	characteristic
76	#13063282	—	2	1	no	—
77	C₄²×D₄₃	—	2	1	no	—
78	#13063260	—	2	2	no	—
79	#13063260	—	2	2	no	—
80	#13063258	C₂×C₄	1	2	yes	—
81	#13063256	C₂×C₄	1	2	yes	—
82	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
83	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
84	Dic₄₃⋊C₈	—	2	2	no	—
85	Dic₄₃⋊C₈	—	2	2	no	—
86	#13063253	—	2	2	no	—
87	#13063253	—	2	2	no	—
88	#13063249	C₂×C₄	1	2	yes	—
89	#13063248	C₂×C₄	1	2	yes	—
90	#13063246	C₂×C₄	1	2	yes	—
91	#13063245	C₂×C₄	1	2	yes	—
92	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
93	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
94	(C₂×D₄₃)⋊C₈	—	2	2	no	—
95	(C₂×D₄₃)⋊C₈	—	2	2	no	—
96	#13063236	—	2	1	no	—
97	#13063236	—	2	2	no	—
98	#13063236	—	2	2	no	—
99	#13063236	C₂×C₄	1	2	yes	—
100	#13063236	C₂×C₄	1	2	yes	—
101	#13063236	D₄	1	2	yes	—
102	#13063236	D₄	1	2	yes	—
103	C₄×C₄₃⋊C₈	—	2	1	no	—
104	C₄×C₄₃⋊C₈	—	2	2	no	—
105	C₄×C₄₃⋊C₈	—	2	2	no	—
106	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
109	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₄₃	—	2	2	no	—
111	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
112	#117×C₄₃	—	2	1	no	—
113	#117×C₄₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₄₃	—	2	1	no	—
115	C₂×C₄²×C₄₃	—	2	2	no	—
116	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
119	#104×C₄₃	—	2	2	no	—
120	#104×C₄₃	—	2	2	no	—
121	#97×C₄₃	—	2	1	no	—
122	C₄×C₈×C₄₃	—	2	1	no	—
123	#41×C₄₃	—	2	1	no	—
124	#41×C₄₃	—	2	1	no	—
125	#41×C₄₃	—	2	1	no	—
126	#41×C₄₃	—	2	1	no	—
127	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	#41	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₂²⋊D₄₃	—	2	1	no	—
137	#10621898	—	2	1	no	—
138	#10621898	—	2	1	no	—
139	#10621898	—	2	1	no	—
140	#10621898	—	2	1	no	—
141	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₄₃	—	2	1	no	—
143	C₂×C₄×D₄₃	—	2	2	no	—
144	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
145	M₁₆×C₄₃	—	2	1	no	—
146	M₁₆×C₄₃	—	2	1	no	—
147	M₁₆×C₄₃	—	2	1	no	—
148	M₁₆×C₄₃	—	2	1	no	—
149	C₂×C₈×C₄₃	—	2	1	no	—
150	C₂×C₈×C₄₃	—	2	1	no	—
151	C₄⋊C₄×C₄₃	—	2	2	no	—
152	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₄₃	—	2	2	no	—
154	C₂²⋊C₄×C₄₃	—	2	1	no	—
155	C₄²×C₄₃	—	2	2	no	—
156	C₄²×C₄₃	—	2	1	no	—
157	C₄²×C₄₃	—	2	1	no	—
158	C₄²×C₄₃	—	2	1	no	—
159	C₄²×C₄₃	—	4	4	no	—
160	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
161	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₄₃	#41	1	2	yes	—
164	C₄²×C₄₃	#41	1	2	yes	—
165	C₂²⋊Dic₄₃	—	2	1	no	—
166	#10621885	—	2	2	no	—
167	#10621884	—	2	2	no	—
168	#10621883	—	2	2	no	—
169	#10621882	—	2	2	no	—
170	(C₂×D₄₃)⋊C₄	—	2	2	no	—
171	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
172	Dic₄₃⋊C₄	—	2	2	no	—
173	C₄×Dic₄₃	—	2	2	no	—
174	C₄×Dic₄₃	—	2	1	no	—
175	#10621877	—	2	1	no	—
176	#10621877	—	2	1	no	—
177	#10621877	—	2	1	no	—
178	#10621877	—	2	1	no	—
179	C₂×C₄₃⋊C₈	—	2	1	no	—
180	C₂×C₄₃⋊C₈	—	2	1	no	—
181	C₂×C₄₃⋊C₈	—	2	1	no	—
182	C₂×C₄₃⋊C₈	—	2	1	no	—
183	C₂×C₄₃⋊C₈	—	2	1	no	—
184	C₂×C₄₃⋊C₈	—	2	1	no	—
185	C₂×C₄₃⋊C₈	—	2	1	no	—
186	C₂×C₄₃⋊C₈	—	2	1	no	—
187	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
188	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
191	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
192	C₂×C₄₃⋊C₈	#41	1	2	yes	—
193	C₂×C₄₃⋊C₈	#41	1	2	yes	—
194	C₂³×C₄₃	—	2	1	no	—
195	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂²×D₄₃	—	2	1	no	—
197	Q₈×C₄₃	—	2	1	no	—
198	Q₈×C₄₃	—	2	1	no	—
199	D₄×C₄₃	—	2	1	no	—
200	D₄×C₄₃	—	2	1	no	—
201	D₄×C₄₃	—	4	1	no	—
202	D₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	2	4	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	1	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	8	2	no	—
213	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
221	C₂²⋊D₄₃	—	4	1	no	—
222	C₂²⋊D₄₃	—	4	1	no	—
223	C₂×Dic₄₃	—	2	1	no	—
224	C₂×Dic₄₃	—	2	2	no	—
225	D₁₇₂	—	2	1	no	—
226	D₁₇₂	—	2	1	no	—
227	C₄×D₄₃	—	4	1	no	—
228	C₄×D₄₃	—	4	1	no	—
229	C₄×D₄₃	—	8	2	no	—
230	Dic₈₆	—	2	1	no	—
231	Dic₈₆	—	2	1	no	—
232	C₈×C₄₃	—	4	1	no	—
233	C₈×C₄₃	—	4	1	no	—
234	C₄₃⋊C₈	—	2	2	no	—
235	C₄₃⋊C₈	—	2	2	no	—
236	C₄₃⋊C₈	—	2	2	no	—
237	C₄₃⋊C₈	—	4	1	no	—
238	C₄₃⋊C₈	—	4	1	no	—
239	C₄₃⋊C₈	#117	1	2	yes	—
240	C₄₃⋊C₈	#117	1	2	yes	—
241	#21297	—	43	1	no	maximal, Sylow
242	C₂²×C₄₃	—	2	2	no	—
243	C₂²×C₄₃	—	4	2	no	—
244	C₂²×C₄₃	—	4	1	no	—
245	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₄₃	#529	1	1	yes	characteristic
247	C₂²×C₄₃	#529	1	1	yes	characteristic
248	C₂×D₄₃	—	4	2	no	—
249	C₂×D₄₃	—	4	1	no	—
250	C₄×C₄₃	—	2	4	no	—
251	C₄×C₄₃	—	2	2	no	—
252	C₄×C₄₃	—	2	2	no	—
253	C₄×C₄₃	—	4	2	no	—
254	C₄×C₄₃	—	4	2	no	—
255	C₄×C₄₃	—	4	1	no	—
256	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
257	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
258	C₄×C₄₃	#532	1	1	yes	characteristic
259	C₄×C₄₃	#532	1	1	yes	characteristic
260	Dic₄₃	—	4	2	no	—
261	Dic₄₃	—	4	1	no	—
262	#2943	—	43	1	no	—
263	#2923	—	43	1	no	—
264	#2923	—	43	1	no	—
265	#1975	—	43	1	no	—
266	#1974	—	43	1	no	—
267	#1946	—	43	1	no	—
268	#1945	—	43	1	no	—
269	#1938	—	43	1	no	—
270	#1938	—	43	1	no	—
271	#1937	—	43	1	no	—
272	#1937	—	43	1	no	—
273	#1778	—	43	1	no	—
274	C₄×#104	—	43	1	no	—
275	C₄×#104	D₄₃	1	1	yes	characteristic, complemented
276	C₄×#97	—	43	1	no	—
277	C₂×C₄₃	—	2	1	no	—
278	C₂×C₄₃	—	2	1	no	—
279	C₂×C₄₃	—	8	1	no	—
280	C₂×C₄₃	#2293	1	1	yes	characteristic
281	C₂×C₄₃	#2956	1	2	yes	—
282	D₄₃	—	8	1	no	—
283	C₂×#135	—	43	1	no	—
284	C₄×#41	—	43	1	no	—
285	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
286	#442	—	43	2	no	—
287	#441	—	43	2	no	—
288	#440	—	43	2	no	—
289	#440	—	43	2	no	—
290	#433	—	86	2	no	—
291	#433	—	86	2	no	—
292	#432	—	86	2	no	—
293	#432	—	86	2	no	—
294	C₂×#108	—	43	1	no	—
295	C₂×#108	—	43	1	no	—
296	#427	—	43	1	no	—
297	#424	—	43	1	no	—
298	#424	—	43	1	no	—
299	#424	—	43	1	no	—
300	#424	—	43	1	no	—
301	C₂×#104	—	43	1	no	—
302	C₂×#104	—	43	1	no	—
303	C₂×#104	C₂×D₄₃	1	1	yes	characteristic
304	C₂×#104	C₂×D₄₃	1	1	yes	characteristic
305	#416	—	43	1	no	—
306	#416	—	43	1	no	—
307	#408	—	43	1	no	—
308	#408	—	43	1	no	—
309	#408	—	43	1	no	—
310	#408	—	43	1	no	—
311	C₄×M₁₆	—	43	1	no	—
312	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
313	C₂×#97	—	43	1	no	—
314	C₂×#97	—	43	1	no	—
315	C₂×#97	—	43	1	no	—
316	C₂×#97	—	43	1	no	—
317	C₂×C₄×C₈	—	43	1	no	—
318	C₂×C₄×C₈	—	43	1	no	—
319	C₄³	C₂×D₄₃	1	1	yes	characteristic
320	#341	—	43	1	no	—
321	#341	—	43	1	no	—
322	#339	—	43	1	no	—
323	#339	—	43	1	no	—
324	#339	C₂×D₄₃	1	1	yes	characteristic
325	#339	C₂×D₄₃	1	1	yes	characteristic
326	C₄₃	#21297	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	43	1	no	—
328	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
329	#135	—	86	2	no	—
330	#135	—	86	2	no	—
331	C₂×Q₁₆	—	43	1	no	—
332	C₂×SD₁₆	—	43	1	no	—
333	C₂×SD₁₆	—	43	1	no	—
334	C₂×D₈	—	43	1	no	—
335	C₂×M₁₆	—	43	1	no	—
336	C₂×M₁₆	—	43	1	no	—
337	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
338	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
339	C₂²×C₈	—	43	1	no	—
340	C₂²×C₈	—	43	1	no	—
341	C₂²×C₈	—	43	1	no	—
342	C₂²×C₈	—	43	1	no	—
343	C₄×Q₈	—	43	2	no	—
344	C₄×Q₈	C₄×D₄₃	1	2	yes	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	—	43	2	no	—
347	C₄×D₄	—	86	2	no	—
348	C₄×D₄	C₄×D₄₃	1	2	yes	—
349	#117	—	2	1	no	—
350	#117	—	43	1	no	—
351	#117	—	86	1	no	—
352	#117	C₂²×D₄₃	1	1	yes	characteristic
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	—	86	1	no	—
356	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
358	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
359	#108	—	86	2	no	—
360	#108	—	86	2	no	—
361	#107	—	43	2	no	—
362	#106	—	43	2	no	—
363	C₄⋊C₈	—	86	2	no	—
364	C₄⋊C₈	—	86	2	no	—
365	C₄⋊C₈	—	86	2	no	—
366	C₄⋊C₈	—	86	2	no	—
367	#104	—	2	2	no	—
368	#104	—	2	2	no	—
369	#104	—	86	2	no	—
370	#104	—	86	2	no	—
371	#103	—	43	2	no	—
372	#103	—	43	2	no	—
373	#102	—	43	2	no	—
374	#102	—	43	2	no	—
375	C₂²⋊C₈	—	86	2	no	—
376	C₂²⋊C₈	—	86	2	no	—
377	C₂²⋊C₈	—	86	2	no	—
378	C₂²⋊C₈	—	86	2	no	—
379	#97	—	2	1	no	—
380	#97	—	43	2	no	—
381	#97	—	43	2	no	—
382	#97	—	43	2	no	—
383	#97	—	43	2	no	—
384	#97	—	86	2	no	—
385	#97	—	86	2	no	—
386	#97	—	86	1	no	—
387	C₄×C₈	—	2	1	no	—
388	C₄×C₈	—	86	2	no	—
389	C₄×C₈	—	86	2	no	—
390	C₄×C₈	—	86	1	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	86	1	no	—
396	#41	—	86	1	no	—
397	#41	—	86	1	no	—
398	#41	—	86	1	no	—
399	C₂×Q₈	—	43	1	no	—
400	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	43	1	no	—
403	C₂×D₄	—	86	1	no	—
404	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	86	2	no	—
410	C₂²×C₄	—	86	1	no	—
411	C₂²×C₄	#10621900	1	2	yes	—
412	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
413	Q₁₆	—	86	2	no	—
414	SD₁₆	—	86	2	no	—
415	SD₁₆	—	86	2	no	—
416	D₈	—	86	2	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	2	1	no	—
421	M₁₆	—	86	1	no	—
422	M₁₆	—	86	1	no	—
423	M₁₆	—	86	1	no	—
424	M₁₆	—	86	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	43	1	no	—
428	C₂×C₈	—	43	1	no	—
429	C₂×C₈	—	43	2	no	—
430	C₂×C₈	—	43	2	no	—
431	C₂×C₈	—	43	2	no	—
432	C₂×C₈	—	43	2	no	—
433	C₂×C₈	—	43	2	no	—
434	C₂×C₈	—	86	1	no	—
435	C₂×C₈	—	86	1	no	—
436	C₂×C₈	—	86	1	no	—
437	C₂×C₈	—	86	1	no	—
438	C₂×C₈	—	86	1	no	—
439	C₂×C₈	—	86	1	no	—
440	C₂×C₈	—	86	1	no	—
441	C₂×C₈	—	86	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	43	2	no	—
444	C₄⋊C₄	—	86	2	no	—
445	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	86	1	no	—
449	C₂²⋊C₄	—	86	2	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	4	4	no	—
455	C₄²	—	86	2	no	—
456	C₄²	—	86	1	no	—
457	C₄²	C₂×C₄×D₄₃	1	2	yes	—
458	C₄²	#10621898	1	2	yes	—
459	C₄²	#10621898	1	2	yes	—
460	C₄²	D₄×D₄₃	1	1	yes	characteristic
461	C₄²	D₄×D₄₃	1	1	yes	characteristic
462	C₂³	—	2	1	no	—
463	C₂³	—	86	1	no	—
464	C₂³	C₂×#10621900	1	1	yes	characteristic
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	86	1	no	—
468	Q₈	—	86	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	1	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	86	1	no	—
474	D₄	—	86	1	no	—
475	D₄	—	172	1	no	—
476	D₄	—	172	1	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	—	86	2	no	—
488	C₂×C₄	—	86	1	no	—
489	C₂×C₄	—	344	2	no	—
490	C₂×C₄	—	172	1	no	—
491	C₂×C₄	—	172	1	no	—
492	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
493	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
494	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
496	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
497	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
498	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
499	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
500	C₈	—	4	1	no	—
501	C₈	—	4	1	no	—
502	C₈	—	43	2	no	—
503	C₈	—	43	2	no	—
504	C₈	—	86	2	no	—
505	C₈	—	86	2	no	—
506	C₈	—	86	2	no	—
507	C₈	—	172	1	no	—
508	C₈	—	172	1	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	172	1	no	—
513	C₂²	—	172	2	no	—
514	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
515	C₂²	#14583429	1	1	yes	characteristic
516	C₂²	#14583429	1	1	yes	characteristic
517	C₄	—	2	4	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	172	1	no	—
524	C₄	—	172	2	no	—
525	C₄	#117×D₄₃	1	1	yes	characteristic
526	C₄	C₄×#10621898	1	1	yes	characteristic
527	C₄	#14583446	1	1	yes	characteristic
528	C₄	#14583446	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	344	1	no	—
533	C₂	#19137058	1	1	yes	characteristic
534	C₂	#19143501	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#104×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063345	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#104	D₄₃
hypocenter	C₄₃	#21297
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
2. #19143247	C₂	semidirect
3. #19143246	C₂	semidirect
6. #19135347	C₂	semidirect
7. #19135342	C₂	semidirect
8. #19135307	C₂	semidirect
9. #19135303	C₂	semidirect
10. #19135300	C₂	semidirect
11. #19135296	C₂	semidirect
12. #19134502	C₂	semidirect
13. C₄×#13063253	C₂	semidirect
14. C₄×#13063236	C₂	semidirect
15. C₄×#104×C₄₃	C₂	semidirect
18. #14583009	C₄	semidirect
19. #14583004	C₄	semidirect
20. #14582999	C₄	semidirect
21. #14582997	C₄	semidirect
275. C₄×#104	D₄₃	semidirect
326. C₄₃	#21297	semidirect

Maximal subgroups

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

subgroup	index
#19143393	2
#19143247	2
#19143246	2
#19135485	2
#19135480	2
#19135347	2
#19135342	2
#19135307	2
#19135303	2
#19135300	2
#19135296	2
#19134502	2
C₄×#13063253	2
C₄×#13063236	2
C₄×#104×C₄₃	2
#21297	43