Subgroups — #25103428

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144203	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583013	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143301	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143297	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×#10621872	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135487	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135345	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135299	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135037	C₂	1	1	yes	maximal, characteristic, complemented
10	#19135035	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134636	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134473	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134442	C₂	1	1	yes	maximal, characteristic, complemented
14	#19134438	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1937	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063345	C₂²	1	1	yes	characteristic
17	C₂×#13063333	C₂²	1	1	yes	characteristic
18	C₂×#13063332	C₂²	1	1	yes	characteristic
19	C₂²×#10621872	C₂²	1	1	yes	characteristic
20	C₂²×#10621872	C₂²	1	1	yes	characteristic
21	#14583411	C₂²	1	1	yes	characteristic
22	#14583406	C₂²	1	1	yes	characteristic
23	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
24	#14583156	C₄	1	2	yes	complemented
25	#14583151	C₄	1	2	yes	complemented
26	#14583148	C₄	1	2	yes	complemented
27	#14583144	C₄	1	2	yes	complemented
28	#14583013	—	2	4	no	—
29	#14582976	—	2	2	no	—
30	#14582974	—	2	2	no	—
31	#14582969	—	2	2	no	—
32	#14582967	—	2	2	no	—
33	C₂×#13063260	C₂²	1	1	yes	characteristic
34	C₂×#13063260	C₂²	1	1	yes	characteristic
35	#14582935	C₂²	1	1	yes	characteristic
36	#14582925	C₂²	1	1	yes	characteristic
37	C₂×#13063253	C₂²	1	1	yes	characteristic
38	C₂×#13063252	C₂²	1	1	yes	characteristic
39	C₂×#13063251	C₂²	1	1	yes	characteristic
40	#14582896	C₂²	1	1	yes	characteristic
41	#14582865	C₂²	1	1	yes	characteristic
42	#14582862	C₂²	1	1	yes	characteristic
43	#14582862	C₂²	1	1	yes	characteristic
44	#14582857	C₂²	1	1	yes	characteristic
45	#14582855	C₂²	1	1	yes	characteristic
46	C₄×#10621872	—	2	4	no	—
47	C₂×#13063235	C₂²	1	1	yes	characteristic
48	C₂×#13063235	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
50	#14582664	C₂²	1	1	yes	characteristic
51	#14582660	C₂²	1	1	yes	characteristic
52	#14582659	C₂²	1	1	yes	characteristic
53	#14582658	C₂²	1	1	yes	characteristic
54	C₄₃×#424	C₂²	1	1	yes	characteristic
55	C₂×#104×C₄₃	C₂²	1	1	yes	characteristic
56	C₄₃×#416	C₂²	1	1	yes	characteristic
57	C₄₃×#408	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
59	C₄₃×#341	C₂²	1	1	yes	characteristic
60	C₄₃×#339	C₂²	1	1	yes	characteristic
61	C₂×#10621898	C₂³	1	1	yes	characteristic
62	C₂²×C₄×D₄₃	—	2	1	no	—
63	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
64	#13063345	—	2	2	no	—
65	#13063345	—	2	2	no	—
66	C₂×#10621885	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#10621883	C₂×C₄	1	1	yes	characteristic, complemented
68	C₂×#10621884	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂×#10621882	C₂×C₄	1	1	yes	characteristic, complemented
70	#13063333	—	2	2	no	—
71	#13063333	—	2	2	no	—
72	#13063332	—	2	2	no	—
73	#13063332	—	2	2	no	—
74	C₂×#10621877	—	2	1	no	—
75	C₂×#10621877	C₂³	1	1	yes	characteristic
76	C₂×#10621877	C₂³	1	1	yes	characteristic
77	C₂×#10621872	—	2	2	no	—
78	C₂×#10621872	—	2	2	no	—
79	C₂×#10621872	—	2	2	no	—
80	C₂×#10621872	—	2	2	no	—
81	C₂×#10621872	—	2	1	no	—
82	C₂×#10621872	C₂×C₄	1	2	yes	—
83	C₂×#10621872	C₂×C₄	1	2	yes	—
84	C₂×#10621872	D₄	1	2	yes	—
85	C₂×#10621872	D₄	1	2	yes	—
86	C₂²×C₄₃⋊C₈	—	2	1	no	—
87	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₈×D₄₃	—	2	1	no	—
90	#13063309	—	2	1	no	—
91	#13063306	—	2	1	no	—
92	#13063305	C₂×C₄	1	2	yes	—
93	#13063301	C₂×C₄	1	2	yes	—
94	#13063300	C₂×C₄	1	2	yes	—
95	#13063296	C₂×C₄	1	2	yes	—
96	#13063295	—	2	1	no	—
97	#13063293	—	2	1	no	—
98	C₄×D₁₇₂	—	2	2	no	—
99	C₄×C₂²⋊D₄₃	—	2	2	no	—
100	#13063284	C₂³	1	1	yes	characteristic
101	C₂×C₄×Dic₄₃	—	2	1	no	—
102	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
103	C₄²×D₄₃	—	2	2	no	—
104	C₄²×D₄₃	—	2	2	no	—
105	#13063260	—	2	2	no	—
106	#13063260	—	2	2	no	—
107	#13063258	C₂×C₄	1	2	yes	complemented
108	#13063256	C₂×C₄	1	2	yes	complemented
109	Dic₄₃⋊C₈	—	2	2	no	—
110	#13063253	—	2	2	no	—
111	#13063252	—	2	2	no	—
112	#13063251	—	2	2	no	—
113	#13063250	C₂×C₄	1	2	yes	complemented
114	#13063247	C₂×C₄	1	2	yes	complemented
115	(C₂×D₄₃)⋊C₈	—	2	2	no	—
116	(C₂×D₄₃)⋊C₈	—	2	2	no	—
117	(C₂×D₄₃)⋊C₈	—	2	2	no	—
118	#13063236	—	2	1	no	—
119	#13063235	—	2	2	no	—
120	#13063235	—	2	2	no	—
121	#13063235	—	2	1	no	—
122	C₄×C₄₃⋊C₈	—	2	1	no	—
123	C₄×C₄₃⋊C₈	D₄	1	4	yes	complemented
124	C₈×Dic₄₃	—	2	1	no	—
125	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
130	#117×C₄₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
132	C₄⋊C₈×C₄₃	—	2	2	no	—
133	#104×C₄₃	—	2	2	no	—
134	#103×C₄₃	C₂×C₄	1	2	yes	complemented
135	#102×C₄₃	C₂×C₄	1	2	yes	complemented
136	C₂²⋊C₈×C₄₃	—	2	2	no	—
137	C₄×C₈×C₄₃	—	2	2	no	—
138	C₂³×D₄₃	#41	1	1	yes	characteristic
139	#41×C₄₃	—	2	1	no	—
140	#41×C₄₃	—	2	1	no	—
141	#41×C₄₃	—	2	1	no	—
142	#41×C₄₃	—	2	1	no	—
143	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×D₄×C₄₃	—	2	1	no	—
145	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
149	C₂×C₂²⋊D₄₃	—	2	1	no	—
150	C₂×C₂²⋊D₄₃	—	2	2	no	—
151	C₂²×Dic₄₃	—	2	1	no	—
152	C₂²×Dic₄₃	#41	1	1	yes	characteristic
153	#10621898	—	2	1	no	—
154	#10621898	—	2	1	no	—
155	#10621898	—	2	1	no	—
156	#10621898	—	2	1	no	—
157	C₂×D₁₇₂	—	2	2	no	—
158	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₄₃	—	2	1	no	—
160	C₂×C₄×D₄₃	—	2	1	no	—
161	C₂×C₄×D₄₃	—	2	1	no	—
162	C₂×C₄×D₄₃	—	2	1	no	—
163	C₂×C₄×D₄₃	—	2	4	no	—
164	C₂×C₄×D₄₃	—	2	1	no	—
165	C₂×C₄×D₄₃	—	4	4	no	—
166	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
167	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
168	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
169	M₁₆×C₄₃	—	2	1	no	—
170	M₁₆×C₄₃	—	2	1	no	—
171	M₁₆×C₄₃	—	2	1	no	—
172	M₁₆×C₄₃	—	2	1	no	—
173	C₂×C₈×C₄₃	—	2	1	no	—
174	C₂×C₈×C₄₃	—	2	1	no	—
175	C₂×C₈×C₄₃	—	2	1	no	—
176	C₂×C₈×C₄₃	—	2	1	no	—
177	C₂×C₈×C₄₃	—	2	1	no	—
178	C₂×C₈×C₄₃	—	2	1	no	—
179	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
180	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
182	C₂²⋊C₄×C₄₃	—	2	1	no	—
183	C₄²×C₄₃	—	2	1	no	—
184	C₄²×C₄₃	—	2	1	no	—
185	C₄²×C₄₃	C₂×D₄	1	2	yes	—
186	C₂²⋊Dic₄₃	—	2	2	no	—
187	C₂²⋊Dic₄₃	—	2	1	no	—
188	#10621885	—	2	2	no	—
189	#10621884	—	2	2	no	—
190	#10621883	—	2	2	no	—
191	#10621882	—	2	2	no	—
192	(C₂×D₄₃)⋊C₄	—	2	2	no	—
193	(C₂×D₄₃)⋊C₄	—	2	2	no	—
194	(C₂×D₄₃)⋊C₄	—	2	2	no	—
195	C₄⋊Dic₄₃	—	2	2	no	—
196	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
197	Dic₄₃⋊C₄	—	2	2	no	—
198	C₄×Dic₄₃	—	2	4	no	—
199	C₄×Dic₄₃	—	2	1	no	—
200	C₄×Dic₄₃	—	2	1	no	—
201	C₄×Dic₄₃	#41	1	2	yes	—
202	#10621877	—	2	1	no	—
203	#10621877	—	2	1	no	—
204	#10621877	—	2	1	no	—
205	#10621877	—	2	1	no	—
206	#10621877	—	4	2	no	—
207	C₂×C₄₃⋊C₈	—	2	1	no	—
208	C₂×C₄₃⋊C₈	—	2	1	no	—
209	C₂×C₄₃⋊C₈	—	4	2	no	—
210	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
213	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
214	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
215	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
216	C₂×C₄₃⋊C₈	#41	1	2	yes	—
217	C₂×C₄₃⋊C₈	#41	1	2	yes	—
218	#10621872	—	2	4	no	—
219	#10621872	—	2	4	no	—
220	#10621872	—	2	4	no	—
221	#10621872	—	2	4	no	—
222	#10621872	—	4	2	no	—
223	C₈×D₄₃	—	4	2	no	—
224	C₂³×C₄₃	—	2	1	no	—
225	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
226	C₂²×D₄₃	—	2	1	no	—
227	C₂²×D₄₃	—	2	1	no	—
228	C₂²×D₄₃	—	2	1	no	—
229	C₂²×D₄₃	—	4	2	no	—
230	C₂²×D₄₃	C₄×D₄	1	2	yes	—
231	Q₈×C₄₃	—	2	1	no	—
232	Q₈×C₄₃	—	2	1	no	—
233	D₄×C₄₃	—	2	1	no	—
234	D₄×C₄₃	—	2	1	no	—
235	D₄×C₄₃	—	4	1	no	—
236	D₄×C₄₃	—	4	1	no	—
237	C₂×C₄×C₄₃	—	2	4	no	—
238	C₂×C₄×C₄₃	—	2	2	no	—
239	C₂×C₄×C₄₃	—	2	1	no	—
240	C₂×C₄×C₄₃	—	2	2	no	—
241	C₂×C₄×C₄₃	—	4	1	no	—
242	C₂×C₄×C₄₃	—	4	1	no	—
243	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
249	C₂²⋊D₄₃	—	4	1	no	—
250	C₂²⋊D₄₃	—	4	1	no	—
251	C₂²⋊D₄₃	—	8	2	no	—
252	C₂×Dic₄₃	—	2	1	no	—
253	C₂×Dic₄₃	—	2	1	no	—
254	C₂×Dic₄₃	—	2	2	no	—
255	C₂×Dic₄₃	—	2	1	no	—
256	C₂×Dic₄₃	—	2	2	no	—
257	C₂×Dic₄₃	—	4	2	no	—
258	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
259	D₁₇₂	—	2	1	no	—
260	D₁₇₂	—	2	1	no	—
261	D₁₇₂	—	8	2	no	—
262	C₄×D₄₃	—	2	2	no	—
263	C₄×D₄₃	—	2	2	no	—
264	C₄×D₄₃	—	2	2	no	—
265	C₄×D₄₃	—	2	2	no	—
266	C₄×D₄₃	—	4	8	no	—
267	C₄×D₄₃	—	4	1	no	—
268	C₄×D₄₃	—	4	1	no	—
269	Dic₈₆	—	2	1	no	—
270	Dic₈₆	—	2	1	no	—
271	C₈×C₄₃	—	2	2	no	—
272	C₈×C₄₃	—	2	2	no	—
273	C₈×C₄₃	—	4	1	no	—
274	C₈×C₄₃	—	4	1	no	—
275	C₄₃⋊C₈	—	4	1	no	—
276	C₄₃⋊C₈	—	4	1	no	—
277	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
278	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
279	C₄₃⋊C₈	#121	1	2	yes	—
280	C₄₃⋊C₈	#121	1	2	yes	—
281	#21549	—	43	1	no	maximal, Sylow
282	C₂²×C₄₃	—	2	2	no	—
283	C₂²×C₄₃	—	4	2	no	—
284	C₂²×C₄₃	—	4	1	no	—
285	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂²×C₄₃	#525	1	1	yes	characteristic
287	C₂²×C₄₃	#529	1	1	yes	characteristic
288	C₂×D₄₃	—	2	2	no	—
289	C₂×D₄₃	—	2	2	no	—
290	C₂×D₄₃	—	2	2	no	—
291	C₂×D₄₃	—	4	2	no	—
292	C₂×D₄₃	—	4	2	no	—
293	C₂×D₄₃	—	4	2	no	—
294	C₂×D₄₃	—	4	1	no	—
295	C₄×C₄₃	—	2	4	no	—
296	C₄×C₄₃	—	4	2	no	—
297	C₄×C₄₃	—	4	1	no	—
298	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
299	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
300	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
301	C₄×C₄₃	#532	1	1	yes	characteristic
302	Dic₄₃	—	2	2	no	—
303	Dic₄₃	—	4	2	no	—
304	Dic₄₃	—	4	2	no	—
305	Dic₄₃	—	4	1	no	—
306	#3054	—	43	1	no	—
307	C₂×#443	—	43	1	no	—
308	#2930	—	43	1	no	—
309	#2930	—	43	1	no	—
310	C₂×C₄×M₁₆	—	43	1	no	—
311	#1975	—	43	1	no	—
312	#1946	—	43	1	no	—
313	#1937	—	43	1	no	—
314	#1937	D₄₃	1	1	yes	characteristic, complemented
315	#1896	—	43	1	no	—
316	#1896	—	43	1	no	—
317	#1811	—	43	1	no	—
318	#1772	—	43	1	no	—
319	#1765	—	43	1	no	—
320	#1765	—	43	1	no	—
321	C₂×C₄₃	—	2	1	no	—
322	C₂×C₄₃	—	2	1	no	—
323	C₂×C₄₃	—	8	1	no	—
324	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
325	C₂×C₄₃	#2956	1	2	yes	—
326	D₄₃	—	4	2	no	—
327	D₄₃	—	8	1	no	—
328	C₂×#135	—	43	1	no	—
329	C₂×#131	—	43	1	no	—
330	C₂×#131	—	43	1	no	—
331	C₂²×M₁₆	—	43	1	no	—
332	C₂²×M₁₆	—	43	1	no	—
333	#525	—	43	1	no	—
334	#525	—	43	1	no	—
335	C₂²×C₄²	—	43	1	no	—
336	#470	—	43	2	no	—
337	#469	—	43	2	no	—
338	#468	—	43	2	no	—
339	#468	—	43	2	no	—
340	#443	—	86	4	no	—
341	#436	—	86	2	no	—
342	#436	—	86	2	no	—
343	#435	—	86	2	no	—
344	#435	—	86	2	no	—
345	C₂×#108	—	43	1	no	—
346	C₂×#108	—	43	1	no	—
347	#427	—	43	1	no	—
348	#424	—	43	1	no	—
349	#424	C₂×D₄₃	1	1	yes	characteristic
350	C₂×#104	—	43	1	no	—
351	C₂×#104	—	43	1	no	—
352	C₂×#104	—	43	1	no	—
353	C₂×#104	C₂×D₄₃	1	1	yes	characteristic
354	#416	—	43	1	no	—
355	#416	C₂×D₄₃	1	1	yes	characteristic
356	#408	—	43	1	no	—
357	#408	C₂×D₄₃	1	1	yes	characteristic
358	#407	—	43	1	no	—
359	#407	—	43	1	no	—
360	#405	—	43	1	no	—
361	#405	—	43	1	no	—
362	C₄×M₁₆	—	86	4	no	—
363	C₂×#97	—	43	1	no	—
364	C₂×#97	—	43	1	no	—
365	C₂×C₄×C₈	—	43	1	no	—
366	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
367	#341	—	43	1	no	—
368	#341	C₂×D₄₃	1	1	yes	characteristic
369	#339	—	43	1	no	—
370	#339	—	43	1	no	—
371	#339	—	43	1	no	—
372	#339	C₂×D₄₃	1	1	yes	characteristic
373	C₄₃	#21549	1	1	yes	characteristic, complemented, Sylow
374	C₂×#41	—	43	1	no	—
375	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
376	C₂³×C₄	—	43	1	no	—
377	C₂³×C₄	—	86	1	no	—
378	#135	—	86	2	no	—
379	#135	—	86	2	no	—
380	C₂×Q₁₆	—	43	1	no	—
381	C₂×SD₁₆	—	43	1	no	—
382	C₂×SD₁₆	—	43	1	no	—
383	C₂×D₈	—	43	1	no	—
384	#131	—	86	2	no	—
385	#131	—	86	2	no	—
386	#131	—	86	2	no	—
387	#131	—	86	2	no	—
388	C₂×M₁₆	—	43	2	no	—
389	C₂×M₁₆	—	43	2	no	—
390	C₂×M₁₆	—	43	2	no	—
391	C₂×M₁₆	—	43	2	no	—
392	C₂×M₁₆	—	43	1	no	—
393	C₂×M₁₆	—	43	1	no	—
394	C₂×M₁₆	—	86	2	no	—
395	C₂×M₁₆	—	86	2	no	—
396	C₂×M₁₆	—	86	2	no	—
397	C₂×M₁₆	—	86	2	no	—
398	C₂×M₁₆	—	86	1	no	—
399	C₂×M₁₆	—	86	1	no	—
400	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
401	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
402	C₂²×C₈	—	43	1	no	—
403	C₂²×C₈	—	43	1	no	—
404	C₂²×C₈	—	86	1	no	—
405	C₂²×C₈	—	86	1	no	—
406	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
407	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
408	#123	—	86	1	no	—
409	#123	—	86	1	no	—
410	C₂²⋊Q₈	—	43	2	no	—
411	C₂²⋊Q₈	—	43	2	no	—
412	#121	—	43	2	no	—
413	#121	—	43	2	no	—
414	#120	—	86	1	no	—
415	#120	—	86	1	no	—
416	C₄×D₄	—	86	2	no	—
417	C₄×D₄	—	86	2	no	—
418	#117	—	43	1	no	—
419	#117	C₂²×D₄₃	1	1	yes	characteristic
420	C₂×C₄²	—	43	1	no	—
421	C₂×C₄²	—	86	2	no	—
422	C₂×C₄²	—	86	1	no	—
423	C₂×C₄²	—	86	2	no	—
424	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
425	#108	—	86	2	no	—
426	#108	—	86	2	no	—
427	#107	—	43	2	no	—
428	#106	—	43	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₄⋊C₈	—	86	2	no	—
431	#104	—	2	2	no	—
432	#104	—	86	2	no	—
433	#104	—	86	2	no	—
434	#104	—	86	2	no	—
435	#103	—	43	2	no	—
436	#103	C₄×D₄₃	1	2	yes	complemented
437	#102	—	43	2	no	—
438	#102	C₄×D₄₃	1	2	yes	complemented
439	C₂²⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	—	86	2	no	—
441	C₂²⋊C₈	—	86	2	no	—
442	C₂²⋊C₈	—	86	2	no	—
443	#97	—	86	1	no	—
444	#97	—	86	2	no	—
445	#97	—	86	2	no	—
446	#97	—	86	1	no	—
447	C₄×C₈	—	2	2	no	—
448	C₄×C₈	—	43	4	no	—
449	C₄×C₈	—	86	1	no	—
450	C₄×C₈	—	86	1	no	—
451	C₂⁴	—	43	1	no	—
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	2	1	no	—
455	#41	—	2	1	no	—
456	#41	—	86	1	no	—
457	#41	—	86	1	no	—
458	#41	—	86	1	no	—
459	#41	—	86	1	no	—
460	C₂×Q₈	—	43	1	no	—
461	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	43	1	no	—
464	C₂×D₄	—	86	2	no	—
465	C₂×D₄	—	86	2	no	—
466	C₂×D₄	—	86	1	no	—
467	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	43	1	no	—
471	C₂²×C₄	—	43	2	no	—
472	C₂²×C₄	—	43	2	no	—
473	C₂²×C₄	—	86	4	no	—
474	C₂²×C₄	—	86	1	no	—
475	C₂²×C₄	—	86	1	no	—
476	C₂²×C₄	—	86	1	no	—
477	C₂²×C₄	—	86	1	no	—
478	C₂²×C₄	—	86	1	no	—
479	C₂²×C₄	—	86	1	no	—
480	C₂²×C₄	—	172	4	no	—
481	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
482	Q₁₆	—	86	2	no	—
483	SD₁₆	—	86	2	no	—
484	SD₁₆	—	86	2	no	—
485	D₈	—	86	2	no	—
486	M₁₆	—	2	1	no	—
487	M₁₆	—	2	1	no	—
488	M₁₆	—	2	1	no	—
489	M₁₆	—	2	1	no	—
490	M₁₆	—	86	4	no	—
491	M₁₆	—	86	4	no	—
492	M₁₆	—	86	4	no	—
493	M₁₆	—	86	4	no	—
494	M₁₆	—	86	1	no	—
495	M₁₆	—	86	1	no	—
496	M₁₆	—	86	1	no	—
497	M₁₆	—	86	1	no	—
498	M₁₆	—	172	2	no	—
499	M₁₆	—	172	2	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	43	1	no	—
507	C₂×C₈	—	43	1	no	—
508	C₂×C₈	—	43	2	no	—
509	C₂×C₈	—	43	2	no	—
510	C₂×C₈	—	43	1	no	—
511	C₂×C₈	—	43	1	no	—
512	C₂×C₈	—	43	2	no	—
513	C₂×C₈	—	43	2	no	—
514	C₂×C₈	—	86	1	no	—
515	C₂×C₈	—	86	1	no	—
516	C₂×C₈	—	172	2	no	—
517	C₂×C₈	—	172	2	no	—
518	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
519	C₂×C₈	D₄×D₄₃	1	2	yes	—
520	C₄⋊C₄	—	43	2	no	—
521	C₄⋊C₄	—	86	2	no	—
522	C₄⋊C₄	—	86	2	no	—
523	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	86	2	no	—
526	C₂²⋊C₄	—	86	2	no	—
527	C₂²⋊C₄	—	86	2	no	—
528	C₂²⋊C₄	—	86	2	no	—
529	C₂²⋊C₄	—	86	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	43	2	no	—
533	C₄²	—	86	4	no	—
534	C₄²	—	86	1	no	—
535	C₄²	—	86	1	no	—
536	C₄²	D₄×D₄₃	1	2	yes	—
537	C₂³	—	2	1	no	—
538	C₂³	—	43	2	no	—
539	C₂³	—	86	1	no	—
540	C₂³	—	86	1	no	—
541	C₂³	—	86	1	no	—
542	C₂³	—	172	2	no	—
543	C₂³	#41×D₄₃	1	1	yes	characteristic
544	Q₈	—	2	1	no	—
545	Q₈	—	2	1	no	—
546	Q₈	—	86	1	no	—
547	Q₈	—	86	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	86	1	no	—
553	D₄	—	86	1	no	—
554	D₄	—	344	2	no	—
555	D₄	—	344	2	no	—
556	D₄	—	172	1	no	—
557	D₄	—	172	1	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	43	2	no	—
565	C₂×C₄	—	86	1	no	—
566	C₂×C₄	—	86	1	no	—
567	C₂×C₄	—	86	2	no	—
568	C₂×C₄	—	86	2	no	—
569	C₂×C₄	—	86	2	no	—
570	C₂×C₄	—	86	2	no	—
571	C₂×C₄	—	86	2	no	—
572	C₂×C₄	—	86	1	no	—
573	C₂×C₄	—	86	2	no	—
574	C₂×C₄	—	172	8	no	—
575	C₂×C₄	—	172	2	no	—
576	C₂×C₄	—	172	1	no	—
577	C₂×C₄	—	172	1	no	—
578	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
579	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
580	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
581	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
582	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
583	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
584	C₈	—	2	2	no	—
585	C₈	—	2	2	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₈	—	43	2	no	—
589	C₈	—	43	2	no	—
590	C₈	—	43	2	no	—
591	C₈	—	43	2	no	—
592	C₈	—	172	1	no	—
593	C₈	—	172	1	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	86	2	no	—
598	C₂²	—	86	2	no	—
599	C₂²	—	86	2	no	—
600	C₂²	—	172	2	no	—
601	C₂²	—	172	2	no	—
602	C₂²	—	172	2	no	—
603	C₂²	—	172	1	no	—
604	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
605	C₂²	#14583407	1	1	yes	characteristic
606	C₂²	#14583432	1	1	yes	characteristic
607	C₄	—	2	4	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	86	2	no	—
611	C₄	—	172	2	no	—
612	C₄	—	172	2	no	—
613	C₄	—	172	1	no	—
614	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
615	C₄	#14583367	1	1	yes	characteristic
616	C₄	#121×D₄₃	1	1	yes	characteristic
617	C₄	#14583448	1	1	yes	characteristic
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	8	1	no	—
621	C₂	—	344	1	no	—
622	C₂	—	172	2	no	—
623	C₂	#19137107	1	1	yes	characteristic
624	C₂	#19143500	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1937	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19144203	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1937	D₄₃
hypocenter	C₄₃	#21549
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1937

Complements

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

N	H ≅ G/N	type
2. C₂×#14583013	C₂	semidirect
3. #19143301	C₂	semidirect
4. #19143297	C₂	semidirect
5. C₂×C₄×#10621872	C₂	semidirect
6. #19135487	C₂	semidirect
7. #19135345	C₂	semidirect
8. #19135299	C₂	semidirect
9. #19135037	C₂	semidirect
10. #19135035	C₂	semidirect
11. #19134636	C₂	semidirect
12. #19134473	C₂	semidirect
13. #19134442	C₂	semidirect
14. #19134438	C₂	semidirect
15. C₄₃×#1937	C₂	semidirect
24. #14583156	C₄	semidirect
25. #14583151	C₄	semidirect
26. #14583148	C₄	semidirect
27. #14583144	C₄	semidirect
66. C₂×#10621885	C₂×C₄	semidirect
67. C₂×#10621883	C₂×C₄	semidirect
68. C₂×#10621884	C₂×C₄	semidirect
69. C₂×#10621882	C₂×C₄	semidirect
107. #13063258	C₂×C₄	semidirect
108. #13063256	C₂×C₄	semidirect
113. #13063250	C₂×C₄	semidirect
114. #13063247	C₂×C₄	semidirect
123. C₄×C₄₃⋊C₈	D₄	semidirect
134. #103×C₄₃	C₂×C₄	semidirect
135. #102×C₄₃	C₂×C₄	semidirect
314. #1937	D₄₃	semidirect
373. C₄₃	#21549	semidirect
436. #103	C₄×D₄₃	semidirect
438. #102	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19144203	2
C₂×#14583013	2
#19143301	2
#19143297	2
C₂×C₄×#10621872	2
#19135487	2
#19135345	2
#19135299	2
#19135037	2
#19135035	2
#19134636	2
#19134473	2
#19134442	2
#19134438	2
C₄₃×#1937	2
#21549	43