Subgroups — #25097442

Order 11008.

1296 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	C₂×#14583665	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582881	C₂	1	1	yes	maximal, characteristic
4	#19143039	C₂	1	1	yes	maximal, characteristic
5	#19134813	C₂	1	8	yes	maximal, complemented
6	#19134321	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134321	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10621898	C₂²	1	1	yes	characteristic
10	#14583665	—	2	2	no	—
11	#14583665	—	2	2	no	—
12	#14583665	—	2	2	no	—
13	#14583665	C₂²	1	4	yes	—
14	C₂×#13063333	—	2	2	no	—
15	C₂×#13063331	—	2	2	no	—
16	C₂²×#10621877	C₂²	1	1	yes	characteristic
17	C₂²×#10621877	C₂²	1	1	yes	characteristic
18	C₂²×#10621877	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×D₄₃	—	2	2	no	—
20	#14582947	—	2	2	no	—
21	#14582947	C₂²	1	4	yes	complemented
22	C₂×#13063260	—	2	2	no	—
23	#14582881	C₄	1	4	yes	—
24	#14582881	C₂²	1	4	yes	—
25	C₂×#13063243	C₄	1	2	yes	—
26	C₂×#13063241	C₄	1	2	yes	—
27	#14582867	C₂²	1	4	yes	—
28	#14582865	—	2	2	no	—
29	#14582862	—	2	2	no	—
30	#14582663	C₂²	1	4	yes	complemented
31	#14582663	C₂²	1	4	yes	complemented
32	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
33	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×#430	—	2	2	no	—
36	C₄₃×#430	C₂²	1	4	yes	complemented
37	C₂×#108×C₄₃	—	2	2	no	—
38	C₂×#10621898	—	2	1	no	—
39	C₂×#10621898	—	2	1	no	—
40	C₂×#10621898	—	2	1	no	—
41	C₂×#10621898	—	2	1	no	—
42	C₂×#10621898	—	2	1	no	—
43	C₂×#10621898	—	2	1	no	—
44	C₂×#10621898	—	2	1	no	—
45	C₂×#10621898	—	2	1	no	—
46	C₂×#10621898	C₂×C₄	1	2	yes	—
47	C₂×#10621898	D₄	1	2	yes	—
48	C₂×#10621898	Q₈	1	2	yes	—
49	C₂×#10621898	C₂³	1	2	yes	—
50	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₂²⋊D₄₃	Q₈	1	2	yes	—
53	C₂²×C₄×D₄₃	D₄	1	2	yes	—
54	#13063333	—	2	8	no	—
55	#13063333	—	2	8	no	—
56	#13063331	—	2	8	no	—
57	#13063331	—	2	8	no	—
58	C₂×#10621877	—	2	1	no	—
59	C₂×#10621877	—	2	1	no	—
60	C₂×#10621877	—	2	1	no	—
61	C₂×#10621877	—	2	1	no	—
62	C₂×#10621877	—	2	1	no	—
63	C₂×#10621877	—	2	1	no	—
64	C₂×#10621877	—	2	1	no	—
65	C₂×#10621877	—	2	1	no	—
66	C₂×#10621877	—	2	1	no	—
67	C₂×#10621877	—	2	1	no	—
68	C₂×#10621877	—	2	1	no	—
69	C₂×#10621877	—	2	1	no	—
70	C₂×#10621877	C₂×C₄	1	2	yes	—
71	C₂×#10621877	C₂×C₄	1	2	yes	—
72	C₂×#10621877	D₄	1	2	yes	—
73	C₂×#10621877	D₄	1	2	yes	—
74	C₂×#10621877	C₂³	1	2	yes	—
75	C₂×#10621877	C₂³	1	2	yes	—
76	C₂×#10621872	—	2	4	no	—
77	M₁₆×D₄₃	—	2	8	no	—
78	M₁₆×D₄₃	—	2	8	no	—
79	C₂²×C₄₃⋊C₈	—	2	1	no	—
80	C₂²×C₄₃⋊C₈	—	2	1	no	—
81	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
82	C₂×C₈×D₄₃	—	2	4	no	—
83	#13063260	—	2	8	no	—
84	#13063243	C₂×C₄	1	8	yes	—
85	#13063241	C₂×C₄	1	8	yes	—
86	(C₂×D₄₃)⋊C₈	—	2	8	no	—
87	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₂×M₁₆×C₄₃	—	2	1	no	—
91	C₂×M₁₆×C₄₃	—	2	1	no	—
92	C₂×M₁₆×C₄₃	—	2	1	no	—
93	C₂×M₁₆×C₄₃	—	2	1	no	—
94	C₂×M₁₆×C₄₃	—	2	1	no	—
95	C₂×M₁₆×C₄₃	—	2	1	no	—
96	C₂×M₁₆×C₄₃	—	2	1	no	—
97	C₂×M₁₆×C₄₃	—	2	1	no	—
98	C₂×M₁₆×C₄₃	—	2	1	no	—
99	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
100	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
101	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
102	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
103	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
104	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
106	C₂²×C₈×C₄₃	—	2	1	no	—
107	C₂²×C₈×C₄₃	—	2	1	no	—
108	C₂²×C₈×C₄₃	—	2	1	no	—
109	#108×C₄₃	—	2	8	no	—
110	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
111	C₂³×D₄₃	C₄⋊C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
126	C₂×C₂²⋊D₄₃	—	2	2	no	—
127	C₂×C₂²⋊D₄₃	—	2	2	no	—
128	C₂×C₂²⋊D₄₃	—	2	2	no	—
129	C₂×C₂²⋊D₄₃	—	2	2	no	—
130	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	4	yes	—
131	C₂×C₂²⋊D₄₃	C₂×Q₈	1	4	yes	—
132	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	#10621898	—	2	2	no	—
136	#10621898	—	2	2	no	—
137	#10621898	—	2	2	no	—
138	#10621898	—	2	2	no	—
139	#10621898	—	2	2	no	—
140	#10621898	—	2	2	no	—
141	#10621898	—	2	2	no	—
142	#10621898	—	2	2	no	—
143	#10621898	—	2	2	no	—
144	#10621898	—	2	2	no	—
145	#10621898	—	2	2	no	—
146	#10621898	—	2	2	no	—
147	#10621898	—	2	2	no	—
148	#10621898	—	2	2	no	—
149	C₂×D₁₇₂	—	2	1	no	—
150	C₂×D₁₇₂	—	2	1	no	—
151	C₂×D₁₇₂	—	2	1	no	—
152	C₂×D₁₇₂	—	2	1	no	—
153	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
154	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
155	C₂×C₄×D₄₃	—	2	2	no	—
156	C₂×C₄×D₄₃	—	2	2	no	—
157	C₂×C₄×D₄₃	—	2	2	no	—
158	C₂×C₄×D₄₃	—	2	2	no	—
159	C₂×C₄×D₄₃	C₄⋊C₄	1	4	yes	—
160	C₂×C₄×D₄₃	C₂×D₄	1	4	yes	—
161	C₂×Dic₈₆	—	2	1	no	—
162	C₂×Dic₈₆	—	2	1	no	—
163	C₂×Dic₈₆	—	2	1	no	—
164	C₂×Dic₈₆	—	2	1	no	—
165	C₂×Dic₈₆	C₄⋊C₄	1	2	yes	—
166	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
167	M₁₆×C₄₃	—	2	2	no	—
168	M₁₆×C₄₃	—	2	2	no	—
169	M₁₆×C₄₃	—	2	2	no	—
170	M₁₆×C₄₃	—	2	2	no	—
171	M₁₆×C₄₃	—	2	2	no	—
172	M₁₆×C₄₃	—	2	2	no	—
173	M₁₆×C₄₃	—	2	2	no	—
174	M₁₆×C₄₃	—	2	2	no	—
175	M₁₆×C₄₃	—	4	1	no	—
176	M₁₆×C₄₃	—	4	1	no	—
177	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
178	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
179	C₂×C₈×C₄₃	—	2	2	no	—
180	C₂×C₈×C₄₃	—	2	2	no	—
181	C₂×C₈×C₄₃	—	2	2	no	—
182	C₂×C₈×C₄₃	—	2	2	no	—
183	C₂×C₈×C₄₃	—	2	2	no	—
184	C₂×C₈×C₄₃	—	2	2	no	—
185	C₂×C₈×C₄₃	—	2	2	no	—
186	C₂×C₈×C₄₃	—	4	1	no	—
187	C₂×C₈×C₄₃	—	4	1	no	—
188	#10621877	—	2	2	no	—
189	#10621877	—	2	2	no	—
190	#10621877	—	2	2	no	—
191	#10621877	—	2	2	no	—
192	#10621877	—	2	2	no	—
193	#10621877	—	2	2	no	—
194	#10621877	—	4	1	no	—
195	#10621877	—	4	1	no	—
196	#10621877	—	4	1	no	—
197	#10621877	—	4	1	no	—
198	#10621877	C₂²×C₄	1	4	yes	—
199	#10621877	C₂×D₄	1	4	yes	—
200	C₂×C₄₃⋊C₈	—	2	2	no	—
201	C₂×C₄₃⋊C₈	—	2	2	no	—
202	C₂×C₄₃⋊C₈	—	2	2	no	—
203	C₂×C₄₃⋊C₈	—	2	2	no	—
204	C₂×C₄₃⋊C₈	—	2	2	no	—
205	C₂×C₄₃⋊C₈	—	2	2	no	—
206	C₂×C₄₃⋊C₈	—	2	2	no	—
207	C₂×C₄₃⋊C₈	—	2	2	no	—
208	C₂×C₄₃⋊C₈	—	2	2	no	—
209	#10621872	—	2	16	no	—
210	C₈×D₄₃	—	2	16	no	—
211	C₂³×C₄₃	—	8	1	no	—
212	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
215	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
216	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
217	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
219	C₂²×D₄₃	—	2	2	no	—
220	C₂²×D₄₃	—	2	2	no	—
221	C₂²×D₄₃	—	8	2	no	—
222	C₂²×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
223	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
234	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
235	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
242	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
243	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
244	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
251	C₂²⋊D₄₃	—	2	4	no	—
252	C₂²⋊D₄₃	—	2	4	no	—
253	C₂²⋊D₄₃	—	2	4	no	—
254	C₂²⋊D₄₃	—	2	4	no	—
255	C₂×Dic₄₃	—	2	2	no	—
256	C₂×Dic₄₃	—	2	2	no	—
257	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
258	D₁₇₂	—	2	2	no	—
259	D₁₇₂	—	2	2	no	—
260	D₁₇₂	—	2	2	no	—
261	D₁₇₂	—	2	2	no	—
262	C₄×D₄₃	—	2	4	no	—
263	C₄×D₄₃	—	2	4	no	—
264	C₄×D₄₃	—	2	4	no	—
265	C₄×D₄₃	—	2	4	no	—
266	Dic₈₆	—	2	2	no	—
267	Dic₈₆	—	2	2	no	—
268	Dic₈₆	—	2	2	no	—
269	Dic₈₆	—	2	2	no	—
270	C₈×C₄₃	—	2	4	no	—
271	C₈×C₄₃	—	2	4	no	—
272	C₈×C₄₃	—	4	2	no	—
273	C₄₃⋊C₈	—	2	4	no	—
274	C₄₃⋊C₈	—	2	4	no	—
275	C₄₃⋊C₈	—	4	2	no	—
276	#20860	—	43	1	no	maximal, Sylow
277	C₂²×C₄₃	—	4	1	no	—
278	C₂²×C₄₃	—	4	1	no	—
279	C₂²×C₄₃	—	4	1	no	—
280	C₂²×C₄₃	—	4	1	no	—
281	C₂²×C₄₃	—	4	1	no	—
282	C₂²×C₄₃	—	4	1	no	—
283	C₂²×C₄₃	—	4	1	no	—
284	C₂²×C₄₃	#385	1	1	yes	characteristic
285	C₂²×C₄₃	#385	1	1	yes	characteristic
286	C₂²×C₄₃	#385	1	1	yes	characteristic
287	C₂²×C₄₃	#385	1	1	yes	characteristic
288	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
289	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
290	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
291	C₂×D₄₃	—	2	4	no	—
292	C₂×D₄₃	—	4	4	no	—
293	C₂×D₄₃	—	4	4	no	—
294	C₂×D₄₃	—	8	2	no	—
295	C₄×C₄₃	#385	1	1	yes	characteristic
296	C₄×C₄₃	#385	1	1	yes	characteristic
297	C₄×C₄₃	#385	1	1	yes	characteristic
298	C₄×C₄₃	#385	1	1	yes	characteristic
299	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
300	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
301	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
302	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
303	Dic₄₃	—	2	4	no	—
304	C₂×#568	—	43	1	no	—
305	C₂×#430	—	43	1	no	—
306	C₂×#430	D₄₃	1	1	yes	characteristic, complemented
307	C₂×#413	—	43	1	no	—
308	#2879	—	43	1	no	—
309	#1858	—	43	8	no	—
310	#1738	—	43	1	no	—
311	#1738	—	43	1	no	—
312	C₂×C₄₃	—	2	1	no	—
313	C₂×C₄₃	—	2	1	no	—
314	C₂×C₄₃	—	2	1	no	—
315	C₂×C₄₃	—	2	1	no	—
316	C₂×C₄₃	—	2	1	no	—
317	C₂×C₄₃	—	2	1	no	—
318	C₂×C₄₃	—	2	1	no	—
319	C₂×C₄₃	C₂×#385	1	1	yes	characteristic
320	D₄₃	—	4	4	no	—
321	C₂²×#41	—	43	1	no	—
322	#568	—	43	4	no	—
323	#568	—	86	2	no	—
324	#568	—	86	2	no	—
325	#568	—	86	2	no	—
326	C₂×#131	—	86	2	no	—
327	C₂×#131	—	86	2	no	—
328	C₂²×M₁₆	—	43	1	no	—
329	C₂²×M₁₆	—	43	1	no	—
330	C₂²×M₁₆	—	43	1	no	—
331	C₂²×M₁₆	—	86	2	no	—
332	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
333	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
334	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
335	#430	—	2	2	no	—
336	#430	—	43	4	no	—
337	#430	—	86	2	no	—
338	#430	C₂×D₄₃	1	4	yes	complemented
339	C₂×#108	—	2	2	no	—
340	C₂×#108	—	86	2	no	—
341	#413	—	43	4	no	—
342	#413	—	43	4	no	—
343	C₂×#101	—	43	2	no	—
344	C₂×#100	—	43	2	no	—
345	#408	—	43	4	no	—
346	#408	—	86	2	no	—
347	#407	—	86	2	no	—
348	#341	—	43	4	no	—
349	#341	—	43	4	no	—
350	C₄₃	#20860	1	1	yes	characteristic, complemented, Sylow
351	C₂×#41	—	43	2	no	—
352	C₂×#41	—	43	2	no	—
353	C₂×#41	—	43	2	no	—
354	C₂×#41	—	43	2	no	—
355	C₂×#41	—	86	1	no	—
356	C₂×#41	—	86	1	no	—
357	C₂×#41	—	86	1	no	—
358	C₂×#41	—	86	1	no	—
359	C₂×#41	—	86	1	no	—
360	C₂×#41	—	86	1	no	—
361	C₂×#41	—	86	1	no	—
362	C₂×#41	—	86	1	no	—
363	C₂²×Q₈	—	43	1	no	—
364	C₂²×D₄	—	43	2	no	—
365	C₂²×D₄	—	43	1	no	—
366	C₂³×C₄	—	43	2	no	—
367	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
368	#131	—	86	8	no	—
369	#131	—	86	8	no	—
370	#131	—	86	8	no	—
371	#131	—	86	8	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	43	2	no	—
384	C₂×M₁₆	—	43	2	no	—
385	C₂×M₁₆	—	43	2	no	—
386	C₂×M₁₆	—	43	2	no	—
387	C₂×M₁₆	—	43	2	no	—
388	C₂×M₁₆	—	43	2	no	—
389	C₂×M₁₆	—	86	4	no	—
390	C₂×M₁₆	—	86	8	no	—
391	C₂×M₁₆	—	86	8	no	—
392	C₂×M₁₆	—	86	1	no	—
393	C₂×M₁₆	—	86	1	no	—
394	C₂×M₁₆	—	86	1	no	—
395	C₂×M₁₆	—	86	1	no	—
396	C₂×M₁₆	—	86	1	no	—
397	C₂×M₁₆	—	86	1	no	—
398	C₂×M₁₆	—	86	1	no	—
399	C₂×M₁₆	—	86	1	no	—
400	C₂×M₁₆	—	86	1	no	—
401	C₂×M₁₆	—	86	1	no	—
402	C₂×M₁₆	—	86	1	no	—
403	C₂×M₁₆	—	86	1	no	—
404	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
405	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
406	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
407	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
408	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
409	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
410	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
411	C₂²×C₈	—	2	1	no	—
412	C₂²×C₈	—	2	1	no	—
413	C₂²×C₈	—	2	1	no	—
414	C₂²×C₈	—	43	2	no	—
415	C₂²×C₈	—	86	4	no	—
416	C₂²×C₈	—	86	1	no	—
417	C₂²×C₈	—	86	1	no	—
418	#108	—	2	8	no	—
419	#108	—	86	8	no	—
420	#101	—	43	8	no	—
421	#100	—	43	8	no	—
422	C₂²⋊C₈	—	86	8	no	—
423	C₂⁴	—	43	2	no	—
424	C₂⁴	Q₈×D₄₃	1	1	yes	characteristic
425	#41	—	86	2	no	—
426	#41	—	86	2	no	—
427	#41	—	86	2	no	—
428	#41	—	86	2	no	—
429	#41	—	86	2	no	—
430	#41	—	86	2	no	—
431	#41	—	86	2	no	—
432	#41	—	86	2	no	—
433	#41	—	86	2	no	—
434	#41	—	86	2	no	—
435	#41	—	86	2	no	—
436	#41	—	86	2	no	—
437	#41	—	86	2	no	—
438	#41	—	86	2	no	—
439	#41	—	86	2	no	—
440	#41	—	86	2	no	—
441	C₂×Q₈	—	43	2	no	—
442	C₂×Q₈	—	43	2	no	—
443	C₂×Q₈	—	86	1	no	—
444	C₂×Q₈	—	86	1	no	—
445	C₂×Q₈	—	86	1	no	—
446	C₂×Q₈	—	86	1	no	—
447	C₂×D₄	—	43	4	no	—
448	C₂×D₄	—	43	4	no	—
449	C₂×D₄	—	43	2	no	—
450	C₂×D₄	—	43	2	no	—
451	C₂×D₄	—	86	2	no	—
452	C₂×D₄	—	86	2	no	—
453	C₂×D₄	—	86	2	no	—
454	C₂×D₄	—	86	2	no	—
455	C₂×D₄	—	86	1	no	—
456	C₂×D₄	—	86	1	no	—
457	C₂×D₄	—	86	1	no	—
458	C₂×D₄	—	86	1	no	—
459	C₂²×C₄	—	43	2	no	—
460	C₂²×C₄	—	43	4	no	—
461	C₂²×C₄	—	43	4	no	—
462	C₂²×C₄	—	86	2	no	—
463	C₂²×C₄	—	86	2	no	—
464	C₂²×C₄	—	86	2	no	—
465	C₂²×C₄	—	86	2	no	—
466	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
468	C₂²×C₄	#10621898	1	1	yes	characteristic
469	C₂²×C₄	#10621898	1	1	yes	characteristic
470	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
471	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
472	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
473	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
474	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
475	C₂²×C₄	#10621902	1	1	yes	characteristic
476	C₂²×C₄	#10621902	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
479	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	4	1	no	—
490	M₁₆	—	43	4	no	—
491	M₁₆	—	43	4	no	—
492	M₁₆	—	86	16	no	—
493	M₁₆	—	86	2	no	—
494	M₁₆	—	86	2	no	—
495	M₁₆	—	86	2	no	—
496	M₁₆	—	86	2	no	—
497	M₁₆	—	86	2	no	—
498	M₁₆	—	86	2	no	—
499	M₁₆	—	172	1	no	—
500	M₁₆	—	172	1	no	—
501	M₁₆	—	172	1	no	—
502	M₁₆	—	172	1	no	—
503	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
504	M₁₆	C₂×C₂²⋊D₄₃	1	4	yes	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	4	1	no	—
513	C₂×C₈	—	4	1	no	—
514	C₂×C₈	—	86	16	no	—
515	C₂×C₈	—	86	2	no	—
516	C₂×C₈	—	86	2	no	—
517	C₂×C₈	—	86	2	no	—
518	C₂×C₈	—	86	2	no	—
519	C₂×C₈	—	86	2	no	—
520	C₂×C₈	—	86	2	no	—
521	C₂×C₈	—	86	2	no	—
522	C₂×C₈	—	86	2	no	—
523	C₂×C₈	—	86	2	no	—
524	C₂³	—	8	1	no	—
525	C₂³	—	43	4	no	—
526	C₂³	—	86	2	no	—
527	C₂³	—	86	2	no	—
528	C₂³	—	344	2	no	—
529	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
530	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
531	C₂³	#13063301	1	1	yes	characteristic
532	C₂³	#13063301	1	1	yes	characteristic
533	C₂³	#13063303	1	1	yes	characteristic
534	C₂³	#13063303	1	1	yes	characteristic
535	C₂³	C₂×Q₈×D₄₃	1	1	yes	characteristic
536	Q₈	—	86	2	no	—
537	Q₈	—	86	2	no	—
538	Q₈	—	86	2	no	—
539	Q₈	—	86	2	no	—
540	D₄	—	86	4	no	—
541	D₄	—	86	4	no	—
542	D₄	—	86	4	no	—
543	D₄	—	86	4	no	—
544	D₄	—	86	2	no	—
545	D₄	—	86	2	no	—
546	D₄	—	86	2	no	—
547	D₄	—	86	2	no	—
548	C₂×C₄	—	43	4	no	—
549	C₂×C₄	—	86	2	no	—
550	C₂×C₄	—	86	2	no	—
551	C₂×C₄	—	86	4	no	—
552	C₂×C₄	—	86	4	no	—
553	C₂×C₄	—	86	4	no	—
554	C₂×C₄	—	86	4	no	—
555	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
556	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
557	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
558	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
559	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
560	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
561	C₂×C₄	#13063287	1	1	yes	characteristic
562	C₂×C₄	#13063287	1	1	yes	characteristic
563	C₂×C₄	#13063287	1	1	yes	characteristic
564	C₂×C₄	#13063287	1	1	yes	characteristic
565	C₂×C₄	#13063293	1	1	yes	characteristic
566	C₂×C₄	#13063293	1	1	yes	characteristic
567	C₂×C₄	#13063293	1	1	yes	characteristic
568	C₂×C₄	#13063293	1	1	yes	characteristic
569	C₂×C₄	#13063301	1	1	yes	characteristic
570	C₂×C₄	#13063301	1	1	yes	characteristic
571	C₂×C₄	#13063303	1	1	yes	characteristic
572	C₂×C₄	#13063303	1	1	yes	characteristic
573	C₂×C₄	#13063310	1	1	yes	characteristic
574	C₂×C₄	#13063310	1	1	yes	characteristic
575	C₂×C₄	#13063310	1	1	yes	characteristic
576	C₂×C₄	#13063310	1	1	yes	characteristic
577	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
578	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
579	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
580	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
581	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
582	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
583	C₈	—	2	4	no	—
584	C₈	—	2	4	no	—
585	C₈	—	4	2	no	—
586	C₈	—	86	4	no	—
587	C₈	—	86	4	no	—
588	C₈	—	172	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	86	4	no	—
597	C₂²	—	344	2	no	—
598	C₂²	—	172	4	no	—
599	C₂²	—	172	4	no	—
600	C₂²	#14582770	1	1	yes	characteristic
601	C₂²	#14582770	1	1	yes	characteristic
602	C₂²	#14582770	1	1	yes	characteristic
603	C₂²	#14582770	1	1	yes	characteristic
604	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
605	C₂²	C₂×#13063301	1	1	yes	characteristic
606	C₂²	C₂×#13063303	1	1	yes	characteristic
607	C₄	—	86	4	no	—
608	C₄	#14582770	1	1	yes	characteristic
609	C₄	#14582770	1	1	yes	characteristic
610	C₄	#14582770	1	1	yes	characteristic
611	C₄	#14582770	1	1	yes	characteristic
612	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
613	C₄	C₂×#13063287	1	1	yes	characteristic
614	C₄	C₂×#13063293	1	1	yes	characteristic
615	C₄	C₂×#13063310	1	1	yes	characteristic
616	C₂	—	2	1	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	172	4	no	—
624	C₂	C₂×#14582770	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13063293
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#430	C₂
socle	C₂×C₄₃	C₂×#385
prime radical	C₂²×#10621898	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#430	D₄₃
hypocenter	C₄₃	#20860
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#430

Complements

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

N	H ≅ G/N	type
2. C₂×#14582947	C₂	semidirect
5. #19134813	C₂	semidirect
6. #19134321	C₂	semidirect
7. #19134321	C₂	semidirect
8. C₂×C₄₃×#430	C₂	semidirect
21. #14582947	C₂²	semidirect
30. #14582663	C₂²	semidirect
31. #14582663	C₂²	semidirect
36. C₄₃×#430	C₂²	semidirect
306. C₂×#430	D₄₃	semidirect
338. #430	C₂×D₄₃	semidirect
350. C₄₃	#20860	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583665	2
C₂×#14582947	2
C₂×#14582881	2
#19143039	2
#19134813	2
#19134321	2
C₂×C₄₃×#430	2
#20860	43