Subgroups — #25002910

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063251	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582893	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582865	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582663	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582658	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×#13063251	—	2	2	no	—
13	C₂×#13063251	—	2	2	no	—
14	C₂×#13063251	C₄	1	4	yes	complemented
15	#14582893	—	2	2	no	—
16	#14582893	—	2	2	no	—
17	C₂×#13063248	C₄	1	2	yes	complemented
18	C₂×#13063245	C₄	1	2	yes	complemented
19	#14582865	—	2	2	no	—
20	#14582865	C₄	1	4	yes	complemented
21	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
22	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
23	#14582663	—	2	2	no	—
24	#14582658	—	2	2	no	—
25	#14582653	—	2	2	no	—
26	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#405	—	2	2	no	—
30	C₄₃×#405	—	2	2	no	—
31	C₂×#97×C₄₃	—	2	1	no	—
32	C₂×C₄×C₈×C₄₃	—	2	1	no	—
33	C₂×#10621898	—	2	1	no	—
34	C₂×#10621898	—	2	1	no	—
35	C₂×#10621898	—	2	1	no	—
36	C₂×#10621898	—	2	1	no	—
37	C₂×#10621898	—	2	1	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	C₂×C₄	1	2	yes	—
44	C₂×#10621898	C₂×C₄	1	2	yes	—
45	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₄₃	—	2	1	no	—
48	C₂³×Dic₄₃	—	2	1	no	—
49	C₂²×C₄×D₄₃	—	2	1	no	—
50	C₂×#10621877	—	2	1	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂×#10621877	—	2	1	no	—
53	C₂×#10621877	—	2	1	no	—
54	C₂×#10621877	—	2	1	no	—
55	C₂×#10621877	C₂×C₄	1	2	yes	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	C₂²×C₄₃⋊C₈	—	2	1	no	—
58	C₂²×C₄₃⋊C₈	—	2	1	no	—
59	C₂²×C₄₃⋊C₈	—	2	1	no	—
60	C₂²×C₄₃⋊C₈	—	2	1	no	—
61	C₂²×C₄₃⋊C₈	—	2	1	no	—
62	C₂²×C₄₃⋊C₈	—	2	1	no	—
63	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₄₃	—	2	1	no	—
65	C₂×C₄×Dic₄₃	—	2	1	no	—
66	C₂×C₄×Dic₄₃	—	2	1	no	—
67	C₂×C₄×Dic₄₃	—	2	1	no	—
68	C₂×C₄×Dic₄₃	—	2	1	no	—
69	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
70	#13063251	—	2	8	no	—
71	#13063248	—	2	4	no	—
72	#13063245	—	2	4	no	—
73	(C₂×D₄₃)⋊C₈	—	2	4	no	—
74	(C₂×D₄₃)⋊C₈	—	2	4	no	—
75	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₄₃	—	2	1	no	—
77	C₂×M₁₆×C₄₃	—	2	1	no	—
78	C₂×M₁₆×C₄₃	—	2	1	no	—
79	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
81	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
82	C₂²×C₈×C₄₃	—	2	1	no	—
83	C₂²×C₈×C₄₃	—	2	1	no	—
84	C₂²×C₈×C₄₃	—	2	1	no	—
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	C₂²×C₈×C₄₃	—	2	1	no	—
87	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₄₃	D₄	1	2	yes	—
89	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
90	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
91	#117×C₄₃	—	2	1	no	—
92	#117×C₄₃	—	2	1	no	—
93	#117×C₄₃	D₄	1	2	yes	—
94	#117×C₄₃	D₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₄²×C₄₃	—	2	1	no	—
98	#97×C₄₃	—	2	4	no	—
99	C₄×C₈×C₄₃	—	2	4	no	—
100	C₂⁴×C₄₃	#41	1	1	yes	characteristic
101	C₂³×D₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₃	—	2	2	no	—
118	C₂×C₂²⋊D₄₃	—	2	2	no	—
119	C₂×C₂²⋊D₄₃	—	4	1	no	—
120	C₂×C₂²⋊D₄₃	—	4	1	no	—
121	C₂×C₂²⋊D₄₃	—	4	1	no	—
122	C₂×C₂²⋊D₄₃	—	4	1	no	—
123	C₂²×Dic₄₃	—	2	4	no	—
124	C₂²×Dic₄₃	—	2	2	no	—
125	C₂²×Dic₄₃	—	2	1	no	—
126	C₂²×Dic₄₃	—	4	2	no	—
127	C₂²×Dic₄₃	—	4	1	no	—
128	C₂²×Dic₄₃	—	4	1	no	—
129	#10621898	—	2	2	no	—
130	#10621898	—	2	2	no	—
131	#10621898	—	2	2	no	—
132	#10621898	—	2	2	no	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	#10621898	—	2	2	no	—
136	#10621898	—	2	2	no	—
137	#10621898	—	4	1	no	—
138	#10621898	—	4	1	no	—
139	#10621898	—	4	1	no	—
140	#10621898	—	4	1	no	—
141	#10621898	—	4	1	no	—
142	#10621898	—	4	1	no	—
143	#10621898	—	4	1	no	—
144	#10621898	—	4	1	no	—
145	C₂×D₁₇₂	—	2	1	no	—
146	C₂×D₁₇₂	—	2	1	no	—
147	C₂×D₁₇₂	—	2	1	no	—
148	C₂×D₁₇₂	—	2	1	no	—
149	C₂×D₁₇₂	—	2	1	no	—
150	C₂×D₁₇₂	C₄²	1	2	yes	—
151	C₂×C₄×D₄₃	—	2	2	no	—
152	C₂×C₄×D₄₃	—	2	2	no	—
153	C₂×C₄×D₄₃	—	4	1	no	—
154	C₂×C₄×D₄₃	—	4	1	no	—
155	C₂×C₄×D₄₃	—	4	1	no	—
156	C₂×C₄×D₄₃	—	4	1	no	—
157	C₂×Dic₈₆	—	2	1	no	—
158	C₂×Dic₈₆	—	2	1	no	—
159	C₂×Dic₈₆	—	2	1	no	—
160	C₂×Dic₈₆	—	2	1	no	—
161	C₂×Dic₈₆	—	2	1	no	—
162	C₂×Dic₈₆	C₄²	1	2	yes	—
163	M₁₆×C₄₃	—	2	2	no	—
164	M₁₆×C₄₃	—	2	2	no	—
165	M₁₆×C₄₃	—	2	2	no	—
166	M₁₆×C₄₃	C₂²⋊C₄	1	4	yes	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	1	no	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	2	1	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	2	1	no	—
177	C₂×C₈×C₄₃	—	2	1	no	—
178	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
179	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
180	C₄⋊C₄×C₄₃	—	2	2	no	—
181	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
182	C₂²⋊C₄×C₄₃	—	2	2	no	—
183	C₂²⋊C₄×C₄₃	—	2	2	no	—
184	C₄²×C₄₃	—	2	2	no	—
185	C₄²×C₄₃	—	2	2	no	—
186	C₄×Dic₄₃	—	2	2	no	—
187	C₄×Dic₄₃	—	2	2	no	—
188	C₄×Dic₄₃	—	4	1	no	—
189	C₄×Dic₄₃	—	4	1	no	—
190	#10621877	—	2	2	no	—
191	#10621877	—	2	2	no	—
192	#10621877	—	4	1	no	—
193	#10621877	—	4	1	no	—
194	C₂×C₄₃⋊C₈	—	2	2	no	—
195	C₂×C₄₃⋊C₈	—	2	2	no	—
196	C₂×C₄₃⋊C₈	—	2	2	no	—
197	C₂×C₄₃⋊C₈	—	2	2	no	—
198	C₂×C₄₃⋊C₈	—	4	1	no	—
199	C₂×C₄₃⋊C₈	—	4	1	no	—
200	C₂×C₄₃⋊C₈	—	4	1	no	—
201	C₂×C₄₃⋊C₈	—	4	1	no	—
202	C₂×C₄₃⋊C₈	—	4	1	no	—
203	C₂×C₄₃⋊C₈	—	4	1	no	—
204	C₂³×C₄₃	—	2	2	no	—
205	C₂³×C₄₃	—	2	2	no	—
206	C₂³×C₄₃	#117	1	1	yes	characteristic
207	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
208	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
209	C₂³×C₄₃	#121	1	1	yes	characteristic
210	C₂³×C₄₃	#123	1	1	yes	characteristic
211	C₂³×C₄₃	#124	1	1	yes	characteristic
212	C₂³×C₄₃	#126	1	1	yes	characteristic
213	C₂²×D₄₃	—	2	2	no	—
214	C₂²×D₄₃	—	4	1	no	—
215	C₂²×D₄₃	—	4	1	no	—
216	C₂²×D₄₃	—	4	2	no	—
217	C₂²×D₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
226	C₂×C₄×C₄₃	#117	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	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
238	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
239	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
240	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₃	#121	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	#124	1	1	yes	characteristic
246	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
247	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
248	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
249	C₂²⋊D₄₃	—	4	2	no	—
250	C₂²⋊D₄₃	—	4	2	no	—
251	C₂²⋊D₄₃	—	4	2	no	—
252	C₂²⋊D₄₃	—	4	2	no	—
253	C₂×Dic₄₃	—	2	4	no	—
254	C₂×Dic₄₃	—	2	2	no	—
255	C₂×Dic₄₃	—	4	4	no	—
256	C₂×Dic₄₃	—	4	4	no	—
257	C₂×Dic₄₃	—	4	2	no	—
258	C₂×Dic₄₃	—	4	1	no	—
259	C₂×Dic₄₃	—	4	1	no	—
260	C₂×Dic₄₃	—	4	2	no	—
261	D₁₇₂	—	2	2	no	—
262	D₁₇₂	—	2	2	no	—
263	D₁₇₂	—	4	1	no	—
264	D₁₇₂	—	4	1	no	—
265	C₄×D₄₃	—	4	2	no	—
266	C₄×D₄₃	—	4	2	no	—
267	C₄×D₄₃	—	4	2	no	—
268	C₄×D₄₃	—	4	2	no	—
269	Dic₈₆	—	2	2	no	—
270	Dic₈₆	—	2	2	no	—
271	Dic₈₆	—	4	1	no	—
272	Dic₈₆	—	4	1	no	—
273	C₈×C₄₃	—	2	2	no	—
274	C₈×C₄₃	—	2	2	no	—
275	C₈×C₄₃	—	2	4	no	—
276	C₄₃⋊C₈	—	4	2	no	—
277	C₄₃⋊C₈	—	4	2	no	—
278	#10934	—	43	1	no	maximal, Sylow
279	C₂²×C₄₃	—	2	2	no	—
280	C₂²×C₄₃	—	2	2	no	—
281	C₂²×C₄₃	—	2	2	no	—
282	C₂²×C₄₃	—	2	2	no	—
283	C₂²×C₄₃	—	2	1	no	—
284	C₂²×C₄₃	—	2	1	no	—
285	C₂²×C₄₃	—	2	1	no	—
286	C₂²×C₄₃	—	2	1	no	—
287	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
288	C₂²×C₄₃	#386	1	1	yes	characteristic
289	C₂²×C₄₃	#388	1	1	yes	characteristic
290	C₂²×C₄₃	#388	1	1	yes	characteristic
291	C₂²×C₄₃	#388	1	1	yes	characteristic
292	C₂²×C₄₃	#388	1	1	yes	characteristic
293	C₂²×C₄₃	#390	1	1	yes	characteristic
294	C₂²×C₄₃	#443	1	2	yes	—
295	C₂²×C₄₃	#444	1	2	yes	—
296	C₂×D₄₃	—	4	2	no	—
297	C₂×D₄₃	—	4	2	no	—
298	C₂×D₄₃	—	4	2	no	—
299	C₂×D₄₃	—	8	2	no	—
300	C₂×D₄₃	—	8	2	no	—
301	C₄×C₄₃	—	4	4	no	—
302	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
303	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×C₄₃	#386	1	1	yes	characteristic
305	C₄×C₄₃	#386	1	1	yes	characteristic
306	C₄×C₄₃	#388	1	1	yes	characteristic
307	C₄×C₄₃	#388	1	1	yes	characteristic
308	C₄×C₄₃	#390	1	1	yes	characteristic
309	C₄×C₄₃	#390	1	1	yes	characteristic
310	Dic₄₃	—	4	4	no	—
311	Dic₄₃	—	4	2	no	—
312	C₂²×#104	—	43	1	no	—
313	C₂×#416	—	43	1	no	—
314	C₂×#408	—	43	1	no	—
315	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
316	C₂×#341	—	43	1	no	—
317	C₂×#339	—	43	1	no	—
318	C₂×#336	—	43	1	no	—
319	C₂×C₄₃	—	2	1	no	—
320	C₂×C₄₃	—	2	1	no	—
321	C₂×C₄₃	—	2	1	no	—
322	C₂×C₄₃	—	2	1	no	—
323	C₂×C₄₃	#1437	1	1	yes	characteristic
324	C₂×C₄₃	#1764	1	1	yes	characteristic
325	C₂×C₄₃	#1765	1	1	yes	characteristic
326	C₂×C₄₃	#1876	1	2	yes	—
327	C₂×C₄₃	#1929	1	2	yes	—
328	D₄₃	—	8	2	no	—
329	C₂²×#41	—	43	1	no	—
330	C₂²×M₁₆	—	43	1	no	—
331	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
332	C₂³×C₈	—	43	1	no	—
333	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
334	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
335	C₂²×C₄²	—	43	1	no	—
336	C₂×#104	—	43	4	no	—
337	C₂×#104	—	86	2	no	—
338	C₂×#104	—	86	2	no	—
339	#416	—	86	2	no	—
340	#416	—	86	2	no	—
341	C₂×#103	—	43	2	no	—
342	C₂×#102	—	43	2	no	—
343	#408	—	43	4	no	—
344	#408	—	86	2	no	—
345	C₂×C₂²⋊C₈	—	86	1	no	—
346	C₂×C₂²⋊C₈	—	86	1	no	—
347	#405	—	2	2	no	—
348	#405	—	2	2	no	—
349	C₂×#97	—	2	1	no	—
350	C₂×C₄×C₈	—	2	1	no	—
351	#341	—	86	2	no	—
352	#339	—	86	2	no	—
353	#336	—	86	2	no	—
354	C₄₃	#10934	1	1	yes	characteristic, complemented, Sylow
355	C₂×#41	—	43	2	no	—
356	C₂×#41	—	43	2	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	C₂×#41	—	86	1	no	—
364	C₂×#41	—	86	1	no	—
365	C₂×#41	—	86	1	no	—
366	C₂×#41	—	86	1	no	—
367	C₂²×Q₈	—	43	1	no	—
368	C₂²×D₄	—	43	1	no	—
369	C₂²×D₄	—	86	1	no	—
370	C₂³×C₄	—	86	1	no	—
371	C₂³×C₄	—	86	1	no	—
372	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	43	2	no	—
377	C₂×M₁₆	—	86	1	no	—
378	C₂×M₁₆	—	86	1	no	—
379	C₂×M₁₆	—	86	1	no	—
380	C₂×M₁₆	—	86	1	no	—
381	C₂×M₁₆	—	86	1	no	—
382	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
383	C₂×M₁₆	D₁₇₂	1	2	yes	—
384	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	43	2	no	—
391	C₂²×C₈	—	86	1	no	—
392	C₂²×C₈	—	86	1	no	—
393	C₂²×C₈	—	86	1	no	—
394	C₂²×C₈	—	86	1	no	—
395	C₂²×C₈	—	86	1	no	—
396	C₂²×C₈	—	86	1	no	—
397	C₂²×C₈	—	86	1	no	—
398	C₂²×C₈	C₄×D₄₃	1	2	yes	—
399	C₂²×C₈	D₁₇₂	1	2	yes	—
400	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
401	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	D₁₇₂	1	2	yes	—
405	#117	C₂²⋊D₄₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₄²	—	2	1	no	—
409	C₂×C₄²	—	43	2	no	—
410	C₂×C₄²	—	86	1	no	—
411	C₂×C₄²	—	86	1	no	—
412	C₂×C₄²	—	86	1	no	—
413	C₂×C₄²	—	86	1	no	—
414	C₂×C₄²	—	86	1	no	—
415	#104	—	86	8	no	—
416	#103	—	86	4	no	—
417	#102	—	86	4	no	—
418	C₂²⋊C₈	—	86	4	no	—
419	C₂²⋊C₈	—	86	4	no	—
420	#97	—	2	4	no	—
421	C₄×C₈	—	2	4	no	—
422	C₂⁴	—	86	1	no	—
423	C₂⁴	#10621898	1	1	yes	characteristic
424	#41	—	86	2	no	—
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	—	172	1	no	—
433	#41	—	172	1	no	—
434	#41	—	172	1	no	—
435	#41	—	172	1	no	—
436	#41	—	172	1	no	—
437	#41	—	172	1	no	—
438	#41	—	172	1	no	—
439	#41	—	172	1	no	—
440	C₂×Q₈	—	43	2	no	—
441	C₂×Q₈	—	86	1	no	—
442	C₂×Q₈	—	86	1	no	—
443	C₂×Q₈	—	86	1	no	—
444	C₂×Q₈	—	86	1	no	—
445	C₂×Q₈	—	86	1	no	—
446	C₂×D₄	—	43	2	no	—
447	C₂×D₄	—	86	2	no	—
448	C₂×D₄	—	86	2	no	—
449	C₂×D₄	—	86	1	no	—
450	C₂×D₄	—	86	1	no	—
451	C₂×D₄	—	86	1	no	—
452	C₂×D₄	—	86	1	no	—
453	C₂×D₄	—	86	1	no	—
454	C₂×D₄	—	172	1	no	—
455	C₂×D₄	—	172	1	no	—
456	C₂×D₄	—	172	1	no	—
457	C₂×D₄	—	172	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	86	4	no	—
460	C₂²×C₄	—	86	1	no	—
461	C₂²×C₄	—	86	2	no	—
462	C₂²×C₄	—	86	2	no	—
463	C₂²×C₄	—	86	2	no	—
464	C₂²×C₄	—	172	2	no	—
465	C₂²×C₄	—	172	1	no	—
466	C₂²×C₄	—	172	1	no	—
467	C₂²×C₄	—	172	1	no	—
468	C₂²×C₄	—	172	1	no	—
469	C₂²×C₄	—	172	1	no	—
470	C₂²×C₄	—	172	1	no	—
471	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
477	C₂²×C₄	#10621898	1	1	yes	characteristic
478	C₂²×C₄	#10621898	1	1	yes	characteristic
479	C₂²×C₄	#10621898	1	1	yes	characteristic
480	C₂²×C₄	#10621898	1	1	yes	characteristic
481	C₂²×C₄	#10621898	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	86	2	no	—
489	M₁₆	—	86	2	no	—
490	M₁₆	—	172	1	no	—
491	M₁₆	—	172	1	no	—
492	M₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	86	2	no	—
505	C₂×C₈	—	86	2	no	—
506	C₂×C₈	—	86	2	no	—
507	C₂×C₈	—	86	2	no	—
508	C₂×C₈	—	172	1	no	—
509	C₂×C₈	—	172	1	no	—
510	C₂×C₈	—	172	1	no	—
511	C₂×C₈	—	172	1	no	—
512	C₂×C₈	—	172	1	no	—
513	C₂×C₈	—	172	1	no	—
514	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
515	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	86	2	no	—
523	C₄²	—	86	2	no	—
524	C₄²	—	172	1	no	—
525	C₄²	—	172	1	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	86	2	no	—
529	C₂³	—	172	1	no	—
530	C₂³	—	172	2	no	—
531	C₂³	—	172	2	no	—
532	C₂³	—	172	1	no	—
533	C₂³	#13063282	1	1	yes	characteristic
534	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
535	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
536	C₂³	#13063299	1	1	yes	characteristic
537	C₂³	#13063308	1	1	yes	characteristic
538	C₂³	#13063313	1	1	yes	characteristic
539	C₂³	#13063319	1	1	yes	characteristic
540	Q₈	—	86	2	no	—
541	Q₈	—	86	2	no	—
542	Q₈	—	172	1	no	—
543	Q₈	—	172	1	no	—
544	D₄	—	86	2	no	—
545	D₄	—	86	2	no	—
546	D₄	—	172	2	no	—
547	D₄	—	172	2	no	—
548	D₄	—	172	2	no	—
549	D₄	—	172	2	no	—
550	D₄	—	172	1	no	—
551	D₄	—	172	1	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	86	4	no	—
556	C₂×C₄	—	86	2	no	—
557	C₂×C₄	—	172	4	no	—
558	C₂×C₄	—	172	4	no	—
559	C₂×C₄	—	172	2	no	—
560	C₂×C₄	—	172	1	no	—
561	C₂×C₄	—	172	2	no	—
562	C₂×C₄	—	172	1	no	—
563	C₂×C₄	—	172	2	no	—
564	C₂×C₄	—	172	2	no	—
565	C₂×C₄	—	172	2	no	—
566	C₂×C₄	—	172	2	no	—
567	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
568	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
569	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
570	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
571	C₂×C₄	#13063282	1	1	yes	characteristic
572	C₂×C₄	#13063282	1	1	yes	characteristic
573	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
574	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
575	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
576	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
577	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
578	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
579	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
580	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
581	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
582	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
583	C₂×C₄	#13063294	1	1	yes	characteristic
584	C₂×C₄	#13063299	1	1	yes	characteristic
585	C₂×C₄	#13063299	1	1	yes	characteristic
586	C₂×C₄	#13063299	1	1	yes	characteristic
587	C₂×C₄	#13063299	1	1	yes	characteristic
588	C₂×C₄	#13063299	1	1	yes	characteristic
589	C₂×C₄	#13063308	1	1	yes	characteristic
590	C₂×C₄	#13063308	1	1	yes	characteristic
591	C₂×C₄	#13063313	1	1	yes	characteristic
592	C₂×C₄	#13063313	1	1	yes	characteristic
593	C₂×C₄	#13063319	1	1	yes	characteristic
594	C₂×C₄	#13063322	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	4	no	—
598	C₈	—	172	2	no	—
599	C₈	—	172	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	344	2	no	—
609	C₂²	—	344	2	no	—
610	C₂²	—	172	2	no	—
611	C₂²	—	172	2	no	—
612	C₂²	—	172	2	no	—
613	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
614	C₂²	#14582778	1	1	yes	characteristic
615	C₂²	#14582790	1	1	yes	characteristic
616	C₂²	#14582790	1	1	yes	characteristic
617	C₂²	#14582790	1	1	yes	characteristic
618	C₂²	#14582790	1	1	yes	characteristic
619	C₂²	#14582801	1	1	yes	characteristic
620	C₂²	#14583014	1	2	yes	—
621	C₂²	#14583019	1	2	yes	—
622	C₄	—	4	4	no	—
623	C₄	—	172	4	no	—
624	C₄	—	172	2	no	—
625	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
626	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
627	C₄	#14582778	1	1	yes	characteristic
628	C₄	#14582778	1	1	yes	characteristic
629	C₄	#14582790	1	1	yes	characteristic
630	C₄	#14582790	1	1	yes	characteristic
631	C₄	#14582801	1	1	yes	characteristic
632	C₄	#14582801	1	1	yes	characteristic
633	C₂	—	2	1	no	—
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	344	2	no	—
638	C₂	#19132833	1	1	yes	characteristic
639	C₂	#19134434	1	1	yes	characteristic
640	C₂	#19134441	1	1	yes	characteristic
641	C₂	#19134922	1	2	yes	—
642	C₂	#19135243	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#10934
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
4. C₂×#14582663	C₂	semidirect
5. C₂×#14582658	C₂	semidirect
6. C₂×#14582653	C₂	semidirect
7. C₂×C₄₃×#405	C₂	semidirect
14. C₂×#13063251	C₄	semidirect
17. C₂×#13063248	C₄	semidirect
18. C₂×#13063245	C₄	semidirect
20. #14582865	C₄	semidirect
315. C₂×#405	D₄₃	semidirect
354. C₄₃	#10934	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063251	2
C₂×#14582893	2
C₂×#14582865	2
C₂×#14582663	2
C₂×#14582658	2
C₂×#14582653	2
C₂×C₄₃×#405	2
#10934	43