Subgroups — #25977243

Order 11008.

1750 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148405	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148398	C₂	1	1	yes	maximal, characteristic
3	#19147536	C₂	1	4	yes	maximal, complemented
4	#19147514	C₂	1	2	yes	maximal, complemented
5	#19147503	C₂	1	2	yes	maximal, complemented
6	#19147471	C₂	1	4	yes	maximal, complemented
7	#19147468	C₂	1	2	yes	maximal, complemented
8	SD₁₆×Dic₈₆	C₂	1	2	yes	maximal, complemented
9	#19145123	C₂	1	2	yes	maximal, complemented
10	#19145109	C₂	1	1	yes	maximal, characteristic, complemented
11	#19144433	C₂	1	2	yes	maximal, complemented
12	#19144422	C₂	1	2	yes	maximal
13	#19144400	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144392	C₂	1	1	yes	maximal, characteristic
15	#19143529	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143455	C₂	1	2	yes	maximal
17	C₂×C₄×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
18	Q₈×Dic₈₆	—	2	1	no	—
19	Q₈×Dic₈₆	C₂²	1	2	yes	complemented
20	#14583628	—	2	1	no	—
21	#14583628	C₂²	1	2	yes	complemented
22	#14583625	—	2	2	no	—
23	#14583625	C₂²	1	4	yes	complemented
24	#14583608	—	2	2	no	—
25	#14583608	C₂²	1	4	yes	—
26	#14583606	—	2	1	no	—
27	#14583606	C₂²	1	2	yes	—
28	D₄×Dic₈₆	—	2	1	no	—
29	D₄×Dic₈₆	C₂²	1	2	yes	—
30	#14583530	—	2	2	no	—
31	#14583530	C₂²	1	2	yes	—
32	#14583530	C₂²	1	2	yes	—
33	#14583525	—	2	2	no	—
34	#14583456	—	2	2	no	—
35	#14583456	C₂²	1	1	yes	characteristic
36	#14583456	C₂²	1	1	yes	characteristic
37	#14583456	C₂²	1	1	yes	characteristic
38	C₂×#13063304	—	2	2	no	—
39	#14583377	C₂²	1	2	yes	—
40	#14583374	C₂²	1	2	yes	—
41	#14583306	C₂²	1	4	yes	complemented
42	#14583306	C₂²	1	4	yes	complemented
43	#14583304	C₂²	1	1	yes	characteristic, complemented
44	#14583304	C₂²	1	1	yes	characteristic, complemented
45	#14583301	C₂²	1	2	yes	complemented
46	#14583301	C₂²	1	2	yes	complemented
47	#14583299	C₂²	1	4	yes	complemented
48	#14583297	C₂²	1	1	yes	characteristic, complemented
49	#14583297	C₂²	1	1	yes	characteristic, complemented
50	#14583296	C₂²	1	4	yes	complemented
51	#14583208	C₂²	1	4	yes	complemented
52	#14583206	C₂²	1	4	yes	complemented
53	#14583204	C₂²	1	4	yes	complemented
54	#14583201	C₂²	1	4	yes	—
55	#14583199	C₂²	1	4	yes	—
56	#14583197	C₂²	1	4	yes	—
57	#14583194	C₂²	1	2	yes	complemented
58	#14583192	C₂²	1	4	yes	complemented
59	#14583189	C₂²	1	2	yes	—
60	#14583187	C₂²	1	4	yes	—
61	#14583184	C₂²	1	2	yes	complemented
62	#14583182	C₂²	1	4	yes	complemented
63	#14583179	C₂²	1	2	yes	—
64	#14583177	C₂²	1	4	yes	—
65	#14583029	C₂²	1	2	yes	complemented
66	#14583029	C₂²	1	2	yes	complemented
67	C₈×Dic₈₆	C₂²	1	2	yes	complemented
68	C₈×Dic₈₆	C₂²	1	2	yes	complemented
69	#14583000	C₂²	1	4	yes	—
70	#14583000	C₂²	1	4	yes	—
71	SD₁₆×Dic₄₃	C₂²	1	4	yes	—
72	SD₁₆×Dic₄₃	C₂²	1	4	yes	—
73	#14582939	C₂²	1	2	yes	—
74	#14582939	C₂²	1	2	yes	—
75	#14582937	C₂²	1	2	yes	—
76	#14582937	C₂²	1	2	yes	—
77	#14582925	C₂²	1	2	yes	—
78	#14582923	C₂²	1	1	yes	characteristic
79	#14582908	C₂²	1	2	yes	—
80	#14582904	C₂²	1	2	yes	—
81	#14582854	C₂²	1	2	yes	—
82	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
83	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
84	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
85	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	—
87	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	—
88	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	—
89	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
90	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
91	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
92	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
93	C₂²×Dic₈₆	—	2	2	no	—
94	C₂×#10621877	C₂³	1	2	yes	—
95	#13063325	—	2	2	no	—
96	#13063325	—	2	2	no	—
97	#13063325	D₄	1	1	yes	characteristic
98	#13063325	D₄	1	1	yes	characteristic
99	#13063325	C₂³	1	1	yes	characteristic
100	#13063325	C₂³	1	1	yes	characteristic
101	#13063325	C₂³	1	1	yes	characteristic
102	#13063325	C₂³	1	1	yes	characteristic
103	#13063324	—	2	4	no	—
104	#13063324	—	2	2	no	—
105	#13063324	—	2	2	no	—
106	#13063324	—	2	4	no	—
107	#13063324	C₂³	1	4	yes	—
108	#13063324	C₂³	1	4	yes	—
109	#13063317	—	2	4	no	—
110	#13063317	D₄	1	2	yes	—
111	#13063317	C₂³	1	2	yes	—
112	#13063317	C₂³	1	2	yes	—
113	#13063316	—	2	2	no	—
114	#13063316	—	2	2	no	—
115	#13063316	—	2	4	no	—
116	#13063316	—	2	4	no	—
117	#13063316	C₂³	1	4	yes	—
118	#13063316	C₂³	1	4	yes	—
119	#13063304	—	2	1	no	—
120	#13063304	—	2	1	no	—
121	#13063304	—	2	1	no	—
122	#13063304	—	2	1	no	—
123	#13063304	—	2	2	no	—
124	#13063304	—	2	4	no	—
125	#13063304	—	2	4	no	—
126	#13063304	—	2	2	no	—
127	#13063304	—	2	4	no	—
128	#13063304	D₄	1	2	yes	—
129	#13063304	D₄	1	2	yes	—
130	#13063302	—	2	4	no	—
131	#13063302	—	2	4	no	—
132	#13063302	—	2	4	no	—
133	#13063302	—	2	4	no	—
134	Q₈×Dic₄₃	—	2	2	no	—
135	Q₈×Dic₄₃	—	2	2	no	—
136	Q₈×Dic₄₃	C₂³	1	4	yes	—
137	Q₈×Dic₄₃	C₂³	1	4	yes	—
138	C₄×Dic₈₆	—	2	2	no	—
139	C₄×Dic₈₆	—	2	1	no	—
140	C₄×Dic₈₆	—	2	1	no	—
141	C₄×Dic₈₆	—	2	1	no	—
142	C₄×Dic₈₆	—	2	1	no	—
143	C₄×Dic₈₆	—	2	2	no	—
144	C₄×Dic₈₆	—	2	4	no	—
145	C₄×Dic₈₆	C₂³	1	2	yes	—
146	C₄×Dic₈₆	C₂³	1	2	yes	—
147	D₄×Dic₄₃	—	2	2	no	—
148	D₄×Dic₄₃	—	2	2	no	—
149	D₄×Dic₄₃	C₂³	1	4	yes	—
150	D₄×Dic₄₃	C₂³	1	4	yes	—
151	#13063284	—	2	4	no	—
152	#13063284	C₂³	1	2	yes	—
153	#13063284	C₂³	1	2	yes	—
154	#13063284	C₂³	1	2	yes	—
155	C₂×C₄⋊Dic₄₃	—	2	2	no	—
156	C₂×Dic₄₃⋊C₄	—	2	4	no	—
157	C₂×C₂²⋊Dic₄₃	—	2	4	no	—
158	#13063259	C₂³	1	2	yes	—
159	#13063259	C₂³	1	2	yes	—
160	#13063259	C₂³	1	2	yes	—
161	#13063259	C₂³	1	2	yes	—
162	#13063258	C₂³	1	4	yes	—
163	#13063258	C₂³	1	4	yes	—
164	#13063257	C₂³	1	2	yes	—
165	#13063257	C₂³	1	2	yes	—
166	#13063257	C₂³	1	2	yes	—
167	#13063257	C₂³	1	2	yes	—
168	#13063256	C₂³	1	4	yes	—
169	#13063256	C₂³	1	4	yes	—
170	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
171	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
172	Dic₄₃⋊C₈	C₂³	1	4	yes	—
173	Dic₄₃⋊C₈	C₂³	1	4	yes	—
174	#13063249	C₂³	1	4	yes	—
175	#13063249	C₂³	1	4	yes	—
176	#13063246	C₂³	1	4	yes	—
177	#13063246	C₂³	1	4	yes	—
178	#13063235	C₂³	1	4	yes	—
179	C₈×Dic₄₃	C₂³	1	4	yes	—
180	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
181	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
182	C₂³×C₄×C₄₃	—	2	1	no	—
183	C₂×SD₁₆×C₄₃	Q₈	1	8	yes	complemented
184	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
185	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
186	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
188	C₄×Q₈×C₄₃	—	2	1	no	—
189	C₄×Q₈×C₄₃	—	2	1	no	—
190	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
192	C₄×D₄×C₄₃	—	2	1	no	—
193	C₄×D₄×C₄₃	—	2	1	no	—
194	C₄×D₄×C₄₃	C₂³	1	2	yes	—
195	C₄×D₄×C₄₃	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
200	C₂×C₄²×C₄₃	—	2	1	no	—
201	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
202	#106×C₄₃	C₂³	1	2	yes	—
203	#106×C₄₃	C₂³	1	2	yes	—
204	#103×C₄₃	C₂³	1	2	yes	—
205	#103×C₄₃	C₂³	1	2	yes	—
206	#102×C₄₃	C₂³	1	2	yes	—
207	#102×C₄₃	C₂³	1	2	yes	—
208	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
212	C₂⁴×C₄₃	—	2	1	no	—
213	C₂×Q₈×C₄₃	—	2	1	no	—
214	C₂×Q₈×C₄₃	—	2	2	no	—
215	C₂×Q₈×C₄₃	C₂×Q₈	1	4	yes	complemented
216	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
217	C₂×D₄×C₄₃	—	2	1	no	—
218	C₂×D₄×C₄₃	—	2	2	no	—
219	C₂×D₄×C₄₃	C₂×Q₈	1	4	yes	—
220	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₄₃	—	2	2	no	—
222	C₂²×C₄×C₄₃	—	2	2	no	—
223	C₂²×C₄×C₄₃	—	2	1	no	—
224	C₂²×C₄×C₄₃	—	2	1	no	—
225	C₂²×C₄×C₄₃	—	2	1	no	—
226	C₂²×C₄×C₄₃	—	8	2	no	—
227	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
230	C₂²×Dic₄₃	—	2	4	no	—
231	C₂²×Dic₄₃	—	2	4	no	—
232	C₂×Dic₈₆	—	2	1	no	—
233	C₂×Dic₈₆	—	2	1	no	—
234	C₂×Dic₈₆	—	2	1	no	—
235	C₂×Dic₈₆	—	2	1	no	—
236	C₂×Dic₈₆	—	2	4	no	—
237	C₂×Dic₈₆	—	2	4	no	—
238	C₂×Dic₈₆	—	8	4	no	—
239	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
240	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
241	SD₁₆×C₄₃	C₂×Q₈	1	8	yes	complemented
242	SD₁₆×C₄₃	C₂×Q₈	1	8	yes	complemented
243	C₂×C₈×C₄₃	—	2	2	no	—
244	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	complemented
245	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₄₃	—	2	2	no	—
250	C₄⋊C₄×C₄₃	—	2	2	no	—
251	C₄⋊C₄×C₄₃	—	2	1	no	—
252	C₄⋊C₄×C₄₃	—	2	1	no	—
253	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
255	C₂²⋊C₄×C₄₃	—	2	2	no	—
256	C₂²⋊C₄×C₄₃	—	2	2	no	—
257	C₄²×C₄₃	—	2	2	no	—
258	C₄²×C₄₃	—	2	2	no	—
259	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
262	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
263	C₂²⋊Dic₄₃	—	2	4	no	—
264	C₂²⋊Dic₄₃	—	2	4	no	—
265	C₂²⋊Dic₄₃	—	2	2	no	—
266	C₂²⋊Dic₄₃	—	2	2	no	—
267	C₂²⋊Dic₄₃	C₂×D₄	1	4	yes	—
268	C₄⋊Dic₄₃	—	2	1	no	—
269	C₄⋊Dic₄₃	—	2	1	no	—
270	C₄⋊Dic₄₃	—	2	1	no	—
271	C₄⋊Dic₄₃	—	2	1	no	—
272	C₄⋊Dic₄₃	—	2	4	no	—
273	C₄⋊Dic₄₃	—	2	4	no	—
274	C₄⋊Dic₄₃	—	2	4	no	—
275	C₄⋊Dic₄₃	—	2	4	no	—
276	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
277	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
278	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
279	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
280	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
281	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
282	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
283	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
284	Dic₄₃⋊C₄	—	2	2	no	—
285	Dic₄₃⋊C₄	—	2	2	no	—
286	Dic₄₃⋊C₄	—	2	2	no	—
287	Dic₄₃⋊C₄	—	2	2	no	—
288	Dic₄₃⋊C₄	—	2	4	no	—
289	Dic₄₃⋊C₄	—	2	4	no	—
290	Dic₄₃⋊C₄	—	2	4	no	—
291	Dic₄₃⋊C₄	—	2	4	no	—
292	Dic₄₃⋊C₄	C₂×D₄	1	4	yes	—
293	Dic₄₃⋊C₄	C₂×D₄	1	4	yes	—
294	C₄×Dic₄₃	—	2	2	no	—
295	C₄×Dic₄₃	—	2	2	no	—
296	C₄×Dic₄₃	—	2	4	no	—
297	C₄×Dic₄₃	—	2	4	no	—
298	C₄×Dic₄₃	C₂⁴	1	4	yes	—
299	#10621877	—	2	4	no	—
300	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
301	C₂³×C₄₃	—	2	2	no	—
302	C₂³×C₄₃	—	2	4	no	—
303	C₂³×C₄₃	—	8	1	no	—
304	C₂³×C₄₃	—	8	1	no	—
305	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
306	Q₈×C₄₃	—	2	4	no	—
307	Q₈×C₄₃	—	2	2	no	—
308	Q₈×C₄₃	C₂²×Q₈	1	4	yes	—
309	D₄×C₄₃	—	2	4	no	—
310	D₄×C₄₃	—	2	2	no	—
311	D₄×C₄₃	C₂²×Q₈	1	4	yes	—
312	C₂×C₄×C₄₃	—	2	4	no	—
313	C₂×C₄×C₄₃	—	2	2	no	—
314	C₂×C₄×C₄₃	—	2	2	no	—
315	C₂×C₄×C₄₃	—	2	2	no	—
316	C₂×C₄×C₄₃	—	2	2	no	—
317	C₂×C₄×C₄₃	—	4	1	no	—
318	C₂×C₄×C₄₃	—	4	4	no	—
319	C₂×C₄×C₄₃	—	8	2	no	—
320	C₂×C₄×C₄₃	—	8	1	no	—
321	C₂×C₄×C₄₃	—	8	1	no	—
322	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
328	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
329	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
330	C₂×Dic₄₃	—	2	2	no	—
331	C₂×Dic₄₃	—	2	2	no	—
332	C₂×Dic₄₃	—	2	2	no	—
333	C₂×Dic₄₃	—	2	2	no	—
334	C₂×Dic₄₃	—	8	4	no	—
335	C₂×Dic₄₃	—	8	4	no	—
336	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
337	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
338	Dic₈₆	—	2	4	no	—
339	Dic₈₆	—	4	2	no	—
340	Dic₈₆	—	4	2	no	—
341	Dic₈₆	—	4	2	no	—
342	Dic₈₆	—	8	4	no	—
343	Dic₈₆	—	8	4	no	—
344	Dic₈₆	—	8	1	no	—
345	Dic₈₆	—	8	1	no	—
346	C₈×C₄₃	—	2	1	no	—
347	C₈×C₄₃	—	2	1	no	—
348	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
349	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
350	C₄₃⋊C₈	—	2	4	no	—
351	#61371	—	43	1	no	maximal, Sylow
352	C₂²×C₄₃	—	2	1	no	—
353	C₂²×C₄₃	—	2	1	no	—
354	C₂²×C₄₃	—	2	4	no	—
355	C₂²×C₄₃	—	4	2	no	—
356	C₂²×C₄₃	—	4	2	no	—
357	C₂²×C₄₃	—	8	4	no	—
358	C₂²×C₄₃	D₄×Q₈	1	2	yes	—
359	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
360	C₄×C₄₃	—	2	1	no	—
361	C₄×C₄₃	—	2	1	no	—
362	C₄×C₄₃	—	2	4	no	—
363	C₄×C₄₃	—	2	1	no	—
364	C₄×C₄₃	—	4	2	no	—
365	C₄×C₄₃	—	4	2	no	—
366	C₄×C₄₃	D₄×Q₈	1	2	yes	—
367	C₄×C₄₃	#577	1	2	yes	—
368	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
369	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
370	Dic₄₃	—	2	4	no	—
371	Dic₄₃	—	2	4	no	—
372	Dic₄₃	—	4	2	no	—
373	Dic₄₃	—	4	2	no	—
374	Dic₄₃	—	4	2	no	—
375	Dic₄₃	—	4	2	no	—
376	#3502	—	43	1	no	—
377	#3501	—	43	1	no	—
378	#3388	—	43	4	no	—
379	#3386	—	43	2	no	—
380	#3385	—	43	2	no	—
381	#3381	—	43	2	no	—
382	#3381	—	43	4	no	—
383	Q₈×SD₁₆	—	43	2	no	—
384	#3163	—	43	2	no	—
385	#3160	—	43	1	no	—
386	#3082	—	43	2	no	—
387	#3081	—	43	2	no	—
388	#3078	—	43	1	no	—
389	#3077	—	43	1	no	—
390	#2960	—	43	1	no	—
391	#2949	—	43	2	no	—
392	C₂×C₄×SD₁₆	D₄₃	1	1	yes	characteristic
393	C₂×C₄₃	—	2	2	no	—
394	C₂×C₄₃	—	4	4	no	—
395	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
396	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
397	C₂×C₄₃	#3584	1	1	yes	characteristic
398	C₂²×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
399	Q₈²	—	43	2	no	—
400	Q₈²	—	86	1	no	—
401	#557	—	43	2	no	—
402	#557	—	43	4	no	—
403	#557	—	86	2	no	—
404	#557	—	86	1	no	—
405	#554	—	43	2	no	—
406	#554	—	43	4	no	—
407	#554	—	86	2	no	—
408	#554	—	86	1	no	—
409	D₄×Q₈	—	43	2	no	—
410	D₄×Q₈	—	86	1	no	—
411	#544	—	43	2	no	—
412	#544	—	43	2	no	—
413	#544	—	86	2	no	—
414	#543	—	86	2	no	—
415	#533	—	43	1	no	—
416	#533	—	43	1	no	—
417	#533	—	43	1	no	—
418	#533	—	86	2	no	—
419	C₂×C₂²⋊Q₈	—	86	2	no	—
420	#519	—	43	2	no	—
421	#518	—	43	2	no	—
422	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
424	#501	—	43	4	no	—
425	#501	—	43	4	no	—
426	#500	—	43	1	no	—
427	#500	—	43	1	no	—
428	#499	—	43	4	no	—
429	#499	—	43	2	no	—
430	#499	—	43	2	no	—
431	#498	—	43	4	no	—
432	#498	—	43	1	no	—
433	#498	—	43	1	no	—
434	#479	—	43	4	no	—
435	#479	—	43	4	no	—
436	#479	—	43	4	no	—
437	#478	—	43	4	no	—
438	#478	—	43	4	no	—
439	#478	—	43	4	no	—
440	#477	—	43	2	no	—
441	#477	—	43	4	no	—
442	#476	—	43	2	no	—
443	#476	—	43	4	no	—
444	#475	—	43	2	no	—
445	#475	—	43	4	no	—
446	#474	—	43	2	no	—
447	#474	—	43	4	no	—
448	#446	—	43	2	no	—
449	#446	—	43	2	no	—
450	C₈×Q₈	—	43	2	no	—
451	C₈×Q₈	—	43	2	no	—
452	#440	—	43	4	no	—
453	#440	—	43	4	no	—
454	C₄×SD₁₆	—	43	4	no	—
455	C₄×SD₁₆	—	43	4	no	—
456	C₄×SD₁₆	C₂×D₄₃	1	2	yes	—
457	C₄×SD₁₆	C₂×D₄₃	1	2	yes	—
458	C₄×SD₁₆	C₂×D₄₃	1	2	yes	—
459	C₄×SD₁₆	C₂×D₄₃	1	2	yes	—
460	#428	—	43	2	no	—
461	#428	—	43	2	no	—
462	#427	—	43	2	no	—
463	#427	—	43	2	no	—
464	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
465	#424	—	43	2	no	—
466	#423	—	43	1	no	—
467	#419	—	43	2	no	—
468	#418	—	43	2	no	—
469	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
470	C₂×#102	C₂×D₄₃	1	1	yes	characteristic
471	#405	—	43	2	no	—
472	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
473	C₄₃	#61371	1	1	yes	characteristic, complemented, Sylow
474	C₂²×Q₈	—	86	2	no	—
475	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
476	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
477	C₂³×C₄	—	2	1	no	—
478	C₂×SD₁₆	Dic₈₆	1	8	yes	complemented
479	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
480	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
481	C₂×M₁₆	—	43	2	no	—
482	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
483	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
484	C₄⋊Q₈	—	43	4	no	—
485	C₄⋊Q₈	—	43	4	no	—
486	C₄⋊Q₈	—	43	1	no	—
487	C₄⋊Q₈	—	43	1	no	—
488	C₄⋊Q₈	—	43	1	no	—
489	C₄⋊Q₈	—	43	1	no	—
490	C₄⋊Q₈	—	43	1	no	—
491	C₄⋊Q₈	—	43	1	no	—
492	C₄⋊Q₈	—	86	2	no	—
493	C₄⋊Q₈	—	86	2	no	—
494	C₄⋊Q₈	—	86	2	no	—
495	C₄⋊Q₈	—	86	2	no	—
496	C₄⋊Q₈	—	86	4	no	—
497	C₄⋊Q₈	—	86	4	no	—
498	#125	—	43	4	no	—
499	#125	—	43	4	no	—
500	#125	—	43	2	no	—
501	#125	—	43	2	no	—
502	#125	—	43	2	no	—
503	#125	—	86	4	no	—
504	#125	—	86	2	no	—
505	#125	—	86	2	no	—
506	#125	—	86	4	no	—
507	#125	—	86	4	no	—
508	C₂²⋊Q₈	—	43	2	no	—
509	C₂²⋊Q₈	—	43	2	no	—
510	C₂²⋊Q₈	—	86	4	no	—
511	C₂²⋊Q₈	—	86	4	no	—
512	C₂²⋊Q₈	—	86	4	no	—
513	C₂²⋊Q₈	—	86	4	no	—
514	C₂²⋊Q₈	—	86	4	no	—
515	C₂²⋊Q₈	—	86	4	no	—
516	C₂²⋊Q₈	—	86	2	no	—
517	C₂²⋊Q₈	—	86	4	no	—
518	C₂²⋊Q₈	—	86	2	no	—
519	C₂²⋊Q₈	—	86	1	no	—
520	C₂²⋊Q₈	—	86	1	no	—
521	C₂²⋊Q₈	—	86	1	no	—
522	C₂²⋊Q₈	—	86	1	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	—	43	2	no	—
526	C₄×Q₈	—	43	2	no	—
527	C₄×Q₈	—	43	4	no	—
528	C₄×Q₈	—	43	4	no	—
529	C₄×Q₈	—	86	4	no	—
530	C₄×Q₈	—	86	2	no	—
531	C₄×Q₈	—	86	2	no	—
532	C₄×Q₈	—	86	2	no	—
533	C₄×Q₈	—	86	2	no	—
534	C₄×Q₈	—	86	1	no	—
535	C₄×Q₈	—	86	1	no	—
536	C₄×Q₈	—	86	1	no	—
537	C₄×Q₈	—	86	1	no	—
538	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
539	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	43	4	no	—
543	C₄×D₄	—	43	4	no	—
544	C₄×D₄	—	86	2	no	—
545	C₄×D₄	—	86	2	no	—
546	C₄×D₄	C₂²×D₄₃	1	2	yes	—
547	C₄×D₄	C₂²×D₄₃	1	2	yes	—
548	#117	—	43	2	no	—
549	#117	—	43	2	no	—
550	#117	—	43	2	no	—
551	#117	—	86	4	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	86	4	no	—
554	C₂×C₄⋊C₄	—	86	2	no	—
555	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	—	2	1	no	—
558	C₂×C₂²⋊C₄	—	86	4	no	—
559	C₂×C₄²	—	2	1	no	—
560	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
561	#107	—	43	2	no	—
562	#107	—	43	2	no	—
563	#107	—	43	2	no	—
564	#107	—	43	2	no	—
565	#107	—	43	4	no	—
566	#107	—	43	4	no	—
567	#106	—	43	2	no	—
568	#106	—	43	2	no	—
569	#106	—	43	2	no	—
570	#106	—	43	2	no	—
571	#106	—	43	4	no	—
572	#106	—	43	4	no	—
573	#106	C₂²×D₄₃	1	2	yes	—
574	#106	C₂²×D₄₃	1	2	yes	—
575	C₄⋊C₈	—	43	4	no	—
576	C₄⋊C₈	—	43	4	no	—
577	C₄⋊C₈	—	43	2	no	—
578	C₄⋊C₈	—	43	2	no	—
579	#103	—	43	4	no	—
580	#103	—	43	4	no	—
581	#103	C₂²×D₄₃	1	2	yes	—
582	#103	C₂²×D₄₃	1	2	yes	—
583	#102	—	43	4	no	—
584	#102	—	43	4	no	—
585	#102	C₂²×D₄₃	1	2	yes	—
586	#102	C₂²×D₄₃	1	2	yes	—
587	#97	—	43	4	no	—
588	C₄×C₈	—	43	4	no	—
589	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
590	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
591	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
592	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
593	C₂⁴	—	2	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	2	2	no	—
596	C₂×Q₈	—	43	2	no	—
597	C₂×Q₈	—	43	2	no	—
598	C₂×Q₈	—	86	4	no	—
599	C₂×Q₈	—	86	4	no	—
600	C₂×Q₈	—	86	1	no	—
601	C₂×Q₈	—	86	1	no	—
602	C₂×Q₈	—	86	1	no	—
603	C₂×Q₈	—	86	1	no	—
604	C₂×Q₈	—	344	4	no	—
605	C₂×Q₈	C₂×Dic₈₆	1	4	yes	complemented
606	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	C₂×Dic₈₆	1	4	yes	—
610	C₂×D₄	C₂³×D₄₃	1	2	yes	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	8	2	no	—
617	C₂²×C₄	—	86	4	no	—
618	C₂²×C₄	—	86	4	no	—
619	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
620	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
621	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
622	SD₁₆	C₂×Dic₈₆	1	8	yes	complemented
623	SD₁₆	C₂×Dic₈₆	1	8	yes	complemented
624	M₁₆	—	86	4	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	—	43	4	no	—
627	C₂×C₈	C₂×Dic₈₆	1	4	yes	complemented
628	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
629	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
630	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
631	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	43	4	no	—
637	C₄⋊C₄	—	43	2	no	—
638	C₄⋊C₄	—	43	2	no	—
639	C₄⋊C₄	—	43	2	no	—
640	C₄⋊C₄	—	43	4	no	—
641	C₄⋊C₄	—	43	2	no	—
642	C₄⋊C₄	—	43	2	no	—
643	C₄⋊C₄	—	43	2	no	—
644	C₄⋊C₄	—	43	2	no	—
645	C₄⋊C₄	—	43	2	no	—
646	C₄⋊C₄	—	86	4	no	—
647	C₄⋊C₄	—	86	4	no	—
648	C₄⋊C₄	—	86	4	no	—
649	C₄⋊C₄	—	86	4	no	—
650	C₄⋊C₄	—	86	4	no	—
651	C₄⋊C₄	—	86	4	no	—
652	C₄⋊C₄	—	86	4	no	—
653	C₄⋊C₄	—	86	4	no	—
654	C₄⋊C₄	—	86	2	no	—
655	C₄⋊C₄	—	86	1	no	—
656	C₄⋊C₄	—	86	2	no	—
657	C₄⋊C₄	—	86	1	no	—
658	C₄⋊C₄	—	86	2	no	—
659	C₄⋊C₄	—	86	1	no	—
660	C₄⋊C₄	—	86	2	no	—
661	C₄⋊C₄	—	86	1	no	—
662	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
663	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	43	4	no	—
667	C₂²⋊C₄	—	86	4	no	—
668	C₂²⋊C₄	—	86	4	no	—
669	C₂²⋊C₄	—	86	2	no	—
670	C₂²⋊C₄	—	86	2	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	2	no	—
673	C₄²	—	43	4	no	—
674	C₄²	—	86	4	no	—
675	C₄²	—	86	4	no	—
676	C₄²	—	86	2	no	—
677	C₄²	—	86	2	no	—
678	C₄²	D₄×D₄₃	1	1	yes	characteristic
679	C₄²	D₄×D₄₃	1	1	yes	characteristic
680	C₄²	C₂³×D₄₃	1	1	yes	characteristic
681	C₄²	C₂³×D₄₃	1	1	yes	characteristic
682	C₂³	—	2	2	no	—
683	C₂³	—	2	4	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
687	Q₈	—	2	4	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	86	4	no	—
690	Q₈	—	344	1	no	—
691	Q₈	—	344	1	no	—
692	Q₈	—	344	4	no	—
693	Q₈	—	344	4	no	—
694	Q₈	—	172	2	no	—
695	Q₈	—	172	2	no	—
696	Q₈	—	172	2	no	—
697	Q₈	C₂²×Dic₈₆	1	4	yes	—
698	D₄	—	2	4	no	—
699	D₄	—	2	2	no	—
700	D₄	C₂²×Dic₈₆	1	4	yes	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	8	2	no	—
709	C₂×C₄	—	8	1	no	—
710	C₂×C₄	—	8	1	no	—
711	C₂×C₄	—	43	4	no	—
712	C₂×C₄	—	43	4	no	—
713	C₂×C₄	—	86	2	no	—
714	C₂×C₄	—	86	2	no	—
715	C₂×C₄	—	86	2	no	—
716	C₂×C₄	—	86	2	no	—
717	C₂×C₄	—	344	4	no	—
718	C₂×C₄	—	344	4	no	—
719	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
720	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
721	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
722	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
723	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
725	C₂×C₄	#13063372	1	2	yes	—
726	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
727	C₈	—	2	1	no	—
728	C₈	—	2	1	no	—
729	C₈	—	86	4	no	—
730	C₈	C₂²×Dic₈₆	1	2	yes	—
731	C₈	C₂²×Dic₈₆	1	2	yes	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	4	no	—
738	C₂²	D₄×Dic₈₆	1	2	yes	—
739	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
740	C₄	—	2	4	no	—
741	C₄	—	2	1	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	1	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	86	4	no	—
747	C₄	—	86	4	no	—
748	C₄	—	172	2	no	—
749	C₄	—	172	2	no	—
750	C₄	—	172	2	no	—
751	C₄	—	172	2	no	—
752	C₄	D₄×Dic₈₆	1	2	yes	—
753	C₄	#14583705	1	2	yes	—
754	C₄	C₂³×Dic₈₆	1	1	yes	characteristic
755	C₄	C₂×#13063372	1	1	yes	characteristic
756	C₂	—	2	2	no	—
757	C₂	—	4	4	no	—
758	C₂	C₂×D₄×Dic₈₆	1	1	yes	characteristic
759	C₂	C₂×#14583705	1	1	yes	characteristic
760	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×SD₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂²×D₄×C₄₃	C₂³
hypercenter	C₂×C₄×SD₁₆	D₄₃
hypocenter	C₄₃	#61371
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #19148405	C₂	semidirect
3. #19147536	C₂	semidirect
4. #19147514	C₂	semidirect
5. #19147503	C₂	semidirect
6. #19147471	C₂	semidirect
7. #19147468	C₂	semidirect
8. SD₁₆×Dic₈₆	C₂	semidirect
9. #19145123	C₂	semidirect
10. #19145109	C₂	semidirect
11. #19144433	C₂	semidirect
13. #19144400	C₂	semidirect
15. #19143529	C₂	semidirect
19. Q₈×Dic₈₆	C₂²	semidirect
21. #14583628	C₂²	semidirect
23. #14583625	C₂²	semidirect
41. #14583306	C₂²	semidirect
42. #14583306	C₂²	semidirect
43. #14583304	C₂²	semidirect
44. #14583304	C₂²	semidirect
45. #14583301	C₂²	semidirect
46. #14583301	C₂²	semidirect
47. #14583299	C₂²	semidirect
48. #14583297	C₂²	semidirect
49. #14583297	C₂²	semidirect
50. #14583296	C₂²	semidirect
51. #14583208	C₂²	semidirect
52. #14583206	C₂²	semidirect
53. #14583204	C₂²	semidirect
57. #14583194	C₂²	semidirect
58. #14583192	C₂²	semidirect
61. #14583184	C₂²	semidirect
62. #14583182	C₂²	semidirect
65. #14583029	C₂²	semidirect
66. #14583029	C₂²	semidirect
67. C₈×Dic₈₆	C₂²	semidirect
68. C₈×Dic₈₆	C₂²	semidirect
183. C₂×SD₁₆×C₄₃	Q₈	semidirect
215. C₂×Q₈×C₄₃	C₂×Q₈	semidirect
241. SD₁₆×C₄₃	C₂×Q₈	semidirect
242. SD₁₆×C₄₃	C₂×Q₈	semidirect
244. C₂×C₈×C₄₃	C₂×Q₈	semidirect
473. C₄₃	#61371	semidirect
478. C₂×SD₁₆	Dic₈₆	semidirect
605. C₂×Q₈	C₂×Dic₈₆	semidirect
622. SD₁₆	C₂×Dic₈₆	semidirect
623. SD₁₆	C₂×Dic₈₆	semidirect
627. C₂×C₈	C₂×Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
#19148405	2
#19148398	2
#19147536	2
#19147514	2
#19147503	2
#19147471	2
#19147468	2
SD₁₆×Dic₈₆	2
#19145123	2
#19145109	2
#19144433	2
#19144422	2
#19144400	2
#19144392	2
#19143529	2
#19143455	2
C₂×C₄×SD₁₆×C₄₃	2
#61371	43