Subgroups — #25977230

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148398	C₂	1	2	yes	maximal, complemented
2	#19147551	C₂	1	4	yes	maximal, complemented
3	#19147492	C₂	1	4	yes	maximal, complemented
4	#19147462	C₂	1	4	yes	maximal, complemented
5	#19147460	C₂	1	2	yes	maximal, complemented
6	D₈×Dic₈₆	C₂	1	2	yes	maximal, complemented
7	#19145131	C₂	1	2	yes	maximal, complemented
8	#19145109	C₂	1	1	yes	maximal, characteristic, complemented
9	#19144422	C₂	1	4	yes	maximal, complemented
10	#19144392	C₂	1	2	yes	maximal, complemented
11	#19143529	C₂	1	1	yes	maximal, characteristic, complemented
12	#19143447	C₂	1	2	yes	maximal
13	C₂×C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
14	#14583608	—	2	4	no	—
15	#14583608	C₂²	1	8	yes	complemented
16	#14583606	—	2	2	no	—
17	#14583606	C₂²	1	4	yes	complemented
18	D₄×Dic₈₆	—	2	2	no	—
19	D₄×Dic₈₆	C₂²	1	4	yes	complemented
20	#14583530	C₂²	1	4	yes	—
21	#14583525	—	2	4	no	—
22	#14583456	C₂²	1	2	yes	—
23	#14583456	C₂²	1	1	yes	characteristic
24	C₂×#13063304	—	2	4	no	—
25	#14583374	C₂²	1	4	yes	—
26	#14583307	C₂²	1	8	yes	complemented
27	#14583304	C₂²	1	1	yes	characteristic, complemented
28	#14583304	C₂²	1	1	yes	characteristic, complemented
29	#14583303	C₂²	1	4	yes	complemented
30	#14583301	C₂²	1	2	yes	complemented
31	#14583301	C₂²	1	2	yes	complemented
32	#14583300	C₂²	1	4	yes	complemented
33	#14583297	C₂²	1	2	yes	complemented
34	#14583201	C₂²	1	8	yes	complemented
35	#14583199	C₂²	1	8	yes	complemented
36	#14583197	C₂²	1	8	yes	complemented
37	#14583189	C₂²	1	4	yes	complemented
38	#14583187	C₂²	1	8	yes	complemented
39	#14583179	C₂²	1	4	yes	complemented
40	#14583177	C₂²	1	8	yes	complemented
41	#14583029	C₂²	1	2	yes	complemented
42	#14583029	C₂²	1	2	yes	complemented
43	C₈×Dic₈₆	C₂²	1	2	yes	complemented
44	C₈×Dic₈₆	C₂²	1	2	yes	complemented
45	#14583011	C₂²	1	8	yes	—
46	D₈×Dic₄₃	C₂²	1	4	yes	—
47	D₈×Dic₄₃	C₂²	1	4	yes	—
48	#14582939	C₂²	1	4	yes	—
49	#14582937	C₂²	1	2	yes	—
50	#14582937	C₂²	1	2	yes	—
51	#14582925	C₂²	1	2	yes	—
52	#14582923	C₂²	1	1	yes	characteristic
53	#14582904	C₂²	1	4	yes	—
54	#14582854	C₂²	1	2	yes	—
55	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
57	C₄×D₈×C₄₃	C₂²	1	2	yes	—
58	C₄×D₈×C₄₃	C₂²	1	2	yes	—
59	C₄×D₈×C₄₃	C₂²	1	2	yes	—
60	C₄×D₈×C₄₃	C₂²	1	2	yes	—
61	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
62	C₂×#102×C₄₃	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
64	C₂²×Dic₈₆	—	2	4	no	—
65	C₂×#10621877	C₂³	1	2	yes	—
66	#13063325	D₄	1	1	yes	characteristic
67	#13063325	D₄	1	1	yes	characteristic
68	#13063325	C₂³	1	2	yes	—
69	#13063325	C₂³	1	2	yes	—
70	#13063324	—	2	4	no	—
71	#13063324	C₂³	1	8	yes	—
72	#13063317	D₄	1	2	yes	—
73	#13063317	C₂³	1	4	yes	—
74	#13063316	—	2	4	no	—
75	#13063316	C₂³	1	8	yes	—
76	#13063304	—	2	2	no	—
77	#13063304	—	2	2	no	—
78	#13063304	—	2	4	no	—
79	#13063304	—	2	8	no	—
80	#13063304	—	2	4	no	—
81	#13063304	—	2	8	no	—
82	#13063304	D₄	1	2	yes	—
83	#13063304	D₄	1	2	yes	—
84	#13063302	—	2	8	no	—
85	#13063302	—	2	8	no	—
86	#13063302	—	2	8	no	—
87	#13063302	—	2	8	no	—
88	C₄×Dic₈₆	—	2	2	no	—
89	C₄×Dic₈₆	—	2	2	no	—
90	C₄×Dic₈₆	C₂³	1	2	yes	—
91	C₄×Dic₈₆	C₂³	1	2	yes	—
92	D₄×Dic₄₃	—	2	4	no	—
93	D₄×Dic₄₃	—	2	4	no	—
94	D₄×Dic₄₃	C₂³	1	8	yes	—
95	D₄×Dic₄₃	C₂³	1	8	yes	—
96	#13063284	C₂³	1	4	yes	—
97	#13063284	C₂³	1	2	yes	—
98	C₂×C₄⋊Dic₄₃	—	2	4	no	—
99	C₂×Dic₄₃⋊C₄	—	2	8	no	—
100	C₂×C₂²⋊Dic₄₃	—	2	8	no	—
101	#13063259	C₂³	1	2	yes	—
102	#13063259	C₂³	1	2	yes	—
103	#13063259	C₂³	1	2	yes	—
104	#13063259	C₂³	1	2	yes	—
105	#13063258	C₂³	1	8	yes	—
106	#13063257	C₂³	1	4	yes	—
107	#13063257	C₂³	1	4	yes	—
108	#13063256	C₂³	1	8	yes	—
109	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
110	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
111	Dic₄₃⋊C₈	C₂³	1	4	yes	—
112	Dic₄₃⋊C₈	C₂³	1	4	yes	—
113	#13063246	C₂³	1	8	yes	—
114	#13063246	C₂³	1	8	yes	—
115	#13063235	C₂³	1	4	yes	—
116	C₈×Dic₄₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₄₃	—	2	2	no	—
119	C₂×D₈×C₄₃	Q₈	1	8	yes	complemented
120	C₂×D₈×C₄₃	C₂³	1	2	yes	—
121	C₂×D₈×C₄₃	C₂³	1	2	yes	—
122	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₄×D₄×C₄₃	—	2	2	no	—
125	C₄×D₄×C₄₃	—	2	2	no	—
126	C₄×D₄×C₄₃	C₂³	1	4	yes	—
127	C₄×D₄×C₄₃	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
130	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
131	#107×C₄₃	C₂³	1	2	yes	—
132	#107×C₄₃	C₂³	1	2	yes	—
133	#102×C₄₃	C₂³	1	4	yes	—
134	#102×C₄₃	C₂³	1	4	yes	—
135	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₂⁴×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	4	no	—
142	C₂×D₄×C₄₃	C₂×Q₈	1	8	yes	complemented
143	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₄₃	—	2	4	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	8	4	no	—
148	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂²×Dic₄₃	—	2	8	no	—
152	C₂²×Dic₄₃	—	2	8	no	—
153	C₂×Dic₈₆	—	2	2	no	—
154	C₂×Dic₈₆	—	2	2	no	—
155	C₂×Dic₈₆	—	2	8	no	—
156	C₂×Dic₈₆	—	8	8	no	—
157	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
158	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
159	D₈×C₄₃	C₂×Q₈	1	8	yes	complemented
160	D₈×C₄₃	C₂×Q₈	1	8	yes	complemented
161	C₂×C₈×C₄₃	—	2	2	no	—
162	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	complemented
163	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
169	C₂²⋊C₄×C₄₃	—	2	4	no	—
170	C₂²⋊C₄×C₄₃	—	2	4	no	—
171	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
175	C₂²⋊Dic₄₃	—	2	8	no	—
176	C₂²⋊Dic₄₃	—	2	8	no	—
177	C₂²⋊Dic₄₃	—	2	4	no	—
178	C₂²⋊Dic₄₃	C₂×D₄	1	4	yes	—
179	C₄⋊Dic₄₃	—	2	2	no	—
180	C₄⋊Dic₄₃	—	2	2	no	—
181	C₄⋊Dic₄₃	—	2	8	no	—
182	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
183	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
184	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
185	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
186	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
187	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
188	Dic₄₃⋊C₄	—	2	4	no	—
189	Dic₄₃⋊C₄	—	2	4	no	—
190	Dic₄₃⋊C₄	—	2	8	no	—
191	Dic₄₃⋊C₄	—	2	8	no	—
192	Dic₄₃⋊C₄	C₂×D₄	1	4	yes	—
193	Dic₄₃⋊C₄	C₂×D₄	1	4	yes	—
194	C₄×Dic₄₃	—	2	4	no	—
195	C₄×Dic₄₃	C₂⁴	1	4	yes	—
196	#10621877	—	2	4	no	—
197	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
198	C₂³×C₄₃	—	2	4	no	—
199	C₂³×C₄₃	—	2	8	no	—
200	C₂³×C₄₃	—	8	2	no	—
201	C₂³×C₄₃	—	8	2	no	—
202	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	D₄×C₄₃	—	2	8	no	—
204	D₄×C₄₃	—	2	4	no	—
205	D₄×C₄₃	C₂²×Q₈	1	8	yes	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	8	no	—
210	C₂×C₄×C₄₃	—	8	4	no	—
211	C₂×C₄×C₄₃	—	8	2	no	—
212	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
218	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
219	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
220	C₂×Dic₄₃	—	2	4	no	—
221	C₂×Dic₄₃	—	2	4	no	—
222	C₂×Dic₄₃	—	8	8	no	—
223	C₂×Dic₄₃	—	8	8	no	—
224	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
225	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
226	Dic₈₆	—	2	4	no	—
227	Dic₈₆	—	4	2	no	—
228	Dic₈₆	—	4	4	no	—
229	Dic₈₆	—	8	8	no	—
230	Dic₈₆	—	8	2	no	—
231	C₈×C₄₃	—	2	1	no	—
232	C₈×C₄₃	—	2	1	no	—
233	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
234	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
235	C₄₃⋊C₈	—	2	4	no	—
236	#61370	—	43	1	no	maximal, Sylow
237	C₂²×C₄₃	—	2	1	no	—
238	C₂²×C₄₃	—	2	1	no	—
239	C₂²×C₄₃	—	2	8	no	—
240	C₂²×C₄₃	—	4	4	no	—
241	C₂²×C₄₃	—	4	4	no	—
242	C₂²×C₄₃	—	8	8	no	—
243	C₂²×C₄₃	D₄×Q₈	1	2	yes	—
244	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
245	C₄×C₄₃	—	2	1	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	2	1	no	—
248	C₄×C₄₃	—	4	4	no	—
249	C₄×C₄₃	D₄×Q₈	1	2	yes	—
250	C₄×C₄₃	#576	1	2	yes	—
251	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
252	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
253	Dic₄₃	—	2	4	no	—
254	Dic₄₃	—	2	4	no	—
255	Dic₄₃	—	4	4	no	—
256	Dic₄₃	—	4	4	no	—
257	#3501	—	43	2	no	—
258	#3389	—	43	4	no	—
259	#3384	—	43	4	no	—
260	#3380	—	43	2	no	—
261	#3380	—	43	4	no	—
262	Q₈×D₈	—	43	2	no	—
263	#3164	—	43	2	no	—
264	#3160	—	43	1	no	—
265	#3081	—	43	4	no	—
266	#3077	—	43	2	no	—
267	#2960	—	43	1	no	—
268	#2948	—	43	2	no	—
269	C₂×C₄×D₈	D₄₃	1	1	yes	characteristic
270	C₂×C₄₃	—	2	2	no	—
271	C₂×C₄₃	—	4	8	no	—
272	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
273	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
274	C₂×C₄₃	#3584	1	1	yes	characteristic
275	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
276	#554	—	43	4	no	—
277	#554	—	43	8	no	—
278	#554	—	86	4	no	—
279	#554	—	86	2	no	—
280	D₄×Q₈	—	43	4	no	—
281	D₄×Q₈	—	86	2	no	—
282	#544	—	43	4	no	—
283	#543	—	86	4	no	—
284	#533	—	43	1	no	—
285	#533	—	43	2	no	—
286	C₂×C₂²⋊Q₈	—	86	4	no	—
287	#518	—	43	4	no	—
288	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
289	#501	—	43	8	no	—
290	#500	—	43	4	no	—
291	#500	—	43	1	no	—
292	#500	—	43	1	no	—
293	#499	—	43	4	no	—
294	#499	—	43	2	no	—
295	#499	—	43	2	no	—
296	#498	—	43	2	no	—
297	#478	—	43	8	no	—
298	#478	—	43	8	no	—
299	#478	—	43	8	no	—
300	#476	—	43	4	no	—
301	#476	—	43	8	no	—
302	#474	—	43	4	no	—
303	#474	—	43	8	no	—
304	#446	—	43	2	no	—
305	#446	—	43	2	no	—
306	C₈×Q₈	—	43	2	no	—
307	C₈×Q₈	—	43	2	no	—
308	#442	—	43	8	no	—
309	C₄×D₈	—	43	4	no	—
310	C₄×D₈	—	43	4	no	—
311	C₄×D₈	C₂×D₄₃	1	2	yes	—
312	C₄×D₈	C₂×D₄₃	1	2	yes	—
313	C₄×D₈	C₂×D₄₃	1	2	yes	—
314	C₄×D₈	C₂×D₄₃	1	2	yes	—
315	#428	—	43	4	no	—
316	#427	—	43	2	no	—
317	#427	—	43	2	no	—
318	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
319	#424	—	43	2	no	—
320	#423	—	43	1	no	—
321	#418	—	43	4	no	—
322	C₂×#102	C₂×D₄₃	1	2	yes	—
323	#405	—	43	2	no	—
324	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
325	C₄₃	#61370	1	1	yes	characteristic, complemented, Sylow
326	C₂²×Q₈	—	86	4	no	—
327	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
328	C₂³×C₄	—	2	2	no	—
329	C₂×D₈	Dic₈₆	1	8	yes	complemented
330	C₂×D₈	C₂²×D₄₃	1	2	yes	—
331	C₂×D₈	C₂²×D₄₃	1	2	yes	—
332	C₂×M₁₆	—	43	2	no	—
333	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
335	C₄⋊Q₈	—	43	8	no	—
336	C₄⋊Q₈	—	43	1	no	—
337	C₄⋊Q₈	—	43	1	no	—
338	C₄⋊Q₈	—	43	2	no	—
339	C₄⋊Q₈	—	43	2	no	—
340	C₄⋊Q₈	—	86	4	no	—
341	#125	—	43	8	no	—
342	#125	—	43	2	no	—
343	#125	—	43	4	no	—
344	#125	—	86	4	no	—
345	C₂²⋊Q₈	—	43	2	no	—
346	C₂²⋊Q₈	—	43	2	no	—
347	C₂²⋊Q₈	—	86	8	no	—
348	C₂²⋊Q₈	—	86	8	no	—
349	C₂²⋊Q₈	—	86	8	no	—
350	C₂²⋊Q₈	—	86	8	no	—
351	C₂²⋊Q₈	—	86	8	no	—
352	C₂²⋊Q₈	—	86	4	no	—
353	C₂²⋊Q₈	—	86	8	no	—
354	C₂²⋊Q₈	—	86	4	no	—
355	C₂²⋊Q₈	—	86	2	no	—
356	C₂²⋊Q₈	—	86	2	no	—
357	C₄×Q₈	—	43	2	no	—
358	C₄×Q₈	—	43	2	no	—
359	C₄×Q₈	—	86	2	no	—
360	C₄×Q₈	—	86	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	—	43	8	no	—
364	C₄×D₄	—	43	8	no	—
365	C₄×D₄	—	86	4	no	—
366	C₄×D₄	—	86	4	no	—
367	C₄×D₄	C₂²×D₄₃	1	4	yes	—
368	C₄×D₄	C₂²×D₄₃	1	4	yes	—
369	#117	—	43	2	no	—
370	#117	—	43	4	no	—
371	C₂×C₄⋊C₄	—	86	8	no	—
372	C₂×C₄⋊C₄	—	86	4	no	—
373	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₂²⋊C₄	—	86	8	no	—
376	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
377	#107	—	43	2	no	—
378	#107	—	43	2	no	—
379	#107	—	43	2	no	—
380	#107	—	43	2	no	—
381	#107	—	43	8	no	—
382	#107	C₂²×D₄₃	1	2	yes	—
383	#107	C₂²×D₄₃	1	2	yes	—
384	#106	—	43	4	no	—
385	#106	—	43	4	no	—
386	#106	—	43	8	no	—
387	C₄⋊C₈	—	43	4	no	—
388	C₄⋊C₈	—	43	4	no	—
389	C₄⋊C₈	—	43	2	no	—
390	C₄⋊C₈	—	43	2	no	—
391	#102	—	43	8	no	—
392	#102	—	43	8	no	—
393	#102	C₂²×D₄₃	1	4	yes	—
394	#102	C₂²×D₄₃	1	4	yes	—
395	#97	—	43	4	no	—
396	C₄×C₈	—	43	4	no	—
397	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
399	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
400	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
401	C₂⁴	—	2	2	no	—
402	C₂×Q₈	—	43	2	no	—
403	C₂×Q₈	—	43	2	no	—
404	C₂×Q₈	—	86	8	no	—
405	C₂×Q₈	—	86	2	no	—
406	C₂×Q₈	—	86	2	no	—
407	C₂×Q₈	—	344	8	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	C₂×Dic₈₆	1	8	yes	complemented
411	C₂×D₄	C₂³×D₄₃	1	4	yes	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	8	4	no	—
416	C₂²×C₄	—	86	8	no	—
417	C₂²×C₄	—	86	8	no	—
418	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
419	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
420	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
421	D₈	C₂×Dic₈₆	1	8	yes	complemented
422	D₈	C₂×Dic₈₆	1	8	yes	complemented
423	M₁₆	—	86	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	43	4	no	—
426	C₂×C₈	C₂×Dic₈₆	1	4	yes	complemented
427	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
428	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
429	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
430	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	43	4	no	—
433	C₄⋊C₄	—	43	2	no	—
434	C₄⋊C₄	—	43	2	no	—
435	C₄⋊C₄	—	43	2	no	—
436	C₄⋊C₄	—	43	4	no	—
437	C₄⋊C₄	—	43	2	no	—
438	C₄⋊C₄	—	43	4	no	—
439	C₄⋊C₄	—	43	4	no	—
440	C₄⋊C₄	—	86	8	no	—
441	C₄⋊C₄	—	86	8	no	—
442	C₄⋊C₄	—	86	8	no	—
443	C₄⋊C₄	—	86	4	no	—
444	C₄⋊C₄	—	86	2	no	—
445	C₄⋊C₄	—	86	4	no	—
446	C₄⋊C₄	—	86	2	no	—
447	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	43	4	no	—
451	C₂²⋊C₄	—	86	8	no	—
452	C₂²⋊C₄	—	86	8	no	—
453	C₂²⋊C₄	—	86	4	no	—
454	C₄²	—	43	4	no	—
455	C₄²	—	86	4	no	—
456	C₄²	D₄×D₄₃	1	1	yes	characteristic
457	C₄²	D₄×D₄₃	1	1	yes	characteristic
458	C₄²	C₂³×D₄₃	1	1	yes	characteristic
459	C₄²	C₂³×D₄₃	1	1	yes	characteristic
460	C₂³	—	2	4	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	8	2	no	—
463	C₂³	—	8	2	no	—
464	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
465	Q₈	—	86	4	no	—
466	Q₈	—	344	2	no	—
467	Q₈	—	344	8	no	—
468	Q₈	—	172	2	no	—
469	Q₈	—	172	4	no	—
470	D₄	—	2	8	no	—
471	D₄	—	2	4	no	—
472	D₄	C₂²×Dic₈₆	1	8	yes	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	8	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	—	43	4	no	—
480	C₂×C₄	—	43	4	no	—
481	C₂×C₄	—	86	4	no	—
482	C₂×C₄	—	86	4	no	—
483	C₂×C₄	—	344	8	no	—
484	C₂×C₄	—	344	8	no	—
485	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
486	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
489	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
491	C₂×C₄	#13063372	1	2	yes	—
492	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	86	4	no	—
496	C₈	C₂²×Dic₈₆	1	2	yes	—
497	C₈	C₂²×Dic₈₆	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	8	8	no	—
504	C₂²	D₄×Dic₈₆	1	2	yes	—
505	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	4	no	—
510	C₄	—	86	4	no	—
511	C₄	—	86	4	no	—
512	C₄	—	172	4	no	—
513	C₄	—	172	4	no	—
514	C₄	D₄×Dic₈₆	1	2	yes	—
515	C₄	#14583700	1	2	yes	—
516	C₄	C₂³×Dic₈₆	1	1	yes	characteristic
517	C₄	C₂×#13063372	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	4	8	no	—
520	C₂	C₂×D₄×Dic₈₆	1	1	yes	characteristic
521	C₂	C₂×#14583700	1	1	yes	characteristic
522	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×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂²×D₈×C₄₃	C₂²
hypercenter	C₂×C₄×D₈	D₄₃
hypocenter	C₄₃	#61370
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #19148398	C₂	semidirect
2. #19147551	C₂	semidirect
3. #19147492	C₂	semidirect
4. #19147462	C₂	semidirect
5. #19147460	C₂	semidirect
6. D₈×Dic₈₆	C₂	semidirect
7. #19145131	C₂	semidirect
8. #19145109	C₂	semidirect
9. #19144422	C₂	semidirect
10. #19144392	C₂	semidirect
11. #19143529	C₂	semidirect
15. #14583608	C₂²	semidirect
17. #14583606	C₂²	semidirect
19. D₄×Dic₈₆	C₂²	semidirect
26. #14583307	C₂²	semidirect
27. #14583304	C₂²	semidirect
28. #14583304	C₂²	semidirect
29. #14583303	C₂²	semidirect
30. #14583301	C₂²	semidirect
31. #14583301	C₂²	semidirect
32. #14583300	C₂²	semidirect
33. #14583297	C₂²	semidirect
34. #14583201	C₂²	semidirect
35. #14583199	C₂²	semidirect
36. #14583197	C₂²	semidirect
37. #14583189	C₂²	semidirect
38. #14583187	C₂²	semidirect
39. #14583179	C₂²	semidirect
40. #14583177	C₂²	semidirect
41. #14583029	C₂²	semidirect
42. #14583029	C₂²	semidirect
43. C₈×Dic₈₆	C₂²	semidirect
44. C₈×Dic₈₆	C₂²	semidirect
119. C₂×D₈×C₄₃	Q₈	semidirect
142. C₂×D₄×C₄₃	C₂×Q₈	semidirect
159. D₈×C₄₃	C₂×Q₈	semidirect
160. D₈×C₄₃	C₂×Q₈	semidirect
162. C₂×C₈×C₄₃	C₂×Q₈	semidirect
325. C₄₃	#61370	semidirect
329. C₂×D₈	Dic₈₆	semidirect
410. C₂×D₄	C₂×Dic₈₆	semidirect
421. D₈	C₂×Dic₈₆	semidirect
422. D₈	C₂×Dic₈₆	semidirect
426. 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
#19148398	2
#19147551	2
#19147492	2
#19147462	2
#19147460	2
D₈×Dic₈₆	2
#19145131	2
#19145109	2
#19144422	2
#19144392	2
#19143529	2
#19143447	2
C₂×C₄×D₈×C₄₃	2
#61370	43