Subgroups — #24988096

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583454	C₂	1	1	yes	maximal, characteristic
2	#19134572	C₂	1	1	yes	maximal, characteristic
3	#19134572	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582647	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582647	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582645	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583454	—	2	2	no	—
9	#14583454	—	2	2	no	—
10	#14583454	—	2	2	no	—
11	#14583454	—	2	2	no	—
12	C₂×#13063325	C₂²	1	1	yes	characteristic
13	C₂×#13063316	—	2	1	no	—
14	C₂×#13063305	C₄	1	2	yes	—
15	C₂×#13063301	—	2	1	no	—
16	C₂×Q₈×Dic₄₃	—	2	1	no	—
17	C₂×#13063290	C₄	1	2	yes	—
18	C₂×#13063283	—	2	1	no	—
19	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
23	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
24	#14582653	—	2	1	no	—
25	#14582653	—	2	1	no	—
26	#14582647	—	2	2	no	—
27	#14582647	—	2	2	no	—
28	#14582645	—	2	2	no	—
29	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#332	—	2	2	no	—
33	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
34	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
37	C₂²×C₄₃⋊C₈	—	2	1	no	—
38	C₂²×C₄₃⋊C₈	—	2	1	no	—
39	#13063325	—	2	1	no	—
40	#13063325	—	2	1	no	—
41	#13063325	D₄	1	2	yes	—
42	#13063325	D₄	1	2	yes	—
43	#13063316	—	2	4	no	—
44	#13063316	—	2	4	no	—
45	#13063305	—	2	4	no	—
46	#13063305	—	2	4	no	—
47	#13063301	—	2	4	no	—
48	#13063301	—	2	4	no	—
49	Q₈×Dic₄₃	—	2	4	no	—
50	Q₈×Dic₄₃	—	2	4	no	—
51	#13063290	—	2	4	no	—
52	#13063290	—	2	4	no	—
53	#13063283	—	2	4	no	—
54	#13063283	—	2	4	no	—
55	C₂×C₄⋊Dic₄₃	—	2	1	no	—
56	C₂×C₄⋊Dic₄₃	—	2	1	no	—
57	C₂×C₄⋊Dic₄₃	—	2	2	no	—
58	C₂×Dic₄₃⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
60	C₂×C₄×Dic₄₃	—	2	2	no	—
61	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
64	C₄²×D₄₃	—	2	1	no	—
65	C₄²×D₄₃	—	2	1	no	—
66	C₄²×D₄₃	—	2	1	no	—
67	C₄²×D₄₃	—	2	1	no	—
68	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
72	(C₂×D₄₃)⋊C₈	—	4	2	no	—
73	(C₂×D₄₃)⋊C₈	—	4	2	no	—
74	C₂²×Q₈×C₄₃	—	2	1	no	—
75	C₂²×C₈×C₄₃	—	2	1	no	—
76	C₂²×C₈×C₄₃	—	2	1	no	—
77	C₄⋊Q₈×C₄₃	—	2	1	no	—
78	C₄⋊Q₈×C₄₃	—	2	1	no	—
79	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
80	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₃	—	2	1	no	—
85	C₄⋊C₈×C₄₃	—	2	1	no	—
86	C₄⋊C₈×C₄₃	—	2	1	no	—
87	C₄⋊C₈×C₄₃	—	2	1	no	—
88	C₂³×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	4	1	no	—
92	C₂×Q₈×C₄₃	—	4	1	no	—
93	C₂×Q₈×C₄₃	—	4	1	no	—
94	C₂×Q₈×C₄₃	—	4	1	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₄₃	—	2	2	no	—
100	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₃	—	2	1	no	—
104	C₂×C₄×D₄₃	—	2	1	no	—
105	C₂×C₄×D₄₃	—	2	1	no	—
106	C₂×C₄×D₄₃	—	2	1	no	—
107	C₂×C₄×D₄₃	—	2	1	no	—
108	C₂×C₄×D₄₃	—	2	1	no	—
109	C₂×C₄×D₄₃	—	2	1	no	—
110	C₂×C₄×D₄₃	—	2	1	no	—
111	C₂×C₄×D₄₃	—	2	1	no	—
112	C₂×C₄×D₄₃	—	2	1	no	—
113	C₂×C₄×D₄₃	—	2	1	no	—
114	C₂×C₄×D₄₃	—	2	1	no	—
115	C₂×C₄×D₄₃	—	4	1	no	—
116	C₂×C₄×D₄₃	—	4	1	no	—
117	C₂×C₄×D₄₃	SD₁₆	1	2	yes	—
118	C₂×C₄×D₄₃	Q₁₆	1	2	yes	—
119	C₂×Dic₈₆	—	2	2	no	—
120	C₂×Dic₈₆	—	4	2	no	—
121	C₂×Dic₈₆	—	4	2	no	—
122	C₂×Dic₈₆	C₂²⋊C₄	1	4	yes	—
123	C₂×C₈×C₄₃	—	4	1	no	—
124	C₂×C₈×C₄₃	—	4	1	no	—
125	C₂×C₈×C₄₃	—	4	1	no	—
126	C₂×C₈×C₄₃	—	4	1	no	—
127	C₂×C₈×C₄₃	—	4	1	no	—
128	C₂×C₈×C₄₃	—	4	1	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
133	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	(C₂×D₄₃)⋊C₄	—	2	8	no	—
138	C₄⋊Dic₄₃	—	2	8	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	Dic₄₃⋊C₄	—	2	8	no	—
144	C₄×Dic₄₃	—	2	8	no	—
145	C₄×Dic₄₃	—	2	1	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	—	2	1	no	—
148	C₄×Dic₄₃	—	2	1	no	—
149	C₄×Dic₄₃	—	2	1	no	—
150	C₄×Dic₄₃	—	2	1	no	—
151	C₂×C₄₃⋊C₈	—	4	1	no	—
152	C₂×C₄₃⋊C₈	—	4	1	no	—
153	C₂×C₄₃⋊C₈	—	4	1	no	—
154	C₂×C₄₃⋊C₈	—	4	1	no	—
155	C₂×C₄₃⋊C₈	—	4	1	no	—
156	C₂×C₄₃⋊C₈	—	4	1	no	—
157	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×D₄₃	—	2	1	no	—
159	C₂²×D₄₃	—	2	1	no	—
160	C₂²×D₄₃	—	2	1	no	—
161	C₂²×D₄₃	—	2	1	no	—
162	C₂²×D₄₃	—	2	1	no	—
163	C₂²×D₄₃	—	2	1	no	—
164	C₂²×D₄₃	#103	1	2	yes	—
165	Q₈×C₄₃	—	4	2	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	Q₈×C₄₃	—	4	2	no	—
168	Q₈×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	4	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
179	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
183	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
184	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
186	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
188	C₂×Dic₄₃	—	2	1	no	—
189	C₂×Dic₄₃	—	2	1	no	—
190	C₂×Dic₄₃	—	2	1	no	—
191	C₂×Dic₄₃	—	2	1	no	—
192	C₂×Dic₄₃	—	2	4	no	—
193	C₂×Dic₄₃	—	2	1	no	—
194	C₂×Dic₄₃	—	2	1	no	—
195	C₂×Dic₄₃	—	2	1	no	—
196	C₂×Dic₄₃	—	2	1	no	—
197	C₂×Dic₄₃	—	4	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	#103	1	2	yes	—
200	C₄×D₄₃	—	2	2	no	—
201	C₄×D₄₃	—	2	2	no	—
202	C₄×D₄₃	—	2	2	no	—
203	C₄×D₄₃	—	2	2	no	—
204	C₄×D₄₃	—	4	2	no	—
205	C₄×D₄₃	—	4	2	no	—
206	C₄×D₄₃	—	4	1	no	—
207	C₄×D₄₃	—	4	1	no	—
208	C₄×D₄₃	—	4	1	no	—
209	C₄×D₄₃	—	4	1	no	—
210	Dic₈₆	—	4	4	no	—
211	Dic₈₆	—	4	4	no	—
212	C₈×C₄₃	—	8	1	no	—
213	C₈×C₄₃	—	8	1	no	—
214	C₄₃⋊C₈	—	8	1	no	—
215	C₄₃⋊C₈	—	8	1	no	—
216	#8343	—	43	1	no	maximal, Sylow
217	C₂²×C₄₃	#379	1	1	yes	characteristic
218	C₂²×C₄₃	#413	1	1	yes	characteristic
219	C₂²×C₄₃	#413	1	1	yes	characteristic
220	C₂²×C₄₃	C₂×#103	1	1	yes	characteristic
221	C₂²×C₄₃	#416	1	1	yes	characteristic
222	C₂²×C₄₃	#417	1	1	yes	characteristic
223	C₂²×C₄₃	#419	1	1	yes	characteristic
224	C₂×D₄₃	—	2	2	no	—
225	C₂×D₄₃	—	2	2	no	—
226	C₂×D₄₃	—	2	2	no	—
227	C₂×D₄₃	—	4	1	no	—
228	C₂×D₄₃	—	4	1	no	—
229	C₂×D₄₃	—	4	1	no	—
230	C₂×D₄₃	—	4	1	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	—	4	4	no	—
234	C₄×C₄₃	#448	1	1	yes	characteristic
235	C₄×C₄₃	#448	1	1	yes	characteristic
236	C₄×C₄₃	#449	1	1	yes	characteristic
237	C₄×C₄₃	#449	1	1	yes	characteristic
238	C₄×C₄₃	#451	1	1	yes	characteristic
239	C₄×C₄₃	#451	1	1	yes	characteristic
240	C₄×C₄₃	#452	1	1	yes	characteristic
241	C₄×C₄₃	#452	1	1	yes	characteristic
242	Dic₄₃	—	2	2	no	—
243	Dic₄₃	—	4	4	no	—
244	Dic₄₃	—	4	1	no	—
245	Dic₄₃	—	4	1	no	—
246	C₂×#533	—	43	1	no	—
247	#1797	—	43	1	no	—
248	#1797	—	43	1	no	—
249	C₂×#333	—	43	1	no	—
250	C₂×#333	—	43	1	no	—
251	C₂×#332	—	43	1	no	—
252	C₂×#332	D₄₃	1	1	yes	characteristic, complemented
253	C₂×C₄₃	#1542	1	1	yes	characteristic
254	C₂×C₄₃	#1550	1	1	yes	characteristic
255	C₂×C₄₃	#1554	1	1	yes	characteristic
256	C₂×C₄₃	#1559	1	1	yes	characteristic
257	C₂×C₄₃	#1785	1	1	yes	characteristic
258	C₂×C₄₃	#1787	1	1	yes	characteristic
259	C₂×C₄₃	#1788	1	1	yes	characteristic
260	D₄₃	—	4	2	no	—
261	#533	—	86	2	no	—
262	#533	—	86	2	no	—
263	#533	—	86	2	no	—
264	#533	—	86	2	no	—
265	C₂×C₄⋊Q₈	—	43	1	no	—
266	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
267	C₂×#125	—	86	1	no	—
268	C₂×C₂²⋊Q₈	—	43	2	no	—
269	C₂×C₂²⋊Q₈	—	86	1	no	—
270	C₂×C₄×Q₈	—	43	2	no	—
271	C₂×C₄×Q₈	—	86	1	no	—
272	C₂×#117	—	86	1	no	—
273	C₂²×C₄²	—	43	1	no	—
274	C₂×C₄⋊C₈	—	43	1	no	—
275	C₂×C₄⋊C₈	—	43	1	no	—
276	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	—	86	1	no	—
279	C₂×C₂²⋊C₈	—	86	1	no	—
280	#336	—	86	1	no	—
281	#336	—	86	1	no	—
282	#333	—	86	2	no	—
283	#333	—	86	2	no	—
284	#332	—	2	2	no	—
285	#332	—	86	2	no	—
286	C₄₃	#8343	1	1	yes	characteristic, complemented, Sylow
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	—	43	2	no	—
289	C₂³×C₄	—	43	1	no	—
290	C₂³×C₄	—	43	1	no	—
291	C₂³×C₄	—	43	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	86	1	no	—
295	C₂²×C₈	—	86	1	no	—
296	C₄⋊Q₈	—	2	1	no	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	43	2	no	—
299	C₄⋊Q₈	—	43	2	no	—
300	C₄⋊Q₈	—	86	1	no	—
301	C₄⋊Q₈	—	86	1	no	—
302	C₄⋊Q₈	D₁₇₂	1	2	yes	—
303	C₄⋊Q₈	C₂²⋊D₄₃	1	2	yes	—
304	#125	—	86	4	no	—
305	#125	—	86	4	no	—
306	C₂²⋊Q₈	—	86	4	no	—
307	C₂²⋊Q₈	—	86	4	no	—
308	C₂²⋊Q₈	—	86	4	no	—
309	C₂²⋊Q₈	—	86	4	no	—
310	C₄×Q₈	—	86	4	no	—
311	C₄×Q₈	—	86	4	no	—
312	C₄×Q₈	—	86	4	no	—
313	C₄×Q₈	—	86	4	no	—
314	#117	—	86	4	no	—
315	#117	—	86	4	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	86	2	no	—
318	C₂×C₄⋊C₄	—	86	2	no	—
319	C₂×C₄⋊C₄	—	86	1	no	—
320	C₂×C₄⋊C₄	—	86	1	no	—
321	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
322	C₂×C₂²⋊C₄	—	86	2	no	—
323	C₂×C₄²	—	43	1	no	—
324	C₂×C₄²	—	43	1	no	—
325	C₂×C₄²	—	43	1	no	—
326	C₂×C₄²	—	86	2	no	—
327	C₂×C₄²	—	86	1	no	—
328	C₂×C₄²	—	86	1	no	—
329	C₂×C₄²	—	86	1	no	—
330	C₂×C₄²	—	86	1	no	—
331	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	2	1	no	—
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	—	2	1	no	—
336	C₄⋊C₈	—	86	1	no	—
337	C₄⋊C₈	—	86	1	no	—
338	C₄⋊C₈	—	86	1	no	—
339	C₄⋊C₈	—	86	1	no	—
340	C₂²⋊C₈	—	172	2	no	—
341	C₂²⋊C₈	—	172	2	no	—
342	C₂⁴	—	43	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×Q₈	—	4	1	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×Q₈	—	4	1	no	—
349	C₂×Q₈	—	43	4	no	—
350	C₂×Q₈	—	86	2	no	—
351	C₂×Q₈	—	172	2	no	—
352	C₂×Q₈	—	172	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	43	1	no	—
355	C₂²×C₄	—	43	2	no	—
356	C₂²×C₄	—	43	2	no	—
357	C₂²×C₄	—	43	1	no	—
358	C₂²×C₄	—	43	1	no	—
359	C₂²×C₄	—	86	1	no	—
360	C₂²×C₄	—	86	1	no	—
361	C₂²×C₄	—	86	1	no	—
362	C₂²×C₄	—	86	1	no	—
363	C₂²×C₄	—	86	2	no	—
364	C₂²×C₄	—	86	1	no	—
365	C₂²×C₄	—	86	1	no	—
366	C₂²×C₄	—	86	1	no	—
367	C₂²×C₄	—	86	1	no	—
368	C₂²×C₄	—	86	1	no	—
369	C₂²×C₄	—	86	1	no	—
370	C₂²×C₄	—	86	1	no	—
371	C₂²×C₄	—	86	1	no	—
372	C₂²×C₄	—	172	1	no	—
373	C₂²×C₄	—	172	1	no	—
374	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
375	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
377	C₂×C₈	—	4	1	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	—	4	1	no	—
380	C₂×C₈	—	4	1	no	—
381	C₂×C₈	—	4	1	no	—
382	C₂×C₈	—	4	1	no	—
383	C₂×C₈	—	172	1	no	—
384	C₂×C₈	—	172	1	no	—
385	C₂×C₈	—	172	1	no	—
386	C₂×C₈	—	172	1	no	—
387	C₂×C₈	—	172	1	no	—
388	C₂×C₈	—	172	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	86	8	no	—
393	C₄⋊C₄	—	86	8	no	—
394	C₄⋊C₄	—	86	2	no	—
395	C₄⋊C₄	—	86	2	no	—
396	C₄⋊C₄	—	86	2	no	—
397	C₄⋊C₄	—	86	2	no	—
398	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
399	C₂²⋊C₄	—	86	8	no	—
400	C₄²	—	86	8	no	—
401	C₄²	—	86	1	no	—
402	C₄²	—	86	1	no	—
403	C₄²	—	86	1	no	—
404	C₄²	—	86	1	no	—
405	C₄²	—	86	1	no	—
406	C₄²	—	86	1	no	—
407	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
408	C₄²	D₄×D₄₃	1	1	yes	characteristic
409	C₄²	D₄×D₄₃	1	1	yes	characteristic
410	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
411	C₂³	—	43	2	no	—
412	C₂³	—	86	1	no	—
413	C₂³	—	86	1	no	—
414	C₂³	—	86	1	no	—
415	C₂³	—	86	1	no	—
416	C₂³	—	86	1	no	—
417	C₂³	—	86	1	no	—
418	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	172	4	no	—
424	Q₈	—	172	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	43	2	no	—
431	C₂×C₄	—	86	1	no	—
432	C₂×C₄	—	86	1	no	—
433	C₂×C₄	—	86	2	no	—
434	C₂×C₄	—	86	2	no	—
435	C₂×C₄	—	86	2	no	—
436	C₂×C₄	—	86	2	no	—
437	C₂×C₄	—	86	1	no	—
438	C₂×C₄	—	86	1	no	—
439	C₂×C₄	—	86	1	no	—
440	C₂×C₄	—	86	1	no	—
441	C₂×C₄	—	86	1	no	—
442	C₂×C₄	—	86	1	no	—
443	C₂×C₄	—	86	4	no	—
444	C₂×C₄	—	172	2	no	—
445	C₂×C₄	—	172	2	no	—
446	C₂×C₄	—	172	2	no	—
447	C₂×C₄	—	172	2	no	—
448	C₂×C₄	—	172	1	no	—
449	C₂×C₄	—	172	1	no	—
450	C₂×C₄	—	172	1	no	—
451	C₂×C₄	—	172	1	no	—
452	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
454	C₂×C₄	#13063293	1	1	yes	characteristic
455	C₂×C₄	#13063293	1	1	yes	characteristic
456	C₂×C₄	#13063295	1	1	yes	characteristic
457	C₂×C₄	#13063295	1	1	yes	characteristic
458	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
459	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
460	C₂×C₄	#13063344	1	1	yes	characteristic
461	C₂×C₄	#13063346	1	1	yes	characteristic
462	C₂×C₄	#13063349	1	1	yes	characteristic
463	C₂×C₄	#13063354	1	1	yes	characteristic
464	C₂×C₄	#13063354	1	1	yes	characteristic
465	C₂×C₄	#13063357	1	1	yes	characteristic
466	C₈	—	8	1	no	—
467	C₈	—	8	1	no	—
468	C₈	—	344	1	no	—
469	C₈	—	344	1	no	—
470	C₂²	—	86	2	no	—
471	C₂²	—	86	2	no	—
472	C₂²	—	86	2	no	—
473	C₂²	—	172	1	no	—
474	C₂²	—	172	1	no	—
475	C₂²	—	172	1	no	—
476	C₂²	—	172	1	no	—
477	C₂²	#14582754	1	1	yes	characteristic
478	C₂²	#14582882	1	1	yes	characteristic
479	C₂²	#14582882	1	1	yes	characteristic
480	C₂²	#103×D₄₃	1	1	yes	characteristic
481	C₂²	#14582892	1	1	yes	characteristic
482	C₂²	#14582897	1	1	yes	characteristic
483	C₂²	#14582906	1	1	yes	characteristic
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	4	4	no	—
487	C₄	—	86	2	no	—
488	C₄	—	172	1	no	—
489	C₄	—	172	4	no	—
490	C₄	—	172	1	no	—
491	C₄	#14583036	1	1	yes	characteristic
492	C₄	#14583039	1	1	yes	characteristic
493	C₄	#14583041	1	1	yes	characteristic
494	C₄	#14583045	1	1	yes	characteristic
495	C₄	#14583053	1	1	yes	characteristic
496	C₄	#14583056	1	1	yes	characteristic
497	C₄	#14583058	1	1	yes	characteristic
498	C₄	#14583062	1	1	yes	characteristic
499	C₂	—	172	2	no	—
500	C₂	#19133251	1	1	yes	characteristic
501	C₂	#19133284	1	1	yes	characteristic
502	C₂	#19133302	1	1	yes	characteristic
503	C₂	#19133324	1	1	yes	characteristic
504	C₂	#19134522	1	1	yes	characteristic
505	C₂	#19134528	1	1	yes	characteristic
506	C₂	#19134532	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×#332	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×#332	D₄₃
hypocenter	C₄₃	#8343
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
4. C₂×#14582647	C₂	semidirect
5. C₂×#14582647	C₂	semidirect
6. C₂×#14582645	C₂	semidirect
7. C₂×C₄₃×#332	C₂	semidirect
252. C₂×#332	D₄₃	semidirect
286. C₄₃	#8343	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583454	2
#19134572	2
C₂×#14582647	2
C₂×#14582645	2
C₂×C₄₃×#332	2
#8343	43