Subgroups — #19149377

Order 5504.

1412 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583734	C₂	1	1	yes	maximal, characteristic, complemented
2	2₋¹⁺⁴×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583716	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583715	C₂	1	3	yes	maximal, complemented
5	#14583714	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583713	C₂	1	3	yes	maximal, complemented
7	#14583710	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583709	C₂	1	3	yes	maximal, complemented
9	#14583705	C₂	1	3	yes	maximal, complemented
10	#14583696	C₂	1	3	yes	maximal, complemented
11	#14583695	C₂	1	3	yes	maximal, complemented
12	C₂×#13063354	C₂	1	3	yes	maximal, complemented
13	#137×D₄₃	C₂	1	3	yes	maximal, complemented
14	#14583664	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
16	#13063373	—	2	1	no	—
17	#13063373	C₂²	1	3	yes	complemented
18	#13063372	—	2	1	no	—
19	#13063372	—	2	3	no	—
20	#13063372	C₂²	1	3	yes	complemented
21	#13063372	C₂²	1	3	yes	complemented
22	#13063372	C₂²	1	1	yes	characteristic, complemented
23	#13063372	C₂²	1	1	yes	characteristic, complemented
24	#13063370	—	2	3	no	—
25	#13063370	C₂²	1	3	yes	complemented
26	C₂×#10621900	—	2	3	no	—
27	C₂×#10621900	C₂²	1	3	yes	—
28	#41×D₄₃	—	2	1	no	—
29	#41×D₄₃	—	2	3	no	—
30	#41×D₄₃	C₂²	1	3	yes	—
31	#41×D₄₃	C₂²	1	1	yes	characteristic
32	#41×D₄₃	C₂²	1	3	yes	complemented
33	C₂×Q₈×D₄₃	—	2	1	no	—
34	C₂×Q₈×D₄₃	C₂²	1	3	yes	complemented
35	#13063358	C₂²	1	3	yes	complemented
36	#13063358	C₂²	1	3	yes	complemented
37	#13063357	C₂²	1	3	yes	complemented
38	#13063357	C₂²	1	3	yes	complemented
39	#13063356	C₂²	1	3	yes	complemented
40	#13063355	C₂²	1	3	yes	complemented
41	#13063355	C₂²	1	3	yes	complemented
42	#13063354	C₂²	1	6	yes	complemented
43	#13063354	C₂²	1	3	yes	complemented
44	#13063354	C₂²	1	6	yes	complemented
45	#13063354	C₂²	1	6	yes	complemented
46	#13063354	C₂²	1	3	yes	complemented
47	#13063352	C₂²	1	1	yes	characteristic, complemented
48	#13063352	C₂²	1	3	yes	complemented
49	#13063351	C₂²	1	3	yes	complemented
50	#13063349	C₂²	1	3	yes	complemented
51	#13063349	C₂²	1	3	yes	complemented
52	#13063347	C₂²	1	3	yes	complemented
53	#13063346	C₂²	1	6	yes	complemented
54	#13063345	C₂²	1	3	yes	complemented
55	#13063345	C₂²	1	3	yes	complemented
56	#13063344	C₂²	1	6	yes	complemented
57	C₂×Dic₁₇₂	C₂²	1	3	yes	complemented
58	C₂×#10621885	C₂²	1	3	yes	complemented
59	Q₁₆×D₄₃	C₂²	1	6	yes	complemented
60	C₂×#10621883	C₂²	1	3	yes	complemented
61	SD₁₆×D₄₃	C₂²	1	6	yes	complemented
62	#13063333	C₂²	1	3	yes	complemented
63	#13063332	C₂²	1	1	yes	characteristic, complemented
64	#13063331	C₂²	1	3	yes	complemented
65	C₂×#10621872	C₂²	1	3	yes	complemented
66	M₁₆×D₄₃	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₄₃	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₄₃	C₂²	1	1	yes	characteristic, complemented
69	#137×C₄₃	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₄₃	C₂²	1	3	yes	complemented
71	#135×C₄₃	C₂²	1	3	yes	complemented
72	C₂×SD₁₆×C₄₃	C₂²	1	3	yes	complemented
73	#131×C₄₃	C₂²	1	1	yes	characteristic, complemented
74	#41×C₄₃	—	2	1	no	—
75	#41×C₄₃	—	2	3	no	—
76	#41×C₄₃	C₂³	1	3	yes	—
77	#41×C₄₃	C₂³	1	3	yes	—
78	#41×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×Q₈×C₄₃	—	2	1	no	—
80	C₂×Q₈×C₄₃	C₂³	1	3	yes	—
81	C₂×D₄×C₄₃	—	2	3	no	—
82	C₂×D₄×C₄₃	C₂³	1	3	yes	—
83	C₂×C₂²⋊D₄₃	—	2	6	no	—
84	C₂×C₂²⋊D₄₃	—	2	3	no	—
85	C₂²×Dic₄₃	—	2	3	no	—
86	#10621902	—	2	3	no	—
87	#10621902	D₄	1	1	yes	characteristic
88	#10621902	C₂³	1	3	yes	—
89	#10621902	C₂³	1	1	yes	characteristic
90	Q₈×D₄₃	—	2	1	no	—
91	Q₈×D₄₃	—	2	1	no	—
92	Q₈×D₄₃	—	2	3	no	—
93	Q₈×D₄₃	—	2	3	no	—
94	Q₈×D₄₃	—	2	3	no	—
95	Q₈×D₄₃	D₄	1	1	yes	characteristic
96	Q₈×D₄₃	C₂³	1	6	yes	—
97	Q₈×D₄₃	C₂³	1	3	yes	—
98	Q₈×D₄₃	C₂³	1	3	yes	—
99	#10621900	—	2	3	no	—
100	#10621900	—	2	3	no	—
101	#10621900	—	2	6	no	—
102	#10621900	—	2	6	no	—
103	#10621900	—	2	3	no	—
104	#10621900	—	2	3	no	—
105	#10621900	—	2	3	no	—
106	#10621900	—	2	3	no	—
107	#10621900	—	2	3	no	—
108	#10621900	D₄	1	3	yes	—
109	#10621900	C₂³	1	3	yes	—
110	#10621900	C₂³	1	6	yes	—
111	#10621900	C₂³	1	3	yes	—
112	D₄×D₄₃	—	2	3	no	—
113	D₄×D₄₃	—	2	3	no	—
114	D₄×D₄₃	—	2	3	no	—
115	D₄×D₄₃	D₄	1	3	yes	—
116	D₄×D₄₃	C₂³	1	3	yes	—
117	D₄×D₄₃	C₂³	1	1	yes	characteristic
118	#10621898	—	2	6	no	—
119	#10621898	—	2	3	no	—
120	#10621898	—	2	3	no	—
121	#10621898	—	2	3	no	—
122	#10621898	—	2	3	no	—
123	#10621898	C₂³	1	3	yes	—
124	#10621898	C₂³	1	3	yes	—
125	#10621898	C₂³	1	3	yes	—
126	C₂×C₄×D₄₃	—	2	3	no	—
127	C₂×C₄×D₄₃	—	2	3	no	—
128	C₂×C₄×D₄₃	—	2	3	no	—
129	C₂×C₄×D₄₃	C₂³	1	3	yes	—
130	C₂×Dic₈₆	—	2	3	no	—
131	C₂×Dic₈₆	—	2	3	no	—
132	C₂×Dic₈₆	—	2	3	no	—
133	C₂×Dic₈₆	C₂³	1	3	yes	—
134	C₂×Dic₈₆	C₂³	1	3	yes	—
135	Q₁₆×C₄₃	C₂³	1	3	yes	—
136	SD₁₆×C₄₃	C₂³	1	3	yes	—
137	SD₁₆×C₄₃	C₂³	1	6	yes	—
138	SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
139	D₈×C₄₃	C₂³	1	3	yes	—
140	M₁₆×C₄₃	C₂³	1	3	yes	—
141	C₂×C₈×C₄₃	C₂³	1	3	yes	—
142	#10621885	C₂³	1	3	yes	—
143	#10621885	C₂³	1	6	yes	—
144	#10621885	C₂³	1	3	yes	—
145	#10621884	C₂³	1	3	yes	—
146	#10621884	C₂³	1	1	yes	characteristic
147	#10621883	C₂³	1	6	yes	—
148	#10621883	C₂³	1	3	yes	—
149	#10621883	C₂³	1	3	yes	—
150	#10621882	C₂³	1	1	yes	characteristic
151	#10621882	C₂³	1	3	yes	—
152	#10621877	C₂³	1	3	yes	—
153	C₂×C₄₃⋊C₈	C₂³	1	3	yes	—
154	Dic₁₇₂	C₂³	1	6	yes	—
155	Dic₁₇₂	C₂³	1	3	yes	—
156	D₃₄₄	C₂³	1	1	yes	characteristic
157	#10621873	C₂³	1	3	yes	—
158	#10621873	C₂³	1	3	yes	—
159	#10621872	C₂³	1	3	yes	—
160	#10621872	C₂³	1	1	yes	characteristic
161	#10621872	C₂³	1	3	yes	—
162	#10621872	C₂³	1	3	yes	—
163	C₈×D₄₃	C₂³	1	6	yes	—
164	C₂³×C₄₃	—	2	3	no	—
165	C₂²×D₄₃	—	2	1	no	—
166	C₂²×D₄₃	—	2	3	no	—
167	C₂²×D₄₃	C₂×D₄	1	3	yes	—
168	Q₈×C₄₃	—	2	3	no	—
169	Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
170	Q₈×C₄₃	C₂⁴	1	3	yes	—
171	Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
172	D₄×C₄₃	—	2	3	no	—
173	D₄×C₄₃	—	2	3	no	—
174	D₄×C₄₃	—	2	3	no	—
175	D₄×C₄₃	C₂×D₄	1	3	yes	—
176	D₄×C₄₃	C₂⁴	1	1	yes	characteristic
177	D₄×C₄₃	C₂⁴	1	3	yes	—
178	C₂×C₄×C₄₃	—	2	3	no	—
179	C₂×C₄×C₄₃	—	2	3	no	—
180	C₂×C₄×C₄₃	—	2	3	no	—
181	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
182	C₂²⋊D₄₃	—	2	3	no	—
183	C₂²⋊D₄₃	—	2	3	no	—
184	C₂²⋊D₄₃	—	2	3	no	—
185	C₂²⋊D₄₃	—	2	3	no	—
186	C₂²⋊D₄₃	—	2	6	no	—
187	C₂²⋊D₄₃	—	2	1	no	—
188	C₂²⋊D₄₃	—	2	3	no	—
189	C₂²⋊D₄₃	C₂×D₄	1	6	yes	—
190	C₂×Dic₄₃	—	2	3	no	—
191	C₂×Dic₄₃	—	2	3	no	—
192	C₂×Dic₄₃	—	2	3	no	—
193	C₂×Dic₄₃	—	2	6	no	—
194	C₂×Dic₄₃	—	2	3	no	—
195	C₂×Dic₄₃	C₂×D₄	1	3	yes	—
196	D₁₇₂	—	2	1	no	—
197	D₁₇₂	—	2	3	no	—
198	D₁₇₂	C₂×D₄	1	3	yes	—
199	D₁₇₂	C₂⁴	1	1	yes	characteristic
200	D₁₇₂	C₂⁴	1	1	yes	characteristic
201	C₄×D₄₃	—	2	3	no	—
202	C₄×D₄₃	—	2	3	no	—
203	C₄×D₄₃	—	2	6	no	—
204	C₄×D₄₃	—	2	3	no	—
205	C₄×D₄₃	—	2	3	no	—
206	C₄×D₄₃	—	2	1	no	—
207	C₄×D₄₃	—	2	3	no	—
208	C₄×D₄₃	C₂×D₄	1	3	yes	—
209	C₄×D₄₃	C₂×D₄	1	3	yes	—
210	C₄×D₄₃	C₂⁴	1	3	yes	—
211	C₄×D₄₃	C₂⁴	1	1	yes	characteristic
212	Dic₈₆	—	2	3	no	—
213	Dic₈₆	—	2	3	no	—
214	Dic₈₆	—	2	3	no	—
215	Dic₈₆	—	2	6	no	—
216	Dic₈₆	—	2	3	no	—
217	Dic₈₆	C₂×D₄	1	3	yes	—
218	Dic₈₆	C₂⁴	1	3	yes	—
219	Dic₈₆	C₂⁴	1	3	yes	—
220	C₈×C₄₃	C₂⁴	1	3	yes	—
221	C₈×C₄₃	C₂⁴	1	1	yes	characteristic
222	C₄₃⋊C₈	C₂⁴	1	3	yes	—
223	C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄₃	—	2	3	no	—
225	C₂²×C₄₃	—	2	1	no	—
226	C₂²×C₄₃	—	8	3	no	—
227	C₂²×C₄₃	C₂²×D₄	1	3	yes	—
228	C₂×D₄₃	—	2	1	no	—
229	C₂×D₄₃	—	2	1	no	—
230	C₂×D₄₃	—	4	3	no	—
231	C₂×D₄₃	—	4	2	no	—
232	C₂×D₄₃	—	8	3	no	—
233	C₂×D₄₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×D₄₃	C₂²×D₄	1	3	yes	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	2	3	no	—
237	C₄×C₄₃	C₂²×D₄	1	3	yes	—
238	C₄×C₄₃	C₂⁵	1	1	yes	characteristic
239	Dic₄₃	—	2	3	no	—
240	Dic₄₃	—	2	3	no	—
241	Dic₄₃	C₂²×D₄	1	3	yes	—
242	Dic₄₃	C₂²×D₄	1	1	yes	characteristic
243	#3586	—	43	1	no	maximal, Sylow
244	C₂×C₄₃	—	2	3	no	—
245	C₂×C₄₃	—	4	1	no	—
246	C₂×C₄₃	—	4	3	no	—
247	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
248	D₄₃	—	2	1	no	—
249	D₄₃	—	2	3	no	—
250	D₄₃	—	4	1	no	—
251	D₄₃	—	4	1	no	—
252	#585	—	43	1	no	—
253	C₂×2₋¹⁺⁴	—	43	1	no	—
254	#578	—	43	1	no	—
255	#578	—	43	3	no	—
256	#578	—	43	3	no	—
257	#578	—	43	1	no	—
258	#577	—	43	1	no	—
259	#577	—	43	3	no	—
260	#577	—	43	3	no	—
261	#577	D₄₃	1	1	yes	characteristic, complemented
262	#575	—	43	3	no	—
263	#575	—	43	3	no	—
264	C₂×#137	—	43	3	no	—
265	C₂×#137	—	43	3	no	—
266	#568	—	43	1	no	—
267	C₄₃	#3586	1	1	yes	characteristic, complemented, Sylow
268	2₋¹⁺⁴	—	43	3	no	—
269	2₋¹⁺⁴	—	43	3	no	—
270	2₋¹⁺⁴	—	43	1	no	—
271	2₋¹⁺⁴	—	43	1	no	—
272	2₋¹⁺⁴	—	43	3	no	—
273	2₋¹⁺⁴	—	86	1	no	—
274	2₋¹⁺⁴	—	86	1	no	—
275	2₋¹⁺⁴	—	86	3	no	—
276	2₋¹⁺⁴	C₂×D₄₃	1	1	yes	characteristic, complemented
277	H(5,𝔽₂)	—	43	3	no	—
278	H(5,𝔽₂)	—	86	3	no	—
279	H(5,𝔽₂)	C₂×D₄₃	1	1	yes	characteristic, complemented
280	C₂×#41	—	43	1	no	—
281	C₂×#41	—	43	3	no	—
282	C₂×#41	—	43	3	no	—
283	C₂×#41	—	43	3	no	—
284	C₂×#41	—	86	3	no	—
285	C₂×#41	—	86	3	no	—
286	C₂×#41	—	86	1	no	—
287	C₂²×Q₈	—	43	3	no	—
288	C₂²×Q₈	—	86	1	no	—
289	#137	—	43	3	no	—
290	#137	—	43	3	no	—
291	#137	—	43	3	no	—
292	#137	—	43	3	no	—
293	#137	—	43	3	no	—
294	#137	—	43	6	no	—
295	#137	—	43	3	no	—
296	#137	—	43	6	no	—
297	#137	—	43	6	no	—
298	#137	—	43	3	no	—
299	#137	—	43	3	no	—
300	#137	—	43	3	no	—
301	#137	C₂×D₄₃	1	3	yes	complemented
302	AGL(1,ℤ/8)	—	43	3	no	—
303	AGL(1,ℤ/8)	—	43	1	no	—
304	AGL(1,ℤ/8)	—	43	3	no	—
305	AGL(1,ℤ/8)	—	43	3	no	—
306	AGL(1,ℤ/8)	—	43	3	no	—
307	AGL(1,ℤ/8)	C₂×D₄₃	1	3	yes	complemented
308	#135	—	43	3	no	—
309	#135	—	43	3	no	—
310	#135	—	43	6	no	—
311	#135	—	43	6	no	—
312	#135	—	43	3	no	—
313	#135	C₂×D₄₃	1	3	yes	complemented
314	C₂×Q₁₆	—	43	3	no	—
315	C₂×Q₁₆	—	43	6	no	—
316	C₂×Q₁₆	—	43	3	no	—
317	C₂×SD₁₆	—	43	3	no	—
318	C₂×SD₁₆	—	43	6	no	—
319	C₂×SD₁₆	C₂×D₄₃	1	3	yes	complemented
320	#131	—	43	1	no	—
321	#131	—	43	3	no	—
322	#131	—	43	3	no	—
323	#131	C₂×D₄₃	1	1	yes	characteristic, complemented
324	C₂×M₁₆	—	43	3	no	—
325	C₂×M₁₆	—	43	3	no	—
326	#41	—	2	1	no	—
327	#41	—	2	3	no	—
328	#41	—	43	1	no	—
329	#41	—	43	3	no	—
330	#41	—	43	3	no	—
331	#41	—	43	3	no	—
332	#41	—	43	1	no	—
333	#41	—	43	3	no	—
334	#41	—	43	6	no	—
335	#41	—	43	3	no	—
336	#41	—	43	3	no	—
337	#41	—	43	3	no	—
338	#41	—	86	3	no	—
339	#41	—	86	3	no	—
340	#41	—	86	3	no	—
341	#41	—	86	6	no	—
342	#41	—	86	3	no	—
343	#41	—	86	3	no	—
344	#41	—	86	3	no	—
345	#41	—	86	3	no	—
346	#41	—	86	3	no	—
347	#41	—	86	6	no	—
348	#41	—	86	6	no	—
349	#41	—	86	3	no	—
350	#41	—	86	3	no	—
351	#41	—	86	3	no	—
352	#41	—	86	3	no	—
353	#41	C₂²×D₄₃	1	3	yes	—
354	#41	C₂²×D₄₃	1	3	yes	—
355	#41	C₂²×D₄₃	1	1	yes	characteristic
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	43	1	no	—
358	C₂×Q₈	—	43	6	no	—
359	C₂×Q₈	—	43	3	no	—
360	C₂×Q₈	—	43	3	no	—
361	C₂×Q₈	—	43	3	no	—
362	C₂×Q₈	—	43	3	no	—
363	C₂×Q₈	—	86	3	no	—
364	C₂×Q₈	—	86	3	no	—
365	C₂×Q₈	—	86	3	no	—
366	C₂×Q₈	—	86	3	no	—
367	C₂×Q₈	—	86	3	no	—
368	C₂×Q₈	—	86	3	no	—
369	C₂×Q₈	—	86	1	no	—
370	C₂×Q₈	—	86	1	no	—
371	C₂×Q₈	C₂²×D₄₃	1	3	yes	—
372	C₂×D₄	—	2	3	no	—
373	C₂×D₄	—	43	3	no	—
374	C₂×D₄	—	43	3	no	—
375	C₂×D₄	—	43	1	no	—
376	C₂×D₄	—	86	3	no	—
377	C₂×D₄	—	86	3	no	—
378	C₂×D₄	—	86	3	no	—
379	C₂×D₄	—	86	6	no	—
380	C₂×D₄	—	86	3	no	—
381	C₂×D₄	C₂²×D₄₃	1	3	yes	—
382	C₂²×C₄	—	43	3	no	—
383	C₂²×C₄	—	86	3	no	—
384	C₂²×C₄	—	86	3	no	—
385	C₂²×C₄	—	86	3	no	—
386	C₂²×C₄	—	86	3	no	—
387	Q₁₆	—	43	3	no	—
388	Q₁₆	—	43	3	no	—
389	Q₁₆	—	43	6	no	—
390	Q₁₆	—	43	6	no	—
391	Q₁₆	—	43	3	no	—
392	Q₁₆	C₂²×D₄₃	1	3	yes	—
393	SD₁₆	—	43	3	no	—
394	SD₁₆	—	43	1	no	—
395	SD₁₆	—	43	3	no	—
396	SD₁₆	—	43	6	no	—
397	SD₁₆	—	43	3	no	—
398	SD₁₆	—	43	3	no	—
399	SD₁₆	—	43	3	no	—
400	SD₁₆	C₂²×D₄₃	1	6	yes	—
401	SD₁₆	C₂²×D₄₃	1	3	yes	—
402	SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
403	D₈	—	43	3	no	—
404	D₈	—	43	1	no	—
405	D₈	—	43	1	no	—
406	D₈	C₂²×D₄₃	1	3	yes	—
407	M₁₆	—	43	3	no	—
408	M₁₆	—	43	3	no	—
409	M₁₆	—	43	1	no	—
410	M₁₆	—	43	3	no	—
411	M₁₆	—	43	3	no	—
412	M₁₆	C₂²×D₄₃	1	3	yes	—
413	C₂×C₈	—	43	3	no	—
414	C₂×C₈	—	43	6	no	—
415	C₂×C₈	C₂²×D₄₃	1	3	yes	—
416	C₂³	—	2	3	no	—
417	C₂³	—	43	3	no	—
418	C₂³	—	86	3	no	—
419	C₂³	—	86	1	no	—
420	Q₈	—	2	3	no	—
421	Q₈	—	43	3	no	—
422	Q₈	—	43	3	no	—
423	Q₈	—	43	3	no	—
424	Q₈	—	86	3	no	—
425	Q₈	—	86	6	no	—
426	Q₈	—	86	3	no	—
427	Q₈	—	86	3	no	—
428	Q₈	—	86	3	no	—
429	Q₈	D₄×D₄₃	1	1	yes	characteristic
430	Q₈	C₂³×D₄₃	1	3	yes	—
431	Q₈	C₂³×D₄₃	1	1	yes	characteristic
432	D₄	—	2	3	no	—
433	D₄	—	2	3	no	—
434	D₄	—	2	3	no	—
435	D₄	—	43	6	no	—
436	D₄	—	43	3	no	—
437	D₄	—	43	1	no	—
438	D₄	—	43	1	no	—
439	D₄	—	86	1	no	—
440	D₄	—	86	3	no	—
441	D₄	—	86	3	no	—
442	D₄	—	86	1	no	—
443	D₄	—	86	3	no	—
444	D₄	—	86	6	no	—
445	D₄	—	86	3	no	—
446	D₄	—	86	3	no	—
447	D₄	—	86	3	no	—
448	D₄	D₄×D₄₃	1	3	yes	—
449	D₄	C₂³×D₄₃	1	1	yes	characteristic
450	D₄	C₂³×D₄₃	1	3	yes	—
451	C₂×C₄	—	2	3	no	—
452	C₂×C₄	—	2	3	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	43	3	no	—
455	C₂×C₄	—	43	3	no	—
456	C₂×C₄	—	43	3	no	—
457	C₂×C₄	—	43	3	no	—
458	C₂×C₄	—	43	1	no	—
459	C₂×C₄	—	86	1	no	—
460	C₂×C₄	—	86	3	no	—
461	C₂×C₄	—	86	3	no	—
462	C₂×C₄	—	86	3	no	—
463	C₂×C₄	—	86	6	no	—
464	C₂×C₄	—	86	3	no	—
465	C₂×C₄	—	86	6	no	—
466	C₂×C₄	—	86	3	no	—
467	C₂×C₄	—	86	3	no	—
468	C₂×C₄	—	86	3	no	—
469	C₂×C₄	—	86	3	no	—
470	C₂×C₄	—	86	3	no	—
471	C₂×C₄	C₂³×D₄₃	1	3	yes	—
472	C₈	—	43	1	no	—
473	C₈	—	43	3	no	—
474	C₈	C₂³×D₄₃	1	3	yes	—
475	C₈	C₂³×D₄₃	1	1	yes	characteristic
476	C₂²	—	2	1	no	—
477	C₂²	—	2	3	no	—
478	C₂²	—	8	3	no	—
479	C₂²	—	43	1	no	—
480	C₂²	—	43	3	no	—
481	C₂²	—	86	1	no	—
482	C₂²	—	86	1	no	—
483	C₂²	—	344	3	no	—
484	C₂²	—	172	3	no	—
485	C₂²	—	172	2	no	—
486	C₂²	C₂×D₄×D₄₃	1	3	yes	—
487	C₄	—	2	1	no	—
488	C₄	—	2	3	no	—
489	C₄	—	43	1	no	—
490	C₄	—	43	3	no	—
491	C₄	—	86	3	no	—
492	C₄	—	86	3	no	—
493	C₄	C₂×D₄×D₄₃	1	3	yes	—
494	C₄	C₂⁴×D₄₃	1	1	yes	characteristic
495	C₂	—	2	3	no	—
496	C₂	—	4	3	no	—
497	C₂	—	4	1	no	—
498	C₂	—	86	3	no	—
499	C₂	—	86	1	no	—
500	C₂	—	172	1	no	—
501	C₂	—	172	1	no	—
502	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁵
Frattini	C₄	C₂⁴×D₄₃
Fitting	C₄₃×#577	C₂
socle	C₂×C₄₃	C₂³×D₄
hypercenter	#577	D₄₃
hypocenter	C₄₃	#3586
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. #14583734	C₂	semidirect
2. 2₋¹⁺⁴×D₄₃	C₂	semidirect
3. #14583716	C₂	semidirect
4. #14583715	C₂	semidirect
5. #14583714	C₂	semidirect
6. #14583713	C₂	semidirect
7. #14583710	C₂	semidirect
8. #14583709	C₂	semidirect
9. #14583705	C₂	semidirect
10. #14583696	C₂	semidirect
11. #14583695	C₂	semidirect
12. C₂×#13063354	C₂	semidirect
13. #137×D₄₃	C₂	semidirect
14. #14583664	C₂	semidirect
15. C₄₃×#577	C₂	semidirect
17. #13063373	C₂²	semidirect
20. #13063372	C₂²	semidirect
21. #13063372	C₂²	semidirect
22. #13063372	C₂²	semidirect
23. #13063372	C₂²	semidirect
25. #13063370	C₂²	semidirect
32. #41×D₄₃	C₂²	semidirect
34. C₂×Q₈×D₄₃	C₂²	semidirect
35. #13063358	C₂²	semidirect
36. #13063358	C₂²	semidirect
37. #13063357	C₂²	semidirect
38. #13063357	C₂²	semidirect
39. #13063356	C₂²	semidirect
40. #13063355	C₂²	semidirect
41. #13063355	C₂²	semidirect
42. #13063354	C₂²	semidirect
43. #13063354	C₂²	semidirect
44. #13063354	C₂²	semidirect
45. #13063354	C₂²	semidirect
46. #13063354	C₂²	semidirect
47. #13063352	C₂²	semidirect
48. #13063352	C₂²	semidirect
49. #13063351	C₂²	semidirect
50. #13063349	C₂²	semidirect
51. #13063349	C₂²	semidirect
52. #13063347	C₂²	semidirect
53. #13063346	C₂²	semidirect
54. #13063345	C₂²	semidirect
55. #13063345	C₂²	semidirect
56. #13063344	C₂²	semidirect
57. C₂×Dic₁₇₂	C₂²	semidirect
58. C₂×#10621885	C₂²	semidirect
59. Q₁₆×D₄₃	C₂²	semidirect
60. C₂×#10621883	C₂²	semidirect
61. SD₁₆×D₄₃	C₂²	semidirect
62. #13063333	C₂²	semidirect
63. #13063332	C₂²	semidirect
64. #13063331	C₂²	semidirect
65. C₂×#10621872	C₂²	semidirect
66. M₁₆×D₄₃	C₂²	semidirect
67. 2₋¹⁺⁴×C₄₃	C₂²	semidirect
68. H(5,𝔽₂)×C₄₃	C₂²	semidirect
69. #137×C₄₃	C₂²	semidirect
70. AGL(1,ℤ/8)×C₄₃	C₂²	semidirect
71. #135×C₄₃	C₂²	semidirect
72. C₂×SD₁₆×C₄₃	C₂²	semidirect
73. #131×C₄₃	C₂²	semidirect
261. #577	D₄₃	semidirect
267. C₄₃	#3586	semidirect
276. 2₋¹⁺⁴	C₂×D₄₃	semidirect
279. H(5,𝔽₂)	C₂×D₄₃	semidirect
301. #137	C₂×D₄₃	semidirect
307. AGL(1,ℤ/8)	C₂×D₄₃	semidirect
313. #135	C₂×D₄₃	semidirect
319. C₂×SD₁₆	C₂×D₄₃	semidirect
323. #131	C₂×D₄₃	semidirect