Subgroups — #25250988

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147727	C₂	1	2	yes	maximal, complemented
2	#19145022	C₂	1	1	yes	maximal, characteristic, complemented
3	#443×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136677	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136676	C₂	1	1	yes	maximal, characteristic, complemented
6	#19136668	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136663	C₂	1	2	yes	maximal, complemented
8	#19136662	C₂	1	2	yes	maximal, complemented
9	#364×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#19136341	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2213	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063344	—	2	1	no	—
13	C₂×#13063344	C₂²	1	2	yes	—
14	#135×D₄₃	C₂²	1	1	yes	characteristic
15	#131×D₄₃	—	2	1	no	—
16	#14583447	—	2	1	no	—
17	#14583342	C₂²	1	2	yes	—
18	#14583339	C₂²	1	2	yes	—
19	#14583338	—	2	2	no	—
20	#14583335	C₂²	1	2	yes	—
21	#14583333	—	2	2	no	—
22	#14583330	—	2	2	no	—
23	#14583328	—	2	2	no	—
24	M₃₂×D₄₃	C₂²	1	2	yes	—
25	#14583282	—	2	1	no	—
26	#14583282	C₂²	1	2	yes	complemented
27	#14583279	C₂²	1	1	yes	characteristic, complemented
28	#14583271	—	2	1	no	—
29	#14583017	C₂²	1	1	yes	characteristic
30	#14583016	C₂²	1	1	yes	characteristic
31	#14583015	C₂²	1	1	yes	characteristic
32	#14583014	—	2	1	no	—
33	#14583013	—	2	1	no	—
34	#108×D₄₃	C₂²	1	1	yes	characteristic
35	#104×D₄₃	—	2	1	no	—
36	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
37	#14582720	C₂²	1	1	yes	characteristic, complemented
38	#14582719	C₂²	1	2	yes	complemented
39	#14582716	C₂²	1	2	yes	complemented
40	#14582714	C₂²	1	2	yes	complemented
41	#14582712	C₂²	1	2	yes	complemented
42	C₄₃×#509	C₂²	1	2	yes	—
43	C₄₃×#493	C₂²	1	1	yes	characteristic, complemented
44	C₄₃×#443	C₂²	1	1	yes	characteristic
45	C₄₃×#364	C₂²	1	1	yes	characteristic, complemented
46	C₄₃×#361	C₂²	1	2	yes	complemented
47	C₂×#10621900	—	2	2	no	—
48	#41×D₄₃	—	2	1	no	—
49	#13063348	D₄	1	1	yes	characteristic, complemented
50	#13063347	C₂³	1	1	yes	characteristic
51	#13063346	—	2	1	no	—
52	#13063345	—	2	1	no	—
53	#13063344	—	2	2	no	—
54	#13063344	—	2	2	no	—
55	#13063344	—	2	2	no	—
56	#13063344	—	2	2	no	—
57	#13063344	—	4	1	no	—
58	#13063344	—	4	1	no	—
59	#13063344	—	4	1	no	—
60	#13063344	—	4	1	no	—
61	#13063344	D₄	1	1	yes	characteristic, complemented
62	C₂×Dic₁₇₂	—	2	1	no	—
63	C₂×Dic₁₇₂	C₂³	1	2	yes	—
64	Q₁₆×D₄₃	D₄	1	1	yes	characteristic, complemented
65	C₂×#10621883	—	2	2	no	—
66	C₂×#10621883	—	2	2	no	—
67	SD₁₆×D₄₃	—	2	1	no	—
68	D₈×D₄₃	D₄	1	1	yes	characteristic, complemented
69	#13063333	—	2	1	no	—
70	#13063333	—	4	1	no	—
71	#13063332	—	2	1	no	—
72	#13063331	—	2	1	no	—
73	#13063331	—	4	1	no	—
74	M₁₆×D₄₃	—	2	1	no	—
75	M₁₆×D₄₃	—	4	1	no	—
76	C₂×C₈×D₄₃	—	4	1	no	—
77	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
78	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
79	#13063325	—	2	1	no	—
80	#13063312	—	2	2	no	—
81	#13063296	—	4	2	no	—
82	D₄×Dic₄₃	—	4	2	no	—
83	C₄²×D₄₃	D₄	1	1	yes	characteristic
84	Dic₃₄₄	—	2	2	no	—
85	#13063271	—	2	2	no	—
86	#13063270	—	2	2	no	—
87	#13063269	—	2	2	no	—
88	#13063269	—	2	2	no	—
89	#13063266	—	2	2	no	—
90	#13063265	C₂³	1	2	yes	—
91	#13063264	—	2	2	no	—
92	C₁₆×D₄₃	—	2	2	no	—
93	#13063261	C₂³	1	1	yes	characteristic
94	#13063260	—	2	1	no	—
95	#13063253	—	2	1	no	—
96	#13063252	—	2	1	no	—
97	#13063251	—	2	1	no	—
98	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
99	C₈×Dic₄₃	D₄	1	1	yes	characteristic
100	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
101	#135×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₄₃	—	2	1	no	—
103	C₂×D₈×C₄₃	C₂³	1	2	yes	—
104	#131×C₄₃	—	2	1	no	—
105	#127×C₄₃	—	2	1	no	—
106	SD₃₂×C₄₃	—	2	2	no	—
107	D₁₆×C₄₃	—	2	2	no	—
108	M₃₂×C₄₃	C₂³	1	2	yes	—
109	#108×C₄₃	C₂³	1	1	yes	characteristic
110	#104×C₄₃	—	2	1	no	—
111	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
112	#41×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	4	2	no	—
115	C₂×C₂²⋊D₄₃	—	4	2	no	—
116	C₂²×Dic₄₃	—	4	2	no	—
117	#10621902	—	2	1	no	—
118	Q₈×D₄₃	—	2	1	no	—
119	#10621900	—	2	1	no	—
120	#10621900	—	4	1	no	—
121	#10621900	—	4	2	no	—
122	#10621900	—	4	2	no	—
123	#10621900	—	4	2	no	—
124	#10621900	—	4	2	no	—
125	D₄×D₄₃	—	2	1	no	—
126	D₄×D₄₃	—	4	1	no	—
127	#10621898	—	2	1	no	—
128	#10621898	—	4	1	no	—
129	C₂×C₄×D₄₃	—	2	1	no	—
130	C₂×C₄×D₄₃	—	4	1	no	—
131	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂×Dic₈₆	—	2	2	no	—
133	Q₁₆×C₄₃	C₂×D₄	1	1	yes	characteristic
134	SD₁₆×C₄₃	—	2	1	no	—
135	D₈×C₄₃	—	2	2	no	—
136	D₈×C₄₃	—	2	2	no	—
137	D₈×C₄₃	—	4	1	no	—
138	D₈×C₄₃	—	4	1	no	—
139	D₈×C₄₃	C₂×D₄	1	1	yes	characteristic
140	M₁₆×C₄₃	—	2	1	no	—
141	M₁₆×C₄₃	—	4	1	no	—
142	C₂×C₈×C₄₃	—	4	1	no	—
143	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
145	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²⋊Dic₄₃	—	4	4	no	—
147	#10621885	—	2	1	no	—
148	#10621884	—	2	1	no	—
149	#10621883	—	2	1	no	—
150	#10621883	—	4	2	no	—
151	#10621883	—	4	2	no	—
152	#10621883	—	4	2	no	—
153	#10621883	—	4	2	no	—
154	#10621882	—	2	1	no	—
155	C₄⋊Dic₄₃	—	4	2	no	—
156	C₄×Dic₄₃	—	2	1	no	—
157	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
158	#10621877	—	2	1	no	—
159	#10621877	—	4	1	no	—
160	C₂×C₄₃⋊C₈	—	4	1	no	—
161	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
163	Dic₁₇₂	—	2	2	no	—
164	Dic₁₇₂	—	2	2	no	—
165	Dic₁₇₂	—	4	1	no	—
166	Dic₁₇₂	—	4	1	no	—
167	Dic₁₇₂	C₂×D₄	1	1	yes	characteristic
168	D₃₄₄	C₂×D₄	1	1	yes	characteristic
169	#10621873	—	2	1	no	—
170	#10621872	—	4	1	no	—
171	#10621872	—	4	1	no	—
172	#10621872	—	4	1	no	—
173	C₈×D₄₃	—	4	1	no	—
174	C₈×D₄₃	—	4	1	no	—
175	C₈×D₄₃	—	4	1	no	—
176	C₈×D₄₃	D₈	1	1	yes	characteristic
177	C₈×D₄₃	D₈	1	1	yes	characteristic
178	C₈×D₄₃	D₈	1	1	yes	characteristic
179	C₈×D₄₃	D₈	1	1	yes	characteristic
180	C₈×D₄₃	C₂×D₄	1	1	yes	characteristic
181	C₈×D₄₃	C₂×D₄	1	1	yes	characteristic
182	C₈×D₄₃	#41	1	1	yes	characteristic
183	C₈×D₄₃	#41	1	1	yes	characteristic
184	C₁₆×C₄₃	—	2	2	no	—
185	C₄₃⋊C₁₆	—	2	2	no	—
186	C₂³×C₄₃	—	4	2	no	—
187	C₂²×D₄₃	—	4	1	no	—
188	C₂²×D₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
189	Q₈×C₄₃	—	2	1	no	—
190	D₄×C₄₃	—	2	1	no	—
191	D₄×C₄₃	—	4	1	no	—
192	D₄×C₄₃	—	4	2	no	—
193	D₄×C₄₃	—	4	2	no	—
194	D₄×C₄₃	—	8	4	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
198	C₂²⋊D₄₃	—	4	1	no	—
199	C₂²⋊D₄₃	—	4	1	no	—
200	C₂²⋊D₄₃	—	4	1	no	—
201	C₂²⋊D₄₃	—	8	2	no	—
202	C₂²⋊D₄₃	—	8	2	no	—
203	C₂×Dic₄₃	—	2	1	no	—
204	C₂×Dic₄₃	—	4	1	no	—
205	C₂×Dic₄₃	—	4	2	no	—
206	C₂×Dic₄₃	—	8	2	no	—
207	C₂×Dic₄₃	—	8	2	no	—
208	C₂×Dic₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
209	D₁₇₂	—	2	1	no	—
210	D₁₇₂	—	4	1	no	—
211	C₄×D₄₃	—	4	2	no	—
212	C₄×D₄₃	—	4	1	no	—
213	C₄×D₄₃	—	4	1	no	—
214	C₄×D₄₃	—	4	1	no	—
215	C₄×D₄₃	#121	1	1	yes	characteristic
216	C₄×D₄₃	#121	1	1	yes	characteristic
217	C₄×D₄₃	C₂×D₈	1	1	yes	characteristic
218	C₄×D₄₃	C₂×D₈	1	1	yes	characteristic
219	Dic₈₆	—	2	1	no	—
220	Dic₈₆	—	4	1	no	—
221	Dic₈₆	—	4	2	no	—
222	Dic₈₆	—	4	2	no	—
223	C₈×C₄₃	—	4	1	no	—
224	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
225	C₈×C₄₃	C₂×D₈	1	1	yes	characteristic
226	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
227	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
228	C₄₃⋊C₈	—	4	1	no	—
229	C₄₃⋊C₈	#121	1	1	yes	characteristic
230	C₄₃⋊C₈	#121	1	1	yes	characteristic
231	C₄₃⋊C₈	C₂×D₈	1	1	yes	characteristic
232	C₄₃⋊C₈	C₂×D₈	1	1	yes	characteristic
233	#33594	—	43	1	no	maximal, Sylow
234	C₂²×C₄₃	—	4	1	no	—
235	C₂²×C₄₃	—	8	4	no	—
236	C₂²×C₄₃	—	8	2	no	—
237	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₂×D₄₃	—	4	1	no	—
239	C₂×D₄₃	—	4	1	no	—
240	C₂×D₄₃	—	8	2	no	—
241	C₂×D₄₃	#459	1	1	yes	characteristic
242	C₂×D₄₃	#459	1	1	yes	characteristic
243	C₄×C₄₃	—	2	2	no	—
244	C₄×C₄₃	—	4	1	no	—
245	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
246	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
247	Dic₄₃	—	4	1	no	—
248	Dic₄₃	—	4	1	no	—
249	Dic₄₃	—	8	2	no	—
250	Dic₄₃	#459	1	1	yes	characteristic
251	Dic₄₃	#459	1	1	yes	characteristic
252	#3414	—	43	2	no	—
253	#3147	—	43	1	no	—
254	C₂×#443	—	43	1	no	—
255	#2214	—	43	1	no	—
256	#2214	—	43	1	no	—
257	#2213	—	43	1	no	—
258	#2213	D₄₃	1	1	yes	characteristic, complemented
259	#2212	—	43	2	no	—
260	#2212	—	43	2	no	—
261	C₂×#364	—	43	1	no	—
262	#2148	—	43	2	no	—
263	C₂×C₄₃	—	2	1	no	—
264	C₂×C₄₃	—	8	1	no	—
265	C₂×C₄₃	—	16	2	no	—
266	C₂×C₄₃	C₂×#459	1	1	yes	characteristic
267	D₄₃	—	2	1	no	—
268	D₄₃	—	2	1	no	—
269	D₄₃	—	8	1	no	—
270	C₂×#135	—	43	1	no	—
271	C₂×#135	—	43	2	no	—
272	C₂×#135	—	86	1	no	—
273	C₂×#131	—	86	1	no	—
274	#532	—	86	1	no	—
275	#510	—	43	2	no	—
276	#510	—	43	2	no	—
277	#510	—	86	2	no	—
278	#509	—	43	2	no	—
279	#509	—	86	2	no	—
280	#509	C₂×D₄₃	1	2	yes	—
281	#508	—	86	2	no	—
282	#508	—	86	2	no	—
283	C₂×M₃₂	—	43	2	no	—
284	#495	—	43	2	no	—
285	#495	—	86	1	no	—
286	#494	—	43	1	no	—
287	#493	C₂×D₄₃	1	1	yes	characteristic, complemented
288	#492	—	86	1	no	—
289	#443	—	43	1	no	—
290	#443	—	43	1	no	—
291	#443	—	43	1	no	—
292	#443	—	86	1	no	—
293	#443	—	86	1	no	—
294	#443	C₂×D₄₃	1	1	yes	characteristic
295	C₂×#108	—	43	1	no	—
296	C₂×#104	—	86	1	no	—
297	C₂×C₄×C₈	—	43	1	no	—
298	#364	—	43	2	no	—
299	#364	—	43	1	no	—
300	#364	C₂×D₄₃	1	1	yes	characteristic, complemented
301	#362	—	43	2	no	—
302	#362	—	43	2	no	—
303	#361	—	43	2	no	—
304	#361	C₂×D₄₃	1	2	yes	complemented
305	C₄₃	#33594	1	1	yes	characteristic, complemented, Sylow
306	C₂×#41	—	86	2	no	—
307	C₂×#41	—	86	1	no	—
308	#135	—	43	1	no	—
309	#135	—	43	1	no	—
310	#135	—	43	1	no	—
311	#135	—	86	2	no	—
312	#135	—	86	2	no	—
313	#135	—	86	2	no	—
314	#135	—	86	2	no	—
315	#135	—	86	1	no	—
316	#135	—	86	1	no	—
317	#135	—	172	1	no	—
318	#135	—	172	1	no	—
319	#135	—	172	1	no	—
320	#135	—	172	1	no	—
321	#135	C₂²×D₄₃	1	1	yes	characteristic
322	C₂×Q₁₆	—	43	1	no	—
323	C₂×Q₁₆	—	43	2	no	—
324	C₂×Q₁₆	—	86	1	no	—
325	C₂×SD₁₆	—	86	1	no	—
326	C₂×SD₁₆	—	86	2	no	—
327	C₂×SD₁₆	—	86	2	no	—
328	C₂×D₈	—	2	1	no	—
329	C₂×D₈	—	43	1	no	—
330	C₂×D₈	C₂²×D₄₃	1	2	yes	—
331	#131	—	2	1	no	—
332	#131	—	86	1	no	—
333	#131	—	86	1	no	—
334	#131	—	86	1	no	—
335	#131	—	172	1	no	—
336	#131	—	172	1	no	—
337	C₂×M₁₆	—	86	1	no	—
338	C₂×M₁₆	—	172	1	no	—
339	C₂²×C₈	—	43	1	no	—
340	C₂²×C₈	—	43	1	no	—
341	C₂²×C₈	—	172	1	no	—
342	C₄⋊Q₈	—	86	1	no	—
343	#127	—	2	1	no	—
344	#124	—	86	2	no	—
345	#121	—	172	2	no	—
346	C₄×D₄	—	172	2	no	—
347	C₂×C₄²	—	43	1	no	—
348	Q₃₂	—	86	2	no	—
349	Q₃₂	—	86	2	no	—
350	SD₃₂	—	2	2	no	—
351	SD₃₂	—	86	2	no	—
352	SD₃₂	—	86	2	no	—
353	SD₃₂	—	86	2	no	—
354	D₁₆	—	2	2	no	—
355	D₁₆	—	86	2	no	—
356	M₃₂	—	43	2	no	—
357	M₃₂	—	86	2	no	—
358	M₃₂	C₂²×D₄₃	1	2	yes	—
359	C₂×C₁₆	—	86	2	no	—
360	#108	—	43	1	no	—
361	#108	—	86	1	no	—
362	#108	C₂²×D₄₃	1	1	yes	characteristic
363	#104	—	2	1	no	—
364	#104	—	86	1	no	—
365	#104	—	86	1	no	—
366	#104	—	86	1	no	—
367	C₄×C₈	—	43	1	no	—
368	C₄×C₈	—	43	1	no	—
369	C₄×C₈	—	43	1	no	—
370	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
371	#41	—	2	1	no	—
372	#41	—	86	1	no	—
373	#41	—	86	1	no	—
374	#41	—	86	1	no	—
375	#41	—	172	1	no	—
376	#41	—	172	2	no	—
377	#41	—	172	2	no	—
378	#41	—	172	2	no	—
379	#41	—	172	2	no	—
380	#41	—	172	1	no	—
381	C₂×Q₈	—	86	1	no	—
382	C₂×Q₈	—	86	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	86	1	no	—
386	C₂×D₄	—	172	1	no	—
387	C₂×D₄	—	172	2	no	—
388	C₂²×C₄	—	43	1	no	—
389	C₂²×C₄	—	86	1	no	—
390	C₂²×C₄	—	172	1	no	—
391	C₂²×C₄	—	172	2	no	—
392	Q₁₆	—	43	1	no	—
393	Q₁₆	—	86	1	no	—
394	Q₁₆	—	86	2	no	—
395	Q₁₆	—	86	2	no	—
396	Q₁₆	—	172	1	no	—
397	Q₁₆	—	172	1	no	—
398	Q₁₆	D₄×D₄₃	1	1	yes	characteristic
399	SD₁₆	—	2	1	no	—
400	SD₁₆	—	86	1	no	—
401	SD₁₆	—	86	1	no	—
402	SD₁₆	—	86	1	no	—
403	SD₁₆	—	172	2	no	—
404	SD₁₆	—	172	2	no	—
405	SD₁₆	—	172	2	no	—
406	SD₁₆	—	172	2	no	—
407	D₈	—	2	2	no	—
408	D₈	—	2	2	no	—
409	D₈	—	4	1	no	—
410	D₈	—	4	1	no	—
411	D₈	—	43	1	no	—
412	D₈	—	86	1	no	—
413	D₈	D₄×D₄₃	1	1	yes	characteristic
414	M₁₆	—	2	1	no	—
415	M₁₆	—	4	1	no	—
416	M₁₆	—	86	1	no	—
417	M₁₆	—	172	1	no	—
418	M₁₆	—	172	1	no	—
419	M₁₆	—	172	1	no	—
420	M₁₆	—	172	1	no	—
421	C₂×C₈	—	4	1	no	—
422	C₂×C₈	—	43	1	no	—
423	C₂×C₈	—	43	1	no	—
424	C₂×C₈	—	43	1	no	—
425	C₂×C₈	—	43	1	no	—
426	C₂×C₈	—	43	1	no	—
427	C₂×C₈	—	43	1	no	—
428	C₂×C₈	—	43	1	no	—
429	C₂×C₈	—	43	1	no	—
430	C₂×C₈	—	43	1	no	—
431	C₂×C₈	—	43	1	no	—
432	C₂×C₈	—	172	1	no	—
433	C₂×C₈	—	172	1	no	—
434	C₂×C₈	—	172	1	no	—
435	C₂×C₈	—	172	1	no	—
436	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
437	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
438	C₄⋊C₄	—	172	2	no	—
439	C₂²⋊C₄	—	172	4	no	—
440	C₄²	—	43	1	no	—
441	C₄²	—	86	1	no	—
442	C₄²	D₄×D₄₃	1	1	yes	characteristic
443	C₁₆	—	2	2	no	—
444	C₁₆	—	86	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	43	1	no	—
447	C₂³	—	172	1	no	—
448	Q₈	—	2	1	no	—
449	Q₈	—	86	1	no	—
450	Q₈	—	172	1	no	—
451	Q₈	—	172	2	no	—
452	Q₈	—	172	2	no	—
453	D₄	—	2	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	8	4	no	—
458	D₄	—	86	1	no	—
459	D₄	—	344	2	no	—
460	D₄	—	344	2	no	—
461	D₄	—	172	1	no	—
462	D₄	—	172	1	no	—
463	D₄	—	172	1	no	—
464	D₄	—	172	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	43	1	no	—
468	C₂×C₄	—	43	1	no	—
469	C₂×C₄	—	43	1	no	—
470	C₂×C₄	—	43	1	no	—
471	C₂×C₄	—	43	1	no	—
472	C₂×C₄	—	86	1	no	—
473	C₂×C₄	—	344	2	no	—
474	C₂×C₄	—	344	2	no	—
475	C₂×C₄	—	172	2	no	—
476	C₂×C₄	—	172	1	no	—
477	C₂×C₄	—	172	1	no	—
478	C₂×C₄	—	172	1	no	—
479	C₂×C₄	—	172	2	no	—
480	C₂×C₄	—	172	1	no	—
481	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
482	C₈	—	4	1	no	—
483	C₈	—	43	1	no	—
484	C₈	—	43	1	no	—
485	C₈	—	43	1	no	—
486	C₈	—	43	1	no	—
487	C₈	—	172	1	no	—
488	C₈	D₈×D₄₃	1	1	yes	characteristic
489	C₈	D₈×D₄₃	1	1	yes	characteristic
490	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
491	C₈	#41×D₄₃	1	1	yes	characteristic
492	C₂²	—	4	1	no	—
493	C₂²	—	8	4	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	43	1	no	—
496	C₂²	—	43	1	no	—
497	C₂²	—	344	2	no	—
498	C₂²	—	172	1	no	—
499	C₂²	—	172	1	no	—
500	C₂²	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	4	1	no	—
503	C₄	—	43	1	no	—
504	C₄	—	43	1	no	—
505	C₄	—	344	2	no	—
506	C₄	—	172	1	no	—
507	C₄	—	172	1	no	—
508	C₄	#121×D₄₃	1	1	yes	characteristic
509	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	8	1	no	—
512	C₂	—	16	2	no	—
513	C₂	—	86	1	no	—
514	C₂	—	86	1	no	—
515	C₂	—	344	1	no	—
516	C₂	#459×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#459×D₄₃
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₄₃×#2213	C₂
socle	C₂×C₄₃	C₂×#459
hypercenter	#2213	D₄₃
hypocenter	C₄₃	#33594
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2213

Complements

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

N	H ≅ G/N	type
1. #19147727	C₂	semidirect
2. #19145022	C₂	semidirect
3. #443×D₄₃	C₂	semidirect
4. #19136677	C₂	semidirect
5. #19136676	C₂	semidirect
6. #19136668	C₂	semidirect
7. #19136663	C₂	semidirect
8. #19136662	C₂	semidirect
9. #364×D₄₃	C₂	semidirect
10. #19136341	C₂	semidirect
11. C₄₃×#2213	C₂	semidirect
26. #14583282	C₂²	semidirect
27. #14583279	C₂²	semidirect
37. #14582720	C₂²	semidirect
38. #14582719	C₂²	semidirect
39. #14582716	C₂²	semidirect
40. #14582714	C₂²	semidirect
41. #14582712	C₂²	semidirect
43. C₄₃×#493	C₂²	semidirect
45. C₄₃×#364	C₂²	semidirect
46. C₄₃×#361	C₂²	semidirect
49. #13063348	D₄	semidirect
61. #13063344	D₄	semidirect
64. Q₁₆×D₄₃	D₄	semidirect
68. D₈×D₄₃	D₄	semidirect
258. #2213	D₄₃	semidirect
287. #493	C₂×D₄₃	semidirect
300. #364	C₂×D₄₃	semidirect
304. #361	C₂×D₄₃	semidirect
305. C₄₃	#33594	semidirect

Maximal subgroups

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

subgroup	index
#19147727	2
#19145022	2
#443×D₄₃	2
#19136677	2
#19136676	2
#19136668	2
#19136663	2
#19136662	2
#364×D₄₃	2
#19136341	2
C₄₃×#2213	2
#33594	43