Subgroups — #25103540

Order 11008.

868 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	#19144315	C₂	1	1	yes	maximal, characteristic
2	#19143494	C₂	1	2	yes	maximal, complemented
3	C₂×#14583020	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143021	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135491	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135383	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135262	C₂	1	2	yes	maximal, complemented
8	#19135094	C₂	1	2	yes	maximal, complemented
9	#19134481	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134394	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1814	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583697	C₂²	1	2	yes	—
13	C₂×#13063347	C₂²	1	1	yes	characteristic
14	C₂×#13063333	C₂²	1	2	yes	—
15	C₂×#13063332	C₂²	1	1	yes	characteristic
16	#41×Dic₄₃	C₂²	1	1	yes	characteristic
17	#14583174	C₄	1	2	yes	complemented
18	#14583169	C₄	1	2	yes	complemented
19	#14583162	C₄	1	4	yes	complemented
20	#14583020	—	2	1	no	—
21	#14583020	—	2	1	no	—
22	#14583020	—	2	1	no	—
23	#14583020	—	2	1	no	—
24	#14583018	—	2	4	no	—
25	#14583013	—	2	4	no	—
26	#14582947	C₂²	1	2	yes	—
27	C₂×#13063261	C₂²	1	1	yes	characteristic
28	#14582917	C₂²	1	2	yes	—
29	C₂×#13063251	C₂²	1	2	yes	—
30	#14582881	C₂²	1	2	yes	—
31	#14582872	C₂²	1	2	yes	—
32	#14582857	—	2	1	no	—
33	#14582857	C₂²	1	1	yes	characteristic
34	#14582855	C₂²	1	2	yes	—
35	#14582854	—	2	1	no	—
36	#14582854	C₂²	1	1	yes	characteristic
37	M₁₆×Dic₄₃	—	2	1	no	—
38	M₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
39	C₂×#13063235	—	2	1	no	—
40	C₂×#13063235	C₂²	1	1	yes	characteristic
41	#14582670	C₂²	1	2	yes	—
42	#14582658	C₂²	1	2	yes	—
43	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#427	C₂²	1	1	yes	characteristic
46	C₄₃×#421	C₂²	1	2	yes	—
47	C₄₃×#344	C₂²	1	2	yes	—
48	C₂×#10621898	C₂³	1	2	yes	—
49	#13063356	—	2	2	no	—
50	#13063355	C₂×C₄	1	4	yes	—
51	#13063351	—	2	2	no	—
52	#13063350	C₂×C₄	1	4	yes	—
53	#13063347	—	2	1	no	—
54	#13063347	—	2	1	no	—
55	#13063347	—	2	1	no	—
56	#13063347	—	2	1	no	—
57	#13063345	—	2	4	no	—
58	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂×#10621873	C₂×C₄	1	2	yes	complemented
60	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic, complemented
61	#13063333	—	2	2	no	—
62	#13063333	—	2	2	no	—
63	#13063333	—	2	2	no	—
64	#13063333	—	2	2	no	—
65	#13063332	—	2	2	no	—
66	#13063332	D₄	1	4	yes	—
67	C₂×#10621877	—	2	1	no	—
68	C₂×#10621877	C₂³	1	2	yes	—
69	C₂×#10621877	C₂³	1	1	yes	characteristic
70	C₂×#10621872	—	2	2	no	—
71	C₂²×C₄₃⋊C₈	—	2	1	no	—
72	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₄₃	—	2	2	no	—
74	Q₈×Dic₄₃	—	2	1	no	—
75	D₄×Dic₄₃	—	2	1	no	—
76	D₄×Dic₄₃	—	2	2	no	—
77	#13063284	—	2	1	no	—
78	#13063284	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₄₃	—	2	1	no	—
80	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
81	#13063261	C₂×C₄	1	2	yes	complemented
82	#13063261	C₂×C₄	1	2	yes	complemented
83	#13063260	—	2	4	no	—
84	#13063253	—	2	4	no	—
85	#13063251	—	2	2	no	—
86	#13063251	—	2	2	no	—
87	#13063243	C₂×C₄	1	4	yes	complemented
88	#13063241	C₂×C₄	1	4	yes	complemented
89	#13063239	—	2	4	no	—
90	#13063236	—	2	2	no	—
91	#13063235	—	2	1	no	—
92	#13063235	—	2	1	no	—
93	#13063235	—	2	1	no	—
94	#13063235	D₄	1	1	yes	characteristic
95	#13063235	D₄	1	1	yes	characteristic
96	#13063235	D₄	1	1	yes	characteristic
97	#13063235	D₄	1	1	yes	characteristic
98	C₄×C₄₃⋊C₈	—	2	2	no	—
99	C₈×Dic₄₃	—	2	1	no	—
100	C₈×Dic₄₃	—	2	1	no	—
101	C₈×Dic₄₃	—	2	1	no	—
102	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
103	#131×C₄₃	—	2	1	no	—
104	#131×C₄₃	—	2	1	no	—
105	#131×C₄₃	C₂×C₄	1	2	yes	—
106	#131×C₄₃	C₂×C₄	1	2	yes	—
107	C₂×M₁₆×C₄₃	—	2	1	no	—
108	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
109	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₄₃	—	2	1	no	—
111	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
112	#117×C₄₃	C₂³	1	2	yes	—
113	#108×C₄₃	—	2	1	no	—
114	#108×C₄₃	—	2	1	no	—
115	#107×C₄₃	—	2	1	no	—
116	#106×C₄₃	—	2	1	no	—
117	#104×C₄₃	—	2	4	no	—
118	#41×C₄₃	—	2	1	no	—
119	#41×C₄₃	—	2	1	no	—
120	#41×C₄₃	C₂²×C₄	1	2	yes	—
121	#41×C₄₃	C₂×D₄	1	2	yes	—
122	C₂×Q₈×C₄₃	#41	1	1	yes	characteristic
123	C₂×D₄×C₄₃	—	2	1	no	—
124	C₂×D₄×C₄₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₂²⋊D₄₃	—	2	2	no	—
128	C₂²×Dic₄₃	—	2	2	no	—
129	C₂²×Dic₄₃	—	2	1	no	—
130	#10621898	—	2	2	no	—
131	#10621898	—	2	2	no	—
132	#10621898	—	2	2	no	—
133	#10621898	—	2	2	no	—
134	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
135	C₂×C₄×D₄₃	—	2	2	no	—
136	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
137	M₁₆×C₄₃	—	2	1	no	—
138	M₁₆×C₄₃	—	2	2	no	—
139	M₁₆×C₄₃	—	2	2	no	—
140	M₁₆×C₄₃	—	2	2	no	—
141	M₁₆×C₄₃	—	2	2	no	—
142	M₁₆×C₄₃	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₄₃	—	2	1	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	2	no	—
146	C₂×C₈×C₄₃	—	2	2	no	—
147	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
152	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
153	C₄⋊C₄×C₄₃	—	2	2	no	—
154	C₂²⋊C₄×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	2	2	no	—
156	C₂²⋊Dic₄₃	—	2	2	no	—
157	C₂²⋊Dic₄₃	#41	1	2	yes	—
158	#10621885	—	2	4	no	—
159	#10621884	—	2	4	no	—
160	#10621883	—	2	4	no	—
161	#10621882	—	2	4	no	—
162	C₄⋊Dic₄₃	—	2	2	no	—
163	C₄⋊Dic₄₃	—	2	1	no	—
164	C₄×Dic₄₃	—	2	2	no	—
165	C₄×Dic₄₃	—	2	1	no	—
166	C₄×Dic₄₃	—	2	1	no	—
167	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
168	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
169	#10621877	—	2	1	no	—
170	#10621877	—	2	2	no	—
171	#10621877	—	2	4	no	—
172	#10621877	C₂²×C₄	1	4	yes	—
173	#10621877	C₂×D₄	1	2	yes	—
174	C₂×C₄₃⋊C₈	—	2	1	no	—
175	C₂×C₄₃⋊C₈	—	2	2	no	—
176	C₂×C₄₃⋊C₈	—	2	4	no	—
177	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
179	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
180	C₂×C₄₃⋊C₈	#41	1	2	yes	—
181	Dic₁₇₂	—	2	1	no	—
182	Dic₁₇₂	—	2	1	no	—
183	D₃₄₄	—	2	1	no	—
184	D₃₄₄	—	2	1	no	—
185	#10621873	—	2	2	no	—
186	#10621873	—	2	2	no	—
187	#10621872	—	4	2	no	—
188	#10621872	—	4	2	no	—
189	C₈×D₄₃	—	4	2	no	—
190	C₈×D₄₃	—	4	2	no	—
191	C₂³×C₄₃	—	2	1	no	—
192	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
193	C₂²×D₄₃	—	2	2	no	—
194	Q₈×C₄₃	—	2	1	no	—
195	Q₈×C₄₃	C₄×D₄	1	2	yes	—
196	D₄×C₄₃	—	2	2	no	—
197	D₄×C₄₃	—	2	2	no	—
198	D₄×C₄₃	—	2	1	no	—
199	D₄×C₄₃	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	2	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
210	C₂²⋊D₄₃	—	4	2	no	—
211	C₂²⋊D₄₃	—	4	2	no	—
212	C₂×Dic₄₃	—	2	2	no	—
213	C₂×Dic₄₃	—	2	1	no	—
214	C₂×Dic₄₃	—	2	2	no	—
215	C₂×Dic₄₃	—	2	1	no	—
216	C₂×Dic₄₃	—	8	1	no	—
217	C₂×Dic₄₃	—	8	2	no	—
218	D₁₇₂	—	2	2	no	—
219	D₁₇₂	—	2	2	no	—
220	C₄×D₄₃	—	4	2	no	—
221	C₄×D₄₃	—	4	2	no	—
222	Dic₈₆	—	2	2	no	—
223	Dic₈₆	—	2	2	no	—
224	C₈×C₄₃	—	2	2	no	—
225	C₈×C₄₃	—	4	2	no	—
226	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
227	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
228	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
229	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
230	C₄₃⋊C₈	—	2	4	no	—
231	C₄₃⋊C₈	—	2	2	no	—
232	C₄₃⋊C₈	#121	1	2	yes	—
233	C₄₃⋊C₈	#121	1	2	yes	—
234	#21559	—	43	1	no	maximal, Sylow
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	4	1	no	—
237	C₂²×C₄₃	—	4	2	no	—
238	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
239	C₂²×C₄₃	#525	1	1	yes	characteristic
240	C₂²×C₄₃	#532	1	1	yes	characteristic
241	C₂×D₄₃	—	4	2	no	—
242	C₂×D₄₃	—	8	2	no	—
243	C₄×C₄₃	—	2	2	no	—
244	C₄×C₄₃	—	8	2	no	—
245	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
247	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
248	C₄×C₄₃	#529	1	1	yes	characteristic
249	Dic₄₃	—	4	2	no	—
250	Dic₄₃	—	4	1	no	—
251	Dic₄₃	—	4	1	no	—
252	Dic₄₃	—	4	2	no	—
253	#3067	—	43	1	no	—
254	#2955	—	43	2	no	—
255	C₂×#444	—	43	1	no	—
256	#2875	—	43	1	no	—
257	#1976	—	43	1	no	—
258	#1953	—	43	1	no	—
259	#1932	—	43	2	no	—
260	#1906	—	43	2	no	—
261	#1814	D₄₃	1	1	yes	characteristic, complemented
262	#1773	—	43	1	no	—
263	#1757	—	43	2	no	—
264	C₂×C₄₃	—	2	1	no	—
265	C₂×C₄₃	—	2	1	no	—
266	C₂×C₄₃	—	2	1	no	—
267	C₂×C₄₃	—	4	2	no	—
268	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
269	D₄₃	—	8	2	no	—
270	#575	—	43	2	no	—
271	C₂×#135	—	43	1	no	—
272	C₂×#131	—	43	1	no	—
273	C₂×#131	—	43	2	no	—
274	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
275	C₄×#41	—	43	1	no	—
276	#473	—	43	2	no	—
277	#472	—	43	2	no	—
278	#471	—	43	4	no	—
279	#444	—	86	1	no	—
280	#444	—	86	1	no	—
281	#444	—	86	1	no	—
282	#444	—	86	1	no	—
283	#444	—	86	4	no	—
284	#443	—	86	4	no	—
285	#430	—	43	2	no	—
286	C₂×#108	—	43	1	no	—
287	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
288	#427	C₂×D₄₃	1	1	yes	characteristic
289	#421	—	43	2	no	—
290	#421	C₂×D₄₃	1	2	yes	—
291	C₂×#104	—	43	2	no	—
292	#413	—	43	2	no	—
293	#410	—	43	2	no	—
294	#405	—	43	1	no	—
295	#405	—	43	1	no	—
296	#405	—	43	2	no	—
297	#405	—	86	1	no	—
298	#405	—	86	1	no	—
299	C₄×M₁₆	—	43	1	no	—
300	C₄×M₁₆	—	86	1	no	—
301	C₂×#97	—	43	1	no	—
302	C₂×#97	—	86	1	no	—
303	#344	—	43	2	no	—
304	#344	C₂×D₄₃	1	2	yes	—
305	#339	—	43	2	no	—
306	C₄₃	#21559	1	1	yes	characteristic, complemented, Sylow
307	C₂×#41	—	43	2	no	—
308	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
309	#137	—	43	4	no	—
310	#137	—	86	2	no	—
311	AGL(1,ℤ/8)	—	43	4	no	—
312	AGL(1,ℤ/8)	—	86	2	no	—
313	#135	—	86	4	no	—
314	#135	—	86	1	no	—
315	#135	—	86	1	no	—
316	#135	—	86	1	no	—
317	#135	—	86	1	no	—
318	C₂×Q₁₆	—	43	1	no	—
319	C₂×SD₁₆	—	43	2	no	—
320	C₂×D₈	—	43	1	no	—
321	#131	—	2	1	no	—
322	#131	—	2	1	no	—
323	#131	—	43	4	no	—
324	#131	—	86	2	no	—
325	#131	—	86	2	no	—
326	#131	—	86	2	no	—
327	#131	—	86	2	no	—
328	#131	—	86	2	no	—
329	#131	C₄×D₄₃	1	2	yes	—
330	#131	C₄×D₄₃	1	2	yes	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	43	1	no	—
333	C₂×M₁₆	—	43	2	no	—
334	C₂×M₁₆	—	86	2	no	—
335	C₂×M₁₆	—	86	1	no	—
336	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
337	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
338	C₂²×C₈	—	2	1	no	—
339	C₂²×C₈	—	43	1	no	—
340	C₂²×C₈	—	86	2	no	—
341	C₂²×C₈	—	86	1	no	—
342	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
343	C₄×Q₈	—	86	1	no	—
344	C₄×D₄	—	86	2	no	—
345	C₄×D₄	—	86	1	no	—
346	#117	—	43	1	no	—
347	#117	—	86	1	no	—
348	#117	C₂²×D₄₃	1	2	yes	—
349	C₂×C₄²	—	43	1	no	—
350	C₂×C₄²	—	86	1	no	—
351	#108	—	2	1	no	—
352	#108	—	2	1	no	—
353	#108	—	43	2	no	—
354	#108	—	43	2	no	—
355	#108	—	86	4	no	—
356	#107	—	2	1	no	—
357	#106	—	2	1	no	—
358	#104	—	2	4	no	—
359	#104	—	86	4	no	—
360	#104	—	86	2	no	—
361	#104	—	86	2	no	—
362	#101	—	43	4	no	—
363	#100	—	43	4	no	—
364	#99	—	86	4	no	—
365	#97	—	43	1	no	—
366	#97	—	43	1	no	—
367	#97	—	43	1	no	—
368	#97	—	43	1	no	—
369	#97	—	86	2	no	—
370	#97	—	86	1	no	—
371	#97	—	86	1	no	—
372	#97	—	86	1	no	—
373	C₄×C₈	—	86	2	no	—
374	C₄×C₈	—	86	1	no	—
375	C₄×C₈	—	86	1	no	—
376	C₄×C₈	—	86	1	no	—
377	#41	—	2	1	no	—
378	#41	—	2	1	no	—
379	#41	—	86	2	no	—
380	#41	—	86	2	no	—
381	#41	—	86	2	no	—
382	#41	—	86	2	no	—
383	#41	C₂×C₄×D₄₃	1	2	yes	—
384	#41	D₄×D₄₃	1	2	yes	—
385	C₂×Q₈	—	43	2	no	—
386	C₂×Q₈	#10621902	1	1	yes	characteristic
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	43	2	no	—
389	C₂×D₄	—	86	2	no	—
390	C₂×D₄	#10621902	1	1	yes	characteristic
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	86	2	no	—
393	C₂²×C₄	—	86	1	no	—
394	C₂²×C₄	—	86	2	no	—
395	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
396	Q₁₆	—	86	4	no	—
397	Q₁₆	—	86	1	no	—
398	Q₁₆	—	86	1	no	—
399	SD₁₆	—	86	4	no	—
400	SD₁₆	—	86	4	no	—
401	SD₁₆	—	86	2	no	—
402	SD₁₆	—	86	2	no	—
403	D₈	—	86	4	no	—
404	D₈	—	86	1	no	—
405	D₈	—	86	1	no	—
406	M₁₆	—	2	1	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	43	4	no	—
412	M₁₆	—	43	2	no	—
413	M₁₆	—	86	4	no	—
414	M₁₆	—	86	1	no	—
415	M₁₆	—	86	2	no	—
416	M₁₆	—	172	2	no	—
417	M₁₆	—	172	2	no	—
418	M₁₆	C₂×C₄×D₄₃	1	2	yes	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	43	1	no	—
424	C₂×C₈	—	43	2	no	—
425	C₂×C₈	—	43	1	no	—
426	C₂×C₈	—	43	2	no	—
427	C₂×C₈	—	86	4	no	—
428	C₂×C₈	—	86	1	no	—
429	C₂×C₈	—	86	2	no	—
430	C₂×C₈	—	172	2	no	—
431	C₂×C₈	—	172	2	no	—
432	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
433	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
434	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
435	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
436	C₂×C₈	#10621900	1	1	yes	characteristic
437	C₂×C₈	#10621900	1	1	yes	characteristic
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	86	2	no	—
440	C₄⋊C₄	—	86	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	43	2	no	—
443	C₂²⋊C₄	—	86	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	43	1	no	—
446	C₄²	—	43	1	no	—
447	C₄²	—	86	2	no	—
448	C₄²	—	86	1	no	—
449	C₄²	—	86	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	86	2	no	—
452	C₂³	#41×D₄₃	1	1	yes	characteristic
453	Q₈	—	2	1	no	—
454	Q₈	—	86	2	no	—
455	Q₈	—	86	2	no	—
456	Q₈	#13063287	1	2	yes	—
457	D₄	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	1	no	—
460	D₄	—	86	2	no	—
461	D₄	—	86	2	no	—
462	D₄	—	172	2	no	—
463	D₄	—	172	2	no	—
464	D₄	#13063287	1	2	yes	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	86	2	no	—
470	C₂×C₄	—	86	1	no	—
471	C₂×C₄	—	86	1	no	—
472	C₂×C₄	—	86	2	no	—
473	C₂×C₄	—	344	1	no	—
474	C₂×C₄	—	344	2	no	—
475	C₂×C₄	—	172	2	no	—
476	C₂×C₄	—	172	2	no	—
477	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
479	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
480	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
481	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
482	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	4	2	no	—
485	C₈	—	43	2	no	—
486	C₈	—	43	2	no	—
487	C₈	—	86	4	no	—
488	C₈	—	86	2	no	—
489	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
490	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
491	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
492	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
493	C₂²	—	2	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	344	2	no	—
497	C₂²	—	172	2	no	—
498	C₂²	#14583367	1	1	yes	characteristic
499	C₂²	#14583412	1	1	yes	characteristic
500	C₂²	#14583444	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	8	2	no	—
503	C₄	—	172	1	no	—
504	C₄	—	172	1	no	—
505	C₄	—	172	2	no	—
506	C₄	—	172	2	no	—
507	C₄	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
508	C₄	C₂×#13063287	1	1	yes	characteristic
509	C₄	#121×D₄₃	1	1	yes	characteristic
510	C₄	#14583435	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	4	2	no	—
515	C₂	—	344	2	no	—
516	C₂	#19137101	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1814	C₂
socle	C₂×C₄₃	C₄×#121
prime radical	#19144315	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1814	D₄₃
hypocenter	C₄₃	#21559
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1814

Complements

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

N	H ≅ G/N	type
2. #19143494	C₂	semidirect
3. C₂×#14583020	C₂	semidirect
4. #19143021	C₂	semidirect
5. #19135491	C₂	semidirect
6. #19135383	C₂	semidirect
7. #19135262	C₂	semidirect
8. #19135094	C₂	semidirect
9. #19134481	C₂	semidirect
10. #19134394	C₂	semidirect
11. C₄₃×#1814	C₂	semidirect
17. #14583174	C₄	semidirect
18. #14583169	C₄	semidirect
19. #14583162	C₄	semidirect
58. C₂×Dic₁₇₂	C₂×C₄	semidirect
59. C₂×#10621873	C₂×C₄	semidirect
60. C₂×D₃₄₄	C₂×C₄	semidirect
81. #13063261	C₂×C₄	semidirect
82. #13063261	C₂×C₄	semidirect
87. #13063243	C₂×C₄	semidirect
88. #13063241	C₂×C₄	semidirect
261. #1814	D₄₃	semidirect
306. C₄₃	#21559	semidirect

Maximal subgroups

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

subgroup	index
#19144315	2
#19143494	2
C₂×#14583020	2
#19143021	2
#19135491	2
#19135383	2
#19135262	2
#19135094	2
#19134481	2
#19134394	2
C₄₃×#1814	2
#21559	43