Subgroups — #25148154

Order 11008.

892 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144320	C₂	1	2	yes	maximal, complemented
2	#19144311	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583166	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143512	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135865	C₂	1	2	yes	maximal, complemented
6	#19135648	C₂	1	2	yes	maximal, complemented
7	#19135506	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135385	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135143	C₂	1	2	yes	maximal, complemented
10	#19134396	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583697	C₂²	1	2	yes	—
13	C₂×#13063351	C₂²	1	2	yes	—
14	#14583666	C₂²	1	2	yes	—
15	C₂×#13063331	C₂²	1	1	yes	characteristic
16	#14583171	—	2	1	no	—
17	#14583167	—	2	4	no	—
18	#14583166	—	2	2	no	—
19	#14583166	—	2	2	no	—
20	#14583166	—	2	1	no	—
21	#14583160	—	2	4	no	—
22	#14583159	—	2	2	no	—
23	#14583021	—	2	2	no	—
24	#14583016	—	2	2	no	—
25	#14582947	C₂²	1	2	yes	—
26	C₂×#13063261	C₂²	1	1	yes	characteristic
27	C₂×#13063261	C₂²	1	1	yes	characteristic
28	#14582916	C₂²	1	2	yes	—
29	#14582904	C₂²	1	2	yes	—
30	#14582883	C₂²	1	2	yes	—
31	#14582881	C₂²	1	1	yes	characteristic
32	C₂×#13063242	C₂²	1	2	yes	—
33	C₂×#13063242	C₂²	1	2	yes	—
34	#14582872	C₂²	1	1	yes	characteristic
35	#14582854	C₂²	1	1	yes	characteristic
36	#14582671	C₂²	1	1	yes	characteristic
37	#14582669	C₂²	1	2	yes	—
38	#14582669	C₂²	1	1	yes	characteristic
39	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	2	yes	—
40	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
41	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#535	C₂²	1	2	yes	—
43	C₄₃×#496	—	2	2	no	—
44	C₄₃×#495	—	2	1	no	—
45	C₄₃×#493	—	2	1	no	—
46	C₄₃×#405	C₂²	1	1	yes	characteristic
47	C₂×#10621898	C₂³	1	1	yes	characteristic
48	#13063356	—	2	2	no	—
49	#13063355	—	2	2	no	—
50	#13063351	—	2	2	no	—
51	#13063351	—	2	4	no	—
52	#13063351	—	4	2	no	—
53	#13063350	—	2	2	no	—
54	#13063345	—	4	2	no	—
55	C₂×#10621883	—	2	2	no	—
56	C₂×#10621882	—	2	2	no	—
57	#13063332	—	2	4	no	—
58	#13063332	—	2	4	no	—
59	#13063331	—	2	1	no	—
60	#13063331	—	2	1	no	—
61	#13063331	—	2	1	no	—
62	#13063331	—	2	1	no	—
63	C₂×#10621877	—	4	2	no	—
64	C₂×#10621877	C₂³	1	1	yes	characteristic
65	C₂×#10621877	C₂³	1	2	yes	—
66	C₂×#10621877	C₂³	1	1	yes	characteristic
67	C₂×#10621877	C₂³	1	2	yes	—
68	C₂×#10621872	—	2	1	no	—
69	C₂×C₈×D₄₃	—	2	1	no	—
70	#13063284	C₂³	1	1	yes	characteristic
71	#13063261	—	2	1	no	—
72	#13063261	—	2	1	no	—
73	#13063261	D₄	1	2	yes	complemented
74	#13063261	D₄	1	2	yes	complemented
75	#13063260	—	2	4	no	—
76	#13063252	—	2	4	no	—
77	#13063246	—	4	2	no	—
78	#13063244	—	2	2	no	—
79	#13063243	D₄	1	2	yes	complemented
80	#13063242	—	2	2	no	—
81	#13063242	—	2	4	no	—
82	#13063242	—	2	4	no	—
83	#13063241	D₄	1	2	yes	complemented
84	#13063239	—	2	2	no	—
85	#13063235	—	2	1	no	—
86	C₈×Dic₄₃	—	2	1	no	—
87	C₂×#41×C₄₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
89	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
90	AGL(1,ℤ/8)×C₄₃	—	4	2	no	—
91	#135×C₄₃	—	2	1	no	—
92	#135×C₄₃	—	2	1	no	—
93	#135×C₄₃	—	2	1	no	—
94	#135×C₄₃	—	2	1	no	—
95	C₂×Q₁₆×C₄₃	D₄	1	1	yes	characteristic
96	C₂×SD₁₆×C₄₃	—	2	2	no	—
97	C₂×SD₁₆×C₄₃	D₄	1	2	yes	—
98	C₂×D₈×C₄₃	—	2	2	no	—
99	C₂×D₈×C₄₃	—	2	1	no	—
100	C₂×D₈×C₄₃	—	2	1	no	—
101	C₂×D₈×C₄₃	—	2	1	no	—
102	C₂×D₈×C₄₃	—	2	1	no	—
103	C₂×D₈×C₄₃	—	2	1	no	—
104	C₂×D₈×C₄₃	—	2	1	no	—
105	C₂×D₈×C₄₃	D₄	1	1	yes	characteristic
106	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	#127×C₄₃	—	2	2	no	—
109	#124×C₄₃	—	2	2	no	—
110	#121×C₄₃	—	4	2	no	—
111	#120×C₄₃	—	2	4	no	—
112	#117×C₄₃	C₂³	1	1	yes	characteristic
113	#97×C₄₃	—	2	1	no	—
114	C₄×C₈×C₄₃	—	2	1	no	—
115	C₂⁴×C₄₃	—	2	2	no	—
116	#41×C₄₃	—	2	2	no	—
117	#41×C₄₃	—	2	2	no	—
118	#41×C₄₃	—	2	2	no	—
119	#41×C₄₃	—	2	2	no	—
120	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	2	2	no	—
127	C₂×D₄×C₄₃	—	2	2	no	—
128	C₂×D₄×C₄₃	—	4	4	no	—
129	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₂²⋊D₄₃	—	2	1	no	—
133	#10621898	—	2	1	no	—
134	#10621898	—	2	1	no	—
135	#10621898	—	2	1	no	—
136	#10621898	—	2	1	no	—
137	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×D₄₃	—	2	1	no	—
139	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
140	Q₁₆×C₄₃	—	2	1	no	—
141	Q₁₆×C₄₃	—	2	1	no	—
142	SD₁₆×C₄₃	—	2	2	no	—
143	SD₁₆×C₄₃	—	2	2	no	—
144	SD₁₆×C₄₃	—	4	4	no	—
145	D₈×C₄₃	—	2	1	no	—
146	D₈×C₄₃	—	2	1	no	—
147	D₈×C₄₃	—	4	4	no	—
148	D₈×C₄₃	—	4	1	no	—
149	D₈×C₄₃	—	4	1	no	—
150	D₈×C₄₃	—	4	1	no	—
151	D₈×C₄₃	—	4	1	no	—
152	M₁₆×C₄₃	—	2	1	no	—
153	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₄₃	—	2	1	no	—
155	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
160	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
161	C₄⋊C₄×C₄₃	—	2	1	no	—
162	C₂²⋊C₄×C₄₃	—	4	4	no	—
163	C₂²⋊C₄×C₄₃	#41	1	2	yes	—
164	C₄²×C₄₃	—	2	1	no	—
165	C₂²⋊Dic₄₃	—	2	1	no	—
166	#10621885	—	4	2	no	—
167	#10621884	—	4	2	no	—
168	#10621883	—	4	4	no	—
169	#10621883	—	4	2	no	—
170	#10621882	—	4	4	no	—
171	#10621882	—	4	2	no	—
172	C₄⋊Dic₄₃	—	2	1	no	—
173	C₄×Dic₄₃	—	2	1	no	—
174	#10621877	—	2	1	no	—
175	#10621877	—	2	2	no	—
176	#10621877	—	2	1	no	—
177	#10621877	—	2	1	no	—
178	#10621877	—	2	2	no	—
179	#10621877	—	2	2	no	—
180	#10621877	—	4	4	no	—
181	#10621877	C₂×D₄	1	2	yes	—
182	#10621877	C₂×D₄	1	4	yes	—
183	C₂×C₄₃⋊C₈	—	2	1	no	—
184	C₂×C₄₃⋊C₈	—	2	2	no	—
185	C₂×C₄₃⋊C₈	—	2	1	no	—
186	C₂×C₄₃⋊C₈	—	2	2	no	—
187	C₂×C₄₃⋊C₈	—	4	4	no	—
188	#10621872	—	4	1	no	—
189	#10621872	—	4	1	no	—
190	C₈×D₄₃	—	4	1	no	—
191	C₈×D₄₃	—	4	1	no	—
192	C₂³×C₄₃	—	2	2	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	—	4	2	no	—
195	C₂³×C₄₃	—	4	2	no	—
196	C₂³×C₄₃	—	16	2	no	—
197	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
198	C₂²×D₄₃	—	2	1	no	—
199	Q₈×C₄₃	—	2	2	no	—
200	Q₈×C₄₃	—	2	2	no	—
201	D₄×C₄₃	—	2	2	no	—
202	D₄×C₄₃	—	2	2	no	—
203	D₄×C₄₃	—	4	2	no	—
204	D₄×C₄₃	—	4	2	no	—
205	D₄×C₄₃	—	4	2	no	—
206	D₄×C₄₃	—	4	2	no	—
207	D₄×C₄₃	—	4	2	no	—
208	D₄×C₄₃	—	4	2	no	—
209	D₄×C₄₃	—	16	4	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
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	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂²⋊D₄₃	—	4	1	no	—
221	C₂²⋊D₄₃	—	4	1	no	—
222	C₂×Dic₄₃	—	2	1	no	—
223	C₂×Dic₄₃	—	4	1	no	—
224	D₁₇₂	—	2	1	no	—
225	D₁₇₂	—	2	1	no	—
226	C₄×D₄₃	—	4	1	no	—
227	C₄×D₄₃	—	4	1	no	—
228	Dic₈₆	—	2	1	no	—
229	Dic₈₆	—	2	1	no	—
230	C₈×C₄₃	—	2	2	no	—
231	C₈×C₄₃	#121	1	1	yes	characteristic
232	C₈×C₄₃	#121	1	1	yes	characteristic
233	C₈×C₄₃	#121	1	1	yes	characteristic
234	C₈×C₄₃	#121	1	1	yes	characteristic
235	C₄₃⋊C₈	—	2	2	no	—
236	C₄₃⋊C₈	—	2	4	no	—
237	C₄₃⋊C₈	—	4	1	no	—
238	C₄₃⋊C₈	—	4	2	no	—
239	#25447	—	43	1	no	maximal, Sylow
240	C₂²×C₄₃	—	4	1	no	—
241	C₂²×C₄₃	—	4	2	no	—
242	C₂²×C₄₃	—	8	2	no	—
243	C₂²×C₄₃	—	8	4	no	—
244	C₂²×C₄₃	—	8	2	no	—
245	C₂²×C₄₃	—	16	2	no	—
246	C₂²×C₄₃	—	16	2	no	—
247	C₂²×C₄₃	#532	1	1	yes	characteristic
248	C₂²×C₄₃	#546	1	1	yes	characteristic
249	C₂²×C₄₃	#550	1	1	yes	characteristic
250	C₂×D₄₃	—	4	1	no	—
251	C₂×D₄₃	—	8	1	no	—
252	C₄×C₄₃	—	4	2	no	—
253	C₄×C₄₃	—	4	2	no	—
254	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
255	C₄×C₄₃	#540	1	1	yes	characteristic
256	C₄×C₄₃	D₄²	1	1	yes	characteristic
257	C₄×C₄₃	D₄²	1	1	yes	characteristic
258	Dic₄₃	—	4	1	no	—
259	Dic₄₃	—	8	1	no	—
260	#3155	D₄₃	1	1	yes	characteristic, complemented
261	#3068	—	43	2	no	—
262	#3067	—	43	1	no	—
263	C₂×#472	—	43	1	no	—
264	#2957	—	43	1	no	—
265	#2048	—	43	2	no	—
266	#2008	—	43	2	no	—
267	#1978	—	43	1	no	—
268	#1953	—	43	1	no	—
269	#1914	—	43	2	no	—
270	#1757	—	43	1	no	—
271	C₂×C₄₃	—	2	1	no	—
272	C₂×C₄₃	—	2	1	no	—
273	C₂×C₄₃	—	2	1	no	—
274	C₂×C₄₃	—	8	2	no	—
275	C₂×C₄₃	—	16	2	no	—
276	C₂×C₄₃	#2428	1	1	yes	characteristic
277	D₄₃	—	8	1	no	—
278	#575	—	43	2	no	—
279	C₂×AGL(1,ℤ/8)	—	43	2	no	—
280	C₂×AGL(1,ℤ/8)	C₂×D₄₃	1	2	yes	—
281	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
282	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
283	#568	—	43	2	no	—
284	C₂×#131	—	43	1	no	—
285	#535	C₂×D₄₃	1	2	yes	—
286	#496	—	2	2	no	—
287	#495	—	2	1	no	—
288	#493	—	2	1	no	—
289	#473	—	86	1	no	—
290	#472	—	86	4	no	—
291	#472	—	86	2	no	—
292	#472	—	86	2	no	—
293	#472	—	86	1	no	—
294	#471	—	86	4	no	—
295	#471	—	86	2	no	—
296	#444	—	86	2	no	—
297	#443	—	86	2	no	—
298	#430	—	43	2	no	—
299	C₂×#108	—	43	1	no	—
300	C₂×#108	—	43	1	no	—
301	#421	—	43	2	no	—
302	#418	—	43	2	no	—
303	#413	—	43	1	no	—
304	#413	—	43	2	no	—
305	C₂×#100	—	43	2	no	—
306	C₂×#100	—	43	2	no	—
307	#410	—	43	1	no	—
308	#405	—	43	1	no	—
309	#405	C₂×D₄₃	1	1	yes	characteristic
310	#344	—	43	1	no	—
311	#344	—	43	1	no	—
312	#344	—	43	2	no	—
313	C₄₃	#25447	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	—	43	1	no	—
315	C₂×#41	C₂²×D₄₃	1	2	yes	—
316	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
317	#137	—	86	2	no	—
318	#137	—	86	2	no	—
319	AGL(1,ℤ/8)	—	2	4	no	—
320	AGL(1,ℤ/8)	—	4	2	no	—
321	AGL(1,ℤ/8)	—	86	4	no	—
322	AGL(1,ℤ/8)	—	86	2	no	—
323	AGL(1,ℤ/8)	—	86	2	no	—
324	AGL(1,ℤ/8)	—	172	2	no	—
325	#135	—	2	1	no	—
326	#135	—	2	1	no	—
327	#135	—	2	1	no	—
328	#135	—	2	1	no	—
329	#135	—	172	2	no	—
330	C₂×Q₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
331	C₂×SD₁₆	—	2	2	no	—
332	C₂×SD₁₆	—	86	2	no	—
333	C₂×SD₁₆	C₂²⋊D₄₃	1	2	yes	—
334	C₂×D₈	—	2	2	no	—
335	C₂×D₈	—	2	1	no	—
336	C₂×D₈	—	2	1	no	—
337	C₂×D₈	—	2	1	no	—
338	C₂×D₈	—	2	1	no	—
339	C₂×D₈	—	2	1	no	—
340	C₂×D₈	—	2	1	no	—
341	C₂×D₈	—	86	2	no	—
342	C₂×D₈	C₂²⋊D₄₃	1	1	yes	characteristic
343	#131	—	86	4	no	—
344	#131	—	86	4	no	—
345	#131	—	86	1	no	—
346	#131	—	86	1	no	—
347	#131	—	86	1	no	—
348	#131	—	86	1	no	—
349	C₂×M₁₆	—	43	1	no	—
350	C₂×M₁₆	—	43	2	no	—
351	C₂×M₁₆	—	43	1	no	—
352	C₂×M₁₆	—	43	2	no	—
353	C₂×M₁₆	—	86	1	no	—
354	C₂×M₁₆	—	172	2	no	—
355	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
356	C₂²×C₈	—	86	1	no	—
357	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
358	#127	—	2	2	no	—
359	#124	—	2	2	no	—
360	#121	—	4	2	no	—
361	#120	—	2	4	no	—
362	#117	—	43	1	no	—
363	#117	C₂²×D₄₃	1	1	yes	characteristic
364	#108	—	43	2	no	—
365	#108	—	43	2	no	—
366	#108	—	86	4	no	—
367	#108	—	86	1	no	—
368	#108	—	86	1	no	—
369	#104	—	86	4	no	—
370	#102	—	172	2	no	—
371	#101	—	43	2	no	—
372	#101	—	86	2	no	—
373	#100	—	43	2	no	—
374	#100	—	86	4	no	—
375	#100	—	86	4	no	—
376	#100	—	86	2	no	—
377	#99	—	86	2	no	—
378	#97	—	2	1	no	—
379	#97	—	86	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	—	86	1	no	—
382	C₂⁴	—	2	2	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	86	1	no	—
388	#41	—	86	1	no	—
389	#41	—	86	1	no	—
390	#41	—	86	1	no	—
391	C₂×Q₈	—	43	1	no	—
392	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	43	1	no	—
402	C₂×D₄	—	86	1	no	—
403	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	86	1	no	—
406	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	2	1	no	—
409	Q₁₆	—	172	2	no	—
410	SD₁₆	—	2	2	no	—
411	SD₁₆	—	2	2	no	—
412	SD₁₆	—	4	4	no	—
413	SD₁₆	—	172	4	no	—
414	SD₁₆	—	172	2	no	—
415	SD₁₆	—	172	2	no	—
416	D₈	—	2	1	no	—
417	D₈	—	2	1	no	—
418	D₈	—	4	4	no	—
419	D₈	—	4	1	no	—
420	D₈	—	4	1	no	—
421	D₈	—	4	1	no	—
422	D₈	—	4	1	no	—
423	D₈	—	172	4	no	—
424	D₈	—	172	2	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	43	2	no	—
427	M₁₆	—	43	4	no	—
428	M₁₆	—	86	1	no	—
429	M₁₆	—	86	2	no	—
430	M₁₆	—	86	1	no	—
431	M₁₆	—	86	2	no	—
432	M₁₆	—	86	1	no	—
433	M₁₆	—	86	2	no	—
434	M₁₆	—	172	4	no	—
435	M₁₆	—	172	1	no	—
436	M₁₆	—	172	1	no	—
437	M₁₆	D₄×D₄₃	1	2	yes	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	86	1	no	—
440	C₂×C₈	—	86	2	no	—
441	C₂×C₈	—	86	1	no	—
442	C₂×C₈	—	86	2	no	—
443	C₂×C₈	—	172	4	no	—
444	C₂×C₈	—	172	1	no	—
445	C₂×C₈	—	172	1	no	—
446	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
447	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
448	C₂×C₈	#10621900	1	1	yes	characteristic
449	C₂×C₈	#10621900	1	1	yes	characteristic
450	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
451	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	86	1	no	—
454	C₂²⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	86	1	no	—
456	C₂²⋊C₄	#10621900	1	2	yes	—
457	C₄²	—	2	1	no	—
458	C₄²	—	86	1	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	16	2	no	—
464	C₂³	—	86	1	no	—
465	C₂³	C₂×#10621900	1	1	yes	characteristic
466	Q₈	—	2	2	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	86	1	no	—
469	Q₈	—	86	1	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	16	4	no	—
479	D₄	—	86	1	no	—
480	D₄	—	86	1	no	—
481	D₄	—	172	1	no	—
482	D₄	—	172	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	86	1	no	—
488	C₂×C₄	—	172	1	no	—
489	C₂×C₄	—	172	1	no	—
490	C₂×C₄	—	172	1	no	—
491	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
493	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
494	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
495	C₂×C₄	#13063370	1	1	yes	characteristic
496	C₂×C₄	#13063370	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	86	2	no	—
499	C₈	—	86	4	no	—
500	C₈	—	172	1	no	—
501	C₈	—	172	2	no	—
502	C₈	#13063297	1	1	yes	characteristic
503	C₈	#13063297	1	1	yes	characteristic
504	C₈	#13063297	1	1	yes	characteristic
505	C₈	#13063297	1	1	yes	characteristic
506	C₂²	—	4	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	4	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	16	2	no	—
512	C₂²	—	16	2	no	—
513	C₂²	—	344	1	no	—
514	C₂²	—	172	1	no	—
515	C₂²	#14583447	1	1	yes	characteristic
516	C₂²	#14583543	1	1	yes	characteristic
517	C₂²	#14583569	1	1	yes	characteristic
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	344	1	no	—
521	C₄	—	172	1	no	—
522	C₄	C₂×#13063297	1	1	yes	characteristic
523	C₄	#14583503	1	1	yes	characteristic
524	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
525	C₄	#14583534	1	1	yes	characteristic
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	8	2	no	—
530	C₂	—	16	2	no	—
531	C₂	—	344	1	no	—
532	C₂	#19138186	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19138186
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#3155	C₂
socle	C₂×C₄₃	#2428
hypercenter	#3155	D₄₃
hypocenter	C₄₃	#25447
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3155

Complements

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

N	H ≅ G/N	type
1. #19144320	C₂	semidirect
2. #19144311	C₂	semidirect
3. C₂×#14583166	C₂	semidirect
4. #19143512	C₂	semidirect
5. #19135865	C₂	semidirect
6. #19135648	C₂	semidirect
7. #19135506	C₂	semidirect
8. #19135385	C₂	semidirect
9. #19135143	C₂	semidirect
10. #19134396	C₂	semidirect
11. C₄₃×#3155	C₂	semidirect
73. #13063261	D₄	semidirect
74. #13063261	D₄	semidirect
79. #13063243	D₄	semidirect
83. #13063241	D₄	semidirect
260. #3155	D₄₃	semidirect
313. C₄₃	#25447	semidirect

Maximal subgroups

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

subgroup	index
#19144320	2
#19144311	2
C₂×#14583166	2
#19143512	2
#19135865	2
#19135648	2
#19135506	2
#19135385	2
#19135143	2
#19134396	2
C₄₃×#3155	2
#25447	43