Subgroups — #25148151

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	#19145081	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144326	C₂	1	2	yes	maximal, complemented
3	#19144315	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14583169	C₂	1	1	yes	maximal, characteristic, complemented
5	#19143513	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135871	C₂	1	2	yes	maximal, complemented
7	#19135647	C₂	1	2	yes	maximal, complemented
8	#19135505	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135385	C₂	1	1	yes	maximal, characteristic, complemented
10	#19135141	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1757	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583697	C₂²	1	2	yes	—
13	C₂×#13063353	C₂²	1	2	yes	—
14	C₂×#13063350	C₂²	1	2	yes	—
15	C₂×#13063347	C₂²	1	1	yes	characteristic
16	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
17	#14583665	C₂²	1	2	yes	—
18	#14583468	C₂²	1	2	yes	—
19	#14583288	—	2	2	no	—
20	#14583283	—	2	1	no	—
21	#14583276	—	2	1	no	—
22	#14583174	—	2	1	no	—
23	#14583169	—	2	1	no	—
24	#14583169	—	2	2	no	—
25	#14583169	—	2	2	no	—
26	#14583168	—	2	4	no	—
27	#14583165	—	2	4	no	—
28	#14583162	—	2	2	no	—
29	#14583022	—	2	2	no	—
30	#14583017	—	2	2	no	—
31	#14582947	C₂²	1	2	yes	—
32	C₂×#13063261	C₂²	1	1	yes	characteristic
33	C₂×#13063261	C₂²	1	1	yes	characteristic
34	#14582917	C₂²	1	2	yes	—
35	#14582903	C₂²	1	2	yes	—
36	#14582881	C₂²	1	2	yes	—
37	C₂×#13063241	C₂²	1	2	yes	—
38	C₂×#13063241	C₂²	1	2	yes	—
39	#14582669	C₂²	1	2	yes	—
40	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#413	C₂²	1	1	yes	characteristic
42	C₄₃×#410	C₂²	1	1	yes	characteristic
43	C₄₃×#405	C₂²	1	1	yes	characteristic
44	C₄₃×#405	C₂²	1	1	yes	characteristic
45	C₄₃×#344	C₂²	1	1	yes	characteristic
46	C₄₃×#344	C₂²	1	1	yes	characteristic
47	C₂×#10621898	C₂³	1	2	yes	—
48	C₂²×D₁₇₂	C₂³	1	2	yes	—
49	#13063356	—	2	2	no	—
50	#13063355	—	2	2	no	—
51	#13063353	—	2	4	no	—
52	#13063353	—	4	2	no	—
53	#13063351	—	2	2	no	—
54	#13063350	—	2	2	no	—
55	#13063350	—	2	4	no	—
56	#13063350	—	4	2	no	—
57	#13063347	—	2	1	no	—
58	#13063347	—	2	1	no	—
59	#13063347	—	2	1	no	—
60	#13063347	—	2	1	no	—
61	#13063345	—	4	2	no	—
62	C₂×Dic₁₇₂	D₄	1	1	yes	characteristic
63	C₂×#10621873	—	2	2	no	—
64	C₂×#10621873	D₄	1	2	yes	—
65	C₂×#10621884	—	2	2	no	—
66	C₂×D₃₄₄	—	2	2	no	—
67	C₂×D₃₄₄	—	2	1	no	—
68	C₂×D₃₄₄	—	2	1	no	—
69	C₂×D₃₄₄	—	2	1	no	—
70	C₂×D₃₄₄	—	2	1	no	—
71	C₂×D₃₄₄	—	2	1	no	—
72	C₂×D₃₄₄	—	2	1	no	—
73	C₂×D₃₄₄	D₄	1	1	yes	characteristic
74	C₂×#10621882	—	2	2	no	—
75	#13063333	—	2	4	no	—
76	#13063331	—	2	4	no	—
77	C₂×#10621877	C₂³	1	2	yes	—
78	C₂×#10621877	C₂³	1	2	yes	—
79	M₁₆×D₄₃	—	4	2	no	—
80	#13063322	—	2	2	no	—
81	#13063313	—	2	2	no	—
82	#13063300	—	4	2	no	—
83	#13063295	—	2	4	no	—
84	#13063261	—	2	1	no	—
85	#13063261	—	2	1	no	—
86	#13063261	D₄	1	2	yes	complemented
87	#13063261	D₄	1	2	yes	complemented
88	#13063260	—	2	4	no	—
89	#13063253	—	2	4	no	—
90	#13063245	—	4	2	no	—
91	#13063243	—	2	2	no	—
92	#13063241	—	2	2	no	—
93	#13063241	—	2	4	no	—
94	#13063241	—	2	4	no	—
95	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
96	#131×C₄₃	—	2	1	no	—
97	#131×C₄₃	—	2	1	no	—
98	#131×C₄₃	—	2	1	no	—
99	#131×C₄₃	—	2	1	no	—
100	C₂×M₁₆×C₄₃	—	2	1	no	—
101	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₃	—	2	1	no	—
105	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
106	#117×C₄₃	C₂³	1	1	yes	characteristic
107	#117×C₄₃	C₂³	1	1	yes	characteristic
108	#101×C₄₃	D₄	1	2	yes	complemented
109	#100×C₄₃	D₄	1	2	yes	complemented
110	#99×C₄₃	—	2	2	no	—
111	#97×C₄₃	—	2	1	no	—
112	#97×C₄₃	—	2	1	no	—
113	C₄×C₈×C₄₃	—	2	1	no	—
114	C₄×C₈×C₄₃	—	2	1	no	—
115	C₂³×D₄₃	—	2	2	no	—
116	#41×C₄₃	—	2	1	no	—
117	#41×C₄₃	—	2	1	no	—
118	#41×C₄₃	—	2	1	no	—
119	#41×C₄₃	—	2	1	no	—
120	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₄₃	—	2	1	no	—
122	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₃	—	2	2	no	—
126	#10621898	—	2	2	no	—
127	#10621898	—	2	2	no	—
128	#10621898	—	2	2	no	—
129	#10621898	—	2	2	no	—
130	C₂×D₁₇₂	—	2	2	no	—
131	C₂×D₁₇₂	—	2	2	no	—
132	C₂×D₁₇₂	—	2	2	no	—
133	C₂×D₁₇₂	—	2	2	no	—
134	C₂×D₁₇₂	—	2	2	no	—
135	C₂×D₁₇₂	—	2	2	no	—
136	C₂×D₁₇₂	—	4	4	no	—
137	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
138	C₂×C₄×D₄₃	—	2	2	no	—
139	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
140	M₁₆×C₄₃	—	2	1	no	—
141	M₁₆×C₄₃	—	2	1	no	—
142	M₁₆×C₄₃	—	2	1	no	—
143	M₁₆×C₄₃	—	2	1	no	—
144	M₁₆×C₄₃	—	4	1	no	—
145	M₁₆×C₄₃	—	4	1	no	—
146	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
147	M₁₆×C₄₃	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₄₃	—	2	1	no	—
149	C₂×C₈×C₄₃	—	2	1	no	—
150	C₂×C₈×C₄₃	—	2	1	no	—
151	C₂×C₈×C₄₃	—	4	1	no	—
152	C₂×C₈×C₄₃	—	4	1	no	—
153	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
158	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₂²⋊C₄×C₄₃	—	2	1	no	—
162	C₂²⋊C₄×C₄₃	#41	1	2	yes	—
163	C₄²×C₄₃	—	2	1	no	—
164	C₄²×C₄₃	—	2	1	no	—
165	#10621885	—	4	2	no	—
166	#10621884	—	4	4	no	—
167	#10621884	—	4	2	no	—
168	#10621883	—	4	2	no	—
169	#10621882	—	4	4	no	—
170	#10621882	—	4	2	no	—
171	(C₂×D₄₃)⋊C₄	—	4	4	no	—
172	#10621877	—	2	2	no	—
173	#10621877	—	2	2	no	—
174	#10621877	—	2	2	no	—
175	#10621877	C₂×D₄	1	4	yes	—
176	C₂×C₄₃⋊C₈	—	2	2	no	—
177	C₂×C₄₃⋊C₈	—	2	2	no	—
178	Dic₁₇₂	—	2	1	no	—
179	Dic₁₇₂	—	2	1	no	—
180	D₃₄₄	—	2	1	no	—
181	D₃₄₄	—	2	1	no	—
182	D₃₄₄	—	4	4	no	—
183	D₃₄₄	—	4	1	no	—
184	D₃₄₄	—	4	1	no	—
185	D₃₄₄	—	4	1	no	—
186	D₃₄₄	—	4	1	no	—
187	#10621873	—	2	2	no	—
188	#10621873	—	2	2	no	—
189	#10621873	—	4	4	no	—
190	#10621872	—	4	4	no	—
191	C₈×D₄₃	—	4	4	no	—
192	C₂³×C₄₃	—	2	1	no	—
193	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂²×D₄₃	—	2	2	no	—
195	C₂²×D₄₃	—	4	2	no	—
196	C₂²×D₄₃	—	4	2	no	—
197	C₂²×D₄₃	—	4	2	no	—
198	C₂²×D₄₃	—	16	2	no	—
199	Q₈×C₄₃	—	2	1	no	—
200	Q₈×C₄₃	—	2	1	no	—
201	D₄×C₄₃	—	2	1	no	—
202	D₄×C₄₃	—	2	1	no	—
203	D₄×C₄₃	—	4	1	no	—
204	D₄×C₄₃	—	4	1	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²⋊D₄₃	—	4	2	no	—
217	C₂²⋊D₄₃	—	4	2	no	—
218	C₂×Dic₄₃	—	2	2	no	—
219	D₁₇₂	—	2	2	no	—
220	D₁₇₂	—	2	2	no	—
221	D₁₇₂	—	4	2	no	—
222	D₁₇₂	—	4	2	no	—
223	D₁₇₂	—	4	2	no	—
224	D₁₇₂	—	4	2	no	—
225	D₁₇₂	—	16	4	no	—
226	C₄×D₄₃	—	4	2	no	—
227	C₄×D₄₃	—	4	2	no	—
228	Dic₈₆	—	2	2	no	—
229	Dic₈₆	—	2	2	no	—
230	C₈×C₄₃	—	2	2	no	—
231	C₈×C₄₃	—	2	2	no	—
232	C₈×C₄₃	—	4	1	no	—
233	C₈×C₄₃	#121	1	1	yes	characteristic
234	C₈×C₄₃	#121	1	1	yes	characteristic
235	C₈×C₄₃	#121	1	1	yes	characteristic
236	C₈×C₄₃	#121	1	1	yes	characteristic
237	C₄₃⋊C₈	—	2	4	no	—
238	C₄₃⋊C₈	—	4	2	no	—
239	#25447	—	43	1	no	maximal, Sylow
240	C₂²×C₄₃	—	4	1	no	—
241	C₂²×C₄₃	—	4	1	no	—
242	C₂²×C₄₃	—	8	1	no	—
243	C₂²×C₄₃	#532	1	1	yes	characteristic
244	C₂²×C₄₃	#546	1	1	yes	characteristic
245	C₂²×C₄₃	#550	1	1	yes	characteristic
246	C₂×D₄₃	—	4	2	no	—
247	C₂×D₄₃	—	8	2	no	—
248	C₂×D₄₃	—	8	4	no	—
249	C₂×D₄₃	—	8	2	no	—
250	C₂×D₄₃	—	16	2	no	—
251	C₂×D₄₃	—	16	2	no	—
252	C₄×C₄₃	—	4	2	no	—
253	C₄×C₄₃	—	4	1	no	—
254	C₄×C₄₃	—	8	1	no	—
255	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
256	C₄×C₄₃	#540	1	1	yes	characteristic
257	C₄×C₄₃	D₄²	1	1	yes	characteristic
258	C₄×C₄₃	D₄²	1	1	yes	characteristic
259	Dic₄₃	—	4	2	no	—
260	#3155	—	43	1	no	—
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	D₄₃	1	1	yes	characteristic, complemented
271	C₂×C₄₃	—	2	1	no	—
272	C₂×C₄₃	—	2	1	no	—
273	C₂×C₄₃	—	2	1	no	—
274	C₂×C₄₃	—	8	1	no	—
275	C₂×C₄₃	#2428	1	1	yes	characteristic
276	D₄₃	—	8	2	no	—
277	D₄₃	—	16	2	no	—
278	#575	—	43	2	no	—
279	C₂×AGL(1,ℤ/8)	—	43	2	no	—
280	C₂×AGL(1,ℤ/8)	—	43	2	no	—
281	C₂×#135	—	43	1	no	—
282	C₂²×D₈	—	43	1	no	—
283	#568	—	43	2	no	—
284	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
285	#535	—	43	2	no	—
286	#496	—	86	2	no	—
287	#495	—	86	1	no	—
288	#493	—	86	1	no	—
289	#473	—	86	1	no	—
290	#472	—	86	2	no	—
291	#472	—	86	2	no	—
292	#472	—	86	1	no	—
293	#472	—	86	4	no	—
294	#471	—	86	2	no	—
295	#471	—	86	4	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	2	no	—
304	#413	C₂×D₄₃	1	1	yes	characteristic
305	C₂×#100	—	43	2	no	—
306	C₂×#100	—	43	2	no	—
307	#410	C₂×D₄₃	1	1	yes	characteristic
308	#405	C₂×D₄₃	1	1	yes	characteristic
309	#405	C₂×D₄₃	1	1	yes	characteristic
310	#344	—	43	2	no	—
311	#344	C₂×D₄₃	1	1	yes	characteristic
312	#344	C₂×D₄₃	1	1	yes	characteristic
313	C₄₃	#25447	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	—	43	2	no	—
315	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
316	C₂²×D₄	—	43	2	no	—
317	#137	—	86	2	no	—
318	#137	—	86	2	no	—
319	AGL(1,ℤ/8)	—	86	4	no	—
320	AGL(1,ℤ/8)	—	86	2	no	—
321	AGL(1,ℤ/8)	—	86	2	no	—
322	AGL(1,ℤ/8)	—	86	4	no	—
323	AGL(1,ℤ/8)	—	172	2	no	—
324	AGL(1,ℤ/8)	—	172	2	no	—
325	#135	—	86	1	no	—
326	#135	—	86	1	no	—
327	#135	—	86	1	no	—
328	#135	—	86	1	no	—
329	#135	—	172	2	no	—
330	C₂×Q₁₆	—	43	1	no	—
331	C₂×SD₁₆	—	43	2	no	—
332	C₂×SD₁₆	—	86	2	no	—
333	C₂×SD₁₆	—	86	2	no	—
334	C₂×D₈	—	43	1	no	—
335	C₂×D₈	—	86	2	no	—
336	C₂×D₈	—	86	2	no	—
337	C₂×D₈	—	86	1	no	—
338	C₂×D₈	—	86	1	no	—
339	C₂×D₈	—	86	1	no	—
340	C₂×D₈	—	86	1	no	—
341	C₂×D₈	—	86	1	no	—
342	C₂×D₈	—	86	1	no	—
343	#131	—	2	1	no	—
344	#131	—	2	1	no	—
345	#131	—	2	1	no	—
346	#131	—	2	1	no	—
347	#131	—	86	4	no	—
348	#131	—	86	4	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	43	2	no	—
351	C₂×M₁₆	—	43	2	no	—
352	C₂×M₁₆	—	172	2	no	—
353	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
354	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
355	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
358	#127	—	86	2	no	—
359	#124	—	86	2	no	—
360	#121	—	172	2	no	—
361	#120	—	86	4	no	—
362	#117	C₂²×D₄₃	1	1	yes	characteristic
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	—	86	2	no	—
372	#101	D₁₇₂	1	2	yes	complemented
373	#100	—	86	4	no	—
374	#100	—	86	2	no	—
375	#100	—	86	4	no	—
376	#100	D₁₇₂	1	2	yes	complemented
377	#99	—	2	2	no	—
378	#97	—	2	1	no	—
379	#97	—	2	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	—	2	1	no	—
382	C₂⁴	—	86	2	no	—
383	#41	—	2	1	no	—
384	#41	—	2	1	no	—
385	#41	—	2	1	no	—
386	#41	—	2	1	no	—
387	#41	—	86	2	no	—
388	#41	—	86	2	no	—
389	#41	—	86	2	no	—
390	#41	—	86	2	no	—
391	C₂×Q₈	—	43	2	no	—
392	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	43	2	no	—
395	C₂×D₄	—	86	2	no	—
396	C₂×D₄	—	86	2	no	—
397	C₂×D₄	—	86	2	no	—
398	C₂×D₄	—	86	2	no	—
399	C₂×D₄	—	86	2	no	—
400	C₂×D₄	—	86	2	no	—
401	C₂×D₄	—	86	2	no	—
402	C₂×D₄	—	172	4	no	—
403	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	86	2	no	—
406	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
407	Q₁₆	—	86	1	no	—
408	Q₁₆	—	86	1	no	—
409	Q₁₆	—	172	2	no	—
410	SD₁₆	—	86	2	no	—
411	SD₁₆	—	86	2	no	—
412	SD₁₆	—	172	4	no	—
413	SD₁₆	—	172	4	no	—
414	SD₁₆	—	172	2	no	—
415	SD₁₆	—	172	2	no	—
416	D₈	—	86	1	no	—
417	D₈	—	86	1	no	—
418	D₈	—	172	4	no	—
419	D₈	—	172	4	no	—
420	D₈	—	172	2	no	—
421	D₈	—	172	1	no	—
422	D₈	—	172	1	no	—
423	D₈	—	172	1	no	—
424	D₈	—	172	1	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	1	no	—
427	M₁₆	—	2	1	no	—
428	M₁₆	—	2	1	no	—
429	M₁₆	—	4	1	no	—
430	M₁₆	—	4	1	no	—
431	M₁₆	—	43	4	no	—
432	M₁₆	—	86	2	no	—
433	M₁₆	—	86	2	no	—
434	M₁₆	—	86	2	no	—
435	M₁₆	—	172	4	no	—
436	M₁₆	C₂×D₁₇₂	1	2	yes	—
437	M₁₆	C₂×D₁₇₂	1	2	yes	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	4	1	no	—
442	C₂×C₈	—	4	1	no	—
443	C₂×C₈	—	86	2	no	—
444	C₂×C₈	—	86	2	no	—
445	C₂×C₈	—	172	4	no	—
446	C₂×C₈	#10621898	1	1	yes	characteristic
447	C₂×C₈	#10621898	1	1	yes	characteristic
448	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
449	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
450	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
451	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	172	4	no	—
456	C₂²⋊C₄	#10621898	1	2	yes	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	86	2	no	—
461	C₂³	—	172	2	no	—
462	C₂³	—	172	2	no	—
463	C₂³	—	172	2	no	—
464	C₂³	—	688	2	no	—
465	C₂³	C₂×#10621898	1	1	yes	characteristic
466	Q₈	—	2	1	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	86	2	no	—
469	Q₈	—	86	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	86	2	no	—
475	D₄	—	86	2	no	—
476	D₄	—	172	2	no	—
477	D₄	—	172	2	no	—
478	D₄	—	172	2	no	—
479	D₄	—	172	2	no	—
480	D₄	—	172	2	no	—
481	D₄	—	172	2	no	—
482	D₄	—	688	4	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	86	2	no	—
489	C₂×C₄	—	172	2	no	—
490	C₂×C₄	—	172	2	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×D₁₇₂	1	1	yes	characteristic
494	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
495	C₂×C₄	#13063371	1	1	yes	characteristic
496	C₂×C₄	#13063371	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	2	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	86	4	no	—
501	C₈	—	172	2	no	—
502	C₈	#13063298	1	1	yes	characteristic
503	C₈	#13063298	1	1	yes	characteristic
504	C₈	#13063298	1	1	yes	characteristic
505	C₈	#13063298	1	1	yes	characteristic
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	344	2	no	—
510	C₂²	—	344	4	no	—
511	C₂²	—	344	2	no	—
512	C₂²	—	172	2	no	—
513	C₂²	—	688	2	no	—
514	C₂²	—	688	2	no	—
515	C₂²	#14583449	1	1	yes	characteristic
516	C₂²	#14583545	1	1	yes	characteristic
517	C₂²	#14583570	1	1	yes	characteristic
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	8	1	no	—
521	C₄	—	172	2	no	—
522	C₄	C₂×#13063298	1	1	yes	characteristic
523	C₄	#14583504	1	1	yes	characteristic
524	C₄	D₄×D₁₇₂	1	1	yes	characteristic
525	C₄	D₄×D₁₇₂	1	1	yes	characteristic
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	8	1	no	—
530	C₂	—	344	2	no	—
531	C₂	—	688	2	no	—
532	C₂	#19138183	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19138183
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1757	C₂
socle	C₂×C₄₃	#2428
hypercenter	#1757	D₄₃
hypocenter	C₄₃	#25447
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1757

Complements

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

N	H ≅ G/N	type
1. #19145081	C₂	semidirect
2. #19144326	C₂	semidirect
3. #19144315	C₂	semidirect
4. C₂×#14583169	C₂	semidirect
5. #19143513	C₂	semidirect
6. #19135871	C₂	semidirect
7. #19135647	C₂	semidirect
8. #19135505	C₂	semidirect
9. #19135385	C₂	semidirect
10. #19135141	C₂	semidirect
11. C₄₃×#1757	C₂	semidirect
86. #13063261	D₄	semidirect
87. #13063261	D₄	semidirect
108. #101×C₄₃	D₄	semidirect
109. #100×C₄₃	D₄	semidirect
270. #1757	D₄₃	semidirect
313. C₄₃	#25447	semidirect
372. #101	D₁₇₂	semidirect
376. #100	D₁₇₂	semidirect

Maximal subgroups

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

subgroup	index
#19145081	2
#19144326	2
#19144315	2
C₂×#14583169	2
#19143513	2
#19135871	2
#19135647	2
#19135505	2
#19135385	2
#19135141	2
C₄₃×#1757	2
#25447	43