Subgroups — #25080086

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145902	C₂	1	1	yes	maximal, characteristic
2	#19145716	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143341	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134081	C₂	1	2	yes	maximal, complemented
5	#19134057	C₂	1	2	yes	maximal, complemented
6	#19133957	C₂	1	2	yes	maximal, complemented
7	#19133933	C₂	1	2	yes	maximal, complemented
8	#19133347	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133244	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063333	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583302	—	2	1	no	—
15	#14583247	—	2	1	no	—
16	#14583212	—	2	2	no	—
17	#14583179	—	2	1	no	—
18	#14583176	C₂²	1	2	yes	—
19	#14583176	C₂²	1	2	yes	—
20	#14583176	C₂²	1	2	yes	—
21	#14583133	—	2	2	no	—
22	#14583094	—	2	1	no	—
23	#14583091	C₂²	1	2	yes	—
24	#14582978	C₂²	1	2	yes	—
25	#14582972	—	2	2	no	—
26	C₈×D₁₇₂	C₂²	1	2	yes	—
27	#14582952	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#14582867	—	2	1	no	—
31	#14582652	C₂²	1	2	yes	—
32	#14582650	C₂²	1	2	yes	—
33	#14582645	C₂²	1	1	yes	characteristic
34	#14582645	C₂²	1	2	yes	—
35	#14582645	C₂²	1	2	yes	—
36	#14582645	C₂²	1	1	yes	characteristic
37	#14582643	C₂²	1	1	yes	characteristic
38	#14582643	C₂²	1	1	yes	characteristic
39	C₂×#137×C₄₃	—	2	1	no	—
40	C₂×#137×C₄₃	—	2	1	no	—
41	C₄₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#497	—	2	2	no	—
44	C₄₃×#494	C₂²	1	2	yes	—
45	C₄₃×#492	C₂²	1	2	yes	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621882	—	2	2	no	—
49	#13063333	—	4	4	no	—
50	C₂×#10621872	—	2	2	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂×C₈×D₄₃	—	2	2	no	—
54	#13063325	D₄	1	1	yes	characteristic
55	#13063322	D₄	1	1	yes	characteristic
56	#13063313	—	2	1	no	—
57	#13063299	—	2	1	no	—
58	#13063299	D₄	1	2	yes	—
59	C₄×D₁₇₂	—	2	1	no	—
60	C₄×D₁₇₂	C₂³	1	2	yes	—
61	#13063258	—	2	2	no	—
62	#13063258	—	2	2	no	—
63	#13063258	—	2	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
71	#13063246	—	2	2	no	—
72	#13063245	—	2	2	no	—
73	#13063245	—	2	2	no	—
74	#13063245	—	2	2	no	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
76	(C₂×D₄₃)⋊C₈	—	2	2	no	—
77	(C₂×D₄₃)⋊C₈	—	2	2	no	—
78	C₄×C₄₃⋊C₈	—	2	1	no	—
79	C₂×#41×C₄₃	—	2	1	no	—
80	C₂²×Q₈×C₄₃	—	2	1	no	—
81	#137×C₄₃	—	4	4	no	—
82	#137×C₄₃	—	4	4	no	—
83	C₂×Q₁₆×C₄₃	—	2	2	no	—
84	C₂×Q₁₆×C₄₃	—	2	2	no	—
85	C₂×SD₁₆×C₄₃	—	2	2	no	—
86	C₂×SD₁₆×C₄₃	—	2	2	no	—
87	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
88	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
89	C₄⋊Q₈×C₄₃	—	2	1	no	—
90	C₄⋊Q₈×C₄₃	—	2	1	no	—
91	C₄⋊Q₈×C₄₃	—	2	1	no	—
92	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
93	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
94	#127×C₄₃	C₂³	1	1	yes	characteristic
95	#124×C₄₃	—	2	1	no	—
96	#121×C₄₃	—	2	1	no	—
97	#121×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	—	2	1	no	—
99	C₄×D₄×C₄₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	#97×C₄₃	D₄	1	2	yes	—
104	C₄×C₈×C₄₃	C₂³	1	2	yes	—
105	#41×C₄₃	—	4	2	no	—
106	#41×C₄₃	—	4	2	no	—
107	C₂×Q₈×C₄₃	—	2	1	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	4	1	no	—
110	C₂×Q₈×C₄₃	—	4	2	no	—
111	C₂×Q₈×C₄₃	—	4	2	no	—
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	4	1	no	—
116	C₂²×C₄×C₄₃	—	4	1	no	—
117	C₂²×C₄×C₄₃	—	4	1	no	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂×C₂²⋊D₄₃	—	2	2	no	—
122	#10621898	—	4	2	no	—
123	#10621898	—	4	2	no	—
124	C₂×D₁₇₂	—	2	1	no	—
125	C₂×D₁₇₂	—	2	1	no	—
126	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
127	C₂×C₄×D₄₃	—	2	2	no	—
128	C₂×Dic₈₆	—	2	1	no	—
129	Q₁₆×C₄₃	—	4	4	no	—
130	Q₁₆×C₄₃	—	4	4	no	—
131	SD₁₆×C₄₃	—	4	4	no	—
132	SD₁₆×C₄₃	—	4	4	no	—
133	M₁₆×C₄₃	—	2	2	no	—
134	M₁₆×C₄₃	D₈	1	4	yes	complemented
135	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	4	1	no	—
142	C₄⋊C₄×C₄₃	—	4	1	no	—
143	C₂²⋊C₄×C₄₃	—	4	1	no	—
144	C₂²⋊C₄×C₄₃	—	4	1	no	—
145	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	#41	1	1	yes	characteristic
148	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
149	#10621882	—	8	2	no	—
150	(C₂×D₄₃)⋊C₄	—	2	2	no	—
151	(C₂×D₄₃)⋊C₄	—	2	2	no	—
152	C₄⋊Dic₄₃	—	2	1	no	—
153	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
154	C₂×C₄₃⋊C₈	—	2	1	no	—
155	C₂×C₄₃⋊C₈	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	1	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	4	2	no	—
160	C₂×C₄₃⋊C₈	—	8	1	no	—
161	#10621872	—	4	4	no	—
162	C₈×D₄₃	—	4	4	no	—
163	C₂³×C₄₃	—	4	1	no	—
164	C₂³×C₄₃	#121	1	1	yes	characteristic
165	C₂²×D₄₃	—	2	2	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	Q₈×C₄₃	—	4	1	no	—
168	Q₈×C₄₃	—	4	2	no	—
169	Q₈×C₄₃	—	4	1	no	—
170	Q₈×C₄₃	—	8	2	no	—
171	D₄×C₄₃	—	4	1	no	—
172	D₄×C₄₃	—	4	1	no	—
173	D₄×C₄₃	—	4	1	no	—
174	D₄×C₄₃	—	4	1	no	—
175	D₄×C₄₃	—	8	1	no	—
176	D₄×C₄₃	—	8	2	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	4	1	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	8	2	no	—
183	C₂×C₄×C₄₃	—	8	2	no	—
184	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
188	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
192	C₂²⋊D₄₃	—	4	4	no	—
193	C₂×Dic₄₃	—	2	2	no	—
194	D₁₇₂	—	2	2	no	—
195	D₁₇₂	—	2	2	no	—
196	D₁₇₂	—	4	2	no	—
197	D₁₇₂	—	8	1	no	—
198	C₄×D₄₃	—	4	2	no	—
199	C₄×D₄₃	—	4	2	no	—
200	Dic₈₆	—	4	2	no	—
201	C₈×C₄₃	—	2	2	no	—
202	C₈×C₄₃	C₂×D₈	1	4	yes	—
203	C₄₃⋊C₈	—	4	1	no	—
204	C₄₃⋊C₈	—	4	1	no	—
205	C₄₃⋊C₈	—	4	1	no	—
206	C₄₃⋊C₈	—	4	2	no	—
207	C₄₃⋊C₈	—	4	1	no	—
208	#19231	—	43	1	no	maximal, Sylow
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	—	8	1	no	—
212	C₂²×C₄₃	—	8	1	no	—
213	C₂²×C₄₃	—	8	1	no	—
214	C₂²×C₄₃	#459	1	2	yes	—
215	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
216	C₂×D₄₃	—	4	2	no	—
217	C₂×D₄₃	—	4	2	no	—
218	C₂×D₄₃	—	4	2	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	2	1	no	—
222	C₄×C₄₃	—	8	1	no	—
223	C₄×C₄₃	—	8	2	no	—
224	C₄×C₄₃	#459	1	2	yes	—
225	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
226	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₄₃	#577	1	1	yes	characteristic
228	C₄×C₄₃	#578	1	1	yes	characteristic
229	Dic₄₃	—	4	2	no	—
230	#3245	—	43	1	no	—
231	#3226	—	43	1	no	—
232	#3152	D₄₃	1	1	yes	characteristic, complemented
233	#2935	—	43	1	no	—
234	#1689	—	43	2	no	—
235	#1685	—	43	2	no	—
236	#1669	—	43	2	no	—
237	#1665	—	43	2	no	—
238	#1565	—	43	1	no	—
239	#1540	—	43	1	no	—
240	C₂×#332	—	43	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	—	16	1	no	—
243	C₂×C₄₃	C₂×#459	1	1	yes	characteristic
244	C₂×C₄₃	#3063	1	1	yes	characteristic
245	C₂×C₄₃	#3069	1	1	yes	characteristic
246	D₄₃	—	8	2	no	—
247	C₂×#137	—	2	1	no	—
248	C₂×#137	—	2	1	no	—
249	C₂×#131	—	86	1	no	—
250	#532	—	43	1	no	—
251	#532	C₂×D₄₃	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
253	#500	—	86	1	no	—
254	#497	—	2	2	no	—
255	#494	C₂×D₄₃	1	2	yes	—
256	#492	C₂×D₄₃	1	2	yes	—
257	#486	—	86	1	no	—
258	#480	—	86	2	no	—
259	#474	—	43	2	no	—
260	#474	—	43	2	no	—
261	#474	—	43	2	no	—
262	#474	—	86	1	no	—
263	#466	—	86	2	no	—
264	#459	—	43	2	no	—
265	#459	—	86	1	no	—
266	#436	—	43	2	no	—
267	#435	—	86	2	no	—
268	C₈×D₄	—	43	2	no	—
269	#431	—	43	1	no	—
270	C₂×C₄⋊C₈	—	43	1	no	—
271	C₂×C₄⋊C₈	—	43	1	no	—
272	#408	—	86	1	no	—
273	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
274	#335	—	43	2	no	—
275	#334	—	43	2	no	—
276	#332	—	43	2	no	—
277	#332	—	43	2	no	—
278	#332	—	43	1	no	—
279	#332	—	43	1	no	—
280	#331	—	43	1	no	—
281	#331	—	43	1	no	—
282	C₄₃	#19231	1	1	yes	characteristic, complemented, Sylow
283	C₂×#41	—	2	1	no	—
284	C₂×#41	—	86	1	no	—
285	C₂²×Q₈	—	2	1	no	—
286	#137	—	4	4	no	—
287	#137	—	4	4	no	—
288	C₂×Q₁₆	—	2	2	no	—
289	C₂×Q₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×D₈	—	86	2	no	—
293	#131	—	172	4	no	—
294	C₂×M₁₆	—	86	2	no	—
295	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
296	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
297	C₂²×C₈	—	86	1	no	—
298	C₂²×C₈	—	86	1	no	—
299	C₂²×C₈	—	86	2	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	43	1	no	—
304	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
305	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
306	#127	—	43	1	no	—
307	#127	C₂²×D₄₃	1	1	yes	characteristic
308	#124	—	2	1	no	—
309	#124	—	86	1	no	—
310	#121	—	2	1	no	—
311	#121	—	2	1	no	—
312	#121	—	43	2	no	—
313	#121	—	86	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	43	2	no	—
317	C₄×D₄	—	86	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	#107	—	86	2	no	—
322	#107	—	86	2	no	—
323	#107	—	86	2	no	—
324	C₄⋊C₈	—	43	1	no	—
325	C₄⋊C₈	—	43	1	no	—
326	C₄⋊C₈	—	43	1	no	—
327	C₄⋊C₈	—	43	1	no	—
328	C₄⋊C₈	—	43	2	no	—
329	C₄⋊C₈	—	86	1	no	—
330	C₄⋊C₈	—	86	1	no	—
331	#102	—	86	2	no	—
332	#102	—	86	2	no	—
333	#102	—	86	2	no	—
334	#102	—	86	2	no	—
335	C₂²⋊C₈	—	86	1	no	—
336	C₂²⋊C₈	—	86	2	no	—
337	C₂²⋊C₈	—	86	2	no	—
338	#97	C₂²⋊D₄₃	1	2	yes	—
339	C₄×C₈	—	86	1	no	—
340	C₄×C₈	C₂²×D₄₃	1	2	yes	—
341	#41	—	4	2	no	—
342	#41	—	4	2	no	—
343	#41	—	172	2	no	—
344	#41	—	172	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	4	1	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	—	86	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	4	1	no	—
355	C₂×D₄	—	43	2	no	—
356	C₂×D₄	—	86	2	no	—
357	C₂×D₄	—	86	1	no	—
358	C₂×D₄	—	86	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	86	2	no	—
362	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
363	C₂²×C₄	#10621900	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
365	Q₁₆	—	4	4	no	—
366	Q₁₆	—	4	4	no	—
367	SD₁₆	—	4	4	no	—
368	SD₁₆	—	4	4	no	—
369	D₈	—	344	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	172	4	no	—
372	M₁₆	#10621882	1	4	yes	complemented
373	C₂×C₈	—	86	1	no	—
374	C₂×C₈	—	86	1	no	—
375	C₂×C₈	—	86	2	no	—
376	C₂×C₈	—	86	1	no	—
377	C₂×C₈	—	86	1	no	—
378	C₂×C₈	—	344	1	no	—
379	C₂×C₈	—	172	2	no	—
380	C₂×C₈	—	172	4	no	—
381	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
382	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	43	2	no	—
390	C₄⋊C₄	—	86	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	86	2	no	—
394	C₂²⋊C₄	—	86	2	no	—
395	C₄²	D₄×D₄₃	1	1	yes	characteristic
396	C₄²	#10621900	1	1	yes	characteristic
397	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
398	C₄²	C₂³×D₄₃	1	1	yes	characteristic
399	C₂³	—	4	1	no	—
400	C₂³	—	86	2	no	—
401	C₂³	#13063296	1	1	yes	characteristic
402	Q₈	—	4	2	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	8	2	no	—
407	Q₈	—	172	2	no	—
408	D₄	—	4	1	no	—
409	D₄	—	4	1	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	D₄	—	8	1	no	—
413	D₄	—	8	2	no	—
414	D₄	—	86	2	no	—
415	D₄	—	86	2	no	—
416	D₄	—	344	1	no	—
417	D₄	—	172	4	no	—
418	D₄	—	172	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	86	2	no	—
427	C₂×C₄	—	172	2	no	—
428	C₂×C₄	—	172	2	no	—
429	C₂×C₄	#13063296	1	1	yes	characteristic
430	C₂×C₄	#13063296	1	1	yes	characteristic
431	C₂×C₄	#13063296	1	1	yes	characteristic
432	C₂×C₄	C₂×#10621882	1	2	yes	—
433	C₂×C₄	#13063351	1	2	yes	—
434	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	172	1	no	—
439	C₈	—	172	1	no	—
440	C₈	—	172	2	no	—
441	C₈	—	172	1	no	—
442	C₈	—	172	1	no	—
443	C₈	C₂×#10621882	1	4	yes	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	8	1	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	172	2	no	—
450	C₂²	—	172	2	no	—
451	C₂²	—	172	2	no	—
452	C₂²	#14583091	1	2	yes	—
453	C₂²	C₂×#13063296	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	2	no	—
459	C₄	—	172	2	no	—
460	C₄	#14583091	1	2	yes	—
461	C₄	C₂²×#10621882	1	1	yes	characteristic
462	C₄	C₂×#13063351	1	1	yes	characteristic
463	C₄	#14583708	1	1	yes	characteristic
464	C₄	#14583715	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	16	1	no	—
467	C₂	—	344	2	no	—
468	C₂	C₂×#14583091	1	1	yes	characteristic
469	C₂	#19144280	1	1	yes	characteristic
470	C₂	#19144328	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3152	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145902	C₂
hypercenter	#3152	D₄₃
hypocenter	C₄₃	#19231
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3152

Complements

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

N	H ≅ G/N	type
2. #19145716	C₂	semidirect
3. #19143341	C₂	semidirect
4. #19134081	C₂	semidirect
5. #19134057	C₂	semidirect
6. #19133957	C₂	semidirect
7. #19133933	C₂	semidirect
8. #19133347	C₂	semidirect
9. #19133244	C₂	semidirect
10. C₂×#14582645	C₂	semidirect
11. C₄₃×#3152	C₂	semidirect
134. M₁₆×C₄₃	D₈	semidirect
232. #3152	D₄₃	semidirect
282. C₄₃	#19231	semidirect
372. M₁₆	#10621882	semidirect

Maximal subgroups

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

subgroup	index
#19145902	2
#19145716	2
#19143341	2
#19134081	2
#19134057	2
#19133957	2
#19133933	2
#19133347	2
#19133244	2
C₂×#14582645	2
C₄₃×#3152	2
#19231	43