Subgroups — #25080088

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	#19145052	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143339	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134082	C₂	1	2	yes	maximal, complemented
5	#19134062	C₂	1	2	yes	maximal, complemented
6	#19133958	C₂	1	2	yes	maximal, complemented
7	#19133938	C₂	1	2	yes	maximal, complemented
8	#19133348	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133242	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	—	2	1	no	—
13	C₂×#13063356	—	2	1	no	—
14	C₂×#13063332	—	2	1	no	—
15	#14583449	C₂²	1	1	yes	characteristic
16	#14583291	—	2	2	no	—
17	#14583278	C₂²	1	2	yes	—
18	#14583273	C₂²	1	2	yes	—
19	#14583179	C₂²	1	2	yes	—
20	#14583176	—	2	1	no	—
21	#14583133	—	2	2	no	—
22	#14583094	C₂²	1	2	yes	—
23	#14583091	—	2	1	no	—
24	#14582977	C₂²	1	2	yes	—
25	#14582971	—	2	2	no	—
26	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
27	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	#14582866	—	2	1	no	—
30	C₄×#10621877	C₂²	1	1	yes	characteristic
31	#14582651	C₂²	1	2	yes	—
32	#14582649	C₂²	1	2	yes	—
33	#14582645	C₂²	1	2	yes	—
34	#14582645	C₂²	1	2	yes	—
35	#14582644	C₂²	1	1	yes	characteristic
36	#14582644	C₂²	1	1	yes	characteristic
37	#14582642	C₂²	1	1	yes	characteristic
38	#14582642	C₂²	1	1	yes	characteristic
39	C₄₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#500	—	2	1	no	—
42	C₄₃×#486	—	2	1	no	—
43	C₄₃×#480	—	2	2	no	—
44	C₄₃×#474	C₂²	1	2	yes	—
45	C₄₃×#474	C₂²	1	2	yes	—
46	C₄₃×#431	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	#13063356	—	4	4	no	—
49	#13063356	—	4	4	no	—
50	C₂×#10621885	—	2	2	no	—
51	C₂×#10621885	—	2	2	no	—
52	C₂×#10621884	—	2	2	no	—
53	C₂×#10621884	—	2	2	no	—
54	C₂×#10621882	—	2	2	no	—
55	#13063332	—	4	4	no	—
56	C₂×#10621877	—	2	2	no	—
57	C₂×#10621877	D₄	1	1	yes	characteristic
58	C₂×#10621877	D₄	1	1	yes	characteristic
59	C₂²×C₄₃⋊C₈	—	2	1	no	—
60	C₂²×C₄₃⋊C₈	—	2	1	no	—
61	C₂²×C₄₃⋊C₈	—	2	2	no	—
62	#13063325	C₂³	1	1	yes	characteristic
63	#13063322	C₂³	1	1	yes	characteristic
64	#13063313	—	2	1	no	—
65	#13063299	—	2	1	no	—
66	#13063299	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	C₄×D₁₇₂	—	2	1	no	—
69	#13063258	—	2	2	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
72	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
75	#13063246	—	2	2	no	—
76	#13063245	—	2	2	no	—
77	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
79	#13063236	D₄	1	2	yes	—
80	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
81	C₂×#41×C₄₃	—	2	1	no	—
82	C₂²×Q₈×C₄₃	—	2	1	no	—
83	C₄⋊Q₈×C₄₃	—	2	1	no	—
84	C₄⋊Q₈×C₄₃	—	2	1	no	—
85	C₄⋊Q₈×C₄₃	—	2	1	no	—
86	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
88	#127×C₄₃	D₄	1	1	yes	characteristic
89	#124×C₄₃	—	2	1	no	—
90	#121×C₄₃	—	2	1	no	—
91	#121×C₄₃	D₄	1	2	yes	—
92	C₄×D₄×C₄₃	—	2	1	no	—
93	C₄×D₄×C₄₃	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	#107×C₄₃	—	2	2	no	—
98	#107×C₄₃	—	2	2	no	—
99	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
101	#102×C₄₃	—	2	2	no	—
102	#102×C₄₃	—	2	2	no	—
103	C₂²⋊C₈×C₄₃	—	2	1	no	—
104	C₄×C₈×C₄₃	—	2	1	no	—
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	2	no	—
115	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	—	2	2	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	—	4	1	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	—	2	1	no	—
127	C₂×C₄×D₄₃	—	4	1	no	—
128	C₂×Dic₈₆	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	4	1	no	—
135	C₄⋊C₄×C₄₃	—	4	1	no	—
136	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₄₃	—	2	2	no	—
138	C₂²⋊C₄×C₄₃	—	2	2	no	—
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₃	#41	1	1	yes	characteristic
142	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
143	#10621885	—	4	4	no	—
144	#10621885	—	4	4	no	—
145	#10621884	—	4	4	no	—
146	#10621884	—	4	4	no	—
147	#10621882	—	8	2	no	—
148	(C₂×D₄₃)⋊C₄	—	4	1	no	—
149	(C₂×D₄₃)⋊C₄	—	4	1	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	#10621877	—	2	2	no	—
153	#10621877	—	4	4	no	—
154	#10621877	D₈	1	4	yes	complemented
155	C₂×C₄₃⋊C₈	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	4	2	no	—
159	C₂×C₄₃⋊C₈	—	4	4	no	—
160	C₂×C₄₃⋊C₈	—	8	1	no	—
161	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
162	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
163	C₂³×C₄₃	—	2	2	no	—
164	C₂³×C₄₃	#121	1	1	yes	characteristic
165	C₂²×D₄₃	—	4	1	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	Q₈×C₄₃	—	4	2	no	—
168	Q₈×C₄₃	—	4	2	no	—
169	Q₈×C₄₃	—	8	2	no	—
170	D₄×C₄₃	—	2	2	no	—
171	D₄×C₄₃	—	2	2	no	—
172	D₄×C₄₃	—	4	4	no	—
173	D₄×C₄₃	—	4	2	no	—
174	D₄×C₄₃	—	8	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	8	2	no	—
183	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
191	C₂²⋊D₄₃	—	8	2	no	—
192	C₂×Dic₄₃	—	4	1	no	—
193	D₁₇₂	—	4	1	no	—
194	D₁₇₂	—	4	1	no	—
195	D₁₇₂	—	4	1	no	—
196	D₁₇₂	—	4	1	no	—
197	D₁₇₂	—	8	1	no	—
198	C₄×D₄₃	—	8	2	no	—
199	Dic₈₆	—	4	1	no	—
200	Dic₈₆	—	4	1	no	—
201	C₈×C₄₃	—	4	1	no	—
202	C₈×C₄₃	—	4	1	no	—
203	C₄₃⋊C₈	—	2	2	no	—
204	C₄₃⋊C₈	—	4	1	no	—
205	C₄₃⋊C₈	—	4	1	no	—
206	C₄₃⋊C₈	—	4	2	no	—
207	C₄₃⋊C₈	C₂×D₈	1	4	yes	—
208	#19231	—	43	1	no	maximal, Sylow
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	—	4	2	no	—
212	C₂²×C₄₃	—	4	2	no	—
213	C₂²×C₄₃	—	4	2	no	—
214	C₂²×C₄₃	#459	1	2	yes	—
215	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
216	C₂×D₄₃	—	8	1	no	—
217	C₂×D₄₃	—	8	1	no	—
218	C₂×D₄₃	—	8	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	2	1	no	—
222	C₄×C₄₃	—	4	2	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	—	8	1	no	—
230	#3245	—	43	1	no	—
231	#3226	D₄₃	1	1	yes	characteristic, complemented
232	#3152	—	43	1	no	—
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	—	8	2	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	—	16	1	no	—
247	C₂×#137	—	86	1	no	—
248	C₂×#137	—	86	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	—	2	1	no	—
254	#497	—	86	2	no	—
255	#494	—	43	2	no	—
256	#492	—	43	2	no	—
257	#486	—	2	1	no	—
258	#480	—	2	2	no	—
259	#474	—	43	2	no	—
260	#474	—	86	1	no	—
261	#474	C₂×D₄₃	1	2	yes	—
262	#474	C₂×D₄₃	1	2	yes	—
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	C₂×D₄₃	1	1	yes	characteristic
270	C₂×C₄⋊C₈	—	43	1	no	—
271	C₂×C₄⋊C₈	—	43	1	no	—
272	#408	—	86	1	no	—
273	C₄×M₁₆	—	43	1	no	—
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	—	172	4	no	—
287	#137	—	172	4	no	—
288	C₂×Q₁₆	—	86	2	no	—
289	C₂×Q₁₆	—	86	2	no	—
290	C₂×SD₁₆	—	86	2	no	—
291	C₂×SD₁₆	—	86	2	no	—
292	C₂×D₈	—	86	2	no	—
293	#131	—	172	4	no	—
294	C₂×M₁₆	—	43	1	no	—
295	C₂×M₁₆	—	43	1	no	—
296	C₂×M₁₆	—	86	2	no	—
297	C₂²×C₈	—	86	2	no	—
298	C₂²×C₈	—	86	1	no	—
299	C₂²×C₈	—	86	1	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	1	yes	characteristic
305	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
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	—	86	1	no	—
312	#121	—	86	1	no	—
313	#121	C₂²⋊D₄₃	1	2	yes	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	86	1	no	—
316	C₄×D₄	—	86	1	no	—
317	C₄×D₄	C₂²×D₄₃	1	2	yes	—
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	—	2	2	no	—
322	#107	—	2	2	no	—
323	#107	—	86	2	no	—
324	C₄⋊C₈	—	43	1	no	—
325	C₄⋊C₈	—	43	1	no	—
326	C₄⋊C₈	—	43	2	no	—
327	C₄⋊C₈	—	86	1	no	—
328	C₄⋊C₈	—	86	1	no	—
329	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
330	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	86	2	no	—
334	#102	—	86	2	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	86	2	no	—
337	C₂²⋊C₈	—	86	2	no	—
338	#97	—	43	2	no	—
339	C₄×C₈	—	2	1	no	—
340	C₄×C₈	—	43	2	no	—
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	2	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	86	1	no	—
355	C₂×D₄	—	86	1	no	—
356	C₂×D₄	—	86	1	no	—
357	C₂×D₄	—	172	1	no	—
358	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	172	1	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	—	172	4	no	—
366	Q₁₆	—	172	4	no	—
367	SD₁₆	—	172	4	no	—
368	SD₁₆	—	172	4	no	—
369	D₈	—	344	2	no	—
370	M₁₆	—	43	4	no	—
371	M₁₆	—	86	2	no	—
372	M₁₆	—	172	4	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	43	2	no	—
376	C₂×C₈	—	43	2	no	—
377	C₂×C₈	—	86	1	no	—
378	C₂×C₈	—	86	1	no	—
379	C₂×C₈	—	86	2	no	—
380	C₂×C₈	—	344	1	no	—
381	C₂×C₈	—	172	4	no	—
382	C₂×C₈	—	172	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	86	1	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	172	1	no	—
394	C₂²⋊C₄	—	172	1	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	—	2	2	no	—
400	C₂³	—	172	1	no	—
401	C₂³	#13063297	1	1	yes	characteristic
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	8	2	no	—
406	Q₈	—	172	1	no	—
407	Q₈	—	172	1	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	2	no	—
412	D₄	—	8	1	no	—
413	D₄	—	344	1	no	—
414	D₄	—	344	2	no	—
415	D₄	—	172	1	no	—
416	D₄	—	172	1	no	—
417	D₄	—	172	1	no	—
418	D₄	—	172	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	344	2	no	—
428	C₂×C₄	—	172	1	no	—
429	C₂×C₄	#13063297	1	1	yes	characteristic
430	C₂×C₄	#13063297	1	1	yes	characteristic
431	C₂×C₄	#13063297	1	1	yes	characteristic
432	C₂×C₄	D₈×D₄₃	1	2	yes	—
433	C₂×C₄	#13063349	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	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₈	—	43	4	no	—
440	C₈	—	86	2	no	—
441	C₈	—	172	1	no	—
442	C₈	—	172	1	no	—
443	C₈	—	172	2	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	344	1	no	—
450	C₂²	—	344	1	no	—
451	C₂²	—	344	1	no	—
452	C₂²	#14583092	1	2	yes	—
453	C₂²	C₂×#13063297	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	344	1	no	—
460	C₄	#14583092	1	2	yes	—
461	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
462	C₄	C₂×#13063349	1	1	yes	characteristic
463	C₄	#14583707	1	1	yes	characteristic
464	C₄	#14583714	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	2	no	—
467	C₂	—	688	1	no	—
468	C₂	C₂×#14583092	1	1	yes	characteristic
469	C₂	#19144282	1	1	yes	characteristic
470	C₂	#19144329	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3226	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145902	C₂
hypercenter	#3226	D₄₃
hypocenter	C₄₃	#19231
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3226

Complements

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

N	H ≅ G/N	type
2. #19145052	C₂	semidirect
3. #19143339	C₂	semidirect
4. #19134082	C₂	semidirect
5. #19134062	C₂	semidirect
6. #19133958	C₂	semidirect
7. #19133938	C₂	semidirect
8. #19133348	C₂	semidirect
9. #19133242	C₂	semidirect
10. C₂×#14582645	C₂	semidirect
11. C₄₃×#3226	C₂	semidirect
154. #10621877	D₈	semidirect
231. #3226	D₄₃	semidirect
282. C₄₃	#19231	semidirect

Maximal subgroups

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

subgroup	index
#19145902	2
#19145052	2
#19143339	2
#19134082	2
#19134062	2
#19133958	2
#19133938	2
#19133348	2
#19133242	2
C₂×#14582645	2
C₄₃×#3226	2
#19231	43