Subgroups — #25080393

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145177	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144394	C₂	1	1	yes	maximal, characteristic
3	#19144388	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582964	C₂	1	1	yes	maximal, characteristic
5	#19134049	C₂	1	2	yes	maximal, complemented
6	#19134045	C₂	1	2	yes	maximal, complemented
7	#19133993	C₂	1	2	yes	maximal, complemented
8	#19133959	C₂	1	2	yes	maximal, complemented
9	#19133353	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₃	—	2	1	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	#14583302	C₂²	1	1	yes	characteristic, complemented
16	#14583278	C₂²	1	1	yes	characteristic, complemented
17	#14583251	C₂²	1	1	yes	characteristic, complemented
18	#14583249	C₂²	1	1	yes	characteristic, complemented
19	#14583200	—	2	2	no	—
20	#14583196	—	2	2	no	—
21	#14583190	C₂²	1	2	yes	—
22	#14583186	C₂²	1	2	yes	—
23	#14583180	C₂²	1	2	yes	—
24	#14583176	C₂²	1	2	yes	—
25	#14583138	—	2	1	no	—
26	#14583138	—	2	1	no	—
27	C₄×#10621885	—	2	1	no	—
28	C₄×#10621885	—	2	1	no	—
29	#14582964	—	2	1	no	—
30	#14582964	—	2	1	no	—
31	#14582964	C₂²	1	2	yes	—
32	#14582964	C₂²	1	2	yes	—
33	#14582942	—	2	1	no	—
34	#14582941	—	2	1	no	—
35	#14582923	C₂²	1	1	yes	characteristic
36	#14582905	—	2	1	no	—
37	#14582903	—	2	1	no	—
38	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
40	#14582651	C₂²	1	2	yes	complemented
41	#14582651	C₂²	1	2	yes	complemented
42	#14582647	C₂²	1	2	yes	complemented
43	#14582646	C₂²	1	2	yes	complemented
44	C₄₃×#533	C₂²	1	1	yes	characteristic
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#333	C₂²	1	2	yes	complemented
48	C₄₃×#332	C₂²	1	2	yes	complemented
49	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₃	—	2	1	no	—
51	C₂×#10621885	—	2	1	no	—
52	C₂×#10621885	—	2	1	no	—
53	C₂×#10621877	—	2	1	no	—
54	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
55	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
56	C₂×C₈×D₄₃	—	2	2	no	—
57	C₂×C₈×D₄₃	—	2	2	no	—
58	C₂×C₈×D₄₃	—	4	4	no	—
59	#13063325	C₂³	1	1	yes	characteristic
60	#13063325	C₂³	1	1	yes	characteristic
61	#13063317	—	2	1	no	—
62	#13063304	—	2	1	no	—
63	#13063304	—	2	1	no	—
64	C₄×Dic₈₆	—	2	1	no	—
65	C₄×Dic₈₆	—	2	1	no	—
66	C₄×D₁₇₂	—	2	1	no	—
67	C₄×D₁₇₂	—	2	1	no	—
68	C₄×D₁₇₂	D₄	1	2	yes	—
69	C₄×D₁₇₂	C₂³	1	2	yes	—
70	#13063284	—	2	1	no	—
71	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
72	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
73	#13063259	—	2	2	no	—
74	#13063258	—	2	2	no	—
75	#13063258	—	2	1	no	—
76	#13063258	—	2	1	no	—
77	#13063257	—	2	2	no	—
78	#13063256	—	2	2	no	—
79	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
80	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
81	#13063249	—	2	1	no	—
82	#13063249	—	2	1	no	—
83	#13063248	—	2	1	no	—
84	#13063248	—	2	1	no	—
85	#13063247	—	2	2	no	—
86	#13063247	—	2	2	no	—
87	#13063245	—	2	2	no	—
88	#13063245	—	2	2	no	—
89	(C₂×D₄₃)⋊C₈	—	2	2	no	—
90	(C₂×D₄₃)⋊C₈	—	2	2	no	—
91	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₄₃	—	2	1	no	—
96	C₂²×C₈×C₄₃	—	2	1	no	—
97	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
99	#125×C₄₃	—	2	1	no	—
100	C₂²⋊Q₈×C₄₃	—	2	1	no	—
101	C₂²⋊Q₈×C₄₃	—	2	1	no	—
102	C₄×Q₈×C₄₃	—	2	1	no	—
103	C₄×Q₈×C₄₃	—	2	1	no	—
104	#117×C₄₃	—	2	1	no	—
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₄₃	—	2	1	no	—
107	C₄⋊C₈×C₄₃	—	2	1	no	—
108	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
109	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
110	C₂³×D₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
116	C₂²×Dic₄₃	—	2	1	no	—
117	C₂×D₁₇₂	—	2	1	no	—
118	C₂×D₁₇₂	—	2	2	no	—
119	C₂×D₁₇₂	Q₁₆	1	4	yes	complemented
120	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
121	C₂×C₄×D₄₃	—	2	2	no	—
122	C₂×C₄×D₄₃	—	2	2	no	—
123	C₂×C₄×D₄₃	—	4	2	no	—
124	C₂×C₄×D₄₃	—	4	2	no	—
125	C₂×Dic₈₆	—	2	1	no	—
126	C₂×Dic₈₆	—	2	1	no	—
127	M₁₆×C₄₃	—	4	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	4	2	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	1	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	4	1	no	—
136	C₄⋊C₄×C₄₃	—	4	1	no	—
137	C₂²⋊C₄×C₄₃	—	4	1	no	—
138	C₄²×C₄₃	—	4	1	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	C₂²⋊Dic₄₃	—	4	1	no	—
144	#10621885	—	4	2	no	—
145	#10621885	—	4	2	no	—
146	(C₂×D₄₃)⋊C₄	—	2	2	no	—
147	(C₂×D₄₃)⋊C₄	—	2	2	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	C₄⋊Dic₄₃	—	2	1	no	—
153	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
154	Dic₄₃⋊C₄	—	4	1	no	—
155	Dic₄₃⋊C₄	—	4	1	no	—
156	C₄×Dic₄₃	—	4	1	no	—
157	#10621877	—	4	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	4	1	no	—
161	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₈×D₄₃	—	4	4	no	—
166	C₈×D₄₃	—	4	4	no	—
167	C₂³×C₄₃	#121	1	1	yes	characteristic
168	C₂²×D₄₃	—	2	2	no	—
169	C₂²×D₄₃	—	2	4	no	—
170	C₂²×D₄₃	—	4	2	no	—
171	C₂²×D₄₃	—	4	2	no	—
172	Q₈×C₄₃	—	4	1	no	—
173	Q₈×C₄₃	—	4	1	no	—
174	Q₈×C₄₃	—	8	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	1	no	—
180	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
184	C₂×C₄×C₄₃	#135	1	2	yes	—
185	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	4	2	no	—
190	C₂×Dic₄₃	—	4	1	no	—
191	C₂×Dic₄₃	—	4	1	no	—
192	D₁₇₂	—	2	2	no	—
193	D₁₇₂	—	2	4	no	—
194	D₁₇₂	C₂×Q₁₆	1	4	yes	—
195	C₄×D₄₃	—	4	4	no	—
196	C₄×D₄₃	—	4	2	no	—
197	C₄×D₄₃	—	4	2	no	—
198	Dic₈₆	—	4	1	no	—
199	Dic₈₆	—	4	1	no	—
200	Dic₈₆	—	8	1	no	—
201	C₈×C₄₃	—	4	2	no	—
202	C₈×C₄₃	—	4	2	no	—
203	C₄₃⋊C₈	—	2	1	no	—
204	C₄₃⋊C₈	—	2	1	no	—
205	C₄₃⋊C₈	—	2	1	no	—
206	C₄₃⋊C₈	—	4	2	no	—
207	C₄₃⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
208	#19256	—	43	1	no	maximal, Sylow
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	#467	1	2	yes	—
212	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
213	C₂×D₄₃	—	2	4	no	—
214	C₂×D₄₃	—	4	8	no	—
215	C₂×D₄₃	—	4	2	no	—
216	C₂×D₄₃	—	4	2	no	—
217	C₄×C₄₃	—	2	1	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	8	1	no	—
221	C₄×C₄₃	—	8	1	no	—
222	C₄×C₄₃	#467	1	2	yes	—
223	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
224	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
225	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₄×C₄₃	#575	1	1	yes	characteristic
227	Dic₄₃	—	4	2	no	—
228	Dic₄₃	—	8	1	no	—
229	Dic₄₃	—	8	1	no	—
230	#3170	—	43	1	no	—
231	#3077	—	43	1	no	—
232	#3077	—	43	1	no	—
233	C₂×C₈×D₄	—	43	1	no	—
234	#1683	—	43	2	no	—
235	#1683	—	43	2	no	—
236	#1675	—	43	2	no	—
237	#1669	—	43	2	no	—
238	#1567	—	43	1	no	—
239	#1550	—	43	1	no	—
240	#1550	D₄₃	1	1	yes	characteristic, complemented
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	#3036	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#467	1	1	yes	characteristic
244	C₂×C₄₃	#3067	1	1	yes	characteristic
245	D₄₃	—	4	4	no	—
246	C₂³×C₈	—	86	1	no	—
247	#533	—	43	1	no	—
248	#533	C₂×D₄₃	1	1	yes	characteristic
249	C₂×C₄×D₄	—	43	1	no	—
250	#500	—	43	1	no	—
251	#494	—	43	1	no	—
252	#487	—	43	1	no	—
253	#487	—	43	1	no	—
254	#478	—	86	2	no	—
255	#478	—	86	2	no	—
256	#476	—	43	2	no	—
257	#476	—	43	2	no	—
258	#474	—	43	2	no	—
259	#474	—	43	2	no	—
260	#467	—	86	1	no	—
261	#467	—	86	1	no	—
262	C₄×Q₁₆	—	86	1	no	—
263	C₄×Q₁₆	—	86	1	no	—
264	C₈×D₄	—	43	2	no	—
265	C₈×D₄	—	43	2	no	—
266	C₈×D₄	—	86	1	no	—
267	C₈×D₄	—	86	1	no	—
268	#428	—	86	1	no	—
269	#428	—	86	1	no	—
270	#423	—	43	1	no	—
271	#423	C₂×D₄₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
273	#418	—	86	1	no	—
274	#418	—	86	1	no	—
275	C₂×C₂²⋊C₈	—	86	1	no	—
276	C₂×C₄×C₈	—	43	1	no	—
277	#335	—	43	2	no	—
278	#335	—	43	2	no	—
279	#333	—	43	2	no	—
280	#333	C₂×D₄₃	1	2	yes	complemented
281	#332	—	43	2	no	—
282	#332	C₂×D₄₃	1	2	yes	complemented
283	C₄₃	#19256	1	1	yes	characteristic, complemented, Sylow
284	C₂²×D₄	—	43	1	no	—
285	C₂³×C₄	—	86	1	no	—
286	C₂×Q₁₆	—	86	1	no	—
287	C₂×Q₁₆	—	86	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	86	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	43	1	no	—
292	C₂²×C₈	—	43	1	no	—
293	C₂²×C₈	—	86	2	no	—
294	C₂²×C₈	—	86	2	no	—
295	C₂²×C₈	—	172	4	no	—
296	C₄⋊Q₈	—	43	1	no	—
297	C₄⋊Q₈	—	43	1	no	—
298	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
299	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
300	#125	—	2	1	no	—
301	#125	—	86	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	86	1	no	—
305	C₂²⋊Q₈	—	86	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	86	1	no	—
309	C₄×Q₈	—	86	1	no	—
310	C₄×D₄	—	43	2	no	—
311	C₄×D₄	—	43	2	no	—
312	C₄×D₄	—	86	1	no	—
313	C₄×D₄	—	86	1	no	—
314	#117	—	2	1	no	—
315	#117	—	86	1	no	—
316	C₂×C₄⋊C₄	—	43	1	no	—
317	C₂×C₂²⋊C₄	—	86	1	no	—
318	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
319	#107	—	86	2	no	—
320	#107	—	86	1	no	—
321	#107	—	86	1	no	—
322	#107	—	86	2	no	—
323	#106	—	86	2	no	—
324	#106	—	86	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	43	2	no	—
328	C₄⋊C₈	—	86	1	no	—
329	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
330	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
331	#103	—	86	1	no	—
332	#103	—	86	1	no	—
333	#103	—	86	1	no	—
334	#103	—	86	1	no	—
335	#102	—	86	2	no	—
336	#102	—	86	2	no	—
337	#102	—	86	2	no	—
338	#102	—	86	2	no	—
339	C₂²⋊C₈	—	86	2	no	—
340	C₂²⋊C₈	—	86	2	no	—
341	C₄×C₈	—	43	1	no	—
342	C₄×C₈	—	43	1	no	—
343	C₄×C₈	—	43	1	no	—
344	C₄×C₈	—	43	1	no	—
345	C₂⁴	—	86	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	86	1	no	—
349	C₂×Q₈	—	86	1	no	—
350	C₂×D₄	—	43	4	no	—
351	C₂×D₄	—	43	2	no	—
352	C₂×D₄	—	86	1	no	—
353	C₂×D₄	—	86	2	no	—
354	C₂²×C₄	—	86	1	no	—
355	C₂²×C₄	—	86	2	no	—
356	C₂²×C₄	—	86	2	no	—
357	C₂²×C₄	—	172	2	no	—
358	C₂²×C₄	—	172	2	no	—
359	C₂²×C₄	#10621898	1	1	yes	characteristic
360	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
361	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
362	Q₁₆	—	172	2	no	—
363	Q₁₆	—	172	2	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	172	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	43	1	no	—
370	C₂×C₈	—	43	1	no	—
371	C₂×C₈	—	43	1	no	—
372	C₂×C₈	—	43	1	no	—
373	C₂×C₈	—	86	2	no	—
374	C₂×C₈	—	86	2	no	—
375	C₂×C₈	—	172	4	no	—
376	C₂×C₈	—	172	4	no	—
377	C₂×C₈	—	172	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	43	2	no	—
385	C₄⋊C₄	—	86	1	no	—
386	C₄⋊C₄	—	86	1	no	—
387	C₄⋊C₄	—	86	1	no	—
388	C₄⋊C₄	—	86	1	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₄⋊C₄	—	172	1	no	—
391	C₄⋊C₄	—	172	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	86	2	no	—
394	C₂²⋊C₄	—	86	2	no	—
395	C₂²⋊C₄	—	172	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	172	1	no	—
398	C₄²	#10621898	1	1	yes	characteristic
399	C₄²	D₄×D₄₃	1	1	yes	characteristic
400	C₄²	D₄×D₄₃	1	1	yes	characteristic
401	C₄²	C₂³×D₄₃	1	1	yes	characteristic
402	C₂³	—	86	2	no	—
403	C₂³	—	86	4	no	—
404	C₂³	—	172	2	no	—
405	C₂³	—	172	2	no	—
406	C₂³	#13063298	1	1	yes	characteristic
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	8	1	no	—
410	Q₈	—	344	1	no	—
411	Q₈	—	172	1	no	—
412	Q₈	—	172	1	no	—
413	D₄	—	43	4	no	—
414	D₄	—	86	4	no	—
415	D₄	—	86	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	86	2	no	—
422	C₂×C₄	—	172	4	no	—
423	C₂×C₄	—	172	1	no	—
424	C₂×C₄	—	172	1	no	—
425	C₂×C₄	—	172	2	no	—
426	C₂×C₄	—	172	2	no	—
427	C₂×C₄	—	172	2	no	—
428	C₂×C₄	#13063298	1	1	yes	characteristic
429	C₂×C₄	#13063298	1	1	yes	characteristic
430	C₂×C₄	#13063298	1	1	yes	characteristic
431	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
432	C₂×C₄	#13063346	1	2	yes	—
433	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
434	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	43	2	no	—
439	C₈	—	86	1	no	—
440	C₈	—	86	1	no	—
441	C₈	—	86	1	no	—
442	C₈	—	172	2	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	86	4	no	—
446	C₂²	—	172	8	no	—
447	C₂²	—	172	2	no	—
448	C₂²	—	172	2	no	—
449	C₂²	#14583139	1	2	yes	—
450	C₂²	C₂×#13063298	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	—	344	1	no	—
457	C₄	—	344	1	no	—
458	C₄	—	172	2	no	—
459	C₄	#14583139	1	2	yes	—
460	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
461	C₄	C₂×#13063346	1	1	yes	characteristic
462	C₄	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
463	C₄	#14583698	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	172	4	no	—
466	C₂	#19144058	1	1	yes	characteristic
467	C₂	C₂×#14583139	1	1	yes	characteristic
468	C₂	#19144314	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063298
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1550	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂²×D₁₇₂	D₄
hypercenter	#1550	D₄₃
hypocenter	C₄₃	#19256
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1550

Complements

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

N	H ≅ G/N	type
1. #19145177	C₂	semidirect
5. #19134049	C₂	semidirect
6. #19134045	C₂	semidirect
7. #19133993	C₂	semidirect
8. #19133959	C₂	semidirect
9. #19133353	C₂	semidirect
10. #19133283	C₂	semidirect
11. C₄₃×#1550	C₂	semidirect
15. #14583302	C₂²	semidirect
16. #14583278	C₂²	semidirect
17. #14583251	C₂²	semidirect
18. #14583249	C₂²	semidirect
40. #14582651	C₂²	semidirect
41. #14582651	C₂²	semidirect
42. #14582647	C₂²	semidirect
43. #14582646	C₂²	semidirect
47. C₄₃×#333	C₂²	semidirect
48. C₄₃×#332	C₂²	semidirect
119. C₂×D₁₇₂	Q₁₆	semidirect
240. #1550	D₄₃	semidirect
280. #333	C₂×D₄₃	semidirect
282. #332	C₂×D₄₃	semidirect
283. C₄₃	#19256	semidirect

Maximal subgroups

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

subgroup	index
#19145177	2
#19144394	2
#19144388	2
C₂×#14582964	2
#19134049	2
#19134045	2
#19133993	2
#19133959	2
#19133353	2
#19133283	2
C₄₃×#1550	2
#19256	43