Subgroups — #25084441

Order 11008.

900 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145723	C₂	1	1	yes	maximal, characteristic, complemented
2	#19145533	C₂	1	1	yes	maximal, characteristic, complemented
3	#19145155	C₂	1	1	yes	maximal, characteristic, complemented
4	#19145047	C₂	1	1	yes	maximal, characteristic
5	C₂×#14583273	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134224	C₂	1	2	yes	maximal, complemented
7	#19134218	C₂	1	2	yes	maximal, complemented
8	#19134188	C₂	1	2	yes	maximal, complemented
9	#19134183	C₂	1	2	yes	maximal, complemented
10	M₁₆×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063353	—	2	2	no	—
13	C₂²×#10621884	—	2	2	no	—
14	#14583449	C₂²	1	1	yes	characteristic
15	C₂×#13063322	C₂²	1	1	yes	characteristic
16	#14583295	C₂²	1	2	yes	complemented
17	#14583295	C₂²	1	1	yes	characteristic, complemented
18	#14583288	—	2	2	no	—
19	#14583276	C₂²	1	2	yes	—
20	#14583273	—	2	2	no	—
21	#14583273	C₂²	1	2	yes	—
22	#14583273	C₂²	1	2	yes	—
23	#14583273	C₂²	1	2	yes	—
24	#14583273	C₂²	1	1	yes	characteristic, complemented
25	#14583272	C₂²	1	2	yes	—
26	#14583249	C₂²	1	1	yes	characteristic, complemented
27	#14583247	C₂²	1	2	yes	—
28	#14583247	C₂²	1	1	yes	characteristic, complemented
29	#14583247	C₂²	1	2	yes	complemented
30	#14583217	—	2	2	no	—
31	#14583186	—	2	2	no	—
32	#14583130	—	2	2	no	—
33	#14583099	—	2	2	no	—
34	#14583049	—	2	2	no	—
35	C₄×#10621884	—	2	2	no	—
36	#14582952	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	#14582620	C₂²	1	2	yes	complemented
39	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
40	C₄₃×#533	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#501	—	2	2	no	—
43	C₄₃×#500	C₂²	1	2	yes	complemented
44	C₄₃×#498	C₂²	1	2	yes	complemented
45	C₄₃×#428	—	2	2	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂²×D₁₇₂	—	2	1	no	—
49	C₂²×D₁₇₂	—	2	1	no	—
50	C₂²×D₁₇₂	—	2	1	no	—
51	#13063353	—	4	8	no	—
52	C₂×#10621873	—	2	4	no	—
53	C₂×#10621884	—	2	2	no	—
54	C₂×#10621884	—	2	4	no	—
55	C₂×#10621884	—	2	4	no	—
56	C₂×#10621884	—	2	4	no	—
57	C₂×#10621884	—	4	8	no	—
58	C₂×D₃₄₄	—	2	4	no	—
59	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
60	#13063325	C₂³	1	1	yes	characteristic
61	#13063322	—	2	1	no	—
62	#13063322	—	2	1	no	—
63	#13063322	—	2	1	no	—
64	#13063322	C₂³	1	2	yes	—
65	#13063322	C₂³	1	1	yes	characteristic
66	#13063313	—	2	1	no	—
67	#13063299	—	2	1	no	—
68	#13063299	—	2	1	no	—
69	C₄×D₁₇₂	—	2	1	no	—
70	C₄×D₁₇₂	—	2	1	no	—
71	#13063256	—	2	2	no	—
72	#13063256	—	2	4	no	—
73	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
74	#13063249	—	2	2	no	—
75	#13063245	—	2	4	no	—
76	#13063245	—	2	2	no	—
77	#13063245	—	2	4	no	—
78	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
79	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
80	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
83	C₂²×Q₈×C₄₃	—	2	1	no	—
84	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
85	C₄⋊Q₈×C₄₃	—	2	1	no	—
86	C₄⋊Q₈×C₄₃	—	2	1	no	—
87	C₄⋊Q₈×C₄₃	—	2	1	no	—
88	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
90	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
91	#125×C₄₃	—	2	1	no	—
92	C₂²⋊Q₈×C₄₃	—	2	1	no	—
93	C₂²⋊Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	—	2	1	no	—
95	C₄×Q₈×C₄₃	—	2	1	no	—
96	#117×C₄₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
100	#107×C₄₃	—	2	4	no	—
101	#106×C₄₃	—	2	4	no	—
102	#97×C₄₃	D₄	1	2	yes	—
103	C₄×C₈×C₄₃	C₂³	1	2	yes	—
104	C₂³×D₄₃	—	4	1	no	—
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	4	4	no	—
109	C₂×Q₈×C₄₃	—	4	1	no	—
110	C₂²×C₄×C₄₃	—	4	1	no	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₃	—	4	1	no	—
115	#10621898	—	4	4	no	—
116	C₂×D₁₇₂	—	2	1	no	—
117	C₂×D₁₇₂	—	2	1	no	—
118	C₂×D₁₇₂	—	2	2	no	—
119	C₂×D₁₇₂	—	2	1	no	—
120	C₂×D₁₇₂	—	2	2	no	—
121	C₂×D₁₇₂	—	2	2	no	—
122	C₂×D₁₇₂	—	4	1	no	—
123	C₂×D₁₇₂	—	4	1	no	—
124	C₂×D₁₇₂	—	4	1	no	—
125	C₂×D₁₇₂	—	4	4	no	—
126	C₂×D₁₇₂	—	4	4	no	—
127	C₂×D₁₇₂	—	8	2	no	—
128	C₂×C₄×D₄₃	—	4	1	no	—
129	C₂×Dic₈₆	—	2	1	no	—
130	M₁₆×C₄₃	SD₁₆	1	8	yes	complemented
131	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	4	1	no	—
139	C₄⋊C₄×C₄₃	—	4	1	no	—
140	C₄⋊C₄×C₄₃	—	4	1	no	—
141	C₄⋊C₄×C₄₃	—	4	1	no	—
142	C₂²⋊C₄×C₄₃	—	4	1	no	—
143	C₄²×C₄₃	—	4	1	no	—
144	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
148	#10621884	—	4	8	no	—
149	#10621884	—	4	4	no	—
150	#10621884	—	4	8	no	—
151	#10621884	—	8	4	no	—
152	(C₂×D₄₃)⋊C₄	—	4	1	no	—
153	(C₂×D₄₃)⋊C₄	—	4	1	no	—
154	C₄⋊Dic₄₃	—	2	1	no	—
155	C₄⋊Dic₄₃	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	2	4	no	—
157	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
158	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
159	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
160	D₃₄₄	—	4	8	no	—
161	#10621873	—	4	8	no	—
162	C₂³×C₄₃	#127	1	1	yes	characteristic
163	C₂²×D₄₃	—	4	1	no	—
164	C₂²×D₄₃	—	4	2	no	—
165	C₂²×D₄₃	—	8	2	no	—
166	C₂²×D₄₃	—	8	2	no	—
167	C₂²×D₄₃	—	8	2	no	—
168	Q₈×C₄₃	—	4	4	no	—
169	Q₈×C₄₃	—	4	2	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	Q₈×C₄₃	—	8	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	8	2	no	—
178	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
179	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
180	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
182	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂²⋊D₄₃	—	8	2	no	—
186	C₂×Dic₄₃	—	4	1	no	—
187	D₁₇₂	—	4	4	no	—
188	D₁₇₂	—	4	2	no	—
189	D₁₇₂	—	4	4	no	—
190	D₁₇₂	—	4	2	no	—
191	D₁₇₂	—	4	4	no	—
192	D₁₇₂	—	4	2	no	—
193	D₁₇₂	—	8	2	no	—
194	D₁₇₂	—	8	2	no	—
195	D₁₇₂	—	8	2	no	—
196	C₄×D₄₃	—	8	2	no	—
197	Dic₈₆	—	4	2	no	—
198	C₈×C₄₃	C₂×SD₁₆	1	8	yes	complemented
199	C₄₃⋊C₈	—	2	2	no	—
200	C₄₃⋊C₈	—	2	4	no	—
201	C₄₃⋊C₈	AGL(1,ℤ/8)	1	4	yes	complemented
202	#19621	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	1	no	—
205	C₂²×C₄₃	#492	1	2	yes	—
206	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
207	C₂×D₄₃	—	8	2	no	—
208	C₂×D₄₃	—	8	1	no	—
209	C₂×D₄₃	—	8	2	no	—
210	C₂×D₄₃	—	8	1	no	—
211	C₂×D₄₃	—	8	2	no	—
212	C₂×D₄₃	—	8	1	no	—
213	C₂×D₄₃	—	16	4	no	—
214	C₄×C₄₃	—	2	1	no	—
215	C₄×C₄₃	—	2	1	no	—
216	C₄×C₄₃	—	8	2	no	—
217	C₄×C₄₃	—	8	1	no	—
218	C₄×C₄₃	—	8	1	no	—
219	C₄×C₄₃	#492	1	2	yes	—
220	C₄×C₄₃	C₂²×SD₁₆	1	2	yes	—
221	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
222	C₄×C₄₃	#577	1	2	yes	—
223	Dic₄₃	—	8	1	no	—
224	#3227	—	43	1	no	—
225	#3208	—	43	1	no	—
226	#3167	—	43	1	no	—
227	#3165	D₄₃	1	1	yes	characteristic, complemented
228	#3151	—	43	1	no	—
229	C₂×#492	—	43	1	no	—
230	#1715	—	43	2	no	—
231	#1714	—	43	2	no	—
232	#1706	—	43	2	no	—
233	#1705	—	43	2	no	—
234	C₈×M₁₆	—	43	1	no	—
235	C₂×C₄₃	—	2	2	no	—
236	C₂×C₄₃	C₂×#492	1	1	yes	characteristic
237	C₂×C₄₃	#3151	1	1	yes	characteristic
238	C₂×C₄₃	#3154	1	1	yes	characteristic
239	D₄₃	—	16	1	no	—
240	D₄₃	—	16	2	no	—
241	C₂×AGL(1,ℤ/8)	—	86	2	no	—
242	C₂²×SD₁₆	—	86	2	no	—
243	#533	C₂×D₄₃	1	1	yes	characteristic
244	#532	—	43	1	no	—
245	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
246	C₂×#127	—	43	1	no	—
247	#501	—	2	2	no	—
248	#500	C₂×D₄₃	1	2	yes	complemented
249	#498	—	43	1	no	—
250	#498	—	43	2	no	—
251	#498	C₂×D₄₃	1	2	yes	complemented
252	#496	—	86	2	no	—
253	#493	—	43	2	no	—
254	#492	—	43	2	no	—
255	#492	—	43	2	no	—
256	#492	—	43	1	no	—
257	#492	—	43	2	no	—
258	#492	—	43	2	no	—
259	#492	—	86	2	no	—
260	#487	—	43	1	no	—
261	#486	—	43	1	no	—
262	#486	—	43	2	no	—
263	#486	—	43	2	no	—
264	#481	—	86	2	no	—
265	#476	—	86	2	no	—
266	#465	—	86	2	no	—
267	#460	—	86	2	no	—
268	#450	—	86	2	no	—
269	C₄×SD₁₆	—	86	2	no	—
270	#431	—	43	1	no	—
271	#428	—	2	2	no	—
272	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
273	C₂×C₄×C₈	—	43	1	no	—
274	#322	—	43	2	no	—
275	C₈²	—	43	2	no	—
276	C₄₃	#19621	1	1	yes	characteristic, complemented, Sylow
277	C₂×#41	—	86	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×D₄	—	86	1	no	—
280	C₂²×D₄	—	86	1	no	—
281	C₂²×D₄	—	86	1	no	—
282	AGL(1,ℤ/8)	—	172	8	no	—
283	C₂×SD₁₆	—	86	4	no	—
284	C₂×SD₁₆	—	86	4	no	—
285	C₂×SD₁₆	—	86	4	no	—
286	C₂×SD₁₆	—	86	2	no	—
287	C₂×SD₁₆	—	86	4	no	—
288	C₂×SD₁₆	—	172	8	no	—
289	C₂×D₈	—	86	4	no	—
290	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
291	C₂²×C₈	—	43	2	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	43	1	no	—
296	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
297	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
298	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
299	#127	—	43	2	no	—
300	#127	—	43	1	no	—
301	#127	—	86	1	no	—
302	#127	—	86	1	no	—
303	#127	—	86	1	no	—
304	#125	—	2	1	no	—
305	#124	—	86	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	#121	—	86	1	no	—
309	#121	—	86	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×D₄	—	86	1	no	—
313	C₄×D₄	—	86	1	no	—
314	#117	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
318	#107	—	2	4	no	—
319	#106	—	2	4	no	—
320	#106	—	86	2	no	—
321	#106	—	86	4	no	—
322	C₄⋊C₈	—	43	2	no	—
323	#103	—	86	2	no	—
324	#102	—	86	2	no	—
325	#102	—	86	4	no	—
326	#102	—	86	4	no	—
327	C₂²⋊C₈	—	43	2	no	—
328	#97	C₂²⋊D₄₃	1	2	yes	—
329	C₄×C₈	—	43	2	no	—
330	C₄×C₈	—	43	1	no	—
331	C₄×C₈	—	43	2	no	—
332	C₄×C₈	—	43	1	no	—
333	C₄×C₈	C₂²×D₄₃	1	2	yes	—
334	C₂⁴	—	172	1	no	—
335	#41	—	172	4	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	4	4	no	—
340	C₂×Q₈	—	4	1	no	—
341	C₂×Q₈	—	86	1	no	—
342	C₂×D₄	—	86	1	no	—
343	C₂×D₄	—	86	1	no	—
344	C₂×D₄	—	86	2	no	—
345	C₂×D₄	—	86	2	no	—
346	C₂×D₄	—	86	1	no	—
347	C₂×D₄	—	86	2	no	—
348	C₂×D₄	—	344	2	no	—
349	C₂×D₄	—	172	4	no	—
350	C₂×D₄	—	172	1	no	—
351	C₂×D₄	—	172	1	no	—
352	C₂×D₄	—	172	1	no	—
353	C₂×D₄	—	172	1	no	—
354	C₂×D₄	—	172	4	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	172	1	no	—
357	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
358	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
360	SD₁₆	—	344	4	no	—
361	SD₁₆	—	172	8	no	—
362	SD₁₆	—	172	4	no	—
363	SD₁₆	—	172	8	no	—
364	SD₁₆	—	172	8	no	—
365	D₈	—	172	8	no	—
366	M₁₆	#10621884	1	8	yes	complemented
367	C₂×C₈	—	43	2	no	—
368	C₂×C₈	—	43	2	no	—
369	C₂×C₈	—	43	4	no	—
370	C₂×C₈	—	86	4	no	—
371	C₂×C₈	C₂×C₂²⋊D₄₃	1	4	yes	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	86	1	no	—
383	C₄⋊C₄	—	86	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	172	1	no	—
386	C₂²⋊C₄	—	172	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	D₄×D₄₃	1	1	yes	characteristic
389	C₄²	D₄×D₄₃	1	1	yes	characteristic
390	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
391	C₄²	C₂³×D₄₃	1	1	yes	characteristic
392	C₂³	—	344	2	no	—
393	C₂³	—	344	2	no	—
394	C₂³	—	344	2	no	—
395	C₂³	—	172	1	no	—
396	C₂³	—	172	2	no	—
397	C₂³	#13063321	1	1	yes	characteristic
398	Q₈	—	4	4	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	8	2	no	—
402	Q₈	—	172	2	no	—
403	D₄	—	344	2	no	—
404	D₄	—	344	2	no	—
405	D₄	—	344	2	no	—
406	D₄	—	344	2	no	—
407	D₄	—	172	2	no	—
408	D₄	—	172	4	no	—
409	D₄	—	172	4	no	—
410	D₄	—	172	2	no	—
411	D₄	—	172	4	no	—
412	D₄	—	172	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	344	2	no	—
420	C₂×C₄	—	172	1	no	—
421	C₂×C₄	#13063321	1	1	yes	characteristic
422	C₂×C₄	#13063321	1	1	yes	characteristic
423	C₂×C₄	#13063321	1	1	yes	characteristic
424	C₂×C₄	C₂×#10621884	1	4	yes	—
425	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
428	C₈	—	43	4	no	—
429	C₈	—	86	2	no	—
430	C₈	—	86	4	no	—
431	C₈	C₂×#10621884	1	8	yes	complemented
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	344	1	no	—
435	C₂²	—	344	2	no	—
436	C₂²	—	344	2	no	—
437	C₂²	—	344	1	no	—
438	C₂²	—	344	2	no	—
439	C₂²	—	344	1	no	—
440	C₂²	—	688	4	no	—
441	C₂²	#14583273	1	2	yes	—
442	C₂²	C₂×#13063321	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	344	1	no	—
449	C₄	#14583273	1	2	yes	—
450	C₄	C₂²×#10621884	1	2	yes	—
451	C₄	AGL(1,ℤ/8)×D₄₃	1	2	yes	—
452	C₄	#14583708	1	2	yes	—
453	C₂	—	2	2	no	—
454	C₂	—	688	2	no	—
455	C₂	—	688	1	no	—
456	C₂	C₂×#14583273	1	1	yes	characteristic
457	C₂	#19145043	1	1	yes	characteristic
458	C₂	#19145074	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063321
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3165	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	#19145047	C₂
hypercenter	#3165	D₄₃
hypocenter	C₄₃	#19621
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3165

Complements

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

N	H ≅ G/N	type
1. #19145723	C₂	semidirect
2. #19145533	C₂	semidirect
3. #19145155	C₂	semidirect
5. C₂×#14583273	C₂	semidirect
6. #19134224	C₂	semidirect
7. #19134218	C₂	semidirect
8. #19134188	C₂	semidirect
9. #19134183	C₂	semidirect
10. M₁₆×C₄₃⋊C₈	C₂	semidirect
11. C₄₃×#3165	C₂	semidirect
16. #14583295	C₂²	semidirect
17. #14583295	C₂²	semidirect
24. #14583273	C₂²	semidirect
26. #14583249	C₂²	semidirect
28. #14583247	C₂²	semidirect
29. #14583247	C₂²	semidirect
38. #14582620	C₂²	semidirect
39. C₈×C₄₃⋊C₈	C₂²	semidirect
43. C₄₃×#500	C₂²	semidirect
44. C₄₃×#498	C₂²	semidirect
130. M₁₆×C₄₃	SD₁₆	semidirect
198. C₈×C₄₃	C₂×SD₁₆	semidirect
201. C₄₃⋊C₈	AGL(1,ℤ/8)	semidirect
227. #3165	D₄₃	semidirect
248. #500	C₂×D₄₃	semidirect
251. #498	C₂×D₄₃	semidirect
276. C₄₃	#19621	semidirect
366. M₁₆	#10621884	semidirect
431. C₈	C₂×#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145723	2
#19145533	2
#19145155	2
#19145047	2
C₂×#14583273	2
#19134224	2
#19134218	2
#19134188	2
#19134183	2
M₁₆×C₄₃⋊C₈	2
C₄₃×#3165	2
#19621	43