Subgroups — #25115085

Order 11008.

846 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583014	C₂	1	1	yes	maximal, characteristic
2	#19143476	C₂	1	2	yes	maximal
3	#19143192	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135372	C₂	1	2	yes	maximal, complemented
5	#19134828	C₂	1	2	yes	maximal, complemented
6	#19134825	C₂	1	2	yes	maximal, complemented
7	#19134758	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134660	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134659	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063345	C₂²	1	1	yes	characteristic
13	C₂×#13063331	C₂²	1	1	yes	characteristic
14	#14583379	C₂²	1	2	yes	—
15	#14583014	C₄	1	8	yes	complemented
16	#14583009	—	2	2	no	—
17	#14583004	—	2	2	no	—
18	C₄×#10621884	—	2	2	no	—
19	C₄×#10621883	—	2	2	no	—
20	C₂×#13063261	C₂²	1	1	yes	characteristic
21	C₂×#13063260	C₂²	1	1	yes	characteristic
22	#14582942	C₂²	1	2	yes	—
23	#14582938	—	2	2	no	—
24	#14582936	—	2	1	no	—
25	C₂×#13063259	C₂²	1	1	yes	characteristic
26	#107×D₄₃	—	2	1	no	—
27	C₂×#13063256	C₂²	1	2	yes	—
28	C₂×#13063252	C₂²	1	1	yes	characteristic
29	C₂×#13063251	C₂²	1	1	yes	characteristic
30	#14582900	C₂²	1	2	yes	—
31	#14582898	C₂²	1	2	yes	—
32	#14582855	C₂²	1	2	yes	—
33	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
34	#14582764	C₂²	1	2	yes	—
35	#14582668	C₂²	1	2	yes	—
36	#14582667	C₂²	1	2	yes	—
37	#14582658	C₂²	1	2	yes	—
38	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#520	C₂²	1	2	yes	—
40	C₄₃×#428	—	2	2	no	—
41	C₄₃×#428	C₂²	1	2	yes	—
42	C₄₃×#427	—	2	1	no	—
43	C₄₃×#427	C₂²	1	1	yes	characteristic
44	C₂×#107×C₄₃	—	2	1	no	—
45	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#10621898	C₂³	1	1	yes	characteristic
47	#13063345	C₂×C₄	1	4	yes	—
48	#13063345	Q₈	1	4	yes	—
49	C₂×#10621885	D₄	1	1	yes	characteristic
50	C₂×#10621883	D₄	1	1	yes	characteristic
51	C₂×#10621884	D₄	1	1	yes	characteristic
52	C₂×#10621882	D₄	1	1	yes	characteristic
53	#13063331	—	2	2	no	—
54	#13063331	C₂×C₄	1	4	yes	complemented
55	C₂×#10621877	C₂³	1	2	yes	—
56	C₂×#10621877	C₂³	1	1	yes	characteristic
57	C₂×#10621872	—	2	1	no	—
58	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₄₃	—	2	1	no	—
60	C₄×Dic₈₆	—	2	2	no	—
61	C₄×D₁₇₂	—	2	2	no	—
62	(C₂²⋊D₄₃)⋊C₄	—	4	2	no	—
63	#13063283	—	2	2	no	—
64	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
65	C₄⋊C₄×D₄₃	—	2	2	no	—
66	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
67	#13063261	—	2	2	no	—
68	#13063260	C₂×C₄	1	4	yes	complemented
69	#13063259	—	2	1	no	—
70	#13063259	—	2	1	no	—
71	#13063258	—	2	2	no	—
72	#13063256	—	2	2	no	—
73	#13063256	—	2	2	no	—
74	#13063256	—	2	2	no	—
75	#13063252	C₂×C₄	1	4	yes	complemented
76	#13063251	C₂×C₄	1	4	yes	complemented
77	#13063249	—	2	2	no	—
78	#13063248	—	2	2	no	—
79	#13063246	—	2	2	no	—
80	#13063245	—	2	2	no	—
81	#13063236	—	2	2	no	—
82	C₄×C₄₃⋊C₈	—	2	2	no	—
83	C₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
84	C₄₃⋊#95	—	4	2	no	—
85	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
86	#131×C₄₃	—	2	2	no	—
87	#131×C₄₃	C₂×C₄	1	4	yes	complemented
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₃	—	2	1	no	—
91	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₄×Q₈×C₄₃	—	2	2	no	—
93	C₄×D₄×C₄₃	—	2	2	no	—
94	C₄×D₄×C₄₃	—	4	2	no	—
95	#117×C₄₃	—	2	2	no	—
96	#117×C₄₃	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
98	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
99	#107×C₄₃	—	2	1	no	—
100	#107×C₄₃	—	2	1	no	—
101	#107×C₄₃	—	2	2	no	—
102	#107×C₄₃	D₄	1	1	yes	characteristic
103	#107×C₄₃	D₄	1	1	yes	characteristic
104	#106×C₄₃	—	2	2	no	—
105	#106×C₄₃	D₄	1	2	yes	—
106	#41×C₄₃	—	2	1	no	—
107	#41×C₄₃	—	2	1	no	—
108	#41×C₄₃	C₂²×C₄	1	2	yes	—
109	#41×C₄₃	C₂×Q₈	1	2	yes	—
110	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂×D₄×C₄₃	—	2	1	no	—
112	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	4	2	no	—
116	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₃	—	2	1	no	—
118	C₂²×Dic₄₃	—	2	1	no	—
119	C₂²×Dic₄₃	—	2	2	no	—
120	#10621898	—	2	1	no	—
121	#10621898	—	2	1	no	—
122	#10621898	C₂²×C₄	1	2	yes	—
123	#10621898	C₂×Q₈	1	2	yes	—
124	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₄₃	—	2	1	no	—
126	C₂×C₄×D₄₃	—	4	2	no	—
127	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
128	M₁₆×C₄₃	—	2	1	no	—
129	M₁₆×C₄₃	—	2	4	no	—
130	M₁₆×C₄₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	4	no	—
133	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₃	#41	1	2	yes	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	4	2	no	—
140	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₄₃	—	2	2	no	—
143	C₂²⋊C₄×C₄₃	—	4	2	no	—
144	C₄²×C₄₃	—	2	2	no	—
145	C₄²×C₄₃	—	4	2	no	—
146	#10621885	C₄⋊C₄	1	4	yes	—
147	#10621884	C₄⋊C₄	1	4	yes	—
148	#10621883	C₄⋊C₄	1	4	yes	—
149	#10621882	C₄⋊C₄	1	4	yes	—
150	(C₂×D₄₃)⋊C₄	—	4	2	no	—
151	C₄⋊Dic₄₃	—	2	2	no	—
152	C₄⋊Dic₄₃	—	2	2	no	—
153	Dic₄₃⋊C₄	—	4	2	no	—
154	C₄×Dic₄₃	—	2	1	no	—
155	C₄×Dic₄₃	—	4	2	no	—
156	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
157	#10621877	—	2	1	no	—
158	#10621877	—	2	2	no	—
159	#10621877	—	2	2	no	—
160	#10621877	C₂²×C₄	1	2	yes	—
161	C₂×C₄₃⋊C₈	—	2	1	no	—
162	C₂×C₄₃⋊C₈	—	2	2	no	—
163	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
164	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
167	#10621872	—	2	4	no	—
168	C₈×D₄₃	—	2	4	no	—
169	C₂³×C₄₃	—	2	1	no	—
170	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²×D₄₃	—	2	1	no	—
172	Q₈×C₄₃	—	2	1	no	—
173	Q₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
174	D₄×C₄₃	—	2	2	no	—
175	D₄×C₄₃	—	2	2	no	—
176	D₄×C₄₃	—	2	1	no	—
177	D₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	8	2	no	—
185	C₂×C₄×C₄₃	—	16	2	no	—
186	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
192	C₂²⋊D₄₃	—	2	2	no	—
193	C₂²⋊D₄₃	—	2	2	no	—
194	C₂×Dic₄₃	—	2	1	no	—
195	C₂×Dic₄₃	—	2	2	no	—
196	C₂×Dic₄₃	—	4	1	no	—
197	C₂×Dic₄₃	—	4	1	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	—	8	2	no	—
200	D₁₇₂	—	2	1	no	—
201	D₁₇₂	C₂×C₄⋊C₄	1	2	yes	—
202	C₄×D₄₃	—	2	2	no	—
203	C₄×D₄₃	—	2	2	no	—
204	C₄×D₄₃	—	16	2	no	—
205	Dic₈₆	—	2	1	no	—
206	Dic₈₆	C₂×C₄⋊C₄	1	2	yes	—
207	C₈×C₄₃	—	2	2	no	—
208	C₈×C₄₃	C₄×D₄	1	2	yes	—
209	C₈×C₄₃	C₄×D₄	1	2	yes	—
210	C₄₃⋊C₈	—	2	2	no	—
211	C₄₃⋊C₈	—	4	2	no	—
212	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
213	C₄₃⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
214	#22691	—	43	1	no	maximal, Sylow
215	C₂²×C₄₃	—	2	1	no	—
216	C₂²×C₄₃	—	2	1	no	—
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	4	1	no	—
219	C₂²×C₄₃	—	4	1	no	—
220	C₂²×C₄₃	#520	1	1	yes	characteristic
221	C₂²×C₄₃	D₄²	1	1	yes	characteristic
222	C₂²×C₄₃	#554	1	1	yes	characteristic
223	C₂×D₄₃	—	2	2	no	—
224	C₂×D₄₃	—	4	1	no	—
225	C₂×D₄₃	—	4	1	no	—
226	C₄×C₄₃	—	2	2	no	—
227	C₄×C₄₃	—	4	2	no	—
228	C₄×C₄₃	—	4	2	no	—
229	C₄×C₄₃	—	8	2	no	—
230	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
231	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
232	C₄×C₄₃	#547	1	1	yes	characteristic
233	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
234	Dic₄₃	—	2	2	no	—
235	Dic₄₃	—	4	2	no	—
236	Dic₄₃	—	8	2	no	—
237	C₂×#443	—	43	1	no	—
238	#2952	—	43	2	no	—
239	#2913	—	43	1	no	—
240	#2913	D₄₃	1	1	yes	characteristic, complemented
241	#1951	—	43	2	no	—
242	#1860	—	43	2	no	—
243	#1860	—	43	2	no	—
244	#1846	—	43	1	no	—
245	#1816	—	43	1	no	—
246	#1816	—	43	1	no	—
247	#1772	—	43	1	no	—
248	C₂×C₄₃	—	2	1	no	—
249	C₂×C₄₃	—	2	1	no	—
250	C₂×C₄₃	—	4	2	no	—
251	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₄₃	#3290	1	1	yes	characteristic
253	C₂×C₄₃	#3290	1	1	yes	characteristic
254	D₄₃	—	4	2	no	—
255	C₂×#135	—	43	1	no	—
256	C₂×#131	—	43	1	no	—
257	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
258	#520	—	43	2	no	—
259	#520	C₂×D₄₃	1	2	yes	—
260	#443	—	43	8	no	—
261	#442	—	86	2	no	—
262	#441	—	86	2	no	—
263	C₄×SD₁₆	—	86	2	no	—
264	C₄×SD₁₆	—	86	2	no	—
265	C₂×#108	—	43	1	no	—
266	C₂×#108	—	43	1	no	—
267	#428	—	2	2	no	—
268	#428	—	43	2	no	—
269	#428	—	86	2	no	—
270	#428	C₂×D₄₃	1	2	yes	—
271	#427	—	2	1	no	—
272	#427	—	86	1	no	—
273	#427	C₂×D₄₃	1	1	yes	characteristic
274	C₂×#107	—	2	1	no	—
275	C₂×#107	—	43	1	no	—
276	C₂×#107	—	86	1	no	—
277	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
278	C₂×#106	—	43	2	no	—
279	C₂×#104	—	43	1	no	—
280	C₂×#104	—	43	1	no	—
281	#417	—	43	2	no	—
282	#417	—	43	2	no	—
283	#405	—	43	2	no	—
284	C₂×C₄×C₈	—	43	1	no	—
285	#382	—	43	2	no	—
286	#343	—	43	2	no	—
287	#343	—	43	2	no	—
288	#339	—	43	2	no	—
289	C₄₃	#22691	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	43	1	no	—
291	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
292	#135	—	43	4	no	—
293	#135	—	43	4	no	—
294	C₂×Q₁₆	—	43	1	no	—
295	C₂×SD₁₆	—	43	1	no	—
296	C₂×SD₁₆	—	43	1	no	—
297	C₂×D₈	—	43	1	no	—
298	#131	—	2	2	no	—
299	#131	—	43	4	no	—
300	#131	—	86	2	no	—
301	#131	C₄×D₄₃	1	4	yes	complemented
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	43	1	no	—
304	C₂×M₁₆	—	43	2	no	—
305	C₂×M₁₆	—	86	1	no	—
306	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	43	1	no	—
309	C₂²×C₈	—	86	1	no	—
310	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	—	86	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	4	2	no	—
315	C₄×D₄	—	86	2	no	—
316	C₄×D₄	—	172	2	no	—
317	#117	—	2	2	no	—
318	#117	—	86	2	no	—
319	#117	C₂²×D₄₃	1	2	yes	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	43	2	no	—
322	C₂×C₄⋊C₄	—	86	2	no	—
323	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
324	C₂×C₄²	—	43	1	no	—
325	#108	—	43	4	no	—
326	#108	—	86	2	no	—
327	#107	—	2	1	no	—
328	#107	—	2	1	no	—
329	#107	—	2	2	no	—
330	#107	—	86	1	no	—
331	#107	—	86	1	no	—
332	#107	—	86	2	no	—
333	#107	C₂²⋊D₄₃	1	1	yes	characteristic
334	#107	C₂²⋊D₄₃	1	1	yes	characteristic
335	#106	—	2	2	no	—
336	#106	—	86	2	no	—
337	#106	—	86	2	no	—
338	#106	—	86	2	no	—
339	#106	C₂²⋊D₄₃	1	2	yes	—
340	#104	—	43	4	no	—
341	#104	—	43	4	no	—
342	#103	—	86	2	no	—
343	#103	—	86	2	no	—
344	#102	—	86	2	no	—
345	#102	—	86	2	no	—
346	#97	—	86	2	no	—
347	C₄×C₈	—	43	4	no	—
348	C₄×C₈	—	86	2	no	—
349	#95	—	172	2	no	—
350	#41	—	2	1	no	—
351	#41	—	2	1	no	—
352	#41	—	43	2	no	—
353	#41	—	43	2	no	—
354	#41	—	86	1	no	—
355	#41	—	86	1	no	—
356	#41	C₂×C₄×D₄₃	1	2	yes	—
357	#41	Q₈×D₄₃	1	2	yes	—
358	C₂×Q₈	—	43	1	no	—
359	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	43	1	no	—
362	C₂×D₄	—	86	1	no	—
363	C₂×D₄	D₄×D₄₃	1	1	yes	characteristic
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	86	1	no	—
368	C₂²×C₄	—	86	1	no	—
369	C₂²×C₄	—	86	2	no	—
370	C₂²×C₄	—	172	2	no	—
371	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
372	Q₁₆	—	43	4	no	—
373	SD₁₆	—	43	4	no	—
374	SD₁₆	—	43	4	no	—
375	D₈	—	43	4	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	4	no	—
378	M₁₆	—	43	2	no	—
379	M₁₆	—	86	1	no	—
380	M₁₆	—	86	4	no	—
381	M₁₆	—	86	2	no	—
382	M₁₆	—	86	2	no	—
383	M₁₆	C₂×C₄×D₄₃	1	2	yes	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	43	2	no	—
387	C₂×C₈	—	43	1	no	—
388	C₂×C₈	—	43	1	no	—
389	C₂×C₈	—	43	2	no	—
390	C₂×C₈	—	86	1	no	—
391	C₂×C₈	—	86	4	no	—
392	C₂×C₈	—	86	2	no	—
393	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
394	C₂×C₈	#10621898	1	2	yes	—
395	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
396	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	86	2	no	—
401	C₄⋊C₄	—	86	2	no	—
402	C₄⋊C₄	—	172	2	no	—
403	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
404	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₂²⋊C₄	—	172	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	4	2	no	—
410	C₄²	—	43	2	no	—
411	C₄²	—	86	1	no	—
412	C₄²	—	172	2	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	86	1	no	—
415	C₂³	#13063370	1	1	yes	characteristic
416	Q₈	—	2	1	no	—
417	Q₈	—	43	2	no	—
418	Q₈	—	86	1	no	—
419	Q₈	C₄⋊C₄×D₄₃	1	2	yes	—
420	D₄	—	2	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	1	no	—
423	D₄	—	43	2	no	—
424	D₄	—	86	2	no	—
425	D₄	—	86	2	no	—
426	D₄	—	86	1	no	—
427	D₄	C₄⋊C₄×D₄₃	1	2	yes	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	8	2	no	—
435	C₂×C₄	—	16	2	no	—
436	C₂×C₄	—	86	1	no	—
437	C₂×C₄	—	86	2	no	—
438	C₂×C₄	—	86	2	no	—
439	C₂×C₄	—	86	2	no	—
440	C₂×C₄	—	344	2	no	—
441	C₂×C₄	—	172	2	no	—
442	C₂×C₄	—	172	1	no	—
443	C₂×C₄	—	172	1	no	—
444	C₂×C₄	—	688	2	no	—
445	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
446	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
448	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
449	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
450	C₂×C₄	#13063373	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	43	2	no	—
453	C₈	—	43	2	no	—
454	C₈	—	86	2	no	—
455	C₈	—	172	2	no	—
456	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
457	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	86	2	no	—
464	C₂²	—	172	1	no	—
465	C₂²	—	172	1	no	—
466	C₂²	#14583380	1	1	yes	characteristic
467	C₂²	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
468	C₂²	#14583604	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	86	2	no	—
474	C₄	—	344	2	no	—
475	C₄	—	172	2	no	—
476	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
477	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
478	C₄	#14583550	1	1	yes	characteristic
479	C₄	Q₈×C₂²⋊D₄₃	1	1	yes	characteristic
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	4	2	no	—
483	C₂	—	172	2	no	—
484	C₂	C₄⋊C₄×C₂²⋊D₄₃	1	1	yes	characteristic
485	C₂	#19146377	1	1	yes	characteristic
486	C₂	#19146381	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2913	C₂
socle	C₂²×C₄₃	D₄²
prime radical	C₂×#13063345	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2913	D₄₃
hypocenter	C₄₃	#22691
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #2913

Complements

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

N	H ≅ G/N	type
3. #19143192	C₂	semidirect
4. #19135372	C₂	semidirect
5. #19134828	C₂	semidirect
6. #19134825	C₂	semidirect
7. #19134758	C₂	semidirect
8. #19134660	C₂	semidirect
9. #19134659	C₂	semidirect
10. #19134476	C₂	semidirect
11. C₄₃×#2913	C₂	semidirect
15. #14583014	C₄	semidirect
54. #13063331	C₂×C₄	semidirect
68. #13063260	C₂×C₄	semidirect
75. #13063252	C₂×C₄	semidirect
76. #13063251	C₂×C₄	semidirect
83. C₈×Dic₄₃	C₂×C₄	semidirect
87. #131×C₄₃	C₂×C₄	semidirect
240. #2913	D₄₃	semidirect
289. C₄₃	#22691	semidirect
301. #131	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583014	2
#19143476	2
#19143192	2
#19135372	2
#19134828	2
#19134825	2
#19134758	2
#19134660	2
#19134659	2
#19134476	2
C₄₃×#2913	2
#22691	43