Subgroups — #25103504

Order 11008.

874 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	C₂×#14583171	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063356	C₂	1	2	yes	maximal
3	#19143020	C₂	1	1	yes	maximal, characteristic
4	#19135511	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135373	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135247	C₂	1	2	yes	maximal, complemented
7	#19135113	C₂	1	2	yes	maximal
8	#19134655	C₂	1	1	yes	maximal, characteristic
9	#19134501	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063244	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	C₂²	1	2	yes	—
13	C₂×#13063331	C₂²	1	1	yes	characteristic
14	C₂×#13063331	C₂²	1	1	yes	characteristic
15	C₄×#10621898	C₂²	1	1	yes	characteristic
16	#14583171	C₄	1	8	yes	complemented
17	#14583004	—	2	2	no	—
18	#14582997	—	2	2	no	—
19	C₄×#10621885	—	2	2	no	—
20	C₄×#10621884	—	2	2	no	—
21	C₂×#13063261	C₂²	1	1	yes	characteristic
22	C₂×#13063261	C₂²	1	1	yes	characteristic
23	#14582939	C₂²	1	2	yes	—
24	#14582908	C₂²	1	2	yes	—
25	#14582898	C₂²	1	2	yes	—
26	C₂×#13063244	C₂²	1	2	yes	—
27	C₂×#13063244	C₂²	1	2	yes	—
28	#14582856	—	2	1	no	—
29	#14582856	—	2	1	no	—
30	#14582854	C₂²	1	1	yes	characteristic
31	#14582854	C₂²	1	1	yes	characteristic
32	C₄×#10621877	C₂²	1	2	yes	—
33	C₄×#10621877	C₂²	1	1	yes	characteristic
34	#14582851	—	2	1	no	—
35	#97×D₄₃	—	2	1	no	—
36	#14582668	C₂²	1	2	yes	—
37	#14582668	C₂²	1	2	yes	—
38	#14582664	C₂²	1	2	yes	—
39	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
41	C₄₃×#441	—	2	1	no	—
42	C₄₃×#441	—	2	1	no	—
43	C₄₃×#441	—	2	1	no	—
44	C₄₃×#441	—	2	1	no	—
45	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#103×C₄₃	C₂²	1	2	yes	—
47	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
48	C₂×#10621898	C₂³	1	1	yes	characteristic
49	#13063356	—	2	4	no	—
50	#13063356	C₂×C₄	1	8	yes	—
51	C₂×#10621885	—	2	2	no	—
52	C₂×#10621884	—	2	2	no	—
53	#13063331	—	2	2	no	—
54	#13063331	—	2	2	no	—
55	#13063331	—	2	2	no	—
56	#13063331	C₂×C₄	1	4	yes	—
57	C₂×#10621877	C₂³	1	2	yes	—
58	C₂×#10621877	C₂³	1	1	yes	characteristic
59	C₂×#10621877	C₂³	1	2	yes	—
60	C₂×#10621877	C₂³	1	1	yes	characteristic
61	C₂×#10621872	—	2	1	no	—
62	C₂×#10621872	—	2	1	no	—
63	C₂×C₈×D₄₃	—	2	1	no	—
64	C₂×C₈×D₄₃	—	2	1	no	—
65	C₄×Dic₈₆	D₄	1	2	yes	—
66	C₄×D₁₇₂	D₄	1	2	yes	—
67	C₄×C₂²⋊D₄₃	—	2	2	no	—
68	#13063284	C₂³	1	1	yes	characteristic
69	#13063282	—	2	1	no	—
70	C₄²×D₄₃	—	2	1	no	—
71	#13063261	—	2	2	no	—
72	#13063261	C₂×C₄	1	4	yes	complemented
73	#13063258	—	2	2	no	—
74	#13063256	—	2	2	no	—
75	#13063249	—	2	2	no	—
76	#13063249	—	2	2	no	—
77	#13063248	—	2	2	no	—
78	#13063245	—	2	2	no	—
79	#13063244	—	2	4	no	—
80	#13063244	C₂×C₄	1	8	yes	complemented
81	#13063236	—	2	1	no	—
82	#13063236	—	2	2	no	—
83	#13063235	—	2	1	no	—
84	#13063235	—	2	1	no	—
85	C₄×C₄₃⋊C₈	—	2	1	no	—
86	C₄×C₄₃⋊C₈	—	2	2	no	—
87	C₈×Dic₄₃	—	2	1	no	—
88	C₈×Dic₄₃	—	2	1	no	—
89	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
90	C₂×Q₁₆×C₄₃	—	2	1	no	—
91	C₂×Q₁₆×C₄₃	—	2	1	no	—
92	C₂×Q₁₆×C₄₃	—	2	2	no	—
93	C₂×Q₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
94	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₄₃	—	2	2	no	—
97	C₄×Q₈×C₄₃	—	2	2	no	—
98	C₄×Q₈×C₄₃	—	2	2	no	—
99	C₄×Q₈×C₄₃	—	2	2	no	—
100	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
101	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
102	C₂×C₄²×C₄₃	—	2	2	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#106×C₄₃	—	2	1	no	—
105	#106×C₄₃	—	2	1	no	—
106	#103×C₄₃	—	2	2	no	—
107	#103×C₄₃	—	2	2	no	—
108	#97×C₄₃	D₄	1	1	yes	characteristic
109	#97×C₄₃	D₄	1	1	yes	characteristic
110	#97×C₄₃	D₄	1	1	yes	characteristic
111	#97×C₄₃	D₄	1	1	yes	characteristic
112	C₂×Q₈×C₄₃	—	2	2	no	—
113	C₂×Q₈×C₄₃	—	2	2	no	—
114	C₂×Q₈×C₄₃	—	2	2	no	—
115	C₂×Q₈×C₄₃	—	2	2	no	—
116	C₂×Q₈×C₄₃	—	2	2	no	—
117	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	#41	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
122	C₂×C₂²⋊D₄₃	—	2	1	no	—
123	#10621898	—	2	1	no	—
124	#10621898	—	2	1	no	—
125	#10621898	C₂²×C₄	1	2	yes	—
126	#10621898	#41	1	2	yes	—
127	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×D₄₃	—	2	1	no	—
129	C₂×C₄×D₄₃	—	2	2	no	—
130	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
131	Q₁₆×C₄₃	—	2	4	no	—
132	Q₁₆×C₄₃	—	2	4	no	—
133	C₂×C₈×C₄₃	—	2	1	no	—
134	C₂×C₈×C₄₃	—	2	1	no	—
135	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₃	#41	1	2	yes	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	4	2	no	—
144	C₄⋊C₄×C₄₃	—	4	2	no	—
145	C₄²×C₄₃	—	4	2	no	—
146	C₄²×C₄₃	—	4	2	no	—
147	C₄²×C₄₃	C₂×D₄	1	2	yes	—
148	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂²⋊Dic₄₃	—	2	1	no	—
151	#10621885	—	2	8	no	—
152	#10621884	—	2	8	no	—
153	(C₂×D₄₃)⋊C₄	—	2	2	no	—
154	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
155	Dic₄₃⋊C₄	—	2	2	no	—
156	C₄×Dic₄₃	—	2	2	no	—
157	C₄×Dic₄₃	—	2	1	no	—
158	#10621877	—	2	1	no	—
159	#10621877	—	2	1	no	—
160	#10621877	—	2	2	no	—
161	#10621877	—	2	2	no	—
162	#10621877	—	2	2	no	—
163	#10621877	C₂²×C₄	1	2	yes	—
164	#10621877	C₂²×C₄	1	4	yes	—
165	#10621877	#41	1	2	yes	—
166	C₂×C₄₃⋊C₈	—	2	1	no	—
167	C₂×C₄₃⋊C₈	—	2	1	no	—
168	C₂×C₄₃⋊C₈	—	2	2	no	—
169	C₂×C₄₃⋊C₈	—	2	2	no	—
170	#10621872	—	2	4	no	—
171	#10621872	—	2	4	no	—
172	C₈×D₄₃	—	2	4	no	—
173	C₈×D₄₃	—	2	4	no	—
174	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂²×D₄₃	—	2	1	no	—
176	Q₈×C₄₃	—	2	4	no	—
177	Q₈×C₄₃	—	2	4	no	—
178	Q₈×C₄₃	—	4	2	no	—
179	Q₈×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	8	2	no	—
186	C₂×C₄×C₄₃	#121	1	2	yes	—
187	C₂×C₄×C₄₃	#121	1	2	yes	—
188	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
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	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂²⋊D₄₃	—	2	2	no	—
195	C₂²⋊D₄₃	—	2	2	no	—
196	C₂×Dic₄₃	—	2	1	no	—
197	C₂×Dic₄₃	—	2	2	no	—
198	D₁₇₂	—	2	1	no	—
199	D₁₇₂	C₄×D₄	1	2	yes	—
200	C₄×D₄₃	—	2	2	no	—
201	C₄×D₄₃	—	2	2	no	—
202	C₄×D₄₃	—	8	2	no	—
203	Dic₈₆	—	2	1	no	—
204	Dic₈₆	C₄×D₄	1	2	yes	—
205	C₈×C₄₃	—	2	1	no	—
206	C₈×C₄₃	—	2	1	no	—
207	C₈×C₄₃	C₄×D₄	1	2	yes	—
208	C₈×C₄₃	C₄×D₄	1	2	yes	—
209	C₄₃⋊C₈	—	2	2	no	—
210	C₄₃⋊C₈	—	2	4	no	—
211	C₄₃⋊C₈	—	2	2	no	—
212	C₄₃⋊C₈	—	4	2	no	—
213	#21556	—	43	1	no	maximal, Sylow
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
216	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
217	C₂²×C₄₃	#529	1	1	yes	characteristic
218	C₂×D₄₃	—	2	2	no	—
219	C₂×D₄₃	—	4	2	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	4	4	no	—
223	C₄×C₄₃	—	8	2	no	—
224	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₄₃	#525	1	1	yes	characteristic
227	C₄×C₄₃	#532	1	1	yes	characteristic
228	Dic₄₃	—	2	2	no	—
229	Dic₄₃	—	4	2	no	—
230	C₂×#473	—	43	1	no	—
231	C₄×#137	—	43	2	no	—
232	C₂×#441	D₄₃	1	1	yes	characteristic, complemented
233	#2875	—	43	1	no	—
234	#1979	—	43	1	no	—
235	#1951	—	43	1	no	—
236	#1930	—	43	2	no	—
237	#1908	—	43	2	no	—
238	#1815	—	43	1	no	—
239	#1778	—	43	1	no	—
240	C₄×#101	—	43	2	no	—
241	C₂×C₄₃	—	2	1	no	—
242	C₂×C₄₃	—	2	1	no	—
243	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
244	C₂×C₄₃	#3069	1	2	yes	—
245	D₄₃	—	4	2	no	—
246	C₂×#137	—	43	2	no	—
247	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
248	C₂×#131	—	43	1	no	—
249	C₂×#131	—	43	1	no	—
250	C₄×#41	—	43	1	no	—
251	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
252	#473	—	43	8	no	—
253	#441	—	2	1	no	—
254	#441	—	2	1	no	—
255	#441	—	2	1	no	—
256	#441	—	2	1	no	—
257	#441	—	86	2	no	—
258	#440	—	86	2	no	—
259	C₄×Q₁₆	—	86	2	no	—
260	C₄×SD₁₆	—	86	2	no	—
261	C₂×#108	—	43	1	no	—
262	C₂×#108	—	43	1	no	—
263	#428	—	43	2	no	—
264	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
265	#419	—	43	2	no	—
266	#417	—	43	2	no	—
267	C₂×#103	C₂×D₄₃	1	2	yes	—
268	C₂×#101	—	43	2	no	—
269	C₂×#101	—	43	2	no	—
270	#405	—	43	1	no	—
271	#405	—	43	1	no	—
272	#405	—	86	1	no	—
273	#405	—	86	1	no	—
274	C₄×M₁₆	—	43	1	no	—
275	C₄×M₁₆	—	43	2	no	—
276	C₄×M₁₆	—	86	1	no	—
277	C₂×#97	—	86	1	no	—
278	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
279	#343	—	43	2	no	—
280	#343	—	43	2	no	—
281	#341	—	43	2	no	—
282	C₄₃	#21556	1	1	yes	characteristic, complemented, Sylow
283	C₂×#41	—	43	1	no	—
284	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
285	#137	—	43	8	no	—
286	#137	—	86	4	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×Q₁₆	—	2	1	no	—
289	C₂×Q₁₆	—	2	1	no	—
290	C₂×Q₁₆	—	86	2	no	—
291	C₂×Q₁₆	C₄×D₄₃	1	4	yes	complemented
292	C₂×SD₁₆	—	86	2	no	—
293	#131	—	43	4	no	—
294	#131	—	86	2	no	—
295	#131	—	86	2	no	—
296	#131	—	86	2	no	—
297	C₂×M₁₆	—	43	1	no	—
298	C₂×M₁₆	—	43	1	no	—
299	C₂×M₁₆	—	43	2	no	—
300	C₂×M₁₆	—	43	2	no	—
301	C₂×M₁₆	—	86	1	no	—
302	C₂×M₁₆	—	86	1	no	—
303	C₂²×C₈	—	86	1	no	—
304	C₂²×C₈	—	86	1	no	—
305	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	43	2	no	—
312	C₄×D₄	—	43	2	no	—
313	C₄×D₄	—	86	2	no	—
314	#117	—	43	1	no	—
315	#117	—	86	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	86	1	no	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	#108	—	43	4	no	—
322	#108	—	86	2	no	—
323	#107	—	86	2	no	—
324	#106	—	2	1	no	—
325	#106	—	2	1	no	—
326	#106	—	86	2	no	—
327	#103	—	2	2	no	—
328	#103	—	2	2	no	—
329	#103	—	86	2	no	—
330	#103	—	86	2	no	—
331	#103	—	86	2	no	—
332	#102	—	86	2	no	—
333	#101	—	43	8	no	—
334	#101	—	86	4	no	—
335	#97	—	86	1	no	—
336	#97	—	86	1	no	—
337	#97	—	86	2	no	—
338	#97	—	86	1	no	—
339	#97	C₂²⋊D₄₃	1	1	yes	characteristic
340	#97	C₂²⋊D₄₃	1	1	yes	characteristic
341	#97	C₂²⋊D₄₃	1	1	yes	characteristic
342	#97	C₂²⋊D₄₃	1	1	yes	characteristic
343	C₄×C₈	—	86	1	no	—
344	C₄×C₈	—	86	1	no	—
345	C₄×C₈	—	86	2	no	—
346	C₄×C₈	—	86	1	no	—
347	#41	—	43	2	no	—
348	#41	—	43	2	no	—
349	#41	—	86	1	no	—
350	#41	—	86	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	43	1	no	—
357	C₂×Q₈	C₂×C₄×D₄₃	1	4	yes	—
358	C₂×D₄	—	43	1	no	—
359	C₂×D₄	—	86	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	86	1	no	—
363	C₂²×C₄	—	86	2	no	—
364	C₂²×C₄	#10621900	1	2	yes	—
365	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
366	Q₁₆	—	2	4	no	—
367	Q₁₆	—	2	4	no	—
368	Q₁₆	—	86	8	no	—
369	SD₁₆	—	86	8	no	—
370	M₁₆	—	43	2	no	—
371	M₁₆	—	43	4	no	—
372	M₁₆	—	43	2	no	—
373	M₁₆	—	86	4	no	—
374	M₁₆	—	86	1	no	—
375	M₁₆	—	86	2	no	—
376	M₁₆	—	86	1	no	—
377	M₁₆	—	86	4	no	—
378	M₁₆	—	86	2	no	—
379	M₁₆	—	86	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	86	4	no	—
383	C₂×C₈	—	86	2	no	—
384	C₂×C₈	—	86	1	no	—
385	C₂×C₈	—	86	1	no	—
386	C₂×C₈	—	86	4	no	—
387	C₂×C₈	—	86	2	no	—
388	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
389	C₂×C₈	#10621898	1	2	yes	—
390	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
391	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
392	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
393	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	43	2	no	—
399	C₄⋊C₄	—	86	2	no	—
400	C₂²⋊C₄	—	86	1	no	—
401	C₂²⋊C₄	—	86	2	no	—
402	C₄²	—	4	2	no	—
403	C₄²	—	4	2	no	—
404	C₄²	—	86	2	no	—
405	C₄²	—	86	1	no	—
406	C₄²	D₄×D₄₃	1	2	yes	—
407	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
409	C₂³	—	86	1	no	—
410	C₂³	C₂×#10621900	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	43	2	no	—
416	Q₈	—	86	1	no	—
417	D₄	—	43	2	no	—
418	D₄	—	86	2	no	—
419	D₄	—	86	2	no	—
420	D₄	—	86	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	2	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	—	86	1	no	—
428	C₂×C₄	—	86	2	no	—
429	C₂×C₄	—	86	2	no	—
430	C₂×C₄	—	86	2	no	—
431	C₂×C₄	—	344	2	no	—
432	C₂×C₄	#13063296	1	2	yes	—
433	C₂×C₄	#13063296	1	2	yes	—
434	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
437	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
438	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
440	C₈	—	2	1	no	—
441	C₈	—	2	1	no	—
442	C₈	—	86	4	no	—
443	C₈	—	86	2	no	—
444	C₈	—	86	2	no	—
445	C₈	—	172	2	no	—
446	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
447	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
448	C₂²	—	2	2	no	—
449	C₂²	—	86	2	no	—
450	C₂²	—	172	2	no	—
451	C₂²	C₄×#10621900	1	1	yes	characteristic
452	C₂²	C₂×#13063296	1	1	yes	characteristic
453	C₂²	#14583431	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	—	86	2	no	—
459	C₄	—	172	2	no	—
460	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
461	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
462	C₄	#14583406	1	1	yes	characteristic
463	C₄	#14583446	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	172	2	no	—
467	C₂	C₄×#13063296	1	1	yes	characteristic
468	C₂	#19144328	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#441	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂×#10621898	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#441	D₄₃
hypocenter	C₄₃	#21556
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#441

Complements

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

N	H ≅ G/N	type
4. #19135511	C₂	semidirect
5. #19135373	C₂	semidirect
6. #19135247	C₂	semidirect
9. #19134501	C₂	semidirect
10. C₄×#13063244	C₂	semidirect
11. C₂×C₄₃×#441	C₂	semidirect
16. #14583171	C₄	semidirect
72. #13063261	C₂×C₄	semidirect
80. #13063244	C₂×C₄	semidirect
93. C₂×Q₁₆×C₄₃	C₂×C₄	semidirect
232. C₂×#441	D₄₃	semidirect
282. C₄₃	#21556	semidirect
291. C₂×Q₁₆	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×#14583171	2
C₄×#13063356	2
#19143020	2
#19135511	2
#19135373	2
#19135247	2
#19135113	2
#19134655	2
#19134501	2
C₄×#13063244	2
C₂×C₄₃×#441	2
#21556	43