Subgroups — #25079728

Order 11008.

638 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	#19145912	C₂	1	1	yes	maximal, characteristic
2	#19145907	C₂	1	1	yes	maximal, characteristic
3	#19145105	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143306	C₂	1	1	yes	maximal, characteristic
5	#19134097	C₂	1	2	yes	maximal, complemented
6	#19134093	C₂	1	2	yes	maximal, complemented
7	#19133993	C₂	1	2	yes	maximal, complemented
8	#19133983	C₂	1	2	yes	maximal, complemented
9	C₂×#14582651	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133286	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063333	—	2	1	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	#14583449	C₂²	1	1	yes	characteristic
15	#14583302	C₂²	1	1	yes	characteristic
16	#14583302	C₂²	1	1	yes	characteristic
17	#14583298	—	2	1	no	—
18	#14583298	—	2	1	no	—
19	#14583295	C₂²	1	1	yes	characteristic
20	#14583295	C₂²	1	1	yes	characteristic
21	#14583190	C₂²	1	2	yes	—
22	#14583186	C₂²	1	2	yes	—
23	#14583185	—	2	1	no	—
24	#14583184	—	2	1	no	—
25	#14583130	—	2	2	no	—
26	#14583128	—	2	2	no	—
27	#14583105	C₂²	1	2	yes	—
28	#14583101	C₂²	1	2	yes	—
29	#14583100	—	2	1	no	—
30	#14583099	—	2	1	no	—
31	#14582976	—	2	1	no	—
32	#14582976	C₂²	1	2	yes	—
33	#14582964	—	2	1	no	—
34	#14582964	C₂²	1	2	yes	—
35	#14582935	—	2	1	no	—
36	#14582935	—	2	1	no	—
37	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
38	#14582867	—	2	1	no	—
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
40	#14582651	C₂²	1	2	yes	—
41	#14582651	C₂²	1	2	yes	—
42	#14582647	C₂²	1	2	yes	—
43	#14582644	C₂²	1	2	yes	—
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	—
48	C₄₃×#332	C₂²	1	2	yes	—
49	C₂×#10621898	—	2	1	no	—
50	C₂×#10621873	—	2	2	no	—
51	C₂×#10621884	—	2	2	no	—
52	#13063333	—	4	4	no	—
53	C₂×#10621872	—	2	2	no	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
56	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
57	C₂×C₈×D₄₃	—	2	2	no	—
58	#13063325	D₄	1	1	yes	characteristic
59	#13063325	C₂³	1	1	yes	characteristic
60	#13063325	C₂³	1	1	yes	characteristic
61	#13063322	D₄	1	1	yes	characteristic
62	#13063317	—	2	1	no	—
63	#13063313	—	2	1	no	—
64	#13063304	—	2	1	no	—
65	#13063304	—	2	1	no	—
66	#13063299	—	2	1	no	—
67	#13063299	D₄	1	2	yes	—
68	C₄×Dic₈₆	—	2	1	no	—
69	C₄×Dic₈₆	—	2	1	no	—
70	C₄×D₁₇₂	—	2	1	no	—
71	C₄×D₁₇₂	C₂³	1	2	yes	—
72	#13063284	—	2	1	no	—
73	#13063258	—	2	1	no	—
74	#13063258	—	2	1	no	—
75	#13063258	—	2	1	no	—
76	#13063258	—	2	1	no	—
77	#13063257	—	2	2	no	—
78	#13063256	—	2	2	no	—
79	#13063256	—	2	1	no	—
80	#13063256	—	2	1	no	—
81	#13063256	—	2	1	no	—
82	#13063256	—	2	1	no	—
83	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
84	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
85	#13063250	—	2	2	no	—
86	#13063249	—	2	2	no	—
87	#13063247	—	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	C₂×Q₈×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
115	C₂×C₂²⋊D₄₃	—	2	2	no	—
116	#10621898	—	4	2	no	—
117	#10621898	—	4	2	no	—
118	C₂×D₁₇₂	—	2	1	no	—
119	C₂×D₁₇₂	—	2	1	no	—
120	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
121	C₂×C₄×D₄₃	—	2	2	no	—
122	C₂×Dic₈₆	—	2	1	no	—
123	C₂×Dic₈₆	—	2	1	no	—
124	C₂×Dic₈₆	—	2	1	no	—
125	M₁₆×C₄₃	—	4	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	8	1	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	4	1	no	—
134	C₄⋊C₄×C₄₃	—	4	1	no	—
135	C₂²⋊C₄×C₄₃	—	4	1	no	—
136	C₄²×C₄₃	—	4	1	no	—
137	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	#41	1	1	yes	characteristic
140	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
141	C₂²⋊Dic₄₃	—	4	1	no	—
142	#10621884	—	8	2	no	—
143	(C₂×D₄₃)⋊C₄	—	2	2	no	—
144	(C₂×D₄₃)⋊C₄	—	2	2	no	—
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
151	Dic₄₃⋊C₄	—	4	1	no	—
152	Dic₄₃⋊C₄	—	4	1	no	—
153	C₄×Dic₄₃	—	4	1	no	—
154	C₂×C₄₃⋊C₈	—	2	2	no	—
155	C₂×C₄₃⋊C₈	—	2	2	no	—
156	C₂×C₄₃⋊C₈	—	8	1	no	—
157	C₂×C₄₃⋊C₈	SD₁₆	1	4	yes	complemented
158	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	#10621873	—	8	2	no	—
163	#10621872	—	4	4	no	—
164	C₈×D₄₃	—	4	4	no	—
165	C₂³×C₄₃	#121	1	1	yes	characteristic
166	C₂²×D₄₃	—	2	2	no	—
167	Q₈×C₄₃	—	4	1	no	—
168	Q₈×C₄₃	—	4	1	no	—
169	Q₈×C₄₃	—	8	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₄₃	#137	1	2	yes	—
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂²⋊D₄₃	—	4	4	no	—
184	C₂×Dic₄₃	—	2	2	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	4	1	no	—
187	D₁₇₂	—	2	2	no	—
188	D₁₇₂	—	2	2	no	—
189	D₁₇₂	—	4	2	no	—
190	D₁₇₂	—	4	2	no	—
191	C₄×D₄₃	—	4	2	no	—
192	C₄×D₄₃	—	4	2	no	—
193	Dic₈₆	—	4	2	no	—
194	Dic₈₆	—	4	1	no	—
195	Dic₈₆	—	4	1	no	—
196	Dic₈₆	—	8	1	no	—
197	C₈×C₄₃	—	4	2	no	—
198	C₈×C₄₃	—	4	2	no	—
199	C₄₃⋊C₈	—	2	1	no	—
200	C₄₃⋊C₈	—	2	1	no	—
201	C₄₃⋊C₈	—	4	2	no	—
202	C₄₃⋊C₈	C₂×SD₁₆	1	2	yes	—
203	C₄₃⋊C₈	C₂×SD₁₆	1	2	yes	—
204	#19195	—	43	1	no	maximal, Sylow
205	C₂²×C₄₃	—	2	1	no	—
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	#461	1	2	yes	—
208	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
209	C₂×D₄₃	—	4	2	no	—
210	C₂×D₄₃	—	4	2	no	—
211	C₂×D₄₃	—	4	2	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	2	1	no	—
214	C₄×C₄₃	—	2	1	no	—
215	C₄×C₄₃	—	8	1	no	—
216	C₄×C₄₃	—	8	1	no	—
217	C₄×C₄₃	#461	1	2	yes	—
218	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
219	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
220	C₄×C₄₃	#576	1	1	yes	characteristic
221	C₄×C₄₃	#578	1	1	yes	characteristic
222	Dic₄₃	—	4	2	no	—
223	Dic₄₃	—	8	1	no	—
224	Dic₄₃	—	8	1	no	—
225	#3246	—	43	1	no	—
226	#3246	—	43	1	no	—
227	#3160	—	43	1	no	—
228	#2931	—	43	1	no	—
229	#1691	—	43	2	no	—
230	#1691	—	43	2	no	—
231	#1675	—	43	2	no	—
232	#1673	—	43	2	no	—
233	C₂×#335	—	43	1	no	—
234	#1550	—	43	1	no	—
235	#1550	D₄₃	1	1	yes	characteristic, complemented
236	C₂×C₄₃	—	2	2	no	—
237	C₂×C₄₃	C₂×#461	1	1	yes	characteristic
238	C₂×C₄₃	#3061	1	1	yes	characteristic
239	C₂×C₄₃	#3067	1	1	yes	characteristic
240	D₄₃	—	8	2	no	—
241	C₂×#131	—	86	1	no	—
242	#533	—	43	1	no	—
243	#533	C₂×D₄₃	1	1	yes	characteristic
244	#532	—	43	1	no	—
245	#500	—	43	1	no	—
246	#500	—	43	1	no	—
247	#499	—	86	1	no	—
248	#499	—	86	1	no	—
249	#498	—	43	1	no	—
250	#498	—	43	1	no	—
251	#476	—	43	2	no	—
252	#476	—	43	2	no	—
253	#475	—	86	1	no	—
254	#475	—	86	1	no	—
255	#465	—	86	2	no	—
256	#465	—	86	2	no	—
257	#461	—	43	2	no	—
258	#461	—	43	2	no	—
259	#460	—	86	1	no	—
260	#460	—	86	1	no	—
261	#436	—	43	2	no	—
262	#436	—	86	1	no	—
263	C₈×D₄	—	43	2	no	—
264	C₈×D₄	—	86	1	no	—
265	#427	—	86	1	no	—
266	#427	—	86	1	no	—
267	#423	C₂×D₄₃	1	1	yes	characteristic
268	C₂×C₄⋊C₈	—	43	1	no	—
269	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
270	#408	—	86	1	no	—
271	C₂×C₄×C₈	—	43	1	no	—
272	#335	—	43	2	no	—
273	#335	—	43	2	no	—
274	#333	—	43	2	no	—
275	#333	C₂×D₄₃	1	2	yes	—
276	#332	—	43	2	no	—
277	#332	C₂×D₄₃	1	2	yes	—
278	C₄₃	#19195	1	1	yes	characteristic, complemented, Sylow
279	C₂×#41	—	86	1	no	—
280	C₂×SD₁₆	—	86	2	no	—
281	C₂×SD₁₆	—	86	2	no	—
282	#131	—	172	4	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	86	2	no	—
285	C₂²×C₈	—	2	1	no	—
286	C₂²×C₈	—	43	1	no	—
287	C₂²×C₈	—	43	1	no	—
288	C₂²×C₈	—	86	2	no	—
289	C₂²×C₈	—	86	1	no	—
290	C₄⋊Q₈	—	43	1	no	—
291	C₄⋊Q₈	—	43	1	no	—
292	C₄⋊Q₈	—	43	1	no	—
293	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
294	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
295	#127	—	43	1	no	—
296	#125	—	2	1	no	—
297	#125	—	86	1	no	—
298	#124	—	86	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	86	1	no	—
302	C₂²⋊Q₈	—	86	1	no	—
303	#121	—	43	2	no	—
304	#121	—	86	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	86	1	no	—
308	C₄×Q₈	—	86	1	no	—
309	C₄×D₄	—	43	2	no	—
310	C₄×D₄	—	86	1	no	—
311	#117	—	2	1	no	—
312	#117	—	86	1	no	—
313	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
314	#107	—	86	1	no	—
315	#107	—	86	1	no	—
316	#107	—	86	1	no	—
317	#107	—	86	1	no	—
318	#106	—	86	2	no	—
319	#106	—	86	1	no	—
320	#106	—	86	1	no	—
321	#106	—	86	1	no	—
322	#106	—	86	1	no	—
323	#106	—	86	2	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	43	2	no	—
327	C₄⋊C₈	—	86	1	no	—
328	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
329	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
330	#103	—	86	2	no	—
331	#103	—	86	2	no	—
332	#102	—	86	2	no	—
333	#102	—	86	2	no	—
334	C₂²⋊C₈	—	86	2	no	—
335	C₂²⋊C₈	—	86	2	no	—
336	C₄×C₈	—	43	1	no	—
337	C₄×C₈	—	43	1	no	—
338	C₄×C₈	—	43	1	no	—
339	C₄×C₈	—	43	1	no	—
340	#41	—	172	2	no	—
341	#41	—	172	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	86	1	no	—
345	C₂×Q₈	—	86	1	no	—
346	C₂×Q₈	—	86	1	no	—
347	C₂×D₄	—	43	2	no	—
348	C₂×D₄	—	86	2	no	—
349	C₂×D₄	—	86	1	no	—
350	C₂×D₄	—	86	1	no	—
351	C₂²×C₄	—	86	2	no	—
352	C₂²×C₄	#10621898	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
355	SD₁₆	—	344	2	no	—
356	SD₁₆	—	344	2	no	—
357	M₁₆	—	4	2	no	—
358	M₁₆	—	172	4	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	8	1	no	—
362	C₂×C₈	—	43	4	no	—
363	C₂×C₈	—	43	1	no	—
364	C₂×C₈	—	43	1	no	—
365	C₂×C₈	—	43	1	no	—
366	C₂×C₈	—	43	1	no	—
367	C₂×C₈	—	86	2	no	—
368	C₂×C₈	—	86	2	no	—
369	C₂×C₈	—	344	1	no	—
370	C₂×C₈	—	172	4	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	43	2	no	—
378	C₄⋊C₄	—	86	1	no	—
379	C₄⋊C₄	—	86	1	no	—
380	C₄⋊C₄	—	86	1	no	—
381	C₄⋊C₄	—	86	1	no	—
382	C₄⋊C₄	—	86	1	no	—
383	C₄⋊C₄	—	172	1	no	—
384	C₄⋊C₄	—	172	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	86	2	no	—
387	C₂²⋊C₄	—	86	2	no	—
388	C₂²⋊C₄	—	172	1	no	—
389	C₄²	—	4	1	no	—
390	C₄²	—	172	1	no	—
391	C₄²	#10621898	1	1	yes	characteristic
392	C₄²	D₄×D₄₃	1	1	yes	characteristic
393	C₄²	D₄×D₄₃	1	1	yes	characteristic
394	C₄²	C₂³×D₄₃	1	1	yes	characteristic
395	C₂³	—	86	2	no	—
396	C₂³	#13063298	1	1	yes	characteristic
397	Q₈	—	4	1	no	—
398	Q₈	—	4	1	no	—
399	Q₈	—	8	1	no	—
400	Q₈	—	344	1	no	—
401	Q₈	—	172	1	no	—
402	Q₈	—	172	1	no	—
403	Q₈	—	172	2	no	—
404	D₄	—	86	2	no	—
405	D₄	—	86	2	no	—
406	D₄	—	172	2	no	—
407	D₄	—	172	4	no	—
408	D₄	—	172	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	86	2	no	—
415	C₂×C₄	—	172	1	no	—
416	C₂×C₄	—	172	1	no	—
417	C₂×C₄	—	172	2	no	—
418	C₂×C₄	—	172	2	no	—
419	C₂×C₄	#13063298	1	1	yes	characteristic
420	C₂×C₄	#13063298	1	1	yes	characteristic
421	C₂×C₄	#13063298	1	1	yes	characteristic
422	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
423	C₂×C₄	#13063357	1	2	yes	—
424	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
425	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₈	—	43	2	no	—
430	C₈	—	43	2	no	—
431	C₈	—	86	1	no	—
432	C₈	—	86	1	no	—
433	C₈	—	172	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	172	2	no	—
437	C₂²	—	172	2	no	—
438	C₂²	—	172	2	no	—
439	C₂²	#14583103	1	2	yes	—
440	C₂²	C₂×#13063298	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	8	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	344	1	no	—
447	C₄	—	344	1	no	—
448	C₄	—	172	2	no	—
449	C₄	#14583103	1	2	yes	—
450	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
451	C₄	C₂×#13063357	1	1	yes	characteristic
452	C₄	#14583703	1	1	yes	characteristic
453	C₄	#14583715	1	1	yes	characteristic
454	C₂	—	2	2	no	—
455	C₂	—	344	2	no	—
456	C₂	C₂×#14583103	1	1	yes	characteristic
457	C₂	#19144264	1	1	yes	characteristic
458	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	#14583449	C₂²
hypercenter	#1550	D₄₃
hypocenter	C₄₃	#19195
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
3. #19145105	C₂	semidirect
5. #19134097	C₂	semidirect
6. #19134093	C₂	semidirect
7. #19133993	C₂	semidirect
8. #19133983	C₂	semidirect
9. C₂×#14582651	C₂	semidirect
10. #19133286	C₂	semidirect
11. C₄₃×#1550	C₂	semidirect
157. C₂×C₄₃⋊C₈	SD₁₆	semidirect
235. #1550	D₄₃	semidirect
278. C₄₃	#19195	semidirect

Maximal subgroups

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

subgroup	index
#19145912	2
#19145907	2
#19145105	2
#19143306	2
#19134097	2
#19134093	2
#19133993	2
#19133983	2
C₂×#14582651	2
#19133286	2
C₄₃×#1550	2
#19195	43