Subgroups — #25084480

Order 11008.

836 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145746	C₂	1	1	yes	maximal, characteristic, complemented
2	#19145513	C₂	1	1	yes	maximal, characteristic
3	#19145154	C₂	1	1	yes	maximal, characteristic, complemented
4	#19144991	C₂	1	1	yes	maximal, characteristic, complemented
5	#19144969	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134246	C₂	1	2	yes	maximal, complemented
7	#19134232	C₂	1	2	yes	maximal, complemented
8	#19134194	C₂	1	2	yes	maximal, complemented
9	#19134185	C₂	1	2	yes	maximal, complemented
10	C₈×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583456	C₂²	1	1	yes	characteristic
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583302	C₂²	1	2	yes	complemented
15	#14583297	C₂²	1	1	yes	characteristic, complemented
16	#14583275	C₂²	1	2	yes	—
17	#14583272	C₂²	1	1	yes	characteristic, complemented
18	#14583263	—	2	2	no	—
19	#14583261	—	2	2	no	—
20	#14583251	C₂²	1	2	yes	complemented
21	#14583251	C₂²	1	2	yes	complemented
22	#14583250	C₂²	1	1	yes	characteristic, complemented
23	#14583247	C₂²	1	2	yes	complemented
24	#14583246	C₂²	1	1	yes	characteristic, complemented
25	#14583245	C₂²	1	2	yes	—
26	#14583245	C₂²	1	2	yes	—
27	#14583245	C₂²	1	2	yes	—
28	#14583234	—	2	2	no	—
29	#14583191	—	2	2	no	—
30	#14583128	—	2	2	no	—
31	#14583091	—	2	2	no	—
32	#14583033	—	2	2	no	—
33	C₄×#10621873	—	2	2	no	—
34	#14582952	C₂²	1	1	yes	characteristic
35	#14582904	—	2	2	no	—
36	#14582898	—	2	2	no	—
37	C₄×#10621877	C₂²	1	1	yes	characteristic
38	#14582621	C₂²	1	2	yes	complemented
39	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
40	C₂²×SD₁₆×C₄₃	—	2	2	no	—
41	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#492	—	2	2	no	—
44	C₄₃×#492	C₂²	1	2	yes	—
45	C₄₃×#492	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621873	—	2	2	no	—
49	C₂×#10621882	—	2	4	no	—
50	C₂×#10621877	D₄	1	2	yes	—
51	#13063325	C₂³	1	1	yes	characteristic
52	#13063325	C₂³	1	1	yes	characteristic
53	#13063325	C₂³	1	1	yes	characteristic
54	#13063322	C₂³	1	1	yes	characteristic
55	#13063317	—	2	1	no	—
56	#13063313	—	2	1	no	—
57	#13063304	—	2	1	no	—
58	#13063304	—	2	1	no	—
59	#13063299	—	2	1	no	—
60	#13063299	—	2	1	no	—
61	C₄×Dic₈₆	—	2	1	no	—
62	C₄×Dic₈₆	—	2	1	no	—
63	C₄×D₁₇₂	—	2	1	no	—
64	C₄×D₁₇₂	—	2	1	no	—
65	#13063284	—	2	1	no	—
66	#13063258	—	2	4	no	—
67	#13063257	—	2	2	no	—
68	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
69	#13063250	—	2	2	no	—
70	#13063248	—	2	4	no	—
71	#13063248	—	2	4	no	—
72	#13063247	—	2	2	no	—
73	#13063246	—	2	4	no	—
74	#13063246	—	2	4	no	—
75	#13063246	—	2	4	no	—
76	#13063245	—	2	4	no	—
77	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
78	#13063236	D₄	1	2	yes	—
79	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
80	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
81	C₂²×Q₈×C₄₃	—	2	1	no	—
82	C₂²×D₄×C₄₃	—	2	1	no	—
83	C₂²×D₄×C₄₃	—	2	1	no	—
84	C₂²×D₄×C₄₃	—	2	1	no	—
85	C₂×SD₁₆×C₄₃	—	2	4	no	—
86	C₂×SD₁₆×C₄₃	—	2	4	no	—
87	C₂×SD₁₆×C₄₃	—	4	8	no	—
88	C₂²×C₈×C₄₃	D₄	1	2	yes	—
89	C₄⋊Q₈×C₄₃	—	2	1	no	—
90	C₄⋊Q₈×C₄₃	—	2	1	no	—
91	C₄⋊Q₈×C₄₃	—	2	1	no	—
92	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
93	#127×C₄₃	—	2	1	no	—
94	#127×C₄₃	—	2	1	no	—
95	#127×C₄₃	—	2	1	no	—
96	#127×C₄₃	C₂³	1	2	yes	—
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	C₄×C₈×C₄₃	D₄	1	2	yes	—
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂⁴×C₄₃	—	4	1	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	4	4	no	—
106	C₂×Q₈×C₄₃	—	4	1	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	4	1	no	—
111	C₂×D₄×C₄₃	—	4	1	no	—
112	C₂×D₄×C₄₃	—	4	1	no	—
113	C₂×D₄×C₄₃	—	4	4	no	—
114	C₂×D₄×C₄₃	—	4	4	no	—
115	C₂×D₄×C₄₃	—	8	2	no	—
116	C₂²×C₄×C₄₃	—	4	1	no	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₂²⋊D₄₃	—	4	1	no	—
121	#10621898	—	4	4	no	—
122	C₂×D₁₇₂	—	2	1	no	—
123	C₂×D₁₇₂	—	2	1	no	—
124	C₂×D₁₇₂	—	2	1	no	—
125	C₂×C₄×D₄₃	—	4	1	no	—
126	C₂×Dic₈₆	—	2	1	no	—
127	C₂×Dic₈₆	—	2	1	no	—
128	C₂×Dic₈₆	—	2	1	no	—
129	SD₁₆×C₄₃	—	4	8	no	—
130	SD₁₆×C₄₃	—	4	8	no	—
131	C₂×C₈×C₄₃	—	2	4	no	—
132	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	4	1	no	—
137	C₄⋊C₄×C₄₃	—	4	1	no	—
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
142	C₂²⋊Dic₄₃	—	4	1	no	—
143	#10621882	—	8	4	no	—
144	(C₂×D₄₃)⋊C₄	—	4	1	no	—
145	(C₂×D₄₃)⋊C₄	—	4	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	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	Dic₄₃⋊C₄	—	4	1	no	—
153	Dic₄₃⋊C₄	—	4	1	no	—
154	C₄×Dic₄₃	—	4	1	no	—
155	#10621877	—	2	4	no	—
156	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
157	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
158	#10621873	—	4	4	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	—	8	2	no	—
161	C₂³×C₄₃	—	8	2	no	—
162	C₂³×C₄₃	—	8	2	no	—
163	C₂³×C₄₃	#127	1	1	yes	characteristic
164	C₂²×D₄₃	—	4	1	no	—
165	Q₈×C₄₃	—	4	4	no	—
166	Q₈×C₄₃	—	8	2	no	—
167	D₄×C₄₃	—	4	4	no	—
168	D₄×C₄₃	—	4	4	no	—
169	D₄×C₄₃	—	4	4	no	—
170	D₄×C₄₃	—	8	2	no	—
171	D₄×C₄₃	—	8	2	no	—
172	D₄×C₄₃	—	8	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	8	2	no	—
177	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
179	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
180	C₂×C₄×C₄₃	#135	1	4	yes	—
181	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
184	C₂²⋊D₄₃	—	8	2	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	4	1	no	—
187	C₂×Dic₄₃	—	4	1	no	—
188	D₁₇₂	—	4	2	no	—
189	D₁₇₂	—	4	2	no	—
190	D₁₇₂	—	4	2	no	—
191	C₄×D₄₃	—	8	2	no	—
192	Dic₈₆	—	4	2	no	—
193	Dic₈₆	—	4	2	no	—
194	Dic₈₆	—	4	2	no	—
195	C₈×C₄₃	—	2	2	no	—
196	C₈×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
197	C₄₃⋊C₈	—	2	4	no	—
198	C₄₃⋊C₈	—	2	4	no	—
199	#19625	—	43	1	no	maximal, Sylow
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	8	2	no	—
203	C₂²×C₄₃	—	8	2	no	—
204	C₂²×C₄₃	—	8	2	no	—
205	C₂²×C₄₃	—	16	4	no	—
206	C₂²×C₄₃	#495	1	2	yes	—
207	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
208	C₂×D₄₃	—	8	1	no	—
209	C₂×D₄₃	—	8	1	no	—
210	C₂×D₄₃	—	8	1	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	8	2	no	—
214	C₄×C₄₃	#495	1	2	yes	—
215	C₄×C₄₃	C₂×#135	1	2	yes	—
216	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
217	C₄×C₄₃	#577	1	2	yes	—
218	Dic₄₃	—	8	1	no	—
219	Dic₄₃	—	8	1	no	—
220	Dic₄₃	—	8	1	no	—
221	#3230	—	43	1	no	—
222	#3205	—	43	1	no	—
223	#3167	—	43	1	no	—
224	C₂×#492	D₄₃	1	1	yes	characteristic, complemented
225	#3141	—	43	1	no	—
226	#3138	—	43	1	no	—
227	#1719	—	43	2	no	—
228	#1717	—	43	2	no	—
229	#1708	—	43	2	no	—
230	#1706	—	43	2	no	—
231	C₈×M₁₆	—	43	1	no	—
232	C₂×C₄₃	—	2	2	no	—
233	C₂×C₄₃	—	16	2	no	—
234	C₂×C₄₃	C₂×#495	1	1	yes	characteristic
235	C₂×C₄₃	#3151	1	1	yes	characteristic
236	C₂×C₄₃	#3154	1	1	yes	characteristic
237	D₄₃	—	16	1	no	—
238	C₂²×SD₁₆	—	2	2	no	—
239	#533	—	43	1	no	—
240	#532	—	43	1	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
242	C₂×#127	C₂×D₄₃	1	1	yes	characteristic
243	#500	—	43	2	no	—
244	#498	—	43	1	no	—
245	#493	—	43	2	no	—
246	#492	—	2	2	no	—
247	#492	—	43	1	no	—
248	#492	C₂×D₄₃	1	2	yes	—
249	#492	C₂×D₄₃	1	2	yes	—
250	#490	—	86	2	no	—
251	#489	—	86	2	no	—
252	#487	—	43	2	no	—
253	#487	—	43	2	no	—
254	#487	—	43	1	no	—
255	#486	—	43	2	no	—
256	#486	—	43	2	no	—
257	#486	—	43	2	no	—
258	#486	—	43	2	no	—
259	#486	—	43	1	no	—
260	#484	—	86	2	no	—
261	#477	—	86	2	no	—
262	#465	—	86	2	no	—
263	#459	—	86	2	no	—
264	#447	—	86	2	no	—
265	C₄×SD₁₆	—	86	2	no	—
266	#431	—	43	1	no	—
267	#418	—	86	2	no	—
268	#417	—	86	2	no	—
269	C₄×M₁₆	—	43	1	no	—
270	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
271	#322	—	43	2	no	—
272	C₈²	—	43	2	no	—
273	C₄₃	#19625	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	86	1	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂×SD₁₆	—	2	4	no	—
280	C₂×SD₁₆	—	2	4	no	—
281	C₂×SD₁₆	—	4	8	no	—
282	C₂×SD₁₆	—	86	2	no	—
283	C₂×D₈	—	86	4	no	—
284	C₂×M₁₆	—	43	2	no	—
285	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	43	1	no	—
290	C₄⋊Q₈	—	43	1	no	—
291	C₄⋊Q₈	—	43	1	no	—
292	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
293	#127	—	2	1	no	—
294	#127	—	2	1	no	—
295	#127	—	2	1	no	—
296	#127	—	43	1	no	—
297	#127	C₂²×D₄₃	1	2	yes	—
298	#125	—	86	1	no	—
299	#124	—	86	1	no	—
300	C₂²⋊Q₈	—	86	1	no	—
301	C₂²⋊Q₈	—	86	1	no	—
302	#121	—	86	1	no	—
303	#121	—	86	1	no	—
304	C₄×Q₈	—	86	1	no	—
305	C₄×Q₈	—	86	1	no	—
306	C₄×D₄	—	86	1	no	—
307	C₄×D₄	—	86	1	no	—
308	#117	—	86	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
312	#107	—	86	4	no	—
313	#106	—	86	2	no	—
314	C₄⋊C₈	—	43	2	no	—
315	#103	—	86	4	no	—
316	#103	—	86	4	no	—
317	#103	—	86	2	no	—
318	#102	—	86	4	no	—
319	#102	—	86	4	no	—
320	#102	—	86	4	no	—
321	#102	—	86	4	no	—
322	#102	—	86	2	no	—
323	C₂²⋊C₈	—	43	2	no	—
324	#97	—	43	2	no	—
325	C₄×C₈	—	43	2	no	—
326	C₄×C₈	—	43	2	no	—
327	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
328	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
330	C₂⁴	—	4	1	no	—
331	#41	—	172	4	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	4	4	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×Q₈	—	86	1	no	—
336	C₂×Q₈	—	86	1	no	—
337	C₂×Q₈	—	86	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	4	no	—
346	C₂×D₄	—	8	2	no	—
347	C₂×D₄	—	86	1	no	—
348	C₂×D₄	—	86	1	no	—
349	C₂×D₄	—	86	1	no	—
350	C₂×D₄	—	172	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	172	1	no	—
353	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
356	SD₁₆	—	4	8	no	—
357	SD₁₆	—	4	8	no	—
358	SD₁₆	—	172	4	no	—
359	D₈	—	344	4	no	—
360	M₁₆	—	86	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	43	4	no	—
363	C₂×C₈	—	43	4	no	—
364	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
365	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	86	1	no	—
372	C₄⋊C₄	—	86	1	no	—
373	C₄⋊C₄	—	86	1	no	—
374	C₄⋊C₄	—	86	1	no	—
375	C₄⋊C₄	—	86	1	no	—
376	C₄⋊C₄	—	172	1	no	—
377	C₄⋊C₄	—	172	1	no	—
378	C₂²⋊C₄	—	172	1	no	—
379	C₂²⋊C₄	—	172	1	no	—
380	C₂²⋊C₄	—	172	1	no	—
381	C₄²	—	172	1	no	—
382	C₄²	D₄×D₄₃	1	1	yes	characteristic
383	C₄²	D₄×D₄₃	1	1	yes	characteristic
384	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
385	C₄²	C₂³×D₄₃	1	1	yes	characteristic
386	C₂³	—	4	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	—	8	2	no	—
390	C₂³	—	172	1	no	—
391	C₂³	#13063321	1	1	yes	characteristic
392	Q₈	—	4	4	no	—
393	Q₈	—	8	2	no	—
394	Q₈	—	172	2	no	—
395	Q₈	—	172	2	no	—
396	Q₈	—	172	2	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	4	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	344	2	no	—
404	D₄	—	172	2	no	—
405	D₄	—	172	2	no	—
406	D₄	—	172	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	8	2	no	—
411	C₂×C₄	—	344	2	no	—
412	C₂×C₄	—	172	1	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	—	172	1	no	—
415	C₂×C₄	#13063321	1	1	yes	characteristic
416	C₂×C₄	#13063321	1	1	yes	characteristic
417	C₂×C₄	#13063321	1	1	yes	characteristic
418	C₂×C₄	#13063346	1	4	yes	—
419	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	86	4	no	—
424	C₈	—	86	4	no	—
425	C₈	#13063351	1	4	yes	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	16	4	no	—
432	C₂²	—	344	1	no	—
433	C₂²	—	344	1	no	—
434	C₂²	—	344	1	no	—
435	C₂²	#14583280	1	2	yes	—
436	C₂²	C₂×#13063321	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	8	2	no	—
440	C₄	—	344	1	no	—
441	C₄	—	344	1	no	—
442	C₄	—	344	1	no	—
443	C₄	#14583280	1	2	yes	—
444	C₄	C₂×#13063346	1	2	yes	—
445	C₄	C₂×#13063351	1	2	yes	—
446	C₄	#14583705	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	—	16	2	no	—
449	C₂	—	688	1	no	—
450	C₂	C₂×#14583280	1	1	yes	characteristic
451	C₂	#19145045	1	1	yes	characteristic
452	C₂	#19145065	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063321
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#492	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	#19145513	C₂
hypercenter	C₂×#492	D₄₃
hypocenter	C₄₃	#19625
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#492

Complements

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

N	H ≅ G/N	type
1. #19145746	C₂	semidirect
3. #19145154	C₂	semidirect
4. #19144991	C₂	semidirect
5. #19144969	C₂	semidirect
6. #19134246	C₂	semidirect
7. #19134232	C₂	semidirect
8. #19134194	C₂	semidirect
9. #19134185	C₂	semidirect
10. C₈×#10621877	C₂	semidirect
11. C₂×C₄₃×#492	C₂	semidirect
14. #14583302	C₂²	semidirect
15. #14583297	C₂²	semidirect
17. #14583272	C₂²	semidirect
20. #14583251	C₂²	semidirect
21. #14583251	C₂²	semidirect
22. #14583250	C₂²	semidirect
23. #14583247	C₂²	semidirect
24. #14583246	C₂²	semidirect
38. #14582621	C₂²	semidirect
39. C₈×C₄₃⋊C₈	C₂²	semidirect
224. C₂×#492	D₄₃	semidirect
273. C₄₃	#19625	semidirect

Maximal subgroups

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

subgroup	index
#19145746	2
#19145513	2
#19145154	2
#19144991	2
#19144969	2
#19134246	2
#19134232	2
#19134194	2
#19134185	2
C₈×#10621877	2
C₂×C₄₃×#492	2
#19625	43