Subgroups — #25080144

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145902	C₂	1	1	yes	maximal, characteristic
2	#19145725	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144988	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143338	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134169	C₂	1	2	yes	maximal, complemented
6	#19134127	C₂	1	2	yes	maximal, complemented
7	#19134045	C₂	1	2	yes	maximal, complemented
8	#19134003	C₂	1	2	yes	maximal, complemented
9	#19133348	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582647	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1540	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063331	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	C₂×#13063325	C₂²	1	1	yes	characteristic
15	#14583297	—	2	1	no	—
16	#14583258	—	2	2	no	—
17	#14583249	C₂²	1	2	yes	—
18	#14583246	—	2	1	no	—
19	#14583245	C₂²	1	2	yes	—
20	#14583218	—	2	2	no	—
21	#14583190	C₂²	1	2	yes	—
22	#14583190	C₂²	1	2	yes	—
23	#14583179	—	2	1	no	—
24	#14583176	C₂²	1	2	yes	—
25	#14583133	—	2	2	no	—
26	#14583094	—	2	1	no	—
27	#14583091	C₂²	1	2	yes	—
28	#14582976	C₂²	1	2	yes	—
29	#14582969	—	2	2	no	—
30	#14582964	C₂²	1	2	yes	—
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	#14582900	—	2	1	no	—
33	#14582900	—	2	1	no	—
34	#14582865	—	2	1	no	—
35	C₄×#10621877	C₂²	1	1	yes	characteristic
36	#14582651	C₂²	1	2	yes	—
37	#14582649	C₂²	1	2	yes	—
38	#14582647	C₂²	1	2	yes	—
39	#14582647	C₂²	1	2	yes	—
40	C₄₃×#532	C₂²	1	1	yes	characteristic
41	C₄₃×#431	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#332	C₂²	1	1	yes	characteristic
44	C₄₃×#332	C₂²	1	1	yes	characteristic
45	C₄₃×#331	C₂²	1	1	yes	characteristic
46	C₄₃×#331	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂²×Dic₈₆	—	2	1	no	—
49	C₂×#10621882	—	2	2	no	—
50	#13063331	—	4	4	no	—
51	C₂×#10621877	D₄	1	1	yes	characteristic
52	C₂×#10621877	D₄	1	1	yes	characteristic
53	C₂×#10621872	—	2	2	no	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂×C₈×D₄₃	—	2	2	no	—
56	#13063325	—	2	1	no	—
57	#13063325	—	2	1	no	—
58	#13063325	—	2	1	no	—
59	#13063325	D₄	1	1	yes	characteristic
60	#13063325	C₂³	1	2	yes	—
61	#13063322	D₄	1	1	yes	characteristic
62	#13063313	—	2	1	no	—
63	#13063299	—	2	1	no	—
64	#13063299	D₄	1	2	yes	—
65	C₄×D₁₇₂	—	2	1	no	—
66	C₄×D₁₇₂	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₄₃	—	2	1	no	—
68	C₂×C₄⋊Dic₄₃	—	2	1	no	—
69	#13063258	—	2	2	no	—
70	#13063257	—	2	2	no	—
71	#13063257	—	2	2	no	—
72	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
74	#13063249	—	2	2	no	—
75	#13063249	—	2	2	no	—
76	#13063247	—	2	2	no	—
77	#13063247	—	2	2	no	—
78	#13063246	—	2	2	no	—
79	#13063246	—	2	2	no	—
80	#13063246	—	2	2	no	—
81	#13063245	—	2	2	no	—
82	(C₂×D₄₃)⋊C₈	—	2	2	no	—
83	(C₂×D₄₃)⋊C₈	—	2	2	no	—
84	#13063236	D₄	1	2	yes	—
85	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
86	C₂×#41×C₄₃	—	2	1	no	—
87	C₂²×C₈×C₄₃	—	2	1	no	—
88	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
89	#127×C₄₃	C₂³	1	1	yes	characteristic
90	#124×C₄₃	—	2	1	no	—
91	#121×C₄₃	—	2	1	no	—
92	#121×C₄₃	—	2	1	no	—
93	C₄×D₄×C₄₃	—	2	1	no	—
94	C₄×D₄×C₄₃	—	2	1	no	—
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₃	—	2	1	no	—
97	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₂²⋊C₈×C₄₃	—	2	1	no	—
102	C₄×C₈×C₄₃	—	2	1	no	—
103	#41×C₄₃	—	4	2	no	—
104	#41×C₄₃	—	4	2	no	—
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×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	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₃	—	2	2	no	—
115	C₂²×Dic₄₃	—	4	1	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	2	no	—
124	C₂×Dic₈₆	—	4	1	no	—
125	C₂×Dic₈₆	—	8	2	no	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	4	2	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₂²⋊C₄×C₄₃	—	4	1	no	—
134	C₂²⋊C₄×C₄₃	—	4	1	no	—
135	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₃	#41	1	1	yes	characteristic
138	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
139	#10621882	—	8	2	no	—
140	(C₂×D₄₃)⋊C₄	—	2	2	no	—
141	(C₂×D₄₃)⋊C₄	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	1	no	—
143	C₄⋊Dic₄₃	—	2	2	no	—
144	C₄⋊Dic₄₃	—	2	2	no	—
145	C₄⋊Dic₄₃	—	4	1	no	—
146	C₄⋊Dic₄₃	—	4	1	no	—
147	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
148	#10621877	—	2	2	no	—
149	#10621877	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	8	1	no	—
152	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
154	#10621872	—	4	4	no	—
155	C₈×D₄₃	—	4	4	no	—
156	C₂³×C₄₃	—	4	1	no	—
157	C₂³×C₄₃	#121	1	1	yes	characteristic
158	C₂²×D₄₃	—	2	2	no	—
159	Q₈×C₄₃	—	4	1	no	—
160	Q₈×C₄₃	—	4	1	no	—
161	D₄×C₄₃	—	4	1	no	—
162	D₄×C₄₃	—	4	1	no	—
163	D₄×C₄₃	—	4	1	no	—
164	D₄×C₄₃	—	4	1	no	—
165	D₄×C₄₃	—	8	1	no	—
166	D₄×C₄₃	—	8	2	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	8	2	no	—
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₃	#135	1	2	yes	—
176	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₄₃	—	4	4	no	—
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	4	2	no	—
183	C₂×Dic₄₃	—	8	2	no	—
184	D₁₇₂	—	2	2	no	—
185	D₁₇₂	—	2	2	no	—
186	D₁₇₂	—	4	2	no	—
187	D₁₇₂	—	8	1	no	—
188	C₄×D₄₃	—	4	2	no	—
189	C₄×D₄₃	—	4	2	no	—
190	Dic₈₆	—	4	2	no	—
191	Dic₈₆	—	8	2	no	—
192	Dic₈₆	—	8	2	no	—
193	C₈×C₄₃	—	4	1	no	—
194	C₈×C₄₃	—	4	1	no	—
195	C₈×C₄₃	—	4	1	no	—
196	C₈×C₄₃	—	4	1	no	—
197	C₄₃⋊C₈	—	2	2	no	—
198	C₄₃⋊C₈	—	2	2	no	—
199	C₄₃⋊C₈	—	4	2	no	—
200	#19236	—	43	1	no	maximal, Sylow
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	8	1	no	—
204	C₂²×C₄₃	—	8	1	no	—
205	C₂²×C₄₃	—	8	1	no	—
206	C₂²×C₄₃	#463	1	2	yes	—
207	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
208	C₂×D₄₃	—	4	2	no	—
209	C₂×D₄₃	—	4	2	no	—
210	C₂×D₄₃	—	4	2	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	2	1	no	—
214	C₄×C₄₃	—	8	1	no	—
215	C₄×C₄₃	#463	1	2	yes	—
216	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
217	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₄×C₄₃	#577	1	1	yes	characteristic
219	C₄×C₄₃	#578	1	1	yes	characteristic
220	Dic₄₃	—	4	2	no	—
221	Dic₄₃	—	8	2	no	—
222	#3245	—	43	1	no	—
223	#3227	—	43	1	no	—
224	#3141	—	43	1	no	—
225	#2935	—	43	1	no	—
226	#1703	—	43	2	no	—
227	#1697	—	43	2	no	—
228	#1683	—	43	2	no	—
229	#1677	—	43	2	no	—
230	#1565	—	43	1	no	—
231	C₂×#333	—	43	1	no	—
232	#1540	D₄₃	1	1	yes	characteristic, complemented
233	C₂×C₄₃	—	2	2	no	—
234	C₂×C₄₃	—	16	1	no	—
235	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
236	C₂×C₄₃	#3063	1	1	yes	characteristic
237	C₂×C₄₃	#3068	1	1	yes	characteristic
238	D₄₃	—	8	2	no	—
239	C₂×#131	—	86	1	no	—
240	#532	—	43	1	no	—
241	#532	C₂×D₄₃	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	—	43	1	no	—
243	#498	—	86	1	no	—
244	#489	—	86	2	no	—
245	#487	—	43	2	no	—
246	#486	—	43	2	no	—
247	#486	—	86	1	no	—
248	#481	—	86	2	no	—
249	#476	—	43	2	no	—
250	#476	—	43	2	no	—
251	#474	—	43	2	no	—
252	#474	—	86	1	no	—
253	#466	—	86	2	no	—
254	#459	—	43	2	no	—
255	#459	—	86	1	no	—
256	#436	—	43	2	no	—
257	#435	—	86	2	no	—
258	C₈×D₄	—	43	2	no	—
259	#431	C₂×D₄₃	1	1	yes	characteristic
260	C₂×C₄⋊C₈	—	43	1	no	—
261	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
262	#417	—	86	1	no	—
263	#417	—	86	1	no	—
264	#408	—	86	1	no	—
265	C₄×M₁₆	—	43	1	no	—
266	#335	—	43	2	no	—
267	#334	—	43	2	no	—
268	#333	—	43	2	no	—
269	#333	—	43	2	no	—
270	#332	C₂×D₄₃	1	1	yes	characteristic
271	#332	C₂×D₄₃	1	1	yes	characteristic
272	#331	C₂×D₄₃	1	1	yes	characteristic
273	#331	C₂×D₄₃	1	1	yes	characteristic
274	C₄₃	#19236	1	1	yes	characteristic, complemented, Sylow
275	C₂×#41	—	2	1	no	—
276	C₂×#41	—	86	1	no	—
277	C₂²×Q₈	—	86	1	no	—
278	C₂×D₈	—	86	2	no	—
279	#131	—	172	4	no	—
280	C₂×M₁₆	—	43	1	no	—
281	C₂×M₁₆	—	43	1	no	—
282	C₂×M₁₆	—	86	2	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	86	2	no	—
285	C₂²×C₈	—	86	1	no	—
286	C₄⋊Q₈	—	43	1	no	—
287	C₄⋊Q₈	—	43	2	no	—
288	C₄⋊Q₈	—	86	1	no	—
289	C₄⋊Q₈	—	86	1	no	—
290	C₄⋊Q₈	—	86	1	no	—
291	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
292	#127	—	43	1	no	—
293	#127	C₂²×D₄₃	1	1	yes	characteristic
294	#124	—	2	1	no	—
295	#124	—	86	1	no	—
296	#121	—	2	1	no	—
297	#121	—	2	1	no	—
298	#121	—	43	2	no	—
299	#121	—	86	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	43	2	no	—
303	C₄×D₄	—	86	1	no	—
304	C₂×C₄⋊C₄	—	86	1	no	—
305	C₂×C₄⋊C₄	—	86	1	no	—
306	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
307	#107	—	86	2	no	—
308	#106	—	86	2	no	—
309	#106	—	86	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	43	2	no	—
312	C₄⋊C₈	—	86	1	no	—
313	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
314	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
315	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
317	#103	—	86	2	no	—
318	#103	—	86	2	no	—
319	#102	—	86	2	no	—
320	#102	—	86	2	no	—
321	#102	—	86	2	no	—
322	#102	—	86	2	no	—
323	#102	—	86	2	no	—
324	#102	—	86	2	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	86	2	no	—
327	C₂²⋊C₈	—	86	2	no	—
328	#97	—	43	2	no	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	—	43	2	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	#41	—	172	2	no	—
334	#41	—	172	2	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	86	1	no	—
337	C₂×Q₈	—	86	2	no	—
338	C₂×Q₈	—	344	2	no	—
339	C₂×Q₈	—	172	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	43	2	no	—
345	C₂×D₄	—	86	2	no	—
346	C₂×D₄	—	86	1	no	—
347	C₂×D₄	—	86	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	86	2	no	—
350	C₂²×C₄	—	172	1	no	—
351	C₂²×C₄	#10621898	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
354	D₈	—	344	2	no	—
355	M₁₆	—	86	2	no	—
356	M₁₆	—	86	2	no	—
357	M₁₆	—	172	4	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	43	2	no	—
364	C₂×C₈	—	43	2	no	—
365	C₂×C₈	—	86	2	no	—
366	C₂×C₈	—	344	1	no	—
367	C₂×C₈	—	172	4	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	43	2	no	—
371	C₄⋊C₄	—	86	1	no	—
372	C₄⋊C₄	—	86	2	no	—
373	C₄⋊C₄	—	86	2	no	—
374	C₄⋊C₄	—	172	1	no	—
375	C₄⋊C₄	—	172	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	86	2	no	—
379	C₂²⋊C₄	—	86	2	no	—
380	C₄²	#10621898	1	1	yes	characteristic
381	C₄²	D₄×D₄₃	1	1	yes	characteristic
382	C₄²	D₄×D₄₃	1	1	yes	characteristic
383	C₄²	C₂³×D₄₃	1	1	yes	characteristic
384	C₂³	—	4	1	no	—
385	C₂³	—	86	2	no	—
386	C₂³	#13063298	1	1	yes	characteristic
387	Q₈	—	4	1	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	344	2	no	—
390	Q₈	—	344	2	no	—
391	Q₈	—	172	2	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	2	no	—
398	D₄	—	86	2	no	—
399	D₄	—	86	2	no	—
400	D₄	—	344	1	no	—
401	D₄	—	172	4	no	—
402	D₄	—	172	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	—	86	2	no	—
409	C₂×C₄	—	344	2	no	—
410	C₂×C₄	—	172	2	no	—
411	C₂×C₄	—	172	2	no	—
412	C₂×C₄	—	172	2	no	—
413	C₂×C₄	#13063298	1	1	yes	characteristic
414	C₂×C₄	#13063298	1	1	yes	characteristic
415	C₂×C₄	#13063298	1	1	yes	characteristic
416	C₂×C₄	#13063346	1	2	yes	—
417	C₂×C₄	#13063349	1	2	yes	—
418	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
419	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	86	2	no	—
426	C₈	—	86	2	no	—
427	C₈	—	172	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	172	2	no	—
434	C₂²	—	172	2	no	—
435	C₂²	—	172	2	no	—
436	C₂²	#14583113	1	2	yes	—
437	C₂²	C₂×#13063298	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	344	2	no	—
443	C₄	—	172	2	no	—
444	C₄	#14583113	1	2	yes	—
445	C₄	C₂×#13063346	1	1	yes	characteristic
446	C₄	C₂×#13063349	1	1	yes	characteristic
447	C₄	#14583706	1	1	yes	characteristic
448	C₄	#14583713	1	1	yes	characteristic
449	C₂	—	2	2	no	—
450	C₂	—	16	1	no	—
451	C₂	—	344	2	no	—
452	C₂	C₂×#14583113	1	1	yes	characteristic
453	C₂	#19144289	1	1	yes	characteristic
454	C₂	#19144326	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063298
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1540	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145902	C₂
hypercenter	#1540	D₄₃
hypocenter	C₄₃	#19236
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1540

Complements

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

N	H ≅ G/N	type
2. #19145725	C₂	semidirect
3. #19144988	C₂	semidirect
4. #19143338	C₂	semidirect
5. #19134169	C₂	semidirect
6. #19134127	C₂	semidirect
7. #19134045	C₂	semidirect
8. #19134003	C₂	semidirect
9. #19133348	C₂	semidirect
10. C₂×#14582647	C₂	semidirect
11. C₄₃×#1540	C₂	semidirect
232. #1540	D₄₃	semidirect
274. C₄₃	#19236	semidirect

Maximal subgroups

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

subgroup	index
#19145902	2
#19145725	2
#19144988	2
#19143338	2
#19134169	2
#19134127	2
#19134045	2
#19134003	2
#19133348	2
C₂×#14582647	2
C₄₃×#1540	2
#19236	43