Subgroups — #25080038

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145915	C₂	1	2	yes	maximal, complemented
2	#19143570	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134120	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134115	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134076	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134071	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134008	C₂	1	2	yes	maximal, complemented
8	#19134001	C₂	1	2	yes	maximal, complemented
9	C₂×#14582650	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133290	C₂	1	2	yes	maximal, complemented
11	C₄₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583433	C₂²	1	1	yes	characteristic
13	#14583199	—	2	2	no	—
14	#14583191	C₂²	1	2	yes	—
15	#14583186	C₂²	1	2	yes	—
16	#14583133	—	2	2	no	—
17	#14583126	—	2	2	no	—
18	#14583114	—	2	2	no	—
19	#14583096	C₂²	1	2	yes	—
20	#14583091	C₂²	1	2	yes	—
21	#14583029	C₂²	1	1	yes	characteristic
22	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
23	#14582978	C₂²	1	1	yes	characteristic
24	#14582970	—	2	1	no	—
25	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₄₃	—	2	1	no	—
27	#14582958	—	2	1	no	—
28	#14582956	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
30	#14582853	—	2	1	no	—
31	#14582650	C₂²	1	2	yes	—
32	#14582650	C₂²	1	1	yes	characteristic
33	#14582650	C₂²	1	1	yes	characteristic
34	#14582648	C₂²	1	2	yes	—
35	#14582648	C₂²	1	2	yes	—
36	#14582643	C₂²	1	2	yes	—
37	#14582643	C₂²	1	2	yes	—
38	C₄₃×#532	C₂²	1	2	yes	—
39	C₄₃×#500	C₂²	1	1	yes	characteristic
40	C₄₃×#493	C₂²	1	1	yes	characteristic
41	C₄₃×#486	C₂²	1	2	yes	—
42	C₄₃×#466	—	2	1	no	—
43	C₄₃×#466	—	2	1	no	—
44	C₄×D₈×C₄₃	—	2	1	no	—
45	C₄×D₈×C₄₃	—	2	1	no	—
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621883	—	2	2	no	—
48	C₂×#10621882	—	2	2	no	—
49	C₂×#10621872	—	2	1	no	—
50	C₂²×C₄₃⋊C₈	—	2	2	no	—
51	C₂×C₈×D₄₃	—	2	1	no	—
52	#13063319	—	2	1	no	—
53	#13063317	D₄	1	1	yes	characteristic
54	#13063313	D₄	1	1	yes	characteristic
55	#13063308	—	2	1	no	—
56	#13063304	D₄	1	1	yes	characteristic
57	#13063299	D₄	1	1	yes	characteristic
58	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
59	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
60	C₄×C₂²⋊D₄₃	—	2	1	no	—
61	#13063282	—	2	1	no	—
62	#13063258	—	2	2	no	—
63	#13063256	—	2	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
69	Dic₄₃⋊C₈	—	2	1	no	—
70	Dic₄₃⋊C₈	—	2	1	no	—
71	#13063248	—	2	2	no	—
72	#13063246	—	2	2	no	—
73	#13063246	—	2	2	no	—
74	#13063245	—	2	2	no	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
76	(C₂×D₄₃)⋊C₈	—	2	1	no	—
77	(C₂×D₄₃)⋊C₈	—	2	1	no	—
78	#13063236	—	2	1	no	—
79	#13063235	—	2	1	no	—
80	C₈×Dic₄₃	—	2	1	no	—
81	C₂×#41×C₄₃	—	2	2	no	—
82	C₂×D₈×C₄₃	—	2	1	no	—
83	C₂×D₈×C₄₃	—	2	1	no	—
84	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
86	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
87	#127×C₄₃	C₂³	1	2	yes	—
88	#124×C₄₃	—	2	2	no	—
89	#121×C₄₃	—	2	2	no	—
90	#121×C₄₃	—	2	2	no	—
91	C₄×D₄×C₄₃	—	2	2	no	—
92	C₄×D₄×C₄₃	—	2	2	no	—
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	#107×C₄₃	—	2	1	no	—
95	#107×C₄₃	—	2	1	no	—
96	#102×C₄₃	—	2	2	no	—
97	#102×C₄₃	—	2	2	no	—
98	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	#41×C₄₃	—	8	4	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	—	4	2	no	—
108	C₂²×C₄×C₄₃	—	4	2	no	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₃	—	2	1	no	—
113	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₄₃	—	2	1	no	—
115	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
116	D₈×C₄₃	—	4	2	no	—
117	D₈×C₄₃	—	4	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	4	1	no	—
120	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₂²⋊C₄×C₄₃	—	4	2	no	—
127	C₂²⋊C₄×C₄₃	—	4	2	no	—
128	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₃	#41	1	1	yes	characteristic
131	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₄₃	—	2	1	no	—
133	#10621883	—	8	2	no	—
134	#10621882	—	8	2	no	—
135	(C₂×D₄₃)⋊C₄	—	2	1	no	—
136	(C₂×D₄₃)⋊C₄	—	2	1	no	—
137	(C₂×D₄₃)⋊C₄	—	2	1	no	—
138	(C₂×D₄₃)⋊C₄	—	2	1	no	—
139	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
141	Dic₄₃⋊C₄	—	2	1	no	—
142	Dic₄₃⋊C₄	—	2	1	no	—
143	Dic₄₃⋊C₄	—	2	1	no	—
144	Dic₄₃⋊C₄	—	2	1	no	—
145	C₄×Dic₄₃	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	8	2	no	—
151	#10621872	—	4	2	no	—
152	C₈×D₄₃	—	4	2	no	—
153	C₂³×C₄₃	—	4	2	no	—
154	C₂³×C₄₃	#121	1	1	yes	characteristic
155	C₂²×D₄₃	—	2	1	no	—
156	Q₈×C₄₃	—	8	2	no	—
157	D₄×C₄₃	—	4	2	no	—
158	D₄×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	4	2	no	—
160	D₄×C₄₃	—	4	2	no	—
161	D₄×C₄₃	—	8	2	no	—
162	D₄×C₄₃	—	8	4	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	8	4	no	—
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₄₃	—	4	2	no	—
176	C₂×Dic₄₃	—	2	1	no	—
177	C₂×Dic₄₃	—	2	1	no	—
178	C₂×Dic₄₃	—	2	1	no	—
179	D₁₇₂	—	2	2	no	—
180	C₄×D₄₃	—	4	1	no	—
181	C₄×D₄₃	—	4	1	no	—
182	Dic₈₆	—	2	2	no	—
183	C₈×C₄₃	—	2	1	no	—
184	C₈×C₄₃	—	2	1	no	—
185	C₈×C₄₃	—	2	1	no	—
186	C₈×C₄₃	#135	1	2	yes	—
187	C₄₃⋊C₈	—	4	1	no	—
188	C₄₃⋊C₈	—	4	1	no	—
189	C₄₃⋊C₈	—	4	2	no	—
190	C₄₃⋊C₈	—	4	2	no	—
191	#19227	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	8	2	no	—
195	C₂²×C₄₃	—	8	2	no	—
196	C₂²×C₄₃	—	8	2	no	—
197	C₂²×C₄₃	#472	1	2	yes	—
198	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
199	C₂×D₄₃	—	4	1	no	—
200	C₂×D₄₃	—	4	1	no	—
201	C₂×D₄₃	—	4	1	no	—
202	C₄×C₄₃	—	2	1	no	—
203	C₄×C₄₃	—	2	1	no	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	8	2	no	—
207	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
208	C₄×C₄₃	#575	1	1	yes	characteristic
209	C₄×C₄₃	#577	1	2	yes	—
210	Dic₄₃	—	4	1	no	—
211	Dic₄₃	—	4	1	no	—
212	Dic₄₃	—	4	1	no	—
213	#3247	—	43	2	no	—
214	#3169	D₄₃	1	1	yes	characteristic, complemented
215	#2966	—	43	1	no	—
216	#1696	—	43	1	no	—
217	#1695	—	43	1	no	—
218	#1688	—	43	1	no	—
219	#1687	—	43	1	no	—
220	#1678	—	43	2	no	—
221	#1677	—	43	2	no	—
222	C₂×#334	—	43	1	no	—
223	#1551	—	43	2	no	—
224	C₂×C₄₃	—	2	2	no	—
225	C₂×C₄₃	—	16	2	no	—
226	C₂×C₄₃	#3035	1	1	yes	characteristic
227	C₂×C₄₃	#3060	1	1	yes	characteristic
228	C₂×C₄₃	C₂×#472	1	1	yes	characteristic
229	D₄₃	—	8	1	no	—
230	#532	C₂×D₄₃	1	2	yes	—
231	#529	—	43	1	no	—
232	#500	C₂×D₄₃	1	1	yes	characteristic
233	#493	C₂×D₄₃	1	1	yes	characteristic
234	#486	C₂×D₄₃	1	2	yes	—
235	#478	—	86	2	no	—
236	#477	—	43	2	no	—
237	#476	—	43	2	no	—
238	#466	—	2	1	no	—
239	#466	—	2	1	no	—
240	#466	—	86	2	no	—
241	#465	—	86	2	no	—
242	#463	—	86	2	no	—
243	#460	—	43	2	no	—
244	#459	—	43	2	no	—
245	#446	—	43	1	no	—
246	C₈×Q₈	—	43	1	no	—
247	C₄×D₈	—	2	1	no	—
248	C₄×D₈	—	2	1	no	—
249	#436	—	43	1	no	—
250	#435	—	86	1	no	—
251	C₈×D₄	—	43	1	no	—
252	C₈×D₄	—	86	1	no	—
253	#433	—	86	1	no	—
254	#432	—	43	1	no	—
255	C₂×C₄⋊C₈	—	43	2	no	—
256	#405	—	86	1	no	—
257	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
258	#334	—	43	2	no	—
259	#334	—	43	1	no	—
260	#334	—	43	1	no	—
261	#333	—	43	2	no	—
262	#333	—	43	2	no	—
263	#331	—	43	2	no	—
264	#331	—	43	2	no	—
265	C₄₃	#19227	1	1	yes	characteristic, complemented, Sylow
266	C₂×#41	—	2	2	no	—
267	C₂×SD₁₆	—	86	2	no	—
268	C₂×D₈	—	2	1	no	—
269	C₂×D₈	—	2	1	no	—
270	C₂×D₈	—	86	2	no	—
271	C₂×M₁₆	—	86	1	no	—
272	C₂²×C₈	—	86	2	no	—
273	C₂²×C₈	—	86	1	no	—
274	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
276	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
277	#127	C₂²×D₄₃	1	2	yes	—
278	#126	—	86	1	no	—
279	#125	—	43	1	no	—
280	#124	—	2	2	no	—
281	#124	—	43	1	no	—
282	#123	—	86	1	no	—
283	C₂²⋊Q₈	—	43	1	no	—
284	#121	—	2	2	no	—
285	#121	—	2	2	no	—
286	#121	—	43	1	no	—
287	C₄×Q₈	—	43	1	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	43	1	no	—
291	C₄×D₄	—	86	1	no	—
292	#117	—	86	1	no	—
293	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
294	#107	—	2	1	no	—
295	#107	—	2	1	no	—
296	#107	—	86	2	no	—
297	#106	—	86	2	no	—
298	C₄⋊C₈	—	43	1	no	—
299	C₄⋊C₈	—	43	1	no	—
300	C₄⋊C₈	—	43	2	no	—
301	C₄⋊C₈	—	43	2	no	—
302	C₄⋊C₈	—	86	1	no	—
303	C₄⋊C₈	—	86	1	no	—
304	C₄⋊C₈	—	86	2	no	—
305	#103	—	86	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	86	2	no	—
309	#102	—	86	2	no	—
310	#102	—	86	2	no	—
311	C₂²⋊C₈	—	86	1	no	—
312	C₂²⋊C₈	—	86	1	no	—
313	C₂²⋊C₈	—	86	1	no	—
314	#97	—	86	1	no	—
315	#97	—	86	1	no	—
316	C₄×C₈	—	86	1	no	—
317	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
318	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
321	#41	—	8	4	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	43	1	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	43	1	no	—
329	C₂×D₄	—	86	1	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	86	1	no	—
332	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
333	C₂²×C₄	#10621900	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
335	SD₁₆	—	344	2	no	—
336	D₈	—	4	2	no	—
337	D₈	—	4	2	no	—
338	D₈	—	344	2	no	—
339	M₁₆	—	172	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	86	2	no	—
343	C₂×C₈	—	86	2	no	—
344	C₂×C₈	—	86	1	no	—
345	C₂×C₈	—	86	1	no	—
346	C₂×C₈	—	344	2	no	—
347	C₂×C₈	—	172	2	no	—
348	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	43	1	no	—
355	C₄⋊C₄	—	43	1	no	—
356	C₄⋊C₄	—	86	1	no	—
357	C₄⋊C₄	—	86	1	no	—
358	C₄⋊C₄	—	86	1	no	—
359	C₄⋊C₄	—	86	1	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	86	1	no	—
363	C₂²⋊C₄	—	86	1	no	—
364	C₂²⋊C₄	—	86	1	no	—
365	C₂²⋊C₄	—	86	1	no	—
366	C₂²⋊C₄	—	86	1	no	—
367	C₄²	—	86	1	no	—
368	C₄²	D₄×D₄₃	1	1	yes	characteristic
369	C₄²	#10621900	1	1	yes	characteristic
370	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
371	C₄²	C₂³×D₄₃	1	1	yes	characteristic
372	C₂³	—	4	2	no	—
373	C₂³	—	86	1	no	—
374	C₂³	#13063296	1	1	yes	characteristic
375	Q₈	—	8	2	no	—
376	Q₈	—	86	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	8	2	no	—
382	D₄	—	8	4	no	—
383	D₄	—	86	2	no	—
384	D₄	—	172	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	4	no	—
391	C₂×C₄	—	86	1	no	—
392	C₂×C₄	—	86	1	no	—
393	C₂×C₄	—	86	1	no	—
394	C₂×C₄	—	172	1	no	—
395	C₂×C₄	—	172	1	no	—
396	C₂×C₄	#13063296	1	1	yes	characteristic
397	C₂×C₄	#13063296	1	1	yes	characteristic
398	C₂×C₄	#13063296	1	1	yes	characteristic
399	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	172	1	no	—
406	C₈	—	172	1	no	—
407	C₈	—	172	2	no	—
408	C₈	—	172	2	no	—
409	C₈	#13063345	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	172	1	no	—
416	C₂²	—	172	1	no	—
417	C₂²	—	172	1	no	—
418	C₂²	#14583166	1	2	yes	—
419	C₂²	C₂×#13063296	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	8	2	no	—
425	C₄	—	172	1	no	—
426	C₄	—	172	1	no	—
427	C₄	—	172	1	no	—
428	C₄	C₂×#13063345	1	1	yes	characteristic
429	C₄	#14583697	1	1	yes	characteristic
430	C₄	#14583706	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	16	2	no	—
433	C₂	—	344	1	no	—
434	C₂	#19144044	1	1	yes	characteristic
435	C₂	#19144253	1	1	yes	characteristic
436	C₂	C₂×#14583166	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3169	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#3169	D₄₃
hypocenter	C₄₃	#19227
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #19145915	C₂	semidirect
2. #19143570	C₂	semidirect
3. #19134120	C₂	semidirect
4. #19134115	C₂	semidirect
5. #19134076	C₂	semidirect
6. #19134071	C₂	semidirect
7. #19134008	C₂	semidirect
8. #19134001	C₂	semidirect
9. C₂×#14582650	C₂	semidirect
10. #19133290	C₂	semidirect
11. C₄₃×#3169	C₂	semidirect
214. #3169	D₄₃	semidirect
265. C₄₃	#19227	semidirect

Maximal subgroups

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

subgroup	index
#19145915	2
#19143570	2
#19134120	2
#19134115	2
#19134076	2
#19134071	2
#19134008	2
#19134001	2
C₂×#14582650	2
#19133290	2
C₄₃×#3169	2
#19227	43