Subgroups — #25079337

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144649	C₂	1	2	yes	maximal, complemented
2	#19143561	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134132	C₂	1	2	yes	maximal, complemented
4	#19134125	C₂	1	2	yes	maximal, complemented
5	#19134120	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134115	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134076	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134071	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133343	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133257	C₂	1	2	yes	maximal, complemented
11	C₄₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10621898	C₂²	1	1	yes	characteristic
13	#14583220	—	2	2	no	—
14	#14583191	C₂²	1	2	yes	—
15	#14583186	C₂²	1	2	yes	—
16	#14583096	C₂²	1	2	yes	—
17	#14583091	C₂²	1	2	yes	—
18	#14583042	—	2	2	no	—
19	#14583029	C₂²	1	1	yes	characteristic
20	#14583029	C₂²	1	1	yes	characteristic
21	C₄×#10621883	—	2	2	no	—
22	C₄×#10621882	—	2	2	no	—
23	#14582978	C₂²	1	1	yes	characteristic
24	#14582978	C₂²	1	1	yes	characteristic
25	#14582970	—	2	1	no	—
26	#14582970	—	2	1	no	—
27	#14582952	C₂²	1	1	yes	characteristic
28	#14582952	C₂²	1	2	yes	—
29	#14582950	—	2	1	no	—
30	C₄×#10621872	—	2	1	no	—
31	#14582652	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×#10621898	D₄	1	1	yes	characteristic
48	C₂×#10621883	—	2	2	no	—
49	C₂×#10621882	—	2	2	no	—
50	C₂×#10621872	—	2	1	no	—
51	C₂×#10621872	—	2	1	no	—
52	C₄×Dic₈₆	D₄	1	1	yes	characteristic
53	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
54	C₄×D₁₇₂	D₄	1	1	yes	characteristic
55	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₄₃	—	2	1	no	—
57	C₄×C₂²⋊D₄₃	—	2	1	no	—
58	#13063284	D₄	1	1	yes	characteristic
59	#13063282	—	2	1	no	—
60	C₄²×D₄₃	—	2	1	no	—
61	#13063258	—	2	2	no	—
62	#13063256	—	2	2	no	—
63	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
67	Dic₄₃⋊C₈	—	2	1	no	—
68	Dic₄₃⋊C₈	—	2	1	no	—
69	#13063248	—	2	2	no	—
70	#13063246	—	2	2	no	—
71	#13063246	—	2	2	no	—
72	#13063245	—	2	2	no	—
73	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
75	(C₂×D₄₃)⋊C₈	—	2	1	no	—
76	(C₂×D₄₃)⋊C₈	—	2	1	no	—
77	#13063235	—	2	1	no	—
78	#13063235	—	2	1	no	—
79	C₄×C₄₃⋊C₈	—	2	1	no	—
80	C₄×C₄₃⋊C₈	—	2	2	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	#10621898	—	4	2	no	—
114	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₄₃	—	2	1	no	—
116	C₂×C₄×D₄₃	—	2	1	no	—
117	C₂×C₄×D₄₃	—	2	1	no	—
118	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
119	D₈×C₄₃	—	4	2	no	—
120	D₈×C₄₃	—	4	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	4	1	no	—
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₂²⋊C₄×C₄₃	—	4	2	no	—
130	C₂²⋊C₄×C₄₃	—	4	2	no	—
131	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₃	#41	1	1	yes	characteristic
134	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₃	—	2	1	no	—
136	#10621883	—	4	4	no	—
137	#10621882	—	4	4	no	—
138	(C₂×D₄₃)⋊C₄	—	2	1	no	—
139	(C₂×D₄₃)⋊C₄	—	2	1	no	—
140	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
142	Dic₄₃⋊C₄	—	2	1	no	—
143	Dic₄₃⋊C₄	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	C₄×Dic₄₃	—	2	1	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	#10621872	—	4	2	no	—
152	#10621872	—	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	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	2	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	2	no	—
181	C₄×D₄₃	—	4	1	no	—
182	C₄×D₄₃	—	4	1	no	—
183	C₄×D₄₃	—	4	2	no	—
184	Dic₈₆	—	2	2	no	—
185	C₈×C₄₃	—	2	1	no	—
186	C₈×C₄₃	—	2	1	no	—
187	C₈×C₄₃	—	2	1	no	—
188	C₈×C₄₃	#135	1	2	yes	—
189	C₄₃⋊C₈	—	4	1	no	—
190	C₄₃⋊C₈	—	4	1	no	—
191	C₄₃⋊C₈	—	4	2	no	—
192	C₄₃⋊C₈	—	4	2	no	—
193	#19160	—	43	1	no	maximal, Sylow
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	8	2	no	—
198	C₂²×C₄₃	—	8	2	no	—
199	C₂²×C₄₃	—	8	2	no	—
200	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
201	C₂×D₄₃	—	4	1	no	—
202	C₂×D₄₃	—	4	1	no	—
203	C₂×D₄₃	—	4	1	no	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	8	2	no	—
208	C₄×C₄₃	#472	1	2	yes	—
209	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
210	C₄×C₄₃	#575	1	2	yes	—
211	C₄×C₄₃	#575	1	1	yes	characteristic
212	Dic₄₃	—	4	1	no	—
213	Dic₄₃	—	4	1	no	—
214	Dic₄₃	—	4	1	no	—
215	#3169	D₄₃	1	1	yes	characteristic, complemented
216	#3106	—	43	2	no	—
217	#2965	—	43	1	no	—
218	#1698	—	43	2	no	—
219	#1697	—	43	2	no	—
220	#1696	—	43	1	no	—
221	#1695	—	43	1	no	—
222	#1688	—	43	1	no	—
223	#1687	—	43	1	no	—
224	#1564	—	43	1	no	—
225	#1543	—	43	2	no	—
226	C₂×C₄₃	—	4	1	no	—
227	C₂×C₄₃	—	16	2	no	—
228	C₂×C₄₃	#3035	1	1	yes	characteristic
229	C₂×C₄₃	#3054	1	1	yes	characteristic
230	C₂×C₄₃	C₂×#472	1	1	yes	characteristic
231	D₄₃	—	8	1	no	—
232	#532	C₂×D₄₃	1	2	yes	—
233	C₄×#41	—	43	1	no	—
234	#500	C₂×D₄₃	1	1	yes	characteristic
235	#493	C₂×D₄₃	1	1	yes	characteristic
236	#486	C₂×D₄₃	1	2	yes	—
237	#482	—	86	2	no	—
238	#477	—	43	2	no	—
239	#476	—	43	2	no	—
240	#466	—	2	1	no	—
241	#466	—	2	1	no	—
242	#460	—	43	2	no	—
243	#459	—	43	2	no	—
244	#449	—	86	2	no	—
245	#446	—	43	1	no	—
246	#446	—	43	1	no	—
247	C₄×SD₁₆	—	86	2	no	—
248	C₄×D₈	—	2	1	no	—
249	C₄×D₈	—	2	1	no	—
250	C₄×D₈	—	86	2	no	—
251	#436	—	43	1	no	—
252	#436	—	43	1	no	—
253	#435	—	86	1	no	—
254	#435	—	86	1	no	—
255	#431	—	43	1	no	—
256	#431	—	43	2	no	—
257	#431	—	86	1	no	—
258	C₄×M₁₆	—	86	1	no	—
259	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
260	#335	—	43	2	no	—
261	#334	—	43	1	no	—
262	#334	—	43	1	no	—
263	#333	—	43	2	no	—
264	#333	—	43	2	no	—
265	#331	—	43	2	no	—
266	#331	—	43	2	no	—
267	C₄₃	#19160	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	43	1	no	—
270	C₂×SD₁₆	—	86	2	no	—
271	C₂×D₈	—	2	1	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	86	2	no	—
274	C₂×M₁₆	—	86	1	no	—
275	C₂×M₁₆	—	86	1	no	—
276	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
277	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
278	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
279	#127	C₂²×D₄₃	1	2	yes	—
280	#124	—	2	2	no	—
281	#121	—	2	2	no	—
282	#121	—	2	2	no	—
283	C₄×Q₈	—	43	1	no	—
284	C₄×Q₈	—	43	1	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	43	1	no	—
288	C₄×D₄	—	43	1	no	—
289	C₄×D₄	—	86	1	no	—
290	C₄×D₄	—	86	1	no	—
291	#117	—	43	1	no	—
292	#117	—	86	1	no	—
293	C₂×C₄²	—	86	1	no	—
294	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
295	#107	—	2	1	no	—
296	#107	—	2	1	no	—
297	#107	—	86	2	no	—
298	#106	—	86	2	no	—
299	C₄⋊C₈	—	43	1	no	—
300	C₄⋊C₈	—	43	1	no	—
301	C₄⋊C₈	—	43	2	no	—
302	C₄⋊C₈	—	43	2	no	—
303	C₄⋊C₈	—	86	1	no	—
304	C₄⋊C₈	—	86	1	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	2	no	—
312	C₂²⋊C₈	—	86	1	no	—
313	C₂²⋊C₈	—	86	1	no	—
314	C₂²⋊C₈	—	86	1	no	—
315	#97	—	86	1	no	—
316	#97	—	86	1	no	—
317	C₄×C₈	—	86	2	no	—
318	C₄×C₈	—	86	1	no	—
319	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
320	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
323	#41	—	8	4	no	—
324	#41	—	172	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	43	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	43	1	no	—
332	C₂×D₄	—	86	1	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	86	1	no	—
335	C₂²×C₄	—	86	1	no	—
336	C₂²×C₄	—	86	1	no	—
337	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
338	C₂²×C₄	#10621900	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
340	SD₁₆	—	172	4	no	—
341	D₈	—	4	2	no	—
342	D₈	—	4	2	no	—
343	D₈	—	172	4	no	—
344	M₁₆	—	172	2	no	—
345	M₁₆	—	172	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	86	2	no	—
349	C₂×C₈	—	86	2	no	—
350	C₂×C₈	—	86	1	no	—
351	C₂×C₈	—	86	1	no	—
352	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	43	1	no	—
359	C₄⋊C₄	—	43	1	no	—
360	C₄⋊C₄	—	86	1	no	—
361	C₄⋊C₄	—	86	1	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	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	—	86	1	no	—
369	C₄²	—	86	1	no	—
370	C₄²	D₄×D₄₃	1	1	yes	characteristic
371	C₄²	#10621900	1	1	yes	characteristic
372	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
373	C₄²	C₂³×D₄₃	1	1	yes	characteristic
374	C₂³	—	4	2	no	—
375	C₂³	—	86	1	no	—
376	C₂³	#13063296	1	1	yes	characteristic
377	Q₈	—	8	2	no	—
378	Q₈	—	86	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	4	no	—
385	D₄	—	86	2	no	—
386	D₄	—	172	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	8	4	no	—
393	C₂×C₄	—	86	1	no	—
394	C₂×C₄	—	86	1	no	—
395	C₂×C₄	—	86	1	no	—
396	C₂×C₄	—	172	2	no	—
397	C₂×C₄	—	172	2	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	—	172	1	no	—
400	C₂×C₄	#13063296	1	1	yes	characteristic
401	C₂×C₄	#13063296	1	1	yes	characteristic
402	C₂×C₄	#13063296	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	172	1	no	—
410	C₈	—	172	2	no	—
411	C₈	—	172	2	no	—
412	C₈	—	172	1	no	—
413	C₈	#13063345	1	2	yes	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	172	1	no	—
421	C₂²	—	172	1	no	—
422	C₂²	—	172	1	no	—
423	C₂²	C₂×#13063296	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	172	1	no	—
429	C₄	—	172	1	no	—
430	C₄	—	172	1	no	—
431	C₄	#14583166	1	2	yes	—
432	C₄	C₂×#13063345	1	1	yes	characteristic
433	C₄	#14583696	1	2	yes	—
434	C₄	#14583697	1	1	yes	characteristic
435	C₂	—	4	1	no	—
436	C₂	—	16	2	no	—
437	C₂	—	344	1	no	—
438	C₂	#19144044	1	1	yes	characteristic
439	C₂	#19144200	1	1	yes	characteristic
440	C₂	C₂×#14583166	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3169	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#3169	D₄₃
hypocenter	C₄₃	#19160
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #19144649	C₂	semidirect
2. #19143561	C₂	semidirect
3. #19134132	C₂	semidirect
4. #19134125	C₂	semidirect
5. #19134120	C₂	semidirect
6. #19134115	C₂	semidirect
7. #19134076	C₂	semidirect
8. #19134071	C₂	semidirect
9. #19133343	C₂	semidirect
10. #19133257	C₂	semidirect
11. C₄₃×#3169	C₂	semidirect
215. #3169	D₄₃	semidirect
267. C₄₃	#19160	semidirect

Maximal subgroups

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

subgroup	index
#19144649	2
#19143561	2
#19134132	2
#19134125	2
#19134120	2
#19134115	2
#19134076	2
#19134071	2
#19133343	2
#19133257	2
C₄₃×#3169	2
#19160	43