Subgroups — #25080181

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 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	#19145741	C₂	1	1	yes	maximal, characteristic, complemented
3	#19145054	C₂	1	1	yes	maximal, characteristic
4	#19143542	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134090	C₂	1	2	yes	maximal, complemented
6	#19134068	C₂	1	2	yes	maximal, complemented
7	#19133966	C₂	1	2	yes	maximal, complemented
8	#19133944	C₂	1	2	yes	maximal, complemented
9	#19133242	C₂	1	1	yes	maximal, characteristic
10	C₂×#14582644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	—	2	1	no	—
13	C₂×#13063358	—	2	1	no	—
14	#14583456	C₂²	1	1	yes	characteristic
15	#14583449	C₂²	1	1	yes	characteristic
16	C₂×#13063325	C₂²	1	1	yes	characteristic
17	#14583297	—	2	1	no	—
18	#14583293	—	2	2	no	—
19	#14583279	C₂²	1	2	yes	—
20	#14583272	C₂²	1	2	yes	—
21	#14583250	—	2	1	no	—
22	#14583230	—	2	2	no	—
23	#14583190	—	2	1	no	—
24	#14583185	C₂²	1	2	yes	—
25	#14583185	C₂²	1	2	yes	—
26	#14583185	C₂²	1	2	yes	—
27	#14583128	—	2	2	no	—
28	#14583105	—	2	1	no	—
29	#14583100	C₂²	1	2	yes	—
30	#14583029	C₂²	1	2	yes	—
31	#14583027	—	2	2	no	—
32	C₈×Dic₈₆	C₂²	1	2	yes	—
33	#14582927	—	2	1	no	—
34	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
35	#14582857	—	2	1	no	—
36	#14582644	C₂²	1	1	yes	characteristic
37	#14582644	C₂²	1	2	yes	—
38	#14582644	C₂²	1	2	yes	—
39	#14582644	C₂²	1	1	yes	characteristic
40	#14582642	C₂²	1	1	yes	characteristic
41	#14582642	C₂²	1	1	yes	characteristic
42	C₄₃×#431	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	2	yes	—
46	C₄₃×#334	C₂²	1	2	yes	—
47	C₂×#10621898	—	2	1	no	—
48	C₂²×Dic₈₆	—	2	1	no	—
49	#13063358	—	4	4	no	—
50	#13063358	—	4	4	no	—
51	C₂×Dic₁₇₂	—	2	2	no	—
52	C₂×Dic₁₇₂	—	2	2	no	—
53	C₂×#10621873	—	2	2	no	—
54	C₂×#10621873	—	2	2	no	—
55	C₂×#10621873	—	2	2	no	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	#13063325	—	2	1	no	—
58	#13063325	—	2	1	no	—
59	#13063325	—	2	1	no	—
60	#13063325	D₄	1	1	yes	characteristic
61	#13063325	D₄	1	1	yes	characteristic
62	#13063325	C₂³	1	2	yes	—
63	#13063325	C₂³	1	1	yes	characteristic
64	#13063322	C₂³	1	1	yes	characteristic
65	#13063317	—	2	1	no	—
66	#13063313	—	2	1	no	—
67	#13063304	—	2	1	no	—
68	#13063304	D₄	1	2	yes	—
69	#13063299	—	2	1	no	—
70	#13063299	—	2	1	no	—
71	C₄×Dic₈₆	—	2	1	no	—
72	C₄×Dic₈₆	C₂³	1	2	yes	—
73	C₄×D₁₇₂	—	2	1	no	—
74	C₄×D₁₇₂	—	2	1	no	—
75	#13063284	—	2	1	no	—
76	C₂×C₄⋊Dic₄₃	—	2	1	no	—
77	C₂×C₄⋊Dic₄₃	—	2	1	no	—
78	#13063257	—	2	2	no	—
79	#13063257	—	2	2	no	—
80	#13063257	—	2	2	no	—
81	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
82	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
83	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
84	Dic₄₃⋊C₈	—	2	2	no	—
85	Dic₄₃⋊C₈	—	2	2	no	—
86	#13063250	—	2	2	no	—
87	#13063250	—	2	2	no	—
88	#13063250	—	2	2	no	—
89	#13063247	—	2	2	no	—
90	#13063235	—	2	2	no	—
91	C₈×Dic₄₃	—	2	2	no	—
92	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
93	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
94	C₂²×C₈×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	2	yes	—
98	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₂²⋊C₈×C₄₃	—	2	1	no	—
101	#97×C₄₃	D₄	1	2	yes	—
102	C₄×C₈×C₄₃	—	2	1	no	—
103	C₄×C₈×C₄₃	C₂³	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₃	—	4	1	no	—
108	C₂²×Dic₄₃	—	4	1	no	—
109	#10621898	—	4	2	no	—
110	#10621898	—	4	2	no	—
111	C₂×D₁₇₂	—	2	1	no	—
112	C₂×D₁₇₂	—	2	1	no	—
113	C₂×D₁₇₂	—	2	1	no	—
114	C₂×C₄×D₄₃	—	4	1	no	—
115	C₂×Dic₈₆	—	2	1	no	—
116	C₂×Dic₈₆	—	2	2	no	—
117	C₂×Dic₈₆	—	2	1	no	—
118	C₂×Dic₈₆	—	4	2	no	—
119	C₂×Dic₈₆	—	4	2	no	—
120	C₂×Dic₈₆	—	4	1	no	—
121	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
122	M₁₆×C₄₃	—	2	2	no	—
123	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	8	1	no	—
128	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
130	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₃	#41	1	1	yes	characteristic
133	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
134	C₂²⋊Dic₄₃	—	2	2	no	—
135	(C₂×D₄₃)⋊C₄	—	4	1	no	—
136	(C₂×D₄₃)⋊C₄	—	4	1	no	—
137	C₄⋊Dic₄₃	—	2	1	no	—
138	C₄⋊Dic₄₃	—	2	1	no	—
139	C₄⋊Dic₄₃	—	2	1	no	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	—	2	1	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	C₄⋊Dic₄₃	—	2	1	no	—
144	C₄⋊Dic₄₃	—	4	1	no	—
145	C₄⋊Dic₄₃	—	4	1	no	—
146	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
147	Dic₄₃⋊C₄	—	2	2	no	—
148	Dic₄₃⋊C₄	—	2	2	no	—
149	C₄×Dic₄₃	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	1	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	4	2	no	—
153	Dic₁₇₂	—	4	4	no	—
154	Dic₁₇₂	—	4	4	no	—
155	#10621873	—	4	4	no	—
156	#10621873	—	4	4	no	—
157	#10621873	—	8	2	no	—
158	C₂³×C₄₃	#121	1	1	yes	characteristic
159	C₂²×D₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
167	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₂²⋊D₄₃	—	8	2	no	—
172	C₂×Dic₄₃	—	2	2	no	—
173	C₂×Dic₄₃	—	2	2	no	—
174	C₂×Dic₄₃	—	4	2	no	—
175	C₂×Dic₄₃	—	4	1	no	—
176	C₂×Dic₄₃	—	8	2	no	—
177	D₁₇₂	—	4	1	no	—
178	D₁₇₂	—	4	1	no	—
179	D₁₇₂	—	4	1	no	—
180	D₁₇₂	—	4	1	no	—
181	D₁₇₂	—	8	1	no	—
182	C₄×D₄₃	—	8	2	no	—
183	Dic₈₆	—	2	2	no	—
184	Dic₈₆	—	2	2	no	—
185	Dic₈₆	—	4	2	no	—
186	Dic₈₆	—	4	1	no	—
187	Dic₈₆	—	4	2	no	—
188	Dic₈₆	—	4	1	no	—
189	Dic₈₆	—	8	1	no	—
190	Dic₈₆	—	8	2	no	—
191	C₈×C₄₃	—	2	2	no	—
192	C₈×C₄₃	—	4	2	no	—
193	C₈×C₄₃	—	4	1	no	—
194	C₈×C₄₃	—	4	1	no	—
195	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
196	C₄₃⋊C₈	—	4	1	no	—
197	C₄₃⋊C₈	—	4	1	no	—
198	#19239	—	43	1	no	maximal, Sylow
199	C₂²×C₄₃	—	2	1	no	—
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	#460	1	2	yes	—
202	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
203	C₂×D₄₃	—	8	1	no	—
204	C₂×D₄₃	—	8	1	no	—
205	C₂×D₄₃	—	8	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	#460	1	2	yes	—
210	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
211	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₄×C₄₃	#577	1	1	yes	characteristic
213	C₄×C₄₃	#578	1	1	yes	characteristic
214	Dic₄₃	—	4	2	no	—
215	Dic₄₃	—	4	2	no	—
216	Dic₄₃	—	8	2	no	—
217	Dic₄₃	—	8	1	no	—
218	#3246	—	43	1	no	—
219	#3229	—	43	1	no	—
220	#3152	—	43	1	no	—
221	#2962	—	43	1	no	—
222	#1690	—	43	2	no	—
223	#1686	—	43	2	no	—
224	#1670	—	43	2	no	—
225	#1666	—	43	2	no	—
226	#1565	D₄₃	1	1	yes	characteristic, complemented
227	#1540	—	43	1	no	—
228	C₂×#332	—	43	1	no	—
229	C₂×C₄₃	—	2	2	no	—
230	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
231	C₂×C₄₃	#3063	1	1	yes	characteristic
232	C₂×C₄₃	#3069	1	1	yes	characteristic
233	D₄₃	—	16	1	no	—
234	C₂×#137	—	86	1	no	—
235	C₂×#137	—	86	1	no	—
236	#533	—	43	1	no	—
237	#532	—	43	1	no	—
238	C₂×C₄⋊Q₈	—	43	1	no	—
239	#498	—	86	1	no	—
240	#497	—	86	2	no	—
241	#494	—	43	2	no	—
242	#492	—	43	2	no	—
243	#487	—	86	1	no	—
244	#483	—	86	2	no	—
245	#476	—	86	1	no	—
246	#475	—	43	2	no	—
247	#475	—	43	2	no	—
248	#475	—	43	2	no	—
249	#465	—	86	2	no	—
250	#461	—	86	1	no	—
251	#460	—	43	2	no	—
252	#446	—	43	2	no	—
253	#446	—	86	2	no	—
254	C₈×Q₈	—	43	2	no	—
255	#431	C₂×D₄₃	1	1	yes	characteristic
256	#424	—	86	1	no	—
257	C₂×C₄⋊C₈	—	43	1	no	—
258	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
259	#405	—	86	1	no	—
260	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
261	#335	C₂×D₄₃	1	2	yes	—
262	#334	C₂×D₄₃	1	2	yes	—
263	#332	—	43	2	no	—
264	#332	—	43	2	no	—
265	#332	—	43	1	no	—
266	#332	—	43	1	no	—
267	#331	—	43	1	no	—
268	#331	—	43	1	no	—
269	C₄₃	#19239	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	—	86	1	no	—
271	C₂²×Q₈	—	86	1	no	—
272	#137	—	172	4	no	—
273	#137	—	172	4	no	—
274	C₂×Q₁₆	—	86	2	no	—
275	C₂×Q₁₆	—	86	2	no	—
276	C₂×SD₁₆	—	86	2	no	—
277	C₂×SD₁₆	—	86	2	no	—
278	C₂×SD₁₆	—	86	2	no	—
279	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
280	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	86	1	no	—
283	C₄⋊Q₈	—	43	1	no	—
284	C₄⋊Q₈	—	43	1	no	—
285	C₄⋊Q₈	—	43	2	no	—
286	C₄⋊Q₈	—	43	1	no	—
287	C₄⋊Q₈	—	86	1	no	—
288	C₄⋊Q₈	—	86	1	no	—
289	C₄⋊Q₈	—	86	1	no	—
290	#127	—	43	1	no	—
291	#125	—	86	1	no	—
292	#124	—	86	1	no	—
293	C₂²⋊Q₈	—	43	2	no	—
294	C₂²⋊Q₈	—	86	1	no	—
295	#121	—	86	1	no	—
296	#121	—	86	1	no	—
297	C₄×Q₈	—	43	2	no	—
298	C₄×Q₈	—	86	1	no	—
299	C₄×D₄	—	86	1	no	—
300	C₄×D₄	—	86	1	no	—
301	#117	—	86	1	no	—
302	C₂×C₄⋊C₄	—	86	1	no	—
303	C₂×C₄⋊C₄	—	86	1	no	—
304	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
305	#106	—	86	2	no	—
306	#106	—	86	2	no	—
307	#106	—	86	2	no	—
308	C₄⋊C₈	—	2	1	no	—
309	C₄⋊C₈	—	43	1	no	—
310	C₄⋊C₈	—	43	1	no	—
311	C₄⋊C₈	—	86	2	no	—
312	C₄⋊C₈	—	86	2	no	—
313	C₄⋊C₈	—	86	1	no	—
314	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
315	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
317	#103	—	86	2	no	—
318	#103	—	86	2	no	—
319	#103	—	86	2	no	—
320	#102	—	86	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	#97	—	86	2	no	—
323	#97	D₁₇₂	1	2	yes	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	86	2	no	—
326	C₄×C₈	C₂²×D₄₃	1	2	yes	—
327	#41	—	172	2	no	—
328	#41	—	172	2	no	—
329	C₂×Q₈	—	43	2	no	—
330	C₂×Q₈	—	86	1	no	—
331	C₂×Q₈	—	86	1	no	—
332	C₂×Q₈	—	86	2	no	—
333	C₂×Q₈	—	172	2	no	—
334	C₂×Q₈	—	172	2	no	—
335	C₂×Q₈	—	172	1	no	—
336	C₂×D₄	—	86	1	no	—
337	C₂×D₄	—	86	1	no	—
338	C₂×D₄	—	86	1	no	—
339	C₂×D₄	—	172	1	no	—
340	C₂²×C₄	—	172	1	no	—
341	C₂²×C₄	—	172	1	no	—
342	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
344	C₂²×C₄	#10621902	1	1	yes	characteristic
345	Q₁₆	—	172	4	no	—
346	Q₁₆	—	172	4	no	—
347	SD₁₆	—	344	2	no	—
348	SD₁₆	—	172	4	no	—
349	SD₁₆	—	172	4	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	#10621873	1	4	yes	complemented
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	8	1	no	—
356	C₂×C₈	—	86	1	no	—
357	C₂×C₈	—	86	1	no	—
358	C₂×C₈	—	172	2	no	—
359	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
360	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
361	C₄⋊C₄	—	43	2	no	—
362	C₄⋊C₄	—	86	1	no	—
363	C₄⋊C₄	—	86	1	no	—
364	C₄⋊C₄	—	86	2	no	—
365	C₄⋊C₄	—	86	1	no	—
366	C₄⋊C₄	—	86	2	no	—
367	C₄⋊C₄	—	86	2	no	—
368	C₄⋊C₄	—	86	1	no	—
369	C₄⋊C₄	—	86	2	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	172	1	no	—
372	C₄⋊C₄	—	172	1	no	—
373	C₂²⋊C₄	—	86	2	no	—
374	C₂²⋊C₄	—	172	1	no	—
375	C₂²⋊C₄	—	172	1	no	—
376	C₄²	—	86	2	no	—
377	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
378	C₄²	D₄×D₄₃	1	1	yes	characteristic
379	C₄²	#10621902	1	1	yes	characteristic
380	C₄²	C₂³×D₄₃	1	1	yes	characteristic
381	C₂³	—	172	1	no	—
382	C₂³	#13063300	1	1	yes	characteristic
383	Q₈	—	86	2	no	—
384	Q₈	—	86	2	no	—
385	Q₈	—	344	1	no	—
386	Q₈	—	344	2	no	—
387	Q₈	—	172	2	no	—
388	Q₈	—	172	1	no	—
389	Q₈	—	172	2	no	—
390	Q₈	—	172	1	no	—
391	D₄	—	344	1	no	—
392	D₄	—	344	2	no	—
393	D₄	—	172	1	no	—
394	D₄	—	172	1	no	—
395	D₄	—	172	1	no	—
396	D₄	—	172	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	86	2	no	—
401	C₂×C₄	—	86	2	no	—
402	C₂×C₄	—	344	2	no	—
403	C₂×C₄	—	344	2	no	—
404	C₂×C₄	—	172	1	no	—
405	C₂×C₄	—	172	2	no	—
406	C₂×C₄	#13063300	1	1	yes	characteristic
407	C₂×C₄	#13063300	1	1	yes	characteristic
408	C₂×C₄	#13063300	1	1	yes	characteristic
409	C₂×C₄	C₂×#10621873	1	2	yes	—
410	C₂×C₄	#13063353	1	2	yes	—
411	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
413	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	172	1	no	—
419	C₈	—	172	1	no	—
420	C₈	C₂×#10621873	1	4	yes	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	344	1	no	—
424	C₂²	—	344	1	no	—
425	C₂²	—	344	1	no	—
426	C₂²	#14583100	1	2	yes	—
427	C₂²	C₂×#13063300	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	344	1	no	—
432	C₄	—	344	2	no	—
433	C₄	—	172	2	no	—
434	C₄	—	172	2	no	—
435	C₄	#14583100	1	2	yes	—
436	C₄	C₂²×#10621873	1	1	yes	characteristic
437	C₄	C₂×#13063353	1	1	yes	characteristic
438	C₄	#14583709	1	1	yes	characteristic
439	C₄	#14583715	1	1	yes	characteristic
440	C₂	—	2	2	no	—
441	C₂	—	688	1	no	—
442	C₂	C₂×#14583100	1	1	yes	characteristic
443	C₂	#19144287	1	1	yes	characteristic
444	C₂	#19144333	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1565	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#1565	D₄₃
hypocenter	C₄₃	#19239
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
2. #19145741	C₂	semidirect
4. #19143542	C₂	semidirect
5. #19134090	C₂	semidirect
6. #19134068	C₂	semidirect
7. #19133966	C₂	semidirect
8. #19133944	C₂	semidirect
10. C₂×#14582644	C₂	semidirect
11. C₄₃×#1565	C₂	semidirect
123. M₁₆×C₄₃	SD₁₆	semidirect
226. #1565	D₄₃	semidirect
269. C₄₃	#19239	semidirect
351. M₁₆	#10621873	semidirect

Maximal subgroups

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

subgroup	index
#19145912	2
#19145741	2
#19145054	2
#19143542	2
#19134090	2
#19134068	2
#19133966	2
#19133944	2
#19133242	2
C₂×#14582644	2
C₄₃×#1565	2
#19239	43