Subgroups — #25080108

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145907	C₂	1	1	yes	maximal, characteristic
2	#19145723	C₂	1	1	yes	maximal, characteristic
3	#19143341	C₂	1	1	yes	maximal, characteristic
4	#19134115	C₂	1	2	yes	maximal, complemented
5	#19134091	C₂	1	2	yes	maximal, complemented
6	#19133991	C₂	1	2	yes	maximal, complemented
7	#19133967	C₂	1	2	yes	maximal, complemented
8	#19133347	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133252	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582648	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063333	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583295	—	2	1	no	—
15	#14583247	—	2	1	no	—
16	#14583217	—	2	2	no	—
17	#14583186	C₂²	1	2	yes	—
18	#14583186	C₂²	1	2	yes	—
19	#14583186	C₂²	1	2	yes	—
20	#14583184	—	2	1	no	—
21	#14583130	—	2	2	no	—
22	#14583101	C₂²	1	2	yes	—
23	#14583099	—	2	1	no	—
24	#14582978	C₂²	1	2	yes	—
25	#14582972	—	2	2	no	—
26	C₈×D₁₇₂	C₂²	1	2	yes	—
27	#14582952	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#14582867	—	2	1	no	—
31	#14582652	C₂²	1	2	yes	—
32	#14582650	C₂²	1	2	yes	—
33	#14582648	C₂²	1	2	yes	—
34	#14582648	C₂²	1	1	yes	characteristic
35	#14582648	C₂²	1	2	yes	—
36	#14582648	C₂²	1	1	yes	characteristic
37	#14582645	C₂²	1	1	yes	characteristic
38	#14582645	C₂²	1	1	yes	characteristic
39	C₄₃×#533	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#501	—	2	2	no	—
42	C₄₃×#500	C₂²	1	2	yes	—
43	C₄₃×#498	C₂²	1	2	yes	—
44	C₄₃×#428	—	2	1	no	—
45	C₄₃×#428	—	2	1	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621884	—	2	2	no	—
49	#13063333	—	4	4	no	—
50	C₂×#10621872	—	2	2	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂×C₈×D₄₃	—	2	2	no	—
54	#13063325	D₄	1	1	yes	characteristic
55	#13063322	D₄	1	1	yes	characteristic
56	#13063313	—	2	1	no	—
57	#13063299	—	2	1	no	—
58	#13063299	D₄	1	2	yes	—
59	C₄×D₁₇₂	—	2	1	no	—
60	C₄×D₁₇₂	C₂³	1	2	yes	—
61	#13063256	—	2	2	no	—
62	#13063256	—	2	2	no	—
63	#13063256	—	2	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
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	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
71	#13063249	—	2	2	no	—
72	#13063245	—	2	2	no	—
73	#13063245	—	2	2	no	—
74	#13063245	—	2	2	no	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
76	(C₂×D₄₃)⋊C₈	—	2	2	no	—
77	(C₂×D₄₃)⋊C₈	—	2	2	no	—
78	C₄×C₄₃⋊C₈	—	2	1	no	—
79	C₂²×Q₈×C₄₃	—	2	1	no	—
80	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₃	—	2	1	no	—
83	C₄⋊Q₈×C₄₃	—	2	1	no	—
84	C₄⋊Q₈×C₄₃	—	2	1	no	—
85	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
88	#125×C₄₃	—	2	1	no	—
89	C₂²⋊Q₈×C₄₃	—	2	1	no	—
90	C₂²⋊Q₈×C₄₃	—	2	1	no	—
91	C₄×Q₈×C₄₃	—	2	1	no	—
92	C₄×Q₈×C₄₃	—	2	1	no	—
93	#117×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	#107×C₄₃	—	2	2	no	—
98	#107×C₄₃	—	2	2	no	—
99	#106×C₄₃	—	2	2	no	—
100	#106×C₄₃	—	2	2	no	—
101	#97×C₄₃	D₄	1	2	yes	—
102	C₄×C₈×C₄₃	C₂³	1	2	yes	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	—	2	1	no	—
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	—	4	1	no	—
107	C₂×Q₈×C₄₃	—	8	2	no	—
108	C₂²×C₄×C₄₃	—	4	1	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	2	no	—
113	#10621898	—	4	2	no	—
114	#10621898	—	4	2	no	—
115	C₂×D₁₇₂	—	2	1	no	—
116	C₂×D₁₇₂	—	2	1	no	—
117	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
118	C₂×C₄×D₄₃	—	2	2	no	—
119	C₂×Dic₈₆	—	2	1	no	—
120	M₁₆×C₄₃	—	2	2	no	—
121	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
122	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	4	1	no	—
131	C₄⋊C₄×C₄₃	—	4	1	no	—
132	C₄⋊C₄×C₄₃	—	4	1	no	—
133	C₄⋊C₄×C₄₃	—	4	1	no	—
134	C₂²⋊C₄×C₄₃	—	4	1	no	—
135	C₄²×C₄₃	—	4	1	no	—
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₃	#41	1	1	yes	characteristic
139	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
140	#10621884	—	8	2	no	—
141	(C₂×D₄₃)⋊C₄	—	2	2	no	—
142	(C₂×D₄₃)⋊C₄	—	2	2	no	—
143	C₄⋊Dic₄₃	—	2	1	no	—
144	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	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	—	4	2	no	—
151	C₂×C₄₃⋊C₈	—	8	1	no	—
152	#10621872	—	4	4	no	—
153	C₈×D₄₃	—	4	4	no	—
154	C₂³×C₄₃	#121	1	1	yes	characteristic
155	C₂²×D₄₃	—	2	2	no	—
156	Q₈×C₄₃	—	4	1	no	—
157	Q₈×C₄₃	—	4	1	no	—
158	Q₈×C₄₃	—	8	1	no	—
159	Q₈×C₄₃	—	8	2	no	—
160	Q₈×C₄₃	—	8	2	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	8	2	no	—
168	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
172	C₂×C₄×C₄₃	#137	1	2	yes	—
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₄₃	—	4	4	no	—
177	C₂×Dic₄₃	—	2	2	no	—
178	D₁₇₂	—	2	2	no	—
179	D₁₇₂	—	2	2	no	—
180	D₁₇₂	—	4	2	no	—
181	D₁₇₂	—	8	1	no	—
182	C₄×D₄₃	—	4	2	no	—
183	C₄×D₄₃	—	4	2	no	—
184	Dic₈₆	—	4	2	no	—
185	C₈×C₄₃	—	2	2	no	—
186	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
187	C₄₃⋊C₈	—	4	1	no	—
188	C₄₃⋊C₈	—	4	1	no	—
189	C₄₃⋊C₈	—	4	1	no	—
190	C₄₃⋊C₈	—	4	2	no	—
191	C₄₃⋊C₈	—	4	1	no	—
192	#19233	—	43	1	no	maximal, Sylow
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	#461	1	2	yes	—
196	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
197	C₂×D₄₃	—	4	2	no	—
198	C₂×D₄₃	—	4	2	no	—
199	C₂×D₄₃	—	4	2	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	2	1	no	—
202	C₄×C₄₃	—	2	1	no	—
203	C₄×C₄₃	—	8	1	no	—
204	C₄×C₄₃	—	8	2	no	—
205	C₄×C₄₃	—	8	1	no	—
206	C₄×C₄₃	#461	1	2	yes	—
207	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
208	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
209	C₄×C₄₃	#577	1	1	yes	characteristic
210	C₄×C₄₃	#578	1	1	yes	characteristic
211	Dic₄₃	—	4	2	no	—
212	#3246	—	43	1	no	—
213	#3227	—	43	1	no	—
214	#3165	D₄₃	1	1	yes	characteristic, complemented
215	#2935	—	43	1	no	—
216	#1695	—	43	2	no	—
217	#1691	—	43	2	no	—
218	#1675	—	43	2	no	—
219	#1671	—	43	2	no	—
220	#1565	—	43	1	no	—
221	#1542	—	43	1	no	—
222	C₂×#333	—	43	1	no	—
223	C₂×C₄₃	—	2	2	no	—
224	C₂×C₄₃	C₂×#461	1	1	yes	characteristic
225	C₂×C₄₃	#3063	1	1	yes	characteristic
226	C₂×C₄₃	#3068	1	1	yes	characteristic
227	D₄₃	—	8	2	no	—
228	C₂×#131	—	86	1	no	—
229	#533	C₂×D₄₃	1	1	yes	characteristic
230	#532	—	43	1	no	—
231	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
232	#501	—	2	2	no	—
233	#500	C₂×D₄₃	1	2	yes	—
234	#498	—	86	1	no	—
235	#498	C₂×D₄₃	1	2	yes	—
236	#486	—	86	1	no	—
237	#481	—	86	2	no	—
238	#476	—	43	2	no	—
239	#476	—	43	2	no	—
240	#476	—	43	2	no	—
241	#475	—	86	1	no	—
242	#465	—	86	2	no	—
243	#461	—	43	2	no	—
244	#460	—	86	1	no	—
245	#436	—	43	2	no	—
246	#435	—	86	2	no	—
247	C₈×D₄	—	43	2	no	—
248	#431	—	43	1	no	—
249	#428	—	2	1	no	—
250	#428	—	2	1	no	—
251	C₂×C₄⋊C₈	—	43	1	no	—
252	C₂×C₄⋊C₈	—	43	1	no	—
253	#408	—	86	1	no	—
254	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
255	#335	—	43	2	no	—
256	#334	—	43	2	no	—
257	#333	—	43	2	no	—
258	#333	—	43	2	no	—
259	#333	—	43	1	no	—
260	#333	—	43	1	no	—
261	#332	—	43	1	no	—
262	#332	—	43	1	no	—
263	C₄₃	#19233	1	1	yes	characteristic, complemented, Sylow
264	C₂×#41	—	86	1	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂×SD₁₆	—	86	2	no	—
267	#131	—	172	4	no	—
268	C₂×M₁₆	—	86	2	no	—
269	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
270	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
271	C₂²×C₈	—	86	1	no	—
272	C₂²×C₈	—	86	1	no	—
273	C₂²×C₈	—	86	2	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	43	1	no	—
278	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
279	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
280	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
281	#127	—	43	1	no	—
282	#125	—	2	1	no	—
283	#124	—	86	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	#121	—	43	2	no	—
287	#121	—	86	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×D₄	—	43	2	no	—
291	C₄×D₄	—	86	1	no	—
292	#117	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
296	#107	—	2	2	no	—
297	#107	—	2	2	no	—
298	#106	—	2	2	no	—
299	#106	—	2	2	no	—
300	#106	—	86	2	no	—
301	#106	—	86	2	no	—
302	#106	—	86	2	no	—
303	C₄⋊C₈	—	43	1	no	—
304	C₄⋊C₈	—	43	1	no	—
305	C₄⋊C₈	—	43	1	no	—
306	C₄⋊C₈	—	43	1	no	—
307	C₄⋊C₈	—	43	2	no	—
308	C₄⋊C₈	—	86	1	no	—
309	C₄⋊C₈	—	86	1	no	—
310	#103	—	86	2	no	—
311	#102	—	86	2	no	—
312	#102	—	86	2	no	—
313	#102	—	86	2	no	—
314	C₂²⋊C₈	—	86	1	no	—
315	C₂²⋊C₈	—	86	2	no	—
316	C₂²⋊C₈	—	86	2	no	—
317	#97	C₂²⋊D₄₃	1	2	yes	—
318	C₄×C₈	—	86	1	no	—
319	C₄×C₈	C₂²×D₄₃	1	2	yes	—
320	#41	—	172	2	no	—
321	#41	—	172	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	8	2	no	—
327	C₂×Q₈	—	86	1	no	—
328	C₂×D₄	—	43	2	no	—
329	C₂×D₄	—	86	2	no	—
330	C₂×D₄	—	86	1	no	—
331	C₂×D₄	—	86	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	86	2	no	—
334	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
335	C₂²×C₄	#10621900	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
337	SD₁₆	—	344	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	172	4	no	—
340	M₁₆	#10621884	1	4	yes	complemented
341	C₂×C₈	—	86	1	no	—
342	C₂×C₈	—	86	1	no	—
343	C₂×C₈	—	86	2	no	—
344	C₂×C₈	—	86	1	no	—
345	C₂×C₈	—	86	1	no	—
346	C₂×C₈	—	344	1	no	—
347	C₂×C₈	—	172	2	no	—
348	C₂×C₈	—	172	4	no	—
349	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
350	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	43	2	no	—
362	C₄⋊C₄	—	86	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	86	2	no	—
365	C₂²⋊C₄	—	86	2	no	—
366	C₄²	—	4	1	no	—
367	C₄²	D₄×D₄₃	1	1	yes	characteristic
368	C₄²	#10621900	1	1	yes	characteristic
369	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
370	C₄²	C₂³×D₄₃	1	1	yes	characteristic
371	C₂³	—	86	2	no	—
372	C₂³	#13063296	1	1	yes	characteristic
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	Q₈	—	8	2	no	—
376	Q₈	—	8	1	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	172	2	no	—
379	D₄	—	86	2	no	—
380	D₄	—	86	2	no	—
381	D₄	—	344	1	no	—
382	D₄	—	172	4	no	—
383	D₄	—	172	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	86	2	no	—
392	C₂×C₄	—	172	2	no	—
393	C₂×C₄	—	172	2	no	—
394	C₂×C₄	#13063296	1	1	yes	characteristic
395	C₂×C₄	#13063296	1	1	yes	characteristic
396	C₂×C₄	#13063296	1	1	yes	characteristic
397	C₂×C₄	C₂×#10621884	1	2	yes	—
398	C₂×C₄	#13063356	1	2	yes	—
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	2	no	—
403	C₈	—	172	1	no	—
404	C₈	—	172	1	no	—
405	C₈	—	172	2	no	—
406	C₈	—	172	1	no	—
407	C₈	—	172	1	no	—
408	C₈	C₂×#10621884	1	4	yes	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	172	2	no	—
412	C₂²	—	172	2	no	—
413	C₂²	—	172	2	no	—
414	C₂²	#14583101	1	2	yes	—
415	C₂²	C₂×#13063296	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	1	no	—
422	C₄	—	172	2	no	—
423	C₄	#14583101	1	2	yes	—
424	C₄	C₂²×#10621884	1	1	yes	characteristic
425	C₄	C₂×#13063356	1	1	yes	characteristic
426	C₄	#14583708	1	1	yes	characteristic
427	C₄	#14583715	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	344	2	no	—
430	C₂	C₂×#14583101	1	1	yes	characteristic
431	C₂	#19144280	1	1	yes	characteristic
432	C₂	#19144319	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3165	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#3165	D₄₃
hypocenter	C₄₃	#19233
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3165

Complements

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

N	H ≅ G/N	type
4. #19134115	C₂	semidirect
5. #19134091	C₂	semidirect
6. #19133991	C₂	semidirect
7. #19133967	C₂	semidirect
8. #19133347	C₂	semidirect
9. #19133252	C₂	semidirect
10. C₂×#14582648	C₂	semidirect
11. C₄₃×#3165	C₂	semidirect
121. M₁₆×C₄₃	SD₁₆	semidirect
214. #3165	D₄₃	semidirect
263. C₄₃	#19233	semidirect
340. M₁₆	#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145907	2
#19145723	2
#19143341	2
#19134115	2
#19134091	2
#19133991	2
#19133967	2
#19133347	2
#19133252	2
C₂×#14582648	2
C₄₃×#3165	2
#19233	43