Subgroups — #25079354

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145181	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144666	C₂	1	2	yes	maximal
3	#19134149	C₂	1	2	yes	maximal, complemented
4	#19134142	C₂	1	2	yes	maximal, complemented
5	#19134113	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134108	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134089	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134084	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133343	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133259	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2965	C₂	1	1	yes	maximal, characteristic
12	#14583456	C₂²	1	2	yes	—
13	#14583304	C₂²	1	1	yes	characteristic
14	#14583279	C₂²	1	1	yes	characteristic
15	#14583250	C₂²	1	2	yes	—
16	#14583240	—	2	2	no	—
17	#14583184	C₂²	1	2	yes	—
18	#14583179	C₂²	1	2	yes	—
19	#14583140	—	2	1	no	—
20	#14583140	—	2	1	no	—
21	#14583109	C₂²	1	2	yes	—
22	#14583104	C₂²	1	2	yes	—
23	#14583061	—	2	2	no	—
24	C₄×Dic₁₇₂	—	2	1	no	—
25	C₄×Dic₁₇₂	—	2	1	no	—
26	C₄×#10621885	—	2	2	no	—
27	C₄×#10621883	—	2	2	no	—
28	#14582952	C₂²	1	2	yes	—
29	#14582652	C₂²	1	2	yes	—
30	#14582650	C₂²	1	1	yes	characteristic
31	#14582650	C₂²	1	1	yes	characteristic
32	#14582646	C₂²	1	2	yes	—
33	#14582646	C₂²	1	2	yes	—
34	#14582644	C₂²	1	2	yes	—
35	#14582644	C₂²	1	2	yes	—
36	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#446	C₂²	1	1	yes	characteristic
38	C₄₃×#446	C₂²	1	1	yes	characteristic
39	C₄₃×#436	C₂²	1	1	yes	characteristic
40	C₄₃×#436	C₂²	1	1	yes	characteristic
41	C₄₃×#435	—	2	1	no	—
42	C₄₃×#435	—	2	1	no	—
43	C₄₃×#431	—	2	1	no	—
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₃	—	2	1	no	—
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×Dic₁₇₂	—	2	1	no	—
48	C₂×Dic₁₇₂	—	2	1	no	—
49	C₂×#10621885	—	2	2	no	—
50	C₂×#10621883	—	2	2	no	—
51	#13063325	C₂³	1	2	yes	—
52	#13063325	C₂³	1	2	yes	—
53	#13063317	—	2	2	no	—
54	#13063304	—	2	2	no	—
55	#13063304	—	2	2	no	—
56	C₄×Dic₈₆	—	2	2	no	—
57	C₄×Dic₈₆	—	2	2	no	—
58	#13063284	—	2	2	no	—
59	#13063259	—	2	1	no	—
60	#13063259	—	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	#13063250	—	2	2	no	—
66	#13063250	—	2	2	no	—
67	#13063249	—	2	2	no	—
68	#13063248	—	2	2	no	—
69	#13063248	—	2	2	no	—
70	#13063246	—	2	2	no	—
71	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
72	C₄×C₄₃⋊C₈	—	2	2	no	—
73	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
74	C₂×M₁₆×C₄₃	—	2	1	no	—
75	C₂×M₁₆×C₄₃	—	2	1	no	—
76	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₄₃	—	2	1	no	—
81	C₄×D₄×C₄₃	—	2	1	no	—
82	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
83	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
84	#117×C₄₃	—	2	1	no	—
85	#117×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₃	—	2	1	no	—
89	C₄⋊C₈×C₄₃	—	2	1	no	—
90	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₄₃	—	2	1	no	—
93	C₂²⋊C₈×C₄₃	—	2	1	no	—
94	C₂²⋊C₈×C₄₃	—	2	1	no	—
95	#97×C₄₃	—	2	1	no	—
96	#97×C₄₃	—	2	1	no	—
97	C₄×C₈×C₄₃	—	2	1	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	—	4	2	no	—
103	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	—	2	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×Dic₈₆	—	2	2	no	—
113	C₂×Dic₈₆	—	2	2	no	—
114	M₁₆×C₄₃	—	4	2	no	—
115	M₁₆×C₄₃	—	4	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	1	no	—
118	C₂×C₈×C₄₃	—	2	1	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	1	no	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₄₃	—	2	1	no	—
129	C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂²⋊C₄×C₄₃	—	2	1	no	—
131	C₄²×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₃	#41	1	1	yes	characteristic
137	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₄₃	—	4	2	no	—
139	#10621885	—	4	4	no	—
140	#10621883	—	4	4	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	C₄⋊Dic₄₃	—	2	2	no	—
144	C₄⋊Dic₄₃	—	2	2	no	—
145	Dic₄₃⋊C₄	—	4	2	no	—
146	Dic₄₃⋊C₄	—	4	2	no	—
147	C₄×Dic₄₃	—	4	2	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	Dic₁₇₂	—	4	2	no	—
151	Dic₁₇₂	—	4	2	no	—
152	C₂³×C₄₃	—	2	1	no	—
153	C₂³×C₄₃	#121	1	1	yes	characteristic
154	Q₈×C₄₃	—	2	2	no	—
155	D₄×C₄₃	—	2	2	no	—
156	D₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	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	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₄₃	—	4	2	no	—
175	C₂×Dic₄₃	—	4	2	no	—
176	Dic₈₆	—	4	2	no	—
177	Dic₈₆	—	4	2	no	—
178	Dic₈₆	—	4	2	no	—
179	Dic₈₆	—	4	2	no	—
180	C₈×C₄₃	—	2	1	no	—
181	C₈×C₄₃	—	2	1	no	—
182	C₈×C₄₃	—	2	1	no	—
183	C₈×C₄₃	—	4	1	no	—
184	C₈×C₄₃	—	4	1	no	—
185	C₈×C₄₃	#135	1	2	yes	—
186	C₄₃⋊C₈	—	4	2	no	—
187	C₄₃⋊C₈	—	4	2	no	—
188	#19161	—	43	1	no	maximal, Sylow
189	C₂²×C₄₃	—	2	1	no	—
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	4	1	no	—
193	C₂²×C₄₃	—	4	1	no	—
194	C₂²×C₄₃	—	4	1	no	—
195	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	4	1	no	—
200	C₄×C₄₃	—	4	1	no	—
201	C₄×C₄₃	—	4	1	no	—
202	C₄×C₄₃	#473	1	2	yes	—
203	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
204	C₄×C₄₃	#575	1	1	yes	characteristic
205	C₄×C₄₃	#575	1	2	yes	—
206	Dic₄₃	—	8	2	no	—
207	Dic₄₃	—	8	2	no	—
208	#3170	—	43	1	no	—
209	#3107	—	43	2	no	—
210	#2965	D₄₃	1	1	yes	characteristic
211	#1700	—	43	2	no	—
212	#1699	—	43	2	no	—
213	#1694	—	43	1	no	—
214	#1693	—	43	1	no	—
215	#1690	—	43	1	no	—
216	#1689	—	43	1	no	—
217	#1564	—	43	1	no	—
218	#1544	—	43	2	no	—
219	C₂×C₄₃	—	4	1	no	—
220	C₂×C₄₃	—	8	1	no	—
221	C₂×C₄₃	#3035	1	1	yes	characteristic
222	C₂×C₄₃	#3054	1	1	yes	characteristic
223	C₂×C₄₃	C₂×#473	1	1	yes	characteristic
224	#533	—	43	2	no	—
225	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
226	#500	—	43	1	no	—
227	#494	—	43	1	no	—
228	#487	—	43	2	no	—
229	#485	—	86	2	no	—
230	#475	—	43	2	no	—
231	#474	—	43	2	no	—
232	#467	—	86	1	no	—
233	#467	—	86	1	no	—
234	#462	—	43	2	no	—
235	#461	—	43	2	no	—
236	#452	—	86	2	no	—
237	#446	C₂×D₄₃	1	1	yes	characteristic
238	#446	C₂×D₄₃	1	1	yes	characteristic
239	C₄×Q₁₆	—	86	2	no	—
240	C₄×Q₁₆	—	86	1	no	—
241	C₄×Q₁₆	—	86	1	no	—
242	C₄×SD₁₆	—	86	2	no	—
243	#436	C₂×D₄₃	1	1	yes	characteristic
244	#436	C₂×D₄₃	1	1	yes	characteristic
245	#435	—	2	1	no	—
246	#435	—	2	1	no	—
247	#431	—	2	1	no	—
248	#431	—	43	2	no	—
249	#431	C₂×D₄₃	1	1	yes	characteristic
250	C₄×M₁₆	—	2	1	no	—
251	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
252	#335	—	43	2	no	—
253	#334	—	43	1	no	—
254	#334	—	43	1	no	—
255	#332	—	43	2	no	—
256	#332	—	43	2	no	—
257	#332	—	43	2	no	—
258	#332	—	43	2	no	—
259	C₄₃	#19161	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	D₁₇₂	1	1	yes	characteristic
261	C₂×Q₁₆	—	86	2	no	—
262	C₂×Q₁₆	—	86	1	no	—
263	C₂×Q₁₆	—	86	1	no	—
264	C₂×SD₁₆	—	86	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
269	C₄⋊Q₈	—	43	2	no	—
270	C₄⋊Q₈	—	43	2	no	—
271	#125	—	86	2	no	—
272	C₂²⋊Q₈	—	86	2	no	—
273	C₂²⋊Q₈	—	86	2	no	—
274	C₄×Q₈	—	86	2	no	—
275	C₄×Q₈	—	86	2	no	—
276	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
277	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₁₇₂	1	1	yes	characteristic
281	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	86	2	no	—
284	#117	D₁₇₂	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
287	#107	—	86	1	no	—
288	#107	—	86	1	no	—
289	#107	—	86	2	no	—
290	#106	—	86	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	43	2	no	—
294	C₄⋊C₈	—	43	2	no	—
295	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
296	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
297	#103	—	86	2	no	—
298	#103	—	86	2	no	—
299	#103	—	86	2	no	—
300	#103	—	86	2	no	—
301	#103	—	86	2	no	—
302	#102	—	86	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	86	2	no	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	86	2	no	—
311	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
312	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
315	#41	—	4	2	no	—
316	C₂×Q₈	—	86	2	no	—
317	C₂×Q₈	—	86	2	no	—
318	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
325	C₂²×C₄	#10621898	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
327	Q₁₆	—	172	2	no	—
328	Q₁₆	—	172	4	no	—
329	Q₁₆	—	172	2	no	—
330	SD₁₆	—	172	4	no	—
331	M₁₆	—	4	2	no	—
332	M₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	86	2	no	—
338	C₂×C₈	—	86	2	no	—
339	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	86	2	no	—
346	C₄⋊C₄	—	86	2	no	—
347	C₄⋊C₄	—	86	2	no	—
348	C₄⋊C₄	—	86	2	no	—
349	C₄⋊C₄	—	172	2	no	—
350	C₄⋊C₄	—	172	2	no	—
351	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
352	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	172	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	172	2	no	—
361	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
362	C₄²	#10621898	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
364	C₄²	C₂³×D₄₃	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	#13063299	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	172	2	no	—
369	Q₈	—	172	2	no	—
370	Q₈	—	172	2	no	—
371	Q₈	—	172	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	#13063299	1	1	yes	characteristic
388	C₂×C₄	#13063299	1	1	yes	characteristic
389	C₂×C₄	#13063299	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
392	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	172	2	no	—
399	C₈	—	172	2	no	—
400	C₈	#13063345	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₂×#13063299	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	344	2	no	—
415	C₄	—	344	2	no	—
416	C₄	#14583174	1	2	yes	—
417	C₄	C₂×#13063345	1	1	yes	characteristic
418	C₄	#14583697	1	1	yes	characteristic
419	C₄	#14583699	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	8	1	no	—
422	C₂	#19144050	1	1	yes	characteristic
423	C₂	#19144204	1	1	yes	characteristic
424	C₂	C₂×#14583174	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063299
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2965	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂×#41×C₄₃	D₄
hypercenter	#2965	D₄₃
hypocenter	C₄₃	#19161
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
1. #19145181	C₂	semidirect
3. #19134149	C₂	semidirect
4. #19134142	C₂	semidirect
5. #19134113	C₂	semidirect
6. #19134108	C₂	semidirect
7. #19134089	C₂	semidirect
8. #19134084	C₂	semidirect
9. #19133343	C₂	semidirect
10. #19133259	C₂	semidirect
259. C₄₃	#19161	semidirect

Maximal subgroups

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

subgroup	index
#19145181	2
#19144666	2
#19134149	2
#19134142	2
#19134113	2
#19134108	2
#19134089	2
#19134084	2
#19133343	2
#19133259	2
C₄₃×#2965	2
#19161	43