Subgroups — #25110478

Order 11008.

818 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	#19145040	C₂	1	1	yes	maximal, characteristic
2	#19143308	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135428	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135426	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134925	C₂	1	4	yes	maximal, complemented
6	#19134922	C₂	1	4	yes	maximal, complemented
7	#19134735	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063345	C₂²	1	4	yes	—
11	C₂×#13063331	C₂²	1	2	yes	—
12	#14583449	C₂²	1	1	yes	characteristic
13	#14583294	C₄	1	2	yes	complemented
14	#14583291	C₄	1	2	yes	complemented
15	#14583289	C₄	1	2	yes	complemented
16	#14583286	C₄	1	2	yes	complemented
17	#14582978	—	2	1	no	—
18	#14582978	—	2	1	no	—
19	C₈×D₁₇₂	—	2	1	no	—
20	C₈×D₁₇₂	—	2	1	no	—
21	#14582923	C₂²	1	1	yes	characteristic
22	C₂×#13063252	C₂²	1	4	yes	—
23	C₂×#13063251	C₂²	1	4	yes	—
24	#14582865	C₂²	1	2	yes	—
25	C₂×#13063236	C₂²	1	1	yes	characteristic
26	#14582745	C₂²	1	1	yes	characteristic
27	#14582663	C₂²	1	4	yes	—
28	#14582653	C₂²	1	2	yes	—
29	#14582653	C₂²	1	2	yes	—
30	C₂×#131×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#532	C₂²	1	1	yes	characteristic
32	C₄₃×#436	—	2	1	no	—
33	C₄₃×#436	—	2	1	no	—
34	C₈×D₄×C₄₃	—	2	1	no	—
35	C₈×D₄×C₄₃	—	2	1	no	—
36	C₄₃×#423	C₂²	1	1	yes	characteristic
37	C₄₃×#408	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#10621898	C₂³	1	2	yes	—
40	#13063345	—	4	4	no	—
41	#13063345	—	4	4	no	—
42	C₂×#10621885	C₂×C₄	1	4	yes	—
43	C₂×#10621883	C₂×C₄	1	4	yes	—
44	C₂×#10621884	C₂×C₄	1	4	yes	—
45	C₂×#10621882	C₂×C₄	1	4	yes	—
46	#13063331	—	4	4	no	—
47	C₂×#10621877	C₂³	1	2	yes	—
48	C₂×#10621872	—	2	2	no	—
49	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
50	C₂×C₈×D₄₃	—	2	2	no	—
51	#13063325	C₂×C₄	1	1	yes	characteristic
52	#13063322	C₂×C₄	1	1	yes	characteristic
53	#13063313	C₂×C₄	1	2	yes	—
54	#13063299	—	2	1	no	—
55	#13063299	—	2	1	no	—
56	C₄×D₁₇₂	—	2	1	no	—
57	C₄×D₁₇₂	—	2	1	no	—
58	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
59	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
60	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
61	#13063252	—	4	4	no	—
62	#13063251	—	4	4	no	—
63	(C₂×D₄₃)⋊C₈	—	2	2	no	—
64	(C₂×D₄₃)⋊C₈	—	2	2	no	—
65	#13063236	C₂×C₄	1	2	yes	—
66	#13063236	C₂×C₄	1	2	yes	—
67	C₄₃⋊#95	—	2	1	no	—
68	C₄₃⋊#95	—	2	1	no	—
69	C₂×#41×C₄₃	C₂³	1	2	yes	—
70	#131×C₄₃	—	4	4	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₃	—	2	2	no	—
74	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
77	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
78	#124×C₄₃	C₂×C₄	1	2	yes	—
79	#121×C₄₃	—	2	1	no	—
80	#121×C₄₃	—	2	1	no	—
81	C₄×D₄×C₄₃	—	2	1	no	—
82	C₄×D₄×C₄₃	—	2	1	no	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₃	—	2	1	no	—
85	C₄⋊C₈×C₄₃	—	2	1	no	—
86	C₂²⋊C₈×C₄₃	—	2	2	no	—
87	C₂²⋊C₈×C₄₃	—	2	2	no	—
88	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
89	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
92	#41×C₄₃	—	2	4	no	—
93	#41×C₄₃	—	2	4	no	—
94	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₄₃	—	2	1	no	—
96	C₂×D₄×C₄₃	—	2	1	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
103	C₂×C₂²⋊D₄₃	—	2	2	no	—
104	C₂²×Dic₄₃	—	2	2	no	—
105	#10621898	—	2	4	no	—
106	#10621898	—	2	4	no	—
107	C₂×D₁₇₂	—	2	1	no	—
108	C₂×D₁₇₂	—	2	1	no	—
109	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₄₃	—	2	2	no	—
111	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
112	M₁₆×C₄₃	—	2	4	no	—
113	M₁₆×C₄₃	—	4	4	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	4	4	no	—
118	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₄₃	—	2	1	no	—
123	C₄⋊C₄×C₄₃	—	2	1	no	—
124	C₂²⋊C₄×C₄₃	—	2	2	no	—
125	C₂²⋊C₄×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
130	#10621885	—	4	4	no	—
131	#10621884	—	4	4	no	—
132	#10621883	—	4	4	no	—
133	#10621882	—	4	4	no	—
134	(C₂×D₄₃)⋊C₄	—	2	2	no	—
135	(C₂×D₄₃)⋊C₄	—	2	2	no	—
136	C₄⋊Dic₄₃	—	2	1	no	—
137	C₄⋊Dic₄₃	—	2	1	no	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	#10621877	—	2	4	no	—
141	C₂×C₄₃⋊C₈	—	2	2	no	—
142	C₂×C₄₃⋊C₈	—	2	2	no	—
143	C₂×C₄₃⋊C₈	—	2	2	no	—
144	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
145	#10621872	—	4	4	no	—
146	C₈×D₄₃	—	4	4	no	—
147	C₂³×C₄₃	—	2	2	no	—
148	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
149	C₂²×D₄₃	—	2	2	no	—
150	Q₈×C₄₃	—	2	4	no	—
151	D₄×C₄₃	—	2	4	no	—
152	D₄×C₄₃	—	4	2	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	4	4	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	4	1	no	—
157	C₂×C₄×C₄₃	—	4	1	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
167	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
168	C₂²⋊D₄₃	—	4	4	no	—
169	C₂×Dic₄₃	—	2	2	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	C₂×Dic₄₃	—	4	2	no	—
173	D₁₇₂	—	2	4	no	—
174	D₁₇₂	—	4	2	no	—
175	D₁₇₂	—	4	2	no	—
176	C₄×D₄₃	—	4	2	no	—
177	C₄×D₄₃	—	4	2	no	—
178	Dic₈₆	—	2	4	no	—
179	C₈×C₄₃	—	2	1	no	—
180	C₈×C₄₃	—	2	1	no	—
181	C₈×C₄₃	—	2	1	no	—
182	C₈×C₄₃	—	2	1	no	—
183	C₈×C₄₃	—	4	2	no	—
184	C₄₃⋊C₈	—	2	4	no	—
185	C₄₃⋊C₈	—	4	2	no	—
186	#22281	—	43	1	no	maximal, Sylow
187	C₂²×C₄₃	—	2	1	no	—
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	—	4	2	no	—
190	C₂²×C₄₃	—	4	2	no	—
191	C₂²×C₄₃	—	4	2	no	—
192	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₄₃	#540	1	2	yes	—
194	C₂×D₄₃	—	4	2	no	—
195	C₂×D₄₃	—	4	2	no	—
196	C₂×D₄₃	—	4	2	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	4	2	no	—
202	C₄×C₄₃	#518	1	2	yes	—
203	C₄×C₄₃	#535	1	1	yes	characteristic
204	C₄×C₄₃	#535	1	1	yes	characteristic
205	Dic₄₃	—	4	2	no	—
206	Dic₄₃	—	8	2	no	—
207	#3150	—	43	1	no	—
208	#2931	—	43	1	no	—
209	#2931	D₄₃	1	1	yes	characteristic, complemented
210	#1963	—	43	1	no	—
211	#1963	—	43	1	no	—
212	#1876	—	43	4	no	—
213	#1876	—	43	4	no	—
214	#1838	—	43	1	no	—
215	#1746	—	43	1	no	—
216	C₂×C₄₃	—	2	2	no	—
217	C₂×C₄₃	—	8	2	no	—
218	C₂×C₄₃	#2328	1	1	yes	characteristic
219	C₂×C₄₃	#2955	1	1	yes	characteristic
220	C₂×C₄₃	#2955	1	1	yes	characteristic
221	D₄₃	—	8	2	no	—
222	C₂×#135	—	43	4	no	—
223	C₂×#131	—	43	2	no	—
224	C₂×#131	C₂×D₄₃	1	2	yes	—
225	#532	—	43	1	no	—
226	#532	C₂×D₄₃	1	1	yes	characteristic
227	#497	—	43	2	no	—
228	#497	—	43	2	no	—
229	#496	—	43	2	no	—
230	#496	—	43	2	no	—
231	#436	—	2	1	no	—
232	#436	—	2	1	no	—
233	#436	—	86	1	no	—
234	#436	—	86	1	no	—
235	C₈×D₄	—	2	1	no	—
236	C₈×D₄	—	2	1	no	—
237	C₈×D₄	—	86	1	no	—
238	C₈×D₄	—	86	1	no	—
239	#423	—	43	1	no	—
240	#423	C₂×D₄₃	1	1	yes	characteristic
241	C₂×#104	—	43	4	no	—
242	C₂×#104	—	43	4	no	—
243	#408	—	43	2	no	—
244	#408	C₂×D₄₃	1	2	yes	—
245	C₂×#97	—	43	1	no	—
246	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
247	#376	—	43	1	no	—
248	#341	—	43	4	no	—
249	#336	—	43	2	no	—
250	#336	—	43	2	no	—
251	C₄₃	#22281	1	1	yes	characteristic, complemented, Sylow
252	C₂×#41	—	43	2	no	—
253	C₂×#41	C₂²×D₄₃	1	2	yes	—
254	#135	—	172	4	no	—
255	#135	—	172	4	no	—
256	C₂×Q₁₆	—	43	4	no	—
257	C₂×SD₁₆	—	43	4	no	—
258	C₂×SD₁₆	—	43	4	no	—
259	C₂×D₈	—	43	4	no	—
260	#131	—	4	4	no	—
261	#131	—	172	4	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	43	2	no	—
264	C₂×M₁₆	—	86	2	no	—
265	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	43	2	no	—
268	C₂²×C₈	—	86	2	no	—
269	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
271	C₄⋊Q₈	—	43	1	no	—
272	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
273	#127	—	43	1	no	—
274	#127	C₄×D₄₃	1	1	yes	characteristic
275	#124	—	43	2	no	—
276	#124	C₄×D₄₃	1	2	yes	—
277	#121	—	2	1	no	—
278	#121	—	2	1	no	—
279	#121	—	86	1	no	—
280	#121	—	86	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	86	1	no	—
284	C₄×D₄	—	86	1	no	—
285	C₂×C₄²	—	43	2	no	—
286	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	86	1	no	—
290	C₄⋊C₈	—	86	1	no	—
291	#104	—	172	4	no	—
292	#104	—	172	4	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	86	2	no	—
296	C₂²⋊C₈	—	86	2	no	—
297	#97	—	43	2	no	—
298	#97	—	43	2	no	—
299	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
300	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
301	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
302	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
303	#95	—	86	1	no	—
304	#95	—	86	1	no	—
305	#41	—	2	4	no	—
306	#41	—	2	4	no	—
307	#41	—	86	4	no	—
308	#41	—	86	4	no	—
309	C₂×Q₈	—	43	2	no	—
310	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	43	2	no	—
315	C₂×D₄	—	86	2	no	—
316	C₂×D₄	—	86	1	no	—
317	C₂×D₄	—	86	1	no	—
318	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	86	2	no	—
321	C₂²×C₄	—	86	2	no	—
322	C₂²×C₄	#10621898	1	1	yes	characteristic
323	C₂²×C₄	#10621898	1	1	yes	characteristic
324	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
325	Q₁₆	—	172	4	no	—
326	SD₁₆	—	172	4	no	—
327	SD₁₆	—	172	4	no	—
328	D₈	—	172	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	4	4	no	—
331	M₁₆	—	86	4	no	—
332	M₁₆	—	172	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	—	43	4	no	—
338	C₂×C₈	—	86	2	no	—
339	C₂×C₈	—	86	2	no	—
340	C₂×C₈	—	86	2	no	—
341	C₂×C₈	—	172	4	no	—
342	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	86	1	no	—
349	C₄⋊C₄	—	86	1	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	86	2	no	—
353	C₂²⋊C₄	—	86	2	no	—
354	C₄²	—	86	2	no	—
355	C₄²	—	86	2	no	—
356	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
358	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
359	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
360	C₂³	—	2	2	no	—
361	C₂³	—	86	2	no	—
362	C₂³	C₂×#10621898	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	86	4	no	—
365	D₄	—	2	4	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	86	4	no	—
370	D₄	—	172	2	no	—
371	D₄	—	172	2	no	—
372	D₄	—	172	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	86	2	no	—
379	C₂×C₄	—	172	2	no	—
380	C₂×C₄	—	172	2	no	—
381	C₂×C₄	—	172	2	no	—
382	C₂×C₄	—	172	2	no	—
383	C₂×C₄	—	172	2	no	—
384	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
385	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
389	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
390	C₂×C₄	#13063370	1	2	yes	—
391	C₂×C₄	#13063371	1	2	yes	—
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	2	no	—
397	C₈	—	86	4	no	—
398	C₈	—	172	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	172	2	no	—
405	C₂²	—	172	2	no	—
406	C₂²	—	172	2	no	—
407	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
408	C₂²	#14583500	1	2	yes	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	344	2	no	—
415	C₄	—	172	2	no	—
416	C₄	#14583371	1	2	yes	—
417	C₄	#14583463	1	1	yes	characteristic
418	C₄	#14583466	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	—	8	2	no	—
421	C₂	—	344	2	no	—
422	C₂	#19137317	1	1	yes	characteristic
423	C₂	#19143496	1	1	yes	characteristic
424	C₂	#19143496	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2931	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19145040	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2931	D₄₃
hypocenter	C₄₃	#22281
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. #19143308	C₂	semidirect
3. #19135428	C₂	semidirect
4. #19135426	C₂	semidirect
5. #19134925	C₂	semidirect
6. #19134922	C₂	semidirect
7. #19134735	C₂	semidirect
8. #19134346	C₂	semidirect
9. C₄₃×#2931	C₂	semidirect
13. #14583294	C₄	semidirect
14. #14583291	C₄	semidirect
15. #14583289	C₄	semidirect
16. #14583286	C₄	semidirect
209. #2931	D₄₃	semidirect
251. C₄₃	#22281	semidirect

Maximal subgroups

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

subgroup	index
#19145040	2
#19143308	2
#19135428	2
#19135426	2
#19134925	2
#19134922	2
#19134735	2
#19134346	2
C₄₃×#2931	2
#22281	43