Subgroups — #25114213

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143252	C₂	1	2	yes	maximal
2	#19143183	C₂	1	1	yes	maximal, characteristic
3	#19135344	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135197	C₂	1	2	yes	maximal, complemented
5	#19135191	C₂	1	2	yes	maximal, complemented
6	#19134693	C₂	1	2	yes	maximal
7	#19134634	C₂	1	1	yes	maximal, characteristic
8	#19134479	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134477	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134380	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621872	C₂²	1	1	yes	characteristic
13	#117×D₄₃	C₂²	1	2	yes	—
14	#14582959	—	2	2	no	—
15	#14582959	—	2	2	no	—
16	#14582955	—	2	2	no	—
17	#14582951	—	2	2	no	—
18	C₂×#13063261	C₂²	1	1	yes	characteristic
19	#14582940	C₄	1	2	yes	complemented
20	#14582940	C₄	1	2	yes	complemented
21	#14582938	C₄	1	2	yes	complemented
22	#14582938	C₄	1	2	yes	complemented
23	#14582937	C₂²	1	1	yes	characteristic
24	#14582935	C₂²	1	2	yes	—
25	#14582926	C₂²	1	2	yes	—
26	#14582862	C₂²	1	2	yes	—
27	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
28	#14582857	C₂²	1	2	yes	—
29	#14582854	C₂²	1	2	yes	—
30	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
31	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
32	#14582663	C₂²	1	2	yes	—
33	#14582660	C₂²	1	2	yes	—
34	#14582659	C₂²	1	2	yes	—
35	#14582658	C₂²	1	2	yes	—
36	#14582654	C₂²	1	1	yes	characteristic
37	#14582653	C₂²	1	1	yes	characteristic
38	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#427	C₂²	1	1	yes	characteristic
40	C₄₃×#424	C₂²	1	2	yes	—
41	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#339	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
44	C₂×#10621877	C₂³	1	2	yes	—
45	C₂×#10621872	—	2	2	no	—
46	C₂×#10621872	—	2	2	no	—
47	C₂×#10621872	C₂×C₄	1	2	yes	—
48	C₂×#10621872	C₂×C₄	1	2	yes	—
49	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
51	#13063284	C₂³	1	2	yes	—
52	#13063283	C₂×C₄	1	2	yes	—
53	#13063283	C₂×C₄	1	2	yes	—
54	#13063282	—	2	2	no	—
55	#13063281	—	2	2	no	—
56	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
57	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
58	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
59	C₂²⋊C₄×D₄₃	—	2	2	no	—
60	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
61	C₄²×D₄₃	—	2	2	no	—
62	#13063261	—	2	2	no	—
63	#13063259	C₂×C₄	1	1	yes	characteristic
64	#13063259	C₂×C₄	1	1	yes	characteristic
65	#13063258	C₂×C₄	1	2	yes	—
66	#13063258	C₂×C₄	1	2	yes	—
67	#13063257	C₂×C₄	1	2	yes	—
68	#13063256	C₂×C₄	1	2	yes	—
69	#13063256	C₂×C₄	1	2	yes	—
70	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
72	(C₂×D₄₃)⋊C₈	—	2	2	no	—
73	(C₂×D₄₃)⋊C₈	—	2	2	no	—
74	(C₂×D₄₃)⋊C₈	D₄	1	2	yes	—
75	(C₂×D₄₃)⋊C₈	D₄	1	2	yes	—
76	#13063235	—	2	2	no	—
77	#13063235	—	2	2	no	—
78	C₈×Dic₄₃	—	2	2	no	—
79	C₈×Dic₄₃	—	2	2	no	—
80	C₈×Dic₄₃	—	2	2	no	—
81	C₄₃⋊#95	—	2	1	no	—
82	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
85	#117×C₄₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
87	#108×C₄₃	—	2	2	no	—
88	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
89	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
90	#106×C₄₃	C₂×C₄	1	2	yes	—
91	C₄⋊C₈×C₄₃	—	2	2	no	—
92	C₄⋊C₈×C₄₃	—	2	2	no	—
93	#97×C₄₃	—	2	2	no	—
94	C₂³×D₄₃	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	—	2	1	no	—
96	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₃	—	2	1	no	—
98	C₂²×Dic₄₃	#41	1	1	yes	characteristic
99	C₂×C₄×D₄₃	—	2	1	no	—
100	C₂×C₄×D₄₃	—	2	1	no	—
101	C₂×C₄×D₄₃	—	2	1	no	—
102	C₂×C₄×D₄₃	—	2	1	no	—
103	C₂×C₄×D₄₃	—	2	2	no	—
104	C₂×C₄×D₄₃	—	2	2	no	—
105	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
107	M₁₆×C₄₃	—	2	2	no	—
108	M₁₆×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	—	2	1	no	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₄₃	#41	1	2	yes	—
116	C₂×C₈×C₄₃	#41	1	2	yes	—
117	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
118	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂²⋊C₄×C₄₃	—	2	2	no	—
120	C₄²×C₄₃	—	2	2	no	—
121	C₄²×C₄₃	—	2	1	no	—
122	C₄²×C₄₃	—	2	1	no	—
123	C₂²⋊Dic₄₃	—	2	2	no	—
124	(C₂×D₄₃)⋊C₄	—	2	2	no	—
125	(C₂×D₄₃)⋊C₄	—	2	2	no	—
126	(C₂×D₄₃)⋊C₄	—	4	2	no	—
127	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
128	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
129	Dic₄₃⋊C₄	—	2	2	no	—
130	Dic₄₃⋊C₄	—	2	2	no	—
131	C₄×Dic₄₃	—	2	2	no	—
132	C₄×Dic₄₃	—	2	2	no	—
133	C₄×Dic₄₃	—	2	2	no	—
134	C₄×Dic₄₃	—	2	1	no	—
135	C₄×Dic₄₃	—	2	1	no	—
136	#10621877	—	2	2	no	—
137	#10621877	—	2	2	no	—
138	C₂×C₄₃⋊C₈	—	2	1	no	—
139	C₂×C₄₃⋊C₈	—	2	1	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	2	no	—
143	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
146	#10621872	—	2	4	no	—
147	#10621872	—	2	4	no	—
148	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
149	C₂²×D₄₃	—	2	1	no	—
150	C₂²×D₄₃	—	2	1	no	—
151	C₂²×D₄₃	—	4	1	no	—
152	C₂²×D₄₃	—	4	1	no	—
153	C₂²×D₄₃	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₄₃	—	2	2	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	1	no	—
159	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×Dic₄₃	—	2	1	no	—
166	C₂×Dic₄₃	—	2	1	no	—
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	2	2	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
173	C₄×D₄₃	—	2	2	no	—
174	C₄×D₄₃	—	2	2	no	—
175	C₄×D₄₃	—	2	2	no	—
176	C₄×D₄₃	—	2	2	no	—
177	C₄×D₄₃	—	4	4	no	—
178	C₄×D₄₃	—	8	2	no	—
179	C₈×C₄₃	—	2	2	no	—
180	C₈×C₄₃	—	4	2	no	—
181	C₈×C₄₃	#117	1	2	yes	—
182	C₈×C₄₃	#117	1	2	yes	—
183	C₄₃⋊C₈	—	2	2	no	—
184	C₄₃⋊C₈	—	2	1	no	—
185	C₄₃⋊C₈	—	2	1	no	—
186	C₄₃⋊C₈	—	4	2	no	—
187	#22608	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	—	2	1	no	—
190	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂²×C₄₃	#552	1	1	yes	characteristic
192	C₂²×C₄₃	#552	1	1	yes	characteristic
193	C₂×D₄₃	—	2	2	no	—
194	C₂×D₄₃	—	2	2	no	—
195	C₂×D₄₃	—	2	2	no	—
196	C₂×D₄₃	—	8	1	no	—
197	C₂×D₄₃	—	8	1	no	—
198	C₄×C₄₃	—	4	2	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	8	1	no	—
201	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
202	C₄×C₄₃	#519	1	1	yes	characteristic
203	C₄×C₄₃	#547	1	1	yes	characteristic
204	C₄×C₄₃	#547	1	1	yes	characteristic
205	Dic₄₃	—	2	2	no	—
206	Dic₄₃	—	4	2	no	—
207	Dic₄₃	—	4	2	no	—
208	Dic₄₃	—	4	2	no	—
209	#2924	—	43	2	no	—
210	#2911	—	43	1	no	—
211	#1946	D₄₃	1	1	yes	characteristic, complemented
212	#1945	—	43	1	no	—
213	#1922	—	43	2	no	—
214	#1922	—	43	2	no	—
215	#1826	—	43	2	no	—
216	#1811	—	43	1	no	—
217	#1773	—	43	1	no	—
218	#1772	—	43	1	no	—
219	#1753	—	43	1	no	—
220	C₂×C₄₃	—	2	1	no	—
221	C₂×C₄₃	—	2	1	no	—
222	C₂×C₄₃	#2344	1	1	yes	characteristic
223	C₂×C₄₃	#2955	1	1	yes	characteristic
224	C₂×C₄₃	#2956	1	1	yes	characteristic
225	D₄₃	—	4	2	no	—
226	C₂²×M₁₆	—	43	1	no	—
227	C₂×#117	—	43	2	no	—
228	#433	—	86	2	no	—
229	#433	—	86	2	no	—
230	#432	—	86	2	no	—
231	#431	—	86	2	no	—
232	C₂×#108	—	43	1	no	—
233	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
234	#428	—	43	2	no	—
235	#428	—	43	2	no	—
236	#428	—	43	2	no	—
237	#428	—	43	2	no	—
238	#427	—	43	1	no	—
239	#427	—	43	2	no	—
240	#427	C₂×D₄₃	1	1	yes	characteristic
241	#424	—	43	2	no	—
242	#424	C₂×D₄₃	1	2	yes	—
243	#407	—	43	2	no	—
244	C₂×C₂²⋊C₈	—	43	1	no	—
245	#405	—	43	2	no	—
246	#405	—	43	2	no	—
247	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
248	C₂×C₄×C₈	—	43	1	no	—
249	C₄×C₂²⋊C₄	—	43	1	no	—
250	#341	—	43	2	no	—
251	#339	—	43	2	no	—
252	#339	—	43	2	no	—
253	#339	—	43	2	no	—
254	#339	C₂×D₄₃	1	2	yes	—
255	#336	—	43	1	no	—
256	#336	—	43	1	no	—
257	C₄₃	#22608	1	1	yes	characteristic, complemented, Sylow
258	C₂³×C₄	—	43	1	no	—
259	C₂×M₁₆	—	43	2	no	—
260	C₂×M₁₆	—	43	2	no	—
261	C₂×M₁₆	—	43	2	no	—
262	C₂×M₁₆	—	86	2	no	—
263	C₂×M₁₆	—	86	2	no	—
264	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
265	C₂²×C₈	—	43	1	no	—
266	C₂²×C₈	—	43	1	no	—
267	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
269	#117	—	43	2	no	—
270	#117	—	43	2	no	—
271	#117	—	43	2	no	—
272	#117	—	86	2	no	—
273	#117	—	86	2	no	—
274	#117	C₂²×D₄₃	1	2	yes	—
275	C₂×C₄⋊C₄	—	43	2	no	—
276	C₂×C₄⋊C₄	—	43	2	no	—
277	C₂×C₂²⋊C₄	—	86	2	no	—
278	C₂×C₂²⋊C₄	—	86	1	no	—
279	C₂×C₄²	—	43	1	no	—
280	C₂×C₄²	—	86	2	no	—
281	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
282	#108	—	2	2	no	—
283	#108	—	86	2	no	—
284	#107	—	43	1	no	—
285	#107	—	43	1	no	—
286	#107	—	43	2	no	—
287	#107	—	43	2	no	—
288	#107	C₄×D₄₃	1	1	yes	characteristic
289	#107	C₄×D₄₃	1	1	yes	characteristic
290	#106	—	43	2	no	—
291	#106	—	43	2	no	—
292	#106	—	43	2	no	—
293	#106	C₄×D₄₃	1	2	yes	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	86	2	no	—
297	C₄⋊C₈	—	86	2	no	—
298	C₂²⋊C₈	—	43	2	no	—
299	C₂²⋊C₈	—	43	2	no	—
300	C₂²⋊C₈	—	86	2	no	—
301	C₂²⋊C₈	—	86	2	no	—
302	#97	—	2	2	no	—
303	#97	—	86	2	no	—
304	#97	—	86	2	no	—
305	C₄×C₈	—	86	2	no	—
306	C₄×C₈	—	86	2	no	—
307	C₄×C₈	—	86	2	no	—
308	#95	—	86	1	no	—
309	C₂⁴	—	43	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	43	1	no	—
312	C₂²×C₄	—	43	2	no	—
313	C₂²×C₄	—	43	2	no	—
314	C₂²×C₄	—	86	2	no	—
315	C₂²×C₄	—	86	2	no	—
316	C₂²×C₄	—	86	1	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	—	86	1	no	—
319	C₂²×C₄	—	86	1	no	—
320	C₂²×C₄	—	86	1	no	—
321	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	86	4	no	—
325	M₁₆	—	86	4	no	—
326	M₁₆	—	86	2	no	—
327	M₁₆	—	86	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	43	2	no	—
332	C₂×C₈	—	43	1	no	—
333	C₂×C₈	—	43	1	no	—
334	C₂×C₈	—	86	1	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	—	86	1	no	—
337	C₂×C₈	—	86	1	no	—
338	C₂×C₈	—	86	2	no	—
339	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
341	C₂×C₈	D₄×D₄₃	1	2	yes	—
342	C₂×C₈	#10621900	1	2	yes	—
343	C₂×C₈	#10621902	1	2	yes	—
344	C₄⋊C₄	—	43	2	no	—
345	C₄⋊C₄	—	43	2	no	—
346	C₄⋊C₄	—	86	2	no	—
347	C₄⋊C₄	—	86	2	no	—
348	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
349	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	86	2	no	—
352	C₂²⋊C₄	—	86	2	no	—
353	C₂²⋊C₄	—	86	2	no	—
354	C₂²⋊C₄	—	172	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	86	2	no	—
359	C₄²	—	86	2	no	—
360	C₄²	—	86	2	no	—
361	C₄²	—	86	1	no	—
362	C₄²	—	86	1	no	—
363	C₂³	—	43	2	no	—
364	C₂³	—	86	1	no	—
365	C₂³	—	86	1	no	—
366	C₂³	—	172	1	no	—
367	C₂³	—	172	1	no	—
368	C₂³	#41×D₄₃	1	1	yes	characteristic
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	43	2	no	—
375	C₂×C₄	—	86	1	no	—
376	C₂×C₄	—	86	1	no	—
377	C₂×C₄	—	86	2	no	—
378	C₂×C₄	—	86	2	no	—
379	C₂×C₄	—	86	2	no	—
380	C₂×C₄	—	86	2	no	—
381	C₂×C₄	—	86	2	no	—
382	C₂×C₄	—	86	2	no	—
383	C₂×C₄	—	86	2	no	—
384	C₂×C₄	—	344	2	no	—
385	C₂×C₄	—	172	4	no	—
386	C₂×C₄	—	172	1	no	—
387	C₂×C₄	—	172	1	no	—
388	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
390	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
391	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
392	C₂×C₄	#13063372	1	1	yes	characteristic
393	C₂×C₄	#13063373	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	86	1	no	—
397	C₈	—	86	1	no	—
398	C₈	—	86	2	no	—
399	C₈	—	172	2	no	—
400	C₈	#13063283	1	2	yes	—
401	C₈	#13063283	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	86	2	no	—
405	C₂²	—	86	2	no	—
406	C₂²	—	86	2	no	—
407	C₂²	—	344	1	no	—
408	C₂²	—	344	1	no	—
409	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
410	C₂²	#14583583	1	1	yes	characteristic
411	C₂²	#14583587	1	1	yes	characteristic
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	86	2	no	—
416	C₄	—	172	2	no	—
417	C₄	—	172	2	no	—
418	C₄	—	172	2	no	—
419	C₄	C₂×#13063283	1	1	yes	characteristic
420	C₄	#14583375	1	1	yes	characteristic
421	C₄	#14583549	1	1	yes	characteristic
422	C₄	#14583552	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	172	2	no	—
426	C₂	#19137463	1	1	yes	characteristic
427	C₂	#19143495	1	1	yes	characteristic
428	C₂	#19143503	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1946	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂³×D₄₃	#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1946	D₄₃
hypocenter	C₄₃	#22608
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1946

Complements

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

N	H ≅ G/N	type
3. #19135344	C₂	semidirect
4. #19135197	C₂	semidirect
5. #19135191	C₂	semidirect
8. #19134479	C₂	semidirect
9. #19134477	C₂	semidirect
11. C₄₃×#1946	C₂	semidirect
19. #14582940	C₄	semidirect
20. #14582940	C₄	semidirect
21. #14582938	C₄	semidirect
22. #14582938	C₄	semidirect
211. #1946	D₄₃	semidirect
257. C₄₃	#22608	semidirect

Maximal subgroups

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

subgroup	index
#19143252	2
#19143183	2
#19135344	2
#19135197	2
#19135191	2
#19134693	2
#19134634	2
#19134479	2
#19134477	2
#19134380	2
C₄₃×#1946	2
#22608	43