Subgroups — #25095181

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583021	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583016	C₂	1	1	yes	maximal, characteristic
3	#19143023	C₂	1	2	yes	maximal, complemented
4	#19134501	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134481	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134476	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134442	C₂	1	2	yes	maximal, complemented
8	#19134435	C₂	1	2	yes	maximal, complemented
9	C₄×#13063252	C₂	1	2	yes	maximal, complemented
10	#97×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2943	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063332	C₂²	1	2	yes	—
13	C₂×#13063332	C₂²	1	2	yes	—
14	#14583021	C₄	1	8	yes	complemented
15	#14583016	C₄	1	8	yes	complemented
16	C₂×#13063261	C₂²	1	1	yes	characteristic
17	C₂×#13063261	C₂²	1	1	yes	characteristic
18	C₂×#13063252	C₂²	1	2	yes	—
19	C₂×#13063252	C₂²	1	2	yes	—
20	#14582855	—	2	2	no	—
21	#14582855	—	2	2	no	—
22	#14582855	C₂²	1	2	yes	—
23	#14582855	C₂²	1	2	yes	—
24	C₄×#10621877	—	2	2	no	—
25	C₄×#10621877	C₂²	1	2	yes	—
26	C₂×#13063236	—	2	2	no	—
27	C₂×#13063236	C₂²	1	1	yes	characteristic
28	C₂×#13063235	C₂²	1	1	yes	characteristic
29	C₂×#13063235	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
32	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
33	#14582664	C₂²	1	2	yes	—
34	#14582658	C₂²	1	2	yes	—
35	#14582658	C₂²	1	2	yes	—
36	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
37	C₄×#41×C₄₃	C₂²	1	2	yes	—
38	C₄₃×#442	C₄	1	2	yes	complemented
39	C₄₃×#441	C₄	1	2	yes	complemented
40	C₄₃×#440	C₄	1	4	yes	complemented
41	C₄₃×#427	C₂²	1	1	yes	characteristic
42	C₄₃×#416	C₂²	1	2	yes	—
43	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
44	#13063332	—	2	4	no	—
45	#13063332	—	2	4	no	—
46	#13063332	C₂×C₄	1	8	yes	complemented
47	#13063332	C₂×C₄	1	8	yes	complemented
48	C₂×#10621877	—	2	2	no	—
49	C₂×#10621877	—	2	2	no	—
50	C₂×#10621877	C₂³	1	2	yes	—
51	C₂×#10621877	C₂³	1	2	yes	—
52	C₂²×C₄₃⋊C₈	—	2	2	no	—
53	C₂²×C₄₃⋊C₈	—	2	2	no	—
54	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₃	—	2	2	no	—
57	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
59	#13063261	C₂×C₄	1	4	yes	complemented
60	#13063261	C₂×C₄	1	4	yes	complemented
61	#13063252	C₂×C₄	1	8	yes	complemented
62	#13063252	C₂×C₄	1	8	yes	complemented
63	#13063236	—	2	2	no	—
64	#13063236	—	2	2	no	—
65	#13063236	—	2	2	no	—
66	#13063236	D₄	1	2	yes	—
67	#13063236	D₄	1	2	yes	—
68	#13063235	—	2	2	no	—
69	#13063235	C₂×C₄	1	4	yes	complemented
70	C₄×C₄₃⋊C₈	—	2	2	no	—
71	C₄×C₄₃⋊C₈	—	2	2	no	—
72	C₄×C₄₃⋊C₈	—	2	2	no	—
73	C₈×Dic₄₃	—	2	2	no	—
74	C₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
75	C₂×#41×C₄₃	C₂³	1	2	yes	—
76	#135×C₄₃	C₂×C₄	1	4	yes	—
77	#135×C₄₃	C₂×C₄	1	4	yes	—
78	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
79	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
84	C₄×D₄×C₄₃	—	2	4	no	—
85	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
86	#117×C₄₃	—	2	2	no	—
87	#117×C₄₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₃	—	2	2	no	—
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	#107×C₄₃	C₂×C₄	1	2	yes	—
91	#106×C₄₃	C₂×C₄	1	2	yes	—
92	#103×C₄₃	C₂×C₄	1	4	yes	—
93	#102×C₄₃	C₂×C₄	1	4	yes	—
94	#97×C₄₃	C₂×C₄	1	2	yes	—
95	#97×C₄₃	C₂×C₄	1	2	yes	—
96	#41×C₄₃	—	2	2	no	—
97	#41×C₄₃	—	2	2	no	—
98	#41×C₄₃	C₂²×C₄	1	4	yes	—
99	#41×C₄₃	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	#41	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₃	—	2	1	no	—
108	C₂²×Dic₄₃	—	2	1	no	—
109	Q₁₆×C₄₃	C₄²	1	4	yes	complemented
110	SD₁₆×C₄₃	C₄²	1	8	yes	complemented
111	D₈×C₄₃	C₄²	1	4	yes	complemented
112	C₂×C₈×C₄₃	—	2	1	no	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₄⋊C₄×C₄₃	—	2	4	no	—
120	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₄₃	—	2	4	no	—
122	C₂²⋊C₄×C₄₃	—	2	2	no	—
123	C₄²×C₄₃	—	2	4	no	—
124	C₄²×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₃	C₂×D₄	1	2	yes	—
127	C₄×Dic₄₃	—	2	1	no	—
128	C₄×Dic₄₃	—	2	1	no	—
129	C₄×Dic₄₃	—	4	4	no	—
130	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
131	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
132	#10621877	—	2	2	no	—
133	#10621877	—	2	2	no	—
134	#10621877	—	2	8	no	—
135	#10621877	—	2	8	no	—
136	#10621877	C₂²×C₄	1	4	yes	—
137	#10621877	C₂²×C₄	1	4	yes	—
138	C₂×C₄₃⋊C₈	—	2	2	no	—
139	C₂×C₄₃⋊C₈	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	8	no	—
141	C₂×C₄₃⋊C₈	—	2	8	no	—
142	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
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	2	yes	—
146	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄₃⋊C₈	#41	1	2	yes	—
148	C₂×C₄₃⋊C₈	#41	1	2	yes	—
149	C₂³×C₄₃	—	2	2	no	—
150	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
151	Q₈×C₄₃	—	2	2	no	—
152	Q₈×C₄₃	C₂×C₄²	1	4	yes	—
153	D₄×C₄₃	—	2	4	no	—
154	D₄×C₄₃	—	2	4	no	—
155	D₄×C₄₃	—	2	2	no	—
156	D₄×C₄₃	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	8	4	no	—
163	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
164	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₄₃	—	2	4	no	—
171	C₂×Dic₄₃	—	2	2	no	—
172	C₂×Dic₄₃	—	2	2	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₈×C₄₃	—	2	2	no	—
175	C₈×C₄₃	C₂×C₄²	1	2	yes	—
176	C₈×C₄₃	C₂×C₄²	1	2	yes	—
177	C₄₃⋊C₈	—	2	4	no	—
178	C₄₃⋊C₈	—	2	4	no	—
179	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
180	C₄₃⋊C₈	C₄×D₄	1	4	yes	—
181	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
182	#20512	—	43	1	no	maximal, Sylow
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	2	4	no	—
185	C₂²×C₄₃	—	4	4	no	—
186	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
188	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
189	C₄×C₄₃	—	2	4	no	—
190	C₄×C₄₃	—	2	4	no	—
191	C₄×C₄₃	—	4	4	no	—
192	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
193	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
196	Dic₄₃	—	2	4	no	—
197	Dic₄₃	—	4	2	no	—
198	C₂×#444	—	43	1	no	—
199	C₂×#443	—	43	1	no	—
200	#2943	D₄₃	1	1	yes	characteristic
201	#2875	—	43	2	no	—
202	#1778	—	43	1	no	—
203	#1773	—	43	1	no	—
204	#1772	—	43	1	no	—
205	#1765	—	43	2	no	—
206	#1764	—	43	2	no	—
207	C₄×#104	—	43	2	no	—
208	C₄×#97	—	43	1	no	—
209	C₂×C₄₃	—	2	1	no	—
210	C₂×C₄₃	—	2	1	no	—
211	C₂×C₄₃	—	4	4	no	—
212	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
213	C₂×C₄₃	#2956	1	2	yes	—
214	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
215	C₂×#131	—	43	2	no	—
216	C₂×#131	—	43	2	no	—
217	C₄×#41	C₂×D₄₃	1	2	yes	—
218	#444	—	43	8	no	—
219	#443	—	43	8	no	—
220	#442	Dic₄₃	1	2	yes	complemented
221	#441	Dic₄₃	1	2	yes	complemented
222	#440	Dic₄₃	1	4	yes	complemented
223	C₂×#108	—	43	1	no	—
224	C₂×#108	—	43	1	no	—
225	#427	C₂×D₄₃	1	1	yes	characteristic
226	C₂×#104	—	43	2	no	—
227	C₂×#104	—	43	2	no	—
228	#416	C₂×D₄₃	1	2	yes	—
229	#405	—	43	2	no	—
230	#405	—	43	2	no	—
231	#405	—	86	2	no	—
232	#405	—	86	2	no	—
233	C₄×M₁₆	—	43	2	no	—
234	C₄×M₁₆	—	86	2	no	—
235	C₂×#97	—	43	1	no	—
236	C₂×#97	—	43	1	no	—
237	C₂×#97	—	43	1	no	—
238	C₂×#97	—	86	2	no	—
239	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
240	C₂×C₄×C₈	—	43	1	no	—
241	C₂×C₄×C₈	—	43	1	no	—
242	C₄³	—	43	1	no	—
243	#341	—	43	2	no	—
244	#339	—	43	2	no	—
245	#339	—	43	2	no	—
246	C₄₃	#20512	1	1	yes	characteristic, complemented, Sylow
247	C₂×#41	C₂²×D₄₃	1	2	yes	—
248	#135	C₄×D₄₃	1	4	yes	—
249	#135	C₄×D₄₃	1	4	yes	—
250	C₂×Q₁₆	C₂×Dic₄₃	1	1	yes	characteristic
251	C₂×SD₁₆	C₂×Dic₄₃	1	2	yes	—
252	C₂×D₈	C₂×Dic₄₃	1	1	yes	characteristic
253	#131	—	43	8	no	—
254	#131	—	43	8	no	—
255	#131	—	86	4	no	—
256	#131	—	86	4	no	—
257	C₂×M₁₆	—	43	2	no	—
258	C₂×M₁₆	—	43	2	no	—
259	C₂×M₁₆	—	86	2	no	—
260	C₂×M₁₆	—	86	2	no	—
261	C₂²×C₈	—	43	1	no	—
262	C₂²×C₈	—	43	1	no	—
263	C₂²×C₈	—	86	2	no	—
264	C₂²×C₈	—	86	2	no	—
265	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
267	C₄×Q₈	C₂×Dic₄₃	1	4	yes	—
268	C₄×D₄	—	2	4	no	—
269	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
270	#117	—	2	2	no	—
271	#117	C₂²×D₄₃	1	2	yes	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	43	1	no	—
274	C₂×C₄²	—	43	1	no	—
275	C₂×C₄²	—	86	2	no	—
276	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
277	#108	—	43	4	no	—
278	#108	—	43	4	no	—
279	#107	C₂×Dic₄₃	1	2	yes	—
280	#106	C₂×Dic₄₃	1	2	yes	—
281	#104	—	43	8	no	—
282	#104	—	43	8	no	—
283	#103	C₂×Dic₄₃	1	4	yes	—
284	#102	C₂×Dic₄₃	1	4	yes	—
285	#97	—	43	4	no	—
286	#97	—	43	2	no	—
287	#97	—	43	2	no	—
288	#97	—	86	2	no	—
289	#97	—	86	2	no	—
290	#97	—	86	2	no	—
291	#97	—	86	2	no	—
292	#97	C₂×Dic₄₃	1	2	yes	—
293	#97	C₂×Dic₄₃	1	2	yes	—
294	C₄×C₈	—	43	4	no	—
295	C₄×C₈	—	86	2	no	—
296	C₄×C₈	—	86	2	no	—
297	C₄×C₈	—	86	2	no	—
298	C₄×C₈	—	86	2	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	C₂×C₄×D₄₃	1	4	yes	—
302	#41	C₂×C₄×D₄₃	1	4	yes	—
303	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	86	1	no	—
309	C₂²×C₄	—	86	1	no	—
310	C₂²×C₄	#10621900	1	2	yes	—
311	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
312	Q₁₆	C₄×Dic₄₃	1	4	yes	complemented
313	SD₁₆	C₄×Dic₄₃	1	8	yes	complemented
314	D₈	C₄×Dic₄₃	1	4	yes	complemented
315	M₁₆	—	43	4	no	—
316	M₁₆	—	43	4	no	—
317	M₁₆	—	86	8	no	—
318	M₁₆	—	86	8	no	—
319	M₁₆	—	86	2	no	—
320	M₁₆	—	86	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	43	2	no	—
324	C₂×C₈	—	43	2	no	—
325	C₂×C₈	—	43	1	no	—
326	C₂×C₈	—	43	2	no	—
327	C₂×C₈	—	43	1	no	—
328	C₂×C₈	—	43	2	no	—
329	C₂×C₈	—	43	2	no	—
330	C₂×C₈	—	86	8	no	—
331	C₂×C₈	—	86	8	no	—
332	C₂×C₈	—	86	2	no	—
333	C₂×C₈	—	86	2	no	—
334	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
335	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
336	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
337	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
338	C₂×C₈	C₂²×Dic₄₃	1	1	yes	characteristic
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	43	2	no	—
346	C₄²	—	43	2	no	—
347	C₄²	—	86	1	no	—
348	C₄²	—	86	1	no	—
349	C₄²	—	172	4	no	—
350	C₄²	D₄×D₄₃	1	2	yes	—
351	C₄²	C₂²×Dic₄₃	1	2	yes	—
352	C₂³	—	2	2	no	—
353	C₂³	C₂×#10621900	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	C₂×C₄×Dic₄₃	1	4	yes	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	2	no	—
359	D₄	C₂×C₄×Dic₄₃	1	4	yes	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	86	4	no	—
367	C₂×C₄	—	86	2	no	—
368	C₂×C₄	—	86	2	no	—
369	C₂×C₄	—	172	2	no	—
370	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
371	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
373	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
375	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
376	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	43	2	no	—
379	C₈	—	43	4	no	—
380	C₈	—	43	2	no	—
381	C₈	—	86	4	no	—
382	C₈	—	86	4	no	—
383	C₈	C₂×C₄×Dic₄₃	1	2	yes	—
384	C₈	C₂×C₄×Dic₄₃	1	2	yes	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
389	C₂²	C₄×#10621900	1	1	yes	characteristic
390	C₂²	C₄×#10621900	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	4	4	no	—
394	C₄	—	86	4	no	—
395	C₄	—	172	2	no	—
396	C₄	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
397	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
398	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
399	C₄	#41×Dic₄₃	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	4	4	no	—
403	C₂	C₄×D₄×Dic₄₃	1	1	yes	characteristic
404	C₂	#19143505	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2943	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#135×C₄₃	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2943	D₄₃
hypocenter	C₄₃	#20512
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
3. #19143023	C₂	semidirect
4. #19134501	C₂	semidirect
5. #19134481	C₂	semidirect
6. #19134476	C₂	semidirect
7. #19134442	C₂	semidirect
8. #19134435	C₂	semidirect
9. C₄×#13063252	C₂	semidirect
10. #97×Dic₄₃	C₂	semidirect
14. #14583021	C₄	semidirect
15. #14583016	C₄	semidirect
38. C₄₃×#442	C₄	semidirect
39. C₄₃×#441	C₄	semidirect
40. C₄₃×#440	C₄	semidirect
46. #13063332	C₂×C₄	semidirect
47. #13063332	C₂×C₄	semidirect
59. #13063261	C₂×C₄	semidirect
60. #13063261	C₂×C₄	semidirect
61. #13063252	C₂×C₄	semidirect
62. #13063252	C₂×C₄	semidirect
69. #13063235	C₂×C₄	semidirect
74. C₈×Dic₄₃	C₂×C₄	semidirect
109. Q₁₆×C₄₃	C₄²	semidirect
110. SD₁₆×C₄₃	C₄²	semidirect
111. D₈×C₄₃	C₄²	semidirect
220. #442	Dic₄₃	semidirect
221. #441	Dic₄₃	semidirect
222. #440	Dic₄₃	semidirect
246. C₄₃	#20512	semidirect
312. Q₁₆	C₄×Dic₄₃	semidirect
313. SD₁₆	C₄×Dic₄₃	semidirect
314. D₈	C₄×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583021	2
C₂×#14583016	2
#19143023	2
#19134501	2
#19134481	2
#19134476	2
#19134442	2
#19134435	2
C₄×#13063252	2
#97×Dic₄₃	2
C₄₃×#2943	2
#20512	43