Subgroups — #25115067

Order 11008.

862 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	C₂×#14583016	C₂	1	1	yes	maximal, characteristic
2	#19143479	C₂	1	1	yes	maximal, characteristic
3	#19143188	C₂	1	2	yes	maximal, complemented
4	#19135375	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135373	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134821	C₂	1	2	yes	maximal, complemented
7	#19134819	C₂	1	2	yes	maximal, complemented
8	#19134750	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134652	C₂	1	2	yes	maximal, complemented
10	#19134475	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2952	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063332	C₂²	1	2	yes	—
13	#14583382	C₂²	1	2	yes	—
14	#14583016	C₄	1	8	yes	complemented
15	#14583011	—	2	1	no	—
16	#14583006	—	2	1	no	—
17	SD₁₆×Dic₄₃	—	2	2	no	—
18	C₂×#13063261	C₂²	1	1	yes	characteristic
19	C₂×#13063260	C₂²	1	1	yes	characteristic
20	#14582942	—	2	2	no	—
21	#14582942	C₂²	1	2	yes	—
22	#14582939	—	2	2	no	—
23	#14582939	C₂²	1	2	yes	—
24	#14582935	—	2	2	no	—
25	#14582935	C₂²	1	1	yes	characteristic
26	C₂×#13063257	C₂²	1	1	yes	characteristic
27	C₂×#13063256	—	2	2	no	—
28	C₂×#13063256	C₂²	1	2	yes	—
29	C₂×#13063252	C₂²	1	2	yes	—
30	#14582900	C₂²	1	2	yes	—
31	#14582854	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	#14582768	C₂²	1	2	yes	—
34	#14582668	C₂²	1	2	yes	—
35	#14582667	C₂²	1	2	yes	—
36	#14582660	C₂²	1	1	yes	characteristic
37	#14582658	C₂²	1	1	yes	characteristic
38	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#520	C₂²	1	2	yes	—
40	C₄₃×#442	—	2	1	no	—
41	C₄₃×#441	—	2	1	no	—
42	C₄×SD₁₆×C₄₃	—	2	2	no	—
43	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#417	C₂²	1	2	yes	—
45	C₄₃×#405	C₂²	1	1	yes	characteristic
46	#13063332	—	2	4	no	—
47	#13063332	C₂×C₄	1	8	yes	complemented
48	C₂×#10621877	—	2	2	no	—
49	C₂×#10621877	C₂³	1	1	yes	characteristic
50	C₂×#10621877	C₂³	1	2	yes	—
51	C₂²×C₄₃⋊C₈	—	2	2	no	—
52	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
53	Q₈×Dic₄₃	—	2	2	no	—
54	D₄×Dic₄₃	—	2	2	no	—
55	D₄×Dic₄₃	—	4	2	no	—
56	#13063284	—	2	2	no	—
57	#13063284	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₃	—	2	2	no	—
59	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
60	C₂×Dic₄₃⋊C₄	—	4	2	no	—
61	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
62	#13063261	C₂×C₄	1	4	yes	complemented
63	#13063260	—	2	2	no	—
64	#13063258	—	2	2	no	—
65	#13063258	—	2	2	no	—
66	#13063258	D₄	1	2	yes	—
67	#13063257	—	2	1	no	—
68	#13063257	—	2	1	no	—
69	#13063256	—	2	2	no	—
70	#13063256	—	2	2	no	—
71	#13063256	—	2	2	no	—
72	#13063256	—	2	2	no	—
73	#13063256	D₄	1	2	yes	—
74	#13063252	C₂×C₄	1	8	yes	complemented
75	#13063249	—	2	2	no	—
76	#13063246	—	2	2	no	—
77	#13063235	—	2	1	no	—
78	C₈×Dic₄₃	—	2	1	no	—
79	C₈×Dic₄₃	C₂×C₄	1	4	yes	complemented
80	C₂×#41×C₄₃	C₂³	1	2	yes	—
81	#135×C₄₃	C₂×C₄	1	4	yes	—
82	#135×C₄₃	Q₈	1	4	yes	—
83	C₂×Q₁₆×C₄₃	D₄	1	1	yes	characteristic
84	C₂×SD₁₆×C₄₃	D₄	1	2	yes	—
85	C₂×D₈×C₄₃	D₄	1	1	yes	characteristic
86	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₄×Q₈×C₄₃	—	2	2	no	—
89	C₄×D₄×C₄₃	—	2	2	no	—
90	C₄×D₄×C₄₃	—	4	2	no	—
91	#117×C₄₃	—	2	2	no	—
92	#117×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
95	#106×C₄₃	—	2	1	no	—
96	#106×C₄₃	—	2	1	no	—
97	#103×C₄₃	—	2	2	no	—
98	#102×C₄₃	—	2	2	no	—
99	#97×C₄₃	—	2	1	no	—
100	C₄×C₈×C₄₃	—	2	1	no	—
101	#41×C₄₃	—	2	2	no	—
102	#41×C₄₃	—	2	2	no	—
103	#41×C₄₃	C₂²×C₄	1	4	yes	—
104	#41×C₄₃	C₂×Q₈	1	4	yes	—
105	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	4	2	no	—
111	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂²×Dic₄₃	—	2	1	no	—
113	C₂²×Dic₄₃	—	2	2	no	—
114	C₂²×Dic₄₃	—	4	2	no	—
115	Q₁₆×C₄₃	C₄⋊C₄	1	4	yes	complemented
116	SD₁₆×C₄₃	C₄⋊C₄	1	8	yes	complemented
117	D₈×C₄₃	C₄⋊C₄	1	4	yes	complemented
118	M₁₆×C₄₃	—	2	1	no	—
119	M₁₆×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	4	2	no	—
128	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂²⋊C₄×C₄₃	—	4	2	no	—
131	C₄²×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	4	2	no	—
133	C₂²⋊Dic₄₃	—	2	1	no	—
134	C₂²⋊Dic₄₃	—	4	2	no	—
135	C₄⋊Dic₄₃	—	2	2	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	4	2	no	—
138	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
139	Dic₄₃⋊C₄	—	8	4	no	—
140	C₄×Dic₄₃	—	2	1	no	—
141	C₄×Dic₄₃	—	2	1	no	—
142	C₄×Dic₄₃	—	4	2	no	—
143	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
144	#10621877	—	2	2	no	—
145	#10621877	—	2	8	no	—
146	#10621877	—	2	1	no	—
147	#10621877	—	2	1	no	—
148	#10621877	C₂²×C₄	1	4	yes	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	8	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄₃⋊C₈	#41	1	2	yes	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
158	Q₈×C₄₃	—	2	2	no	—
159	Q₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
160	D₄×C₄₃	—	2	4	no	—
161	D₄×C₄₃	—	2	4	no	—
162	D₄×C₄₃	—	2	2	no	—
163	D₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	8	2	no	—
170	C₂×C₄×C₄₃	—	16	2	no	—
171	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×Dic₄₃	—	2	4	no	—
178	C₂×Dic₄₃	—	2	2	no	—
179	C₂×Dic₄₃	—	2	2	no	—
180	C₂×Dic₄₃	—	4	2	no	—
181	C₂×Dic₄₃	—	8	2	no	—
182	C₂×Dic₄₃	—	16	2	no	—
183	C₈×C₄₃	—	4	1	no	—
184	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
185	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
186	C₄₃⋊C₈	—	2	4	no	—
187	C₄₃⋊C₈	—	4	1	no	—
188	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
189	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
190	#22689	—	43	1	no	maximal, Sylow
191	C₂²×C₄₃	—	2	2	no	—
192	C₂²×C₄₃	—	2	4	no	—
193	C₂²×C₄₃	—	4	2	no	—
194	C₂²×C₄₃	—	4	2	no	—
195	C₂²×C₄₃	#520	1	1	yes	characteristic
196	C₂²×C₄₃	D₄²	1	1	yes	characteristic
197	C₂²×C₄₃	#554	1	1	yes	characteristic
198	C₄×C₄₃	—	2	4	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	8	2	no	—
201	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₄₃	#547	1	1	yes	characteristic
204	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
205	Dic₄₃	—	2	4	no	—
206	Dic₄₃	—	4	2	no	—
207	Dic₄₃	—	8	2	no	—
208	C₂×#443	—	43	1	no	—
209	#2952	—	43	1	no	—
210	#2952	D₄₃	1	1	yes	characteristic
211	#2912	—	43	2	no	—
212	#1951	—	43	1	no	—
213	#1951	—	43	1	no	—
214	#1859	—	43	2	no	—
215	#1859	—	43	2	no	—
216	#1844	—	43	1	no	—
217	#1815	—	43	2	no	—
218	#1772	—	43	1	no	—
219	C₂×C₄₃	—	2	1	no	—
220	C₂×C₄₃	—	2	1	no	—
221	C₂×C₄₃	—	4	4	no	—
222	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₄₃	#3291	1	2	yes	—
224	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
225	C₂×#131	—	43	2	no	—
226	#520	—	43	2	no	—
227	#520	C₂×D₄₃	1	2	yes	—
228	#443	—	43	8	no	—
229	#442	—	2	1	no	—
230	#442	—	86	1	no	—
231	#441	—	2	1	no	—
232	#441	—	86	1	no	—
233	C₄×SD₁₆	—	2	2	no	—
234	C₄×SD₁₆	—	86	2	no	—
235	C₂×#108	—	43	1	no	—
236	C₂×#108	—	43	1	no	—
237	#428	—	43	2	no	—
238	#428	—	43	2	no	—
239	#428	—	86	2	no	—
240	#428	—	86	2	no	—
241	#427	—	43	1	no	—
242	#427	—	86	2	no	—
243	C₂×#106	—	43	1	no	—
244	C₂×#106	—	43	2	no	—
245	C₂×#106	—	86	2	no	—
246	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
247	C₂×#104	—	43	2	no	—
248	#417	—	43	2	no	—
249	#417	C₂×D₄₃	1	2	yes	—
250	#405	—	43	1	no	—
251	#405	C₂×D₄₃	1	1	yes	characteristic
252	C₂×C₄×C₈	—	43	1	no	—
253	#384	—	43	2	no	—
254	#343	—	43	2	no	—
255	#343	—	43	2	no	—
256	#339	—	43	1	no	—
257	#339	—	43	1	no	—
258	C₄₃	#22689	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	C₂²×D₄₃	1	2	yes	—
260	#135	Dic₈₆	1	4	yes	—
261	#135	C₄×D₄₃	1	4	yes	—
262	C₂×Q₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
263	C₂×SD₁₆	C₂²⋊D₄₃	1	2	yes	—
264	C₂×D₈	C₂²⋊D₄₃	1	1	yes	characteristic
265	#131	—	43	8	no	—
266	#131	—	86	4	no	—
267	C₂×M₁₆	—	43	2	no	—
268	C₂×M₁₆	—	43	1	no	—
269	C₂×M₁₆	—	86	2	no	—
270	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
271	C₂²×C₈	—	43	1	no	—
272	C₂²×C₈	—	86	2	no	—
273	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	86	2	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	—	4	2	no	—
278	C₄×D₄	—	86	2	no	—
279	C₄×D₄	—	172	2	no	—
280	#117	—	2	2	no	—
281	#117	—	43	1	no	—
282	#117	—	86	2	no	—
283	#117	C₂²×D₄₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	43	2	no	—
286	C₂×C₄⋊C₄	—	86	2	no	—
287	C₂×C₄⋊C₄	—	172	2	no	—
288	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
289	C₂×C₄²	—	43	1	no	—
290	#108	—	43	4	no	—
291	#108	—	86	2	no	—
292	#107	—	43	2	no	—
293	#107	—	86	2	no	—
294	#107	—	86	2	no	—
295	#106	—	2	1	no	—
296	#106	—	2	1	no	—
297	#106	—	43	2	no	—
298	#106	—	86	2	no	—
299	#106	—	86	2	no	—
300	#106	—	86	2	no	—
301	#106	—	86	1	no	—
302	#106	—	86	1	no	—
303	#106	—	86	2	no	—
304	#104	—	43	8	no	—
305	#103	—	2	2	no	—
306	#103	—	86	2	no	—
307	#102	—	2	2	no	—
308	#102	—	86	2	no	—
309	#97	—	2	1	no	—
310	#97	—	86	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	43	4	no	—
313	C₄×C₈	—	86	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	C₂×Dic₈₆	1	4	yes	—
317	#41	C₂×C₄×D₄₃	1	4	yes	—
318	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	86	1	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	—	172	2	no	—
327	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
328	Q₁₆	Dic₄₃⋊C₄	1	4	yes	complemented
329	SD₁₆	Dic₄₃⋊C₄	1	8	yes	complemented
330	D₈	Dic₄₃⋊C₄	1	4	yes	complemented
331	M₁₆	—	2	1	no	—
332	M₁₆	—	2	1	no	—
333	M₁₆	—	43	4	no	—
334	M₁₆	—	86	8	no	—
335	M₁₆	—	86	2	no	—
336	M₁₆	—	86	1	no	—
337	M₁₆	—	86	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	43	2	no	—
340	C₂×C₈	—	43	1	no	—
341	C₂×C₈	—	43	1	no	—
342	C₂×C₈	—	43	2	no	—
343	C₂×C₈	—	86	8	no	—
344	C₂×C₈	—	86	2	no	—
345	C₂×C₈	—	86	1	no	—
346	C₂×C₈	C₂×Dic₈₆	1	2	yes	—
347	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
348	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	43	2	no	—
354	C₄⋊C₄	—	86	2	no	—
355	C₄⋊C₄	—	86	2	no	—
356	C₄⋊C₄	—	344	4	no	—
357	C₄⋊C₄	—	172	2	no	—
358	C₄⋊C₄	D₄×D₄₃	1	2	yes	—
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	86	1	no	—
362	C₂²⋊C₄	—	172	2	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	4	2	no	—
365	C₄²	—	43	2	no	—
366	C₄²	—	86	1	no	—
367	C₄²	—	86	1	no	—
368	C₄²	—	172	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	#13063370	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	C₂×Dic₄₃⋊C₄	1	4	yes	—
373	D₄	—	2	4	no	—
374	D₄	—	2	4	no	—
375	D₄	—	2	2	no	—
376	D₄	C₂×Dic₄₃⋊C₄	1	4	yes	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	16	2	no	—
384	C₂×C₄	—	86	4	no	—
385	C₂×C₄	—	86	2	no	—
386	C₂×C₄	—	86	2	no	—
387	C₂×C₄	—	344	2	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	—	688	2	no	—
390	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
394	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
395	C₂×C₄	#13063372	1	1	yes	characteristic
396	C₈	—	4	1	no	—
397	C₈	—	43	2	no	—
398	C₈	—	43	2	no	—
399	C₈	—	86	4	no	—
400	C₈	—	172	1	no	—
401	C₈	C₂×Dic₄₃⋊C₄	1	2	yes	—
402	C₈	C₂×Dic₄₃⋊C₄	1	2	yes	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	#14583378	1	1	yes	characteristic
408	C₂²	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
409	C₂²	#14583608	1	1	yes	characteristic
410	C₄	—	2	4	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	2	no	—
413	C₄	—	86	4	no	—
414	C₄	—	344	2	no	—
415	C₄	—	172	2	no	—
416	C₄	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
417	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
418	C₄	#14583548	1	1	yes	characteristic
419	C₄	D₄×Dic₈₆	1	1	yes	characteristic
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	4	4	no	—
423	C₂	D₄×Dic₄₃⋊C₄	1	1	yes	characteristic
424	C₂	#19146386	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2952	C₂
socle	C₂²×C₄₃	D₄²
prime radical	C₂×#135×C₄₃	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2952	D₄₃
hypocenter	C₄₃	#22689
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #2952

Complements

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

N	H ≅ G/N	type
3. #19143188	C₂	semidirect
4. #19135375	C₂	semidirect
5. #19135373	C₂	semidirect
6. #19134821	C₂	semidirect
7. #19134819	C₂	semidirect
8. #19134750	C₂	semidirect
9. #19134652	C₂	semidirect
10. #19134475	C₂	semidirect
14. #14583016	C₄	semidirect
47. #13063332	C₂×C₄	semidirect
62. #13063261	C₂×C₄	semidirect
74. #13063252	C₂×C₄	semidirect
79. C₈×Dic₄₃	C₂×C₄	semidirect
115. Q₁₆×C₄₃	C₄⋊C₄	semidirect
116. SD₁₆×C₄₃	C₄⋊C₄	semidirect
117. D₈×C₄₃	C₄⋊C₄	semidirect
258. C₄₃	#22689	semidirect
328. Q₁₆	Dic₄₃⋊C₄	semidirect
329. SD₁₆	Dic₄₃⋊C₄	semidirect
330. D₈	Dic₄₃⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583016	2
#19143479	2
#19143188	2
#19135375	2
#19135373	2
#19134821	2
#19134819	2
#19134750	2
#19134652	2
#19134475	2
C₄₃×#2952	2
#22689	43