Subgroups — #25067813

Order 11008.

598 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	#19144667	C₂	1	1	yes	maximal, characteristic
2	#19143725	C₂	1	1	yes	maximal, characteristic
3	#19143696	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133484	C₂	1	2	yes	maximal, complemented
5	#19133472	C₂	1	2	yes	maximal, complemented
6	#19133465	C₂	1	2	yes	maximal, complemented
7	#19133401	C₂	1	2	yes	maximal, complemented
8	#19133049	C₂	1	1	yes	maximal, characteristic, complemented
9	#19132975	C₂	1	1	yes	maximal, characteristic
10	#19132879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583456	C₂²	1	1	yes	characteristic
13	C₄×#10621898	C₂²	1	1	yes	characteristic
14	#14583241	C₄	1	2	yes	—
15	#14583185	C₄	1	1	yes	characteristic
16	#14583180	C₄	1	1	yes	characteristic
17	#14583110	C₄	1	1	yes	characteristic
18	#14583105	C₄	1	1	yes	characteristic
19	#14583063	C₄	1	2	yes	—
20	#14583029	—	2	1	no	—
21	#14583026	C₂²	1	2	yes	—
22	C₈×Dic₈₆	—	2	1	no	—
23	#14583023	C₂²	1	2	yes	—
24	#14583023	C₂²	1	2	yes	—
25	C₄×Dic₁₇₂	C₂²	1	2	yes	—
26	C₄×#10621873	C₂²	1	2	yes	—
27	#14582976	C₂²	1	2	yes	—
28	#14582975	—	2	2	no	—
29	#14582957	—	2	2	no	—
30	#14582952	C₂²	1	1	yes	characteristic
31	#14582951	—	2	1	no	—
32	#14582921	—	2	1	no	—
33	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
34	#14582629	C₂²	1	1	yes	characteristic
35	#14582629	C₂²	1	2	yes	—
36	#14582629	C₂²	1	2	yes	—
37	#14582629	C₂²	1	1	yes	characteristic
38	#14582626	C₂²	1	1	yes	characteristic
39	#14582626	C₂²	1	1	yes	characteristic
40	#14582621	C₂²	1	2	yes	—
41	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
42	C₄₃×#431	C₂²	1	1	yes	characteristic
43	C₄₃×#431	C₂²	1	1	yes	characteristic
44	C₄₃×#423	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	2	yes	—
46	C₄₃×#334	C₂²	1	2	yes	—
47	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
48	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
49	C₂×#10621873	C₂×C₄	1	2	yes	—
50	C₂×#10621872	—	2	2	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	#13063325	C₂×C₄	1	1	yes	characteristic
53	#13063325	C₂×C₄	1	1	yes	characteristic
54	#13063317	—	2	1	no	—
55	#13063304	—	2	1	no	—
56	#13063304	C₂×C₄	1	2	yes	—
57	C₄×Dic₈₆	—	2	1	no	—
58	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
60	C₄×Dic₈₆	C₂³	1	2	yes	—
61	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
62	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
63	C₄×C₂²⋊D₄₃	—	2	1	no	—
64	C₄×C₂²⋊D₄₃	—	2	1	no	—
65	#13063284	—	2	1	no	—
66	#13063284	C₂×C₄	1	1	yes	characteristic
67	#13063282	—	2	1	no	—
68	C₄²×D₄₃	—	2	1	no	—
69	#13063259	C₂×C₄	1	2	yes	—
70	#13063257	C₂×C₄	1	2	yes	—
71	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
72	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
73	Dic₄₃⋊C₈	—	2	2	no	—
74	Dic₄₃⋊C₈	—	2	2	no	—
75	Dic₄₃⋊C₈	—	2	2	no	—
76	#13063250	C₂×C₄	1	2	yes	—
77	#13063250	C₂×C₄	1	2	yes	—
78	#13063250	C₂×C₄	1	2	yes	—
79	#13063247	C₂×C₄	1	2	yes	—
80	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
81	(C₂×D₄₃)⋊C₈	—	2	2	no	—
82	#13063235	—	2	2	no	—
83	C₄×C₄₃⋊C₈	—	2	1	no	—
84	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
87	C₈×Dic₄₃	—	2	2	no	—
88	C₈×Dic₄₃	—	2	2	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₃	—	2	1	no	—
92	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
96	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₂²⋊C₈×C₄₃	—	2	1	no	—
98	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
99	C₄×C₈×C₄₃	—	2	1	no	—
100	C₄×C₈×C₄₃	C₂³	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₃	—	2	1	no	—
105	#10621898	—	2	2	no	—
106	#10621898	—	4	1	no	—
107	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₄₃	—	2	1	no	—
109	C₂×C₄×D₄₃	—	2	1	no	—
110	C₂×C₄×D₄₃	—	2	1	no	—
111	C₂×Dic₈₆	—	2	1	no	—
112	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
113	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
114	M₁₆×C₄₃	—	8	1	no	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₃	#41	1	1	yes	characteristic
123	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₄₃	—	2	2	no	—
125	C₂²⋊Dic₄₃	—	2	1	no	—
126	(C₂×D₄₃)⋊C₄	—	2	1	no	—
127	(C₂×D₄₃)⋊C₄	—	2	1	no	—
128	C₄⋊Dic₄₃	—	2	1	no	—
129	C₄⋊Dic₄₃	—	2	1	no	—
130	C₄⋊Dic₄₃	—	2	1	no	—
131	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
132	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
134	Dic₄₃⋊C₄	—	2	1	no	—
135	Dic₄₃⋊C₄	—	2	2	no	—
136	Dic₄₃⋊C₄	—	2	1	no	—
137	Dic₄₃⋊C₄	—	2	2	no	—
138	C₄×Dic₄₃	—	2	1	no	—
139	C₄×Dic₄₃	—	2	1	no	—
140	C₄×Dic₄₃	—	2	1	no	—
141	C₄×Dic₄₃	—	2	2	no	—
142	C₂×C₄₃⋊C₈	—	2	4	no	—
143	C₂×C₄₃⋊C₈	—	2	1	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
147	Dic₁₇₂	—	2	4	no	—
148	#10621873	—	4	2	no	—
149	#10621872	—	8	2	no	—
150	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
151	C₂²×D₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂²⋊D₄₃	—	4	2	no	—
164	C₂×Dic₄₃	—	2	1	no	—
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	D₁₇₂	—	2	1	no	—
170	D₁₇₂	—	2	1	no	—
171	C₄×D₄₃	—	4	2	no	—
172	C₄×D₄₃	—	4	1	no	—
173	C₄×D₄₃	—	4	1	no	—
174	C₄×D₄₃	—	4	2	no	—
175	Dic₈₆	—	2	1	no	—
176	Dic₈₆	—	2	2	no	—
177	Dic₈₆	—	2	2	no	—
178	Dic₈₆	—	4	2	no	—
179	Dic₈₆	#131	1	2	yes	—
180	C₈×C₄₃	—	2	2	no	—
181	C₈×C₄₃	—	2	2	no	—
182	C₈×C₄₃	—	4	2	no	—
183	C₈×C₄₃	—	4	1	no	—
184	C₈×C₄₃	—	4	1	no	—
185	C₄₃⋊C₈	—	2	2	no	—
186	C₄₃⋊C₈	—	2	2	no	—
187	C₄₃⋊C₈	—	2	2	no	—
188	C₄₃⋊C₈	—	2	2	no	—
189	#18019	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	—	2	1	no	—
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₄₃	—	4	1	no	—
195	C₂×D₄₃	—	4	1	no	—
196	C₂×D₄₃	—	4	1	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	#443	1	2	yes	—
201	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
202	C₄×C₄₃	#568	1	1	yes	characteristic
203	C₄×C₄₃	#577	1	1	yes	characteristic
204	C₄×C₄₃	#578	1	1	yes	characteristic
205	Dic₄₃	—	2	2	no	—
206	Dic₄₃	—	4	2	no	—
207	Dic₄₃	—	4	1	no	—
208	Dic₄₃	—	4	2	no	—
209	Dic₄₃	—	4	1	no	—
210	#3107	—	43	1	no	—
211	#2991	—	43	1	no	—
212	#2986	—	43	1	no	—
213	#1590	—	43	2	no	—
214	#1588	—	43	2	no	—
215	#1587	—	43	2	no	—
216	C₈×Q₁₆	—	43	2	no	—
217	#1574	D₄₃	1	1	yes	characteristic, complemented
218	#1493	—	43	1	no	—
219	#1476	—	43	1	no	—
220	#1450	—	43	1	no	—
221	C₂×C₄₃	—	4	1	no	—
222	C₂×C₄₃	#2933	1	1	yes	characteristic
223	C₂×C₄₃	#2947	1	1	yes	characteristic
224	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
225	D₄₃	—	8	1	no	—
226	#533	—	43	1	no	—
227	C₄×#41	—	43	1	no	—
228	#485	—	43	2	no	—
229	#475	—	43	1	no	—
230	#474	—	43	1	no	—
231	#462	—	43	1	no	—
232	#461	—	43	1	no	—
233	#452	—	43	2	no	—
234	#446	—	43	2	no	—
235	#446	—	86	1	no	—
236	C₈×Q₈	—	43	2	no	—
237	C₈×Q₈	—	43	2	no	—
238	C₈×Q₈	—	86	1	no	—
239	C₄×Q₁₆	—	43	2	no	—
240	C₄×SD₁₆	—	43	2	no	—
241	#436	—	43	2	no	—
242	#436	—	86	2	no	—
243	#433	—	86	2	no	—
244	#431	—	43	1	no	—
245	#431	—	86	1	no	—
246	#431	C₂×D₄₃	1	1	yes	characteristic
247	#431	C₂×D₄₃	1	1	yes	characteristic
248	#423	—	86	1	no	—
249	#423	C₂×D₄₃	1	1	yes	characteristic
250	C₂×C₄×C₈	—	43	1	no	—
251	#335	C₂×D₄₃	1	2	yes	—
252	#334	C₂×D₄₃	1	2	yes	—
253	Q₈⋊C₈	—	43	1	no	—
254	Q₈⋊C₈	—	43	2	no	—
255	Q₈⋊C₈	—	43	1	no	—
256	Q₈⋊C₈	—	43	2	no	—
257	D₄⋊C₈	—	43	1	no	—
258	D₄⋊C₈	—	43	1	no	—
259	#322	—	43	2	no	—
260	C₈²	—	43	2	no	—
261	C₄₃	#18019	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	43	1	no	—
263	C₂×Q₁₆	—	43	2	no	—
264	C₂×SD₁₆	—	43	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	86	2	no	—
267	C₂²×C₈	—	86	1	no	—
268	C₄⋊Q₈	—	43	1	no	—
269	C₄⋊Q₈	—	43	1	no	—
270	#125	—	86	1	no	—
271	C₂²⋊Q₈	—	43	2	no	—
272	C₂²⋊Q₈	—	86	1	no	—
273	C₄×Q₈	—	43	1	no	—
274	C₄×Q₈	—	43	1	no	—
275	C₄×Q₈	—	43	2	no	—
276	C₄×Q₈	—	86	1	no	—
277	C₄×D₄	—	43	1	no	—
278	C₄×D₄	—	43	1	no	—
279	C₄×D₄	—	86	1	no	—
280	C₄×D₄	—	86	1	no	—
281	#117	—	43	1	no	—
282	#117	—	86	1	no	—
283	#117	—	86	1	no	—
284	C₂×C₄²	—	86	1	no	—
285	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
286	#107	—	43	2	no	—
287	#106	—	43	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	43	1	no	—
290	C₄⋊C₈	—	43	1	no	—
291	C₄⋊C₈	—	86	2	no	—
292	C₄⋊C₈	—	86	2	no	—
293	C₄⋊C₈	—	86	2	no	—
294	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
295	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
296	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
298	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
299	#103	—	43	2	no	—
300	#103	—	43	2	no	—
301	#103	—	43	2	no	—
302	#102	—	43	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	43	2	no	—
305	C₂²⋊C₈	—	86	2	no	—
306	C₂²⋊C₈	C₄×D₄₃	1	2	yes	—
307	#97	—	86	2	no	—
308	C₄×C₈	—	2	1	no	—
309	C₄×C₈	—	43	2	no	—
310	C₄×C₈	—	43	1	no	—
311	C₄×C₈	—	43	1	no	—
312	C₄×C₈	—	86	2	no	—
313	C₄×C₈	—	86	2	no	—
314	C₄×C₈	—	86	1	no	—
315	C₄×C₈	C₂²×D₄₃	1	2	yes	—
316	#41	—	86	2	no	—
317	#41	—	172	1	no	—
318	C₂×Q₈	—	43	1	no	—
319	C₂×Q₈	—	43	2	no	—
320	C₂×Q₈	—	86	1	no	—
321	C₂×D₄	—	43	1	no	—
322	C₂×D₄	—	86	1	no	—
323	C₂²×C₄	—	86	1	no	—
324	C₂²×C₄	—	86	1	no	—
325	C₂²×C₄	—	86	1	no	—
326	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
328	C₂²×C₄	#10621902	1	1	yes	characteristic
329	Q₁₆	—	86	4	no	—
330	SD₁₆	—	172	2	no	—
331	M₁₆	—	8	1	no	—
332	M₁₆	—	344	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	43	2	no	—
337	C₂×C₈	—	43	2	no	—
338	C₂×C₈	—	86	4	no	—
339	C₂×C₈	—	86	1	no	—
340	C₂×C₈	—	86	1	no	—
341	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
342	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
343	C₄⋊C₄	—	43	2	no	—
344	C₄⋊C₄	—	43	1	no	—
345	C₄⋊C₄	—	43	1	no	—
346	C₄⋊C₄	—	86	1	no	—
347	C₄⋊C₄	—	86	1	no	—
348	C₄⋊C₄	—	86	1	no	—
349	C₄⋊C₄	—	86	2	no	—
350	C₄⋊C₄	—	86	1	no	—
351	C₄⋊C₄	—	86	1	no	—
352	C₄⋊C₄	—	86	2	no	—
353	C₂²⋊C₄	—	86	1	no	—
354	C₂²⋊C₄	—	86	2	no	—
355	C₂²⋊C₄	—	86	1	no	—
356	C₂²⋊C₄	—	86	1	no	—
357	C₄²	—	86	1	no	—
358	C₄²	—	86	1	no	—
359	C₄²	—	86	1	no	—
360	C₄²	—	86	2	no	—
361	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
362	C₄²	D₄×D₄₃	1	1	yes	characteristic
363	C₄²	#10621902	1	1	yes	characteristic
364	C₄²	C₂³×D₄₃	1	1	yes	characteristic
365	C₂³	—	86	1	no	—
366	C₂³	#13063287	1	1	yes	characteristic
367	Q₈	—	43	2	no	—
368	Q₈	—	86	1	no	—
369	Q₈	—	86	2	no	—
370	Q₈	—	86	2	no	—
371	Q₈	—	172	2	no	—
372	D₄	—	86	1	no	—
373	D₄	—	86	1	no	—
374	D₄	—	172	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	86	1	no	—
381	C₂×C₄	—	86	1	no	—
382	C₂×C₄	—	86	1	no	—
383	C₂×C₄	—	86	2	no	—
384	C₂×C₄	—	86	2	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	1	no	—
387	C₂×C₄	—	172	1	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	#13063287	1	1	yes	characteristic
390	C₂×C₄	#13063287	1	1	yes	characteristic
391	C₂×C₄	#13063287	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
394	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	86	2	no	—
401	C₈	—	86	2	no	—
402	C₈	—	86	2	no	—
403	C₈	—	86	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	172	1	no	—
408	C₂²	—	172	1	no	—
409	C₂²	—	172	1	no	—
410	C₂²	C₂×#13063287	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	86	2	no	—
415	C₄	—	172	1	no	—
416	C₄	—	172	1	no	—
417	C₄	—	172	2	no	—
418	C₄	—	172	2	no	—
419	C₄	#14583015	1	2	yes	—
420	C₄	#131×D₄₃	1	1	yes	characteristic
421	C₄	#14583664	1	1	yes	characteristic
422	C₄	#14583709	1	1	yes	characteristic
423	C₄	#14583715	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	344	1	no	—
426	C₂	#19143319	1	1	yes	characteristic
427	C₂	#19143436	1	1	yes	characteristic
428	C₂	C₂×#14583015	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1574	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#10621898	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1574	D₄₃
hypocenter	C₄₃	#18019
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1574

Complements

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

N	H ≅ G/N	type
3. #19143696	C₂	semidirect
4. #19133484	C₂	semidirect
5. #19133472	C₂	semidirect
6. #19133465	C₂	semidirect
7. #19133401	C₂	semidirect
8. #19133049	C₂	semidirect
10. #19132879	C₂	semidirect
11. C₄₃×#1574	C₂	semidirect
217. #1574	D₄₃	semidirect
261. C₄₃	#18019	semidirect

Maximal subgroups

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

subgroup	index
#19144667	2
#19143725	2
#19143696	2
#19133484	2
#19133472	2
#19133465	2
#19133401	2
#19133049	2
#19132975	2
#19132879	2
C₄₃×#1574	2
#18019	43