Subgroups — #25068363

Order 11008.

654 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145155	C₂	1	1	yes	maximal, characteristic
2	#19143341	C₂	1	1	yes	maximal, characteristic
3	#19133485	C₂	1	2	yes	maximal, complemented
4	#19133438	C₂	1	2	yes	maximal, complemented
5	#19133429	C₂	1	2	yes	maximal, complemented
6	C₈×#10621884	C₂	1	2	yes	maximal, complemented
7	C₂×#14582649	C₂	1	1	yes	maximal, characteristic, complemented
8	#19132998	C₂	1	1	yes	maximal, characteristic, complemented
9	#19132993	C₂	1	1	yes	maximal, characteristic
10	M₁₆×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063333	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583295	C₄	1	1	yes	characteristic
15	#14583273	C₄	1	1	yes	characteristic
16	#14583249	C₄	1	1	yes	characteristic
17	#14583247	C₄	1	1	yes	characteristic
18	#14583130	C₄	1	2	yes	—
19	#14583130	C₄	1	2	yes	—
20	C₄×#10621884	C₂²	1	2	yes	—
21	C₄×#10621884	C₂²	1	2	yes	—
22	#14582978	C₂²	1	2	yes	—
23	#14582972	—	2	2	no	—
24	C₈×D₁₇₂	C₂²	1	2	yes	—
25	#14582952	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
27	#14582867	—	2	1	no	—
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	#14582649	C₂²	1	1	yes	characteristic
30	#14582649	C₂²	1	1	yes	characteristic
31	#14582649	C₂²	1	1	yes	characteristic
32	#14582649	C₂²	1	1	yes	characteristic
33	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
34	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
35	#14582626	C₂²	1	2	yes	—
36	#14582626	C₂²	1	2	yes	—
37	#14582620	C₂²	1	2	yes	—
38	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
39	C₄₃×#533	C₂²	1	1	yes	characteristic
40	C₄₃×#446	—	2	2	no	—
41	C₄₃×#446	C₂²	1	2	yes	—
42	C₈×Q₈×C₄₃	C₂²	1	2	yes	—
43	C₄₃×#424	—	2	1	no	—
44	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#405	—	2	1	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621884	C₂×C₄	1	2	yes	—
49	C₂×#10621884	C₂×C₄	1	2	yes	—
50	#13063333	—	4	4	no	—
51	C₂×#10621872	—	2	2	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₄₃	—	2	2	no	—
56	#13063325	C₂×C₄	1	1	yes	characteristic
57	#13063322	C₂×C₄	1	1	yes	characteristic
58	#13063313	—	2	1	no	—
59	#13063299	—	2	1	no	—
60	#13063299	C₂×C₄	1	2	yes	—
61	C₄×D₁₇₂	—	2	1	no	—
62	C₄×D₁₇₂	C₂³	1	2	yes	—
63	#13063256	C₂×C₄	1	2	yes	—
64	#13063256	C₂×C₄	1	2	yes	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
69	#13063249	C₂×C₄	1	2	yes	—
70	#13063249	C₂×C₄	1	2	yes	—
71	#13063245	C₂×C₄	1	2	yes	—
72	#13063245	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
74	(C₂×D₄₃)⋊C₈	—	2	2	no	—
75	(C₂×D₄₃)⋊C₈	—	2	2	no	—
76	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
79	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
82	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
83	C₂²×C₈×C₄₃	—	2	1	no	—
84	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
86	#125×C₄₃	—	2	1	no	—
87	C₂²⋊Q₈×C₄₃	—	2	1	no	—
88	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
89	C₄×Q₈×C₄₃	—	2	1	no	—
90	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
91	#117×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	—	2	2	no	—
94	C₄⋊C₈×C₄₃	—	2	2	no	—
95	C₄⋊C₈×C₄₃	—	2	1	no	—
96	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
98	#97×C₄₃	—	2	2	no	—
99	#97×C₄₃	D₄	1	2	yes	—
100	C₄×C₈×C₄₃	—	2	2	no	—
101	C₄×C₈×C₄₃	C₂³	1	2	yes	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₃	—	2	2	no	—
108	#10621898	—	4	2	no	—
109	#10621898	—	4	2	no	—
110	C₂×D₁₇₂	—	2	1	no	—
111	C₂×D₁₇₂	—	2	1	no	—
112	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₄₃	—	2	2	no	—
114	C₂×Dic₈₆	—	2	1	no	—
115	M₁₆×C₄₃	—	2	2	no	—
116	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
117	C₂×C₈×C₄₃	—	2	1	no	—
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	—	4	2	no	—
120	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₄₃	—	2	1	no	—
123	C₄⋊C₄×C₄₃	—	2	1	no	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₃	#41	1	1	yes	characteristic
133	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
134	#10621884	—	2	4	no	—
135	#10621884	—	4	2	no	—
136	(C₂×D₄₃)⋊C₄	—	2	2	no	—
137	(C₂×D₄₃)⋊C₄	—	2	2	no	—
138	C₄⋊Dic₄₃	—	2	1	no	—
139	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
140	C₂×C₄₃⋊C₈	—	2	2	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	2	no	—
144	C₂×C₄₃⋊C₈	—	4	1	no	—
145	C₂×C₄₃⋊C₈	—	4	2	no	—
146	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	#10621872	—	4	4	no	—
151	C₈×D₄₃	—	4	4	no	—
152	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
153	C₂²×D₄₃	—	2	2	no	—
154	Q₈×C₄₃	—	2	2	no	—
155	Q₈×C₄₃	—	2	2	no	—
156	Q₈×C₄₃	—	8	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₄₃	#135	1	2	yes	—
167	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₄₃	—	4	4	no	—
171	C₂×Dic₄₃	—	2	2	no	—
172	D₁₇₂	—	2	2	no	—
173	D₁₇₂	—	2	2	no	—
174	D₁₇₂	—	4	2	no	—
175	D₁₇₂	—	8	1	no	—
176	C₄×D₄₃	—	4	2	no	—
177	C₄×D₄₃	—	4	2	no	—
178	Dic₈₆	—	4	2	no	—
179	C₈×C₄₃	—	2	2	no	—
180	C₈×C₄₃	—	4	1	no	—
181	C₈×C₄₃	—	4	1	no	—
182	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
183	C₄₃⋊C₈	—	2	1	no	—
184	C₄₃⋊C₈	—	2	1	no	—
185	C₄₃⋊C₈	—	2	1	no	—
186	C₄₃⋊C₈	—	4	2	no	—
187	C₄₃⋊C₈	—	4	1	no	—
188	C₄₃⋊C₈	—	4	1	no	—
189	C₄₃⋊C₈	#131	1	2	yes	complemented
190	#18067	—	43	1	no	maximal, Sylow
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
194	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂×D₄₃	—	4	2	no	—
196	C₂×D₄₃	—	4	2	no	—
197	C₂×D₄₃	—	4	2	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	—	4	2	no	—
203	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
204	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
205	C₄×C₄₃	#568	1	1	yes	characteristic
206	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
207	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
208	Dic₄₃	—	4	2	no	—
209	#3167	—	43	1	no	—
210	#2962	D₄₃	1	1	yes	characteristic, complemented
211	#2935	—	43	1	no	—
212	#1590	—	43	2	no	—
213	#1583	—	43	2	no	—
214	#1582	—	43	2	no	—
215	C₈×SD₁₆	—	43	2	no	—
216	C₂×#334	—	43	1	no	—
217	#1481	—	43	1	no	—
218	#1480	—	43	1	no	—
219	C₈×M₁₆	—	43	1	no	—
220	C₂×C₄₃	—	2	2	no	—
221	C₂×C₄₃	#2935	1	1	yes	characteristic
222	C₂×C₄₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
223	C₂×C₄₃	#2957	1	1	yes	characteristic
224	D₄₃	—	8	2	no	—
225	C₂×#131	—	86	1	no	—
226	#533	C₂×D₄₃	1	1	yes	characteristic
227	#532	—	43	1	no	—
228	#498	—	43	1	no	—
229	#492	—	43	1	no	—
230	#487	—	43	1	no	—
231	#486	—	43	1	no	—
232	#465	—	43	2	no	—
233	#465	—	43	2	no	—
234	#446	—	2	2	no	—
235	#446	C₂×D₄₃	1	2	yes	—
236	C₈×Q₈	C₂×D₄₃	1	2	yes	—
237	C₄×SD₁₆	—	43	2	no	—
238	C₄×SD₁₆	—	43	2	no	—
239	#436	—	43	2	no	—
240	#435	—	86	2	no	—
241	C₈×D₄	—	43	2	no	—
242	#431	—	43	1	no	—
243	#424	—	2	1	no	—
244	C₂×C₄⋊C₈	—	43	1	no	—
245	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
246	#408	—	86	1	no	—
247	#405	—	2	1	no	—
248	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
249	C₂×C₄×C₈	—	43	1	no	—
250	#334	—	43	1	no	—
251	#334	—	43	1	no	—
252	#334	—	43	1	no	—
253	#334	—	43	1	no	—
254	Q₈⋊C₈	—	43	2	no	—
255	Q₈⋊C₈	—	43	2	no	—
256	D₄⋊C₈	—	43	2	no	—
257	D₄⋊C₈	—	43	2	no	—
258	#322	—	43	2	no	—
259	C₈²	—	43	2	no	—
260	C₄₃	#18067	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	86	1	no	—
262	C₂×SD₁₆	—	43	2	no	—
263	C₂×SD₁₆	—	43	2	no	—
264	#131	—	172	4	no	—
265	C₂×M₁₆	—	86	2	no	—
266	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
267	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	43	1	no	—
270	C₂²×C₈	—	43	1	no	—
271	C₂²×C₈	—	86	1	no	—
272	C₂²×C₈	—	86	2	no	—
273	C₄⋊Q₈	—	43	1	no	—
274	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
275	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
276	#127	—	43	1	no	—
277	#125	—	2	1	no	—
278	#124	—	86	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	C₄×D₄₃	1	2	yes	—
281	#121	—	43	2	no	—
282	#121	—	86	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
285	C₄×D₄	—	43	2	no	—
286	C₄×D₄	—	86	1	no	—
287	#117	—	2	1	no	—
288	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
289	#106	—	43	2	no	—
290	#106	—	43	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	43	1	no	—
295	C₄⋊C₈	—	43	1	no	—
296	C₄⋊C₈	—	86	1	no	—
297	C₄⋊C₈	—	86	1	no	—
298	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
300	#103	—	43	2	no	—
301	#103	—	43	2	no	—
302	#102	—	43	2	no	—
303	#102	—	43	2	no	—
304	C₂²⋊C₈	—	86	1	no	—
305	C₂²⋊C₈	—	86	2	no	—
306	C₂²⋊C₈	—	86	2	no	—
307	#97	—	2	2	no	—
308	#97	C₂²⋊D₄₃	1	2	yes	—
309	C₄×C₈	—	2	2	no	—
310	C₄×C₈	—	43	1	no	—
311	C₄×C₈	—	43	1	no	—
312	C₄×C₈	—	43	1	no	—
313	C₄×C₈	—	43	1	no	—
314	C₄×C₈	—	43	2	no	—
315	C₄×C₈	C₂²×D₄₃	1	2	yes	—
316	#41	—	172	2	no	—
317	#41	—	172	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	86	1	no	—
320	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
321	C₂×D₄	—	43	2	no	—
322	C₂×D₄	—	86	2	no	—
323	C₂×D₄	—	86	1	no	—
324	C₂×D₄	—	86	1	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
327	C₂²×C₄	#10621898	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
329	SD₁₆	—	86	4	no	—
330	SD₁₆	—	172	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	172	4	no	—
333	M₁₆	#10621884	1	4	yes	complemented
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	43	1	no	—
338	C₂×C₈	—	43	1	no	—
339	C₂×C₈	—	43	1	no	—
340	C₂×C₈	—	43	1	no	—
341	C₂×C₈	—	86	2	no	—
342	C₂×C₈	—	86	1	no	—
343	C₂×C₈	—	86	1	no	—
344	C₂×C₈	—	86	2	no	—
345	C₂×C₈	—	172	1	no	—
346	C₂×C₈	—	172	2	no	—
347	C₂×C₈	—	172	4	no	—
348	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
349	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	43	2	no	—
356	C₄⋊C₄	—	86	1	no	—
357	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	86	2	no	—
360	C₂²⋊C₄	—	86	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
363	C₄²	#10621898	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
365	C₄²	C₂³×D₄₃	1	1	yes	characteristic
366	C₂³	—	86	2	no	—
367	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	172	2	no	—
372	D₄	—	86	2	no	—
373	D₄	—	86	2	no	—
374	D₄	—	344	1	no	—
375	D₄	—	172	4	no	—
376	D₄	—	172	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	86	2	no	—
383	C₂×C₄	—	172	2	no	—
384	C₂×C₄	—	172	2	no	—
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	C₂×#10621884	1	2	yes	—
389	C₂×C₄	#13063345	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
392	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	43	2	no	—
397	C₈	—	86	1	no	—
398	C₈	—	86	1	no	—
399	C₈	—	86	1	no	—
400	C₈	—	172	2	no	—
401	C₈	—	172	1	no	—
402	C₈	—	172	1	no	—
403	C₈	C₂×#10621884	1	4	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	172	2	no	—
407	C₂²	—	172	2	no	—
408	C₂²	—	172	2	no	—
409	C₂²	C₄×#10621884	1	2	yes	—
410	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	172	2	no	—
417	C₄	C₄×#10621884	1	2	yes	—
418	C₄	#131×D₄₃	1	1	yes	characteristic
419	C₄	#14583664	1	1	yes	characteristic
420	C₄	C₂²×#10621884	1	1	yes	characteristic
421	C₄	C₂×#13063345	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	344	2	no	—
424	C₂	#19143337	1	1	yes	characteristic
425	C₂	C₂×C₄×#10621884	1	1	yes	characteristic
426	C₂	#19143510	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2962	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#14583449	C₂²
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2962	D₄₃
hypocenter	C₄₃	#18067
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2962

Complements

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

N	H ≅ G/N	type
3. #19133485	C₂	semidirect
4. #19133438	C₂	semidirect
5. #19133429	C₂	semidirect
6. C₈×#10621884	C₂	semidirect
7. C₂×#14582649	C₂	semidirect
8. #19132998	C₂	semidirect
10. M₁₆×C₄₃⋊C₈	C₂	semidirect
11. C₄₃×#2962	C₂	semidirect
116. M₁₆×C₄₃	SD₁₆	semidirect
189. C₄₃⋊C₈	#131	semidirect
210. #2962	D₄₃	semidirect
260. C₄₃	#18067	semidirect
333. M₁₆	#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145155	2
#19143341	2
#19133485	2
#19133438	2
#19133429	2
C₈×#10621884	2
C₂×#14582649	2
#19132998	2
#19132993	2
M₁₆×C₄₃⋊C₈	2
C₄₃×#2962	2
#18067	43