Subgroups — #25062233

Order 11008.

742 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143226	C₂	1	1	yes	maximal, characteristic
2	#19143223	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582950	C₂	1	1	yes	maximal, characteristic
4	#19132896	C₂	1	2	yes	maximal, complemented
5	#19132896	C₂	1	2	yes	maximal, complemented
6	#19132893	C₂	1	2	yes	maximal, complemented
7	#19132891	C₂	1	2	yes	maximal, complemented
8	#19132884	C₂	1	1	yes	maximal, characteristic, complemented
9	#19132876	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
13	#14582955	C₄	1	2	yes	—
14	#14582954	C₄	1	2	yes	—
15	#14582954	C₄	1	2	yes	—
16	#14582953	C₄	1	2	yes	—
17	#14582952	C₂²	1	1	yes	characteristic
18	#14582950	C₄	1	2	yes	—
19	#14582950	C₄	1	2	yes	—
20	#14582950	C₂²	1	1	yes	characteristic
21	#14582950	C₂²	1	1	yes	characteristic
22	#14582950	C₂²	1	1	yes	characteristic
23	#14582950	C₂²	1	1	yes	characteristic
24	#14582950	C₂²	1	2	yes	—
25	#14582950	C₂²	1	2	yes	—
26	#14582950	C₂²	1	2	yes	—
27	#14582922	C₄	1	2	yes	—
28	#14582921	C₄	1	2	yes	—
29	C₂×Dic₄₃⋊C₈	C₄	1	2	yes	—
30	#14582862	C₄	1	2	yes	—
31	#14582861	C₄	1	2	yes	—
32	C₂×(C₂×D₄₃)⋊C₈	C₄	1	2	yes	—
33	C₄×#10621877	C₂²	1	1	yes	characteristic
34	C₄×#10621872	C₂²	1	2	yes	—
35	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
36	#14582621	C₂²	1	2	yes	complemented
37	#14582621	C₂²	1	2	yes	complemented
38	#14582620	C₂²	1	2	yes	complemented
39	#14582620	C₂²	1	2	yes	complemented
40	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
41	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
42	C₄₃×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#322	C₂²	1	2	yes	complemented
46	C₄₃×#322	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂×#10621877	C₂×C₄	1	2	yes	—
51	C₂×#10621872	C₂×C₄	1	4	yes	—
52	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₄₃	C₂³	1	1	yes	characteristic
63	C₄²×D₄₃	C₂³	1	1	yes	characteristic
64	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
65	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
66	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
67	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
68	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
69	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
70	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
71	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
72	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
73	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
74	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
75	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
76	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
78	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
79	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
80	#13063236	C₂×C₄	1	2	yes	—
81	#13063235	C₂×C₄	1	4	yes	—
82	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
83	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
86	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
87	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
92	#97×C₄₃	C₂×C₄	1	2	yes	—
93	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₄₃	C₂³	1	2	yes	—
95	C₄×C₈×C₄₃	C₂³	1	2	yes	—
96	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₂³×D₄₃	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₄₃	C₄²	1	1	yes	characteristic
103	C₂²×Dic₄₃	C₄²	1	1	yes	characteristic
104	C₂²×Dic₄₃	C₄²	1	1	yes	characteristic
105	C₂×C₄×D₄₃	—	2	4	no	—
106	C₂×C₄×D₄₃	—	4	2	no	—
107	C₂×C₄×D₄₃	—	4	2	no	—
108	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
113	C₂×C₄×D₄₃	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
120	M₁₆×C₄₃	—	2	4	no	—
121	C₂×C₈×C₄₃	—	4	2	no	—
122	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
125	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
126	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
130	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
131	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
132	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₄₃	C₄²	1	1	yes	characteristic
136	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
142	#10621877	—	2	4	no	—
143	C₂×C₄₃⋊C₈	—	4	2	no	—
144	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
147	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
148	#10621872	—	4	4	no	—
149	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
150	C₂²×D₄₃	—	2	2	no	—
151	C₂²×D₄₃	—	4	1	no	—
152	C₂²×D₄₃	—	4	1	no	—
153	C₂²×D₄₃	C₂×C₄²	1	1	yes	characteristic
154	C₂²×D₄₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#131	1	4	yes	—
161	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	4	1	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×Dic₄₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×Dic₄₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×Dic₄₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×Dic₄₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×Dic₄₃	C₂×C₄²	1	1	yes	characteristic
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	—	2	2	no	—
178	C₄×D₄₃	—	2	2	no	—
179	C₄×D₄₃	—	2	2	no	—
180	C₄×D₄₃	—	2	2	no	—
181	C₄×D₄₃	—	4	1	no	—
182	C₄×D₄₃	—	4	1	no	—
183	C₄×D₄₃	—	4	1	no	—
184	C₄×D₄₃	—	4	1	no	—
185	C₈×C₄₃	—	2	4	no	—
186	C₈×C₄₃	—	2	4	no	—
187	C₈×C₄₃	—	2	2	no	—
188	C₈×C₄₃	—	2	2	no	—
189	C₄₃⋊C₈	—	2	4	no	—
190	C₄₃⋊C₈	—	2	4	no	—
191	C₄₃⋊C₈	—	2	2	no	—
192	C₄₃⋊C₈	—	2	2	no	—
193	#17324	—	43	1	no	maximal, Sylow
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	#405	1	2	yes	—
197	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
198	C₂×D₄₃	—	2	1	no	—
199	C₂×D₄₃	—	2	1	no	—
200	C₂×D₄₃	—	2	1	no	—
201	C₂×D₄₃	—	2	1	no	—
202	C₂×D₄₃	—	2	1	no	—
203	C₂×D₄₃	—	2	1	no	—
204	C₂×D₄₃	—	4	4	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	#405	1	2	yes	—
208	C₄×C₄₃	C₂×#131	1	2	yes	—
209	C₄×C₄₃	#568	1	2	yes	—
210	C₄×C₄₃	#568	1	2	yes	—
211	Dic₄₃	—	2	1	no	—
212	Dic₄₃	—	2	1	no	—
213	Dic₄₃	—	2	1	no	—
214	Dic₄₃	—	2	1	no	—
215	Dic₄₃	—	2	1	no	—
216	Dic₄₃	—	2	1	no	—
217	#2920	—	43	1	no	—
218	#2920	—	43	1	no	—
219	C₂×#431	—	43	1	no	—
220	#1454	—	43	2	no	—
221	#1454	—	43	2	no	—
222	#1453	—	43	2	no	—
223	#1453	—	43	2	no	—
224	#1451	—	43	1	no	—
225	#1451	D₄₃	1	1	yes	characteristic, complemented
226	C₈×M₁₆	—	43	1	no	—
227	C₈×M₁₆	—	43	1	no	—
228	C₂×C₄₃	—	2	2	no	—
229	C₂×C₄₃	C₂×#405	1	1	yes	characteristic
230	C₂×C₄₃	#2873	1	1	yes	characteristic
231	C₂×C₄₃	#2873	1	1	yes	characteristic
232	D₄₃	—	4	1	no	—
233	D₄₃	—	4	1	no	—
234	C₂²×C₄²	—	43	1	no	—
235	#432	—	43	2	no	—
236	#432	—	43	2	no	—
237	#432	—	43	2	no	—
238	#432	—	43	2	no	—
239	#431	—	43	1	no	—
240	#431	—	43	1	no	—
241	#431	—	43	1	no	—
242	#431	—	43	1	no	—
243	#431	—	43	1	no	—
244	#431	—	43	2	no	—
245	#431	—	43	2	no	—
246	#431	—	43	2	no	—
247	#431	—	43	2	no	—
248	#431	—	43	2	no	—
249	#431	C₂×D₄₃	1	1	yes	characteristic
250	#423	—	43	2	no	—
251	#423	—	43	2	no	—
252	C₂×C₄⋊C₈	—	43	2	no	—
253	#407	—	43	2	no	—
254	#407	—	43	2	no	—
255	C₂×C₂²⋊C₈	—	43	2	no	—
256	C₄×M₁₆	—	43	1	no	—
257	C₄×M₁₆	—	43	2	no	—
258	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
259	C₂×C₄×C₈	—	43	1	no	—
260	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
261	#322	—	43	2	no	—
262	#322	—	43	2	no	—
263	#322	—	43	2	no	—
264	#322	—	43	2	no	—
265	#322	C₂×D₄₃	1	2	yes	complemented
266	#322	C₂×D₄₃	1	2	yes	complemented
267	C₈²	—	43	2	no	—
268	C₈²	—	43	2	no	—
269	C₄₃	#17324	1	1	yes	characteristic, complemented, Sylow
270	C₂³×C₄	—	43	1	no	—
271	C₂³×C₄	—	43	1	no	—
272	C₂³×C₄	—	43	1	no	—
273	C₂×M₁₆	—	43	2	no	—
274	C₂×M₁₆	—	43	4	no	—
275	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
276	C₂²×C₈	—	43	2	no	—
277	C₂²×C₈	C₄×D₄₃	1	2	yes	—
278	C₂×C₄²	—	43	1	no	—
279	C₂×C₄²	—	43	1	no	—
280	C₂×C₄²	—	43	1	no	—
281	C₂×C₄²	—	43	1	no	—
282	C₂×C₄²	—	43	1	no	—
283	C₂×C₄²	—	43	1	no	—
284	C₂×C₄²	—	43	1	no	—
285	C₂×C₄²	—	43	1	no	—
286	C₂×C₄²	—	43	1	no	—
287	C₂×C₄²	—	43	1	no	—
288	C₂×C₄²	—	43	1	no	—
289	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
290	C₄⋊C₈	—	43	2	no	—
291	C₄⋊C₈	—	43	2	no	—
292	C₄⋊C₈	—	43	2	no	—
293	C₄⋊C₈	—	43	2	no	—
294	C₄⋊C₈	—	43	4	no	—
295	C₄⋊C₈	—	43	4	no	—
296	C₄⋊C₈	—	43	4	no	—
297	C₄⋊C₈	—	43	2	no	—
298	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
299	C₂²⋊C₈	—	43	2	no	—
300	C₂²⋊C₈	—	43	2	no	—
301	C₂²⋊C₈	—	43	2	no	—
302	C₂²⋊C₈	—	43	2	no	—
303	C₂²⋊C₈	—	43	2	no	—
304	C₂²⋊C₈	—	43	4	no	—
305	C₂²⋊C₈	—	43	4	no	—
306	C₂²⋊C₈	—	43	4	no	—
307	C₂²⋊C₈	C₄×D₄₃	1	2	yes	—
308	#97	—	43	4	no	—
309	#97	—	43	2	no	—
310	#97	C₄×D₄₃	1	2	yes	—
311	C₄×C₈	—	43	2	no	—
312	C₄×C₈	—	43	1	no	—
313	C₄×C₈	—	43	1	no	—
314	C₄×C₈	—	43	2	no	—
315	C₄×C₈	—	43	2	no	—
316	C₄×C₈	C₄×D₄₃	1	2	yes	—
317	C₄×C₈	C₂²×D₄₃	1	2	yes	—
318	C₄×C₈	C₂²×D₄₃	1	2	yes	—
319	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
321	C₂⁴	—	43	1	no	—
322	C₂²×C₄	—	43	1	no	—
323	C₂²×C₄	—	43	1	no	—
324	C₂²×C₄	—	43	1	no	—
325	C₂²×C₄	—	43	1	no	—
326	C₂²×C₄	—	43	1	no	—
327	C₂²×C₄	—	43	1	no	—
328	C₂²×C₄	—	43	1	no	—
329	C₂²×C₄	—	43	1	no	—
330	C₂²×C₄	—	43	1	no	—
331	C₂²×C₄	—	43	1	no	—
332	C₂²×C₄	—	43	1	no	—
333	C₂²×C₄	—	43	1	no	—
334	C₂²×C₄	—	43	1	no	—
335	C₂²×C₄	—	43	1	no	—
336	C₂²×C₄	—	43	1	no	—
337	C₂²×C₄	—	86	4	no	—
338	C₂²×C₄	—	172	2	no	—
339	C₂²×C₄	—	172	2	no	—
340	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
343	M₁₆	—	2	4	no	—
344	M₁₆	—	86	4	no	—
345	M₁₆	—	172	4	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	43	2	no	—
348	C₂×C₈	—	43	2	no	—
349	C₂×C₈	—	43	4	no	—
350	C₂×C₈	—	43	4	no	—
351	C₂×C₈	—	172	2	no	—
352	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
353	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
354	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
355	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
356	C₄²	—	43	1	no	—
357	C₄²	—	43	1	no	—
358	C₄²	—	43	1	no	—
359	C₄²	—	43	1	no	—
360	C₄²	—	43	1	no	—
361	C₄²	—	43	1	no	—
362	C₄²	—	43	1	no	—
363	C₄²	—	43	1	no	—
364	C₄²	—	43	1	no	—
365	C₄²	—	43	1	no	—
366	C₄²	—	43	1	no	—
367	C₄²	—	43	1	no	—
368	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
369	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
370	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
371	C₄²	C₂³×D₄₃	1	1	yes	characteristic
372	C₂³	—	43	1	no	—
373	C₂³	—	43	1	no	—
374	C₂³	—	86	2	no	—
375	C₂³	—	172	1	no	—
376	C₂³	—	172	1	no	—
377	C₂³	C₄²×D₄₃	1	1	yes	characteristic
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	43	1	no	—
381	C₂×C₄	—	43	1	no	—
382	C₂×C₄	—	43	1	no	—
383	C₂×C₄	—	43	1	no	—
384	C₂×C₄	—	43	1	no	—
385	C₂×C₄	—	43	1	no	—
386	C₂×C₄	—	86	2	no	—
387	C₂×C₄	—	86	2	no	—
388	C₂×C₄	—	86	2	no	—
389	C₂×C₄	—	86	2	no	—
390	C₂×C₄	—	86	2	no	—
391	C₂×C₄	—	86	2	no	—
392	C₂×C₄	—	86	2	no	—
393	C₂×C₄	—	86	2	no	—
394	C₂×C₄	—	86	2	no	—
395	C₂×C₄	—	172	1	no	—
396	C₂×C₄	—	172	1	no	—
397	C₂×C₄	—	172	1	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	—	172	1	no	—
400	C₂×C₄	—	172	1	no	—
401	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
402	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
403	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
404	C₂×C₄	#13063333	1	4	yes	—
405	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
408	C₈	—	2	4	no	—
409	C₈	—	2	4	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	86	4	no	—
413	C₈	—	86	4	no	—
414	C₈	—	86	2	no	—
415	C₈	—	86	2	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	86	1	no	—
419	C₂²	—	86	1	no	—
420	C₂²	—	86	1	no	—
421	C₂²	—	86	1	no	—
422	C₂²	—	86	1	no	—
423	C₂²	—	86	1	no	—
424	C₂²	—	172	4	no	—
425	C₂²	#14582856	1	2	yes	—
426	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	86	1	no	—
430	C₄	—	86	1	no	—
431	C₄	—	86	1	no	—
432	C₄	—	86	1	no	—
433	C₄	—	86	1	no	—
434	C₄	—	86	1	no	—
435	C₄	#14582856	1	2	yes	—
436	C₄	C₂×#13063333	1	2	yes	—
437	C₄	#14583664	1	2	yes	—
438	C₄	#14583665	1	2	yes	—
439	C₂	—	2	2	no	—
440	C₂	—	172	1	no	—
441	C₂	—	172	1	no	—
442	C₂	C₂×#14582856	1	1	yes	characteristic
443	C₂	#19143011	1	1	yes	characteristic
444	C₂	#19143012	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₄²
Fitting	C₄₃×#1451	C₂
prime radical	C₂³×D₄₃	C₄²
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1451	D₄₃
hypocenter	C₄₃	#17324
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ #1451

Complements

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

N	H ≅ G/N	type
4. #19132896	C₂	semidirect
5. #19132896	C₂	semidirect
6. #19132893	C₂	semidirect
7. #19132891	C₂	semidirect
8. #19132884	C₂	semidirect
9. #19132876	C₂	semidirect
10. M₁₆×C₄₃⋊C₈	C₂	semidirect
11. C₄₃×#1451	C₂	semidirect
36. #14582621	C₂²	semidirect
37. #14582621	C₂²	semidirect
38. #14582620	C₂²	semidirect
39. #14582620	C₂²	semidirect
40. C₈×C₄₃⋊C₈	C₂²	semidirect
41. C₈×C₄₃⋊C₈	C₂²	semidirect
45. C₄₃×#322	C₂²	semidirect
46. C₄₃×#322	C₂²	semidirect
225. #1451	D₄₃	semidirect
265. #322	C₂×D₄₃	semidirect
266. #322	C₂×D₄₃	semidirect
269. C₄₃	#17324	semidirect

Maximal subgroups

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

subgroup	index
#19143226	2
#19143223	2
C₂×#14582950	2
#19132896	2
#19132893	2
#19132891	2
#19132884	2
#19132876	2
M₁₆×C₄₃⋊C₈	2
C₄₃×#1451	2
#17324	43