Subgroups — #25100725

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582957	C₂	1	2	yes	maximal, complemented
2	#19137060	C₂	1	1	yes	maximal, characteristic
3	#19135390	C₂	1	1	yes	maximal, characteristic
4	#19135313	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135311	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135204	C₂	1	2	yes	maximal, complemented
7	#19135198	C₂	1	2	yes	maximal, complemented
8	#19134450	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134363	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1954	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063284	C₂²	1	2	yes	—
13	#14582957	—	2	8	no	—
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
16	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
19	C₂×#13063235	C₂²	1	2	yes	—
20	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
25	#14582802	C₄	1	1	yes	characteristic
26	#14582802	C₄	1	1	yes	characteristic
27	#14582798	C₄	1	1	yes	characteristic
28	#14582798	C₄	1	1	yes	characteristic
29	#14582792	C₄	1	2	yes	—
30	#14582792	C₄	1	2	yes	—
31	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
32	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
33	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
34	#14582653	C₂²	1	2	yes	—
35	#14582653	C₂²	1	2	yes	—
36	#14582653	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
40	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	#13063284	—	2	4	no	—
46	#13063284	—	2	4	no	—
47	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
60	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
62	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
63	Dic₄₃⋊C₈	—	2	4	no	—
64	Dic₄₃⋊C₈	—	2	4	no	—
65	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
66	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
67	#13063235	—	2	4	no	—
68	C₄×C₄₃⋊C₈	—	2	2	no	—
69	C₈×Dic₄₃	—	2	2	no	—
70	C₈×Dic₄₃	—	2	2	no	—
71	C₈×Dic₄₃	—	2	2	no	—
72	C₈×Dic₄₃	D₄	1	4	yes	complemented
73	C₄₃⋊#95	C₂×C₄	1	2	yes	—
74	C₄₃⋊#95	C₂×C₄	1	2	yes	—
75	C₄₃⋊#95	C₂×C₄	1	2	yes	—
76	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₄×D₄×C₄₃	—	2	2	no	—
82	C₄×D₄×C₄₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₃	—	2	2	no	—
87	C₂²⋊C₈×C₄₃	—	2	4	no	—
88	C₂²⋊C₈×C₄₃	—	2	4	no	—
89	C₄×C₈×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	—	2	2	no	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
106	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₄₃	—	2	1	no	—
111	C₂×C₈×C₄₃	—	2	1	no	—
112	C₂×C₈×C₄₃	—	2	1	no	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₃	#41	1	2	yes	—
119	C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₂²⋊C₄×C₄₃	—	2	4	no	—
121	C₄²×C₄₃	#41	1	2	yes	—
122	C₄²×C₄₃	#41	1	2	yes	—
123	C₂²⋊Dic₄₃	—	2	4	no	—
124	C₂²⋊Dic₄₃	—	2	4	no	—
125	C₂²⋊Dic₄₃	—	2	4	no	—
126	C₂²⋊Dic₄₃	—	2	4	no	—
127	C₄⋊Dic₄₃	—	2	2	no	—
128	C₄⋊Dic₄₃	—	2	2	no	—
129	C₄⋊Dic₄₃	—	2	4	no	—
130	C₄⋊Dic₄₃	—	2	4	no	—
131	C₄×Dic₄₃	—	2	2	no	—
132	C₄×Dic₄₃	—	2	2	no	—
133	C₄×Dic₄₃	—	2	2	no	—
134	C₄×Dic₄₃	—	2	1	no	—
135	C₄×Dic₄₃	—	2	1	no	—
136	C₄×Dic₄₃	—	2	2	no	—
137	C₄×Dic₄₃	—	2	2	no	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
140	C₄×Dic₄₃	#41	1	2	yes	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	1	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	2	no	—
146	C₂×C₄₃⋊C₈	—	2	2	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₄₃⋊C₈	#41	1	2	yes	—
150	C₂³×C₄₃	—	2	2	no	—
151	C₂³×C₄₃	—	2	2	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
158	D₄×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	#117	1	2	yes	—
169	C₂×C₄×C₄₃	#117	1	2	yes	—
170	C₂×C₄×C₄₃	#131	1	2	yes	—
171	C₂×C₄×C₄₃	#131	1	2	yes	—
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
178	C₂×Dic₄₃	—	2	1	no	—
179	C₂×Dic₄₃	—	2	1	no	—
180	C₂×Dic₄₃	—	2	1	no	—
181	C₂×Dic₄₃	—	2	1	no	—
182	C₂×Dic₄₃	—	2	1	no	—
183	C₂×Dic₄₃	—	2	1	no	—
184	C₂×Dic₄₃	—	2	1	no	—
185	C₂×Dic₄₃	—	2	1	no	—
186	C₂×Dic₄₃	—	2	2	no	—
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	2	2	no	—
191	C₂×Dic₄₃	—	2	2	no	—
192	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
193	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
194	C₂×Dic₄₃	#131	1	2	yes	—
195	C₂×Dic₄₃	#131	1	2	yes	—
196	C₈×C₄₃	—	2	2	no	—
197	C₈×C₄₃	—	2	2	no	—
198	C₈×C₄₃	—	4	2	no	—
199	C₄₃⋊C₈	—	2	2	no	—
200	C₄₃⋊C₈	—	2	2	no	—
201	C₄₃⋊C₈	—	4	2	no	—
202	#21266	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	—	4	2	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	—	4	2	no	—
208	C₂²×C₄₃	—	4	2	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
211	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
213	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
214	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
215	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
216	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	4	2	no	—
219	C₄×C₄₃	#433	1	4	yes	complemented
220	C₄×C₄₃	#529	1	1	yes	characteristic
221	C₄×C₄₃	#529	1	1	yes	characteristic
222	C₄×C₄₃	#532	1	1	yes	characteristic
223	C₄×C₄₃	#532	1	1	yes	characteristic
224	Dic₄₃	—	2	2	no	—
225	Dic₄₃	—	2	2	no	—
226	Dic₄₃	—	2	2	no	—
227	Dic₄₃	—	2	2	no	—
228	Dic₄₃	—	4	2	no	—
229	Dic₄₃	—	4	2	no	—
230	C₂×#433	—	43	2	no	—
231	#2293	—	43	1	no	—
232	#1954	—	43	1	no	—
233	#1954	D₄₃	1	1	yes	characteristic
234	#1939	—	43	1	no	—
235	#1939	—	43	1	no	—
236	#1923	—	43	2	no	—
237	#1923	—	43	2	no	—
238	#1767	—	43	1	no	—
239	#1750	—	43	2	no	—
240	C₄²×C₈	—	43	1	no	—
241	C₂×C₄₃	—	8	2	no	—
242	C₂×C₄₃	#2293	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#433	1	1	yes	characteristic
244	C₂×C₄₃	#2922	1	1	yes	characteristic
245	C₂×C₄₃	#2931	1	1	yes	characteristic
246	C₂×C₄₃	#2931	1	1	yes	characteristic
247	C₂×C₄₃	#2966	1	1	yes	characteristic
248	C₂×C₄₃	#2966	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
250	C₂×#117	—	43	2	no	—
251	#433	—	86	8	no	—
252	C₂×C₄⋊C₈	—	43	2	no	—
253	C₂×C₄⋊C₈	—	43	2	no	—
254	C₂×C₄⋊C₈	—	43	1	no	—
255	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
256	C₂×C₂²⋊C₈	—	43	2	no	—
257	C₂×C₂²⋊C₈	—	43	2	no	—
258	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
260	C₂×#97	—	43	2	no	—
261	C₂×C₄×C₈	—	43	1	no	—
262	C₂×C₄×C₈	—	43	1	no	—
263	C₂×C₄×C₈	—	43	1	no	—
264	C₂×C₄×C₈	—	43	1	no	—
265	C₂×C₄×C₈	—	43	1	no	—
266	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
267	#390	—	43	1	no	—
268	#390	—	43	1	no	—
269	#389	—	43	1	no	—
270	#389	—	43	1	no	—
271	#388	—	43	2	no	—
272	#388	—	43	2	no	—
273	C₄×C₄⋊C₄	—	43	1	no	—
274	C₄×C₂²⋊C₄	—	43	2	no	—
275	C₄³	—	43	1	no	—
276	#336	—	43	2	no	—
277	#336	—	43	2	no	—
278	#336	—	43	2	no	—
279	C₄₃	#21266	1	1	yes	characteristic, complemented, Sylow
280	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
281	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
282	C₂²×C₈	—	43	1	no	—
283	C₂²×C₈	—	43	1	no	—
284	C₂²×C₈	—	43	2	no	—
285	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
286	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
287	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	#117	—	86	4	no	—
291	#117	—	86	4	no	—
292	C₂×C₄⋊C₄	—	43	2	no	—
293	C₂×C₄⋊C₄	—	43	2	no	—
294	C₂×C₄⋊C₄	—	43	1	no	—
295	C₂×C₄⋊C₄	—	43	1	no	—
296	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	43	2	no	—
298	C₂×C₂²⋊C₄	—	43	2	no	—
299	C₂×C₂²⋊C₄	—	43	2	no	—
300	C₂×C₂²⋊C₄	—	43	2	no	—
301	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
302	C₂×C₄²	—	43	1	no	—
303	C₂×C₄²	—	43	1	no	—
304	C₂×C₄²	—	43	1	no	—
305	C₂×C₄²	—	43	1	no	—
306	C₂×C₄²	—	43	1	no	—
307	C₂×C₄²	—	43	2	no	—
308	C₂×C₄²	—	43	1	no	—
309	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	86	4	no	—
312	C₄⋊C₈	—	86	4	no	—
313	C₄⋊C₈	—	86	2	no	—
314	C₂²⋊C₈	—	2	4	no	—
315	C₂²⋊C₈	—	2	4	no	—
316	C₂²⋊C₈	—	86	4	no	—
317	C₂²⋊C₈	—	86	4	no	—
318	#97	—	86	4	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	43	4	no	—
321	C₄×C₈	—	86	2	no	—
322	C₄×C₈	—	86	2	no	—
323	C₄×C₈	—	86	2	no	—
324	C₄×C₈	—	86	2	no	—
325	#95	—	43	2	no	—
326	#95	—	43	2	no	—
327	#95	—	43	2	no	—
328	C₂⁴	C₂×C₄×D₄₃	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	43	1	no	—
339	C₂²×C₄	—	43	1	no	—
340	C₂²×C₄	—	43	1	no	—
341	C₂²×C₄	—	43	1	no	—
342	C₂²×C₄	—	43	2	no	—
343	C₂²×C₄	—	43	2	no	—
344	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
345	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
347	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	43	2	no	—
356	C₂×C₈	—	43	2	no	—
357	C₂×C₈	—	86	1	no	—
358	C₂×C₈	—	86	1	no	—
359	C₂×C₈	—	86	1	no	—
360	C₂×C₈	—	86	1	no	—
361	C₂×C₈	—	86	2	no	—
362	C₂×C₈	—	86	2	no	—
363	C₂×C₈	—	86	2	no	—
364	C₂×C₈	D₄×D₄₃	1	2	yes	—
365	C₂×C₈	#10621900	1	2	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	86	4	no	—
368	C₄⋊C₄	—	86	4	no	—
369	C₄⋊C₄	—	86	2	no	—
370	C₄⋊C₄	—	86	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	86	4	no	—
373	C₂²⋊C₄	—	86	4	no	—
374	C₂²⋊C₄	—	86	4	no	—
375	C₂²⋊C₄	—	86	4	no	—
376	C₄²	—	43	2	no	—
377	C₄²	—	43	2	no	—
378	C₄²	—	86	2	no	—
379	C₄²	—	86	2	no	—
380	C₄²	—	86	2	no	—
381	C₄²	—	86	2	no	—
382	C₄²	—	86	2	no	—
383	C₄²	—	86	1	no	—
384	C₄²	—	86	2	no	—
385	C₄²	—	86	1	no	—
386	C₄²	#10621900	1	2	yes	—
387	C₄²	#10621900	1	2	yes	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
396	D₄	—	4	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	43	2	no	—
407	C₂×C₄	—	43	2	no	—
408	C₂×C₄	—	43	2	no	—
409	C₂×C₄	—	43	2	no	—
410	C₂×C₄	—	86	1	no	—
411	C₂×C₄	—	86	1	no	—
412	C₂×C₄	—	86	1	no	—
413	C₂×C₄	—	86	1	no	—
414	C₂×C₄	—	86	1	no	—
415	C₂×C₄	—	86	1	no	—
416	C₂×C₄	—	86	1	no	—
417	C₂×C₄	—	86	1	no	—
418	C₂×C₄	—	86	2	no	—
419	C₂×C₄	—	86	2	no	—
420	C₂×C₄	—	86	2	no	—
421	C₂×C₄	—	86	2	no	—
422	C₂×C₄	—	86	2	no	—
423	C₂×C₄	—	86	2	no	—
424	C₂×C₄	#13063281	1	2	yes	—
425	C₂×C₄	#13063281	1	2	yes	—
426	C₂×C₄	#13063331	1	2	yes	—
427	C₂×C₄	#13063333	1	2	yes	—
428	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
429	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
430	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
431	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
432	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
433	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	86	2	no	—
438	C₈	—	86	2	no	—
439	C₈	—	172	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂×#13063281	1	1	yes	characteristic
448	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
449	C₂²	C₄×#10621900	1	1	yes	characteristic
450	C₂²	#131×D₄₃	1	1	yes	characteristic
451	C₂²	#131×D₄₃	1	1	yes	characteristic
452	C₂²	C₂×#13063331	1	1	yes	characteristic
453	C₂²	C₂×#13063333	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	86	2	no	—
457	C₄	—	86	2	no	—
458	C₄	—	86	2	no	—
459	C₄	—	86	2	no	—
460	C₄	—	172	2	no	—
461	C₄	—	172	2	no	—
462	C₄	#14582957	1	4	yes	complemented
463	C₄	#14583428	1	1	yes	characteristic
464	C₄	#14583430	1	1	yes	characteristic
465	C₄	#14583444	1	1	yes	characteristic
466	C₄	#14583447	1	1	yes	characteristic
467	C₂	—	8	2	no	—
468	C₂	#19137057	1	1	yes	characteristic
469	C₂	C₂×#14582957	1	1	yes	characteristic
470	C₂	#19143235	1	1	yes	characteristic
471	C₂	#19143302	1	1	yes	characteristic
472	C₂	#19143304	1	1	yes	characteristic
473	C₂	#19143567	1	1	yes	characteristic
474	C₂	#19143573	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1954	C₂
prime radical	C₂²×D₄×C₄₃	C₂×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1954	D₄₃
hypocenter	C₄₃	#21266
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1954

Complements

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

N	H ≅ G/N	type
1. C₂×#14582957	C₂	semidirect
4. #19135313	C₂	semidirect
5. #19135311	C₂	semidirect
6. #19135204	C₂	semidirect
7. #19135198	C₂	semidirect
8. #19134450	C₂	semidirect
9. #19134363	C₂	semidirect
10. C₄×C₈×Dic₄₃	C₂	semidirect
72. C₈×Dic₄₃	D₄	semidirect
219. C₄×C₄₃	#433	semidirect
279. C₄₃	#21266	semidirect
462. C₄	#14582957	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582957	2
#19137060	2
#19135390	2
#19135313	2
#19135311	2
#19135204	2
#19135198	2
#19134450	2
#19134363	2
C₄×C₈×Dic₄₃	2
C₄₃×#1954	2
#21266	43