Subgroups — #25100876

Order 11008.

862 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	C₂×D₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	#19137232	C₂	1	2	yes	maximal, complemented
3	#19135462	C₂	1	1	yes	maximal, characteristic
4	#19135328	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135326	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135295	C₂	1	2	yes	maximal, complemented
7	#19135289	C₂	1	2	yes	maximal, complemented
8	#107×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134422	C₂	1	2	yes	maximal, complemented
10	#19134281	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1970	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₃	C₂²	1	2	yes	—
13	D₈×Dic₄₃	C₄	1	8	yes	complemented
14	C₂×#13063259	C₂²	1	1	yes	characteristic
15	C₂×#13063259	C₂²	1	1	yes	characteristic
16	C₂×#13063246	C₂²	1	2	yes	—
17	C₂×#13063246	C₂²	1	2	yes	—
18	C₂×#13063236	C₂²	1	1	yes	characteristic
19	C₂×#13063235	C₂²	1	1	yes	characteristic
20	C₂×#13063235	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
23	#14582802	C₂²	1	2	yes	—
24	#14582797	C₂²	1	2	yes	—
25	#14582795	C₂²	1	2	yes	—
26	#14582793	—	2	2	no	—
27	#14582787	—	2	2	no	—
28	#14582760	—	2	2	no	—
29	#14582757	—	2	2	no	—
30	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
31	#14582745	C₂²	1	1	yes	characteristic
32	#14582662	C₂²	1	2	yes	—
33	#14582661	C₂²	1	2	yes	—
34	#14582661	C₂²	1	2	yes	—
35	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#102×C₄₃	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#390	C₂²	1	2	yes	—
40	C₂³×Dic₄₃	—	2	2	no	—
41	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
43	D₄×Dic₄₃	—	2	4	no	—
44	D₄×Dic₄₃	C₂×C₄	1	8	yes	—
45	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
47	C₂×Dic₄₃⋊C₄	—	2	2	no	—
48	C₂×Dic₄₃⋊C₄	—	2	2	no	—
49	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
50	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
52	C₂×C₄×Dic₄₃	—	2	2	no	—
53	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
54	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
55	#13063259	—	2	2	no	—
56	#13063259	C₂×C₄	1	4	yes	—
57	#13063246	—	2	4	no	—
58	#13063246	C₂×C₄	1	8	yes	—
59	#13063236	—	2	2	no	—
60	#13063235	—	2	2	no	—
61	#13063235	—	2	2	no	—
62	C₈×Dic₄₃	—	2	2	no	—
63	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
64	C₄₃⋊#95	—	2	2	no	—
65	C₄₃⋊#95	—	2	2	no	—
66	C₄₃⋊#95	—	2	2	no	—
67	C₄₃⋊#95	D₄	1	1	yes	characteristic
68	C₄₃⋊#95	D₄	1	1	yes	characteristic
69	C₄₃⋊#95	D₄	1	1	yes	characteristic
70	C₄₃⋊#95	D₄	1	1	yes	characteristic
71	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
72	C₂×D₈×C₄₃	—	2	2	no	—
73	C₂×D₈×C₄₃	—	2	2	no	—
74	C₂×D₈×C₄₃	C₂×C₄	1	4	yes	—
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#107×C₄₃	—	2	2	no	—
82	#102×C₄₃	—	2	4	no	—
83	C₄×C₈×C₄₃	—	2	2	no	—
84	C₂⁴×C₄₃	—	2	2	no	—
85	C₂×D₄×C₄₃	—	2	2	no	—
86	C₂×D₄×C₄₃	—	2	2	no	—
87	C₂×D₄×C₄₃	—	2	2	no	—
88	C₂×D₄×C₄₃	—	2	2	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₃	—	2	8	no	—
96	C₂²×Dic₄₃	—	2	2	no	—
97	C₂²×Dic₄₃	—	2	2	no	—
98	C₂²×Dic₄₃	—	8	2	no	—
99	C₂²×Dic₄₃	—	8	2	no	—
100	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
104	D₈×C₄₃	—	2	8	no	—
105	C₂×C₈×C₄₃	—	2	1	no	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₄₃	#41	1	2	yes	—
109	C₂×C₈×C₄₃	#41	1	2	yes	—
110	C₂×C₈×C₄₃	#41	1	2	yes	—
111	C₄⋊C₄×C₄₃	—	2	2	no	—
112	C₄⋊C₄×C₄₃	—	2	2	no	—
113	C₂²⋊C₄×C₄₃	—	8	2	no	—
114	C₂²⋊C₄×C₄₃	—	8	2	no	—
115	C₄²×C₄₃	—	2	1	no	—
116	C₄²×C₄₃	—	2	1	no	—
117	C₂²⋊Dic₄₃	—	2	8	no	—
118	C₂²⋊Dic₄₃	—	8	2	no	—
119	C₂²⋊Dic₄₃	—	8	2	no	—
120	C₄⋊Dic₄₃	—	2	2	no	—
121	C₄⋊Dic₄₃	—	2	2	no	—
122	C₄⋊Dic₄₃	—	2	2	no	—
123	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
124	Dic₄₃⋊C₄	—	8	2	no	—
125	Dic₄₃⋊C₄	—	8	2	no	—
126	C₄×Dic₄₃	—	2	1	no	—
127	C₄×Dic₄₃	—	2	1	no	—
128	C₄×Dic₄₃	—	8	2	no	—
129	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
130	C₄×Dic₄₃	#41	1	2	yes	—
131	C₂×C₄₃⋊C₈	—	2	1	no	—
132	C₂×C₄₃⋊C₈	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₄₃⋊C₈	#41	1	2	yes	—
137	C₂³×C₄₃	—	2	4	no	—
138	C₂³×C₄₃	—	4	2	no	—
139	C₂³×C₄₃	—	4	2	no	—
140	C₂³×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	—	4	2	no	—
143	C₂³×C₄₃	—	4	2	no	—
144	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
145	D₄×C₄₃	—	2	4	no	—
146	D₄×C₄₃	—	2	4	no	—
147	D₄×C₄₃	—	4	2	no	—
148	D₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	1	no	—
151	C₂×C₄×C₄₃	—	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	—	4	2	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₄₃	—	2	1	no	—
165	C₂×Dic₄₃	—	2	1	no	—
166	C₂×Dic₄₃	—	2	1	no	—
167	C₂×Dic₄₃	—	2	1	no	—
168	C₂×Dic₄₃	—	2	4	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	—	2	1	no	—
175	C₂×Dic₄₃	—	4	2	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	C₂×Dic₄₃	—	4	2	no	—
180	C₂×Dic₄₃	—	8	8	no	—
181	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
182	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
183	C₈×C₄₃	—	2	2	no	—
184	C₈×C₄₃	#117	1	4	yes	—
185	C₄₃⋊C₈	—	2	2	no	—
186	C₄₃⋊C₈	—	2	2	no	—
187	#21282	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	—	4	4	no	—
189	C₂²×C₄₃	—	4	4	no	—
190	C₂²×C₄₃	—	4	4	no	—
191	C₂²×C₄₃	—	8	2	no	—
192	C₂²×C₄₃	—	8	2	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	2	no	—
195	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₄₃	#532	1	1	yes	characteristic
197	C₂²×C₄₃	#532	1	1	yes	characteristic
198	C₂²×C₄₃	#576	1	1	yes	characteristic
199	C₂²×C₄₃	#576	1	1	yes	characteristic
200	C₂²×C₄₃	#576	1	1	yes	characteristic
201	C₂²×C₄₃	#578	1	1	yes	characteristic
202	C₄×C₄₃	—	4	1	no	—
203	C₄×C₄₃	—	4	1	no	—
204	C₄×C₄₃	—	8	2	no	—
205	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
206	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
207	C₄×C₄₃	#529	1	1	yes	characteristic
208	C₄×C₄₃	#529	1	1	yes	characteristic
209	Dic₄₃	—	2	2	no	—
210	Dic₄₃	—	2	2	no	—
211	Dic₄₃	—	4	1	no	—
212	Dic₄₃	—	4	1	no	—
213	Dic₄₃	—	4	4	no	—
214	Dic₄₃	—	8	2	no	—
215	C₂×C₄×D₈	—	43	1	no	—
216	#2319	—	43	2	no	—
217	#1970	—	43	1	no	—
218	#1970	D₄₃	1	1	yes	characteristic
219	#1942	—	43	1	no	—
220	#1942	—	43	1	no	—
221	#1936	—	43	2	no	—
222	#1936	—	43	2	no	—
223	C₄×#107	—	43	1	no	—
224	#1762	—	43	2	no	—
225	#1726	—	43	1	no	—
226	C₂×C₄₃	—	8	4	no	—
227	C₂×C₄₃	#2293	1	1	yes	characteristic
228	C₂×C₄₃	#2948	1	1	yes	characteristic
229	C₂×C₄₃	#2951	1	1	yes	characteristic
230	C₂×C₄₃	#3175	1	1	yes	characteristic
231	C₂×C₄₃	#3175	1	1	yes	characteristic
232	C₂×C₄₃	#3176	1	1	yes	characteristic
233	C₂×C₄₃	#3176	1	1	yes	characteristic
234	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
235	C₂×C₄×D₄	—	43	2	no	—
236	C₄×D₈	—	43	8	no	—
237	C₂×#107	—	43	1	no	—
238	C₂×#107	—	43	1	no	—
239	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
240	C₂×#102	—	43	2	no	—
241	C₂×#102	—	43	2	no	—
242	C₂×#102	C₂×D₄₃	1	2	yes	—
243	C₂×#97	—	43	1	no	—
244	C₂×#97	—	43	1	no	—
245	C₂×#97	—	43	1	no	—
246	C₂×C₄×C₈	—	43	1	no	—
247	C₂×C₄×C₈	—	43	1	no	—
248	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
249	#390	—	43	2	no	—
250	#390	C₂×D₄₃	1	2	yes	—
251	#389	—	43	2	no	—
252	#389	—	43	2	no	—
253	#388	—	86	2	no	—
254	#388	—	86	2	no	—
255	#381	—	86	2	no	—
256	#380	—	86	2	no	—
257	C₄×C₄⋊C₄	—	43	2	no	—
258	#376	—	43	1	no	—
259	#340	—	43	2	no	—
260	#340	—	43	2	no	—
261	#340	—	43	2	no	—
262	C₄₃	#21282	1	1	yes	characteristic, complemented, Sylow
263	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
264	C₂³×C₄	—	86	2	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×D₈	—	2	2	no	—
267	C₂×D₈	C₄×D₄₃	1	4	yes	—
268	C₂²×C₈	—	43	1	no	—
269	C₂²×C₈	—	43	1	no	—
270	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
272	C₄×D₄	—	43	8	no	—
273	C₄×D₄	—	86	4	no	—
274	C₂×C₄⋊C₄	—	43	2	no	—
275	C₂×C₄⋊C₄	—	43	2	no	—
276	C₂×C₄⋊C₄	—	86	2	no	—
277	C₂×C₄⋊C₄	—	86	2	no	—
278	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	86	2	no	—
282	C₂×C₂²⋊C₄	—	86	2	no	—
283	C₂×C₂²⋊C₄	—	86	2	no	—
284	C₂×C₄²	—	43	1	no	—
285	C₂×C₄²	—	43	1	no	—
286	C₂×C₄²	—	86	2	no	—
287	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
288	#107	—	2	2	no	—
289	#107	—	43	4	no	—
290	#107	—	86	2	no	—
291	#102	—	2	4	no	—
292	#102	—	43	8	no	—
293	#102	—	86	4	no	—
294	#97	—	86	2	no	—
295	#97	—	86	2	no	—
296	#97	—	86	2	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	43	4	no	—
299	C₄×C₈	—	86	2	no	—
300	#95	—	43	1	no	—
301	#95	—	43	1	no	—
302	#95	—	43	1	no	—
303	#95	—	43	1	no	—
304	#95	—	86	2	no	—
305	#95	—	86	2	no	—
306	#95	—	86	2	no	—
307	C₂⁴	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	C₂×C₄×D₄₃	1	4	yes	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	43	1	no	—
316	C₂²×C₄	—	43	1	no	—
317	C₂²×C₄	—	43	1	no	—
318	C₂²×C₄	—	43	1	no	—
319	C₂²×C₄	—	86	8	no	—
320	C₂²×C₄	—	86	2	no	—
321	C₂²×C₄	—	86	2	no	—
322	C₂²×C₄	—	344	2	no	—
323	C₂²×C₄	—	344	2	no	—
324	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
325	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
326	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
327	D₈	—	2	8	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	43	2	no	—
331	C₂×C₈	—	43	2	no	—
332	C₂×C₈	—	86	1	no	—
333	C₂×C₈	—	86	1	no	—
334	C₂×C₈	—	86	1	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
337	C₂×C₈	#10621900	1	2	yes	—
338	C₂×C₈	#10621900	1	2	yes	—
339	C₂×C₈	#10621900	1	2	yes	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	43	4	no	—
343	C₄⋊C₄	—	86	2	no	—
344	C₄⋊C₄	—	86	2	no	—
345	C₄⋊C₄	—	86	2	no	—
346	C₄⋊C₄	—	344	2	no	—
347	C₄⋊C₄	—	344	2	no	—
348	C₂²⋊C₄	—	8	2	no	—
349	C₂²⋊C₄	—	8	2	no	—
350	C₂²⋊C₄	—	86	8	no	—
351	C₂²⋊C₄	—	344	2	no	—
352	C₂²⋊C₄	—	344	2	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	43	2	no	—
356	C₄²	—	43	2	no	—
357	C₄²	—	86	1	no	—
358	C₄²	—	86	1	no	—
359	C₄²	—	344	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
368	D₄	—	2	4	no	—
369	D₄	—	2	4	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	43	2	no	—
382	C₂×C₄	—	43	2	no	—
383	C₂×C₄	—	86	1	no	—
384	C₂×C₄	—	86	1	no	—
385	C₂×C₄	—	86	1	no	—
386	C₂×C₄	—	86	1	no	—
387	C₂×C₄	—	86	4	no	—
388	C₂×C₄	—	86	1	no	—
389	C₂×C₄	—	86	1	no	—
390	C₂×C₄	—	86	1	no	—
391	C₂×C₄	—	86	1	no	—
392	C₂×C₄	—	86	1	no	—
393	C₂×C₄	—	86	1	no	—
394	C₂×C₄	—	344	8	no	—
395	C₂×C₄	—	172	2	no	—
396	C₂×C₄	—	172	2	no	—
397	C₂×C₄	—	172	2	no	—
398	C₂×C₄	—	172	2	no	—
399	C₂×C₄	—	172	2	no	—
400	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
401	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
402	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
403	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
404	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
405	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	86	2	no	—
408	C₈	—	86	2	no	—
409	C₈	#13063281	1	4	yes	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
418	C₂²	#14583444	1	1	yes	characteristic
419	C₂²	#14583447	1	1	yes	characteristic
420	C₂²	#14583700	1	1	yes	characteristic
421	C₂²	#14583700	1	1	yes	characteristic
422	C₂²	#14583701	1	1	yes	characteristic
423	C₂²	#14583713	1	1	yes	characteristic
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	8	2	no	—
427	C₄	—	86	2	no	—
428	C₄	—	86	2	no	—
429	C₄	—	344	2	no	—
430	C₄	—	172	1	no	—
431	C₄	—	172	4	no	—
432	C₄	—	172	1	no	—
433	C₄	C₂×#13063281	1	1	yes	characteristic
434	C₄	C₄×#10621900	1	1	yes	characteristic
435	C₄	#14583428	1	1	yes	characteristic
436	C₄	#14583430	1	1	yes	characteristic
437	C₂	—	8	4	no	—
438	C₂	#19137057	1	1	yes	characteristic
439	C₂	#19143442	1	1	yes	characteristic
440	C₂	#19143465	1	1	yes	characteristic
441	C₂	#19145227	1	1	yes	characteristic
442	C₂	#19145231	1	1	yes	characteristic
443	C₂	#19145238	1	1	yes	characteristic
444	C₂	#19145242	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1970	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₈×C₄₃	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1970	D₄₃
hypocenter	C₄₃	#21282
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1970

Complements

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

N	H ≅ G/N	type
2. #19137232	C₂	semidirect
4. #19135328	C₂	semidirect
5. #19135326	C₂	semidirect
6. #19135295	C₂	semidirect
7. #19135289	C₂	semidirect
8. #107×Dic₄₃	C₂	semidirect
9. #19134422	C₂	semidirect
10. #19134281	C₂	semidirect
13. D₈×Dic₄₃	C₄	semidirect
262. C₄₃	#21282	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₈×Dic₄₃	2
#19137232	2
#19135462	2
#19135328	2
#19135326	2
#19135295	2
#19135289	2
#107×Dic₄₃	2
#19134422	2
#19134281	2
C₄₃×#1970	2
#21282	43