Subgroups — #25114196

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143250	C₂	1	2	yes	maximal
2	#427×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19135348	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135346	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135194	C₂	1	2	yes	maximal, complemented
6	#19135192	C₂	1	2	yes	maximal, complemented
7	#19134693	C₂	1	2	yes	maximal
8	#19134630	C₂	1	1	yes	maximal, characteristic
9	#19134481	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134372	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
13	#117×D₄₃	C₂²	1	2	yes	—
14	#14582961	—	2	2	no	—
15	#14582958	—	2	2	no	—
16	#14582954	—	2	2	no	—
17	#14582950	—	2	2	no	—
18	C₂×#13063261	C₂²	1	1	yes	characteristic
19	#14582937	C₂²	1	1	yes	characteristic
20	#14582936	C₄	1	1	yes	characteristic, complemented
21	#14582936	C₄	1	1	yes	characteristic, complemented
22	#14582935	C₂²	1	2	yes	—
23	#14582934	C₄	1	2	yes	complemented
24	#107×D₄₃	C₄	1	1	yes	characteristic, complemented
25	#107×D₄₃	C₄	1	1	yes	characteristic, complemented
26	#106×D₄₃	C₄	1	2	yes	complemented
27	#14582927	C₂²	1	2	yes	—
28	#14582925	C₂²	1	2	yes	—
29	#14582862	C₂²	1	2	yes	—
30	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
31	#14582855	C₂²	1	2	yes	—
32	C₂×#13063235	C₂²	1	1	yes	characteristic
33	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
34	#14582663	C₂²	1	2	yes	—
35	#14582660	C₂²	1	2	yes	—
36	#14582659	C₂²	1	2	yes	—
37	#14582658	C₂²	1	2	yes	—
38	#14582654	C₂²	1	1	yes	characteristic
39	#14582653	C₂²	1	1	yes	characteristic
40	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#427	C₂²	1	1	yes	characteristic
42	C₄₃×#405	C₂²	1	2	yes	—
43	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#339	C₂²	1	2	yes	—
45	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
46	C₂×#10621877	C₂³	1	2	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₄₃	—	2	2	no	—
50	C₂×C₈×D₄₃	—	2	2	no	—
51	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
55	#13063284	C₂³	1	2	yes	—
56	#13063283	C₂×C₄	1	2	yes	—
57	#13063283	C₂×C₄	1	2	yes	—
58	#13063282	—	2	2	no	—
59	#13063281	—	2	2	no	—
60	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
61	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
62	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
63	C₂²⋊C₄×D₄₃	—	2	2	no	—
64	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
65	C₄²×D₄₃	—	2	2	no	—
66	#13063261	—	2	2	no	—
67	#13063259	C₂×C₄	1	1	yes	characteristic
68	#13063259	C₂×C₄	1	1	yes	characteristic
69	#13063258	C₂×C₄	1	2	yes	—
70	#13063258	C₂×C₄	1	2	yes	—
71	#13063257	C₂×C₄	1	2	yes	—
72	#13063256	C₂×C₄	1	2	yes	—
73	#13063256	C₂×C₄	1	2	yes	—
74	Dic₄₃⋊C₈	—	2	2	no	—
75	Dic₄₃⋊C₈	—	2	2	no	—
76	Dic₄₃⋊C₈	—	2	2	no	—
77	Dic₄₃⋊C₈	—	2	2	no	—
78	(C₂×D₄₃)⋊C₈	—	2	2	no	—
79	(C₂×D₄₃)⋊C₈	—	2	2	no	—
80	(C₂×D₄₃)⋊C₈	D₄	1	2	yes	—
81	(C₂×D₄₃)⋊C₈	D₄	1	2	yes	—
82	#13063236	—	2	2	no	—
83	#13063235	—	2	2	no	—
84	C₄×C₄₃⋊C₈	—	2	2	no	—
85	C₄₃⋊#95	—	2	1	no	—
86	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	#117×C₄₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	#108×C₄₃	—	2	2	no	—
92	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
93	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
94	#106×C₄₃	C₂×C₄	1	2	yes	—
95	#97×C₄₃	—	2	2	no	—
96	#97×C₄₃	—	2	2	no	—
97	C₄×C₈×C₄₃	—	2	2	no	—
98	C₂³×D₄₃	#41	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₃	—	2	1	no	—
102	C₂²×Dic₄₃	#41	1	1	yes	characteristic
103	C₂×C₄×D₄₃	—	2	1	no	—
104	C₂×C₄×D₄₃	—	2	1	no	—
105	C₂×C₄×D₄₃	—	2	1	no	—
106	C₂×C₄×D₄₃	—	2	1	no	—
107	C₂×C₄×D₄₃	—	2	2	no	—
108	C₂×C₄×D₄₃	—	2	2	no	—
109	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
113	M₁₆×C₄₃	—	2	2	no	—
114	M₁₆×C₄₃	—	2	2	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	1	yes	characteristic
119	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₄₃	#41	1	2	yes	—
122	C₂×C₈×C₄₃	#41	1	2	yes	—
123	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
125	C₂²⋊C₄×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	—	2	2	no	—
127	C₄²×C₄₃	—	2	1	no	—
128	C₄²×C₄₃	—	2	1	no	—
129	C₂²⋊Dic₄₃	—	2	2	no	—
130	(C₂×D₄₃)⋊C₄	—	2	2	no	—
131	(C₂×D₄₃)⋊C₄	—	2	2	no	—
132	(C₂×D₄₃)⋊C₄	—	4	2	no	—
133	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
134	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
135	Dic₄₃⋊C₄	—	2	2	no	—
136	Dic₄₃⋊C₄	—	2	2	no	—
137	C₄×Dic₄₃	—	2	2	no	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	C₄×Dic₄₃	—	2	1	no	—
141	C₄×Dic₄₃	—	2	1	no	—
142	#10621877	—	2	2	no	—
143	#10621877	—	2	2	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
152	C₈×D₄₃	—	2	2	no	—
153	C₈×D₄₃	—	2	2	no	—
154	C₈×D₄₃	—	2	2	no	—
155	C₈×D₄₃	—	2	2	no	—
156	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
157	C₂²×D₄₃	—	2	1	no	—
158	C₂²×D₄₃	—	2	1	no	—
159	C₂²×D₄₃	—	2	2	no	—
160	C₂²×D₄₃	—	4	1	no	—
161	C₂²×D₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂²×D₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×Dic₄₃	—	2	1	no	—
175	C₂×Dic₄₃	—	2	1	no	—
176	C₂×Dic₄₃	—	2	2	no	—
177	C₂×Dic₄₃	—	2	2	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	—	4	1	no	—
181	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
182	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
183	C₄×D₄₃	—	2	1	no	—
184	C₄×D₄₃	—	2	1	no	—
185	C₄×D₄₃	—	2	1	no	—
186	C₄×D₄₃	—	2	1	no	—
187	C₄×D₄₃	—	2	1	no	—
188	C₄×D₄₃	—	2	1	no	—
189	C₄×D₄₃	—	2	1	no	—
190	C₄×D₄₃	—	2	1	no	—
191	C₄×D₄₃	—	4	4	no	—
192	C₄×D₄₃	—	8	2	no	—
193	C₈×C₄₃	—	2	2	no	—
194	C₈×C₄₃	—	4	2	no	—
195	C₈×C₄₃	#117	1	2	yes	—
196	C₈×C₄₃	#117	1	2	yes	—
197	C₄₃⋊C₈	—	2	1	no	—
198	C₄₃⋊C₈	—	2	1	no	—
199	C₄₃⋊C₈	—	2	2	no	—
200	C₄₃⋊C₈	—	4	2	no	—
201	#22607	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₃	#552	1	1	yes	characteristic
206	C₂²×C₄₃	#552	1	1	yes	characteristic
207	C₂×D₄₃	—	2	1	no	—
208	C₂×D₄₃	—	2	1	no	—
209	C₂×D₄₃	—	2	1	no	—
210	C₂×D₄₃	—	2	1	no	—
211	C₂×D₄₃	—	2	1	no	—
212	C₂×D₄₃	—	4	2	no	—
213	C₂×D₄₃	—	4	2	no	—
214	C₂×D₄₃	#444	1	2	yes	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	4	2	no	—
217	C₄×C₄₃	—	8	1	no	—
218	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
219	C₄×C₄₃	#519	1	1	yes	characteristic
220	C₄×C₄₃	#547	1	1	yes	characteristic
221	C₄×C₄₃	#547	1	1	yes	characteristic
222	Dic₄₃	—	2	1	no	—
223	Dic₄₃	—	2	1	no	—
224	Dic₄₃	—	4	2	no	—
225	Dic₄₃	—	4	2	no	—
226	Dic₄₃	—	8	1	no	—
227	#2924	—	43	2	no	—
228	C₂×#427	—	43	1	no	—
229	#1946	—	43	1	no	—
230	#1946	—	43	1	no	—
231	#1922	—	43	2	no	—
232	#1922	—	43	2	no	—
233	#1826	—	43	2	no	—
234	#1810	—	43	1	no	—
235	#1773	—	43	1	no	—
236	#1773	D₄₃	1	1	yes	characteristic, complemented
237	#1752	—	43	1	no	—
238	C₂×C₄₃	—	2	1	no	—
239	C₂×C₄₃	—	2	1	no	—
240	C₂×C₄₃	#2344	1	1	yes	characteristic
241	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
242	C₂×C₄₃	#2957	1	1	yes	characteristic
243	D₄₃	—	2	2	no	—
244	D₄₃	—	4	1	no	—
245	C₂³×C₈	—	43	1	no	—
246	C₂×#117	—	43	2	no	—
247	#433	—	86	2	no	—
248	#433	—	86	2	no	—
249	#432	—	86	2	no	—
250	#431	—	86	2	no	—
251	C₂×#108	—	43	1	no	—
252	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
253	#427	—	43	1	no	—
254	#427	—	43	2	no	—
255	#427	—	43	1	no	—
256	#427	—	43	1	no	—
257	#427	—	43	2	no	—
258	#427	C₂×D₄₃	1	1	yes	characteristic
259	C₂×#107	—	43	1	no	—
260	C₂×#107	—	43	1	no	—
261	C₂×#106	—	43	2	no	—
262	#424	—	43	2	no	—
263	#424	—	43	2	no	—
264	#407	—	43	2	no	—
265	C₂×C₂²⋊C₈	—	43	1	no	—
266	#405	—	43	2	no	—
267	#405	C₂×D₄₃	1	2	yes	—
268	C₂×#97	—	43	1	no	—
269	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
270	C₄×C₂²⋊C₄	—	43	1	no	—
271	#341	—	43	2	no	—
272	#339	—	43	2	no	—
273	#339	—	43	2	no	—
274	#339	—	43	2	no	—
275	#339	C₂×D₄₃	1	2	yes	—
276	#336	—	43	1	no	—
277	#336	—	43	1	no	—
278	C₄₃	#22607	1	1	yes	characteristic, complemented, Sylow
279	C₂³×C₄	—	43	1	no	—
280	C₂×M₁₆	—	43	2	no	—
281	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
282	C₂²×C₈	—	43	1	no	—
283	C₂²×C₈	—	43	1	no	—
284	C₂²×C₈	—	43	1	no	—
285	C₂²×C₈	—	43	1	no	—
286	C₂²×C₈	—	43	1	no	—
287	C₂²×C₈	—	43	1	no	—
288	C₂²×C₈	—	86	2	no	—
289	C₂²×C₈	—	86	2	no	—
290	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
292	#117	—	43	2	no	—
293	#117	—	43	2	no	—
294	#117	—	43	2	no	—
295	#117	—	86	2	no	—
296	#117	—	86	2	no	—
297	#117	C₂²×D₄₃	1	2	yes	—
298	C₂×C₄⋊C₄	—	43	2	no	—
299	C₂×C₄⋊C₄	—	43	2	no	—
300	C₂×C₂²⋊C₄	—	86	2	no	—
301	C₂×C₂²⋊C₄	—	86	1	no	—
302	C₂×C₄²	—	43	1	no	—
303	C₂×C₄²	—	86	2	no	—
304	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
305	#108	—	2	2	no	—
306	#108	—	86	2	no	—
307	#107	—	43	1	no	—
308	#107	—	43	1	no	—
309	#107	—	43	2	no	—
310	#107	—	43	2	no	—
311	#107	C₄×D₄₃	1	1	yes	characteristic
312	#107	C₄×D₄₃	1	1	yes	characteristic
313	#106	—	43	2	no	—
314	#106	—	43	2	no	—
315	#106	—	43	2	no	—
316	#106	C₄×D₄₃	1	2	yes	—
317	C₄⋊C₈	—	86	2	no	—
318	C₄⋊C₈	—	86	2	no	—
319	C₄⋊C₈	—	86	2	no	—
320	C₄⋊C₈	—	86	2	no	—
321	C₂²⋊C₈	—	43	2	no	—
322	C₂²⋊C₈	—	43	2	no	—
323	C₂²⋊C₈	—	86	2	no	—
324	C₂²⋊C₈	—	86	2	no	—
325	#97	—	2	2	no	—
326	#97	—	2	2	no	—
327	#97	—	86	2	no	—
328	#97	—	86	2	no	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	—	86	2	no	—
331	#95	—	86	1	no	—
332	C₂⁴	—	43	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	43	1	no	—
335	C₂²×C₄	—	43	1	no	—
336	C₂²×C₄	—	43	1	no	—
337	C₂²×C₄	—	43	1	no	—
338	C₂²×C₄	—	43	1	no	—
339	C₂²×C₄	—	86	2	no	—
340	C₂²×C₄	—	86	2	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	—	86	1	no	—
344	C₂²×C₄	—	86	1	no	—
345	C₂²×C₄	—	86	1	no	—
346	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	86	2	no	—
350	M₁₆	—	86	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	43	1	no	—
355	C₂×C₈	—	43	1	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	—	86	2	no	—
365	C₂×C₈	—	86	2	no	—
366	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
367	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
368	C₂×C₈	#10621898	1	2	yes	—
369	C₂×C₈	#10621898	1	2	yes	—
370	C₂×C₈	D₄×D₄₃	1	2	yes	—
371	C₄⋊C₄	—	43	2	no	—
372	C₄⋊C₄	—	43	2	no	—
373	C₄⋊C₄	—	86	2	no	—
374	C₄⋊C₄	—	86	2	no	—
375	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
376	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	86	2	no	—
379	C₂²⋊C₄	—	86	2	no	—
380	C₂²⋊C₄	—	86	2	no	—
381	C₂²⋊C₄	—	172	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	86	2	no	—
386	C₄²	—	86	2	no	—
387	C₄²	—	86	2	no	—
388	C₄²	—	86	1	no	—
389	C₄²	—	86	1	no	—
390	C₂³	—	43	1	no	—
391	C₂³	—	43	1	no	—
392	C₂³	—	86	2	no	—
393	C₂³	—	86	1	no	—
394	C₂³	—	86	1	no	—
395	C₂³	—	172	1	no	—
396	C₂³	#41×D₄₃	1	1	yes	characteristic
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	43	1	no	—
403	C₂×C₄	—	43	1	no	—
404	C₂×C₄	—	86	1	no	—
405	C₂×C₄	—	86	1	no	—
406	C₂×C₄	—	86	1	no	—
407	C₂×C₄	—	86	1	no	—
408	C₂×C₄	—	86	1	no	—
409	C₂×C₄	—	86	1	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	2	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	344	2	no	—
417	C₂×C₄	—	172	4	no	—
418	C₂×C₄	—	172	1	no	—
419	C₂×C₄	—	172	1	no	—
420	C₂×C₄	—	172	1	no	—
421	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
422	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
424	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
425	C₂×C₄	#13063372	1	1	yes	characteristic
426	C₂×C₄	#13063373	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	4	2	no	—
429	C₈	—	86	2	no	—
430	C₈	—	86	1	no	—
431	C₈	—	86	1	no	—
432	C₈	—	172	2	no	—
433	C₈	#13063282	1	2	yes	—
434	C₈	#13063282	1	2	yes	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	43	2	no	—
438	C₂²	—	86	1	no	—
439	C₂²	—	86	1	no	—
440	C₂²	—	86	1	no	—
441	C₂²	—	86	1	no	—
442	C₂²	—	86	1	no	—
443	C₂²	—	172	2	no	—
444	C₂²	—	172	2	no	—
445	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
446	C₂²	#14583588	1	1	yes	characteristic
447	C₂²	#14583590	1	1	yes	characteristic
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	86	1	no	—
452	C₄	—	86	1	no	—
453	C₄	—	344	1	no	—
454	C₄	—	172	2	no	—
455	C₄	—	172	2	no	—
456	C₄	C₂×#13063282	1	1	yes	characteristic
457	C₄	#14583375	1	1	yes	characteristic
458	C₄	#14583550	1	1	yes	characteristic
459	C₄	#14583554	1	1	yes	characteristic
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	86	2	no	—
463	C₂	—	172	1	no	—
464	C₂	#19137460	1	1	yes	characteristic
465	C₂	#444×D₄₃	1	1	yes	characteristic
466	C₂	#19143509	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1773	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂³×D₄₃	#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1773	D₄₃
hypocenter	C₄₃	#22607
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
3. #19135348	C₂	semidirect
4. #19135346	C₂	semidirect
5. #19135194	C₂	semidirect
6. #19135192	C₂	semidirect
9. #19134481	C₂	semidirect
11. C₄₃×#1773	C₂	semidirect
20. #14582936	C₄	semidirect
21. #14582936	C₄	semidirect
23. #14582934	C₄	semidirect
24. #107×D₄₃	C₄	semidirect
25. #107×D₄₃	C₄	semidirect
26. #106×D₄₃	C₄	semidirect
236. #1773	D₄₃	semidirect
278. C₄₃	#22607	semidirect

Maximal subgroups

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

subgroup	index
#19143250	2
#427×D₄₃	2
#19135348	2
#19135346	2
#19135194	2
#19135192	2
#19134693	2
#19134630	2
#19134481	2
#19134372	2
C₄₃×#1773	2
#22607	43