Subgroups — #24991122

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582951	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063305	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₄₃)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582631	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582629	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13063305	C₄	1	1	yes	characteristic
9	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
10	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
11	#14582951	—	2	2	no	—
12	#14582951	—	2	2	no	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
15	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
16	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₈×Dic₄₃	—	2	1	no	—
18	#14582804	C₄	1	1	yes	characteristic
19	#14582798	C₄	1	1	yes	characteristic
20	#14582784	—	2	1	no	—
21	#14582773	—	2	1	no	—
22	#14582756	C₄	1	1	yes	characteristic
23	C₄×C₄⋊Dic₄₃	—	2	1	no	—
24	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
25	#14582653	—	2	1	no	—
26	#14582631	—	2	2	no	—
27	#14582629	—	2	2	no	—
28	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	#13063305	—	2	2	no	—
38	#13063305	C₈	1	4	yes	complemented
39	C₄×Dic₈₆	—	2	1	no	—
40	C₄×Dic₈₆	—	2	1	no	—
41	C₄×Dic₈₆	—	2	1	no	—
42	C₄×Dic₈₆	—	2	1	no	—
43	C₂×C₄⋊Dic₄₃	—	2	1	no	—
44	C₂×C₄⋊Dic₄₃	—	2	1	no	—
45	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂×Dic₄₃⋊C₄	—	2	1	no	—
47	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
48	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
49	C₂×C₄×Dic₄₃	—	2	1	no	—
50	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
53	C₄²×D₄₃	—	2	1	no	—
54	C₄²×D₄₃	—	2	1	no	—
55	C₄²×D₄₃	—	2	1	no	—
56	C₄²×D₄₃	—	2	1	no	—
57	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
59	(C₂×D₄₃)⋊C₈	—	2	4	no	—
60	(C₂×D₄₃)⋊C₈	—	2	4	no	—
61	C₄×C₄₃⋊C₈	—	2	1	no	—
62	C₄×C₄₃⋊C₈	—	2	1	no	—
63	C₈×Dic₄₃	—	2	4	no	—
64	C₄₃⋊#95	—	2	1	no	—
65	C₄₃⋊#95	—	2	1	no	—
66	C₄₃⋊#95	—	2	1	no	—
67	C₄₃⋊#95	—	2	1	no	—
68	C₂²×C₈×C₄₃	—	2	1	no	—
69	C₂²×C₈×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	—	2	1	no	—
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₃	—	2	1	no	—
75	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
76	C₄×C₈×C₄₃	—	2	1	no	—
77	C₄×C₈×C₄₃	—	2	1	no	—
78	#95×C₄₃	—	2	1	no	—
79	C₂³×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	—	2	1	no	—
81	C₂²×C₄×C₄₃	—	2	1	no	—
82	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₄₃	—	2	1	no	—
86	C₂²×Dic₄₃	—	2	1	no	—
87	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₄₃	—	2	1	no	—
91	C₂×C₄×D₄₃	—	2	1	no	—
92	C₂×C₄×D₄₃	—	2	1	no	—
93	C₂×C₄×D₄₃	—	2	1	no	—
94	C₂×C₄×D₄₃	—	2	1	no	—
95	C₂×C₄×D₄₃	—	2	1	no	—
96	C₂×C₄×D₄₃	—	2	1	no	—
97	C₂×C₄×D₄₃	—	2	1	no	—
98	C₂×C₄×D₄₃	—	2	1	no	—
99	C₂×C₄×D₄₃	—	2	1	no	—
100	C₂×C₄×D₄₃	—	2	1	no	—
101	C₂×C₄×D₄₃	—	2	1	no	—
102	C₂×C₄×D₄₃	—	2	2	no	—
103	C₂×C₄×D₄₃	—	4	1	no	—
104	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
105	C₂×C₄×D₄₃	M₁₆	1	2	yes	—
106	C₂×Dic₈₆	—	2	1	no	—
107	C₂×Dic₈₆	—	2	1	no	—
108	C₂×Dic₈₆	—	2	1	no	—
109	C₂×Dic₈₆	—	2	1	no	—
110	C₂×Dic₈₆	—	2	1	no	—
111	C₂×Dic₈₆	C₂×C₈	1	2	yes	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	4	1	no	—
115	C₂×C₈×C₄₃	—	4	1	no	—
116	C₂×C₈×C₄₃	—	4	1	no	—
117	C₂×C₈×C₄₃	—	4	1	no	—
118	C₄⋊C₄×C₄₃	—	2	1	no	—
119	C₄⋊C₄×C₄₃	—	2	1	no	—
120	C₄⋊C₄×C₄₃	—	2	1	no	—
121	C₄⋊C₄×C₄₃	C₂×C₈	1	2	yes	—
122	C₄²×C₄₃	—	4	1	no	—
123	C₄²×C₄₃	—	4	1	no	—
124	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₃	#41	1	1	yes	characteristic
127	C₄²×C₄₃	#41	1	1	yes	characteristic
128	(C₂×D₄₃)⋊C₄	—	2	4	no	—
129	(C₂×D₄₃)⋊C₄	—	4	2	no	—
130	C₄⋊Dic₄₃	—	2	4	no	—
131	C₄⋊Dic₄₃	—	2	1	no	—
132	C₄⋊Dic₄₃	—	2	1	no	—
133	C₄⋊Dic₄₃	—	4	2	no	—
134	Dic₄₃⋊C₄	—	4	1	no	—
135	Dic₄₃⋊C₄	—	4	1	no	—
136	C₄×Dic₄₃	—	2	1	no	—
137	C₄×Dic₄₃	—	2	1	no	—
138	C₄×Dic₄₃	—	2	1	no	—
139	C₄×Dic₄₃	—	2	1	no	—
140	C₄×Dic₄₃	—	2	1	no	—
141	C₄×Dic₄₃	—	2	1	no	—
142	C₄×Dic₄₃	—	4	1	no	—
143	C₄×Dic₄₃	—	4	1	no	—
144	C₂×C₄₃⋊C₈	—	2	2	no	—
145	C₂×C₄₃⋊C₈	—	2	2	no	—
146	C₂×C₄₃⋊C₈	—	4	1	no	—
147	C₂×C₄₃⋊C₈	—	4	1	no	—
148	C₂×C₄₃⋊C₈	—	4	1	no	—
149	C₂×C₄₃⋊C₈	—	4	1	no	—
150	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×D₄₃	—	2	1	no	—
152	C₂²×D₄₃	—	2	1	no	—
153	C₂²×D₄₃	—	2	1	no	—
154	C₂²×D₄₃	—	2	1	no	—
155	C₂²×D₄₃	—	2	1	no	—
156	C₂²×D₄₃	—	2	1	no	—
157	C₂²×D₄₃	C₂²⋊C₈	1	2	yes	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
174	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
175	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
179	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
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	2	no	—
186	C₂×Dic₄₃	—	2	1	no	—
187	C₂×Dic₄₃	—	2	1	no	—
188	C₂×Dic₄₃	—	4	1	no	—
189	C₂×Dic₄₃	—	4	1	no	—
190	C₂×Dic₄₃	—	4	1	no	—
191	C₂×Dic₄₃	—	4	1	no	—
192	C₂×Dic₄₃	—	4	1	no	—
193	C₂×Dic₄₃	C₂²⋊C₈	1	2	yes	—
194	C₂×Dic₄₃	#104	1	2	yes	—
195	C₄×D₄₃	—	2	2	no	—
196	C₄×D₄₃	—	2	2	no	—
197	C₄×D₄₃	—	2	2	no	—
198	C₄×D₄₃	—	2	2	no	—
199	C₄×D₄₃	—	4	2	no	—
200	C₄×D₄₃	—	4	2	no	—
201	C₄×D₄₃	—	4	1	no	—
202	C₄×D₄₃	—	4	1	no	—
203	C₄×D₄₃	—	4	1	no	—
204	C₄×D₄₃	—	4	1	no	—
205	Dic₈₆	—	2	2	no	—
206	Dic₈₆	—	2	2	no	—
207	Dic₈₆	—	4	1	no	—
208	Dic₈₆	—	4	1	no	—
209	C₈×C₄₃	—	4	2	no	—
210	C₈×C₄₃	—	4	2	no	—
211	C₄₃⋊C₈	—	4	2	no	—
212	C₄₃⋊C₈	—	4	2	no	—
213	#8938	—	43	1	no	maximal, Sylow
214	C₂²×C₄₃	#386	1	1	yes	characteristic
215	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
216	C₂²×C₄₃	#408	1	1	yes	characteristic
217	C₂²×C₄₃	#416	1	1	yes	characteristic
218	C₂²×C₄₃	#419	1	1	yes	characteristic
219	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
220	C₂²×C₄₃	#421	1	1	yes	characteristic
221	C₂×D₄₃	—	2	2	no	—
222	C₂×D₄₃	—	2	2	no	—
223	C₂×D₄₃	—	2	2	no	—
224	C₂×D₄₃	—	4	1	no	—
225	C₂×D₄₃	—	4	1	no	—
226	C₂×D₄₃	—	4	1	no	—
227	C₂×D₄₃	—	4	1	no	—
228	C₄×C₄₃	—	2	1	no	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	—	4	2	no	—
231	C₄×C₄₃	—	8	1	no	—
232	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
233	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
234	C₄×C₄₃	#435	1	1	yes	characteristic
235	C₄×C₄₃	#435	1	1	yes	characteristic
236	C₄×C₄₃	#452	1	1	yes	characteristic
237	C₄×C₄₃	#452	1	1	yes	characteristic
238	C₄×C₄₃	#485	1	1	yes	characteristic
239	C₄×C₄₃	#485	1	1	yes	characteristic
240	Dic₄₃	—	2	2	no	—
241	Dic₄₃	—	2	2	no	—
242	Dic₄₃	—	4	2	no	—
243	Dic₄₃	—	4	1	no	—
244	Dic₄₃	—	8	1	no	—
245	C₂×#431	—	43	1	no	—
246	C₄×C₂²⋊Q₈	—	43	1	no	—
247	C₄×C₂²⋊C₈	—	43	1	no	—
248	C₂×Q₈⋊C₈	—	43	1	no	—
249	C₂×Q₈⋊C₈	—	43	1	no	—
250	#1279	—	43	1	no	—
251	#1279	D₄₃	1	1	yes	characteristic, complemented
252	C₂×C₄₃	#1476	1	1	yes	characteristic
253	C₂×C₄₃	#1479	1	1	yes	characteristic
254	C₂×C₄₃	#1482	1	1	yes	characteristic
255	C₂×C₄₃	#1485	1	1	yes	characteristic
256	C₂×C₄₃	#1869	1	1	yes	characteristic
257	C₂×C₄₃	#1871	1	1	yes	characteristic
258	C₂×C₄₃	#1873	1	1	yes	characteristic
259	D₄₃	—	4	2	no	—
260	C₂×C₂²⋊Q₈	—	43	1	no	—
261	C₂×C₄×Q₈	—	43	1	no	—
262	C₂²×C₄²	—	43	1	no	—
263	#431	—	86	2	no	—
264	#431	—	86	2	no	—
265	C₂×C₄⋊C₈	—	43	1	no	—
266	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
267	C₂×C₂²⋊C₈	—	86	1	no	—
268	C₂×C₂²⋊C₈	—	86	1	no	—
269	C₂×C₄×C₈	—	43	1	no	—
270	C₂×C₄×C₈	—	86	1	no	—
271	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
272	#391	—	43	1	no	—
273	#389	—	43	1	no	—
274	#387	—	86	1	no	—
275	#385	—	86	1	no	—
276	#380	—	43	1	no	—
277	C₄×C₄⋊C₄	—	86	1	no	—
278	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
279	C₄×C₂²⋊C₄	—	86	1	no	—
280	#336	—	86	1	no	—
281	Q₈⋊C₈	—	86	2	no	—
282	Q₈⋊C₈	—	86	2	no	—
283	C₄₃	#8938	1	1	yes	characteristic, complemented, Sylow
284	C₂²×Q₈	—	43	1	no	—
285	C₂³×C₄	—	43	1	no	—
286	C₂³×C₄	—	43	1	no	—
287	C₂³×C₄	—	43	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	86	1	no	—
291	C₂²×C₈	—	86	1	no	—
292	C₂²⋊Q₈	—	43	4	no	—
293	C₂²⋊Q₈	—	86	2	no	—
294	C₄×Q₈	—	86	1	no	—
295	C₄×Q₈	—	86	1	no	—
296	C₄×Q₈	—	86	1	no	—
297	C₄×Q₈	—	86	1	no	—
298	C₂×C₄⋊C₄	—	43	1	no	—
299	C₂×C₄⋊C₄	—	86	1	no	—
300	C₂×C₄⋊C₄	—	86	1	no	—
301	C₂×C₄⋊C₄	—	86	1	no	—
302	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	86	1	no	—
305	C₂×C₂²⋊C₄	—	86	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	43	1	no	—
308	C₂×C₄²	—	43	1	no	—
309	C₂×C₄²	—	43	1	no	—
310	C₂×C₄²	—	86	1	no	—
311	C₂×C₄²	—	86	1	no	—
312	C₂×C₄²	—	86	1	no	—
313	C₂×C₄²	—	86	1	no	—
314	C₂×C₄²	—	86	1	no	—
315	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	43	2	no	—
318	C₄⋊C₈	—	86	1	no	—
319	C₄⋊C₈	D₁₇₂	1	2	yes	—
320	C₂²⋊C₈	—	86	4	no	—
321	C₂²⋊C₈	—	86	4	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	86	4	no	—
325	C₄×C₈	—	86	1	no	—
326	C₄×C₈	—	86	1	no	—
327	#95	—	2	1	no	—
328	#95	—	86	1	no	—
329	#95	—	86	1	no	—
330	#95	—	86	1	no	—
331	#95	—	86	1	no	—
332	C₂⁴	—	43	1	no	—
333	C₂×Q₈	—	43	2	no	—
334	C₂×Q₈	—	86	1	no	—
335	C₂×Q₈	—	86	1	no	—
336	C₂×Q₈	—	86	1	no	—
337	C₂×Q₈	—	86	1	no	—
338	C₂×Q₈	—	86	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	43	1	no	—
342	C₂²×C₄	—	43	1	no	—
343	C₂²×C₄	—	43	2	no	—
344	C₂²×C₄	—	43	2	no	—
345	C₂²×C₄	—	43	1	no	—
346	C₂²×C₄	—	86	2	no	—
347	C₂²×C₄	—	86	1	no	—
348	C₂²×C₄	—	86	1	no	—
349	C₂²×C₄	—	86	1	no	—
350	C₂²×C₄	—	86	1	no	—
351	C₂²×C₄	—	86	1	no	—
352	C₂²×C₄	—	86	1	no	—
353	C₂²×C₄	—	86	1	no	—
354	C₂²×C₄	—	86	1	no	—
355	C₂²×C₄	—	86	1	no	—
356	C₂²×C₄	—	86	1	no	—
357	C₂²×C₄	—	86	1	no	—
358	C₂²×C₄	—	86	1	no	—
359	C₂²×C₄	—	86	1	no	—
360	C₂²×C₄	—	86	1	no	—
361	C₂²×C₄	—	172	1	no	—
362	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
363	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
364	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	86	2	no	—
372	C₂×C₈	—	86	2	no	—
373	C₂×C₈	—	172	1	no	—
374	C₂×C₈	—	172	1	no	—
375	C₂×C₈	—	172	1	no	—
376	C₂×C₈	—	172	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	86	4	no	—
381	C₄⋊C₄	—	86	1	no	—
382	C₄⋊C₄	—	86	1	no	—
383	C₄⋊C₄	—	172	2	no	—
384	C₄⋊C₄	—	172	1	no	—
385	C₄⋊C₄	—	172	1	no	—
386	C₄⋊C₄	C₈×D₄₃	1	2	yes	—
387	C₂²⋊C₄	—	86	4	no	—
388	C₂²⋊C₄	—	172	2	no	—
389	C₄²	—	4	1	no	—
390	C₄²	—	4	1	no	—
391	C₄²	—	86	1	no	—
392	C₄²	—	86	1	no	—
393	C₄²	—	86	1	no	—
394	C₄²	—	86	1	no	—
395	C₄²	—	86	1	no	—
396	C₄²	—	86	1	no	—
397	C₄²	—	172	1	no	—
398	C₄²	—	172	1	no	—
399	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
400	C₄²	#10621898	1	1	yes	characteristic
401	C₄²	D₄×D₄₃	1	1	yes	characteristic
402	C₄²	#10621902	1	1	yes	characteristic
403	C₂³	—	43	2	no	—
404	C₂³	—	86	1	no	—
405	C₂³	—	86	1	no	—
406	C₂³	—	86	1	no	—
407	C₂³	—	86	1	no	—
408	C₂³	—	86	1	no	—
409	C₂³	—	86	1	no	—
410	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
411	Q₈	—	86	2	no	—
412	Q₈	—	86	2	no	—
413	Q₈	—	172	1	no	—
414	Q₈	—	172	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	43	2	no	—
424	C₂×C₄	—	43	2	no	—
425	C₂×C₄	—	86	1	no	—
426	C₂×C₄	—	86	1	no	—
427	C₂×C₄	—	86	1	no	—
428	C₂×C₄	—	86	1	no	—
429	C₂×C₄	—	86	2	no	—
430	C₂×C₄	—	86	2	no	—
431	C₂×C₄	—	86	2	no	—
432	C₂×C₄	—	86	2	no	—
433	C₂×C₄	—	86	2	no	—
434	C₂×C₄	—	86	1	no	—
435	C₂×C₄	—	86	1	no	—
436	C₂×C₄	—	86	1	no	—
437	C₂×C₄	—	172	2	no	—
438	C₂×C₄	—	172	2	no	—
439	C₂×C₄	—	172	1	no	—
440	C₂×C₄	—	172	1	no	—
441	C₂×C₄	—	172	1	no	—
442	C₂×C₄	—	172	1	no	—
443	C₂×C₄	—	172	1	no	—
444	C₂×C₄	—	172	1	no	—
445	C₂×C₄	—	172	1	no	—
446	C₂×C₄	—	172	1	no	—
447	C₂×C₄	—	172	1	no	—
448	C₂×C₄	#13063287	1	1	yes	characteristic
449	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
450	C₂×C₄	#13063295	1	1	yes	characteristic
451	C₂×C₄	#13063298	1	1	yes	characteristic
452	C₂×C₄	#13063300	1	1	yes	characteristic
453	C₂×C₄	#13063310	1	1	yes	characteristic
454	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
455	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
456	C₂×C₄	#13063331	1	1	yes	characteristic
457	C₂×C₄	#13063333	1	1	yes	characteristic
458	C₂×C₄	#13063344	1	1	yes	characteristic
459	C₂×C₄	#13063346	1	1	yes	characteristic
460	C₂×C₄	#13063354	1	1	yes	characteristic
461	C₂×C₄	#13063357	1	1	yes	characteristic
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	172	2	no	—
465	C₈	—	172	2	no	—
466	C₂²	—	86	2	no	—
467	C₂²	—	86	2	no	—
468	C₂²	—	86	2	no	—
469	C₂²	—	172	1	no	—
470	C₂²	—	172	1	no	—
471	C₂²	—	172	1	no	—
472	C₂²	—	172	1	no	—
473	C₂²	#14582777	1	1	yes	characteristic
474	C₂²	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
475	C₂²	#14582864	1	1	yes	characteristic
476	C₂²	#14582892	1	1	yes	characteristic
477	C₂²	#14582906	1	1	yes	characteristic
478	C₂²	#104×D₄₃	1	1	yes	characteristic
479	C₂²	#14582914	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	86	2	no	—
485	C₄	—	86	2	no	—
486	C₄	—	344	1	no	—
487	C₄	—	172	2	no	—
488	C₄	—	172	1	no	—
489	C₄	#14582964	1	1	yes	characteristic
490	C₄	C₈×D₁₇₂	1	1	yes	characteristic
491	C₄	#14582969	1	1	yes	characteristic
492	C₄	#14582972	1	1	yes	characteristic
493	C₄	#14583062	1	1	yes	characteristic
494	C₄	#14583064	1	1	yes	characteristic
495	C₄	#14583242	1	1	yes	characteristic
496	C₄	#14583243	1	1	yes	characteristic
497	C₂	—	172	2	no	—
498	C₂	#19132974	1	1	yes	characteristic
499	C₂	#19132988	1	1	yes	characteristic
500	C₂	#19133000	1	1	yes	characteristic
501	C₂	#19133014	1	1	yes	characteristic
502	C₂	#19134886	1	1	yes	characteristic
503	C₂	#19134896	1	1	yes	characteristic
504	C₂	#19134906	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1279	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1279	D₄₃
hypocenter	C₄₃	#8938
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. C₂×#14582631	C₂	semidirect
5. C₂×#14582629	C₂	semidirect
6. #19132436	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
38. #13063305	C₈	semidirect
251. #1279	D₄₃	semidirect
283. C₄₃	#8938	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582951	2
C₄×#13063305	2
C₄×(C₂×D₄₃)⋊C₈	2
C₂×#14582631	2
C₂×#14582629	2
#19132436	2
C₄₃×#1279	2
#8938	43