Subgroups — #25002883

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063251	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582893	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582865	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582663	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582658	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×#13063251	—	2	2	no	—
13	C₂×#13063251	—	2	2	no	—
14	C₂×#13063251	C₄	1	4	yes	complemented
15	#14582893	—	2	2	no	—
16	#14582893	—	2	2	no	—
17	C₂×#13063248	C₄	1	2	yes	complemented
18	C₂×#13063245	C₄	1	2	yes	complemented
19	#14582865	—	2	2	no	—
20	#14582865	C₄	1	4	yes	complemented
21	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
22	C₂×C₈×Dic₄₃	—	2	2	no	—
23	C₂×C₈×Dic₄₃	—	2	2	no	—
24	C₂×C₈×Dic₄₃	—	2	2	no	—
25	#14582663	—	2	2	no	—
26	#14582658	—	2	2	no	—
27	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
28	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#336	—	2	2	no	—
31	C₂×#10621898	—	2	1	no	—
32	C₂×#10621898	—	2	1	no	—
33	C₂×#10621898	—	2	1	no	—
34	C₂×#10621898	—	2	1	no	—
35	C₂×#10621898	—	2	1	no	—
36	C₂×#10621898	—	2	1	no	—
37	C₂×#10621898	—	2	1	no	—
38	C₂×#10621898	—	2	1	no	—
39	C₂×#10621898	—	2	1	no	—
40	C₂×#10621898	—	2	1	no	—
41	C₂×#10621898	C₂×C₄	1	2	yes	—
42	C₂×#10621898	C₂×C₄	1	2	yes	—
43	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₂²⋊D₄₃	—	2	1	no	—
46	C₂³×Dic₄₃	—	2	1	no	—
47	C₂²×C₄×D₄₃	—	2	1	no	—
48	C₂×#10621877	—	2	1	no	—
49	C₂×#10621877	—	2	1	no	—
50	C₂×#10621877	—	2	1	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂×#10621877	—	2	1	no	—
53	C₂×#10621877	C₂×C₄	1	2	yes	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×C₄₃⋊C₈	—	2	1	no	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	C₂²×C₄₃⋊C₈	—	2	1	no	—
58	C₂²×C₄₃⋊C₈	—	2	1	no	—
59	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
60	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
61	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
62	C₂×C₄×Dic₄₃	—	2	1	no	—
63	C₂×C₄×Dic₄₃	—	2	1	no	—
64	C₂×C₄×Dic₄₃	—	2	1	no	—
65	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
67	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
68	#13063251	—	2	8	no	—
69	#13063248	—	2	4	no	—
70	#13063245	—	2	4	no	—
71	(C₂×D₄₃)⋊C₈	—	2	8	no	—
72	C₈×Dic₄₃	—	2	8	no	—
73	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₄₃	—	2	1	no	—
75	C₂×M₁₆×C₄₃	—	2	1	no	—
76	C₂×M₁₆×C₄₃	—	2	1	no	—
77	C₂×M₁₆×C₄₃	—	2	1	no	—
78	C₂×M₁₆×C₄₃	—	2	1	no	—
79	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
80	C₂²×C₈×C₄₃	—	2	1	no	—
81	C₂²×C₈×C₄₃	—	2	1	no	—
82	C₂²×C₈×C₄₃	—	2	1	no	—
83	C₂²×C₈×C₄₃	—	2	1	no	—
84	C₂²×C₈×C₄₃	—	2	1	no	—
85	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
86	C₂²×C₈×C₄₃	D₄	1	2	yes	—
87	C₂²×C₈×C₄₃	D₄	1	2	yes	—
88	#117×C₄₃	—	2	1	no	—
89	#117×C₄₃	—	2	1	no	—
90	#117×C₄₃	—	2	1	no	—
91	#117×C₄₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	—	2	1	no	—
95	C₂⁴×C₄₃	#41	1	1	yes	characteristic
96	C₂³×D₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₃	—	2	2	no	—
113	C₂×C₂²⋊D₄₃	—	2	2	no	—
114	C₂×C₂²⋊D₄₃	—	4	1	no	—
115	C₂×C₂²⋊D₄₃	—	4	1	no	—
116	C₂×C₂²⋊D₄₃	—	4	1	no	—
117	C₂×C₂²⋊D₄₃	—	4	1	no	—
118	C₂²×Dic₄₃	—	2	8	no	—
119	C₂²×Dic₄₃	—	2	2	no	—
120	C₂²×Dic₄₃	—	2	1	no	—
121	C₂²×Dic₄₃	—	2	2	no	—
122	C₂²×Dic₄₃	—	2	2	no	—
123	#10621898	—	2	2	no	—
124	#10621898	—	2	2	no	—
125	#10621898	—	2	2	no	—
126	#10621898	—	2	2	no	—
127	#10621898	—	2	2	no	—
128	#10621898	—	2	2	no	—
129	#10621898	—	2	2	no	—
130	#10621898	—	2	2	no	—
131	#10621898	—	4	1	no	—
132	#10621898	—	4	1	no	—
133	#10621898	—	4	1	no	—
134	#10621898	—	4	1	no	—
135	#10621898	—	4	1	no	—
136	#10621898	—	4	1	no	—
137	#10621898	—	4	1	no	—
138	#10621898	—	4	1	no	—
139	C₂×D₁₇₂	—	2	1	no	—
140	C₂×D₁₇₂	—	2	1	no	—
141	C₂×D₁₇₂	—	2	1	no	—
142	C₂×D₁₇₂	—	2	1	no	—
143	C₂×D₁₇₂	—	2	1	no	—
144	C₂×D₁₇₂	C₄²	1	2	yes	—
145	C₂×C₄×D₄₃	—	2	2	no	—
146	C₂×C₄×D₄₃	—	2	2	no	—
147	C₂×C₄×D₄₃	—	4	1	no	—
148	C₂×C₄×D₄₃	—	4	1	no	—
149	C₂×C₄×D₄₃	—	4	1	no	—
150	C₂×C₄×D₄₃	—	4	1	no	—
151	C₂×Dic₈₆	—	2	1	no	—
152	C₂×Dic₈₆	—	2	1	no	—
153	C₂×Dic₈₆	—	2	1	no	—
154	C₂×Dic₈₆	—	2	1	no	—
155	C₂×Dic₈₆	—	2	1	no	—
156	C₂×Dic₈₆	C₄²	1	2	yes	—
157	M₁₆×C₄₃	—	2	2	no	—
158	M₁₆×C₄₃	—	2	2	no	—
159	M₁₆×C₄₃	—	4	1	no	—
160	M₁₆×C₄₃	—	4	1	no	—
161	C₂×C₈×C₄₃	—	2	2	no	—
162	C₂×C₈×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	—	2	2	no	—
164	C₂×C₈×C₄₃	—	2	2	no	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	4	1	no	—
169	C₂×C₈×C₄₃	—	4	1	no	—
170	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
171	C₄⋊C₄×C₄₃	—	2	2	no	—
172	C₄⋊C₄×C₄₃	—	2	2	no	—
173	C₂²⋊C₄×C₄₃	—	4	1	no	—
174	C₂²⋊C₄×C₄₃	—	4	1	no	—
175	C₄²×C₄₃	—	4	1	no	—
176	C₄²×C₄₃	—	4	1	no	—
177	C₄×Dic₄₃	—	2	2	no	—
178	C₄×Dic₄₃	—	2	2	no	—
179	C₄×Dic₄₃	—	2	2	no	—
180	C₄×Dic₄₃	C₂²⋊C₄	1	4	yes	—
181	#10621877	—	2	2	no	—
182	#10621877	—	2	2	no	—
183	#10621877	—	4	1	no	—
184	#10621877	—	4	1	no	—
185	C₂×C₄₃⋊C₈	—	2	2	no	—
186	C₂×C₄₃⋊C₈	—	2	2	no	—
187	C₂×C₄₃⋊C₈	—	2	2	no	—
188	C₂×C₄₃⋊C₈	—	2	2	no	—
189	C₂×C₄₃⋊C₈	—	2	2	no	—
190	C₂×C₄₃⋊C₈	—	2	2	no	—
191	C₂×C₄₃⋊C₈	—	2	2	no	—
192	C₂×C₄₃⋊C₈	—	4	1	no	—
193	C₂×C₄₃⋊C₈	—	4	1	no	—
194	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	4	yes	—
195	C₂³×C₄₃	—	2	4	no	—
196	C₂³×C₄₃	#117	1	1	yes	characteristic
197	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
198	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₄₃	#121	1	1	yes	characteristic
200	C₂³×C₄₃	#123	1	1	yes	characteristic
201	C₂³×C₄₃	#124	1	1	yes	characteristic
202	C₂³×C₄₃	#126	1	1	yes	characteristic
203	C₂²×D₄₃	—	2	2	no	—
204	C₂²×D₄₃	—	4	1	no	—
205	C₂²×D₄₃	—	4	1	no	—
206	C₂²×D₄₃	—	4	4	no	—
207	C₂×C₄×C₄₃	—	4	2	no	—
208	C₂×C₄×C₄₃	—	4	4	no	—
209	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
214	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
226	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
227	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
230	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
231	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
232	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
233	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
234	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
235	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
237	C₂²⋊D₄₃	—	4	2	no	—
238	C₂²⋊D₄₃	—	4	2	no	—
239	C₂²⋊D₄₃	—	4	2	no	—
240	C₂²⋊D₄₃	—	4	2	no	—
241	C₂×Dic₄₃	—	2	8	no	—
242	C₂×Dic₄₃	—	2	8	no	—
243	C₂×Dic₄₃	—	2	8	no	—
244	C₂×Dic₄₃	—	2	4	no	—
245	C₂×Dic₄₃	—	2	2	no	—
246	C₂×Dic₄₃	—	4	1	no	—
247	C₂×Dic₄₃	—	4	1	no	—
248	D₁₇₂	—	2	2	no	—
249	D₁₇₂	—	2	2	no	—
250	D₁₇₂	—	4	1	no	—
251	D₁₇₂	—	4	1	no	—
252	C₄×D₄₃	—	4	2	no	—
253	C₄×D₄₃	—	4	2	no	—
254	C₄×D₄₃	—	4	2	no	—
255	C₄×D₄₃	—	4	2	no	—
256	Dic₈₆	—	2	2	no	—
257	Dic₈₆	—	2	2	no	—
258	Dic₈₆	—	4	1	no	—
259	Dic₈₆	—	4	1	no	—
260	C₈×C₄₃	—	2	4	no	—
261	C₈×C₄₃	—	4	2	no	—
262	C₄₃⋊C₈	—	2	4	no	—
263	C₄₃⋊C₈	—	4	2	no	—
264	#10929	—	43	1	no	maximal, Sylow
265	C₂²×C₄₃	—	2	2	no	—
266	C₂²×C₄₃	—	2	2	no	—
267	C₂²×C₄₃	—	2	2	no	—
268	C₂²×C₄₃	—	2	2	no	—
269	C₂²×C₄₃	—	2	2	no	—
270	C₂²×C₄₃	—	2	2	no	—
271	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄₃	#386	1	1	yes	characteristic
273	C₂²×C₄₃	#388	1	1	yes	characteristic
274	C₂²×C₄₃	#388	1	1	yes	characteristic
275	C₂²×C₄₃	#388	1	1	yes	characteristic
276	C₂²×C₄₃	#388	1	1	yes	characteristic
277	C₂²×C₄₃	#390	1	1	yes	characteristic
278	C₂²×C₄₃	#443	1	4	yes	—
279	C₂×D₄₃	—	4	2	no	—
280	C₂×D₄₃	—	4	4	no	—
281	C₂×D₄₃	—	8	2	no	—
282	C₂×D₄₃	—	8	2	no	—
283	C₄×C₄₃	—	8	2	no	—
284	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
285	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₄₃	#386	1	1	yes	characteristic
287	C₄×C₄₃	#386	1	1	yes	characteristic
288	C₄×C₄₃	#388	1	1	yes	characteristic
289	C₄×C₄₃	#388	1	1	yes	characteristic
290	C₄×C₄₃	#390	1	1	yes	characteristic
291	C₄×C₄₃	#390	1	1	yes	characteristic
292	Dic₄₃	—	2	8	no	—
293	Dic₄₃	—	4	2	no	—
294	C₂²×#104	—	43	1	no	—
295	C₂×#416	—	43	1	no	—
296	C₂×#408	—	43	1	no	—
297	C₂²×C₄×C₈	—	43	1	no	—
298	C₂×#341	—	43	1	no	—
299	C₂×#339	—	43	1	no	—
300	#1729	D₄₃	1	1	yes	characteristic, complemented
301	C₂×C₄₃	—	2	1	no	—
302	C₂×C₄₃	—	2	1	no	—
303	C₂×C₄₃	—	2	1	no	—
304	C₂×C₄₃	—	2	1	no	—
305	C₂×C₄₃	#1437	1	1	yes	characteristic
306	C₂×C₄₃	#1764	1	2	yes	—
307	C₂×C₄₃	#1937	1	2	yes	—
308	C₂×C₄₃	#1974	1	2	yes	—
309	D₄₃	—	8	2	no	—
310	C₂²×#41	—	43	1	no	—
311	C₂²×M₁₆	—	43	1	no	—
312	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
313	C₂³×C₈	—	43	1	no	—
314	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
315	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
316	C₂²×C₄²	—	43	1	no	—
317	C₂×#104	—	43	4	no	—
318	C₂×#104	—	86	2	no	—
319	C₂×#104	—	86	2	no	—
320	#416	—	86	2	no	—
321	#416	—	86	2	no	—
322	C₂×#103	—	43	2	no	—
323	C₂×#102	—	43	2	no	—
324	#408	—	43	4	no	—
325	#408	—	86	2	no	—
326	C₂×C₂²⋊C₈	—	86	2	no	—
327	C₂×C₄×C₈	—	86	2	no	—
328	C₂×C₄×C₈	—	86	2	no	—
329	C₂×C₄×C₈	—	86	2	no	—
330	#341	—	86	2	no	—
331	#339	—	86	2	no	—
332	#336	—	2	2	no	—
333	C₄₃	#10929	1	1	yes	characteristic, complemented, Sylow
334	C₂×#41	—	43	2	no	—
335	C₂×#41	—	43	2	no	—
336	C₂×#41	—	86	1	no	—
337	C₂×#41	—	86	1	no	—
338	C₂×#41	—	86	1	no	—
339	C₂×#41	—	86	1	no	—
340	C₂×#41	—	86	1	no	—
341	C₂×#41	—	86	1	no	—
342	C₂×#41	—	86	1	no	—
343	C₂×#41	—	86	1	no	—
344	C₂×#41	—	86	1	no	—
345	C₂×#41	—	86	1	no	—
346	C₂²×Q₈	—	43	1	no	—
347	C₂²×D₄	—	43	1	no	—
348	C₂²×D₄	—	86	1	no	—
349	C₂³×C₄	—	86	1	no	—
350	C₂³×C₄	—	86	1	no	—
351	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	43	2	no	—
358	C₂×M₁₆	—	86	1	no	—
359	C₂×M₁₆	—	86	1	no	—
360	C₂×M₁₆	—	86	1	no	—
361	C₂×M₁₆	—	86	1	no	—
362	C₂×M₁₆	—	86	1	no	—
363	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	43	2	no	—
370	C₂²×C₈	—	43	2	no	—
371	C₂²×C₈	—	43	2	no	—
372	C₂²×C₈	—	86	1	no	—
373	C₂²×C₈	—	86	1	no	—
374	C₂²×C₈	—	86	1	no	—
375	C₂²×C₈	—	86	1	no	—
376	C₂²×C₈	—	86	1	no	—
377	C₂²×C₈	C₄×D₄₃	1	2	yes	—
378	C₂²×C₈	D₁₇₂	1	2	yes	—
379	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	43	2	no	—
388	C₂×C₄²	—	43	2	no	—
389	C₂×C₄²	—	43	2	no	—
390	C₂×C₄²	—	86	1	no	—
391	C₂×C₄²	—	86	1	no	—
392	C₂×C₄²	—	86	1	no	—
393	#104	—	86	8	no	—
394	#103	—	86	4	no	—
395	#102	—	86	4	no	—
396	C₂²⋊C₈	—	86	8	no	—
397	C₄×C₈	—	86	8	no	—
398	C₂⁴	—	86	1	no	—
399	C₂⁴	#10621898	1	1	yes	characteristic
400	#41	—	86	2	no	—
401	#41	—	86	2	no	—
402	#41	—	86	2	no	—
403	#41	—	86	2	no	—
404	#41	—	86	2	no	—
405	#41	—	86	2	no	—
406	#41	—	86	2	no	—
407	#41	—	86	2	no	—
408	#41	—	172	1	no	—
409	#41	—	172	1	no	—
410	#41	—	172	1	no	—
411	#41	—	172	1	no	—
412	#41	—	172	1	no	—
413	#41	—	172	1	no	—
414	#41	—	172	1	no	—
415	#41	—	172	1	no	—
416	C₂×Q₈	—	43	2	no	—
417	C₂×Q₈	—	86	1	no	—
418	C₂×Q₈	—	86	1	no	—
419	C₂×Q₈	—	86	1	no	—
420	C₂×Q₈	—	86	1	no	—
421	C₂×Q₈	—	86	1	no	—
422	C₂×D₄	—	43	2	no	—
423	C₂×D₄	—	86	2	no	—
424	C₂×D₄	—	86	2	no	—
425	C₂×D₄	—	86	1	no	—
426	C₂×D₄	—	86	1	no	—
427	C₂×D₄	—	86	1	no	—
428	C₂×D₄	—	86	1	no	—
429	C₂×D₄	—	86	1	no	—
430	C₂×D₄	—	172	1	no	—
431	C₂×D₄	—	172	1	no	—
432	C₂×D₄	—	172	1	no	—
433	C₂×D₄	—	172	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	86	8	no	—
436	C₂²×C₄	—	86	2	no	—
437	C₂²×C₄	—	86	2	no	—
438	C₂²×C₄	—	86	2	no	—
439	C₂²×C₄	—	86	1	no	—
440	C₂²×C₄	—	86	2	no	—
441	C₂²×C₄	—	86	2	no	—
442	C₂²×C₄	—	172	1	no	—
443	C₂²×C₄	—	172	1	no	—
444	C₂²×C₄	—	172	1	no	—
445	C₂²×C₄	—	172	1	no	—
446	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
450	C₂²×C₄	#10621898	1	1	yes	characteristic
451	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
452	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
453	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
454	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
455	C₂²×C₄	#10621900	1	1	yes	characteristic
456	C₂²×C₄	#10621900	1	1	yes	characteristic
457	C₂²×C₄	#10621902	1	1	yes	characteristic
458	C₂²×C₄	#10621902	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	4	1	no	—
463	M₁₆	—	4	1	no	—
464	M₁₆	—	86	2	no	—
465	M₁₆	—	86	2	no	—
466	M₁₆	—	172	1	no	—
467	M₁₆	—	172	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	4	1	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	43	4	no	—
478	C₂×C₈	—	86	2	no	—
479	C₂×C₈	—	86	2	no	—
480	C₂×C₈	—	86	2	no	—
481	C₂×C₈	—	86	2	no	—
482	C₂×C₈	—	86	2	no	—
483	C₂×C₈	—	86	2	no	—
484	C₂×C₈	—	86	2	no	—
485	C₂×C₈	—	172	1	no	—
486	C₂×C₈	—	172	1	no	—
487	C₂×C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	4	1	no	—
493	C₄²	—	4	1	no	—
494	C₄²	—	43	4	no	—
495	C₄²	—	86	2	no	—
496	C₄²	—	86	2	no	—
497	C₄²	—	86	2	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	86	2	no	—
500	C₂³	—	172	1	no	—
501	C₂³	—	172	1	no	—
502	C₂³	—	172	4	no	—
503	C₂³	#13063282	1	1	yes	characteristic
504	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
505	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
506	C₂³	#13063298	1	1	yes	characteristic
507	C₂³	#13063310	1	1	yes	characteristic
508	C₂³	#13063311	1	1	yes	characteristic
509	C₂³	#13063320	1	1	yes	characteristic
510	Q₈	—	86	2	no	—
511	Q₈	—	86	2	no	—
512	Q₈	—	172	1	no	—
513	Q₈	—	172	1	no	—
514	D₄	—	86	2	no	—
515	D₄	—	86	2	no	—
516	D₄	—	172	2	no	—
517	D₄	—	172	2	no	—
518	D₄	—	172	2	no	—
519	D₄	—	172	2	no	—
520	D₄	—	172	1	no	—
521	D₄	—	172	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	86	8	no	—
525	C₂×C₄	—	86	8	no	—
526	C₂×C₄	—	86	8	no	—
527	C₂×C₄	—	86	4	no	—
528	C₂×C₄	—	86	2	no	—
529	C₂×C₄	—	172	1	no	—
530	C₂×C₄	—	172	1	no	—
531	C₂×C₄	—	172	2	no	—
532	C₂×C₄	—	172	2	no	—
533	C₂×C₄	—	172	2	no	—
534	C₂×C₄	—	172	2	no	—
535	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
536	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
537	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
538	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
539	C₂×C₄	#13063283	1	1	yes	characteristic
540	C₂×C₄	#13063283	1	1	yes	characteristic
541	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
542	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
543	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
544	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
545	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
546	C₂×C₄	#13063287	1	1	yes	characteristic
547	C₂×C₄	#13063287	1	1	yes	characteristic
548	C₂×C₄	#13063287	1	1	yes	characteristic
549	C₂×C₄	#13063287	1	1	yes	characteristic
550	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
551	C₂×C₄	#13063295	1	1	yes	characteristic
552	C₂×C₄	#13063297	1	1	yes	characteristic
553	C₂×C₄	#13063297	1	1	yes	characteristic
554	C₂×C₄	#13063298	1	1	yes	characteristic
555	C₂×C₄	#13063300	1	1	yes	characteristic
556	C₂×C₄	#13063300	1	1	yes	characteristic
557	C₂×C₄	#13063309	1	1	yes	characteristic
558	C₂×C₄	#13063310	1	1	yes	characteristic
559	C₂×C₄	#13063311	1	1	yes	characteristic
560	C₂×C₄	#13063314	1	1	yes	characteristic
561	C₂×C₄	#13063320	1	1	yes	characteristic
562	C₂×C₄	#13063321	1	1	yes	characteristic
563	C₈	—	2	4	no	—
564	C₈	—	4	2	no	—
565	C₈	—	86	4	no	—
566	C₈	—	172	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	344	2	no	—
574	C₂²	—	344	2	no	—
575	C₂²	—	172	2	no	—
576	C₂²	—	172	4	no	—
577	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
578	C₂²	#14582777	1	1	yes	characteristic
579	C₂²	#14582788	1	1	yes	characteristic
580	C₂²	#14582788	1	1	yes	characteristic
581	C₂²	#14582789	1	1	yes	characteristic
582	C₂²	#14582791	1	1	yes	characteristic
583	C₂²	#14582799	1	1	yes	characteristic
584	C₂²	#14583014	1	4	yes	—
585	C₄	—	8	2	no	—
586	C₄	—	86	8	no	—
587	C₄	—	172	2	no	—
588	C₄	#14582746	1	1	yes	characteristic
589	C₄	#14582746	1	1	yes	characteristic
590	C₄	#14582776	1	1	yes	characteristic
591	C₄	#14582777	1	1	yes	characteristic
592	C₄	#14582789	1	1	yes	characteristic
593	C₄	#14582791	1	1	yes	characteristic
594	C₄	#14582799	1	1	yes	characteristic
595	C₄	#14582800	1	1	yes	characteristic
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	2	1	no	—
599	C₂	—	2	1	no	—
600	C₂	—	344	2	no	—
601	C₂	#19132831	1	1	yes	characteristic
602	C₂	#19134434	1	2	yes	—
603	C₂	#19135298	1	2	yes	—
604	C₂	#19135482	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#1729	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#1729	D₄₃
hypocenter	C₄₃	#10929
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ #1729

Complements

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

N	H ≅ G/N	type
4. C₂²×C₈×Dic₄₃	C₂	semidirect
5. C₂×#14582663	C₂	semidirect
6. C₂×#14582658	C₂	semidirect
7. C₄₃×#1729	C₂	semidirect
14. C₂×#13063251	C₄	semidirect
17. C₂×#13063248	C₄	semidirect
18. C₂×#13063245	C₄	semidirect
20. #14582865	C₄	semidirect
300. #1729	D₄₃	semidirect
333. C₄₃	#10929	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063251	2
C₂×#14582893	2
C₂×#14582865	2
C₂²×C₈×Dic₄₃	2
C₂×#14582663	2
C₂×#14582658	2
C₄₃×#1729	2
#10929	43