Subgroups — #25002978

Order 11008.

946 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582915	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13063253	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582881	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582671	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134321	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582659	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂×#13063284	C₂²	1	1	yes	characteristic
12	#14582915	—	2	2	no	—
13	#14582915	C₄	1	4	yes	complemented
14	C₂×#13063253	—	2	2	no	—
15	C₂×#13063253	—	2	1	no	—
16	C₂×#13063253	—	2	1	no	—
17	C₂×#13063253	C₄	1	4	yes	complemented
18	C₂×#13063251	—	2	2	no	—
19	#14582881	—	2	2	no	—
20	#14582881	—	2	2	no	—
21	C₂×#13063243	C₄	1	2	yes	complemented
22	C₂×#13063241	C₄	1	2	yes	complemented
23	#14582671	—	2	2	no	—
24	#14582663	—	2	2	no	—
25	#14582659	—	2	2	no	—
26	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
29	C₄×M₁₆×C₄₃	—	2	2	no	—
30	C₄×M₁₆×C₄₃	—	2	2	no	—
31	C₂×#97×C₄₃	—	2	1	no	—
32	C₂×C₄×C₈×C₄₃	—	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	—	2	1	no	—
42	C₂×#10621898	—	2	1	no	—
43	C₂×#10621898	C₂×C₄	1	2	yes	—
44	C₂×#10621898	C₂×C₄	1	2	yes	—
45	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₂²⋊D₄₃	—	2	1	no	—
48	C₂²×C₄×D₄₃	—	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	—	2	1	no	—
54	C₂×#10621877	—	2	1	no	—
55	C₂×#10621877	—	2	1	no	—
56	C₂×#10621877	—	2	1	no	—
57	C₂×#10621877	—	2	1	no	—
58	C₂×#10621877	—	2	1	no	—
59	C₂×#10621877	C₂×C₄	1	2	yes	—
60	C₂×#10621877	C₂×C₄	1	2	yes	—
61	C₂²×C₄₃⋊C₈	—	2	1	no	—
62	C₂²×C₄₃⋊C₈	—	2	1	no	—
63	#13063284	—	2	1	no	—
64	#13063284	—	2	1	no	—
65	#13063284	—	2	1	no	—
66	#13063284	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊Dic₄₃	—	2	1	no	—
68	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
69	C₂×C₄×Dic₄₃	—	2	1	no	—
70	#13063253	—	2	4	no	—
71	#13063253	—	2	4	no	—
72	#13063251	—	2	8	no	—
73	#13063243	—	2	4	no	—
74	#13063241	—	2	4	no	—
75	C₂³×C₄×C₄₃	—	2	1	no	—
76	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×C₄₃	—	2	1	no	—
78	C₂×M₁₆×C₄₃	—	2	1	no	—
79	C₂×M₁₆×C₄₃	—	2	1	no	—
80	C₂×M₁₆×C₄₃	—	2	1	no	—
81	C₂×M₁₆×C₄₃	—	2	1	no	—
82	C₂×M₁₆×C₄₃	—	2	1	no	—
83	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
85	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
86	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
87	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
88	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
89	C₂²×C₈×C₄₃	—	2	1	no	—
90	C₂²×C₈×C₄₃	—	2	1	no	—
91	C₂×C₄²×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	—	2	1	no	—
93	C₂×C₄²×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
95	C₂×C₄²×C₄₃	D₄	1	2	yes	—
96	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
98	#97×C₄₃	—	2	4	no	—
99	C₄×C₈×C₄₃	—	2	4	no	—
100	C₂⁴×C₄₃	#41	1	1	yes	characteristic
101	C₂³×D₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	—	2	1	no	—
106	C₂²×C₄×C₄₃	—	4	4	no	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂×C₂²⋊D₄₃	—	2	2	no	—
122	C₂×C₂²⋊D₄₃	—	2	2	no	—
123	C₂×C₂²⋊D₄₃	—	4	1	no	—
124	C₂×C₂²⋊D₄₃	—	4	1	no	—
125	C₂×C₂²⋊D₄₃	—	4	1	no	—
126	C₂×C₂²⋊D₄₃	—	4	1	no	—
127	C₂²×Dic₄₃	—	2	1	no	—
128	C₂²×Dic₄₃	—	4	1	no	—
129	#10621898	—	2	2	no	—
130	#10621898	—	2	2	no	—
131	#10621898	—	2	2	no	—
132	#10621898	—	2	2	no	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	#10621898	—	2	2	no	—
136	#10621898	—	2	2	no	—
137	#10621898	—	4	1	no	—
138	#10621898	—	4	1	no	—
139	#10621898	—	4	1	no	—
140	#10621898	—	4	1	no	—
141	#10621898	—	4	1	no	—
142	#10621898	—	4	1	no	—
143	#10621898	—	4	1	no	—
144	#10621898	—	4	1	no	—
145	C₂×D₁₇₂	—	2	1	no	—
146	C₂×D₁₇₂	—	2	1	no	—
147	C₂×D₁₇₂	—	2	1	no	—
148	C₂×D₁₇₂	—	2	1	no	—
149	C₂×D₁₇₂	—	2	1	no	—
150	C₂×D₁₇₂	C₄²	1	2	yes	—
151	C₂×C₄×D₄₃	—	2	2	no	—
152	C₂×C₄×D₄₃	—	2	2	no	—
153	C₂×C₄×D₄₃	—	4	1	no	—
154	C₂×C₄×D₄₃	—	4	1	no	—
155	C₂×C₄×D₄₃	—	4	1	no	—
156	C₂×C₄×D₄₃	—	4	1	no	—
157	C₂×Dic₈₆	—	2	1	no	—
158	C₂×Dic₈₆	—	2	1	no	—
159	C₂×Dic₈₆	—	2	1	no	—
160	C₂×Dic₈₆	—	2	1	no	—
161	C₂×Dic₈₆	—	2	1	no	—
162	C₂×Dic₈₆	C₄²	1	2	yes	—
163	M₁₆×C₄₃	—	2	2	no	—
164	M₁₆×C₄₃	—	2	2	no	—
165	M₁₆×C₄₃	—	2	2	no	—
166	M₁₆×C₄₃	—	2	2	no	—
167	M₁₆×C₄₃	—	2	2	no	—
168	M₁₆×C₄₃	—	2	2	no	—
169	M₁₆×C₄₃	C₂²⋊C₄	1	4	yes	—
170	M₁₆×C₄₃	C₂²⋊C₄	1	4	yes	—
171	C₂×C₈×C₄₃	—	2	2	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₄²×C₄₃	—	2	2	no	—
178	C₄²×C₄₃	—	2	1	no	—
179	C₄²×C₄₃	—	2	1	no	—
180	C₄²×C₄₃	—	2	2	no	—
181	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
182	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
183	C₂²⋊Dic₄₃	—	2	2	no	—
184	C₂²⋊Dic₄₃	—	4	1	no	—
185	C₄⋊Dic₄₃	—	2	2	no	—
186	C₄⋊Dic₄₃	—	4	1	no	—
187	C₄×Dic₄₃	—	2	2	no	—
188	C₄×Dic₄₃	—	4	1	no	—
189	#10621877	—	2	2	no	—
190	#10621877	—	2	2	no	—
191	#10621877	—	2	2	no	—
192	#10621877	—	2	2	no	—
193	#10621877	—	4	1	no	—
194	#10621877	—	4	1	no	—
195	#10621877	—	4	1	no	—
196	#10621877	—	4	1	no	—
197	C₂×C₄₃⋊C₈	—	2	2	no	—
198	C₂×C₄₃⋊C₈	—	2	2	no	—
199	C₂×C₄₃⋊C₈	—	4	1	no	—
200	C₂×C₄₃⋊C₈	—	4	1	no	—
201	C₂×C₄₃⋊C₈	—	4	1	no	—
202	C₂×C₄₃⋊C₈	—	4	1	no	—
203	C₂³×C₄₃	—	4	2	no	—
204	C₂³×C₄₃	#117	1	1	yes	characteristic
205	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
206	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
207	C₂³×C₄₃	#121	1	1	yes	characteristic
208	C₂³×C₄₃	#123	1	1	yes	characteristic
209	C₂³×C₄₃	#124	1	1	yes	characteristic
210	C₂³×C₄₃	#126	1	1	yes	characteristic
211	C₂²×D₄₃	—	2	2	no	—
212	C₂²×D₄₃	—	4	1	no	—
213	C₂²×D₄₃	—	4	1	no	—
214	C₂²×D₄₃	—	8	2	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	4	4	no	—
219	C₂×C₄×C₄₃	—	4	4	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
226	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
238	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
239	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
240	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
241	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
243	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
244	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
245	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
246	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
247	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
248	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
249	C₂²⋊D₄₃	—	4	2	no	—
250	C₂²⋊D₄₃	—	4	2	no	—
251	C₂²⋊D₄₃	—	4	2	no	—
252	C₂²⋊D₄₃	—	4	2	no	—
253	C₂×Dic₄₃	—	2	2	no	—
254	C₂×Dic₄₃	—	4	1	no	—
255	C₂×Dic₄₃	—	4	1	no	—
256	C₂×Dic₄₃	—	4	2	no	—
257	C₂×Dic₄₃	—	8	2	no	—
258	D₁₇₂	—	2	2	no	—
259	D₁₇₂	—	2	2	no	—
260	D₁₇₂	—	4	1	no	—
261	D₁₇₂	—	4	1	no	—
262	C₄×D₄₃	—	4	2	no	—
263	C₄×D₄₃	—	4	2	no	—
264	C₄×D₄₃	—	4	2	no	—
265	C₄×D₄₃	—	4	2	no	—
266	Dic₈₆	—	2	2	no	—
267	Dic₈₆	—	2	2	no	—
268	Dic₈₆	—	4	1	no	—
269	Dic₈₆	—	4	1	no	—
270	C₈×C₄₃	—	2	4	no	—
271	C₈×C₄₃	—	2	4	no	—
272	C₄₃⋊C₈	—	4	2	no	—
273	C₄₃⋊C₈	—	4	2	no	—
274	#10946	—	43	1	no	maximal, Sylow
275	C₂²×C₄₃	—	2	2	no	—
276	C₂²×C₄₃	—	2	2	no	—
277	C₂²×C₄₃	—	2	2	no	—
278	C₂²×C₄₃	—	4	1	no	—
279	C₂²×C₄₃	—	4	1	no	—
280	C₂²×C₄₃	—	4	1	no	—
281	C₂²×C₄₃	—	4	1	no	—
282	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×C₄₃	#386	1	1	yes	characteristic
284	C₂²×C₄₃	#388	1	1	yes	characteristic
285	C₂²×C₄₃	#388	1	1	yes	characteristic
286	C₂²×C₄₃	#388	1	1	yes	characteristic
287	C₂²×C₄₃	#388	1	1	yes	characteristic
288	C₂²×C₄₃	#390	1	1	yes	characteristic
289	C₂×D₄₃	—	4	2	no	—
290	C₂×D₄₃	—	8	2	no	—
291	C₂×D₄₃	—	8	2	no	—
292	C₂×D₄₃	—	8	2	no	—
293	C₄×C₄₃	—	2	4	no	—
294	C₄×C₄₃	—	4	2	no	—
295	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
296	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
297	C₄×C₄₃	#386	1	1	yes	characteristic
298	C₄×C₄₃	#386	1	1	yes	characteristic
299	C₄×C₄₃	#388	1	1	yes	characteristic
300	C₄×C₄₃	#388	1	1	yes	characteristic
301	C₄×C₄₃	#390	1	1	yes	characteristic
302	C₄×C₄₃	#390	1	1	yes	characteristic
303	Dic₄₃	—	4	2	no	—
304	Dic₄₃	—	8	2	no	—
305	C₂×#421	—	43	1	no	—
306	C₂²×#104	—	43	1	no	—
307	C₂×#413	—	43	1	no	—
308	C₂×C₄×M₁₆	D₄₃	1	1	yes	characteristic, complemented
309	C₂×#344	—	43	1	no	—
310	#1738	—	43	1	no	—
311	C₂×#339	—	43	1	no	—
312	C₂×C₄₃	—	2	1	no	—
313	C₂×C₄₃	—	2	1	no	—
314	C₂×C₄₃	—	2	1	no	—
315	C₂×C₄₃	—	2	1	no	—
316	C₂×C₄₃	—	2	1	no	—
317	C₂×C₄₃	—	2	1	no	—
318	C₂×C₄₃	#1437	1	1	yes	characteristic
319	C₂×C₄₃	#1932	1	2	yes	—
320	D₄₃	—	8	2	no	—
321	C₂²×#41	—	43	1	no	—
322	C₂²×M₁₆	—	43	1	no	—
323	C₂²×M₁₆	—	43	1	no	—
324	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
325	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
326	C₂×#117	—	43	1	no	—
327	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
328	#421	—	43	4	no	—
329	#421	—	86	2	no	—
330	C₂×#104	—	43	4	no	—
331	C₂×#104	—	86	2	no	—
332	C₂×#104	—	86	2	no	—
333	C₂×#104	—	86	1	no	—
334	C₂×#104	—	86	1	no	—
335	#413	—	86	2	no	—
336	#413	—	86	2	no	—
337	C₂×#101	—	43	2	no	—
338	C₂×#100	—	43	2	no	—
339	C₄×M₁₆	—	2	2	no	—
340	C₄×M₁₆	—	2	2	no	—
341	C₂×#97	—	2	1	no	—
342	C₂×C₄×C₈	—	2	1	no	—
343	#344	—	86	2	no	—
344	#341	—	86	2	no	—
345	#339	—	86	2	no	—
346	C₄₃	#10946	1	1	yes	characteristic, complemented, Sylow
347	C₂×#41	—	43	2	no	—
348	C₂×#41	—	43	2	no	—
349	C₂×#41	—	86	1	no	—
350	C₂×#41	—	86	1	no	—
351	C₂×#41	—	86	1	no	—
352	C₂×#41	—	86	1	no	—
353	C₂×#41	—	86	1	no	—
354	C₂×#41	—	86	1	no	—
355	C₂×#41	—	86	1	no	—
356	C₂×#41	—	86	1	no	—
357	C₂×#41	—	86	1	no	—
358	C₂×#41	—	86	1	no	—
359	C₂²×Q₈	—	43	1	no	—
360	C₂²×D₄	—	43	1	no	—
361	C₂²×D₄	—	86	1	no	—
362	C₂³×C₄	—	2	1	no	—
363	C₂³×C₄	—	86	1	no	—
364	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	43	2	no	—
372	C₂×M₁₆	—	43	2	no	—
373	C₂×M₁₆	—	86	1	no	—
374	C₂×M₁₆	—	86	1	no	—
375	C₂×M₁₆	—	86	1	no	—
376	C₂×M₁₆	—	86	1	no	—
377	C₂×M₁₆	—	86	1	no	—
378	C₂×M₁₆	—	86	1	no	—
379	C₂×M₁₆	—	86	1	no	—
380	C₂×M₁₆	—	86	1	no	—
381	C₂×M₁₆	—	86	1	no	—
382	C₂×M₁₆	—	86	1	no	—
383	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
384	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
385	C₂×M₁₆	D₁₇₂	1	2	yes	—
386	C₂×M₁₆	D₁₇₂	1	2	yes	—
387	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
388	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	86	1	no	—
392	C₂²×C₈	—	86	1	no	—
393	#117	—	43	2	no	—
394	#117	—	86	1	no	—
395	#117	—	86	1	no	—
396	#117	—	86	1	no	—
397	C₂×C₄⋊C₄	—	86	1	no	—
398	C₂×C₂²⋊C₄	—	86	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	86	1	no	—
403	C₂×C₄²	C₄×D₄₃	1	2	yes	—
404	C₂×C₄²	D₁₇₂	1	2	yes	—
405	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
406	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
407	#104	—	86	8	no	—
408	#104	—	86	4	no	—
409	#104	—	86	4	no	—
410	#101	—	86	4	no	—
411	#100	—	86	4	no	—
412	#97	—	2	4	no	—
413	C₄×C₈	—	2	4	no	—
414	C₂⁴	—	86	1	no	—
415	C₂⁴	#10621898	1	1	yes	characteristic
416	#41	—	86	2	no	—
417	#41	—	86	2	no	—
418	#41	—	86	2	no	—
419	#41	—	86	2	no	—
420	#41	—	86	2	no	—
421	#41	—	86	2	no	—
422	#41	—	86	2	no	—
423	#41	—	86	2	no	—
424	#41	—	172	1	no	—
425	#41	—	172	1	no	—
426	#41	—	172	1	no	—
427	#41	—	172	1	no	—
428	#41	—	172	1	no	—
429	#41	—	172	1	no	—
430	#41	—	172	1	no	—
431	#41	—	172	1	no	—
432	C₂×Q₈	—	43	2	no	—
433	C₂×Q₈	—	86	1	no	—
434	C₂×Q₈	—	86	1	no	—
435	C₂×Q₈	—	86	1	no	—
436	C₂×Q₈	—	86	1	no	—
437	C₂×Q₈	—	86	1	no	—
438	C₂×D₄	—	43	2	no	—
439	C₂×D₄	—	86	2	no	—
440	C₂×D₄	—	86	2	no	—
441	C₂×D₄	—	86	1	no	—
442	C₂×D₄	—	86	1	no	—
443	C₂×D₄	—	86	1	no	—
444	C₂×D₄	—	86	1	no	—
445	C₂×D₄	—	86	1	no	—
446	C₂×D₄	—	172	1	no	—
447	C₂×D₄	—	172	1	no	—
448	C₂×D₄	—	172	1	no	—
449	C₂×D₄	—	172	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	86	1	no	—
456	C₂²×C₄	—	86	2	no	—
457	C₂²×C₄	—	86	2	no	—
458	C₂²×C₄	—	172	1	no	—
459	C₂²×C₄	—	172	1	no	—
460	C₂²×C₄	—	172	1	no	—
461	C₂²×C₄	—	172	1	no	—
462	C₂²×C₄	—	172	1	no	—
463	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
469	C₂²×C₄	#10621898	1	1	yes	characteristic
470	C₂²×C₄	#10621898	1	1	yes	characteristic
471	C₂²×C₄	#10621898	1	1	yes	characteristic
472	C₂²×C₄	#10621898	1	1	yes	characteristic
473	C₂²×C₄	#10621898	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	86	2	no	—
484	M₁₆	—	86	2	no	—
485	M₁₆	—	86	2	no	—
486	M₁₆	—	86	2	no	—
487	M₁₆	—	172	1	no	—
488	M₁₆	—	172	1	no	—
489	M₁₆	—	172	1	no	—
490	M₁₆	—	172	1	no	—
491	M₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	—
492	M₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	86	2	no	—
500	C₂×C₈	—	86	2	no	—
501	C₂×C₈	—	172	1	no	—
502	C₂×C₈	—	172	1	no	—
503	C₂×C₈	—	172	1	no	—
504	C₂×C₈	—	172	1	no	—
505	C₄⋊C₄	—	86	2	no	—
506	C₄⋊C₄	—	172	1	no	—
507	C₂²⋊C₄	—	86	2	no	—
508	C₂²⋊C₄	—	172	1	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	86	2	no	—
514	C₄²	—	172	1	no	—
515	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
516	C₄²	(C₂×D₄₃)⋊C₄	1	2	yes	—
517	C₂³	—	4	2	no	—
518	C₂³	—	86	2	no	—
519	C₂³	—	344	2	no	—
520	C₂³	—	172	1	no	—
521	C₂³	—	172	1	no	—
522	C₂³	#13063282	1	1	yes	characteristic
523	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
524	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
525	C₂³	#13063299	1	1	yes	characteristic
526	C₂³	#13063308	1	1	yes	characteristic
527	C₂³	#13063313	1	1	yes	characteristic
528	C₂³	#13063319	1	1	yes	characteristic
529	Q₈	—	86	2	no	—
530	Q₈	—	86	2	no	—
531	Q₈	—	172	1	no	—
532	Q₈	—	172	1	no	—
533	D₄	—	86	2	no	—
534	D₄	—	86	2	no	—
535	D₄	—	172	2	no	—
536	D₄	—	172	2	no	—
537	D₄	—	172	2	no	—
538	D₄	—	172	2	no	—
539	D₄	—	172	1	no	—
540	D₄	—	172	1	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	86	2	no	—
548	C₂×C₄	—	344	2	no	—
549	C₂×C₄	—	172	2	no	—
550	C₂×C₄	—	172	1	no	—
551	C₂×C₄	—	172	1	no	—
552	C₂×C₄	—	172	2	no	—
553	C₂×C₄	—	172	2	no	—
554	C₂×C₄	—	172	2	no	—
555	C₂×C₄	—	172	2	no	—
556	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
557	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
558	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
560	C₂×C₄	#13063282	1	1	yes	characteristic
561	C₂×C₄	#13063282	1	1	yes	characteristic
562	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
563	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
564	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
565	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
566	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
567	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
568	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
569	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
570	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
571	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
572	C₂×C₄	#13063294	1	1	yes	characteristic
573	C₂×C₄	#13063299	1	1	yes	characteristic
574	C₂×C₄	#13063299	1	1	yes	characteristic
575	C₂×C₄	#13063299	1	1	yes	characteristic
576	C₂×C₄	#13063299	1	1	yes	characteristic
577	C₂×C₄	#13063299	1	1	yes	characteristic
578	C₂×C₄	#13063308	1	1	yes	characteristic
579	C₂×C₄	#13063308	1	1	yes	characteristic
580	C₂×C₄	#13063313	1	1	yes	characteristic
581	C₂×C₄	#13063313	1	1	yes	characteristic
582	C₂×C₄	#13063319	1	1	yes	characteristic
583	C₂×C₄	#13063322	1	1	yes	characteristic
584	C₈	—	2	4	no	—
585	C₈	—	2	4	no	—
586	C₈	—	172	2	no	—
587	C₈	—	172	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	344	2	no	—
596	C₂²	—	344	2	no	—
597	C₂²	—	344	2	no	—
598	C₂²	—	172	2	no	—
599	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
600	C₂²	#14582778	1	1	yes	characteristic
601	C₂²	#14582790	1	1	yes	characteristic
602	C₂²	#14582790	1	1	yes	characteristic
603	C₂²	#14582790	1	1	yes	characteristic
604	C₂²	#14582790	1	1	yes	characteristic
605	C₂²	#14582801	1	1	yes	characteristic
606	C₄	—	2	4	no	—
607	C₄	—	4	2	no	—
608	C₄	—	344	2	no	—
609	C₄	—	172	2	no	—
610	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
611	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
612	C₄	#14582778	1	1	yes	characteristic
613	C₄	#14582778	1	1	yes	characteristic
614	C₄	#14582790	1	1	yes	characteristic
615	C₄	#14582790	1	1	yes	characteristic
616	C₄	#14582801	1	1	yes	characteristic
617	C₄	#14582801	1	1	yes	characteristic
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	344	2	no	—
625	C₂	#19132833	1	1	yes	characteristic
626	C₂	#19135264	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13063299
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄×M₁₆×C₄₃	C₂
socle	C₂²×C₄₃	#388
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×C₄×M₁₆	D₄₃
hypocenter	C₄₃	#10946
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₂×#14582671	C₂	semidirect
5. #19134321	C₂	semidirect
6. C₂×#14582659	C₂	semidirect
7. C₂×C₄×M₁₆×C₄₃	C₂	semidirect
13. #14582915	C₄	semidirect
17. C₂×#13063253	C₄	semidirect
21. C₂×#13063243	C₄	semidirect
22. C₂×#13063241	C₄	semidirect
308. C₂×C₄×M₁₆	D₄₃	semidirect
346. C₄₃	#10946	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582915	2
C₂²×#13063253	2
C₂×#14582881	2
C₂×#14582671	2
#19134321	2
C₂×#14582659	2
C₂×C₄×M₁₆×C₄₃	2
#10946	43