Subgroups — #25001988

Order 11008.

1210 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583665	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582881	C₂	1	1	yes	maximal, characteristic
3	#19137183	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582669	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582667	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582667	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	#14583665	—	2	2	no	—
10	#14583665	—	2	2	no	—
11	#14583665	—	2	2	no	—
12	#14583665	C₄	1	4	yes	complemented
13	C₂×#13063333	—	2	2	no	—
14	C₂×#13063331	—	2	2	no	—
15	C₂²×#10621877	C₂²	1	1	yes	characteristic
16	C₂²×#10621877	C₂²	1	1	yes	characteristic
17	C₂×M₁₆×D₄₃	—	2	2	no	—
18	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
19	#14582881	—	2	2	no	—
20	#14582881	C₄	1	4	yes	complemented
21	C₂×#13063243	—	2	1	no	—
22	C₂×#13063241	—	2	1	no	—
23	#14582805	—	2	1	no	—
24	#14582801	—	2	1	no	—
25	#14582776	C₄	1	4	yes	—
26	#14582756	—	2	2	no	—
27	#14582669	—	2	2	no	—
28	#14582667	—	2	2	no	—
29	#14582667	—	2	2	no	—
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#344	—	2	2	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	C₂×C₄	1	2	yes	—
43	C₂×#10621898	C₂×C₄	1	2	yes	—
44	C₂×#10621898	D₄	1	2	yes	—
45	C₂×#10621898	Q₈	1	2	yes	—
46	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
47	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
48	C₂²×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
49	C₂³×Dic₄₃	C₂×C₄	1	2	yes	—
50	C₂²×C₄×D₄₃	D₄	1	2	yes	—
51	#13063333	—	2	8	no	—
52	#13063333	—	2	8	no	—
53	#13063331	—	2	8	no	—
54	#13063331	—	2	8	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	—	2	1	no	—
60	C₂×#10621877	—	2	1	no	—
61	C₂×#10621877	—	2	1	no	—
62	C₂×#10621877	—	2	1	no	—
63	C₂×#10621877	C₂×C₄	1	2	yes	—
64	C₂×#10621877	C₂×C₄	1	2	yes	—
65	C₂×#10621877	D₄	1	2	yes	—
66	C₂×#10621877	D₄	1	2	yes	—
67	C₂×#10621872	—	2	4	no	—
68	M₁₆×D₄₃	—	2	8	no	—
69	M₁₆×D₄₃	—	2	8	no	—
70	C₂²×C₄₃⋊C₈	—	2	1	no	—
71	C₂²×C₄₃⋊C₈	—	2	1	no	—
72	C₂×C₈×D₄₃	—	2	4	no	—
73	C₂×C₄⋊Dic₄₃	—	2	1	no	—
74	C₂×C₄⋊Dic₄₃	—	2	1	no	—
75	C₂×C₄⋊Dic₄₃	—	2	1	no	—
76	C₂×C₄⋊Dic₄₃	—	2	1	no	—
77	C₂×C₄⋊Dic₄₃	—	2	1	no	—
78	C₂×C₄⋊Dic₄₃	—	2	1	no	—
79	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
80	#13063243	—	2	4	no	—
81	#13063241	—	2	4	no	—
82	C₄₃⋊#95	—	2	4	no	—
83	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₃	—	2	1	no	—
85	C₂×M₁₆×C₄₃	—	2	1	no	—
86	C₂×M₁₆×C₄₃	—	2	1	no	—
87	C₂×M₁₆×C₄₃	—	2	1	no	—
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₂×M₁₆×C₄₃	—	2	1	no	—
91	C₂×M₁₆×C₄₃	—	2	1	no	—
92	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
93	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
94	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
95	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
96	C₂²×C₈×C₄₃	—	2	1	no	—
97	C₂²×C₈×C₄₃	—	2	1	no	—
98	#117×C₄₃	—	2	1	no	—
99	#117×C₄₃	—	2	1	no	—
100	#117×C₄₃	—	2	1	no	—
101	#117×C₄₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
104	C₂×C₄²×C₄₃	—	2	1	no	—
105	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂³×D₄₃	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×Q₈	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	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
122	C₂×C₂²⋊D₄₃	—	2	2	no	—
123	C₂×C₂²⋊D₄₃	—	2	2	no	—
124	C₂×C₂²⋊D₄₃	—	2	2	no	—
125	C₂×C₂²⋊D₄₃	—	2	2	no	—
126	C₂×C₂²⋊D₄₃	C₄²	1	4	yes	—
127	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	4	yes	—
128	C₂²×Dic₄₃	—	2	2	no	—
129	C₂²×Dic₄₃	—	2	2	no	—
130	C₂²×Dic₄₃	—	2	2	no	—
131	C₂²×Dic₄₃	—	8	2	no	—
132	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	#10621898	—	2	2	no	—
136	#10621898	—	2	2	no	—
137	#10621898	—	2	2	no	—
138	#10621898	—	2	2	no	—
139	#10621898	—	2	2	no	—
140	#10621898	—	2	2	no	—
141	#10621898	—	2	2	no	—
142	#10621898	—	2	2	no	—
143	#10621898	—	2	2	no	—
144	#10621898	—	2	2	no	—
145	#10621898	—	2	2	no	—
146	#10621898	—	2	2	no	—
147	#10621898	—	2	2	no	—
148	#10621898	—	2	2	no	—
149	C₂×D₁₇₂	—	2	1	no	—
150	C₂×D₁₇₂	—	2	1	no	—
151	C₂×D₁₇₂	—	2	1	no	—
152	C₂×D₁₇₂	—	2	1	no	—
153	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
154	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
155	C₂×C₄×D₄₃	—	2	2	no	—
156	C₂×C₄×D₄₃	—	2	2	no	—
157	C₂×C₄×D₄₃	—	2	2	no	—
158	C₂×C₄×D₄₃	—	2	2	no	—
159	C₂×C₄×D₄₃	C₂²⋊C₄	1	4	yes	—
160	C₂×C₄×D₄₃	C₄⋊C₄	1	4	yes	—
161	C₂×Dic₈₆	—	2	1	no	—
162	C₂×Dic₈₆	—	2	1	no	—
163	C₂×Dic₈₆	—	2	1	no	—
164	C₂×Dic₈₆	—	2	1	no	—
165	C₂×Dic₈₆	C₂²⋊C₄	1	2	yes	—
166	C₂×Dic₈₆	C₄⋊C₄	1	2	yes	—
167	M₁₆×C₄₃	—	2	2	no	—
168	M₁₆×C₄₃	—	2	2	no	—
169	M₁₆×C₄₃	—	2	2	no	—
170	M₁₆×C₄₃	—	2	2	no	—
171	M₁₆×C₄₃	—	2	2	no	—
172	M₁₆×C₄₃	—	4	1	no	—
173	M₁₆×C₄₃	—	4	1	no	—
174	M₁₆×C₄₃	C₂²⋊C₄	1	4	yes	complemented
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₂×C₈×C₄₃	—	2	2	no	—
178	C₂×C₈×C₄₃	—	2	2	no	—
179	C₂×C₈×C₄₃	—	4	1	no	—
180	C₂×C₈×C₄₃	—	4	1	no	—
181	C₄⋊C₄×C₄₃	—	4	1	no	—
182	C₄⋊C₄×C₄₃	—	4	1	no	—
183	C₂²⋊C₄×C₄₃	—	2	2	no	—
184	C₂²⋊C₄×C₄₃	—	2	2	no	—
185	C₄²×C₄₃	—	4	1	no	—
186	C₄²×C₄₃	—	4	1	no	—
187	(C₂×D₄₃)⋊C₄	—	8	4	no	—
188	C₄⋊Dic₄₃	—	4	1	no	—
189	C₄⋊Dic₄₃	—	4	1	no	—
190	C₄⋊Dic₄₃	—	4	1	no	—
191	C₄⋊Dic₄₃	—	4	1	no	—
192	#10621877	—	2	2	no	—
193	#10621877	—	2	2	no	—
194	#10621877	—	2	2	no	—
195	#10621877	—	2	2	no	—
196	#10621877	—	2	2	no	—
197	#10621877	—	4	1	no	—
198	#10621877	—	4	1	no	—
199	#10621877	C₂²⋊C₄	1	4	yes	complemented
200	C₂×C₄₃⋊C₈	—	2	2	no	—
201	C₂×C₄₃⋊C₈	—	2	2	no	—
202	C₂×C₄₃⋊C₈	—	2	2	no	—
203	C₂×C₄₃⋊C₈	—	2	2	no	—
204	C₂×C₄₃⋊C₈	—	4	1	no	—
205	C₂×C₄₃⋊C₈	—	4	1	no	—
206	#10621872	—	2	16	no	—
207	C₈×D₄₃	—	2	16	no	—
208	C₂³×C₄₃	—	4	1	no	—
209	C₂³×C₄₃	—	4	1	no	—
210	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
211	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
216	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
217	C₂²×D₄₃	—	2	2	no	—
218	C₂²×D₄₃	—	2	2	no	—
219	C₂²×D₄₃	—	4	2	no	—
220	C₂²×D₄₃	—	4	2	no	—
221	C₂²×D₄₃	#95	1	4	yes	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	2	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
232	C₂×C₄×C₄₃	#117	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	#120	1	1	yes	characteristic
239	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
240	C₂×C₄×C₄₃	#120	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	#121	1	1	yes	characteristic
244	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
250	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
251	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
252	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
253	C₂²⋊D₄₃	—	2	4	no	—
254	C₂²⋊D₄₃	—	2	4	no	—
255	C₂²⋊D₄₃	—	2	4	no	—
256	C₂²⋊D₄₃	—	2	4	no	—
257	C₂×Dic₄₃	—	2	2	no	—
258	C₂×Dic₄₃	—	2	2	no	—
259	C₂×Dic₄₃	—	4	4	no	—
260	C₂×Dic₄₃	—	4	2	no	—
261	C₂×Dic₄₃	—	8	2	no	—
262	C₂×Dic₄₃	—	8	2	no	—
263	C₂×Dic₄₃	#95	1	4	yes	—
264	D₁₇₂	—	2	2	no	—
265	D₁₇₂	—	2	2	no	—
266	D₁₇₂	—	2	2	no	—
267	D₁₇₂	—	2	2	no	—
268	C₄×D₄₃	—	2	4	no	—
269	C₄×D₄₃	—	2	4	no	—
270	C₄×D₄₃	—	2	4	no	—
271	C₄×D₄₃	—	2	4	no	—
272	Dic₈₆	—	2	2	no	—
273	Dic₈₆	—	2	2	no	—
274	Dic₈₆	—	2	2	no	—
275	Dic₈₆	—	2	2	no	—
276	C₈×C₄₃	—	2	4	no	—
277	C₈×C₄₃	—	4	2	no	—
278	C₄₃⋊C₈	—	2	4	no	—
279	C₄₃⋊C₈	—	4	2	no	—
280	#10755	—	43	1	no	maximal, Sylow
281	C₂²×C₄₃	—	2	1	no	—
282	C₂²×C₄₃	—	2	1	no	—
283	C₂²×C₄₃	—	2	1	no	—
284	C₂²×C₄₃	—	2	1	no	—
285	C₂²×C₄₃	—	2	1	no	—
286	C₂²×C₄₃	—	2	1	no	—
287	C₂²×C₄₃	—	4	1	no	—
288	C₂²×C₄₃	—	4	1	no	—
289	C₂²×C₄₃	—	4	1	no	—
290	C₂²×C₄₃	—	4	1	no	—
291	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
292	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
293	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×C₄₃	#385	1	1	yes	characteristic
295	C₂²×C₄₃	#385	1	1	yes	characteristic
296	C₂²×C₄₃	#386	1	1	yes	characteristic
297	C₂²×C₄₃	#386	1	1	yes	characteristic
298	C₂×D₄₃	—	2	4	no	—
299	C₂×D₄₃	—	4	2	no	—
300	C₂×D₄₃	—	4	2	no	—
301	C₂×D₄₃	—	4	4	no	—
302	C₂×D₄₃	—	8	2	no	—
303	C₄×C₄₃	—	8	2	no	—
304	C₄×C₄₃	#379	1	1	yes	characteristic
305	C₄×C₄₃	#380	1	1	yes	characteristic
306	C₄×C₄₃	#380	1	1	yes	characteristic
307	C₄×C₄₃	#381	1	1	yes	characteristic
308	C₄×C₄₃	#385	1	1	yes	characteristic
309	C₄×C₄₃	#385	1	1	yes	characteristic
310	C₄×C₄₃	#386	1	1	yes	characteristic
311	C₄×C₄₃	#386	1	1	yes	characteristic
312	Dic₄₃	—	2	4	no	—
313	Dic₄₃	—	8	2	no	—
314	C₂×#568	—	43	1	no	—
315	C₂×#413	—	43	1	no	—
316	#2311	—	43	1	no	—
317	C₂×#344	—	43	1	no	—
318	C₂×#344	D₄₃	1	1	yes	characteristic, complemented
319	C₂×#343	—	43	1	no	—
320	C₂×#343	—	43	1	no	—
321	C₂×C₄₃	—	2	1	no	—
322	C₂×C₄₃	—	2	1	no	—
323	C₂×C₄₃	—	2	1	no	—
324	C₂×C₄₃	—	2	1	no	—
325	C₂×C₄₃	—	2	1	no	—
326	C₂×C₄₃	—	2	1	no	—
327	C₂×C₄₃	C₂²⋊#95	1	1	yes	characteristic
328	C₂×C₄₃	#1914	1	1	yes	characteristic
329	C₂×C₄₃	#1915	1	1	yes	characteristic
330	D₄₃	—	4	4	no	—
331	C₂²×#41	—	43	1	no	—
332	#568	—	43	4	no	—
333	#568	—	86	2	no	—
334	#568	—	86	2	no	—
335	#568	—	86	2	no	—
336	C₂×#131	—	86	2	no	—
337	C₂×#131	—	86	2	no	—
338	C₂²×M₁₆	—	43	1	no	—
339	C₂²×M₁₆	—	43	1	no	—
340	C₂²×M₁₆	—	86	2	no	—
341	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
342	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
343	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
344	C₂²×C₄⋊C₄	—	43	1	no	—
345	#413	—	43	4	no	—
346	#413	—	86	2	no	—
347	C₂×#101	—	86	1	no	—
348	C₂×#100	—	86	1	no	—
349	#391	—	86	1	no	—
350	#390	—	86	1	no	—
351	#386	—	43	4	no	—
352	#380	—	86	2	no	—
353	#344	—	2	2	no	—
354	#344	—	86	2	no	—
355	#343	—	86	2	no	—
356	#343	—	86	2	no	—
357	C₄₃	#10755	1	1	yes	characteristic, complemented, Sylow
358	C₂×#41	—	43	2	no	—
359	C₂×#41	—	43	2	no	—
360	C₂×#41	—	43	2	no	—
361	C₂×#41	—	43	2	no	—
362	C₂×#41	—	86	1	no	—
363	C₂×#41	—	86	1	no	—
364	C₂×#41	—	86	1	no	—
365	C₂×#41	—	86	1	no	—
366	C₂×#41	—	86	1	no	—
367	C₂×#41	—	86	1	no	—
368	C₂×#41	—	86	1	no	—
369	C₂×#41	—	86	1	no	—
370	C₂²×Q₈	—	43	1	no	—
371	C₂²×D₄	—	43	2	no	—
372	C₂²×D₄	—	43	1	no	—
373	C₂³×C₄	—	43	2	no	—
374	C₂³×C₄	—	43	2	no	—
375	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
376	#131	—	86	8	no	—
377	#131	—	86	8	no	—
378	#131	—	86	8	no	—
379	#131	—	86	8	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	43	2	no	—
389	C₂×M₁₆	—	43	2	no	—
390	C₂×M₁₆	—	43	2	no	—
391	C₂×M₁₆	—	43	2	no	—
392	C₂×M₁₆	—	86	4	no	—
393	C₂×M₁₆	—	86	8	no	—
394	C₂×M₁₆	—	86	8	no	—
395	C₂×M₁₆	—	86	1	no	—
396	C₂×M₁₆	—	86	1	no	—
397	C₂×M₁₆	—	86	1	no	—
398	C₂×M₁₆	—	86	1	no	—
399	C₂×M₁₆	—	86	1	no	—
400	C₂×M₁₆	—	86	1	no	—
401	C₂×M₁₆	—	86	1	no	—
402	C₂×M₁₆	—	86	1	no	—
403	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
404	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
405	C₂×M₁₆	D₁₇₂	1	2	yes	—
406	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
407	C₂²×C₈	—	2	1	no	—
408	C₂²×C₈	—	2	1	no	—
409	C₂²×C₈	—	86	4	no	—
410	C₂²×C₈	—	86	1	no	—
411	C₂²×C₈	—	86	1	no	—
412	#117	—	2	1	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	86	1	no	—
418	C₂×C₄⋊C₄	—	86	1	no	—
419	C₂×C₄⋊C₄	—	86	1	no	—
420	C₂×C₄⋊C₄	—	86	1	no	—
421	C₂×C₄⋊C₄	—	86	1	no	—
422	C₂×C₄⋊C₄	—	86	1	no	—
423	C₂×C₂²⋊C₄	—	86	4	no	—
424	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
425	C₂×C₄²	—	2	1	no	—
426	#101	—	86	4	no	—
427	#100	—	86	4	no	—
428	#95	—	86	4	no	—
429	C₂⁴	—	43	2	no	—
430	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
431	#41	—	86	2	no	—
432	#41	—	86	2	no	—
433	#41	—	86	2	no	—
434	#41	—	86	2	no	—
435	#41	—	86	2	no	—
436	#41	—	86	2	no	—
437	#41	—	86	2	no	—
438	#41	—	86	2	no	—
439	#41	—	86	2	no	—
440	#41	—	86	2	no	—
441	#41	—	86	2	no	—
442	#41	—	86	2	no	—
443	#41	—	86	2	no	—
444	#41	—	86	2	no	—
445	#41	—	86	2	no	—
446	#41	—	86	2	no	—
447	C₂×Q₈	—	43	2	no	—
448	C₂×Q₈	—	43	2	no	—
449	C₂×Q₈	—	86	1	no	—
450	C₂×Q₈	—	86	1	no	—
451	C₂×Q₈	—	86	1	no	—
452	C₂×Q₈	—	86	1	no	—
453	C₂×D₄	—	43	4	no	—
454	C₂×D₄	—	43	4	no	—
455	C₂×D₄	—	43	2	no	—
456	C₂×D₄	—	43	2	no	—
457	C₂×D₄	—	86	2	no	—
458	C₂×D₄	—	86	2	no	—
459	C₂×D₄	—	86	2	no	—
460	C₂×D₄	—	86	2	no	—
461	C₂×D₄	—	86	1	no	—
462	C₂×D₄	—	86	1	no	—
463	C₂×D₄	—	86	1	no	—
464	C₂×D₄	—	86	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	43	2	no	—
467	C₂²×C₄	—	43	4	no	—
468	C₂²×C₄	—	43	4	no	—
469	C₂²×C₄	—	86	2	no	—
470	C₂²×C₄	—	86	2	no	—
471	C₂²×C₄	—	86	2	no	—
472	C₂²×C₄	—	86	2	no	—
473	C₂²×C₄	—	86	2	no	—
474	C₂²×C₄	—	86	2	no	—
475	C₂²×C₄	—	86	2	no	—
476	C₂²×C₄	—	344	2	no	—
477	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
480	C₂²×C₄	#10621898	1	1	yes	characteristic
481	C₂²×C₄	#10621898	1	1	yes	characteristic
482	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
483	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
484	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
485	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
486	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
487	C₂²×C₄	#10621900	1	1	yes	characteristic
488	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
489	C₂²×C₄	#10621902	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
491	M₁₆	—	2	2	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	4	1	no	—
498	M₁₆	—	43	4	no	—
499	M₁₆	—	86	16	no	—
500	M₁₆	—	86	2	no	—
501	M₁₆	—	86	2	no	—
502	M₁₆	—	86	2	no	—
503	M₁₆	—	86	2	no	—
504	M₁₆	—	86	2	no	—
505	M₁₆	—	172	1	no	—
506	M₁₆	—	172	1	no	—
507	M₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	complemented
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	4	1	no	—
513	C₂×C₈	—	4	1	no	—
514	C₂×C₈	—	86	16	no	—
515	C₂×C₈	—	86	2	no	—
516	C₂×C₈	—	86	2	no	—
517	C₂×C₈	—	86	2	no	—
518	C₂×C₈	—	86	2	no	—
519	C₂×C₈	—	172	1	no	—
520	C₂×C₈	—	172	1	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₄⋊C₄	—	172	1	no	—
524	C₄⋊C₄	—	172	1	no	—
525	C₄⋊C₄	—	172	1	no	—
526	C₄⋊C₄	—	172	1	no	—
527	C₂²⋊C₄	—	2	2	no	—
528	C₂²⋊C₄	—	2	2	no	—
529	C₂²⋊C₄	—	344	4	no	—
530	C₄²	—	4	1	no	—
531	C₄²	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	43	4	no	—
535	C₂³	—	86	2	no	—
536	C₂³	—	86	2	no	—
537	C₂³	—	172	2	no	—
538	C₂³	—	172	2	no	—
539	C₂³	C₄²×D₄₃	1	1	yes	characteristic
540	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
541	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
542	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
543	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
544	C₂³	#13063287	1	1	yes	characteristic
545	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
546	Q₈	—	86	2	no	—
547	Q₈	—	86	2	no	—
548	Q₈	—	86	2	no	—
549	Q₈	—	86	2	no	—
550	D₄	—	86	4	no	—
551	D₄	—	86	4	no	—
552	D₄	—	86	4	no	—
553	D₄	—	86	4	no	—
554	D₄	—	86	2	no	—
555	D₄	—	86	2	no	—
556	D₄	—	86	2	no	—
557	D₄	—	86	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	43	4	no	—
562	C₂×C₄	—	86	2	no	—
563	C₂×C₄	—	86	2	no	—
564	C₂×C₄	—	86	4	no	—
565	C₂×C₄	—	86	4	no	—
566	C₂×C₄	—	86	4	no	—
567	C₂×C₄	—	86	4	no	—
568	C₂×C₄	—	344	2	no	—
569	C₂×C₄	—	344	2	no	—
570	C₂×C₄	—	172	4	no	—
571	C₂×C₄	—	172	2	no	—
572	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
573	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
574	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
575	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
576	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
577	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
578	C₂×C₄	#13063282	1	1	yes	characteristic
579	C₂×C₄	#13063283	1	1	yes	characteristic
580	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
581	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
582	C₂×C₄	#13063287	1	1	yes	characteristic
583	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
584	C₂×C₄	#13063293	1	1	yes	characteristic
585	C₂×C₄	#13063293	1	1	yes	characteristic
586	C₂×C₄	#13063295	1	1	yes	characteristic
587	C₂×C₄	#13063295	1	1	yes	characteristic
588	C₂×C₄	#13063296	1	1	yes	characteristic
589	C₂×C₄	#13063298	1	1	yes	characteristic
590	C₂×C₄	#13063298	1	1	yes	characteristic
591	C₂×C₄	#13063300	1	1	yes	characteristic
592	C₂×C₄	#13063301	1	1	yes	characteristic
593	C₂×C₄	#13063303	1	1	yes	characteristic
594	C₂×C₄	#13063303	1	1	yes	characteristic
595	C₂×C₄	#13063305	1	1	yes	characteristic
596	C₂×C₄	#13063307	1	1	yes	characteristic
597	C₂×C₄	#13063307	1	1	yes	characteristic
598	C₂×C₄	#13063310	1	1	yes	characteristic
599	C₂×C₄	#13063310	1	1	yes	characteristic
600	C₈	—	2	4	no	—
601	C₈	—	4	2	no	—
602	C₈	—	86	4	no	—
603	C₈	—	172	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	4	1	no	—
614	C₂²	—	86	4	no	—
615	C₂²	—	344	2	no	—
616	C₂²	—	172	4	no	—
617	C₂²	—	172	2	no	—
618	C₂²	—	172	2	no	—
619	C₂²	#95×D₄₃	1	1	yes	characteristic
620	C₂²	#14582746	1	1	yes	characteristic
621	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
622	C₂²	#14582770	1	1	yes	characteristic
623	C₂²	#14582773	1	1	yes	characteristic
624	C₂²	#14582775	1	1	yes	characteristic
625	C₂²	#14582777	1	1	yes	characteristic
626	C₄	—	8	2	no	—
627	C₄	—	86	4	no	—
628	C₄	—	344	2	no	—
629	C₄	#14582754	1	1	yes	characteristic
630	C₄	#14582756	1	1	yes	characteristic
631	C₄	#14582758	1	1	yes	characteristic
632	C₄	#14582761	1	1	yes	characteristic
633	C₄	#14582770	1	1	yes	characteristic
634	C₄	#14582773	1	1	yes	characteristic
635	C₄	#14582775	1	1	yes	characteristic
636	C₄	#14582777	1	1	yes	characteristic
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	2	1	no	—
642	C₂	—	2	1	no	—
643	C₂	—	172	4	no	—
644	C₂	(C₂×D₄₃)⋊#95	1	1	yes	characteristic
645	C₂	#19135141	1	1	yes	characteristic
646	C₂	#19135146	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14582777
commutator	C₂³×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#344	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#344	D₄₃
hypocenter	C₄₃	#10755
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
4. C₂×#14582669	C₂	semidirect
5. C₂×#14582667	C₂	semidirect
6. C₂×#14582667	C₂	semidirect
7. C₂×C₄₃×#344	C₂	semidirect
12. #14583665	C₄	semidirect
20. #14582881	C₄	semidirect
174. M₁₆×C₄₃	C₂²⋊C₄	semidirect
199. #10621877	C₂²⋊C₄	semidirect
318. C₂×#344	D₄₃	semidirect
357. C₄₃	#10755	semidirect
507. M₁₆	(C₂×D₄₃)⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583665	2
C₂×#14582881	2
#19137183	2
C₂×#14582669	2
C₂×#14582667	2
C₂×C₄₃×#344	2
#10755	43