Subgroups — #25965764

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13063371	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144845	C₂	1	2	yes	maximal, complemented
4	#19144836	C₂	1	2	yes	maximal, complemented
5	#19144808	C₂	1	2	yes	maximal, complemented
6	#19144793	C₂	1	2	yes	maximal, complemented
7	#19144732	C₂	1	2	yes	maximal, complemented
8	#19144703	C₂	1	2	yes	maximal, complemented
9	#19144641	C₂	1	2	yes	maximal, complemented
10	#19144612	C₂	1	2	yes	maximal, complemented
11	#19144582	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144571	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144417	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14583200	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144055	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143895	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143895	C₂	1	1	yes	maximal, characteristic, complemented
18	#19143479	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143471	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143430	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143430	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143260	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063371	C₂²	1	1	yes	characteristic
25	C₂×#13063350	C₂²	1	1	yes	characteristic
26	C₂×#13063350	C₂²	1	1	yes	characteristic
27	#14583595	—	2	1	no	—
28	#14583595	—	2	1	no	—
29	#14583592	—	2	2	no	—
30	#14583592	—	2	2	no	—
31	#14583589	—	2	1	no	—
32	#14583589	—	2	1	no	—
33	#14583510	C₂²	1	2	yes	complemented
34	#14583503	C₂²	1	2	yes	complemented
35	#14583477	C₂²	1	1	yes	characteristic
36	#14583477	C₂²	1	1	yes	characteristic
37	#14583428	C₂²	1	2	yes	complemented
38	#14583428	C₂²	1	2	yes	complemented
39	C₂×#13063317	C₂²	1	1	yes	characteristic, complemented
40	#14583382	C₂²	1	1	yes	characteristic
41	#14583382	C₂²	1	1	yes	characteristic, complemented
42	#14583382	C₂²	1	1	yes	characteristic, complemented
43	#14583381	C₂²	1	2	yes	—
44	#14583379	—	2	1	no	—
45	#14583379	C₂²	1	1	yes	characteristic
46	#14583373	—	2	1	no	—
47	#14583373	C₂²	1	1	yes	characteristic
48	#14583371	—	2	2	no	—
49	#14583371	C₂²	1	2	yes	—
50	C₄×#10621902	C₂²	1	2	yes	—
51	C₄×#10621898	—	2	1	no	—
52	C₄×#10621898	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₁₇₂	—	2	1	no	—
54	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
55	C₄×D₄×D₄₃	—	2	2	no	—
56	C₄×D₄×D₄₃	C₂²	1	2	yes	—
57	#14583239	C₂²	1	2	yes	complemented
58	#14583238	C₂²	1	2	yes	complemented
59	#14583233	C₂²	1	2	yes	complemented
60	#14583228	C₂²	1	2	yes	complemented
61	#14583222	C₂²	1	2	yes	complemented
62	#14583221	C₂²	1	2	yes	complemented
63	#14583216	C₂²	1	2	yes	complemented
64	#14583211	C₂²	1	2	yes	complemented
65	#14583206	C₂²	1	2	yes	complemented
66	#14583206	C₂²	1	2	yes	complemented
67	#14583200	C₂²	1	2	yes	complemented
68	#14583200	C₂²	1	2	yes	complemented
69	#14583200	C₂²	1	2	yes	complemented
70	#14583200	C₂²	1	2	yes	complemented
71	#14583199	C₂²	1	2	yes	complemented
72	#14583199	C₂²	1	2	yes	complemented
73	#14583111	C₂²	1	2	yes	complemented
74	#14583111	C₂²	1	2	yes	complemented
75	#14583101	C₂²	1	2	yes	complemented
76	#14583091	C₂²	1	2	yes	complemented
77	#14583060	C₂²	1	2	yes	—
78	#14583060	C₂²	1	2	yes	—
79	#14583048	C₂²	1	2	yes	—
80	#14583048	C₂²	1	2	yes	—
81	#14583043	C₂²	1	2	yes	—
82	#14583043	C₂²	1	2	yes	—
83	#14583031	C₂²	1	2	yes	—
84	#14583031	C₂²	1	2	yes	—
85	#14583011	C₂²	1	2	yes	complemented
86	#14583008	C₂²	1	2	yes	complemented
87	#14583008	C₂²	1	2	yes	complemented
88	#14583006	C₂²	1	2	yes	complemented
89	#14583002	C₂²	1	2	yes	complemented
90	#14583002	C₂²	1	2	yes	complemented
91	#14583000	C₂²	1	2	yes	complemented
92	#14583000	C₂²	1	2	yes	complemented
93	Q₁₆×Dic₄₃	C₂²	1	2	yes	complemented
94	SD₁₆×Dic₄₃	C₂²	1	2	yes	complemented
95	SD₁₆×Dic₄₃	C₂²	1	2	yes	complemented
96	#14582984	C₂²	1	2	yes	complemented
97	#14582984	C₂²	1	2	yes	complemented
98	D₈×Dic₄₃	C₂²	1	2	yes	complemented
99	#14582979	C₂²	1	2	yes	complemented
100	#14582979	C₂²	1	2	yes	complemented
101	#14582959	C₂²	1	2	yes	complemented
102	#14582959	C₂²	1	2	yes	complemented
103	#14582955	C₂²	1	2	yes	complemented
104	#14582951	C₂²	1	2	yes	complemented
105	#14582942	C₂²	1	1	yes	characteristic, complemented
106	#14582942	C₂²	1	1	yes	characteristic, complemented
107	C₂×#13063259	C₂²	1	1	yes	characteristic, complemented
108	C₂×#13063257	C₂²	1	1	yes	characteristic, complemented
109	#14582923	C₂²	1	1	yes	characteristic, complemented
110	#14582900	C₂²	1	1	yes	characteristic
111	#14582900	C₂²	1	1	yes	characteristic
112	#14582900	C₂²	1	1	yes	characteristic, complemented
113	#14582900	C₂²	1	1	yes	characteristic, complemented
114	C₂×#13063247	C₂²	1	1	yes	characteristic
115	C₂×#13063247	C₂²	1	1	yes	characteristic
116	#14582865	C₂²	1	1	yes	characteristic
117	#14582865	C₂²	1	1	yes	characteristic
118	#14582854	C₂²	1	1	yes	characteristic, complemented
119	#14582854	C₂²	1	1	yes	characteristic, complemented
120	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
121	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#532	C₂²	1	1	yes	characteristic, complemented
123	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
124	C₄₃×#464	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#464	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#463	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#463	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#462	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#461	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#460	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#459	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#416	C₂²	1	1	yes	characteristic, complemented
134	C₄₃×#416	C₂²	1	1	yes	characteristic, complemented
135	#13063371	—	2	4	no	—
136	#13063371	—	2	4	no	—
137	C₂×#10621902	C₂³	1	2	yes	—
138	C₂×#10621898	—	2	1	no	—
139	C₂×#10621898	C₂³	1	1	yes	characteristic
140	C₂²×D₁₇₂	—	2	1	no	—
141	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
142	C₂×D₄×D₄₃	—	2	2	no	—
143	C₂×D₄×D₄₃	C₂³	1	2	yes	—
144	C₂²×C₄×D₄₃	—	2	1	no	—
145	C₂²×C₄×D₄₃	—	2	2	no	—
146	#13063350	—	2	4	no	—
147	#13063350	—	2	4	no	—
148	C₂×#10621884	C₂³	1	2	yes	—
149	C₂×#10621884	C₂³	1	2	yes	—
150	C₂×#10621882	C₂³	1	2	yes	—
151	C₂×#10621882	C₂³	1	2	yes	—
152	C₂×#10621877	C₂³	1	1	yes	characteristic
153	C₂×#10621877	C₂³	1	1	yes	characteristic
154	#13063320	—	2	2	no	—
155	#13063320	—	2	2	no	—
156	#13063318	—	2	2	no	—
157	#13063318	—	2	2	no	—
158	#13063317	—	2	1	no	—
159	#13063317	—	2	1	no	—
160	#13063317	C₂³	1	2	yes	—
161	#13063317	C₂³	1	2	yes	—
162	#13063315	—	2	2	no	—
163	#13063315	—	2	2	no	—
164	#13063307	—	2	2	no	—
165	#13063307	—	2	2	no	—
166	#13063306	—	2	2	no	—
167	#13063306	—	2	2	no	—
168	#13063304	—	2	1	no	—
169	#13063304	—	2	1	no	—
170	#13063301	C₂³	1	2	yes	—
171	#13063301	C₂³	1	2	yes	—
172	#13063299	—	2	1	no	—
173	#13063299	—	2	1	no	—
174	#13063297	—	2	2	no	—
175	#13063297	—	2	2	no	—
176	#13063297	—	2	2	no	—
177	#13063297	—	2	2	no	—
178	#13063296	C₂³	1	2	yes	—
179	#13063296	C₂³	1	2	yes	—
180	Q₈×Dic₄₃	C₂³	1	2	yes	—
181	Q₈×Dic₄₃	C₂³	1	2	yes	—
182	Q₈×Dic₄₃	C₂³	1	2	yes	—
183	C₄×Dic₈₆	—	2	1	no	—
184	C₄×Dic₈₆	D₄	1	1	yes	characteristic
185	C₄×Dic₈₆	D₄	1	1	yes	characteristic
186	C₄×D₁₇₂	—	2	1	no	—
187	C₄×D₁₇₂	—	2	2	no	—
188	C₄×D₁₇₂	—	2	1	no	—
189	C₄×D₁₇₂	—	2	1	no	—
190	C₄×D₁₇₂	—	2	2	no	—
191	C₄×D₁₇₂	—	2	1	no	—
192	C₄×D₁₇₂	—	2	1	no	—
193	C₄×D₁₇₂	D₄	1	1	yes	characteristic
194	C₄×D₁₇₂	D₄	1	1	yes	characteristic
195	C₄×D₁₇₂	C₂³	1	2	yes	—
196	C₄×D₁₇₂	C₂³	1	2	yes	—
197	D₄×Dic₄₃	—	2	2	no	—
198	D₄×Dic₄₃	—	2	2	no	—
199	D₄×Dic₄₃	—	2	2	no	—
200	D₄×Dic₄₃	C₂³	1	2	yes	—
201	D₄×Dic₄₃	C₂³	1	2	yes	—
202	D₄×Dic₄₃	C₂³	1	2	yes	—
203	#13063287	—	2	2	no	—
204	#13063287	—	2	2	no	—
205	#13063287	C₂³	1	2	yes	—
206	#13063287	C₂³	1	2	yes	—
207	C₄×C₂²⋊D₄₃	—	2	2	no	—
208	C₄×C₂²⋊D₄₃	—	2	2	no	—
209	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
210	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
211	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
212	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
213	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
214	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
215	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
216	#13063284	—	2	1	no	—
217	#13063284	—	2	1	no	—
218	#13063284	—	2	1	no	—
219	#13063284	C₂³	1	1	yes	characteristic
220	#13063283	—	2	2	no	—
221	#13063283	C₂³	1	2	yes	—
222	#13063282	—	2	2	no	—
223	#13063282	C₂³	1	2	yes	—
224	#13063281	—	2	2	no	—
225	#13063281	—	2	2	no	—
226	C₂×C₄⋊Dic₄₃	—	2	1	no	—
227	C₂×C₄⋊Dic₄₃	—	2	1	no	—
228	C₂×C₄⋊Dic₄₃	—	2	1	no	—
229	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
232	C₂×Dic₄₃⋊C₄	—	2	1	no	—
233	C₂×Dic₄₃⋊C₄	—	2	1	no	—
234	C₄⋊C₄×D₄₃	—	2	2	no	—
235	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
236	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
237	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
238	C₂²⋊C₄×D₄₃	—	2	2	no	—
239	C₂²⋊C₄×D₄₃	—	2	2	no	—
240	C₂²⋊C₄×D₄₃	—	2	2	no	—
241	C₄²×D₄₃	—	2	2	no	—
242	C₄²×D₄₃	C₂³	1	2	yes	—
243	#13063259	C₂³	1	2	yes	—
244	#13063259	C₂³	1	2	yes	—
245	#13063258	C₂³	1	2	yes	—
246	#13063258	C₂³	1	2	yes	—
247	#13063257	C₂³	1	2	yes	—
248	#13063257	C₂³	1	2	yes	—
249	#13063256	C₂³	1	2	yes	—
250	#13063256	C₂³	1	2	yes	—
251	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
252	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
253	#13063249	C₂³	1	2	yes	—
254	#13063249	C₂³	1	2	yes	—
255	#13063249	C₂³	1	2	yes	—
256	#13063249	C₂³	1	2	yes	—
257	#13063247	C₂³	1	2	yes	—
258	#13063247	C₂³	1	2	yes	—
259	#13063247	C₂³	1	2	yes	—
260	#13063247	C₂³	1	2	yes	—
261	#13063246	C₂³	1	2	yes	—
262	#13063246	C₂³	1	2	yes	—
263	#13063246	C₂³	1	2	yes	—
264	#13063246	C₂³	1	2	yes	—
265	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
268	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
269	#13063235	C₂³	1	2	yes	—
270	#13063235	C₂³	1	2	yes	—
271	C₈×Dic₄₃	C₂³	1	2	yes	—
272	C₈×Dic₄₃	C₂³	1	2	yes	—
273	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
274	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
276	#135×C₄₃	—	2	4	no	—
277	#135×C₄₃	—	2	4	no	—
278	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
279	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
280	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
281	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
282	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
283	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
284	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
286	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	#127×C₄₃	C₂³	1	1	yes	characteristic
290	#124×C₄₃	C₂³	1	1	yes	characteristic
291	#124×C₄₃	C₂³	1	1	yes	characteristic
292	#121×C₄₃	—	2	1	no	—
293	#121×C₄₃	—	2	1	no	—
294	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₄₃	—	2	1	no	—
297	C₄×D₄×C₄₃	—	2	1	no	—
298	C₄×D₄×C₄₃	—	2	1	no	—
299	C₄×D₄×C₄₃	—	2	1	no	—
300	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
301	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
302	#117×C₄₃	—	2	1	no	—
303	#117×C₄₃	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₄₃	—	2	1	no	—
305	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
308	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
310	#103×C₄₃	C₂³	1	1	yes	characteristic
311	#103×C₄₃	C₂³	1	1	yes	characteristic
312	#103×C₄₃	C₂³	1	1	yes	characteristic
313	#103×C₄₃	C₂³	1	1	yes	characteristic
314	#102×C₄₃	C₂³	1	1	yes	characteristic
315	#102×C₄₃	C₂³	1	1	yes	characteristic
316	#102×C₄₃	C₂³	1	1	yes	characteristic
317	#102×C₄₃	C₂³	1	1	yes	characteristic
318	C₂³×D₄₃	—	2	1	no	—
319	C₂³×D₄₃	—	2	2	no	—
320	#41×C₄₃	—	2	2	no	—
321	#41×C₄₃	—	2	2	no	—
322	#41×C₄₃	—	2	2	no	—
323	#41×C₄₃	—	2	2	no	—
324	#41×C₄₃	—	2	2	no	—
325	#41×C₄₃	#41	1	4	yes	—
326	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₄₃	—	2	1	no	—
330	C₂×D₄×C₄₃	—	2	1	no	—
331	C₂×D₄×C₄₃	—	2	1	no	—
332	C₂×D₄×C₄₃	—	2	1	no	—
333	C₂×D₄×C₄₃	—	2	1	no	—
334	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₃	—	2	1	no	—
338	C₂²×C₄×C₄₃	—	2	1	no	—
339	C₂²×C₄×C₄₃	—	2	1	no	—
340	C₂²×C₄×C₄₃	—	2	1	no	—
341	C₂²×C₄×C₄₃	—	2	1	no	—
342	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₂²⋊D₄₃	—	2	2	no	—
346	C₂×C₂²⋊D₄₃	—	2	2	no	—
347	C₂×C₂²⋊D₄₃	—	2	2	no	—
348	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
349	C₂²×Dic₄₃	—	2	2	no	—
350	C₂²×Dic₄₃	—	2	2	no	—
351	C₂²×Dic₄₃	—	2	2	no	—
352	C₂²×Dic₄₃	—	2	1	no	—
353	C₂²×Dic₄₃	—	2	1	no	—
354	C₂²×Dic₄₃	—	2	1	no	—
355	#10621902	—	2	4	no	—
356	#10621902	—	2	4	no	—
357	D₄×D₄₃	—	2	16	no	—
358	D₄×D₄₃	—	2	4	no	—
359	D₄×D₄₃	—	2	4	no	—
360	#10621898	—	2	8	no	—
361	#10621898	—	2	2	no	—
362	#10621898	—	2	2	no	—
363	C₂×D₁₇₂	—	2	8	no	—
364	C₂×D₁₇₂	—	2	1	no	—
365	C₂×D₁₇₂	—	2	2	no	—
366	C₂×D₁₇₂	—	2	2	no	—
367	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
368	C₂×D₁₇₂	#41	1	4	yes	—
369	C₂×D₁₇₂	C₂⁴	1	2	yes	—
370	C₂×C₄×D₄₃	—	2	2	no	—
371	C₂×C₄×D₄₃	—	2	2	no	—
372	C₂×C₄×D₄₃	—	2	2	no	—
373	C₂×C₄×D₄₃	—	2	2	no	—
374	C₂×C₄×D₄₃	—	2	2	no	—
375	C₂×C₄×D₄₃	—	2	2	no	—
376	C₂×C₄×D₄₃	—	8	4	no	—
377	C₂×C₄×D₄₃	—	8	2	no	—
378	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
379	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
380	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
381	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
382	Q₁₆×C₄₃	—	2	2	no	—
383	Q₁₆×C₄₃	—	2	2	no	—
384	SD₁₆×C₄₃	—	2	2	no	—
385	SD₁₆×C₄₃	—	2	2	no	—
386	SD₁₆×C₄₃	—	2	2	no	—
387	SD₁₆×C₄₃	—	2	2	no	—
388	D₈×C₄₃	—	2	2	no	—
389	D₈×C₄₃	—	2	2	no	—
390	C₂×C₈×C₄₃	—	2	2	no	—
391	C₂×C₈×C₄₃	—	2	2	no	—
392	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₄₃	—	2	1	no	—
397	C₄⋊C₄×C₄₃	—	2	1	no	—
398	C₄⋊C₄×C₄₃	—	2	1	no	—
399	C₄⋊C₄×C₄₃	—	2	1	no	—
400	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
402	C₂²⋊C₄×C₄₃	—	2	1	no	—
403	C₂²⋊C₄×C₄₃	—	2	1	no	—
404	C₂²⋊C₄×C₄₃	—	2	1	no	—
405	C₂²⋊C₄×C₄₃	—	2	1	no	—
406	C₂²⋊C₄×C₄₃	—	2	1	no	—
407	C₂²⋊C₄×C₄₃	—	2	1	no	—
408	C₂²⋊C₄×C₄₃	—	2	1	no	—
409	C₄²×C₄₃	—	2	1	no	—
410	C₄²×C₄₃	—	2	1	no	—
411	C₄²×C₄₃	—	2	1	no	—
412	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
413	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
415	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
416	C₂²⋊Dic₄₃	—	2	2	no	—
417	C₂²⋊Dic₄₃	—	2	2	no	—
418	C₂²⋊Dic₄₃	—	2	2	no	—
419	C₂²⋊Dic₄₃	—	2	2	no	—
420	C₂²⋊Dic₄₃	—	2	2	no	—
421	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
422	#10621884	—	2	4	no	—
423	#10621884	—	2	4	no	—
424	#10621882	—	2	4	no	—
425	#10621882	—	2	4	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	2	no	—
428	(C₂×D₄₃)⋊C₄	—	2	2	no	—
429	(C₂×D₄₃)⋊C₄	—	2	2	no	—
430	(C₂×D₄₃)⋊C₄	—	2	2	no	—
431	(C₂×D₄₃)⋊C₄	—	2	2	no	—
432	(C₂×D₄₃)⋊C₄	—	2	2	no	—
433	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
434	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
435	C₄⋊Dic₄₃	—	2	1	no	—
436	C₄⋊Dic₄₃	—	2	1	no	—
437	C₄⋊Dic₄₃	—	2	1	no	—
438	C₄⋊Dic₄₃	—	2	2	no	—
439	C₄⋊Dic₄₃	—	2	2	no	—
440	C₄⋊Dic₄₃	—	2	2	no	—
441	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
442	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
443	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
444	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
445	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
446	Dic₄₃⋊C₄	—	2	2	no	—
447	Dic₄₃⋊C₄	—	2	2	no	—
448	Dic₄₃⋊C₄	—	2	2	no	—
449	Dic₄₃⋊C₄	—	2	2	no	—
450	Dic₄₃⋊C₄	—	2	2	no	—
451	Dic₄₃⋊C₄	—	2	2	no	—
452	Dic₄₃⋊C₄	—	2	2	no	—
453	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
454	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
455	C₄×Dic₄₃	—	2	2	no	—
456	C₄×Dic₄₃	—	2	2	no	—
457	C₄×Dic₄₃	—	2	2	no	—
458	C₄×Dic₄₃	—	2	2	no	—
459	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
460	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
461	C₄×Dic₄₃	C₂⁴	1	2	yes	—
462	#10621877	—	2	2	no	—
463	#10621877	—	2	2	no	—
464	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
465	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
466	C₂³×C₄₃	—	2	1	no	—
467	C₂³×C₄₃	—	2	1	no	—
468	C₂³×C₄₃	—	2	1	no	—
469	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
470	C₂²×D₄₃	—	2	2	no	—
471	C₂²×D₄₃	—	2	8	no	—
472	C₂²×D₄₃	—	2	4	no	—
473	C₂²×D₄₃	—	8	2	no	—
474	C₂²×D₄₃	—	8	2	no	—
475	C₂²×D₄₃	—	8	1	no	—
476	C₂²×D₄₃	—	8	1	no	—
477	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
478	Q₈×C₄₃	—	2	1	no	—
479	Q₈×C₄₃	—	2	1	no	—
480	Q₈×C₄₃	—	2	1	no	—
481	Q₈×C₄₃	—	2	1	no	—
482	Q₈×C₄₃	—	2	1	no	—
483	Q₈×C₄₃	C₂×#41	1	2	yes	—
484	D₄×C₄₃	—	2	4	no	—
485	D₄×C₄₃	—	2	1	no	—
486	D₄×C₄₃	—	2	1	no	—
487	D₄×C₄₃	—	2	1	no	—
488	D₄×C₄₃	—	2	1	no	—
489	D₄×C₄₃	—	2	1	no	—
490	D₄×C₄₃	—	4	2	no	—
491	D₄×C₄₃	—	4	2	no	—
492	D₄×C₄₃	—	8	1	no	—
493	D₄×C₄₃	—	8	1	no	—
494	D₄×C₄₃	C₂×#41	1	2	yes	—
495	C₂×C₄×C₄₃	—	2	1	no	—
496	C₂×C₄×C₄₃	—	2	4	no	—
497	C₂×C₄×C₄₃	—	2	1	no	—
498	C₂×C₄×C₄₃	—	2	1	no	—
499	C₂×C₄×C₄₃	—	2	1	no	—
500	C₂×C₄×C₄₃	—	2	1	no	—
501	C₂×C₄×C₄₃	—	4	1	no	—
502	C₂×C₄×C₄₃	—	4	1	no	—
503	C₂×C₄×C₄₃	—	4	2	no	—
504	C₂×C₄×C₄₃	—	4	2	no	—
505	C₂×C₄×C₄₃	—	4	2	no	—
506	C₂×C₄×C₄₃	—	8	1	no	—
507	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
513	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
514	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
515	C₂²⋊D₄₃	—	2	8	no	—
516	C₂²⋊D₄₃	—	2	4	no	—
517	C₂²⋊D₄₃	—	8	2	no	—
518	C₂²⋊D₄₃	—	8	2	no	—
519	C₂×Dic₄₃	—	2	2	no	—
520	C₂×Dic₄₃	—	2	2	no	—
521	C₂×Dic₄₃	—	2	2	no	—
522	C₂×Dic₄₃	—	8	2	no	—
523	C₂×Dic₄₃	—	8	2	no	—
524	C₂×Dic₄₃	—	8	2	no	—
525	C₂×Dic₄₃	—	8	1	no	—
526	C₂×Dic₄₃	—	8	1	no	—
527	C₂×Dic₄₃	—	8	1	no	—
528	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
529	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
530	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
531	D₁₇₂	—	2	8	no	—
532	D₁₇₂	—	2	2	no	—
533	D₁₇₂	—	2	4	no	—
534	D₁₇₂	—	2	2	no	—
535	D₁₇₂	C₂×#41	1	4	yes	—
536	C₄×D₄₃	—	2	8	no	—
537	C₄×D₄₃	—	2	2	no	—
538	C₄×D₄₃	—	2	2	no	—
539	C₄×D₄₃	—	4	2	no	—
540	C₄×D₄₃	—	4	2	no	—
541	C₄×D₄₃	—	4	4	no	—
542	C₄×D₄₃	—	8	2	no	—
543	C₄×D₄₃	—	8	2	no	—
544	C₄×D₄₃	—	8	2	no	—
545	C₄×D₄₃	—	8	2	no	—
546	Dic₈₆	—	2	2	no	—
547	C₈×C₄₃	—	2	1	no	—
548	C₈×C₄₃	—	2	1	no	—
549	C₈×C₄₃	—	2	1	no	—
550	C₈×C₄₃	—	2	1	no	—
551	C₄₃⋊C₈	—	2	2	no	—
552	C₄₃⋊C₈	—	2	2	no	—
553	#60601	—	43	1	no	maximal, Sylow
554	C₂²×C₄₃	—	2	1	no	—
555	C₂²×C₄₃	—	2	1	no	—
556	C₂²×C₄₃	—	2	2	no	—
557	C₂²×C₄₃	—	4	1	no	—
558	C₂²×C₄₃	—	4	1	no	—
559	C₂²×C₄₃	—	4	1	no	—
560	C₂²×C₄₃	—	4	1	no	—
561	C₂²×C₄₃	—	4	1	no	—
562	C₂²×C₄₃	—	4	1	no	—
563	C₂²×C₄₃	—	4	1	no	—
564	C₂²×C₄₃	—	4	1	no	—
565	C₂²×C₄₃	#525	1	2	yes	—
566	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
567	C₂×D₄₃	—	2	2	no	—
568	C₂×D₄₃	—	2	2	no	—
569	C₂×D₄₃	—	2	4	no	—
570	C₂×D₄₃	—	2	2	no	—
571	C₂×D₄₃	—	4	2	no	—
572	C₂×D₄₃	—	4	2	no	—
573	C₂×D₄₃	—	8	4	no	—
574	C₂×D₄₃	—	8	8	no	—
575	C₄×C₄₃	—	2	1	no	—
576	C₄×C₄₃	—	2	1	no	—
577	C₄×C₄₃	—	2	1	no	—
578	C₄×C₄₃	—	2	1	no	—
579	C₄×C₄₃	—	2	2	no	—
580	C₄×C₄₃	—	4	1	no	—
581	C₄×C₄₃	—	4	1	no	—
582	C₄×C₄₃	—	4	1	no	—
583	C₄×C₄₃	—	4	1	no	—
584	C₄×C₄₃	#525	1	2	yes	—
585	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
586	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
587	Dic₄₃	—	2	2	no	—
588	Dic₄₃	—	2	2	no	—
589	Dic₄₃	—	2	2	no	—
590	Dic₄₃	—	4	2	no	—
591	Dic₄₃	—	4	2	no	—
592	Dic₄₃	—	4	2	no	—
593	#3512	—	43	1	no	—
594	C₄×H(5,𝔽₂)	—	43	1	no	—
595	#3123	—	43	2	no	—
596	#3122	—	43	2	no	—
597	#3120	—	43	2	no	—
598	#3119	—	43	2	no	—
599	#3114	—	43	2	no	—
600	#3111	—	43	2	no	—
601	#3105	—	43	2	no	—
602	#3102	—	43	2	no	—
603	#3099	—	43	1	no	—
604	#3098	—	43	1	no	—
605	#3080	—	43	1	no	—
606	C₂×#478	—	43	1	no	—
607	#3036	—	43	1	no	—
608	#3035	D₄₃	1	1	yes	characteristic, complemented
609	#3012	—	43	1	no	—
610	#3012	—	43	1	no	—
611	#2952	—	43	1	no	—
612	#2951	—	43	1	no	—
613	#2946	—	43	1	no	—
614	#2946	—	43	1	no	—
615	#2925	—	43	1	no	—
616	C₂×C₄₃	—	2	2	no	—
617	C₂×C₄₃	—	4	2	no	—
618	C₂×C₄₃	—	8	1	no	—
619	C₂×C₄₃	—	8	1	no	—
620	C₂×C₄₃	C₂×#525	1	1	yes	characteristic
621	C₂×C₄₃	#3584	1	1	yes	characteristic
622	C₂×C₄₃	#3585	1	1	yes	characteristic
623	D₄₃	—	4	2	no	—
624	D₄₃	—	4	4	no	—
625	C₂×H(5,𝔽₂)	—	43	1	no	—
626	C₂×AGL(1,ℤ/8)	—	43	1	no	—
627	C₂×AGL(1,ℤ/8)	—	43	1	no	—
628	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
629	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
630	#553	—	86	1	no	—
631	#553	—	86	1	no	—
632	#553	—	86	2	no	—
633	#553	—	86	2	no	—
634	#552	—	86	1	no	—
635	#552	—	86	1	no	—
636	#541	—	43	2	no	—
637	#540	—	43	2	no	—
638	#537	—	43	1	no	—
639	#537	—	43	1	no	—
640	#532	C₂×D₄₃	1	1	yes	characteristic, complemented
641	#529	—	43	2	no	—
642	#529	—	43	2	no	—
643	C₂×#125	—	43	1	no	—
644	#520	—	43	1	no	—
645	#520	—	43	1	no	—
646	#520	—	43	1	no	—
647	#520	—	43	1	no	—
648	#520	—	43	2	no	—
649	#520	—	86	1	no	—
650	#518	—	43	2	no	—
651	#518	—	43	1	no	—
652	#518	—	86	1	no	—
653	#518	—	86	2	no	—
654	C₄×#41	—	43	1	no	—
655	C₄×#41	—	43	2	no	—
656	C₄×#41	—	86	1	no	—
657	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
658	C₂×C₄×D₄	—	43	2	no	—
659	C₂×C₄×D₄	—	43	1	no	—
660	C₂×C₄×D₄	—	86	1	no	—
661	C₂×C₄×D₄	—	86	2	no	—
662	#485	—	43	2	no	—
663	#485	—	43	2	no	—
664	#484	—	43	2	no	—
665	#483	—	43	2	no	—
666	#482	—	43	2	no	—
667	#482	—	43	2	no	—
668	#481	—	43	2	no	—
669	#480	—	43	2	no	—
670	#479	—	43	2	no	—
671	#479	—	43	2	no	—
672	#478	—	43	2	no	—
673	#478	—	43	2	no	—
674	#478	—	43	2	no	—
675	#478	—	43	2	no	—
676	#478	—	43	2	no	—
677	#478	—	43	2	no	—
678	#464	C₂×D₄₃	1	1	yes	characteristic, complemented
679	#464	C₂×D₄₃	1	1	yes	characteristic, complemented
680	#463	—	43	2	no	—
681	#463	—	43	2	no	—
682	#463	C₂×D₄₃	1	1	yes	characteristic, complemented
683	#463	C₂×D₄₃	1	1	yes	characteristic, complemented
684	#462	C₂×D₄₃	1	1	yes	characteristic, complemented
685	#461	—	43	2	no	—
686	#461	C₂×D₄₃	1	1	yes	characteristic, complemented
687	#460	C₂×D₄₃	1	1	yes	characteristic, complemented
688	#459	—	43	2	no	—
689	#459	C₂×D₄₃	1	1	yes	characteristic, complemented
690	#452	—	43	2	no	—
691	#452	—	43	2	no	—
692	#450	—	43	2	no	—
693	#450	—	43	2	no	—
694	#449	—	43	2	no	—
695	#449	—	43	2	no	—
696	#447	—	43	2	no	—
697	#447	—	43	2	no	—
698	#442	—	43	2	no	—
699	#442	—	43	2	no	—
700	#442	—	43	2	no	—
701	#441	—	43	2	no	—
702	#440	—	43	2	no	—
703	#440	—	43	2	no	—
704	#440	—	43	2	no	—
705	#440	—	43	2	no	—
706	C₄×Q₁₆	—	43	2	no	—
707	C₄×SD₁₆	—	43	2	no	—
708	C₄×SD₁₆	—	43	2	no	—
709	C₄×SD₁₆	—	43	2	no	—
710	C₄×SD₁₆	—	43	2	no	—
711	C₄×D₈	—	43	2	no	—
712	C₄×D₈	—	43	2	no	—
713	C₄×D₈	—	43	2	no	—
714	#433	—	43	2	no	—
715	#433	—	43	2	no	—
716	#432	—	43	2	no	—
717	#431	—	43	2	no	—
718	#428	—	43	1	no	—
719	#428	—	43	1	no	—
720	C₂×#107	—	43	1	no	—
721	C₂×#106	—	43	1	no	—
722	#423	—	43	1	no	—
723	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
724	#417	—	43	1	no	—
725	#417	—	43	1	no	—
726	#417	—	43	1	no	—
727	#417	—	43	1	no	—
728	#416	C₂×D₄₃	1	1	yes	characteristic, complemented
729	#416	C₂×D₄₃	1	1	yes	characteristic, complemented
730	C₂×#102	—	43	1	no	—
731	C₂×#102	—	43	1	no	—
732	#408	—	43	1	no	—
733	#408	—	43	1	no	—
734	#405	—	43	1	no	—
735	#405	—	43	1	no	—
736	C₄₃	#60601	1	1	yes	characteristic, complemented, Sylow
737	H(5,𝔽₂)	—	86	4	no	—
738	H(5,𝔽₂)	—	86	4	no	—
739	C₂×#41	—	43	1	no	—
740	C₂×#41	—	43	2	no	—
741	C₂×#41	—	86	1	no	—
742	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
743	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
744	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
745	C₂²×D₄	—	43	2	no	—
746	C₂²×D₄	—	43	1	no	—
747	C₂²×D₄	—	86	1	no	—
748	C₂²×D₄	—	86	2	no	—
749	C₂³×C₄	—	86	2	no	—
750	C₂³×C₄	—	86	1	no	—
751	AGL(1,ℤ/8)	—	86	4	no	—
752	AGL(1,ℤ/8)	—	86	4	no	—
753	#135	—	2	4	no	—
754	#135	—	2	4	no	—
755	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
756	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
757	C₂×SD₁₆	—	43	2	no	—
758	C₂×SD₁₆	—	43	2	no	—
759	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
760	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
761	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
762	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
763	C₂×D₈	—	43	2	no	—
764	C₂×D₈	—	43	2	no	—
765	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
766	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
767	C₂×M₁₆	—	43	1	no	—
768	C₂×M₁₆	—	43	1	no	—
769	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
770	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
771	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
772	#127	C₂²×D₄₃	1	1	yes	characteristic
773	#126	—	86	2	no	—
774	#126	—	86	2	no	—
775	#126	—	86	2	no	—
776	#126	—	86	2	no	—
777	#125	—	43	2	no	—
778	#125	—	43	2	no	—
779	#125	—	86	2	no	—
780	#125	—	86	2	no	—
781	#125	—	86	1	no	—
782	#125	—	86	1	no	—
783	#124	C₂²×D₄₃	1	1	yes	characteristic
784	#124	C₂²×D₄₃	1	1	yes	characteristic
785	#123	—	86	2	no	—
786	#123	—	86	2	no	—
787	#123	—	86	2	no	—
788	#123	—	86	2	no	—
789	C₂²⋊Q₈	—	43	2	no	—
790	C₂²⋊Q₈	—	43	2	no	—
791	C₂²⋊Q₈	—	86	1	no	—
792	C₂²⋊Q₈	—	86	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	43	2	no	—
796	#121	—	43	2	no	—
797	#121	—	86	2	no	—
798	#121	—	86	2	no	—
799	#121	—	86	1	no	—
800	#121	—	86	1	no	—
801	#121	—	86	2	no	—
802	#121	—	86	2	no	—
803	C₄×Q₈	—	43	1	no	—
804	C₄×Q₈	—	43	1	no	—
805	C₄×Q₈	—	43	2	no	—
806	C₄×Q₈	—	43	2	no	—
807	C₄×Q₈	—	43	2	no	—
808	C₄×Q₈	—	86	1	no	—
809	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
810	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	43	2	no	—
816	C₄×D₄	—	43	2	no	—
817	C₄×D₄	—	43	2	no	—
818	C₄×D₄	—	43	2	no	—
819	C₄×D₄	—	43	2	no	—
820	C₄×D₄	—	43	2	no	—
821	C₄×D₄	—	43	2	no	—
822	C₄×D₄	—	43	1	no	—
823	C₄×D₄	—	43	1	no	—
824	C₄×D₄	—	43	2	no	—
825	C₄×D₄	—	43	2	no	—
826	C₄×D₄	—	86	2	no	—
827	C₄×D₄	—	86	1	no	—
828	C₄×D₄	—	86	1	no	—
829	C₄×D₄	—	86	2	no	—
830	C₄×D₄	—	86	1	no	—
831	C₄×D₄	—	86	2	no	—
832	C₄×D₄	—	86	2	no	—
833	C₄×D₄	—	86	2	no	—
834	C₄×D₄	—	86	2	no	—
835	C₄×D₄	—	86	2	no	—
836	C₄×D₄	—	86	2	no	—
837	C₄×D₄	—	86	2	no	—
838	C₄×D₄	—	86	2	no	—
839	C₄×D₄	—	86	2	no	—
840	C₄×D₄	—	86	2	no	—
841	C₄×D₄	—	86	2	no	—
842	C₄×D₄	—	86	2	no	—
843	C₄×D₄	—	86	1	no	—
844	C₄×D₄	—	86	1	no	—
845	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
846	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
847	#117	—	2	1	no	—
848	#117	—	43	1	no	—
849	#117	—	43	2	no	—
850	#117	—	43	2	no	—
851	#117	—	86	2	no	—
852	#117	—	86	2	no	—
853	#117	—	86	2	no	—
854	#117	—	86	2	no	—
855	#117	—	86	1	no	—
856	#117	—	86	1	no	—
857	#117	—	86	1	no	—
858	#117	C₂²×D₄₃	1	1	yes	characteristic
859	C₂×C₄⋊C₄	—	43	1	no	—
860	C₂×C₄⋊C₄	—	43	1	no	—
861	C₂×C₄⋊C₄	—	43	1	no	—
862	C₂×C₄⋊C₄	—	43	2	no	—
863	C₂×C₄⋊C₄	—	86	2	no	—
864	C₂×C₄⋊C₄	—	86	1	no	—
865	C₂×C₄⋊C₄	—	86	1	no	—
866	C₂×C₄⋊C₄	—	86	1	no	—
867	C₂×C₄⋊C₄	—	86	1	no	—
868	C₂×C₄⋊C₄	—	86	1	no	—
869	C₂×C₂²⋊C₄	—	86	2	no	—
870	C₂×C₂²⋊C₄	—	86	2	no	—
871	C₂×C₂²⋊C₄	—	86	2	no	—
872	C₂×C₂²⋊C₄	—	86	2	no	—
873	C₂×C₂²⋊C₄	—	86	1	no	—
874	C₂×C₄²	—	2	1	no	—
875	C₂×C₄²	—	43	2	no	—
876	C₂×C₄²	—	86	2	no	—
877	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
878	#107	—	43	2	no	—
879	#107	—	43	2	no	—
880	#107	—	43	2	no	—
881	#107	—	43	2	no	—
882	#106	—	43	2	no	—
883	#106	—	43	2	no	—
884	#106	—	43	2	no	—
885	#106	—	43	2	no	—
886	C₄⋊C₈	—	43	2	no	—
887	C₄⋊C₈	—	43	2	no	—
888	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
889	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
890	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
891	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
892	#103	—	43	2	no	—
893	#103	—	43	2	no	—
894	#103	—	43	2	no	—
895	#103	—	43	2	no	—
896	#103	C₂²×D₄₃	1	1	yes	characteristic
897	#103	C₂²×D₄₃	1	1	yes	characteristic
898	#103	C₂²×D₄₃	1	1	yes	characteristic
899	#103	C₂²×D₄₃	1	1	yes	characteristic
900	#102	—	43	2	no	—
901	#102	—	43	2	no	—
902	#102	—	43	2	no	—
903	#102	—	43	2	no	—
904	#102	—	43	2	no	—
905	#102	—	43	2	no	—
906	#102	—	43	2	no	—
907	#102	—	43	2	no	—
908	#102	C₂²×D₄₃	1	1	yes	characteristic
909	#102	C₂²×D₄₃	1	1	yes	characteristic
910	#102	C₂²×D₄₃	1	1	yes	characteristic
911	#102	C₂²×D₄₃	1	1	yes	characteristic
912	C₂²⋊C₈	—	43	2	no	—
913	C₂²⋊C₈	—	43	2	no	—
914	C₂²⋊C₈	—	43	2	no	—
915	C₂²⋊C₈	—	43	2	no	—
916	#97	—	43	2	no	—
917	#97	—	43	2	no	—
918	C₄×C₈	—	43	2	no	—
919	C₄×C₈	—	43	2	no	—
920	C₂⁴	—	86	2	no	—
921	C₂⁴	—	86	1	no	—
922	#41	—	2	2	no	—
923	#41	—	2	2	no	—
924	#41	—	2	2	no	—
925	#41	—	2	2	no	—
926	#41	—	2	2	no	—
927	#41	—	86	8	no	—
928	#41	—	86	4	no	—
929	#41	—	86	4	no	—
930	#41	—	86	2	no	—
931	#41	—	86	2	no	—
932	#41	#10621900	1	4	yes	—
933	C₂×Q₈	—	43	1	no	—
934	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
935	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
936	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	43	2	no	—
943	C₂×D₄	—	43	1	no	—
944	C₂×D₄	—	43	4	no	—
945	C₂×D₄	—	43	2	no	—
946	C₂×D₄	—	86	2	no	—
947	C₂×D₄	—	86	8	no	—
948	C₂×D₄	—	86	2	no	—
949	C₂×D₄	—	86	4	no	—
950	C₂×D₄	—	86	16	no	—
951	C₂×D₄	—	86	4	no	—
952	C₂×D₄	—	86	2	no	—
953	C₂×D₄	—	86	2	no	—
954	C₂×D₄	—	86	1	no	—
955	C₂×D₄	—	86	2	no	—
956	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
957	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
958	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	43	2	no	—
965	C₂²×C₄	—	43	2	no	—
966	C₂²×C₄	—	43	2	no	—
967	C₂²×C₄	—	86	2	no	—
968	C₂²×C₄	—	86	2	no	—
969	C₂²×C₄	—	86	2	no	—
970	C₂²×C₄	—	86	2	no	—
971	C₂²×C₄	—	86	2	no	—
972	C₂²×C₄	—	86	2	no	—
973	C₂²×C₄	—	86	2	no	—
974	C₂²×C₄	—	86	1	no	—
975	C₂²×C₄	—	86	1	no	—
976	C₂²×C₄	—	86	1	no	—
977	C₂²×C₄	—	86	2	no	—
978	C₂²×C₄	—	86	2	no	—
979	C₂²×C₄	—	344	2	no	—
980	C₂²×C₄	—	344	4	no	—
981	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
982	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
983	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
984	Q₁₆	—	2	2	no	—
985	Q₁₆	—	2	2	no	—
986	SD₁₆	—	2	2	no	—
987	SD₁₆	—	2	2	no	—
988	SD₁₆	—	2	2	no	—
989	SD₁₆	—	2	2	no	—
990	SD₁₆	—	86	4	no	—
991	SD₁₆	—	86	4	no	—
992	D₈	—	2	2	no	—
993	D₈	—	2	2	no	—
994	D₈	—	86	4	no	—
995	D₈	—	86	4	no	—
996	M₁₆	—	86	2	no	—
997	M₁₆	—	86	2	no	—
998	C₂×C₈	—	2	2	no	—
999	C₂×C₈	—	2	2	no	—
1000	C₂×C₈	—	43	2	no	—
1001	C₂×C₈	—	43	2	no	—
1002	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1003	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1004	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1005	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	43	1	no	—
1011	C₄⋊C₄	—	43	1	no	—
1012	C₄⋊C₄	—	43	2	no	—
1013	C₄⋊C₄	—	43	2	no	—
1014	C₄⋊C₄	—	43	2	no	—
1015	C₄⋊C₄	—	43	2	no	—
1016	C₄⋊C₄	—	43	2	no	—
1017	C₄⋊C₄	—	86	2	no	—
1018	C₄⋊C₄	—	86	2	no	—
1019	C₄⋊C₄	—	86	2	no	—
1020	C₄⋊C₄	—	86	2	no	—
1021	C₄⋊C₄	—	86	2	no	—
1022	C₄⋊C₄	—	86	2	no	—
1023	C₄⋊C₄	—	86	1	no	—
1024	C₄⋊C₄	—	86	1	no	—
1025	C₄⋊C₄	—	86	1	no	—
1026	C₄⋊C₄	—	86	2	no	—
1027	C₄⋊C₄	—	86	2	no	—
1028	C₄⋊C₄	—	86	2	no	—
1029	C₄⋊C₄	—	86	2	no	—
1030	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1031	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	43	2	no	—
1040	C₂²⋊C₄	—	43	2	no	—
1041	C₂²⋊C₄	—	43	2	no	—
1042	C₂²⋊C₄	—	86	2	no	—
1043	C₂²⋊C₄	—	86	2	no	—
1044	C₂²⋊C₄	—	86	2	no	—
1045	C₂²⋊C₄	—	86	2	no	—
1046	C₂²⋊C₄	—	86	2	no	—
1047	C₂²⋊C₄	—	86	2	no	—
1048	C₂²⋊C₄	—	86	2	no	—
1049	C₂²⋊C₄	—	86	2	no	—
1050	C₂²⋊C₄	—	86	2	no	—
1051	C₂²⋊C₄	—	86	2	no	—
1052	C₂²⋊C₄	—	86	2	no	—
1053	C₂²⋊C₄	—	86	2	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	1	no	—
1057	C₄²	—	43	2	no	—
1058	C₄²	—	43	2	no	—
1059	C₄²	—	43	2	no	—
1060	C₄²	—	86	2	no	—
1061	C₄²	—	86	2	no	—
1062	C₄²	—	86	2	no	—
1063	C₄²	—	86	2	no	—
1064	C₄²	D₄×D₄₃	1	1	yes	characteristic
1065	C₄²	D₄×D₄₃	1	1	yes	characteristic
1066	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1067	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1068	C₂³	—	2	1	no	—
1069	C₂³	—	2	1	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	43	2	no	—
1072	C₂³	—	86	8	no	—
1073	C₂³	—	86	4	no	—
1074	C₂³	—	86	2	no	—
1075	C₂³	—	344	1	no	—
1076	C₂³	—	344	1	no	—
1077	C₂³	—	344	2	no	—
1078	C₂³	—	344	2	no	—
1079	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1080	Q₈	—	2	1	no	—
1081	Q₈	—	2	1	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	1	no	—
1084	Q₈	—	2	1	no	—
1085	Q₈	—	86	2	no	—
1086	Q₈	C₂×#10621900	1	2	yes	—
1087	D₄	—	2	4	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	8	1	no	—
1096	D₄	—	8	1	no	—
1097	D₄	—	43	4	no	—
1098	D₄	—	86	8	no	—
1099	D₄	—	86	8	no	—
1100	D₄	—	86	4	no	—
1101	D₄	—	86	4	no	—
1102	D₄	—	86	2	no	—
1103	D₄	—	86	2	no	—
1104	D₄	—	344	2	no	—
1105	D₄	—	344	2	no	—
1106	D₄	C₂×#10621900	1	2	yes	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	4	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	43	2	no	—
1120	C₂×C₄	—	43	2	no	—
1121	C₂×C₄	—	43	2	no	—
1122	C₂×C₄	—	86	8	no	—
1123	C₂×C₄	—	86	2	no	—
1124	C₂×C₄	—	86	2	no	—
1125	C₂×C₄	—	86	2	no	—
1126	C₂×C₄	—	86	2	no	—
1127	C₂×C₄	—	86	2	no	—
1128	C₂×C₄	—	344	2	no	—
1129	C₂×C₄	—	344	2	no	—
1130	C₂×C₄	—	344	2	no	—
1131	C₂×C₄	—	344	2	no	—
1132	C₂×C₄	—	344	2	no	—
1133	C₂×C₄	—	344	2	no	—
1134	C₂×C₄	—	344	2	no	—
1135	C₂×C₄	—	344	1	no	—
1136	C₂×C₄	—	344	1	no	—
1137	C₂×C₄	—	344	1	no	—
1138	C₂×C₄	—	172	2	no	—
1139	C₂×C₄	—	172	2	no	—
1140	C₂×C₄	—	172	4	no	—
1141	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1142	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1143	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1144	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1145	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1146	C₂×C₄	#41×D₄₃	1	2	yes	—
1147	C₂×C₄	C₂×#10621900	1	2	yes	—
1148	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1149	C₈	—	2	1	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	86	2	no	—
1154	C₈	—	86	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	1	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	86	2	no	—
1167	C₂²	—	86	4	no	—
1168	C₂²	—	86	2	no	—
1169	C₂²	—	86	2	no	—
1170	C₂²	—	344	4	no	—
1171	C₂²	—	344	8	no	—
1172	C₂²	—	172	2	no	—
1173	C₂²	—	172	2	no	—
1174	C₂²	#14583409	1	2	yes	—
1175	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1176	C₄	—	2	1	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	86	2	no	—
1186	C₄	—	86	2	no	—
1187	C₄	—	86	2	no	—
1188	C₄	—	172	2	no	—
1189	C₄	—	172	2	no	—
1190	C₄	—	172	2	no	—
1191	C₄	#14583409	1	2	yes	—
1192	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1193	C₄	C₂²×#10621900	1	1	yes	characteristic
1194	C₂	—	2	2	no	—
1195	C₂	—	4	2	no	—
1196	C₂	—	8	1	no	—
1197	C₂	—	8	1	no	—
1198	C₂	—	172	2	no	—
1199	C₂	—	172	4	no	—
1200	C₂	C₂×#14583409	1	1	yes	characteristic
1201	C₂	#19149364	1	1	yes	characteristic
1202	C₂	#19149372	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3035	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3035	D₄₃
hypocenter	C₄₃	#60601
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. #19148515	C₂	semidirect
2. C₄×#13063371	C₂	semidirect
3. #19144845	C₂	semidirect
4. #19144836	C₂	semidirect
5. #19144808	C₂	semidirect
6. #19144793	C₂	semidirect
7. #19144732	C₂	semidirect
8. #19144703	C₂	semidirect
9. #19144641	C₂	semidirect
10. #19144612	C₂	semidirect
11. #19144582	C₂	semidirect
12. #19144571	C₂	semidirect
13. #19144417	C₂	semidirect
14. C₂×#14583200	C₂	semidirect
15. #19144055	C₂	semidirect
16. #19143895	C₂	semidirect
17. #19143895	C₂	semidirect
18. #19143479	C₂	semidirect
19. #19143471	C₂	semidirect
20. #19143430	C₂	semidirect
21. #19143430	C₂	semidirect
22. #19143260	C₂	semidirect
23. C₄₃×#3035	C₂	semidirect
33. #14583510	C₂²	semidirect
34. #14583503	C₂²	semidirect
37. #14583428	C₂²	semidirect
38. #14583428	C₂²	semidirect
39. C₂×#13063317	C₂²	semidirect
41. #14583382	C₂²	semidirect
42. #14583382	C₂²	semidirect
57. #14583239	C₂²	semidirect
58. #14583238	C₂²	semidirect
59. #14583233	C₂²	semidirect
60. #14583228	C₂²	semidirect
61. #14583222	C₂²	semidirect
62. #14583221	C₂²	semidirect
63. #14583216	C₂²	semidirect
64. #14583211	C₂²	semidirect
65. #14583206	C₂²	semidirect
66. #14583206	C₂²	semidirect
67. #14583200	C₂²	semidirect
68. #14583200	C₂²	semidirect
69. #14583200	C₂²	semidirect
70. #14583200	C₂²	semidirect
71. #14583199	C₂²	semidirect
72. #14583199	C₂²	semidirect
73. #14583111	C₂²	semidirect
74. #14583111	C₂²	semidirect
75. #14583101	C₂²	semidirect
76. #14583091	C₂²	semidirect
85. #14583011	C₂²	semidirect
86. #14583008	C₂²	semidirect
87. #14583008	C₂²	semidirect
88. #14583006	C₂²	semidirect
89. #14583002	C₂²	semidirect
90. #14583002	C₂²	semidirect
91. #14583000	C₂²	semidirect
92. #14583000	C₂²	semidirect
93. Q₁₆×Dic₄₃	C₂²	semidirect
94. SD₁₆×Dic₄₃	C₂²	semidirect
95. SD₁₆×Dic₄₃	C₂²	semidirect
96. #14582984	C₂²	semidirect
97. #14582984	C₂²	semidirect
98. D₈×Dic₄₃	C₂²	semidirect
99. #14582979	C₂²	semidirect
100. #14582979	C₂²	semidirect
101. #14582959	C₂²	semidirect
102. #14582959	C₂²	semidirect
103. #14582955	C₂²	semidirect
104. #14582951	C₂²	semidirect
105. #14582942	C₂²	semidirect
106. #14582942	C₂²	semidirect
107. C₂×#13063259	C₂²	semidirect
108. C₂×#13063257	C₂²	semidirect
109. #14582923	C₂²	semidirect
112. #14582900	C₂²	semidirect
113. #14582900	C₂²	semidirect
118. #14582854	C₂²	semidirect
119. #14582854	C₂²	semidirect
122. C₄₃×#532	C₂²	semidirect
124. C₄₃×#464	C₂²	semidirect
125. C₄₃×#464	C₂²	semidirect
126. C₄₃×#463	C₂²	semidirect
127. C₄₃×#463	C₂²	semidirect
128. C₄₃×#462	C₂²	semidirect
129. C₄₃×#461	C₂²	semidirect
130. C₄₃×#460	C₂²	semidirect
131. C₄₃×#459	C₂²	semidirect
132. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
133. C₄₃×#416	C₂²	semidirect
134. C₄₃×#416	C₂²	semidirect
608. #3035	D₄₃	semidirect
640. #532	C₂×D₄₃	semidirect
678. #464	C₂×D₄₃	semidirect
679. #464	C₂×D₄₃	semidirect
682. #463	C₂×D₄₃	semidirect
683. #463	C₂×D₄₃	semidirect
684. #462	C₂×D₄₃	semidirect
686. #461	C₂×D₄₃	semidirect
687. #460	C₂×D₄₃	semidirect
689. #459	C₂×D₄₃	semidirect
723. C₂×C₄⋊C₈	C₂×D₄₃	semidirect
728. #416	C₂×D₄₃	semidirect
729. #416	C₂×D₄₃	semidirect
736. C₄₃	#60601	semidirect

Maximal subgroups

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

subgroup	index
#19148515	2
C₄×#13063371	2
#19144845	2
#19144836	2
#19144808	2
#19144793	2
#19144732	2
#19144703	2
#19144641	2
#19144612	2
#19144582	2
#19144571	2
#19144417	2
C₂×#14583200	2
#19144055	2
#19143895	2
#19143479	2
#19143471	2
#19143430	2
#19143260	2
C₄₃×#3035	2
#60601	43