Subgroups — #25978125

Order 11008.

1926 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148217	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148205	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147589	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147468	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147289	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147242	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146975	C₂	1	2	yes	maximal, complemented
8	#19146954	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146498	C₂	1	2	yes	maximal, complemented
10	#19146473	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146431	C₂	1	2	yes	maximal, complemented
12	#19146410	C₂	1	1	yes	maximal, characteristic, complemented
13	#19146296	C₂	1	2	yes	maximal, complemented
14	SD₁₆×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145161	C₂	1	2	yes	maximal, complemented
16	#19145154	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144679	C₂	1	2	yes	maximal, complemented
18	#19144666	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144655	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144640	C₂	1	2	yes	maximal, complemented
21	C₈×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×SD₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₄₃	C₂²	1	2	yes	—
25	#14583634	C₂²	1	1	yes	characteristic
26	#14583628	C₂²	1	1	yes	characteristic, complemented
27	#14583619	—	2	1	no	—
28	#14583619	C₂²	1	1	yes	characteristic, complemented
29	#14583609	C₂²	1	1	yes	characteristic
30	#14583606	C₂²	1	1	yes	characteristic
31	#14583595	—	2	1	no	—
32	#14583593	C₂²	1	2	yes	—
33	#14583588	—	2	2	no	—
34	#14583588	C₂²	1	2	yes	complemented
35	#14583573	—	2	2	no	—
36	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic
37	#14583556	C₂²	1	2	yes	complemented
38	#14583554	—	2	1	no	—
39	#14583554	C₂²	1	1	yes	characteristic
40	#14583545	—	2	1	no	—
41	#14583537	C₂²	1	2	yes	—
42	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
43	#14583456	—	2	1	no	—
44	#14583456	C₂²	1	1	yes	characteristic, complemented
45	#14583449	C₂²	1	1	yes	characteristic
46	#14583436	C₂²	1	2	yes	—
47	#14583433	—	2	1	no	—
48	#14583431	—	2	2	no	—
49	#14583431	C₂²	1	2	yes	complemented
50	#14583408	—	2	2	no	—
51	C₄×#10621898	—	2	1	no	—
52	C₄×#10621898	C₂²	1	1	yes	characteristic
53	C₄×Q₈×D₄₃	C₂²	1	2	yes	complemented
54	C₂×C₄×D₁₇₂	—	2	1	no	—
55	C₄×D₄×D₄₃	C₂²	1	2	yes	—
56	#14583299	C₂²	1	2	yes	complemented
57	#14583297	C₂²	1	1	yes	characteristic, complemented
58	#14583280	C₂²	1	2	yes	complemented
59	#14583272	C₂²	1	1	yes	characteristic
60	#14583255	C₂²	1	2	yes	complemented
61	#14583252	C₂²	1	2	yes	complemented
62	#14583250	C₂²	1	1	yes	characteristic, complemented
63	#14583246	C₂²	1	1	yes	characteristic
64	#14583240	C₂²	1	2	yes	complemented
65	#14583236	C₂²	1	2	yes	complemented
66	#14583228	C₂²	1	2	yes	complemented
67	#14583223	C₂²	1	2	yes	complemented
68	#14583216	C₂²	1	2	yes	complemented
69	#14583214	C₂²	1	2	yes	—
70	#14583205	C₂²	1	2	yes	complemented
71	#14583204	C₂²	1	2	yes	complemented
72	#14583202	C₂²	1	2	yes	complemented
73	#14583201	C₂²	1	2	yes	—
74	#14583194	C₂²	1	1	yes	characteristic, complemented
75	#14583189	C₂²	1	1	yes	characteristic, complemented
76	#14583184	C₂²	1	1	yes	characteristic, complemented
77	#14583179	C₂²	1	1	yes	characteristic
78	#14583139	C₂²	1	2	yes	complemented
79	#14583134	C₂²	1	2	yes	—
80	#14583129	C₂²	1	2	yes	—
81	#14583128	C₂²	1	2	yes	complemented
82	#14583128	C₂²	1	2	yes	complemented
83	#14583125	C₂²	1	2	yes	complemented
84	#14583124	C₂²	1	2	yes	complemented
85	#14583123	C₂²	1	2	yes	complemented
86	#14583113	C₂²	1	2	yes	complemented
87	#14583112	C₂²	1	2	yes	—
88	#14583109	C₂²	1	1	yes	characteristic, complemented
89	#14583104	C₂²	1	1	yes	characteristic
90	#14583099	C₂²	1	1	yes	characteristic
91	#14583094	C₂²	1	1	yes	characteristic
92	#14583061	C₂²	1	2	yes	—
93	#14583053	C₂²	1	2	yes	complemented
94	#14583051	C₂²	1	2	yes	—
95	#14583044	C₂²	1	2	yes	complemented
96	#14583039	C₂²	1	2	yes	—
97	#14583031	C₂²	1	2	yes	—
98	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10621885	C₂²	1	2	yes	complemented
101	#14582990	C₂²	1	2	yes	—
102	C₄×#10621873	C₂²	1	2	yes	complemented
103	C₄×#10621873	C₂²	1	2	yes	complemented
104	SD₁₆×Dic₄₃	C₂²	1	2	yes	—
105	C₄×#10621884	C₂²	1	2	yes	complemented
106	#14582986	C₂²	1	2	yes	complemented
107	C₄×#10621883	C₂²	1	2	yes	—
108	#14582984	C₂²	1	2	yes	complemented
109	C₄×#10621882	C₂²	1	2	yes	complemented
110	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
111	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
112	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
113	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
114	#14582952	C₂²	1	1	yes	characteristic, complemented
115	#14582950	C₂²	1	2	yes	complemented
116	#106×D₄₃	C₂²	1	2	yes	complemented
117	#103×D₄₃	C₂²	1	2	yes	complemented
118	#102×D₄₃	C₂²	1	2	yes	—
119	C₄×C₈×D₄₃	C₂²	1	2	yes	complemented
120	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
124	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
131	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
132	C₄₃×#416	C₂²	1	1	yes	characteristic
133	C₄₃×#416	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621898	—	2	1	no	—
136	C₂×#10621898	—	2	1	no	—
137	C₂×#10621898	D₄	1	1	yes	characteristic
138	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
139	C₂²×D₁₇₂	—	2	1	no	—
140	C₂×D₄×D₄₃	C₂³	1	2	yes	—
141	C₂²×C₄×D₄₃	—	2	2	no	—
142	C₂×#10621885	C₂³	1	2	yes	—
143	C₂×#10621873	C₂³	1	2	yes	—
144	C₂×#10621873	C₂³	1	2	yes	—
145	C₂×#10621883	C₂³	1	2	yes	—
146	C₂×#10621884	C₂³	1	2	yes	—
147	SD₁₆×D₄₃	—	2	8	no	—
148	C₂×#10621882	C₂³	1	2	yes	—
149	C₂×C₈×D₄₃	C₂³	1	2	yes	—
150	C₂×C₈×D₄₃	C₂³	1	2	yes	—
151	#13063325	—	2	1	no	—
152	#13063325	—	2	1	no	—
153	#13063325	C₂³	1	1	yes	characteristic
154	#13063325	C₂³	1	1	yes	characteristic
155	#13063325	C₂³	1	1	yes	characteristic
156	#13063322	C₂³	1	1	yes	characteristic
157	#13063320	—	2	2	no	—
158	#13063319	—	2	2	no	—
159	#13063318	—	2	2	no	—
160	#13063318	—	2	2	no	—
161	#13063318	—	2	2	no	—
162	#13063317	—	2	1	no	—
163	#13063317	—	2	1	no	—
164	#13063317	—	2	2	no	—
165	#13063316	—	2	2	no	—
166	#13063316	C₂³	1	2	yes	—
167	#13063316	C₂³	1	2	yes	—
168	#13063314	C₂³	1	2	yes	—
169	#13063313	—	2	1	no	—
170	#13063313	—	2	1	no	—
171	#13063312	—	2	2	no	—
172	#13063312	C₂³	1	2	yes	—
173	#13063310	—	2	2	no	—
174	#13063310	—	2	2	no	—
175	#13063308	—	2	2	no	—
176	#13063307	—	2	2	no	—
177	#13063307	—	2	2	no	—
178	#13063307	—	2	2	no	—
179	#13063307	—	2	2	no	—
180	#13063305	—	2	2	no	—
181	#13063305	C₂³	1	2	yes	—
182	#13063304	—	2	1	no	—
183	#13063304	—	2	1	no	—
184	#13063304	—	2	1	no	—
185	#13063304	—	2	1	no	—
186	#13063304	—	2	2	no	—
187	#13063304	C₂³	1	2	yes	—
188	#13063303	—	2	2	no	—
189	#13063302	—	2	2	no	—
190	#13063301	C₂³	1	2	yes	—
191	#13063300	C₂³	1	2	yes	—
192	#13063299	—	2	1	no	—
193	#13063299	—	2	1	no	—
194	#13063299	C₂³	1	2	yes	—
195	#13063298	—	2	2	no	—
196	#13063297	—	2	2	no	—
197	#13063296	—	2	2	no	—
198	#13063296	C₂³	1	2	yes	—
199	#13063295	—	2	2	no	—
200	#13063293	—	2	2	no	—
201	Q₈×Dic₄₃	C₂³	1	2	yes	—
202	C₄×Dic₈₆	—	2	1	no	—
203	C₄×Dic₈₆	—	2	1	no	—
204	C₄×Dic₈₆	—	2	2	no	—
205	C₄×Dic₈₆	D₄	1	1	yes	characteristic
206	C₄×Dic₈₆	C₂³	1	2	yes	—
207	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
208	#13063290	—	2	2	no	—
209	#13063290	C₂³	1	2	yes	—
210	C₄×D₁₇₂	—	2	1	no	—
211	C₄×D₁₇₂	—	2	1	no	—
212	C₄×D₁₇₂	—	2	2	no	—
213	C₄×D₁₇₂	—	2	1	no	—
214	C₄×D₁₇₂	—	2	2	no	—
215	C₄×D₁₇₂	—	2	1	no	—
216	C₄×D₁₇₂	D₄	1	1	yes	characteristic
217	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
218	C₄×D₁₇₂	C₂³	1	2	yes	—
219	D₄×Dic₄₃	C₂³	1	2	yes	—
220	#13063287	C₂³	1	2	yes	—
221	C₄×C₂²⋊D₄₃	—	2	2	no	—
222	C₄×C₂²⋊D₄₃	—	2	2	no	—
223	C₄×C₂²⋊D₄₃	—	2	2	no	—
224	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
225	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
226	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
227	#13063284	—	2	1	no	—
228	#13063284	—	2	1	no	—
229	#13063284	—	2	2	no	—
230	#13063284	D₄	1	1	yes	characteristic
231	#13063282	—	2	2	no	—
232	#13063282	—	2	2	no	—
233	#13063282	D₄	1	2	yes	—
234	C₂×C₄⋊Dic₄₃	—	2	1	no	—
235	C₄⋊C₄×D₄₃	—	2	2	no	—
236	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
237	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
238	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
239	C₂²⋊C₄×D₄₃	—	2	2	no	—
240	C₄²×D₄₃	—	2	2	no	—
241	C₄²×D₄₃	C₂³	1	2	yes	—
242	#13063258	C₂³	1	2	yes	—
243	#13063258	C₂³	1	2	yes	—
244	#13063257	C₂³	1	2	yes	—
245	#13063257	C₂³	1	2	yes	—
246	#13063256	C₂³	1	2	yes	—
247	#13063256	C₂³	1	2	yes	—
248	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₃⋊C₈	C₂³	1	2	yes	—
251	Dic₄₃⋊C₈	C₂³	1	2	yes	—
252	#13063250	C₂³	1	2	yes	—
253	#13063250	C₂³	1	2	yes	—
254	#13063249	C₂³	1	2	yes	—
255	#13063249	C₂³	1	2	yes	—
256	#13063248	C₂³	1	2	yes	—
257	#13063248	C₂³	1	2	yes	—
258	#13063247	C₂³	1	2	yes	—
259	#13063247	C₂³	1	2	yes	—
260	#13063246	C₂³	1	2	yes	—
261	#13063246	C₂³	1	2	yes	—
262	#13063245	C₂³	1	2	yes	—
263	#13063245	C₂³	1	2	yes	—
264	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
268	C₈×Dic₄₃	C₂³	1	2	yes	—
269	C₈×Dic₄₃	C₂³	1	2	yes	—
270	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
272	#135×C₄₃	—	2	4	no	—
273	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
274	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
279	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₄₃	—	2	1	no	—
284	C₄×D₄×C₄₃	—	2	1	no	—
285	C₄×D₄×C₄₃	—	2	1	no	—
286	C₄×D₄×C₄₃	—	2	1	no	—
287	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
291	#117×C₄₃	—	2	1	no	—
292	#117×C₄₃	—	2	1	no	—
293	#117×C₄₃	C₂³	1	1	yes	characteristic
294	#117×C₄₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₄₃	—	2	1	no	—
296	C₂×C₄²×C₄₃	—	2	1	no	—
297	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
298	#107×C₄₃	C₂³	1	1	yes	characteristic
299	#107×C₄₃	C₂³	1	1	yes	characteristic
300	#106×C₄₃	C₂³	1	1	yes	characteristic
301	#106×C₄₃	C₂³	1	1	yes	characteristic
302	#103×C₄₃	C₂³	1	1	yes	characteristic
303	#103×C₄₃	C₂³	1	1	yes	characteristic
304	#103×C₄₃	C₂³	1	1	yes	characteristic
305	#103×C₄₃	C₂³	1	1	yes	characteristic
306	#102×C₄₃	C₂³	1	1	yes	characteristic
307	#102×C₄₃	C₂³	1	1	yes	characteristic
308	#102×C₄₃	C₂³	1	1	yes	characteristic
309	#102×C₄₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	C₂³×D₄₃	—	2	2	no	—
315	#41×C₄₃	—	2	2	no	—
316	#41×C₄₃	—	2	2	no	—
317	#41×C₄₃	—	4	1	no	—
318	#41×C₄₃	—	4	1	no	—
319	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₄₃	—	2	1	no	—
322	C₂×D₄×C₄₃	—	2	1	no	—
323	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₃	—	2	1	no	—
326	C₂²×C₄×C₄₃	—	2	1	no	—
327	C₂²×C₄×C₄₃	—	2	1	no	—
328	C₂²×C₄×C₄₃	—	2	1	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₂²⋊D₄₃	—	2	2	no	—
335	C₂×C₂²⋊D₄₃	—	2	2	no	—
336	C₂×C₂²⋊D₄₃	—	2	2	no	—
337	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
338	C₂²×Dic₄₃	—	2	2	no	—
339	Q₈×D₄₃	—	2	4	no	—
340	Q₈×D₄₃	—	4	2	no	—
341	D₄×D₄₃	—	2	4	no	—
342	D₄×D₄₃	—	4	2	no	—
343	#10621898	—	2	4	no	—
344	#10621898	—	4	4	no	—
345	#10621898	—	8	2	no	—
346	C₂×D₁₇₂	—	2	1	no	—
347	C₂×D₁₇₂	—	2	1	no	—
348	C₂×D₁₇₂	—	2	2	no	—
349	C₂×D₁₇₂	—	4	4	no	—
350	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
351	C₂×D₁₇₂	C₂⁴	1	2	yes	—
352	C₂×C₄×D₄₃	—	2	2	no	—
353	C₂×C₄×D₄₃	—	2	2	no	—
354	C₂×C₄×D₄₃	—	2	2	no	—
355	C₂×C₄×D₄₃	—	2	2	no	—
356	C₂×C₄×D₄₃	—	2	2	no	—
357	C₂×C₄×D₄₃	—	8	4	no	—
358	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
359	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
360	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
361	C₂×Dic₈₆	—	2	1	no	—
362	C₂×Dic₈₆	—	2	2	no	—
363	C₂×Dic₈₆	—	2	1	no	—
364	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
365	C₂×Dic₈₆	C₂⁴	1	2	yes	—
366	Q₁₆×C₄₃	—	2	2	no	—
367	SD₁₆×C₄₃	—	2	2	no	—
368	SD₁₆×C₄₃	#41	1	4	yes	complemented
369	D₈×C₄₃	—	2	2	no	—
370	C₂×C₈×C₄₃	—	2	2	no	—
371	C₂×C₈×C₄₃	—	4	1	no	—
372	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₄₃	—	2	1	no	—
377	C₄⋊C₄×C₄₃	—	2	1	no	—
378	C₄⋊C₄×C₄₃	—	2	1	no	—
379	C₄⋊C₄×C₄₃	—	2	1	no	—
380	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
384	C₂²⋊C₄×C₄₃	—	2	1	no	—
385	C₂²⋊C₄×C₄₃	—	2	1	no	—
386	C₂²⋊C₄×C₄₃	—	2	1	no	—
387	C₂²⋊C₄×C₄₃	—	2	1	no	—
388	C₂²⋊C₄×C₄₃	—	2	1	no	—
389	C₂²⋊C₄×C₄₃	—	2	1	no	—
390	C₄²×C₄₃	—	2	1	no	—
391	C₄²×C₄₃	—	2	1	no	—
392	C₄²×C₄₃	—	2	1	no	—
393	C₄²×C₄₃	—	2	1	no	—
394	C₄²×C₄₃	—	2	1	no	—
395	C₄²×C₄₃	—	2	1	no	—
396	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
399	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
400	C₂²⋊Dic₄₃	—	2	2	no	—
401	C₂²⋊Dic₄₃	—	2	2	no	—
402	C₂²⋊Dic₄₃	—	2	2	no	—
403	C₂²⋊Dic₄₃	—	2	2	no	—
404	C₂²⋊Dic₄₃	—	2	2	no	—
405	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
406	#10621885	—	4	2	no	—
407	#10621884	—	2	4	no	—
408	#10621883	—	2	4	no	—
409	#10621882	—	4	2	no	—
410	(C₂×D₄₃)⋊C₄	—	2	2	no	—
411	(C₂×D₄₃)⋊C₄	—	2	2	no	—
412	(C₂×D₄₃)⋊C₄	—	2	2	no	—
413	(C₂×D₄₃)⋊C₄	—	2	2	no	—
414	(C₂×D₄₃)⋊C₄	—	2	2	no	—
415	(C₂×D₄₃)⋊C₄	—	2	2	no	—
416	(C₂×D₄₃)⋊C₄	—	2	2	no	—
417	(C₂×D₄₃)⋊C₄	—	2	2	no	—
418	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
419	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
420	C₄⋊Dic₄₃	—	2	1	no	—
421	C₄⋊Dic₄₃	—	2	1	no	—
422	C₄⋊Dic₄₃	—	2	1	no	—
423	C₄⋊Dic₄₃	—	2	1	no	—
424	C₄⋊Dic₄₃	—	2	2	no	—
425	C₄⋊Dic₄₃	—	2	2	no	—
426	C₄⋊Dic₄₃	—	2	2	no	—
427	C₄⋊Dic₄₃	—	2	2	no	—
428	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
429	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
430	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
431	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
432	Dic₄₃⋊C₄	—	2	2	no	—
433	Dic₄₃⋊C₄	—	2	2	no	—
434	Dic₄₃⋊C₄	—	2	2	no	—
435	Dic₄₃⋊C₄	—	2	2	no	—
436	Dic₄₃⋊C₄	—	2	2	no	—
437	Dic₄₃⋊C₄	—	2	2	no	—
438	Dic₄₃⋊C₄	—	2	2	no	—
439	Dic₄₃⋊C₄	—	2	2	no	—
440	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
441	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
442	C₄×Dic₄₃	—	2	2	no	—
443	C₄×Dic₄₃	—	2	2	no	—
444	C₄×Dic₄₃	—	2	2	no	—
445	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
446	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
447	C₄×Dic₄₃	C₂⁴	1	2	yes	—
448	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
449	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
450	#10621873	—	2	4	no	—
451	#10621873	—	4	2	no	—
452	C₈×D₄₃	—	2	4	no	—
453	C₈×D₄₃	—	4	2	no	—
454	C₂³×C₄₃	—	2	1	no	—
455	C₂³×C₄₃	—	2	1	no	—
456	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
457	C₂²×D₄₃	—	2	2	no	—
458	C₂²×D₄₃	—	4	4	no	—
459	C₂²×D₄₃	—	4	4	no	—
460	C₂²×D₄₃	—	8	2	no	—
461	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
462	Q₈×C₄₃	—	2	1	no	—
463	Q₈×C₄₃	—	2	1	no	—
464	Q₈×C₄₃	—	2	1	no	—
465	Q₈×C₄₃	C₂×#41	1	2	yes	—
466	D₄×C₄₃	—	2	1	no	—
467	D₄×C₄₃	—	2	1	no	—
468	D₄×C₄₃	—	2	1	no	—
469	D₄×C₄₃	—	4	2	no	—
470	D₄×C₄₃	—	4	2	no	—
471	D₄×C₄₃	C₂×#41	1	2	yes	—
472	C₂×C₄×C₄₃	—	2	1	no	—
473	C₂×C₄×C₄₃	—	2	2	no	—
474	C₂×C₄×C₄₃	—	2	2	no	—
475	C₂×C₄×C₄₃	—	2	1	no	—
476	C₂×C₄×C₄₃	—	2	1	no	—
477	C₂×C₄×C₄₃	—	2	1	no	—
478	C₂×C₄×C₄₃	—	2	1	no	—
479	C₂×C₄×C₄₃	—	2	1	no	—
480	C₂×C₄×C₄₃	—	2	1	no	—
481	C₂×C₄×C₄₃	—	2	1	no	—
482	C₂×C₄×C₄₃	—	4	2	no	—
483	C₂×C₄×C₄₃	—	4	2	no	—
484	C₂×C₄×C₄₃	—	4	2	no	—
485	C₂×C₄×C₄₃	—	4	2	no	—
486	C₂×C₄×C₄₃	—	4	2	no	—
487	C₂×C₄×C₄₃	—	4	2	no	—
488	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₄₃	—	2	4	no	—
495	C₂²⋊D₄₃	—	4	4	no	—
496	C₂²⋊D₄₃	—	4	4	no	—
497	C₂²⋊D₄₃	—	8	2	no	—
498	C₂×Dic₄₃	—	2	2	no	—
499	C₂×Dic₄₃	—	2	2	no	—
500	C₂×Dic₄₃	—	2	2	no	—
501	C₂×Dic₄₃	—	8	2	no	—
502	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
503	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
504	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
505	D₁₇₂	—	2	2	no	—
506	D₁₇₂	—	2	2	no	—
507	D₁₇₂	—	4	4	no	—
508	D₁₇₂	—	4	2	no	—
509	D₁₇₂	—	8	1	no	—
510	D₁₇₂	#135	1	4	yes	complemented
511	C₄×D₄₃	—	2	4	no	—
512	C₄×D₄₃	—	2	4	no	—
513	C₄×D₄₃	—	2	2	no	—
514	C₄×D₄₃	—	2	2	no	—
515	C₄×D₄₃	—	4	4	no	—
516	C₄×D₄₃	—	4	4	no	—
517	C₄×D₄₃	—	4	4	no	—
518	C₄×D₄₃	—	8	2	no	—
519	C₄×D₄₃	—	8	2	no	—
520	Dic₈₆	—	2	2	no	—
521	Dic₈₆	—	2	2	no	—
522	Dic₈₆	—	2	2	no	—
523	Dic₈₆	—	4	4	no	—
524	Dic₈₆	—	4	2	no	—
525	Dic₈₆	—	8	1	no	—
526	C₈×C₄₃	—	2	1	no	—
527	C₈×C₄₃	—	2	1	no	—
528	C₈×C₄₃	—	2	1	no	—
529	C₈×C₄₃	C₂×#41	1	2	yes	—
530	C₄₃⋊C₈	—	2	2	no	—
531	C₄₃⋊C₈	—	2	2	no	—
532	#61432	—	43	1	no	maximal, Sylow
533	C₂²×C₄₃	—	2	2	no	—
534	C₂²×C₄₃	—	2	1	no	—
535	C₂²×C₄₃	—	2	1	no	—
536	C₂²×C₄₃	—	2	1	no	—
537	C₂²×C₄₃	—	4	1	no	—
538	C₂²×C₄₃	—	4	1	no	—
539	C₂²×C₄₃	—	4	1	no	—
540	C₂²×C₄₃	—	4	1	no	—
541	C₂²×C₄₃	—	4	1	no	—
542	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
543	C₂×D₄₃	—	2	2	no	—
544	C₂×D₄₃	—	2	2	no	—
545	C₂×D₄₃	—	4	2	no	—
546	C₂×D₄₃	—	4	2	no	—
547	C₂×D₄₃	—	4	2	no	—
548	C₂×D₄₃	—	8	8	no	—
549	C₂×D₄₃	C₂×#135	1	4	yes	—
550	C₄×C₄₃	—	2	2	no	—
551	C₄×C₄₃	—	2	1	no	—
552	C₄×C₄₃	—	2	1	no	—
553	C₄×C₄₃	—	2	1	no	—
554	C₄×C₄₃	—	4	1	no	—
555	C₄×C₄₃	—	4	1	no	—
556	C₄×C₄₃	—	4	1	no	—
557	C₄×C₄₃	—	4	1	no	—
558	C₄×C₄₃	—	4	1	no	—
559	C₄×C₄₃	C₂×#135	1	2	yes	—
560	C₄×C₄₃	#577	1	2	yes	—
561	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
562	C₄×C₄₃	#585	1	1	yes	characteristic
563	Dic₄₃	—	2	2	no	—
564	Dic₄₃	—	2	2	no	—
565	Dic₄₃	—	2	2	no	—
566	Dic₄₃	—	4	2	no	—
567	Dic₄₃	—	4	2	no	—
568	Dic₄₃	—	4	2	no	—
569	#3482	—	43	1	no	—
570	#3481	—	43	1	no	—
571	#3394	—	43	1	no	—
572	#3381	—	43	1	no	—
573	#3365	—	43	1	no	—
574	#3360	—	43	1	no	—
575	#3337	—	43	2	no	—
576	#3335	—	43	1	no	—
577	#3301	—	43	2	no	—
578	#3299	—	43	1	no	—
579	#3296	—	43	2	no	—
580	#3294	—	43	1	no	—
581	#3282	—	43	2	no	—
582	D₄×SD₁₆	—	43	1	no	—
583	#3168	—	43	2	no	—
584	#3167	—	43	1	no	—
585	#3108	—	43	2	no	—
586	#3107	—	43	1	no	—
587	#3106	—	43	1	no	—
588	#3105	—	43	2	no	—
589	C₈×#41	—	43	1	no	—
590	C₄×#135	D₄₃	1	1	yes	characteristic, complemented
591	C₂×C₄×SD₁₆	—	43	2	no	—
592	C₂×C₄₃	—	4	2	no	—
593	C₂×C₄₃	—	4	1	no	—
594	C₂×C₄₃	—	8	1	no	—
595	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
596	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
597	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
598	D₄₃	—	2	4	no	—
599	D₄₃	—	8	2	no	—
600	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
601	C₂²×SD₁₆	—	43	2	no	—
602	#559	—	43	1	no	—
603	#557	—	43	1	no	—
604	#556	—	43	1	no	—
605	#556	—	86	1	no	—
606	#554	—	43	1	no	—
607	#554	—	43	1	no	—
608	#553	—	43	2	no	—
609	#553	—	86	1	no	—
610	#552	—	43	2	no	—
611	#552	—	86	2	no	—
612	#551	—	86	2	no	—
613	D₄×Q₈	—	43	1	no	—
614	#548	—	43	2	no	—
615	#547	—	43	1	no	—
616	#547	—	86	1	no	—
617	#546	—	43	2	no	—
618	#546	—	86	1	no	—
619	D₄²	—	43	1	no	—
620	#533	—	43	1	no	—
621	#533	—	86	1	no	—
622	#532	—	43	1	no	—
623	#529	—	43	2	no	—
624	#529	—	43	2	no	—
625	#529	—	86	1	no	—
626	#529	—	86	2	no	—
627	#525	—	86	2	no	—
628	C₄×#41	—	43	1	no	—
629	C₄×#41	—	86	1	no	—
630	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
631	C₄×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
632	C₂×C₄×Q₈	—	43	2	no	—
633	C₂×C₄×D₄	—	43	2	no	—
634	C₂×C₄×D₄	—	86	1	no	—
635	#499	—	43	2	no	—
636	#498	—	43	1	no	—
637	#495	—	43	2	no	—
638	#492	—	43	1	no	—
639	#488	—	43	2	no	—
640	#488	—	43	2	no	—
641	#487	—	43	1	no	—
642	#486	—	43	1	no	—
643	#485	—	43	2	no	—
644	#484	—	43	2	no	—
645	#483	—	43	2	no	—
646	#482	—	43	2	no	—
647	#481	—	43	2	no	—
648	#480	—	43	2	no	—
649	#479	—	43	2	no	—
650	#479	—	43	2	no	—
651	#478	—	43	2	no	—
652	#478	—	43	2	no	—
653	#477	—	43	1	no	—
654	#476	—	43	1	no	—
655	#475	—	43	1	no	—
656	#474	—	43	1	no	—
657	#467	—	43	2	no	—
658	#466	—	43	2	no	—
659	#465	—	43	2	no	—
660	#465	—	43	2	no	—
661	#465	—	43	2	no	—
662	#465	—	43	2	no	—
663	#464	—	43	2	no	—
664	#464	—	43	2	no	—
665	#463	—	43	2	no	—
666	#463	—	43	2	no	—
667	#462	—	43	1	no	—
668	#461	—	43	1	no	—
669	#460	—	43	1	no	—
670	#459	—	43	1	no	—
671	#452	—	43	2	no	—
672	#451	—	43	2	no	—
673	#450	—	43	2	no	—
674	#449	—	43	2	no	—
675	#448	—	43	2	no	—
676	#447	—	43	2	no	—
677	C₈×Q₈	—	43	1	no	—
678	C₈×Q₈	—	43	1	no	—
679	C₄×Q₁₆	—	43	2	no	—
680	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
681	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
682	C₄×SD₁₆	—	43	2	no	—
683	C₄×SD₁₆	—	43	2	no	—
684	C₄×SD₁₆	—	43	2	no	—
685	C₄×SD₁₆	—	43	2	no	—
686	C₄×SD₁₆	—	43	2	no	—
687	C₄×SD₁₆	—	43	2	no	—
688	C₄×SD₁₆	—	43	2	no	—
689	C₄×SD₁₆	—	43	2	no	—
690	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
691	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
692	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
693	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
694	C₄×D₈	—	43	2	no	—
695	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
696	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
697	C₈×D₄	—	43	2	no	—
698	C₈×D₄	—	43	2	no	—
699	C₈×D₄	—	43	1	no	—
700	C₈×D₄	—	43	1	no	—
701	#431	—	43	1	no	—
702	#431	—	43	2	no	—
703	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
704	C₂×#106	—	43	2	no	—
705	#416	C₂×D₄₃	1	1	yes	characteristic
706	#416	C₂×D₄₃	1	1	yes	characteristic, complemented
707	C₂×#103	—	43	2	no	—
708	C₂×#102	—	43	2	no	—
709	C₂×C₄×C₈	—	43	2	no	—
710	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
711	C₄₃	#61432	1	1	yes	characteristic, complemented, Sylow
712	C₂×#41	—	43	1	no	—
713	C₂×#41	—	86	1	no	—
714	C₂×#41	—	86	1	no	—
715	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
716	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
717	C₂²×Q₈	—	43	2	no	—
718	C₂²×D₄	—	43	2	no	—
719	C₂²×D₄	—	86	1	no	—
720	C₂³×C₄	—	86	2	no	—
721	#135	—	2	4	no	—
722	C₂×Q₁₆	—	43	2	no	—
723	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
724	C₂×SD₁₆	—	43	2	no	—
725	C₂×SD₁₆	—	43	2	no	—
726	C₂×SD₁₆	—	43	2	no	—
727	C₂×SD₁₆	—	43	2	no	—
728	C₂×SD₁₆	—	86	8	no	—
729	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
730	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
731	C₂×D₈	—	43	2	no	—
732	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
733	C₂²×C₈	—	43	2	no	—
734	C₂²×C₈	—	43	2	no	—
735	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
736	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
737	C₄⋊Q₈	—	43	1	no	—
738	C₄⋊Q₈	—	43	1	no	—
739	C₄⋊Q₈	—	43	1	no	—
740	C₄⋊Q₈	—	86	1	no	—
741	C₄⋊Q₈	—	86	1	no	—
742	#127	—	43	1	no	—
743	#126	—	86	2	no	—
744	#126	—	86	2	no	—
745	#126	—	86	2	no	—
746	#126	—	86	2	no	—
747	#126	—	86	2	no	—
748	#125	—	43	2	no	—
749	#125	—	43	2	no	—
750	#125	—	86	1	no	—
751	#125	—	86	2	no	—
752	#125	—	86	2	no	—
753	#125	—	86	1	no	—
754	#124	—	43	2	no	—
755	#124	—	43	2	no	—
756	#124	—	86	1	no	—
757	#124	—	86	2	no	—
758	#124	—	86	1	no	—
759	#123	—	86	2	no	—
760	#123	—	86	2	no	—
761	#123	—	86	2	no	—
762	#123	—	86	2	no	—
763	#123	—	86	2	no	—
764	#123	—	86	2	no	—
765	#123	—	86	2	no	—
766	C₂²⋊Q₈	—	43	2	no	—
767	C₂²⋊Q₈	—	43	2	no	—
768	C₂²⋊Q₈	—	43	2	no	—
769	C₂²⋊Q₈	—	86	2	no	—
770	C₂²⋊Q₈	—	86	2	no	—
771	C₂²⋊Q₈	—	86	2	no	—
772	C₂²⋊Q₈	—	86	1	no	—
773	C₂²⋊Q₈	—	86	2	no	—
774	C₂²⋊Q₈	—	86	1	no	—
775	C₂²⋊Q₈	—	86	1	no	—
776	C₂²⋊Q₈	—	86	1	no	—
777	#121	—	43	2	no	—
778	#121	—	43	2	no	—
779	#121	—	43	2	no	—
780	#121	—	86	2	no	—
781	#121	—	86	2	no	—
782	#121	—	86	1	no	—
783	#121	—	86	2	no	—
784	#121	—	86	1	no	—
785	#120	—	86	2	no	—
786	#120	—	86	2	no	—
787	C₄×Q₈	—	43	1	no	—
788	C₄×Q₈	—	43	1	no	—
789	C₄×Q₈	—	43	2	no	—
790	C₄×Q₈	—	43	2	no	—
791	C₄×Q₈	—	43	2	no	—
792	C₄×Q₈	—	86	2	no	—
793	C₄×Q₈	—	86	1	no	—
794	C₄×Q₈	—	86	2	no	—
795	C₄×Q₈	—	86	1	no	—
796	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
797	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
798	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
799	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	43	2	no	—
805	C₄×D₄	—	43	2	no	—
806	C₄×D₄	—	43	2	no	—
807	C₄×D₄	—	43	2	no	—
808	C₄×D₄	—	43	1	no	—
809	C₄×D₄	—	43	1	no	—
810	C₄×D₄	—	43	2	no	—
811	C₄×D₄	—	86	2	no	—
812	C₄×D₄	—	86	1	no	—
813	C₄×D₄	—	86	2	no	—
814	C₄×D₄	—	86	1	no	—
815	C₄×D₄	—	86	1	no	—
816	C₄×D₄	—	86	2	no	—
817	C₄×D₄	—	86	2	no	—
818	C₄×D₄	—	86	2	no	—
819	C₄×D₄	—	86	2	no	—
820	C₄×D₄	—	86	1	no	—
821	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
822	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
823	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
824	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	43	1	no	—
828	#117	—	43	2	no	—
829	#117	—	86	2	no	—
830	#117	—	86	2	no	—
831	#117	—	86	2	no	—
832	#117	—	86	1	no	—
833	#117	—	86	1	no	—
834	#117	C₂²×D₄₃	1	1	yes	characteristic
835	#117	C₂²×D₄₃	1	1	yes	characteristic
836	C₂×C₄⋊C₄	—	43	2	no	—
837	C₂×C₄⋊C₄	—	43	2	no	—
838	C₂×C₄⋊C₄	—	86	2	no	—
839	C₂×C₄⋊C₄	—	86	1	no	—
840	C₂×C₂²⋊C₄	—	86	2	no	—
841	C₂×C₂²⋊C₄	—	86	2	no	—
842	C₂×C₄²	—	2	1	no	—
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	—	43	2	no	—
845	C₂×C₄²	—	86	2	no	—
846	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
847	#107	—	43	2	no	—
848	#107	—	43	2	no	—
849	#107	C₂²×D₄₃	1	1	yes	characteristic
850	#107	C₂²×D₄₃	1	1	yes	characteristic
851	#106	—	43	2	no	—
852	#106	—	43	2	no	—
853	#106	—	43	2	no	—
854	#106	—	43	2	no	—
855	#106	C₂²×D₄₃	1	1	yes	characteristic
856	#106	C₂²×D₄₃	1	1	yes	characteristic
857	C₄⋊C₈	—	43	2	no	—
858	C₄⋊C₈	—	43	2	no	—
859	C₄⋊C₈	—	43	1	no	—
860	C₄⋊C₈	—	43	1	no	—
861	#103	—	43	2	no	—
862	#103	—	43	2	no	—
863	#103	—	43	2	no	—
864	#103	—	43	2	no	—
865	#103	—	43	2	no	—
866	#103	—	43	2	no	—
867	#103	C₂²×D₄₃	1	1	yes	characteristic
868	#103	C₂²×D₄₃	1	1	yes	characteristic
869	#103	C₂²×D₄₃	1	1	yes	characteristic
870	#103	C₂²×D₄₃	1	1	yes	characteristic
871	#102	—	43	2	no	—
872	#102	—	43	2	no	—
873	#102	—	43	2	no	—
874	#102	—	43	2	no	—
875	#102	—	43	2	no	—
876	#102	—	43	2	no	—
877	#102	C₂²×D₄₃	1	1	yes	characteristic
878	#102	C₂²×D₄₃	1	1	yes	characteristic
879	#102	C₂²×D₄₃	1	1	yes	characteristic
880	#102	C₂²×D₄₃	1	1	yes	characteristic
881	C₂²⋊C₈	—	43	2	no	—
882	C₂²⋊C₈	—	43	2	no	—
883	C₂²⋊C₈	—	43	2	no	—
884	C₄×C₈	—	43	2	no	—
885	C₄×C₈	—	43	2	no	—
886	C₄×C₈	—	43	2	no	—
887	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
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	C₂⁴	—	86	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	4	1	no	—
895	#41	—	4	1	no	—
896	#41	—	86	4	no	—
897	#41	—	344	2	no	—
898	#41	—	172	4	no	—
899	C₂×Q₈	—	43	1	no	—
900	C₂×Q₈	—	43	2	no	—
901	C₂×Q₈	—	86	2	no	—
902	C₂×Q₈	—	86	1	no	—
903	C₂×Q₈	—	86	1	no	—
904	C₂×Q₈	—	86	4	no	—
905	C₂×Q₈	—	172	2	no	—
906	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
907	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	43	2	no	—
911	C₂×D₄	—	43	1	no	—
912	C₂×D₄	—	43	2	no	—
913	C₂×D₄	—	86	2	no	—
914	C₂×D₄	—	86	2	no	—
915	C₂×D₄	—	86	4	no	—
916	C₂×D₄	—	86	2	no	—
917	C₂×D₄	—	86	2	no	—
918	C₂×D₄	—	86	1	no	—
919	C₂×D₄	—	86	1	no	—
920	C₂×D₄	—	172	4	no	—
921	C₂×D₄	—	172	2	no	—
922	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
923	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	1	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	43	2	no	—
931	C₂²×C₄	—	43	2	no	—
932	C₂²×C₄	—	43	2	no	—
933	C₂²×C₄	—	86	2	no	—
934	C₂²×C₄	—	86	2	no	—
935	C₂²×C₄	—	86	2	no	—
936	C₂²×C₄	—	86	2	no	—
937	C₂²×C₄	—	86	2	no	—
938	C₂²×C₄	—	86	2	no	—
939	C₂²×C₄	—	344	4	no	—
940	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
941	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
943	Q₁₆	—	2	2	no	—
944	Q₁₆	—	172	2	no	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	86	4	no	—
947	SD₁₆	—	86	4	no	—
948	SD₁₆	—	86	4	no	—
949	SD₁₆	—	172	2	no	—
950	SD₁₆	#10621898	1	4	yes	complemented
951	D₈	—	2	2	no	—
952	D₈	—	172	2	no	—
953	C₂×C₈	—	2	2	no	—
954	C₂×C₈	—	4	1	no	—
955	C₂×C₈	—	43	2	no	—
956	C₂×C₈	—	43	2	no	—
957	C₂×C₈	—	86	4	no	—
958	C₂×C₈	—	172	2	no	—
959	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
960	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
961	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
962	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	43	1	no	—
968	C₄⋊C₄	—	43	1	no	—
969	C₄⋊C₄	—	43	2	no	—
970	C₄⋊C₄	—	43	2	no	—
971	C₄⋊C₄	—	43	2	no	—
972	C₄⋊C₄	—	43	2	no	—
973	C₄⋊C₄	—	86	2	no	—
974	C₄⋊C₄	—	86	2	no	—
975	C₄⋊C₄	—	86	2	no	—
976	C₄⋊C₄	—	86	2	no	—
977	C₄⋊C₄	—	86	2	no	—
978	C₄⋊C₄	—	86	2	no	—
979	C₄⋊C₄	—	86	2	no	—
980	C₄⋊C₄	—	86	2	no	—
981	C₄⋊C₄	—	86	2	no	—
982	C₄⋊C₄	—	86	2	no	—
983	C₄⋊C₄	—	86	1	no	—
984	C₄⋊C₄	—	86	2	no	—
985	C₄⋊C₄	—	86	2	no	—
986	C₄⋊C₄	—	86	1	no	—
987	C₄⋊C₄	—	86	1	no	—
988	C₄⋊C₄	—	86	1	no	—
989	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	43	2	no	—
1000	C₂²⋊C₄	—	43	2	no	—
1001	C₂²⋊C₄	—	43	2	no	—
1002	C₂²⋊C₄	—	86	2	no	—
1003	C₂²⋊C₄	—	86	2	no	—
1004	C₂²⋊C₄	—	86	2	no	—
1005	C₂²⋊C₄	—	86	2	no	—
1006	C₂²⋊C₄	—	86	2	no	—
1007	C₂²⋊C₄	—	86	2	no	—
1008	C₂²⋊C₄	—	86	2	no	—
1009	C₂²⋊C₄	—	86	2	no	—
1010	C₂²⋊C₄	—	86	2	no	—
1011	C₂²⋊C₄	—	86	2	no	—
1012	C₂²⋊C₄	—	86	2	no	—
1013	C₂²⋊C₄	—	86	2	no	—
1014	C₂²⋊C₄	—	86	2	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	1	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	43	2	no	—
1022	C₄²	—	43	2	no	—
1023	C₄²	—	43	2	no	—
1024	C₄²	—	86	2	no	—
1025	C₄²	—	86	2	no	—
1026	C₄²	—	86	2	no	—
1027	C₄²	D₄×D₄₃	1	1	yes	characteristic
1028	C₄²	D₄×D₄₃	1	1	yes	characteristic
1029	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1030	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	43	2	no	—
1034	C₂³	—	86	2	no	—
1035	C₂³	—	344	2	no	—
1036	C₂³	—	172	4	no	—
1037	C₂³	—	172	4	no	—
1038	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	86	2	no	—
1043	Q₈	—	86	2	no	—
1044	Q₈	—	86	2	no	—
1045	Q₈	—	344	1	no	—
1046	Q₈	—	172	4	no	—
1047	Q₈	—	172	2	no	—
1048	Q₈	C₂×#10621898	1	2	yes	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	1	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	43	4	no	—
1055	D₄	—	86	4	no	—
1056	D₄	—	86	2	no	—
1057	D₄	—	86	2	no	—
1058	D₄	—	344	1	no	—
1059	D₄	—	344	2	no	—
1060	D₄	—	172	4	no	—
1061	D₄	—	172	4	no	—
1062	D₄	—	172	4	no	—
1063	D₄	—	172	2	no	—
1064	D₄	C₂×#10621898	1	2	yes	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	43	2	no	—
1082	C₂×C₄	—	43	2	no	—
1083	C₂×C₄	—	43	2	no	—
1084	C₂×C₄	—	86	4	no	—
1085	C₂×C₄	—	86	4	no	—
1086	C₂×C₄	—	86	2	no	—
1087	C₂×C₄	—	86	2	no	—
1088	C₂×C₄	—	86	2	no	—
1089	C₂×C₄	—	86	2	no	—
1090	C₂×C₄	—	86	2	no	—
1091	C₂×C₄	—	344	2	no	—
1092	C₂×C₄	—	344	2	no	—
1093	C₂×C₄	—	344	2	no	—
1094	C₂×C₄	—	172	4	no	—
1095	C₂×C₄	—	172	4	no	—
1096	C₂×C₄	—	172	4	no	—
1097	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1098	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1099	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1100	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1101	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1102	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1103	C₈	—	2	1	no	—
1104	C₈	—	2	1	no	—
1105	C₈	—	2	1	no	—
1106	C₈	—	86	2	no	—
1107	C₈	—	86	2	no	—
1108	C₈	C₂×#10621898	1	2	yes	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	43	4	no	—
1119	C₂²	—	86	2	no	—
1120	C₂²	—	86	2	no	—
1121	C₂²	—	344	8	no	—
1122	C₂²	—	172	2	no	—
1123	C₂²	—	172	2	no	—
1124	C₂²	—	172	2	no	—
1125	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	86	2	no	—
1136	C₄	—	86	2	no	—
1137	C₄	—	86	2	no	—
1138	C₄	—	172	2	no	—
1139	C₄	—	172	2	no	—
1140	C₄	—	172	2	no	—
1141	C₄	#135×D₄₃	1	2	yes	—
1142	C₄	#14583706	1	2	yes	—
1143	C₄	C₂²×#10621898	1	1	yes	characteristic
1144	C₄	#14583735	1	1	yes	characteristic
1145	C₂	—	4	1	no	—
1146	C₂	—	4	2	no	—
1147	C₂	—	8	1	no	—
1148	C₂	—	86	4	no	—
1149	C₂	—	344	2	no	—
1150	C₂	D₄×#10621898	1	1	yes	characteristic
1151	C₂	C₂×#135×D₄₃	1	1	yes	characteristic
1152	C₂	C₂×#14583706	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₄×#135	D₄₃
hypocenter	C₄₃	#61432
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #19148217	C₂	semidirect
2. #19148205	C₂	semidirect
3. #19147589	C₂	semidirect
4. #19147468	C₂	semidirect
5. #19147289	C₂	semidirect
6. #19147242	C₂	semidirect
7. #19146975	C₂	semidirect
8. #19146954	C₂	semidirect
9. #19146498	C₂	semidirect
10. #19146473	C₂	semidirect
11. #19146431	C₂	semidirect
12. #19146410	C₂	semidirect
13. #19146296	C₂	semidirect
14. SD₁₆×D₁₇₂	C₂	semidirect
15. #19145161	C₂	semidirect
16. #19145154	C₂	semidirect
17. #19144679	C₂	semidirect
18. #19144666	C₂	semidirect
19. #19144655	C₂	semidirect
20. #19144640	C₂	semidirect
21. C₈×#10621898	C₂	semidirect
22. C₄×SD₁₆×D₄₃	C₂	semidirect
23. C₄×#135×C₄₃	C₂	semidirect
26. #14583628	C₂²	semidirect
28. #14583619	C₂²	semidirect
34. #14583588	C₂²	semidirect
37. #14583556	C₂²	semidirect
44. #14583456	C₂²	semidirect
49. #14583431	C₂²	semidirect
53. C₄×Q₈×D₄₃	C₂²	semidirect
56. #14583299	C₂²	semidirect
57. #14583297	C₂²	semidirect
58. #14583280	C₂²	semidirect
60. #14583255	C₂²	semidirect
61. #14583252	C₂²	semidirect
62. #14583250	C₂²	semidirect
64. #14583240	C₂²	semidirect
65. #14583236	C₂²	semidirect
66. #14583228	C₂²	semidirect
67. #14583223	C₂²	semidirect
68. #14583216	C₂²	semidirect
70. #14583205	C₂²	semidirect
71. #14583204	C₂²	semidirect
72. #14583202	C₂²	semidirect
74. #14583194	C₂²	semidirect
75. #14583189	C₂²	semidirect
76. #14583184	C₂²	semidirect
78. #14583139	C₂²	semidirect
81. #14583128	C₂²	semidirect
82. #14583128	C₂²	semidirect
83. #14583125	C₂²	semidirect
84. #14583124	C₂²	semidirect
85. #14583123	C₂²	semidirect
86. #14583113	C₂²	semidirect
88. #14583109	C₂²	semidirect
93. #14583053	C₂²	semidirect
95. #14583044	C₂²	semidirect
98. C₈×Dic₈₆	C₂²	semidirect
99. C₈×Dic₈₆	C₂²	semidirect
100. C₄×#10621885	C₂²	semidirect
102. C₄×#10621873	C₂²	semidirect
103. C₄×#10621873	C₂²	semidirect
105. C₄×#10621884	C₂²	semidirect
106. #14582986	C₂²	semidirect
108. #14582984	C₂²	semidirect
109. C₄×#10621882	C₂²	semidirect
112. C₈×C₂²⋊D₄₃	C₂²	semidirect
113. C₈×C₂²⋊D₄₃	C₂²	semidirect
114. #14582952	C₂²	semidirect
115. #14582950	C₂²	semidirect
116. #106×D₄₃	C₂²	semidirect
117. #103×D₄₃	C₂²	semidirect
119. C₄×C₈×D₄₃	C₂²	semidirect
122. C₄×#41×C₄₃	C₂²	semidirect
123. C₄×Q₁₆×C₄₃	C₂²	semidirect
124. C₄×Q₁₆×C₄₃	C₂²	semidirect
127. C₄×SD₁₆×C₄₃	C₂²	semidirect
128. C₄×SD₁₆×C₄₃	C₂²	semidirect
131. C₄₃×#427	C₂²	semidirect
133. C₄₃×#416	C₂²	semidirect
134. C₂×C₄×C₈×C₄₃	C₂²	semidirect
368. SD₁₆×C₄₃	#41	semidirect
510. D₁₇₂	#135	semidirect
590. C₄×#135	D₄₃	semidirect
631. C₄×#41	C₂×D₄₃	semidirect
680. C₄×Q₁₆	C₂×D₄₃	semidirect
681. C₄×Q₁₆	C₂×D₄₃	semidirect
692. C₄×SD₁₆	C₂×D₄₃	semidirect
693. C₄×SD₁₆	C₂×D₄₃	semidirect
703. #427	C₂×D₄₃	semidirect
706. #416	C₂×D₄₃	semidirect
710. C₂×C₄×C₈	C₂×D₄₃	semidirect
711. C₄₃	#61432	semidirect
950. SD₁₆	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148217	2
#19148205	2
#19147589	2
#19147468	2
#19147289	2
#19147242	2
#19146975	2
#19146954	2
#19146498	2
#19146473	2
#19146431	2
#19146410	2
#19146296	2
SD₁₆×D₁₇₂	2
#19145161	2
#19145154	2
#19144679	2
#19144666	2
#19144655	2
#19144640	2
C₈×#10621898	2
C₄×SD₁₆×D₄₃	2
C₄×#135×C₄₃	2
#61432	43