Subgroups — #25988828

Order 11008.

1952 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148205	C₂	1	1	yes	maximal, characteristic, complemented
2	#19147603	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147591	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147251	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147240	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146497	C₂	1	2	yes	maximal, complemented
7	#19146471	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146445	C₂	1	2	yes	maximal, complemented
9	#19146419	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146303	C₂	1	2	yes	maximal, complemented
11	D₄×#10621884	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146276	C₂	1	2	yes	maximal, complemented
13	D₄×#10621882	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145942	C₂	1	2	yes	maximal, complemented
15	#19145921	C₂	1	1	yes	maximal, characteristic, complemented
16	#19145560	C₂	1	2	yes	maximal, complemented
17	#19145528	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144638	C₂	1	2	yes	maximal, complemented
19	#19144607	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144044	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#14583111	C₂	1	2	yes	maximal, complemented
22	#19143706	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063345	C₂²	1	2	yes	complemented
25	C₂²×#10621884	C₂²	1	2	yes	complemented
26	C₂²×#10621882	C₂²	1	2	yes	—
27	#14583634	C₂²	1	1	yes	characteristic, complemented
28	#14583609	C₂²	1	1	yes	characteristic, complemented
29	#14583606	C₂²	1	1	yes	characteristic
30	#14583595	C₂²	1	2	yes	complemented
31	#14583593	—	2	1	no	—
32	#14583573	—	2	2	no	—
33	#14583545	C₂²	1	2	yes	complemented
34	#14583537	—	2	1	no	—
35	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
36	#14583449	C₂²	1	1	yes	characteristic, complemented
37	#14583436	—	2	1	no	—
38	#14583433	C₂²	1	2	yes	complemented
39	#14583408	—	2	2	no	—
40	C₄×#10621898	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
42	C₄×D₄×D₄₃	—	2	1	no	—
43	#14583281	C₂²	1	2	yes	complemented
44	#14583281	C₂²	1	2	yes	complemented
45	#14583275	C₂²	1	1	yes	characteristic
46	#14583273	C₂²	1	1	yes	characteristic, complemented
47	#14583253	C₂²	1	2	yes	complemented
48	#14583253	C₂²	1	2	yes	complemented
49	#14583249	C₂²	1	1	yes	characteristic, complemented
50	#14583245	C₂²	1	1	yes	characteristic, complemented
51	#14583237	C₂²	1	1	yes	characteristic, complemented
52	#14583232	C₂²	1	2	yes	complemented
53	#14583220	C₂²	1	1	yes	characteristic, complemented
54	#14583215	C₂²	1	2	yes	complemented
55	#14583206	C₂²	1	2	yes	complemented
56	#14583203	C₂²	1	1	yes	characteristic, complemented
57	#14583199	C₂²	1	2	yes	complemented
58	#14583196	C₂²	1	1	yes	characteristic, complemented
59	#14583196	C₂²	1	2	yes	complemented
60	#14583194	C₂²	1	1	yes	characteristic, complemented
61	#14583189	C₂²	1	1	yes	characteristic, complemented
62	#14583138	C₂²	1	2	yes	complemented
63	#14583133	C₂²	1	2	yes	—
64	#14583133	C₂²	1	2	yes	complemented
65	#14583130	C₂²	1	2	yes	complemented
66	#14583130	C₂²	1	2	yes	complemented
67	#14583126	C₂²	1	2	yes	complemented
68	#14583121	C₂²	1	2	yes	complemented
69	#14583118	C₂²	1	1	yes	characteristic, complemented
70	#14583118	C₂²	1	2	yes	complemented
71	#14583114	C₂²	1	2	yes	complemented
72	#14583111	C₂²	1	2	yes	—
73	#14583111	C₂²	1	1	yes	characteristic
74	#14583111	C₂²	1	2	yes	complemented
75	#14583111	C₂²	1	2	yes	complemented
76	#14583111	C₂²	1	2	yes	complemented
77	#14583111	C₂²	1	2	yes	complemented
78	#14583111	C₂²	1	2	yes	complemented
79	#14583111	C₂²	1	2	yes	complemented
80	#14583111	C₂²	1	2	yes	complemented
81	#14583106	C₂²	1	1	yes	characteristic, complemented
82	#14583101	C₂²	1	1	yes	characteristic, complemented
83	#14583099	C₂²	1	1	yes	characteristic, complemented
84	#14583096	C₂²	1	1	yes	characteristic, complemented
85	#14583094	C₂²	1	1	yes	characteristic
86	#14583091	C₂²	1	1	yes	characteristic
87	#14583059	C₂²	1	1	yes	characteristic, complemented
88	#14583055	C₂²	1	2	yes	complemented
89	#14583050	C₂²	1	2	yes	complemented
90	#14583049	C₂²	1	2	yes	complemented
91	#14583044	C₂²	1	2	yes	complemented
92	#14583044	C₂²	1	2	yes	complemented
93	#14583042	C₂²	1	1	yes	characteristic
94	#14583038	C₂²	1	2	yes	complemented
95	#14583033	C₂²	1	2	yes	—
96	#14583032	C₂²	1	2	yes	—
97	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
98	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
99	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10621884	C₂²	1	2	yes	complemented
101	C₄×#10621884	C₂²	1	1	yes	characteristic, complemented
102	C₄×#10621884	C₂²	1	2	yes	complemented
103	C₄×#10621883	C₂²	1	1	yes	characteristic, complemented
104	C₄×#10621882	C₂²	1	1	yes	characteristic
105	C₄×#10621882	C₂²	1	2	yes	complemented
106	C₄×#10621882	C₂²	1	2	yes	complemented
107	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
108	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
109	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
110	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
111	#14582952	C₂²	1	1	yes	characteristic, complemented
112	#14582952	C₂²	1	2	yes	complemented
113	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
114	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
115	#14582895	C₂²	1	2	yes	complemented
116	C₂×#13063249	C₂²	1	2	yes	complemented
117	C₂×#13063246	C₂²	1	2	yes	complemented
118	C₄₃×#559	C₂²	1	1	yes	characteristic, complemented
119	C₄₃×#556	C₂²	1	1	yes	characteristic, complemented
120	C₄₃×#555	—	2	1	no	—
121	C₄₃×#551	—	2	2	no	—
122	D₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
123	C₄₃×#548	C₂²	1	2	yes	complemented
124	C₄₃×#546	—	2	1	no	—
125	C₄₃×#546	C₂²	1	2	yes	complemented
126	D₄²×C₄₃	C₂²	1	1	yes	characteristic
127	C₄₃×#542	—	2	1	no	—
128	C₄₃×#538	—	2	2	no	—
129	C₄₃×#532	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#529	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#529	C₂²	1	2	yes	complemented
132	C₂×#124×C₄₃	C₂²	1	2	yes	complemented
133	C₄₃×#518	—	2	1	no	—
134	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621898	—	2	1	no	—
136	C₂×#10621898	C₂³	1	1	yes	characteristic
137	C₂²×D₁₇₂	C₂³	1	2	yes	—
138	C₂×D₄×D₄₃	—	2	1	no	—
139	C₂²×C₄×D₄₃	—	2	2	no	—
140	#13063345	—	4	4	no	—
141	C₂×#10621885	C₂³	1	1	yes	characteristic
142	C₂×#10621885	C₂³	1	2	yes	—
143	C₂×#10621883	C₂³	1	1	yes	characteristic
144	C₂×#10621883	C₂³	1	2	yes	—
145	C₂×#10621884	—	4	4	no	—
146	C₂×#10621884	C₂³	1	2	yes	—
147	C₂×#10621884	C₂³	1	1	yes	characteristic
148	C₂×#10621884	C₂³	1	2	yes	—
149	C₂×#10621884	C₂³	1	2	yes	—
150	C₂×#10621884	C₂³	1	2	yes	—
151	C₂×#10621882	—	4	4	no	—
152	C₂×#10621882	C₂³	1	1	yes	characteristic
153	C₂×#10621882	C₂³	1	2	yes	—
154	C₂×#10621882	C₂³	1	2	yes	—
155	C₂×#10621882	C₂³	1	2	yes	—
156	C₂×#10621882	C₂³	1	2	yes	—
157	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
158	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
159	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
160	#13063325	C₂³	1	1	yes	characteristic
161	#13063322	C₂³	1	1	yes	characteristic
162	#13063320	—	2	2	no	—
163	#13063319	—	2	2	no	—
164	#13063317	C₂³	1	2	yes	—
165	#13063316	—	2	1	no	—
166	#13063314	—	2	1	no	—
167	#13063313	—	2	1	no	—
168	#13063313	C₂³	1	2	yes	—
169	#13063310	—	2	2	no	—
170	#13063310	—	2	2	no	—
171	#13063308	—	2	2	no	—
172	#13063307	—	2	2	no	—
173	#13063304	C₂³	1	2	yes	—
174	#13063303	—	2	2	no	—
175	#13063302	—	2	2	no	—
176	#13063301	—	2	1	no	—
177	#13063300	—	2	1	no	—
178	#13063299	—	2	1	no	—
179	#13063299	C₂³	1	2	yes	—
180	#13063299	C₂³	1	2	yes	—
181	#13063298	—	2	2	no	—
182	#13063297	—	2	2	no	—
183	#13063295	—	2	2	no	—
184	#13063293	—	2	2	no	—
185	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
186	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
187	C₄×D₁₇₂	—	2	2	no	—
188	C₄×D₁₇₂	—	2	1	no	—
189	C₄×D₁₇₂	—	2	2	no	—
190	C₄×D₁₇₂	C₂³	1	2	yes	—
191	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
192	C₄×D₁₇₂	C₂³	1	2	yes	—
193	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
194	C₄×D₁₇₂	C₂³	1	2	yes	—
195	D₄×Dic₄₃	—	2	1	no	—
196	#13063287	—	2	1	no	—
197	C₄×C₂²⋊D₄₃	—	2	1	no	—
198	C₄×C₂²⋊D₄₃	—	2	2	no	—
199	C₄×C₂²⋊D₄₃	—	2	1	no	—
200	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
201	#13063284	C₂³	1	1	yes	characteristic
202	#13063282	—	2	1	no	—
203	#13063282	—	2	2	no	—
204	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
205	C₄⋊C₄×D₄₃	—	2	1	no	—
206	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
207	C₂²⋊C₄×D₄₃	—	2	2	no	—
208	C₄²×D₄₃	—	2	1	no	—
209	#13063258	C₂³	1	1	yes	characteristic
210	#13063258	C₂³	1	2	yes	—
211	#13063258	C₂³	1	1	yes	characteristic
212	#13063256	C₂³	1	2	yes	—
213	#13063256	C₂³	1	1	yes	characteristic
214	#13063256	C₂³	1	1	yes	characteristic
215	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
218	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
219	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
220	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
221	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
222	#13063249	C₂³	1	2	yes	—
223	#13063249	C₂³	1	2	yes	—
224	#13063249	C₂³	1	2	yes	—
225	#13063249	C₂³	1	2	yes	—
226	#13063249	C₂³	1	2	yes	—
227	#13063249	C₂³	1	1	yes	characteristic
228	#13063249	C₂³	1	1	yes	characteristic
229	#13063248	C₂³	1	1	yes	characteristic
230	#13063248	C₂³	1	1	yes	characteristic
231	#13063246	C₂³	1	2	yes	—
232	#13063246	C₂³	1	2	yes	—
233	#13063246	C₂³	1	2	yes	—
234	#13063246	C₂³	1	2	yes	—
235	#13063246	C₂³	1	2	yes	—
236	#13063246	C₂³	1	1	yes	characteristic
237	#13063246	C₂³	1	1	yes	characteristic
238	#13063245	C₂³	1	1	yes	characteristic
239	#13063245	C₂³	1	2	yes	—
240	#13063245	C₂³	1	1	yes	characteristic
241	#13063245	C₂³	1	2	yes	—
242	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
243	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
244	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
245	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
246	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
248	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
249	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
250	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
251	C₂×#41×C₄₃	C₂³	1	2	yes	—
252	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
253	C₂²×D₄×C₄₃	—	2	1	no	—
254	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
255	C₄⋊Q₈×C₄₃	—	2	1	no	—
256	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
257	#127×C₄₃	C₂³	1	1	yes	characteristic
258	#126×C₄₃	—	2	2	no	—
259	#126×C₄₃	—	2	2	no	—
260	#126×C₄₃	—	2	1	no	—
261	#125×C₄₃	C₂³	1	1	yes	characteristic
262	#124×C₄₃	—	2	1	no	—
263	#124×C₄₃	—	2	2	no	—
264	#124×C₄₃	—	2	2	no	—
265	#124×C₄₃	—	2	2	no	—
266	#124×C₄₃	C₂³	1	1	yes	characteristic
267	#124×C₄₃	C₂³	1	2	yes	—
268	#124×C₄₃	C₂³	1	2	yes	—
269	#124×C₄₃	C₂³	1	2	yes	—
270	#123×C₄₃	—	2	1	no	—
271	#123×C₄₃	—	2	2	no	—
272	#123×C₄₃	—	2	2	no	—
273	#123×C₄₃	—	2	2	no	—
274	C₂²⋊Q₈×C₄₃	—	2	1	no	—
275	C₂²⋊Q₈×C₄₃	—	2	2	no	—
276	C₂²⋊Q₈×C₄₃	—	2	2	no	—
277	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
278	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
279	#121×C₄₃	—	2	2	no	—
280	#121×C₄₃	—	2	1	no	—
281	#121×C₄₃	—	2	1	no	—
282	#121×C₄₃	—	2	1	no	—
283	#121×C₄₃	—	2	2	no	—
284	#121×C₄₃	C₂³	1	1	yes	characteristic
285	#121×C₄₃	C₂³	1	2	yes	—
286	#120×C₄₃	—	2	2	no	—
287	#120×C₄₃	—	2	2	no	—
288	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
289	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
290	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
291	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₃	—	2	1	no	—
293	C₄×D₄×C₄₃	—	2	2	no	—
294	C₄×D₄×C₄₃	—	2	1	no	—
295	C₄×D₄×C₄₃	—	2	1	no	—
296	C₄×D₄×C₄₃	—	2	2	no	—
297	C₄×D₄×C₄₃	—	2	1	no	—
298	C₄×D₄×C₄₃	—	2	1	no	—
299	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
300	C₄×D₄×C₄₃	D₄	1	2	yes	—
301	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
302	C₄×D₄×C₄₃	C₂³	1	2	yes	—
303	C₄×D₄×C₄₃	C₂³	1	2	yes	—
304	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
305	#117×C₄₃	—	2	1	no	—
306	#117×C₄₃	—	2	1	no	—
307	#117×C₄₃	—	2	2	no	—
308	#117×C₄₃	D₄	1	2	yes	—
309	#117×C₄₃	D₄	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
311	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
312	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
313	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
314	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
315	C₂⁴×C₄₃	—	2	2	no	—
316	C₂³×D₄₃	—	2	2	no	—
317	#41×C₄₃	—	2	4	no	—
318	#41×C₄₃	—	4	2	no	—
319	#41×C₄₃	—	4	2	no	—
320	C₂×Q₈×C₄₃	—	2	2	no	—
321	C₂×Q₈×C₄₃	—	4	2	no	—
322	C₂×Q₈×C₄₃	—	4	2	no	—
323	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
326	C₂×D₄×C₄₃	—	2	1	no	—
327	C₂×D₄×C₄₃	—	2	1	no	—
328	C₂×D₄×C₄₃	—	2	2	no	—
329	C₂×D₄×C₄₃	—	2	2	no	—
330	C₂×D₄×C₄₃	—	2	1	no	—
331	C₂×D₄×C₄₃	—	2	2	no	—
332	C₂×D₄×C₄₃	—	4	4	no	—
333	C₂×D₄×C₄₃	—	4	2	no	—
334	C₂×D₄×C₄₃	—	4	2	no	—
335	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₄₃	—	2	1	no	—
340	C₂²×C₄×C₄₃	—	2	2	no	—
341	C₂²×C₄×C₄₃	—	2	2	no	—
342	C₂²×C₄×C₄₃	—	2	2	no	—
343	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
345	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
346	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
348	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₂²⋊D₄₃	—	2	2	no	—
350	C₂×C₂²⋊D₄₃	—	2	1	no	—
351	C₂×C₂²⋊D₄₃	—	2	2	no	—
352	C₂²×Dic₄₃	—	2	2	no	—
353	D₄×D₄₃	—	4	4	no	—
354	#10621898	—	2	2	no	—
355	#10621898	—	4	1	no	—
356	#10621898	—	8	2	no	—
357	C₂×D₁₇₂	—	2	1	no	—
358	C₂×D₁₇₂	—	2	2	no	—
359	C₂×D₁₇₂	—	2	1	no	—
360	C₂×D₁₇₂	—	2	4	no	—
361	C₂×D₁₇₂	—	4	2	no	—
362	C₂×D₁₇₂	C₂⁴	1	2	yes	—
363	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
364	C₂×C₄×D₄₃	—	2	1	no	—
365	C₂×C₄×D₄₃	—	2	1	no	—
366	C₂×C₄×D₄₃	—	2	1	no	—
367	C₂×C₄×D₄₃	—	2	2	no	—
368	C₂×C₄×D₄₃	—	2	2	no	—
369	C₂×C₄×D₄₃	—	2	2	no	—
370	C₂×C₄×D₄₃	—	8	4	no	—
371	C₂×Dic₈₆	—	2	1	no	—
372	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₄₃	—	2	1	no	—
374	C₄⋊C₄×C₄₃	—	2	1	no	—
375	C₄⋊C₄×C₄₃	—	2	1	no	—
376	C₄⋊C₄×C₄₃	—	2	1	no	—
377	C₄⋊C₄×C₄₃	—	2	2	no	—
378	C₄⋊C₄×C₄₃	—	2	1	no	—
379	C₄⋊C₄×C₄₃	—	2	2	no	—
380	C₄⋊C₄×C₄₃	—	2	1	no	—
381	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
384	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
385	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
387	C₂²⋊C₄×C₄₃	—	2	2	no	—
388	C₂²⋊C₄×C₄₃	—	2	1	no	—
389	C₂²⋊C₄×C₄₃	—	2	1	no	—
390	C₂²⋊C₄×C₄₃	—	2	1	no	—
391	C₂²⋊C₄×C₄₃	—	2	2	no	—
392	C₂²⋊C₄×C₄₃	—	2	2	no	—
393	C₂²⋊C₄×C₄₃	—	2	2	no	—
394	C₂²⋊C₄×C₄₃	—	2	2	no	—
395	C₂²⋊C₄×C₄₃	—	2	2	no	—
396	C₂²⋊C₄×C₄₃	—	2	2	no	—
397	C₂²⋊C₄×C₄₃	—	2	1	no	—
398	C₂²⋊C₄×C₄₃	—	2	2	no	—
399	C₂²⋊C₄×C₄₃	—	2	2	no	—
400	C₂²⋊C₄×C₄₃	—	2	1	no	—
401	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
404	C₄²×C₄₃	—	2	2	no	—
405	C₄²×C₄₃	—	2	1	no	—
406	C₄²×C₄₃	C₂×D₄	1	2	yes	—
407	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
408	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
409	C₄²×C₄₃	C₂×D₄	1	2	yes	—
410	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
411	C₄²×C₄₃	C₂⁴	1	2	yes	—
412	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
413	C₂²⋊Dic₄₃	—	2	2	no	—
414	C₂²⋊Dic₄₃	—	2	1	no	—
415	#10621885	—	4	1	no	—
416	#10621885	—	4	2	no	—
417	#10621884	—	2	2	no	—
418	#10621884	—	2	4	no	—
419	#10621884	—	4	2	no	—
420	#10621884	—	4	2	no	—
421	#10621884	—	4	2	no	—
422	#10621883	—	4	1	no	—
423	#10621883	—	4	2	no	—
424	#10621882	—	2	2	no	—
425	#10621882	—	2	4	no	—
426	#10621882	—	4	2	no	—
427	#10621882	—	4	2	no	—
428	#10621882	—	4	2	no	—
429	(C₂×D₄₃)⋊C₄	—	2	2	no	—
430	(C₂×D₄₃)⋊C₄	—	2	2	no	—
431	(C₂×D₄₃)⋊C₄	—	2	1	no	—
432	(C₂×D₄₃)⋊C₄	—	2	2	no	—
433	(C₂×D₄₃)⋊C₄	—	2	2	no	—
434	(C₂×D₄₃)⋊C₄	—	2	2	no	—
435	(C₂×D₄₃)⋊C₄	—	2	1	no	—
436	(C₂×D₄₃)⋊C₄	—	2	2	no	—
437	(C₂×D₄₃)⋊C₄	—	2	2	no	—
438	C₄⋊Dic₄₃	—	2	1	no	—
439	C₄⋊Dic₄₃	—	2	2	no	—
440	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
442	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
443	Dic₄₃⋊C₄	—	2	2	no	—
444	Dic₄₃⋊C₄	—	2	1	no	—
445	Dic₄₃⋊C₄	—	2	1	no	—
446	Dic₄₃⋊C₄	—	2	2	no	—
447	Dic₄₃⋊C₄	—	2	2	no	—
448	C₄×Dic₄₃	—	2	1	no	—
449	C₄×Dic₄₃	—	2	1	no	—
450	C₄×Dic₄₃	—	2	1	no	—
451	C₂×C₄₃⋊C₈	—	4	2	no	—
452	C₂×C₄₃⋊C₈	—	4	2	no	—
453	C₂×C₄₃⋊C₈	—	4	2	no	—
454	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
455	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
456	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
457	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
458	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
459	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
460	C₂³×C₄₃	—	2	1	no	—
461	C₂³×C₄₃	—	2	2	no	—
462	C₂³×C₄₃	—	4	4	no	—
463	C₂³×C₄₃	—	8	2	no	—
464	C₂³×C₄₃	—	8	2	no	—
465	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
467	C₂²×D₄₃	—	2	1	no	—
468	C₂²×D₄₃	—	2	2	no	—
469	C₂²×D₄₃	—	4	4	no	—
470	C₂²×D₄₃	—	4	4	no	—
471	C₂²×D₄₃	—	8	2	no	—
472	Q₈×C₄₃	—	2	2	no	—
473	Q₈×C₄₃	—	2	1	no	—
474	Q₈×C₄₃	—	2	2	no	—
475	Q₈×C₄₃	—	2	2	no	—
476	Q₈×C₄₃	—	2	1	no	—
477	Q₈×C₄₃	—	8	2	no	—
478	D₄×C₄₃	—	2	4	no	—
479	D₄×C₄₃	—	2	1	no	—
480	D₄×C₄₃	—	2	2	no	—
481	D₄×C₄₃	—	2	2	no	—
482	D₄×C₄₃	—	2	1	no	—
483	D₄×C₄₃	—	4	4	no	—
484	D₄×C₄₃	—	4	2	no	—
485	D₄×C₄₃	—	8	1	no	—
486	D₄×C₄₃	—	8	2	no	—
487	D₄×C₄₃	—	8	1	no	—
488	D₄×C₄₃	—	8	2	no	—
489	D₄×C₄₃	#135	1	4	yes	complemented
490	C₂×C₄×C₄₃	—	2	4	no	—
491	C₂×C₄×C₄₃	—	2	2	no	—
492	C₂×C₄×C₄₃	—	2	2	no	—
493	C₂×C₄×C₄₃	—	2	1	no	—
494	C₂×C₄×C₄₃	—	2	2	no	—
495	C₂×C₄×C₄₃	—	2	1	no	—
496	C₂×C₄×C₄₃	—	2	1	no	—
497	C₂×C₄×C₄₃	—	2	1	no	—
498	C₂×C₄×C₄₃	—	2	1	no	—
499	C₂×C₄×C₄₃	—	2	2	no	—
500	C₂×C₄×C₄₃	—	4	2	no	—
501	C₂×C₄×C₄₃	—	4	1	no	—
502	C₂×C₄×C₄₃	—	4	2	no	—
503	C₂×C₄×C₄₃	—	8	2	no	—
504	C₂×C₄×C₄₃	—	8	2	no	—
505	C₂×C₄×C₄₃	—	8	2	no	—
506	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
515	C₂²⋊D₄₃	—	4	2	no	—
516	C₂²⋊D₄₃	—	4	4	no	—
517	C₂²⋊D₄₃	—	8	2	no	—
518	C₂×Dic₄₃	—	2	1	no	—
519	C₂×Dic₄₃	—	2	1	no	—
520	C₂×Dic₄₃	—	2	1	no	—
521	C₂×Dic₄₃	—	2	2	no	—
522	C₂×Dic₄₃	—	8	2	no	—
523	D₁₇₂	—	2	2	no	—
524	D₁₇₂	—	2	1	no	—
525	D₁₇₂	—	2	2	no	—
526	D₁₇₂	—	4	4	no	—
527	D₁₇₂	—	4	2	no	—
528	D₁₇₂	—	8	1	no	—
529	D₁₇₂	H(5,𝔽₂)	1	2	yes	—
530	C₄×D₄₃	—	4	2	no	—
531	C₄×D₄₃	—	4	2	no	—
532	C₄×D₄₃	—	4	4	no	—
533	C₄×D₄₃	—	4	2	no	—
534	C₄×D₄₃	—	8	2	no	—
535	C₄×D₄₃	—	8	2	no	—
536	Dic₈₆	—	2	1	no	—
537	Dic₈₆	—	2	1	no	—
538	Dic₈₆	—	8	1	no	—
539	C₄₃⋊C₈	—	2	1	no	—
540	C₄₃⋊C₈	—	2	2	no	—
541	C₄₃⋊C₈	—	2	2	no	—
542	C₄₃⋊C₈	—	2	1	no	—
543	C₄₃⋊C₈	—	2	1	no	—
544	C₄₃⋊C₈	—	2	1	no	—
545	#61955	—	43	1	no	maximal, Sylow
546	C₂²×C₄₃	—	2	2	no	—
547	C₂²×C₄₃	—	2	2	no	—
548	C₂²×C₄₃	—	2	1	no	—
549	C₂²×C₄₃	—	2	1	no	—
550	C₂²×C₄₃	—	2	1	no	—
551	C₂²×C₄₃	—	4	1	no	—
552	C₂²×C₄₃	—	4	2	no	—
553	C₂²×C₄₃	—	4	1	no	—
554	C₂²×C₄₃	—	4	2	no	—
555	C₂²×C₄₃	—	4	1	no	—
556	C₂²×C₄₃	—	4	2	no	—
557	C₂²×C₄₃	—	16	4	no	—
558	C₂²×C₄₃	C₂×#135	1	4	yes	—
559	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
560	C₂×D₄₃	—	2	2	no	—
561	C₂×D₄₃	—	4	1	no	—
562	C₂×D₄₃	—	4	1	no	—
563	C₂×D₄₃	—	4	2	no	—
564	C₂×D₄₃	—	4	2	no	—
565	C₂×D₄₃	—	4	2	no	—
566	C₂×D₄₃	—	8	8	no	—
567	C₄×C₄₃	—	2	1	no	—
568	C₄×C₄₃	—	2	1	no	—
569	C₄×C₄₃	—	2	2	no	—
570	C₄×C₄₃	—	2	1	no	—
571	C₄×C₄₃	—	2	2	no	—
572	C₄×C₄₃	—	2	1	no	—
573	C₄×C₄₃	—	2	2	no	—
574	C₄×C₄₃	—	4	1	no	—
575	C₄×C₄₃	—	4	2	no	—
576	C₄×C₄₃	—	4	1	no	—
577	C₄×C₄₃	—	4	1	no	—
578	C₄×C₄₃	C₂×#135	1	2	yes	—
579	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₄×C₄₃	#585	1	1	yes	characteristic
581	Dic₄₃	—	4	2	no	—
582	Dic₄₃	—	4	1	no	—
583	Dic₄₃	—	4	1	no	—
584	Dic₄₃	—	4	1	no	—
585	#3514	D₄₃	1	1	yes	characteristic, complemented
586	#3481	—	43	1	no	—
587	#3396	—	43	1	no	—
588	#3394	—	43	1	no	—
589	#3361	—	43	1	no	—
590	#3360	—	43	1	no	—
591	#3301	—	43	2	no	—
592	#3299	—	43	1	no	—
593	#3297	—	43	2	no	—
594	#3295	—	43	1	no	—
595	#3282	—	43	2	no	—
596	D₄×SD₁₆	—	43	1	no	—
597	#3280	—	43	2	no	—
598	D₄×D₈	—	43	1	no	—
599	#3250	—	43	2	no	—
600	#3247	—	43	1	no	—
601	#3211	—	43	2	no	—
602	#3207	—	43	1	no	—
603	#3105	—	43	2	no	—
604	#3102	—	43	1	no	—
605	#3035	—	43	1	no	—
606	C₂×#463	—	43	2	no	—
607	#2988	—	43	1	no	—
608	C₂×C₄₃	—	2	4	no	—
609	C₂×C₄₃	—	4	1	no	—
610	C₂×C₄₃	—	8	2	no	—
611	C₂×C₄₃	—	8	1	no	—
612	C₂×C₄₃	#3488	1	1	yes	characteristic
613	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
614	C₂×C₄₃	#3585	1	1	yes	characteristic
615	D₄₃	—	4	2	no	—
616	D₄₃	—	8	2	no	—
617	C₂×#135	—	43	2	no	—
618	C₂²×SD₁₆	—	43	2	no	—
619	C₂²×D₈	—	43	2	no	—
620	#559	—	43	1	no	—
621	#559	C₂×D₄₃	1	1	yes	characteristic, complemented
622	#556	C₂×D₄₃	1	1	yes	characteristic, complemented
623	#555	—	2	1	no	—
624	#554	—	43	1	no	—
625	#554	—	43	1	no	—
626	#553	—	43	2	no	—
627	#553	—	86	1	no	—
628	#551	—	2	2	no	—
629	#551	—	86	2	no	—
630	D₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
631	#548	C₂×D₄₃	1	2	yes	complemented
632	#546	—	2	1	no	—
633	#546	—	43	2	no	—
634	#546	—	86	1	no	—
635	#546	C₂×D₄₃	1	2	yes	complemented
636	D₄²	—	43	1	no	—
637	D₄²	C₂×D₄₃	1	1	yes	characteristic
638	#542	—	2	1	no	—
639	#538	—	2	2	no	—
640	#532	—	43	1	no	—
641	#532	C₂×D₄₃	1	1	yes	characteristic, complemented
642	#529	—	43	2	no	—
643	#529	—	86	1	no	—
644	#529	C₂×D₄₃	1	1	yes	characteristic, complemented
645	#529	C₂×D₄₃	1	2	yes	complemented
646	C₂×#124	C₂×D₄₃	1	2	yes	complemented
647	#525	—	86	2	no	—
648	#518	—	2	1	no	—
649	C₄×#41	—	43	1	no	—
650	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
651	C₂×C₄×D₄	—	43	2	no	—
652	C₂×C₄×D₄	—	86	1	no	—
653	#495	—	43	2	no	—
654	#495	—	43	2	no	—
655	#493	—	43	1	no	—
656	#492	—	43	1	no	—
657	#488	—	43	2	no	—
658	#488	—	43	2	no	—
659	#487	—	43	1	no	—
660	#486	—	43	1	no	—
661	#485	—	43	1	no	—
662	#484	—	43	2	no	—
663	#482	—	43	1	no	—
664	#481	—	43	2	no	—
665	#479	—	43	1	no	—
666	#479	—	43	2	no	—
667	#478	—	43	1	no	—
668	#478	—	43	2	no	—
669	#478	—	43	2	no	—
670	#477	—	43	1	no	—
671	#476	—	43	1	no	—
672	#467	—	43	2	no	—
673	#466	—	43	2	no	—
674	#466	—	43	2	no	—
675	#465	—	43	2	no	—
676	#465	—	43	2	no	—
677	#465	—	43	2	no	—
678	#464	—	43	1	no	—
679	#464	—	43	2	no	—
680	#464	—	43	2	no	—
681	#463	—	43	1	no	—
682	#463	—	43	2	no	—
683	#463	—	43	2	no	—
684	#463	—	43	2	no	—
685	#463	—	43	2	no	—
686	#463	—	43	2	no	—
687	#463	—	43	2	no	—
688	#463	—	43	2	no	—
689	#463	—	43	2	no	—
690	#463	—	43	2	no	—
691	#462	—	43	1	no	—
692	#461	—	43	1	no	—
693	#460	—	43	1	no	—
694	#460	—	43	1	no	—
695	#459	—	43	1	no	—
696	#459	—	43	1	no	—
697	#452	—	43	1	no	—
698	#451	—	43	2	no	—
699	#450	—	43	2	no	—
700	#450	—	43	2	no	—
701	#449	—	43	2	no	—
702	#449	—	43	2	no	—
703	#449	—	43	1	no	—
704	#448	—	43	2	no	—
705	#447	—	43	2	no	—
706	#447	—	43	2	no	—
707	C₈×Q₈	—	43	1	no	—
708	C₈×Q₈	—	43	1	no	—
709	C₄×Q₁₆	—	43	1	no	—
710	C₄×SD₁₆	—	43	1	no	—
711	C₄×SD₁₆	—	43	2	no	—
712	C₄×SD₁₆	—	43	2	no	—
713	C₄×SD₁₆	—	43	1	no	—
714	C₄×D₈	—	43	1	no	—
715	C₄×D₈	—	43	2	no	—
716	C₄×D₈	—	43	2	no	—
717	C₈×D₄	—	43	1	no	—
718	C₈×D₄	—	43	1	no	—
719	C₈×D₄	—	43	2	no	—
720	C₈×D₄	—	43	2	no	—
721	#431	—	43	1	no	—
722	#431	—	43	2	no	—
723	C₂×C₄⋊C₈	—	43	1	no	—
724	C₂×C₄⋊C₈	—	43	2	no	—
725	#416	—	43	2	no	—
726	C₂×#103	—	43	2	no	—
727	C₂×#102	—	43	2	no	—
728	C₄₃	#61955	1	1	yes	characteristic, complemented, Sylow
729	C₂×#41	—	43	1	no	—
730	C₂×#41	—	86	1	no	—
731	C₂×#41	C₂²⋊D₄₃	1	1	yes	characteristic
732	C₂×#41	C₂²×D₄₃	1	2	yes	—
733	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	—	43	2	no	—
736	C₂²×D₄	—	86	1	no	—
737	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
738	C₂³×C₄	—	86	2	no	—
739	#135	—	172	4	no	—
740	C₂×Q₁₆	—	43	2	no	—
741	C₂×Q₁₆	—	43	1	no	—
742	C₂×SD₁₆	—	43	1	no	—
743	C₂×SD₁₆	—	43	2	no	—
744	C₂×SD₁₆	—	43	2	no	—
745	C₂×SD₁₆	—	43	2	no	—
746	C₂×SD₁₆	—	43	2	no	—
747	C₂×SD₁₆	—	43	2	no	—
748	C₂×SD₁₆	—	43	1	no	—
749	C₂×SD₁₆	—	172	4	no	—
750	C₂×D₈	—	43	1	no	—
751	C₂×D₈	—	43	2	no	—
752	C₂×D₈	—	43	2	no	—
753	C₂×D₈	—	43	2	no	—
754	C₂×D₈	—	43	2	no	—
755	C₂×D₈	—	172	4	no	—
756	C₂²×C₈	—	43	2	no	—
757	C₂²×C₈	—	43	2	no	—
758	C₂²×C₈	—	43	2	no	—
759	C₄⋊Q₈	—	2	1	no	—
760	C₄⋊Q₈	—	43	1	no	—
761	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
762	#127	—	43	1	no	—
763	#127	C₂²×D₄₃	1	1	yes	characteristic
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	1	no	—
767	#126	—	86	2	no	—
768	#126	—	86	2	no	—
769	#125	—	43	2	no	—
770	#125	—	86	1	no	—
771	#125	C₂²×D₄₃	1	1	yes	characteristic
772	#124	—	2	1	no	—
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	—	2	2	no	—
776	#124	—	43	2	no	—
777	#124	—	86	1	no	—
778	#124	—	86	1	no	—
779	#124	C₂²×D₄₃	1	1	yes	characteristic
780	#124	C₂²×D₄₃	1	2	yes	—
781	#124	C₂²×D₄₃	1	2	yes	—
782	#124	C₂²×D₄₃	1	2	yes	—
783	#123	—	2	1	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	86	2	no	—
788	#123	—	86	2	no	—
789	#123	—	86	2	no	—
790	#123	—	86	2	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	43	2	no	—
795	C₂²⋊Q₈	—	86	1	no	—
796	C₂²⋊Q₈	—	86	2	no	—
797	C₂²⋊Q₈	—	86	2	no	—
798	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
799	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
800	#121	—	2	2	no	—
801	#121	—	2	1	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	2	no	—
805	#121	—	43	2	no	—
806	#121	—	43	2	no	—
807	#121	—	86	2	no	—
808	#121	—	86	1	no	—
809	#121	—	86	1	no	—
810	#121	—	86	2	no	—
811	#121	C₂²×D₄₃	1	2	yes	—
812	#121	C₂²×D₄₃	1	1	yes	characteristic
813	#120	—	2	2	no	—
814	#120	—	2	2	no	—
815	#120	—	86	2	no	—
816	#120	—	86	2	no	—
817	C₄×Q₈	—	43	1	no	—
818	C₄×Q₈	—	43	1	no	—
819	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
820	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
821	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
822	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	43	1	no	—
831	C₄×D₄	—	43	2	no	—
832	C₄×D₄	—	43	2	no	—
833	C₄×D₄	—	43	2	no	—
834	C₄×D₄	—	43	1	no	—
835	C₄×D₄	—	86	1	no	—
836	C₄×D₄	—	86	2	no	—
837	C₄×D₄	—	86	1	no	—
838	C₄×D₄	—	86	1	no	—
839	C₄×D₄	—	86	1	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	C₂²⋊D₄₃	1	1	yes	characteristic
845	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
846	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
847	C₄×D₄	C₂²×D₄₃	1	2	yes	—
848	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
849	C₄×D₄	C₂²×D₄₃	1	2	yes	—
850	#117	—	2	1	no	—
851	#117	—	2	1	no	—
852	#117	—	2	2	no	—
853	#117	—	43	1	no	—
854	#117	—	86	1	no	—
855	#117	—	86	2	no	—
856	#117	C₂²⋊D₄₃	1	2	yes	—
857	#117	C₂²⋊D₄₃	1	1	yes	characteristic
858	C₂×C₄⋊C₄	—	43	2	no	—
859	C₂×C₄⋊C₄	—	86	1	no	—
860	C₂×C₂²⋊C₄	—	2	2	no	—
861	C₂×C₂²⋊C₄	—	2	2	no	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	C₂×C₂²⋊C₄	—	86	2	no	—
864	C₂×C₂²⋊C₄	—	86	2	no	—
865	C₂×C₄²	—	86	1	no	—
866	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
867	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
868	#107	—	43	1	no	—
869	#107	—	43	1	no	—
870	#107	—	43	2	no	—
871	#106	—	43	1	no	—
872	#106	—	43	2	no	—
873	#106	—	43	1	no	—
874	C₄⋊C₈	—	43	1	no	—
875	C₄⋊C₈	—	43	2	no	—
876	C₄⋊C₈	—	43	1	no	—
877	C₄⋊C₈	—	43	1	no	—
878	C₄⋊C₈	—	43	2	no	—
879	C₄⋊C₈	—	43	2	no	—
880	C₄⋊C₈	—	43	1	no	—
881	#103	—	43	1	no	—
882	#103	—	43	2	no	—
883	#103	—	43	2	no	—
884	#103	—	43	2	no	—
885	#103	—	43	2	no	—
886	#103	—	43	1	no	—
887	#103	—	43	2	no	—
888	#103	—	43	1	no	—
889	#103	—	43	1	no	—
890	#102	—	43	1	no	—
891	#102	—	43	2	no	—
892	#102	—	43	2	no	—
893	#102	—	43	2	no	—
894	#102	—	43	2	no	—
895	#102	—	43	1	no	—
896	#102	—	43	2	no	—
897	#102	—	43	1	no	—
898	#102	—	43	1	no	—
899	#102	—	43	2	no	—
900	#102	—	43	2	no	—
901	C₂²⋊C₈	—	43	2	no	—
902	C₂²⋊C₈	—	43	2	no	—
903	C₂²⋊C₈	—	43	1	no	—
904	C₂²⋊C₈	—	43	1	no	—
905	C₄×C₈	—	43	2	no	—
906	C₄×C₈	—	43	2	no	—
907	C₄×C₈	—	43	1	no	—
908	C₄×C₈	—	43	1	no	—
909	C₂⁴	—	2	2	no	—
910	C₂⁴	—	86	2	no	—
911	#41	—	2	4	no	—
912	#41	—	4	2	no	—
913	#41	—	4	2	no	—
914	#41	—	86	2	no	—
915	#41	—	344	2	no	—
916	#41	—	172	1	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	4	2	no	—
919	C₂×Q₈	—	4	2	no	—
920	C₂×Q₈	—	43	1	no	—
921	C₂×Q₈	—	86	1	no	—
922	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
923	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
924	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	4	2	no	—
932	C₂×D₄	—	4	2	no	—
933	C₂×D₄	—	4	4	no	—
934	C₂×D₄	—	43	1	no	—
935	C₂×D₄	—	43	2	no	—
936	C₂×D₄	—	86	4	no	—
937	C₂×D₄	—	86	2	no	—
938	C₂×D₄	—	86	1	no	—
939	C₂×D₄	—	86	2	no	—
940	C₂×D₄	—	86	1	no	—
941	C₂×D₄	—	86	2	no	—
942	C₂×D₄	—	86	1	no	—
943	C₂×D₄	—	172	2	no	—
944	C₂×D₄	—	172	4	no	—
945	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
946	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
947	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
948	C₂×D₄	C₂³×D₄₃	1	2	yes	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	86	2	no	—
954	C₂²×C₄	—	86	2	no	—
955	C₂²×C₄	—	86	2	no	—
956	C₂²×C₄	—	86	1	no	—
957	C₂²×C₄	—	86	1	no	—
958	C₂²×C₄	—	86	1	no	—
959	C₂²×C₄	—	86	2	no	—
960	C₂²×C₄	—	344	4	no	—
961	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
962	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
963	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
964	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
965	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
966	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
967	Q₁₆	—	172	2	no	—
968	Q₁₆	—	172	1	no	—
969	SD₁₆	—	86	2	no	—
970	SD₁₆	—	86	4	no	—
971	SD₁₆	—	172	2	no	—
972	SD₁₆	—	172	1	no	—
973	SD₁₆	—	172	2	no	—
974	SD₁₆	—	172	2	no	—
975	SD₁₆	—	172	2	no	—
976	D₈	—	86	2	no	—
977	D₈	—	86	4	no	—
978	D₈	—	172	2	no	—
979	D₈	—	172	2	no	—
980	D₈	—	172	2	no	—
981	C₂×C₈	—	43	1	no	—
982	C₂×C₈	—	43	1	no	—
983	C₂×C₈	—	43	2	no	—
984	C₂×C₈	—	43	1	no	—
985	C₂×C₈	—	43	2	no	—
986	C₂×C₈	—	43	1	no	—
987	C₂×C₈	—	172	2	no	—
988	C₂×C₈	—	172	2	no	—
989	C₂×C₈	—	172	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	43	1	no	—
999	C₄⋊C₄	—	43	2	no	—
1000	C₄⋊C₄	—	43	1	no	—
1001	C₄⋊C₄	—	86	2	no	—
1002	C₄⋊C₄	—	86	1	no	—
1003	C₄⋊C₄	—	86	2	no	—
1004	C₄⋊C₄	—	86	1	no	—
1005	C₄⋊C₄	—	86	1	no	—
1006	C₄⋊C₄	—	86	2	no	—
1007	C₄⋊C₄	—	86	2	no	—
1008	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1011	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1012	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	86	2	no	—
1029	C₂²⋊C₄	—	86	1	no	—
1030	C₂²⋊C₄	—	86	1	no	—
1031	C₂²⋊C₄	—	86	2	no	—
1032	C₂²⋊C₄	—	86	2	no	—
1033	C₂²⋊C₄	—	86	2	no	—
1034	C₂²⋊C₄	—	86	2	no	—
1035	C₂²⋊C₄	—	86	2	no	—
1036	C₂²⋊C₄	—	86	1	no	—
1037	C₂²⋊C₄	—	86	2	no	—
1038	C₂²⋊C₄	—	86	2	no	—
1039	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1040	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1041	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	86	1	no	—
1045	C₄²	—	86	1	no	—
1046	C₄²	—	86	1	no	—
1047	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1048	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1049	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1050	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1051	C₄²	C₂³×D₄₃	1	2	yes	—
1052	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1053	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	2	no	—
1056	C₂³	—	4	4	no	—
1057	C₂³	—	8	2	no	—
1058	C₂³	—	8	2	no	—
1059	C₂³	—	86	1	no	—
1060	C₂³	—	86	2	no	—
1061	C₂³	—	344	2	no	—
1062	C₂³	—	172	4	no	—
1063	C₂³	—	172	4	no	—
1064	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1065	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	8	2	no	—
1072	Q₈	—	86	1	no	—
1073	Q₈	—	86	1	no	—
1074	Q₈	—	344	1	no	—
1075	D₄	—	2	4	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	4	4	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	1	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	1	no	—
1086	D₄	—	43	2	no	—
1087	D₄	—	86	2	no	—
1088	D₄	—	86	1	no	—
1089	D₄	—	86	2	no	—
1090	D₄	—	344	1	no	—
1091	D₄	—	344	2	no	—
1092	D₄	—	172	4	no	—
1093	D₄	—	172	2	no	—
1094	D₄	—	172	4	no	—
1095	D₄	—	172	2	no	—
1096	D₄	#13063345	1	4	yes	complemented
1097	C₂×C₄	—	2	4	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	86	1	no	—
1114	C₂×C₄	—	86	1	no	—
1115	C₂×C₄	—	86	1	no	—
1116	C₂×C₄	—	86	2	no	—
1117	C₂×C₄	—	344	2	no	—
1118	C₂×C₄	—	344	2	no	—
1119	C₂×C₄	—	344	2	no	—
1120	C₂×C₄	—	172	2	no	—
1121	C₂×C₄	—	172	2	no	—
1122	C₂×C₄	—	172	4	no	—
1123	C₂×C₄	—	172	2	no	—
1124	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1125	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1126	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1127	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1128	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1129	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1130	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1131	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1132	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1133	C₈	—	86	1	no	—
1134	C₈	—	86	2	no	—
1135	C₈	—	86	1	no	—
1136	C₈	—	86	2	no	—
1137	C₈	—	86	1	no	—
1138	C₈	—	86	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	16	4	no	—
1151	C₂²	—	86	2	no	—
1152	C₂²	—	344	8	no	—
1153	C₂²	—	172	2	no	—
1154	C₂²	—	172	2	no	—
1155	C₂²	—	172	2	no	—
1156	C₂²	—	172	1	no	—
1157	C₂²	—	172	1	no	—
1158	C₂²	C₂×#13063345	1	4	yes	—
1159	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	172	1	no	—
1172	C₄	—	172	1	no	—
1173	C₄	—	172	2	no	—
1174	C₄	—	172	1	no	—
1175	C₄	C₂×#13063345	1	2	yes	—
1176	C₄	H(5,𝔽₂)×D₄₃	1	1	yes	characteristic
1177	C₄	#14583734	1	1	yes	characteristic
1178	C₂	—	2	4	no	—
1179	C₂	—	4	1	no	—
1180	C₂	—	8	1	no	—
1181	C₂	—	8	2	no	—
1182	C₂	—	344	2	no	—
1183	C₂	—	172	2	no	—
1184	C₂	#19148257	1	1	yes	characteristic
1185	C₂	C₂²×#13063345	1	1	yes	characteristic
1186	C₂	#19149374	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3514	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3514	D₄₃
hypocenter	C₄₃	#61955
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3514

Complements

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

N	H ≅ G/N	type
1. #19148205	C₂	semidirect
2. #19147603	C₂	semidirect
3. #19147591	C₂	semidirect
4. #19147251	C₂	semidirect
5. #19147240	C₂	semidirect
6. #19146497	C₂	semidirect
7. #19146471	C₂	semidirect
8. #19146445	C₂	semidirect
9. #19146419	C₂	semidirect
10. #19146303	C₂	semidirect
11. D₄×#10621884	C₂	semidirect
12. #19146276	C₂	semidirect
13. D₄×#10621882	C₂	semidirect
14. #19145942	C₂	semidirect
15. #19145921	C₂	semidirect
16. #19145560	C₂	semidirect
17. #19145528	C₂	semidirect
18. #19144638	C₂	semidirect
19. #19144607	C₂	semidirect
20. #19144044	C₂	semidirect
21. C₂×#14583111	C₂	semidirect
22. #19143706	C₂	semidirect
23. C₄₃×#3514	C₂	semidirect
24. C₂×#13063345	C₂²	semidirect
25. C₂²×#10621884	C₂²	semidirect
27. #14583634	C₂²	semidirect
28. #14583609	C₂²	semidirect
30. #14583595	C₂²	semidirect
33. #14583545	C₂²	semidirect
36. #14583449	C₂²	semidirect
38. #14583433	C₂²	semidirect
40. C₄×#10621898	C₂²	semidirect
41. C₂×C₄×D₁₇₂	C₂²	semidirect
43. #14583281	C₂²	semidirect
44. #14583281	C₂²	semidirect
46. #14583273	C₂²	semidirect
47. #14583253	C₂²	semidirect
48. #14583253	C₂²	semidirect
49. #14583249	C₂²	semidirect
50. #14583245	C₂²	semidirect
51. #14583237	C₂²	semidirect
52. #14583232	C₂²	semidirect
53. #14583220	C₂²	semidirect
54. #14583215	C₂²	semidirect
55. #14583206	C₂²	semidirect
56. #14583203	C₂²	semidirect
57. #14583199	C₂²	semidirect
58. #14583196	C₂²	semidirect
59. #14583196	C₂²	semidirect
60. #14583194	C₂²	semidirect
61. #14583189	C₂²	semidirect
62. #14583138	C₂²	semidirect
64. #14583133	C₂²	semidirect
65. #14583130	C₂²	semidirect
66. #14583130	C₂²	semidirect
67. #14583126	C₂²	semidirect
68. #14583121	C₂²	semidirect
69. #14583118	C₂²	semidirect
70. #14583118	C₂²	semidirect
71. #14583114	C₂²	semidirect
74. #14583111	C₂²	semidirect
75. #14583111	C₂²	semidirect
76. #14583111	C₂²	semidirect
77. #14583111	C₂²	semidirect
78. #14583111	C₂²	semidirect
79. #14583111	C₂²	semidirect
80. #14583111	C₂²	semidirect
81. #14583106	C₂²	semidirect
82. #14583101	C₂²	semidirect
83. #14583099	C₂²	semidirect
84. #14583096	C₂²	semidirect
87. #14583059	C₂²	semidirect
88. #14583055	C₂²	semidirect
89. #14583050	C₂²	semidirect
90. #14583049	C₂²	semidirect
91. #14583044	C₂²	semidirect
92. #14583044	C₂²	semidirect
94. #14583038	C₂²	semidirect
97. Q₈×C₄₃⋊C₈	C₂²	semidirect
98. Q₈×C₄₃⋊C₈	C₂²	semidirect
99. C₄×#10621885	C₂²	semidirect
100. C₄×#10621884	C₂²	semidirect
101. C₄×#10621884	C₂²	semidirect
102. C₄×#10621884	C₂²	semidirect
103. C₄×#10621883	C₂²	semidirect
105. C₄×#10621882	C₂²	semidirect
106. C₄×#10621882	C₂²	semidirect
109. D₄×C₄₃⋊C₈	C₂²	semidirect
110. D₄×C₄₃⋊C₈	C₂²	semidirect
111. #14582952	C₂²	semidirect
112. #14582952	C₂²	semidirect
113. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
114. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
115. #14582895	C₂²	semidirect
116. C₂×#13063249	C₂²	semidirect
117. C₂×#13063246	C₂²	semidirect
118. C₄₃×#559	C₂²	semidirect
119. C₄₃×#556	C₂²	semidirect
123. C₄₃×#548	C₂²	semidirect
125. C₄₃×#546	C₂²	semidirect
129. C₄₃×#532	C₂²	semidirect
130. C₄₃×#529	C₂²	semidirect
131. C₄₃×#529	C₂²	semidirect
132. C₂×#124×C₄₃	C₂²	semidirect
489. D₄×C₄₃	#135	semidirect
585. #3514	D₄₃	semidirect
621. #559	C₂×D₄₃	semidirect
622. #556	C₂×D₄₃	semidirect
631. #548	C₂×D₄₃	semidirect
635. #546	C₂×D₄₃	semidirect
641. #532	C₂×D₄₃	semidirect
644. #529	C₂×D₄₃	semidirect
645. #529	C₂×D₄₃	semidirect
646. C₂×#124	C₂×D₄₃	semidirect
728. C₄₃	#61955	semidirect
1096. D₄	#13063345	semidirect

Maximal subgroups

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

subgroup	index
#19148205	2
#19147603	2
#19147591	2
#19147251	2
#19147240	2
#19146497	2
#19146471	2
#19146445	2
#19146419	2
#19146303	2
D₄×#10621884	2
#19146276	2
D₄×#10621882	2
#19145942	2
#19145921	2
#19145560	2
#19145528	2
#19144638	2
#19144607	2
#19144044	2
C₂×#14583111	2
#19143706	2
C₄₃×#3514	2
#61955	43