Subgroups — #25988863

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148556	C₂	1	1	yes	maximal, characteristic, complemented
2	#19147591	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147579	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147291	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147280	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146476	C₂	1	2	yes	maximal, complemented
7	#19146454	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146424	C₂	1	2	yes	maximal, complemented
9	#19146402	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#10621885	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146332	C₂	1	2	yes	maximal, complemented
12	#19146303	C₂	1	2	yes	maximal, complemented
13	D₄×#10621884	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145942	C₂	1	2	yes	maximal, complemented
15	#19145926	C₂	1	1	yes	maximal, characteristic, complemented
16	#19145556	C₂	1	2	yes	maximal, complemented
17	#19145547	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144675	C₂	1	2	yes	maximal, complemented
19	#19144613	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144050	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#14583121	C₂	1	2	yes	maximal, complemented
22	#19143706	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063345	C₂²	1	2	yes	complemented
25	C₂²×#10621885	C₂²	1	2	yes	complemented
26	C₂²×#10621884	C₂²	1	2	yes	—
27	#14583634	C₂²	1	1	yes	characteristic
28	#14583622	C₂²	1	1	yes	characteristic
29	#14583612	—	2	1	no	—
30	#14583573	—	2	2	no	—
31	D₄×Dic₈₆	C₂²	1	1	yes	characteristic
32	#14583558	C₂²	1	2	yes	—
33	#14583545	C₂²	1	2	yes	—
34	#14583537	—	2	1	no	—
35	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
36	#14583521	—	2	1	no	—
37	#14583482	—	2	2	no	—
38	#14583449	C₂²	1	1	yes	characteristic
39	#14583433	C₂²	1	1	yes	characteristic
40	#14583433	C₂²	1	2	yes	—
41	C₂×#13063313	C₂²	1	2	yes	—
42	#14583371	—	2	1	no	—
43	#14583281	C₂²	1	2	yes	—
44	#14583281	C₂²	1	2	yes	complemented
45	#14583278	C₂²	1	1	yes	characteristic, complemented
46	#14583273	C₂²	1	1	yes	characteristic
47	#14583256	C₂²	1	2	yes	—
48	#14583256	C₂²	1	2	yes	complemented
49	#14583251	C₂²	1	1	yes	characteristic, complemented
50	#14583247	C₂²	1	1	yes	characteristic
51	#14583240	C₂²	1	1	yes	characteristic, complemented
52	#14583229	C₂²	1	2	yes	complemented
53	#14583223	C₂²	1	1	yes	characteristic
54	#14583212	C₂²	1	2	yes	—
55	#14583206	C₂²	1	1	yes	characteristic, complemented
56	#14583206	C₂²	1	2	yes	complemented
57	#14583203	C₂²	1	2	yes	complemented
58	#14583199	C₂²	1	1	yes	characteristic, complemented
59	#14583196	C₂²	1	2	yes	complemented
60	#14583181	C₂²	1	1	yes	characteristic, complemented
61	#14583176	C₂²	1	1	yes	characteristic
62	#14583138	C₂²	1	2	yes	complemented
63	#14583138	C₂²	1	2	yes	complemented
64	#14583133	C₂²	1	2	yes	—
65	#14583130	C₂²	1	2	yes	—
66	#14583130	C₂²	1	2	yes	—
67	#14583126	C₂²	1	2	yes	complemented
68	#14583121	C₂²	1	2	yes	—
69	#14583121	C₂²	1	2	yes	—
70	#14583121	C₂²	1	2	yes	—
71	#14583121	C₂²	1	1	yes	characteristic
72	#14583121	C₂²	1	2	yes	complemented
73	#14583121	C₂²	1	2	yes	complemented
74	#14583121	C₂²	1	2	yes	complemented
75	#14583121	C₂²	1	2	yes	complemented
76	#14583121	C₂²	1	2	yes	complemented
77	#14583118	C₂²	1	2	yes	complemented
78	#14583114	C₂²	1	1	yes	characteristic
79	#14583114	C₂²	1	2	yes	complemented
80	#14583111	C₂²	1	2	yes	complemented
81	#14583109	C₂²	1	1	yes	characteristic, complemented
82	#14583106	C₂²	1	1	yes	characteristic, complemented
83	#14583104	C₂²	1	1	yes	characteristic, complemented
84	#14583101	C₂²	1	1	yes	characteristic
85	#14583099	C₂²	1	1	yes	characteristic
86	#14583094	C₂²	1	1	yes	characteristic
87	#14583061	C₂²	1	1	yes	characteristic, complemented
88	#14583059	C₂²	1	2	yes	complemented
89	#14583059	C₂²	1	2	yes	complemented
90	#14583055	C₂²	1	2	yes	complemented
91	#14583054	C₂²	1	2	yes	complemented
92	#14583049	C₂²	1	2	yes	—
93	#14583044	C₂²	1	1	yes	characteristic
94	#14583038	C₂²	1	2	yes	—
95	#14583037	C₂²	1	2	yes	complemented
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	2	yes	complemented
100	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
101	C₄×#10621885	C₂²	1	2	yes	complemented
102	C₄×#10621884	C₂²	1	1	yes	characteristic
103	C₄×#10621884	C₂²	1	2	yes	complemented
104	C₄×#10621884	C₂²	1	2	yes	complemented
105	C₄×#10621883	C₂²	1	1	yes	characteristic, complemented
106	C₄×#10621882	C₂²	1	1	yes	characteristic
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	#14582893	C₂²	1	2	yes	complemented
116	C₂×#13063248	C₂²	1	2	yes	complemented
117	C₂×#13063245	C₂²	1	2	yes	—
118	C₄₃×#557	C₂²	1	1	yes	characteristic, complemented
119	C₄₃×#556	—	2	1	no	—
120	C₄₃×#556	C₂²	1	1	yes	characteristic, complemented
121	C₄₃×#552	—	2	2	no	—
122	C₄₃×#552	C₂²	1	2	yes	complemented
123	D₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
124	C₄₃×#548	C₂²	1	2	yes	complemented
125	C₄₃×#547	—	2	1	no	—
126	C₄₃×#547	C₂²	1	1	yes	characteristic
127	C₄₃×#533	—	2	1	no	—
128	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#529	—	2	2	no	—
130	C₄₃×#529	C₂²	1	2	yes	complemented
131	C₄×#41×C₄₃	—	2	1	no	—
132	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
133	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
135	C₂×#10621898	C₂³	1	2	yes	—
136	C₂²×Dic₈₆	C₂³	1	2	yes	—
137	C₂²×D₁₇₂	C₂³	1	2	yes	—
138	C₂×D₄×D₄₃	—	2	1	no	—
139	#13063345	—	4	4	no	—
140	C₂×#10621885	—	4	4	no	—
141	C₂×#10621885	C₂³	1	2	yes	—
142	C₂×#10621885	C₂³	1	1	yes	characteristic
143	C₂×#10621885	C₂³	1	2	yes	—
144	C₂×#10621885	C₂³	1	2	yes	—
145	C₂×#10621885	C₂³	1	2	yes	—
146	C₂×#10621883	C₂³	1	1	yes	characteristic
147	C₂×#10621883	C₂³	1	2	yes	—
148	C₂×#10621884	—	4	4	no	—
149	C₂×#10621884	C₂³	1	1	yes	characteristic
150	C₂×#10621884	C₂³	1	2	yes	—
151	C₂×#10621884	C₂³	1	2	yes	—
152	C₂×#10621884	C₂³	1	2	yes	—
153	C₂×#10621884	C₂³	1	2	yes	—
154	C₂×#10621882	C₂³	1	1	yes	characteristic
155	C₂×#10621882	C₂³	1	2	yes	—
156	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
157	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
158	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
159	#13063325	C₂³	1	1	yes	characteristic
160	#13063324	—	2	1	no	—
161	#13063322	C₂³	1	1	yes	characteristic
162	#13063320	—	2	2	no	—
163	#13063319	—	2	1	no	—
164	#13063319	—	2	2	no	—
165	#13063317	C₂³	1	1	yes	characteristic
166	#13063314	—	2	1	no	—
167	#13063313	—	2	2	no	—
168	#13063313	—	2	2	no	—
169	#13063313	C₂³	1	2	yes	—
170	#13063313	C₂³	1	2	yes	—
171	#13063313	C₂³	1	1	yes	characteristic
172	#13063313	C₂³	1	2	yes	—
173	#13063311	—	2	2	no	—
174	#13063310	—	2	2	no	—
175	#13063310	—	2	2	no	—
176	#13063308	—	2	2	no	—
177	#13063308	—	2	1	no	—
178	#13063304	C₂³	1	1	yes	characteristic
179	#13063304	C₂³	1	2	yes	—
180	#13063303	—	2	2	no	—
181	#13063302	—	2	2	no	—
182	#13063301	—	2	1	no	—
183	#13063300	—	2	1	no	—
184	#13063299	—	2	1	no	—
185	#13063299	—	2	1	no	—
186	#13063299	C₂³	1	1	yes	characteristic
187	#13063299	C₂³	1	2	yes	—
188	#13063298	—	2	2	no	—
189	#13063297	—	2	2	no	—
190	#13063295	—	2	2	no	—
191	#13063293	—	2	2	no	—
192	C₄×Dic₈₆	C₂³	1	2	yes	—
193	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
194	C₄×D₁₇₂	—	2	1	no	—
195	C₄×D₁₇₂	—	2	1	no	—
196	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
197	C₄×D₁₇₂	C₂³	1	2	yes	—
198	D₄×Dic₄₃	—	2	1	no	—
199	#13063287	—	2	1	no	—
200	C₄×C₂²⋊D₄₃	—	2	1	no	—
201	C₄×C₂²⋊D₄₃	—	2	2	no	—
202	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
203	#13063283	—	2	1	no	—
204	#13063282	—	2	2	no	—
205	#13063282	—	2	1	no	—
206	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
207	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
208	C₂²⋊C₄×D₄₃	—	2	2	no	—
209	#13063258	C₂³	1	2	yes	—
210	#13063258	C₂³	1	1	yes	characteristic
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	2	yes	—
218	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
219	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
220	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
221	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
222	#13063249	C₂³	1	1	yes	characteristic
223	#13063249	C₂³	1	2	yes	—
224	#13063249	C₂³	1	1	yes	characteristic
225	#13063249	C₂³	1	2	yes	—
226	#13063248	C₂³	1	1	yes	characteristic
227	#13063248	C₂³	1	2	yes	—
228	#13063248	C₂³	1	2	yes	—
229	#13063248	C₂³	1	2	yes	—
230	#13063248	C₂³	1	2	yes	—
231	#13063248	C₂³	1	1	yes	characteristic
232	#13063248	C₂³	1	2	yes	—
233	#13063246	C₂³	1	1	yes	characteristic
234	#13063246	C₂³	1	1	yes	characteristic
235	#13063245	C₂³	1	1	yes	characteristic
236	#13063245	C₂³	1	2	yes	—
237	#13063245	C₂³	1	2	yes	—
238	#13063245	C₂³	1	2	yes	—
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	2	yes	—
244	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
245	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
251	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
252	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
253	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
254	C₄⋊Q₈×C₄₃	—	2	1	no	—
255	C₄⋊Q₈×C₄₃	—	2	1	no	—
256	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
257	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
258	#126×C₄₃	—	2	2	no	—
259	#126×C₄₃	—	2	2	no	—
260	#126×C₄₃	—	2	2	no	—
261	#125×C₄₃	—	2	2	no	—
262	#125×C₄₃	—	2	2	no	—
263	#125×C₄₃	—	2	1	no	—
264	#125×C₄₃	C₂³	1	2	yes	—
265	#124×C₄₃	—	2	2	no	—
266	#124×C₄₃	C₂³	1	2	yes	—
267	#123×C₄₃	—	2	2	no	—
268	#123×C₄₃	—	2	2	no	—
269	#123×C₄₃	—	2	2	no	—
270	C₂²⋊Q₈×C₄₃	—	2	1	no	—
271	C₂²⋊Q₈×C₄₃	—	2	1	no	—
272	C₂²⋊Q₈×C₄₃	—	2	1	no	—
273	C₂²⋊Q₈×C₄₃	—	2	2	no	—
274	C₂²⋊Q₈×C₄₃	—	2	2	no	—
275	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
276	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
277	#121×C₄₃	—	2	2	no	—
278	#121×C₄₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₄₃	—	2	1	no	—
280	C₄×Q₈×C₄₃	—	2	2	no	—
281	C₄×Q₈×C₄₃	—	2	2	no	—
282	C₄×Q₈×C₄₃	—	2	1	no	—
283	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
284	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
286	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
287	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
288	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	—	2	1	no	—
291	C₄×D₄×C₄₃	—	2	2	no	—
292	C₄×D₄×C₄₃	—	2	1	no	—
293	C₄×D₄×C₄₃	—	2	1	no	—
294	C₄×D₄×C₄₃	—	2	2	no	—
295	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
296	C₄×D₄×C₄₃	D₄	1	2	yes	—
297	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₃	C₂³	1	2	yes	—
300	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
301	#117×C₄₃	—	2	1	no	—
302	#117×C₄₃	—	2	1	no	—
303	#117×C₄₃	—	2	2	no	—
304	#117×C₄₃	—	2	1	no	—
305	#117×C₄₃	—	2	2	no	—
306	#117×C₄₃	D₄	1	2	yes	—
307	#117×C₄₃	D₄	1	1	yes	characteristic
308	#117×C₄₃	C₂³	1	1	yes	characteristic
309	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
310	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
311	C₂×C₄²×C₄₃	—	2	2	no	—
312	C₂×C₄²×C₄₃	—	2	1	no	—
313	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
314	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
315	C₂³×D₄₃	—	2	2	no	—
316	#41×C₄₃	—	2	4	no	—
317	#41×C₄₃	—	2	2	no	—
318	#41×C₄₃	—	4	1	no	—
319	#41×C₄₃	—	4	4	no	—
320	C₂×Q₈×C₄₃	—	2	2	no	—
321	C₂×Q₈×C₄₃	—	2	1	no	—
322	C₂×Q₈×C₄₃	—	2	4	no	—
323	C₂×Q₈×C₄₃	—	4	2	no	—
324	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₄₃	—	2	1	no	—
328	C₂×D₄×C₄₃	—	2	2	no	—
329	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
331	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	—	2	1	no	—
333	C₂²×C₄×C₄₃	—	2	1	no	—
334	C₂²×C₄×C₄₃	—	2	1	no	—
335	C₂²×C₄×C₄₃	—	2	2	no	—
336	C₂²×C₄×C₄₃	—	2	2	no	—
337	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
338	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
340	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₂²⋊D₄₃	—	2	2	no	—
344	C₂×C₂²⋊D₄₃	—	2	1	no	—
345	C₂×C₂²⋊D₄₃	—	2	2	no	—
346	C₂²×Dic₄₃	—	2	2	no	—
347	D₄×D₄₃	—	4	4	no	—
348	#10621898	—	4	2	no	—
349	#10621898	—	4	2	no	—
350	C₂×D₁₇₂	—	2	1	no	—
351	C₂×D₁₇₂	—	2	1	no	—
352	C₂×D₁₇₂	—	2	2	no	—
353	C₂×D₁₇₂	—	4	2	no	—
354	C₂×D₁₇₂	—	4	2	no	—
355	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
356	C₂×D₁₇₂	C₂⁴	1	2	yes	—
357	C₂×C₄×D₄₃	—	2	1	no	—
358	C₂×C₄×D₄₃	—	2	2	no	—
359	C₂×C₄×D₄₃	—	2	2	no	—
360	C₂×Dic₈₆	—	2	2	no	—
361	C₂×Dic₈₆	—	4	2	no	—
362	C₂×Dic₈₆	—	4	2	no	—
363	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
364	C₂×Dic₈₆	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₄₃	—	2	1	no	—
366	C₄⋊C₄×C₄₃	—	2	2	no	—
367	C₄⋊C₄×C₄₃	—	2	2	no	—
368	C₄⋊C₄×C₄₃	—	2	2	no	—
369	C₄⋊C₄×C₄₃	—	2	2	no	—
370	C₄⋊C₄×C₄₃	—	2	1	no	—
371	C₄⋊C₄×C₄₃	—	2	2	no	—
372	C₄⋊C₄×C₄₃	—	2	2	no	—
373	C₄⋊C₄×C₄₃	—	2	1	no	—
374	C₄⋊C₄×C₄₃	—	2	1	no	—
375	C₄⋊C₄×C₄₃	—	2	2	no	—
376	C₄⋊C₄×C₄₃	—	2	1	no	—
377	C₄⋊C₄×C₄₃	—	2	2	no	—
378	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
380	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
385	C₂²⋊C₄×C₄₃	—	2	2	no	—
386	C₂²⋊C₄×C₄₃	—	2	1	no	—
387	C₂²⋊C₄×C₄₃	—	2	1	no	—
388	C₂²⋊C₄×C₄₃	—	2	2	no	—
389	C₂²⋊C₄×C₄₃	—	2	2	no	—
390	C₂²⋊C₄×C₄₃	—	2	2	no	—
391	C₂²⋊C₄×C₄₃	—	2	2	no	—
392	C₂²⋊C₄×C₄₃	—	2	1	no	—
393	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
396	C₄²×C₄₃	—	2	1	no	—
397	C₄²×C₄₃	—	2	1	no	—
398	C₄²×C₄₃	—	2	2	no	—
399	C₄²×C₄₃	—	2	2	no	—
400	C₄²×C₄₃	—	2	1	no	—
401	C₄²×C₄₃	—	2	2	no	—
402	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
403	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₄₃	C₂×D₄	1	2	yes	—
405	C₄²×C₄₃	C₂×D₄	1	2	yes	—
406	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
407	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
408	C₄²×C₄₃	C₂⁴	1	2	yes	—
409	C₂²⋊Dic₄₃	—	2	2	no	—
410	C₂²⋊Dic₄₃	—	2	1	no	—
411	#10621885	—	2	2	no	—
412	#10621885	—	2	4	no	—
413	#10621885	—	4	2	no	—
414	#10621885	—	4	2	no	—
415	#10621885	—	4	2	no	—
416	#10621884	—	2	2	no	—
417	#10621884	—	2	4	no	—
418	#10621884	—	4	2	no	—
419	#10621884	—	4	2	no	—
420	#10621884	—	4	2	no	—
421	#10621883	—	4	1	no	—
422	#10621883	—	4	2	no	—
423	#10621882	—	4	1	no	—
424	#10621882	—	4	2	no	—
425	(C₂×D₄₃)⋊C₄	—	2	1	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	1	no	—
428	(C₂×D₄₃)⋊C₄	—	2	1	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	—	2	2	no	—
434	(C₂×D₄₃)⋊C₄	—	2	2	no	—
435	(C₂×D₄₃)⋊C₄	—	2	2	no	—
436	(C₂×D₄₃)⋊C₄	—	2	1	no	—
437	C₄⋊Dic₄₃	—	2	1	no	—
438	C₄⋊Dic₄₃	—	2	1	no	—
439	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
441	Dic₄₃⋊C₄	—	2	1	no	—
442	Dic₄₃⋊C₄	—	2	1	no	—
443	Dic₄₃⋊C₄	—	2	1	no	—
444	Dic₄₃⋊C₄	—	2	2	no	—
445	Dic₄₃⋊C₄	—	2	2	no	—
446	Dic₄₃⋊C₄	—	2	1	no	—
447	C₄×Dic₄₃	—	2	2	no	—
448	C₄×Dic₄₃	—	2	1	no	—
449	C₂×C₄₃⋊C₈	—	4	2	no	—
450	C₂×C₄₃⋊C₈	—	4	2	no	—
451	C₂×C₄₃⋊C₈	—	4	2	no	—
452	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
453	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
454	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
455	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
456	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
457	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
458	C₂³×C₄₃	—	2	1	no	—
459	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
461	C₂²×D₄₃	—	2	1	no	—
462	C₂²×D₄₃	—	2	2	no	—
463	C₂²×D₄₃	—	4	4	no	—
464	C₂²×D₄₃	—	8	2	no	—
465	C₂²×D₄₃	—	8	2	no	—
466	Q₈×C₄₃	—	2	2	no	—
467	Q₈×C₄₃	—	2	1	no	—
468	Q₈×C₄₃	—	2	2	no	—
469	Q₈×C₄₃	—	2	2	no	—
470	Q₈×C₄₃	—	4	4	no	—
471	Q₈×C₄₃	—	4	2	no	—
472	Q₈×C₄₃	H(5,𝔽₂)	1	2	yes	—
473	D₄×C₄₃	—	2	4	no	—
474	D₄×C₄₃	—	2	1	no	—
475	D₄×C₄₃	—	2	1	no	—
476	D₄×C₄₃	—	4	2	no	—
477	D₄×C₄₃	—	4	4	no	—
478	D₄×C₄₃	#135	1	4	yes	complemented
479	C₂×C₄×C₄₃	—	2	4	no	—
480	C₂×C₄×C₄₃	—	2	1	no	—
481	C₂×C₄×C₄₃	—	2	2	no	—
482	C₂×C₄×C₄₃	—	2	2	no	—
483	C₂×C₄×C₄₃	—	2	1	no	—
484	C₂×C₄×C₄₃	—	2	2	no	—
485	C₂×C₄×C₄₃	—	2	1	no	—
486	C₂×C₄×C₄₃	—	2	1	no	—
487	C₂×C₄×C₄₃	—	2	1	no	—
488	C₂×C₄×C₄₃	—	2	2	no	—
489	C₂×C₄×C₄₃	—	2	2	no	—
490	C₂×C₄×C₄₃	—	4	2	no	—
491	C₂×C₄×C₄₃	—	4	1	no	—
492	C₂×C₄×C₄₃	—	4	2	no	—
493	C₂×C₄×C₄₃	—	4	4	no	—
494	C₂×C₄×C₄₃	—	4	2	no	—
495	C₂×C₄×C₄₃	—	4	4	no	—
496	C₂×C₄×C₄₃	—	4	2	no	—
497	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
506	C₂²⋊D₄₃	—	4	4	no	—
507	C₂²⋊D₄₃	—	8	2	no	—
508	C₂²⋊D₄₃	—	8	1	no	—
509	C₂×Dic₄₃	—	2	1	no	—
510	C₂×Dic₄₃	—	2	1	no	—
511	C₂×Dic₄₃	—	2	2	no	—
512	C₂×Dic₄₃	—	2	1	no	—
513	C₂×Dic₄₃	—	8	2	no	—
514	D₁₇₂	—	2	2	no	—
515	D₁₇₂	—	2	1	no	—
516	D₁₇₂	—	2	1	no	—
517	D₁₇₂	—	2	2	no	—
518	D₁₇₂	—	4	2	no	—
519	D₁₇₂	—	8	1	no	—
520	D₁₇₂	—	8	2	no	—
521	C₄×D₄₃	—	4	2	no	—
522	C₄×D₄₃	—	8	2	no	—
523	C₄×D₄₃	—	8	2	no	—
524	Dic₈₆	—	2	2	no	—
525	Dic₈₆	—	2	1	no	—
526	Dic₈₆	—	2	1	no	—
527	Dic₈₆	—	2	2	no	—
528	Dic₈₆	—	8	2	no	—
529	C₄₃⋊C₈	—	2	2	no	—
530	C₄₃⋊C₈	—	2	2	no	—
531	C₄₃⋊C₈	—	2	1	no	—
532	C₄₃⋊C₈	—	2	1	no	—
533	C₄₃⋊C₈	—	2	1	no	—
534	C₄₃⋊C₈	—	2	1	no	—
535	#61956	—	43	1	no	maximal, Sylow
536	C₂²×C₄₃	—	2	2	no	—
537	C₂²×C₄₃	—	2	2	no	—
538	C₂²×C₄₃	—	2	1	no	—
539	C₂²×C₄₃	—	2	1	no	—
540	C₂²×C₄₃	—	2	1	no	—
541	C₂²×C₄₃	—	4	1	no	—
542	C₂²×C₄₃	—	4	1	no	—
543	C₂²×C₄₃	—	4	1	no	—
544	C₂²×C₄₃	C₂×#135	1	4	yes	—
545	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
546	C₂×D₄₃	—	4	1	no	—
547	C₂×D₄₃	—	4	2	no	—
548	C₂×D₄₃	—	4	1	no	—
549	C₂×D₄₃	—	4	2	no	—
550	C₂×D₄₃	—	4	1	no	—
551	C₂×D₄₃	—	4	2	no	—
552	C₂×D₄₃	—	16	4	no	—
553	C₄×C₄₃	—	2	2	no	—
554	C₄×C₄₃	—	2	1	no	—
555	C₄×C₄₃	—	2	1	no	—
556	C₄×C₄₃	—	2	2	no	—
557	C₄×C₄₃	—	2	1	no	—
558	C₄×C₄₃	—	2	2	no	—
559	C₄×C₄₃	—	2	1	no	—
560	C₄×C₄₃	—	2	2	no	—
561	C₄×C₄₃	—	4	1	no	—
562	C₄×C₄₃	—	4	2	no	—
563	C₄×C₄₃	—	4	1	no	—
564	C₄×C₄₃	—	4	2	no	—
565	C₄×C₄₃	C₂×#135	1	2	yes	—
566	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
567	C₄×C₄₃	#585	1	1	yes	characteristic
568	Dic₄₃	—	4	1	no	—
569	Dic₄₃	—	4	1	no	—
570	Dic₄₃	—	4	2	no	—
571	Dic₄₃	—	4	1	no	—
572	#3514	—	43	1	no	—
573	#3482	D₄₃	1	1	yes	characteristic, complemented
574	#3394	—	43	1	no	—
575	#3393	—	43	1	no	—
576	#3365	—	43	1	no	—
577	#3364	—	43	1	no	—
578	#3300	—	43	2	no	—
579	#3298	—	43	1	no	—
580	#3296	—	43	2	no	—
581	#3294	—	43	1	no	—
582	D₄×Q₁₆	—	43	1	no	—
583	#3285	—	43	2	no	—
584	#3282	—	43	2	no	—
585	D₄×SD₁₆	—	43	1	no	—
586	#3250	—	43	2	no	—
587	#3248	—	43	1	no	—
588	#3211	—	43	2	no	—
589	#3210	—	43	1	no	—
590	#3108	—	43	2	no	—
591	#3102	—	43	1	no	—
592	#3035	—	43	1	no	—
593	C₂×#464	—	43	2	no	—
594	#2988	—	43	1	no	—
595	C₂×C₄₃	—	2	4	no	—
596	C₂×C₄₃	—	4	1	no	—
597	C₂×C₄₃	—	8	1	no	—
598	C₂×C₄₃	#3488	1	1	yes	characteristic
599	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
600	C₂×C₄₃	#3586	1	1	yes	characteristic
601	D₄₃	—	8	2	no	—
602	D₄₃	—	8	1	no	—
603	C₂×#135	—	43	2	no	—
604	C₂²×Q₁₆	—	43	2	no	—
605	C₂²×SD₁₆	—	43	2	no	—
606	#559	—	43	1	no	—
607	#557	C₂×D₄₃	1	1	yes	characteristic, complemented
608	#556	—	2	1	no	—
609	#556	—	43	1	no	—
610	#556	C₂×D₄₃	1	1	yes	characteristic, complemented
611	#555	—	86	1	no	—
612	#552	—	2	2	no	—
613	#552	C₂×D₄₃	1	2	yes	complemented
614	#551	—	86	2	no	—
615	D₄×Q₈	—	43	1	no	—
616	D₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
617	#548	—	43	2	no	—
618	#548	C₂×D₄₃	1	2	yes	complemented
619	#547	—	2	1	no	—
620	#547	C₂×D₄₃	1	1	yes	characteristic
621	#546	—	43	2	no	—
622	#546	—	86	1	no	—
623	D₄²	—	43	1	no	—
624	#542	—	86	1	no	—
625	#538	—	86	2	no	—
626	#533	—	2	1	no	—
627	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
628	#532	—	43	1	no	—
629	#529	—	2	2	no	—
630	#529	—	43	1	no	—
631	#529	—	43	2	no	—
632	#529	C₂×D₄₃	1	2	yes	complemented
633	C₂×#124	—	43	2	no	—
634	#518	—	86	1	no	—
635	C₄×#41	—	2	1	no	—
636	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
637	C₄×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
638	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
639	#495	—	43	2	no	—
640	#495	—	43	2	no	—
641	#494	—	43	1	no	—
642	#492	—	43	1	no	—
643	#488	—	43	2	no	—
644	#488	—	43	2	no	—
645	#487	—	43	1	no	—
646	#486	—	43	1	no	—
647	#485	—	43	1	no	—
648	#483	—	43	2	no	—
649	#482	—	43	1	no	—
650	#480	—	43	2	no	—
651	#479	—	43	2	no	—
652	#479	—	43	1	no	—
653	#479	—	43	2	no	—
654	#478	—	43	2	no	—
655	#478	—	43	1	no	—
656	#475	—	43	1	no	—
657	#474	—	43	1	no	—
658	#467	—	43	2	no	—
659	#467	—	43	2	no	—
660	#466	—	43	2	no	—
661	#465	—	43	2	no	—
662	#465	—	43	2	no	—
663	#465	—	43	2	no	—
664	#464	—	43	2	no	—
665	#464	—	43	1	no	—
666	#464	—	43	2	no	—
667	#464	—	43	2	no	—
668	#464	—	43	2	no	—
669	#464	—	43	2	no	—
670	#464	—	43	2	no	—
671	#464	—	43	2	no	—
672	#464	—	43	2	no	—
673	#464	—	43	2	no	—
674	#463	—	43	2	no	—
675	#463	—	43	1	no	—
676	#463	—	43	2	no	—
677	#462	—	43	1	no	—
678	#462	—	43	1	no	—
679	#461	—	43	1	no	—
680	#461	—	43	1	no	—
681	#460	—	43	1	no	—
682	#459	—	43	1	no	—
683	#452	—	43	1	no	—
684	#452	—	43	2	no	—
685	#452	—	43	2	no	—
686	#451	—	43	2	no	—
687	#451	—	43	2	no	—
688	#450	—	43	2	no	—
689	#449	—	43	1	no	—
690	#448	—	43	2	no	—
691	#448	—	43	2	no	—
692	#447	—	43	2	no	—
693	C₈×Q₈	—	43	1	no	—
694	C₈×Q₈	—	43	1	no	—
695	C₄×Q₁₆	—	43	1	no	—
696	C₄×Q₁₆	—	43	2	no	—
697	C₄×Q₁₆	—	43	2	no	—
698	C₄×SD₁₆	—	43	1	no	—
699	C₄×SD₁₆	—	43	2	no	—
700	C₄×SD₁₆	—	43	2	no	—
701	C₄×SD₁₆	—	43	1	no	—
702	C₄×D₈	—	43	1	no	—
703	C₈×D₄	—	43	1	no	—
704	C₈×D₄	—	43	1	no	—
705	C₈×D₄	—	43	2	no	—
706	C₈×D₄	—	43	2	no	—
707	#431	—	43	1	no	—
708	#431	—	43	2	no	—
709	C₂×C₄⋊C₈	—	43	1	no	—
710	C₂×C₄⋊C₈	—	43	2	no	—
711	#416	—	43	2	no	—
712	C₂×#103	—	43	2	no	—
713	C₂×#102	—	43	2	no	—
714	C₄₃	#61956	1	1	yes	characteristic, complemented, Sylow
715	C₂×#41	—	2	1	no	—
716	C₂×#41	—	43	2	no	—
717	C₂×#41	C₂²⋊D₄₃	1	1	yes	characteristic
718	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
719	C₂²×Q₈	—	43	2	no	—
720	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
721	C₂²×D₄	—	43	2	no	—
722	C₂²×D₄	—	86	1	no	—
723	#135	—	172	4	no	—
724	C₂×Q₁₆	—	43	1	no	—
725	C₂×Q₁₆	—	43	2	no	—
726	C₂×Q₁₆	—	43	2	no	—
727	C₂×Q₁₆	—	43	2	no	—
728	C₂×Q₁₆	—	43	2	no	—
729	C₂×Q₁₆	—	172	4	no	—
730	C₂×SD₁₆	—	43	1	no	—
731	C₂×SD₁₆	—	43	2	no	—
732	C₂×SD₁₆	—	43	2	no	—
733	C₂×SD₁₆	—	43	2	no	—
734	C₂×SD₁₆	—	43	2	no	—
735	C₂×SD₁₆	—	43	2	no	—
736	C₂×SD₁₆	—	43	1	no	—
737	C₂×SD₁₆	—	172	4	no	—
738	C₂×D₈	—	43	2	no	—
739	C₂×D₈	—	43	1	no	—
740	C₂²×C₈	—	43	2	no	—
741	C₂²×C₈	—	43	2	no	—
742	C₂²×C₈	—	43	2	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	—	43	1	no	—
746	C₄⋊Q₈	—	86	1	no	—
747	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
748	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
749	#127	—	43	1	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	86	2	no	—
754	#126	—	86	2	no	—
755	#126	—	86	1	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	1	no	—
759	#125	—	43	1	no	—
760	#125	C₂²×D₄₃	1	2	yes	—
761	#124	—	2	2	no	—
762	#124	—	43	1	no	—
763	#124	—	43	2	no	—
764	#124	—	43	2	no	—
765	#124	—	43	2	no	—
766	#124	—	86	1	no	—
767	#124	—	86	2	no	—
768	#124	—	86	2	no	—
769	#124	—	86	2	no	—
770	#124	C₂²×D₄₃	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	86	1	no	—
775	#123	—	86	2	no	—
776	#123	—	86	2	no	—
777	#123	—	86	2	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	43	2	no	—
784	C₂²⋊Q₈	—	43	1	no	—
785	C₂²⋊Q₈	—	86	1	no	—
786	C₂²⋊Q₈	—	86	2	no	—
787	C₂²⋊Q₈	—	86	2	no	—
788	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
789	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
790	#121	—	2	2	no	—
791	#121	—	43	2	no	—
792	#121	—	43	1	no	—
793	#121	—	86	2	no	—
794	#121	—	86	1	no	—
795	#121	—	86	1	no	—
796	#121	—	86	1	no	—
797	#121	—	86	2	no	—
798	#121	C₂²×D₄₃	1	2	yes	—
799	#120	—	86	2	no	—
800	#120	—	86	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	43	2	no	—
806	C₄×Q₈	—	43	1	no	—
807	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
808	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
809	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
810	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
811	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
812	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
813	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	43	1	no	—
820	C₄×D₄	—	43	2	no	—
821	C₄×D₄	—	86	1	no	—
822	C₄×D₄	—	86	2	no	—
823	C₄×D₄	—	86	1	no	—
824	C₄×D₄	—	86	1	no	—
825	C₄×D₄	—	86	2	no	—
826	C₄×D₄	—	86	1	no	—
827	C₄×D₄	—	86	1	no	—
828	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
829	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
830	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
831	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
832	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
833	C₄×D₄	C₂²×D₄₃	1	2	yes	—
834	#117	—	2	1	no	—
835	#117	—	2	1	no	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	86	1	no	—
840	#117	—	86	1	no	—
841	#117	—	86	2	no	—
842	#117	C₂²⋊D₄₃	1	2	yes	—
843	#117	C₂²⋊D₄₃	1	1	yes	characteristic
844	#117	C₂²×D₄₃	1	1	yes	characteristic
845	C₂×C₄⋊C₄	—	2	2	no	—
846	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
847	C₂×C₂²⋊C₄	—	86	2	no	—
848	C₂×C₂²⋊C₄	—	86	2	no	—
849	C₂×C₂²⋊C₄	—	86	2	no	—
850	C₂×C₄²	—	2	2	no	—
851	C₂×C₄²	—	2	1	no	—
852	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
853	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
854	#107	—	43	1	no	—
855	#107	—	43	2	no	—
856	#107	—	43	1	no	—
857	#106	—	43	1	no	—
858	#106	—	43	2	no	—
859	#106	—	43	1	no	—
860	C₄⋊C₈	—	43	2	no	—
861	C₄⋊C₈	—	43	1	no	—
862	C₄⋊C₈	—	43	1	no	—
863	C₄⋊C₈	—	43	1	no	—
864	C₄⋊C₈	—	43	2	no	—
865	C₄⋊C₈	—	43	2	no	—
866	C₄⋊C₈	—	43	1	no	—
867	#103	—	43	1	no	—
868	#103	—	43	1	no	—
869	#103	—	43	2	no	—
870	#103	—	43	2	no	—
871	#103	—	43	1	no	—
872	#103	—	43	2	no	—
873	#103	—	43	2	no	—
874	#103	—	43	2	no	—
875	#103	—	43	2	no	—
876	#103	—	43	2	no	—
877	#103	—	43	1	no	—
878	#102	—	43	1	no	—
879	#102	—	43	1	no	—
880	#102	—	43	1	no	—
881	#102	—	43	2	no	—
882	#102	—	43	2	no	—
883	#102	—	43	2	no	—
884	#102	—	43	2	no	—
885	#102	—	43	2	no	—
886	#102	—	43	1	no	—
887	C₂²⋊C₈	—	43	2	no	—
888	C₂²⋊C₈	—	43	2	no	—
889	C₂²⋊C₈	—	43	1	no	—
890	C₂²⋊C₈	—	43	1	no	—
891	C₄×C₈	—	43	1	no	—
892	C₄×C₈	—	43	1	no	—
893	C₄×C₈	—	43	2	no	—
894	C₄×C₈	—	43	2	no	—
895	C₂⁴	—	86	2	no	—
896	#41	—	2	4	no	—
897	#41	—	2	2	no	—
898	#41	—	4	1	no	—
899	#41	—	4	4	no	—
900	#41	—	172	2	no	—
901	#41	—	172	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	4	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	43	1	no	—
907	C₂×Q₈	—	43	2	no	—
908	C₂×Q₈	—	86	2	no	—
909	C₂×Q₈	—	172	2	no	—
910	C₂×Q₈	—	172	2	no	—
911	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
912	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
913	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	43	1	no	—
917	C₂×D₄	—	43	2	no	—
918	C₂×D₄	—	86	1	no	—
919	C₂×D₄	—	86	2	no	—
920	C₂×D₄	—	86	2	no	—
921	C₂×D₄	—	86	1	no	—
922	C₂×D₄	—	86	2	no	—
923	C₂×D₄	—	86	1	no	—
924	C₂×D₄	—	172	2	no	—
925	C₂×D₄	—	172	2	no	—
926	C₂×D₄	—	172	4	no	—
927	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
928	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
929	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	86	2	no	—
936	C₂²×C₄	—	86	2	no	—
937	C₂²×C₄	—	86	2	no	—
938	C₂²×C₄	—	86	1	no	—
939	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
940	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
941	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
942	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
943	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
944	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
945	Q₁₆	—	86	2	no	—
946	Q₁₆	—	86	4	no	—
947	Q₁₆	—	172	2	no	—
948	Q₁₆	—	172	2	no	—
949	Q₁₆	—	172	2	no	—
950	SD₁₆	—	86	2	no	—
951	SD₁₆	—	86	4	no	—
952	SD₁₆	—	172	2	no	—
953	SD₁₆	—	172	1	no	—
954	SD₁₆	—	172	2	no	—
955	SD₁₆	—	172	2	no	—
956	SD₁₆	—	172	2	no	—
957	D₈	—	172	2	no	—
958	D₈	—	172	1	no	—
959	C₂×C₈	—	43	1	no	—
960	C₂×C₈	—	43	1	no	—
961	C₂×C₈	—	43	1	no	—
962	C₂×C₈	—	43	2	no	—
963	C₂×C₈	—	43	1	no	—
964	C₂×C₈	—	43	2	no	—
965	C₂×C₈	—	172	2	no	—
966	C₂×C₈	—	172	2	no	—
967	C₂×C₈	—	172	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	43	1	no	—
982	C₄⋊C₄	—	43	1	no	—
983	C₄⋊C₄	—	86	1	no	—
984	C₄⋊C₄	—	86	1	no	—
985	C₄⋊C₄	—	86	1	no	—
986	C₄⋊C₄	—	86	1	no	—
987	C₄⋊C₄	—	86	2	no	—
988	C₄⋊C₄	—	86	1	no	—
989	C₄⋊C₄	—	86	2	no	—
990	C₄⋊C₄	—	86	1	no	—
991	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
994	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
995	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
997	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	86	2	no	—
1007	C₂²⋊C₄	—	86	1	no	—
1008	C₂²⋊C₄	—	86	1	no	—
1009	C₂²⋊C₄	—	86	2	no	—
1010	C₂²⋊C₄	—	86	1	no	—
1011	C₂²⋊C₄	—	86	1	no	—
1012	C₂²⋊C₄	—	86	2	no	—
1013	C₂²⋊C₄	—	86	2	no	—
1014	C₂²⋊C₄	—	86	2	no	—
1015	C₂²⋊C₄	—	86	2	no	—
1016	C₂²⋊C₄	—	86	2	no	—
1017	C₂²⋊C₄	—	86	2	no	—
1018	C₂²⋊C₄	—	86	1	no	—
1019	C₂²⋊C₄	—	86	2	no	—
1020	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1021	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1022	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	86	2	no	—
1030	C₄²	—	86	1	no	—
1031	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1032	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1033	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1034	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1035	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1036	C₄²	C₂³×D₄₃	1	2	yes	—
1037	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	86	1	no	—
1040	C₂³	—	86	2	no	—
1041	C₂³	—	344	2	no	—
1042	C₂³	—	344	2	no	—
1043	C₂³	—	172	4	no	—
1044	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1045	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	4	4	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	86	2	no	—
1053	Q₈	—	86	1	no	—
1054	Q₈	—	86	1	no	—
1055	Q₈	—	86	2	no	—
1056	Q₈	—	344	2	no	—
1057	Q₈	#13063371	1	2	yes	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	4	4	no	—
1063	D₄	—	86	2	no	—
1064	D₄	—	86	1	no	—
1065	D₄	—	86	1	no	—
1066	D₄	—	86	2	no	—
1067	D₄	—	344	2	no	—
1068	D₄	—	344	1	no	—
1069	D₄	—	344	2	no	—
1070	D₄	—	344	1	no	—
1071	D₄	—	172	4	no	—
1072	D₄	—	172	2	no	—
1073	D₄	#13063345	1	4	yes	complemented
1074	C₂×C₄	—	2	4	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	4	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	86	1	no	—
1093	C₂×C₄	—	86	1	no	—
1094	C₂×C₄	—	86	1	no	—
1095	C₂×C₄	—	86	2	no	—
1096	C₂×C₄	—	344	2	no	—
1097	C₂×C₄	—	344	2	no	—
1098	C₂×C₄	—	344	2	no	—
1099	C₂×C₄	—	172	2	no	—
1100	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1102	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1103	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1104	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1105	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1106	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1109	C₈	—	86	2	no	—
1110	C₈	—	86	1	no	—
1111	C₈	—	86	2	no	—
1112	C₈	—	86	1	no	—
1113	C₈	—	86	1	no	—
1114	C₈	—	86	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	172	1	no	—
1124	C₂²	—	172	2	no	—
1125	C₂²	—	172	2	no	—
1126	C₂²	—	172	1	no	—
1127	C₂²	—	172	2	no	—
1128	C₂²	—	172	1	no	—
1129	C₂²	—	688	4	no	—
1130	C₂²	C₂×#13063345	1	4	yes	—
1131	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	172	1	no	—
1145	C₄	—	172	1	no	—
1146	C₄	—	172	2	no	—
1147	C₄	—	172	1	no	—
1148	C₄	C₂×#13063345	1	2	yes	—
1149	C₄	C₂×#13063371	1	1	yes	characteristic
1150	C₄	#14583735	1	1	yes	characteristic
1151	C₂	—	2	4	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	344	1	no	—
1155	C₂	—	344	2	no	—
1156	C₂	#19148264	1	1	yes	characteristic
1157	C₂	C₂²×#13063345	1	1	yes	characteristic
1158	C₂	#19149382	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×#3482	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3482	D₄₃
hypocenter	C₄₃	#61956
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3482

Complements

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

N	H ≅ G/N	type
1. #19148556	C₂	semidirect
2. #19147591	C₂	semidirect
3. #19147579	C₂	semidirect
4. #19147291	C₂	semidirect
5. #19147280	C₂	semidirect
6. #19146476	C₂	semidirect
7. #19146454	C₂	semidirect
8. #19146424	C₂	semidirect
9. #19146402	C₂	semidirect
10. D₄×#10621885	C₂	semidirect
11. #19146332	C₂	semidirect
12. #19146303	C₂	semidirect
13. D₄×#10621884	C₂	semidirect
14. #19145942	C₂	semidirect
15. #19145926	C₂	semidirect
16. #19145556	C₂	semidirect
17. #19145547	C₂	semidirect
18. #19144675	C₂	semidirect
19. #19144613	C₂	semidirect
20. #19144050	C₂	semidirect
21. C₂×#14583121	C₂	semidirect
22. #19143706	C₂	semidirect
23. C₄₃×#3482	C₂	semidirect
24. C₂×#13063345	C₂²	semidirect
25. C₂²×#10621885	C₂²	semidirect
44. #14583281	C₂²	semidirect
45. #14583278	C₂²	semidirect
48. #14583256	C₂²	semidirect
49. #14583251	C₂²	semidirect
51. #14583240	C₂²	semidirect
52. #14583229	C₂²	semidirect
55. #14583206	C₂²	semidirect
56. #14583206	C₂²	semidirect
57. #14583203	C₂²	semidirect
58. #14583199	C₂²	semidirect
59. #14583196	C₂²	semidirect
60. #14583181	C₂²	semidirect
62. #14583138	C₂²	semidirect
63. #14583138	C₂²	semidirect
67. #14583126	C₂²	semidirect
72. #14583121	C₂²	semidirect
73. #14583121	C₂²	semidirect
74. #14583121	C₂²	semidirect
75. #14583121	C₂²	semidirect
76. #14583121	C₂²	semidirect
77. #14583118	C₂²	semidirect
79. #14583114	C₂²	semidirect
80. #14583111	C₂²	semidirect
81. #14583109	C₂²	semidirect
82. #14583106	C₂²	semidirect
83. #14583104	C₂²	semidirect
87. #14583061	C₂²	semidirect
88. #14583059	C₂²	semidirect
89. #14583059	C₂²	semidirect
90. #14583055	C₂²	semidirect
91. #14583054	C₂²	semidirect
95. #14583037	C₂²	semidirect
97. Q₈×C₄₃⋊C₈	C₂²	semidirect
98. Q₈×C₄₃⋊C₈	C₂²	semidirect
99. C₄×#10621885	C₂²	semidirect
100. C₄×#10621885	C₂²	semidirect
101. C₄×#10621885	C₂²	semidirect
103. C₄×#10621884	C₂²	semidirect
104. C₄×#10621884	C₂²	semidirect
105. C₄×#10621883	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. #14582893	C₂²	semidirect
116. C₂×#13063248	C₂²	semidirect
118. C₄₃×#557	C₂²	semidirect
120. C₄₃×#556	C₂²	semidirect
122. C₄₃×#552	C₂²	semidirect
124. C₄₃×#548	C₂²	semidirect
128. C₄₃×#533	C₂²	semidirect
130. C₄₃×#529	C₂²	semidirect
133. C₄×#41×C₄₃	C₂²	semidirect
134. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
478. D₄×C₄₃	#135	semidirect
573. #3482	D₄₃	semidirect
607. #557	C₂×D₄₃	semidirect
610. #556	C₂×D₄₃	semidirect
613. #552	C₂×D₄₃	semidirect
618. #548	C₂×D₄₃	semidirect
627. #533	C₂×D₄₃	semidirect
632. #529	C₂×D₄₃	semidirect
637. C₄×#41	C₂×D₄₃	semidirect
638. C₂×C₄×Q₈	C₂×D₄₃	semidirect
714. C₄₃	#61956	semidirect
1073. D₄	#13063345	semidirect

Maximal subgroups

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

subgroup	index
#19148556	2
#19147591	2
#19147579	2
#19147291	2
#19147280	2
#19146476	2
#19146454	2
#19146424	2
#19146402	2
D₄×#10621885	2
#19146332	2
#19146303	2
D₄×#10621884	2
#19145942	2
#19145926	2
#19145556	2
#19145547	2
#19144675	2
#19144613	2
#19144050	2
C₂×#14583121	2
#19143706	2
C₄₃×#3482	2
#61956	43