Subgroups — #25979557

Order 11008.

1936 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148629	C₂	1	1	yes	maximal, characteristic, complemented
2	#19147633	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147501	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147266	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147251	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147221	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147065	C₂	1	2	yes	maximal, complemented
8	#19146545	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146497	C₂	1	2	yes	maximal, complemented
10	#19146413	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146402	C₂	1	2	yes	maximal, complemented
12	#19146215	C₂	1	1	yes	maximal, characteristic, complemented
13	#19146091	C₂	1	2	yes	maximal, complemented
14	#19145272	C₂	1	2	yes	maximal, complemented
15	#19145170	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144794	C₂	1	2	yes	maximal, complemented
17	#19144773	C₂	1	2	yes	maximal, complemented
18	#19144717	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144682	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143571	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143423	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×#10621884	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063350	C₂²	1	2	yes	—
25	C₂²×#10621884	C₂²	1	1	yes	characteristic
26	#14583614	C₂²	1	1	yes	characteristic
27	#14583609	C₂²	1	1	yes	characteristic
28	#14583602	—	2	1	no	—
29	#14583595	C₂²	1	2	yes	—
30	#14583571	C₂²	1	1	yes	characteristic
31	#14583542	—	2	1	no	—
32	#14583541	—	2	2	no	—
33	D₄×D₁₇₂	C₂²	1	2	yes	—
34	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
35	#14583504	C₂²	1	2	yes	—
36	#14583488	—	2	2	no	—
37	#14583449	C₂²	1	1	yes	characteristic
38	#14583412	—	2	1	no	—
39	#121×D₄₃	—	2	1	no	—
40	#14583373	C₂²	1	2	yes	—
41	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
42	#14583305	C₂²	1	2	yes	complemented
43	#14583302	C₂²	1	1	yes	characteristic, complemented
44	#14583289	C₂²	1	2	yes	complemented
45	#14583275	C₂²	1	1	yes	characteristic, complemented
46	#14583253	C₂²	1	2	yes	complemented
47	#14583247	C₂²	1	2	yes	complemented
48	#14583247	C₂²	1	1	yes	characteristic, complemented
49	#14583245	C₂²	1	1	yes	characteristic, complemented
50	#14583237	C₂²	1	2	yes	complemented
51	#14583220	C₂²	1	2	yes	complemented
52	#14583217	C₂²	1	2	yes	complemented
53	#14583215	C₂²	1	2	yes	complemented
54	#14583212	C₂²	1	2	yes	complemented
55	#14583212	C₂²	1	2	yes	complemented
56	#14583206	C₂²	1	2	yes	complemented
57	#14583199	C₂²	1	2	yes	complemented
58	#14583194	C₂²	1	1	yes	characteristic, complemented
59	#14583194	C₂²	1	1	yes	characteristic, complemented
60	#14583186	C₂²	1	1	yes	characteristic
61	#14583186	C₂²	1	2	yes	complemented
62	#14583186	C₂²	1	1	yes	characteristic, complemented
63	#14583176	C₂²	1	2	yes	—
64	#14583150	C₂²	1	2	yes	complemented
65	#14583147	C₂²	1	2	yes	complemented
66	#14583133	C₂²	1	2	yes	complemented
67	#14583133	C₂²	1	2	yes	complemented
68	#14583133	C₂²	1	2	yes	complemented
69	#14583130	C₂²	1	2	yes	complemented
70	#14583111	C₂²	1	2	yes	—
71	#14583111	C₂²	1	2	yes	complemented
72	#14583099	C₂²	1	1	yes	characteristic, complemented
73	#14583099	C₂²	1	2	yes	complemented
74	#14583099	C₂²	1	1	yes	characteristic, complemented
75	#14583094	C₂²	1	2	yes	complemented
76	#14583091	C₂²	1	1	yes	characteristic
77	#14583091	C₂²	1	1	yes	characteristic, complemented
78	#14583049	C₂²	1	2	yes	—
79	#14583044	C₂²	1	2	yes	complemented
80	#14583044	C₂²	1	2	yes	complemented
81	#14583038	C₂²	1	2	yes	complemented
82	#14583032	C₂²	1	2	yes	—
83	#14583032	C₂²	1	2	yes	—
84	#14583030	C₂²	1	1	yes	characteristic, complemented
85	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	#14583009	C₂²	1	2	yes	—
87	#14583009	C₂²	1	2	yes	complemented
88	#14583009	C₂²	1	2	yes	complemented
89	#14582997	C₂²	1	2	yes	—
90	#14582997	C₂²	1	2	yes	complemented
91	#14582997	C₂²	1	2	yes	complemented
92	C₄×#10621884	C₂²	1	1	yes	characteristic
93	C₄×#10621884	C₂²	1	1	yes	characteristic
94	C₄×#10621884	C₂²	1	1	yes	characteristic
95	C₄×#10621884	C₂²	1	1	yes	characteristic
96	C₄×#10621884	C₂²	1	2	yes	complemented
97	C₄×#10621884	C₂²	1	1	yes	characteristic, complemented
98	C₄×#10621884	C₂²	1	1	yes	characteristic, complemented
99	C₄×#10621884	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10621884	C₂²	1	1	yes	characteristic, complemented
101	C₄×#10621882	C₂²	1	2	yes	—
102	C₄×#10621882	C₂²	1	2	yes	complemented
103	C₄×#10621882	C₂²	1	2	yes	complemented
104	#14582977	C₂²	1	1	yes	characteristic, complemented
105	#14582971	C₂²	1	2	yes	complemented
106	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
107	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
108	#14582960	C₂²	1	2	yes	complemented
109	#14582956	C₂²	1	1	yes	characteristic, complemented
110	#14582939	C₂²	1	2	yes	complemented
111	C₂×#13063256	C₂²	1	1	yes	characteristic, complemented
112	#14582895	C₂²	1	2	yes	complemented
113	C₂×#13063249	C₂²	1	1	yes	characteristic, complemented
114	C₂×#13063245	C₂²	1	1	yes	characteristic
115	C₂×#13063245	C₂²	1	2	yes	—
116	#14582855	C₂²	1	2	yes	complemented
117	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₄₃×#559	—	2	1	no	—
119	C₄₃×#559	C₂²	1	1	yes	characteristic, complemented
120	Q₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
121	C₄₃×#554	—	2	1	no	—
122	C₄₃×#554	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#550	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#548	C₂²	1	2	yes	complemented
125	C₄₃×#547	—	2	2	no	—
126	C₄₃×#547	C₂²	1	2	yes	complemented
127	C₄₃×#542	—	2	2	no	—
128	C₄₃×#542	C₂²	1	2	yes	complemented
129	C₄₃×#532	—	2	1	no	—
130	C₄₃×#532	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#529	—	2	1	no	—
132	C₄₃×#529	C₂²	1	1	yes	characteristic
133	C₄₃×#520	C₂²	1	2	yes	complemented
134	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621902	—	2	1	no	—
136	C₂×#10621898	—	2	1	no	—
137	C₂²×D₁₇₂	C₂³	1	2	yes	—
138	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
139	C₂×D₄×D₄₃	—	2	2	no	—
140	C₂×D₄×D₄₃	—	2	1	no	—
141	C₂²×C₄×D₄₃	—	2	1	no	—
142	#13063350	—	2	8	no	—
143	C₂×#10621884	—	2	4	no	—
144	C₂×#10621884	C₂³	1	1	yes	characteristic
145	C₂×#10621884	C₂³	1	2	yes	—
146	C₂×#10621884	C₂³	1	1	yes	characteristic
147	C₂×#10621884	C₂³	1	1	yes	characteristic
148	C₂×#10621884	C₂³	1	2	yes	—
149	C₂×#10621884	C₂³	1	1	yes	characteristic
150	C₂×#10621882	C₂³	1	2	yes	—
151	C₂×#10621882	C₂³	1	2	yes	—
152	C₂×#10621882	C₂³	1	2	yes	—
153	C₂×#10621882	C₂³	1	2	yes	—
154	C₂×#10621877	C₂³	1	2	yes	—
155	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
157	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
158	#13063325	C₂³	1	1	yes	characteristic
159	#13063322	C₂³	1	2	yes	—
160	#13063322	C₂³	1	1	yes	characteristic
161	#13063320	—	2	2	no	—
162	#13063317	C₂³	1	2	yes	—
163	#13063313	—	2	1	no	—
164	#13063311	—	2	2	no	—
165	#13063310	—	2	2	no	—
166	#13063310	—	2	2	no	—
167	#13063307	—	2	2	no	—
168	#13063303	—	2	2	no	—
169	#13063301	—	2	1	no	—
170	#13063300	—	2	1	no	—
171	#13063300	—	2	2	no	—
172	#13063300	—	2	1	no	—
173	#13063300	—	2	2	no	—
174	#13063299	—	2	1	no	—
175	#13063299	C₂³	1	2	yes	—
176	#13063299	C₂³	1	2	yes	—
177	#13063299	C₂³	1	2	yes	—
178	#13063298	—	2	2	no	—
179	#13063298	—	2	2	no	—
180	#13063297	—	2	2	no	—
181	#13063296	—	2	1	no	—
182	#13063295	—	2	2	no	—
183	#13063295	—	2	2	no	—
184	#13063295	—	2	2	no	—
185	C₄×D₁₇₂	—	2	1	no	—
186	C₄×D₁₇₂	—	2	1	no	—
187	C₄×D₁₇₂	—	2	1	no	—
188	C₄×D₁₇₂	C₂³	1	2	yes	—
189	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
190	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
191	C₄×D₁₇₂	C₂³	1	2	yes	—
192	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
193	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
194	C₄×D₁₇₂	C₂³	1	2	yes	—
195	#13063287	—	2	2	no	—
196	#13063287	—	2	2	no	—
197	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
198	#13063284	C₂³	1	2	yes	—
199	#13063283	—	2	1	no	—
200	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
201	C₄⋊C₄×D₄₃	—	2	1	no	—
202	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
203	C₂²⋊C₄×D₄₃	—	2	2	no	—
204	C₂²⋊C₄×D₄₃	—	2	2	no	—
205	#13063258	C₂³	1	2	yes	—
206	#13063258	C₂³	1	2	yes	—
207	#13063258	C₂³	1	2	yes	—
208	#13063258	C₂³	1	2	yes	—
209	#13063256	C₂³	1	1	yes	characteristic
210	#13063256	C₂³	1	2	yes	—
211	#13063256	C₂³	1	1	yes	characteristic
212	#13063256	C₂³	1	1	yes	characteristic
213	#13063256	C₂³	1	1	yes	characteristic
214	#13063256	C₂³	1	2	yes	—
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	2	yes	—
219	#13063249	C₂³	1	1	yes	characteristic
220	#13063249	C₂³	1	2	yes	—
221	#13063249	C₂³	1	2	yes	—
222	#13063249	C₂³	1	1	yes	characteristic
223	#13063249	C₂³	1	1	yes	characteristic
224	#13063249	C₂³	1	1	yes	characteristic
225	#13063246	C₂³	1	2	yes	—
226	#13063246	C₂³	1	2	yes	—
227	#13063246	C₂³	1	2	yes	—
228	#13063246	C₂³	1	2	yes	—
229	#13063245	C₂³	1	2	yes	—
230	#13063245	C₂³	1	2	yes	—
231	#13063245	C₂³	1	1	yes	characteristic
232	#13063245	C₂³	1	2	yes	—
233	#13063245	C₂³	1	2	yes	—
234	#13063245	C₂³	1	2	yes	—
235	#13063245	C₂³	1	2	yes	—
236	#13063245	C₂³	1	1	yes	characteristic
237	#13063245	C₂³	1	1	yes	characteristic
238	#13063245	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
242	#13063236	C₂³	1	2	yes	—
243	#13063236	C₂³	1	2	yes	—
244	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×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	C₂×#41×C₄₃	—	2	2	no	—
250	C₂×#41×C₄₃	—	2	1	no	—
251	C₂×#41×C₄₃	C₂³	1	2	yes	—
252	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈×C₄₃	—	2	1	no	—
254	C₄⋊Q₈×C₄₃	—	2	2	no	—
255	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
256	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
257	#127×C₄₃	—	2	1	no	—
258	#127×C₄₃	C₂³	1	1	yes	characteristic
259	#126×C₄₃	—	2	2	no	—
260	#126×C₄₃	D₄	1	2	yes	—
261	#125×C₄₃	—	2	1	no	—
262	#125×C₄₃	D₄	1	1	yes	characteristic
263	#124×C₄₃	—	2	1	no	—
264	#124×C₄₃	—	2	2	no	—
265	#124×C₄₃	—	2	2	no	—
266	#124×C₄₃	—	2	1	no	—
267	#124×C₄₃	D₄	1	1	yes	characteristic
268	#124×C₄₃	C₂³	1	2	yes	—
269	#123×C₄₃	—	2	2	no	—
270	#123×C₄₃	—	2	2	no	—
271	#123×C₄₃	—	2	2	no	—
272	#123×C₄₃	—	2	2	no	—
273	#123×C₄₃	D₄	1	2	yes	—
274	C₂²⋊Q₈×C₄₃	—	2	2	no	—
275	C₂²⋊Q₈×C₄₃	—	2	2	no	—
276	C₂²⋊Q₈×C₄₃	—	2	2	no	—
277	C₂²⋊Q₈×C₄₃	—	2	2	no	—
278	C₂²⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
279	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
280	#121×C₄₃	—	2	2	no	—
281	#121×C₄₃	—	2	1	no	—
282	#121×C₄₃	—	2	2	no	—
283	#121×C₄₃	D₄	1	1	yes	characteristic
284	#121×C₄₃	C₂³	1	2	yes	—
285	#121×C₄₃	C₂³	1	2	yes	—
286	C₄×Q₈×C₄₃	—	2	1	no	—
287	C₄×Q₈×C₄₃	—	2	1	no	—
288	C₄×Q₈×C₄₃	—	2	1	no	—
289	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
291	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
293	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
294	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₄₃	—	2	1	no	—
296	C₄×D₄×C₄₃	—	2	1	no	—
297	C₄×D₄×C₄₃	—	2	1	no	—
298	C₄×D₄×C₄₃	—	2	2	no	—
299	C₄×D₄×C₄₃	—	2	2	no	—
300	C₄×D₄×C₄₃	—	2	2	no	—
301	C₄×D₄×C₄₃	—	2	1	no	—
302	C₄×D₄×C₄₃	C₂³	1	2	yes	—
303	C₄×D₄×C₄₃	C₂³	1	2	yes	—
304	C₄×D₄×C₄₃	C₂³	1	2	yes	—
305	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
306	#117×C₄₃	—	2	2	no	—
307	#117×C₄₃	C₂³	1	2	yes	—
308	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
309	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
310	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
311	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
312	C₂×C₄²×C₄₃	—	2	1	no	—
313	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
314	C₂³×D₄₃	—	2	1	no	—
315	C₂³×D₄₃	—	2	2	no	—
316	#41×C₄₃	—	2	4	no	—
317	#41×C₄₃	—	4	2	no	—
318	#41×C₄₃	—	8	2	no	—
319	#41×C₄₃	—	8	4	no	—
320	C₂×Q₈×C₄₃	—	2	1	no	—
321	C₂×Q₈×C₄₃	—	2	2	no	—
322	C₂×Q₈×C₄₃	—	2	1	no	—
323	C₂×Q₈×C₄₃	—	2	2	no	—
324	C₂×Q₈×C₄₃	—	4	1	no	—
325	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₄₃	—	2	1	no	—
329	C₂×D₄×C₄₃	—	2	1	no	—
330	C₂×D₄×C₄₃	—	2	2	no	—
331	C₂×D₄×C₄₃	—	2	2	no	—
332	C₂×D₄×C₄₃	—	2	2	no	—
333	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
334	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
335	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₄₃	—	2	2	no	—
337	C₂²×C₄×C₄₃	—	2	2	no	—
338	C₂²×C₄×C₄₃	—	2	2	no	—
339	C₂²×C₄×C₄₃	—	2	1	no	—
340	C₂²×C₄×C₄₃	—	2	1	no	—
341	C₂²×C₄×C₄₃	—	2	2	no	—
342	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
346	C₂×C₂²⋊D₄₃	—	2	2	no	—
347	C₂×C₂²⋊D₄₃	—	2	2	no	—
348	C₂×C₂²⋊D₄₃	—	2	2	no	—
349	C₂²×Dic₄₃	—	2	1	no	—
350	#10621902	—	8	2	no	—
351	D₄×D₄₃	—	8	4	no	—
352	D₄×D₄₃	—	8	2	no	—
353	#10621898	—	8	2	no	—
354	C₂×D₁₇₂	—	2	2	no	—
355	C₂×D₁₇₂	—	2	1	no	—
356	C₂×D₁₇₂	—	2	1	no	—
357	C₂×D₁₇₂	—	2	2	no	—
358	C₂×D₁₇₂	—	2	1	no	—
359	C₂×D₁₇₂	—	2	2	no	—
360	C₂×D₁₇₂	—	2	2	no	—
361	C₂×D₁₇₂	—	2	4	no	—
362	C₂×D₁₇₂	—	4	1	no	—
363	C₂×D₁₇₂	—	4	2	no	—
364	C₂×D₁₇₂	C₂⁴	1	2	yes	—
365	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
366	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×D₄₃	—	2	1	no	—
368	C₂×C₄×D₄₃	—	2	1	no	—
369	C₂×C₄×D₄₃	—	2	1	no	—
370	C₂×C₄×D₄₃	—	2	2	no	—
371	C₂×C₄×D₄₃	—	2	2	no	—
372	C₂×C₄×D₄₃	—	2	2	no	—
373	C₂×C₄×D₄₃	—	2	1	no	—
374	C₂×C₄×D₄₃	—	8	2	no	—
375	C₂×Dic₈₆	—	2	1	no	—
376	C₄⋊C₄×C₄₃	—	2	1	no	—
377	C₄⋊C₄×C₄₃	—	2	2	no	—
378	C₄⋊C₄×C₄₃	—	2	2	no	—
379	C₄⋊C₄×C₄₃	—	2	1	no	—
380	C₄⋊C₄×C₄₃	—	2	1	no	—
381	C₄⋊C₄×C₄₃	—	2	1	no	—
382	C₄⋊C₄×C₄₃	—	2	1	no	—
383	C₄⋊C₄×C₄₃	—	2	1	no	—
384	C₄⋊C₄×C₄₃	—	2	2	no	—
385	C₄⋊C₄×C₄₃	—	2	2	no	—
386	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
387	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
388	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
394	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
395	C₂²⋊C₄×C₄₃	—	2	2	no	—
396	C₂²⋊C₄×C₄₃	—	2	2	no	—
397	C₂²⋊C₄×C₄₃	—	2	2	no	—
398	C₂²⋊C₄×C₄₃	—	2	2	no	—
399	C₂²⋊C₄×C₄₃	—	2	2	no	—
400	C₂²⋊C₄×C₄₃	—	2	2	no	—
401	C₂²⋊C₄×C₄₃	—	2	2	no	—
402	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
405	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
406	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
407	C₄²×C₄₃	—	2	1	no	—
408	C₄²×C₄₃	—	2	1	no	—
409	C₄²×C₄₃	—	2	1	no	—
410	C₄²×C₄₃	—	2	1	no	—
411	C₄²×C₄₃	—	2	2	no	—
412	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
413	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
415	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
416	C₄²×C₄₃	C₂⁴	1	2	yes	—
417	C₂²⋊Dic₄₃	—	2	2	no	—
418	#10621884	—	2	2	no	—
419	#10621884	—	2	4	no	—
420	#10621884	—	2	2	no	—
421	#10621884	—	2	2	no	—
422	#10621884	—	4	2	no	—
423	#10621884	#41	1	4	yes	complemented
424	#10621882	—	2	4	no	—
425	#10621882	—	2	4	no	—
426	#10621882	—	4	2	no	—
427	#10621882	—	4	2	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	1	no	—
433	(C₂×D₄₃)⋊C₄	—	2	1	no	—
434	(C₂×D₄₃)⋊C₄	—	2	1	no	—
435	(C₂×D₄₃)⋊C₄	—	2	2	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	1	no	—
440	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
442	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
443	Dic₄₃⋊C₄	—	2	2	no	—
444	Dic₄₃⋊C₄	—	2	2	no	—
445	C₄×Dic₄₃	—	2	2	no	—
446	#10621877	—	2	4	no	—
447	C₂×C₄₃⋊C₈	—	2	2	no	—
448	C₂×C₄₃⋊C₈	—	4	1	no	—
449	C₂×C₄₃⋊C₈	—	4	2	no	—
450	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
451	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
453	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
454	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
455	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
456	C₂³×C₄₃	—	2	2	no	—
457	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
458	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
459	C₂²×D₄₃	—	2	1	no	—
460	C₂²×D₄₃	—	2	1	no	—
461	C₂²×D₄₃	—	2	2	no	—
462	C₂²×D₄₃	—	4	2	no	—
463	C₂²×D₄₃	—	4	4	no	—
464	C₂²×D₄₃	—	4	2	no	—
465	C₂²×D₄₃	—	8	1	no	—
466	C₂²×D₄₃	—	8	2	no	—
467	C₂²×D₄₃	—	8	2	no	—
468	Q₈×C₄₃	—	2	2	no	—
469	Q₈×C₄₃	—	2	1	no	—
470	Q₈×C₄₃	—	2	1	no	—
471	Q₈×C₄₃	—	2	1	no	—
472	Q₈×C₄₃	—	4	2	no	—
473	Q₈×C₄₃	—	8	1	no	—
474	Q₈×C₄₃	—	8	2	no	—
475	Q₈×C₄₃	C₂×#41	1	2	yes	—
476	D₄×C₄₃	—	2	4	no	—
477	D₄×C₄₃	—	2	2	no	—
478	D₄×C₄₃	—	2	2	no	—
479	D₄×C₄₃	—	2	2	no	—
480	D₄×C₄₃	—	4	4	no	—
481	D₄×C₄₃	—	4	4	no	—
482	D₄×C₄₃	—	4	2	no	—
483	D₄×C₄₃	—	8	1	no	—
484	D₄×C₄₃	—	8	2	no	—
485	C₂×C₄×C₄₃	—	2	2	no	—
486	C₂×C₄×C₄₃	—	2	1	no	—
487	C₂×C₄×C₄₃	—	2	2	no	—
488	C₂×C₄×C₄₃	—	2	1	no	—
489	C₂×C₄×C₄₃	—	2	2	no	—
490	C₂×C₄×C₄₃	—	2	1	no	—
491	C₂×C₄×C₄₃	—	2	2	no	—
492	C₂×C₄×C₄₃	—	2	1	no	—
493	C₂×C₄×C₄₃	—	2	1	no	—
494	C₂×C₄×C₄₃	—	2	1	no	—
495	C₂×C₄×C₄₃	—	2	2	no	—
496	C₂×C₄×C₄₃	—	4	4	no	—
497	C₂×C₄×C₄₃	—	4	2	no	—
498	C₂×C₄×C₄₃	—	4	2	no	—
499	C₂×C₄×C₄₃	—	8	2	no	—
500	C₂×C₄×C₄₃	—	8	2	no	—
501	C₂×C₄×C₄₃	—	8	2	no	—
502	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
509	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
511	C₂²⋊D₄₃	—	4	4	no	—
512	C₂²⋊D₄₃	—	8	2	no	—
513	C₂²⋊D₄₃	—	8	2	no	—
514	C₂×Dic₄₃	—	2	1	no	—
515	C₂×Dic₄₃	—	2	2	no	—
516	C₂×Dic₄₃	—	2	1	no	—
517	C₂×Dic₄₃	—	8	1	no	—
518	D₁₇₂	—	2	2	no	—
519	D₁₇₂	—	2	1	no	—
520	D₁₇₂	—	2	1	no	—
521	D₁₇₂	—	2	1	no	—
522	D₁₇₂	—	2	2	no	—
523	D₁₇₂	—	4	4	no	—
524	D₁₇₂	—	4	2	no	—
525	D₁₇₂	—	4	2	no	—
526	D₁₇₂	—	8	1	no	—
527	D₁₇₂	—	8	2	no	—
528	D₁₇₂	—	8	2	no	—
529	D₁₇₂	C₂×#41	1	2	yes	—
530	C₄×D₄₃	—	4	2	no	—
531	C₄×D₄₃	—	4	2	no	—
532	C₄×D₄₃	—	8	1	no	—
533	C₄×D₄₃	—	8	1	no	—
534	C₄×D₄₃	—	8	2	no	—
535	C₄×D₄₃	—	8	2	no	—
536	C₄×D₄₃	—	8	2	no	—
537	Dic₈₆	—	8	1	no	—
538	C₄₃⋊C₈	—	2	1	no	—
539	C₄₃⋊C₈	—	2	2	no	—
540	C₄₃⋊C₈	—	2	1	no	—
541	C₄₃⋊C₈	—	2	1	no	—
542	C₄₃⋊C₈	—	2	2	no	—
543	C₄₃⋊C₈	C₂×#41	1	2	yes	—
544	#61498	—	43	1	no	maximal, Sylow
545	C₂²×C₄₃	—	2	1	no	—
546	C₂²×C₄₃	—	2	1	no	—
547	C₂²×C₄₃	—	2	2	no	—
548	C₂²×C₄₃	—	2	2	no	—
549	C₂²×C₄₃	—	2	2	no	—
550	C₂²×C₄₃	—	4	2	no	—
551	C₂²×C₄₃	—	4	2	no	—
552	C₂²×C₄₃	—	4	2	no	—
553	C₂²×C₄₃	#576	1	2	yes	—
554	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
555	C₂×D₄₃	—	2	2	no	—
556	C₂×D₄₃	—	4	1	no	—
557	C₂×D₄₃	—	4	1	no	—
558	C₂×D₄₃	—	4	1	no	—
559	C₂×D₄₃	—	4	2	no	—
560	C₂×D₄₃	—	4	1	no	—
561	C₂×D₄₃	—	4	2	no	—
562	C₂×D₄₃	—	4	1	no	—
563	C₂×D₄₃	—	4	2	no	—
564	C₂×D₄₃	—	8	4	no	—
565	C₂×D₄₃	—	16	4	no	—
566	C₄×C₄₃	—	2	2	no	—
567	C₄×C₄₃	—	2	1	no	—
568	C₄×C₄₃	—	2	2	no	—
569	C₄×C₄₃	—	2	1	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	1	no	—
576	C₄×C₄₃	—	4	1	no	—
577	C₄×C₄₃	—	4	2	no	—
578	C₄×C₄₃	#577	1	2	yes	—
579	C₄×C₄₃	C₂²×#41	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	#3522	D₄₃	1	1	yes	characteristic, complemented
585	#3519	—	43	1	no	—
586	#3399	—	43	1	no	—
587	#3385	—	43	1	no	—
588	#3362	—	43	1	no	—
589	#3361	—	43	1	no	—
590	#3357	—	43	1	no	—
591	#3345	—	43	2	no	—
592	#3305	—	43	1	no	—
593	#3301	—	43	2	no	—
594	#3295	—	43	1	no	—
595	#3294	—	43	2	no	—
596	#3274	—	43	1	no	—
597	#3265	—	43	2	no	—
598	#3179	—	43	2	no	—
599	#3169	—	43	1	no	—
600	#3119	—	43	2	no	—
601	#3118	—	43	2	no	—
602	#3112	—	43	1	no	—
603	#3109	—	43	1	no	—
604	#2966	—	43	1	no	—
605	#2946	—	43	2	no	—
606	C₂×C₄×SD₁₆	—	43	1	no	—
607	C₂×C₄₃	—	2	2	no	—
608	C₂×C₄₃	—	4	2	no	—
609	C₂×C₄₃	—	8	2	no	—
610	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
611	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
612	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
613	D₄₃	—	4	2	no	—
614	D₄₃	—	8	1	no	—
615	D₄₃	—	8	2	no	—
616	C₂×AGL(1,ℤ/8)	—	43	2	no	—
617	C₂²×SD₁₆	—	43	1	no	—
618	#559	—	2	1	no	—
619	#559	C₂×D₄₃	1	1	yes	characteristic, complemented
620	Q₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
621	#555	—	43	1	no	—
622	#554	—	2	1	no	—
623	#554	—	43	1	no	—
624	#554	C₂×D₄₃	1	1	yes	characteristic, complemented
625	#553	—	43	2	no	—
626	#553	—	86	1	no	—
627	#550	—	43	1	no	—
628	#550	C₂×D₄₃	1	1	yes	characteristic, complemented
629	#548	C₂×D₄₃	1	2	yes	complemented
630	#547	—	2	2	no	—
631	#547	C₂×D₄₃	1	2	yes	complemented
632	#546	—	86	1	no	—
633	#546	—	86	2	no	—
634	D₄²	—	43	2	no	—
635	D₄²	—	43	1	no	—
636	#542	—	2	2	no	—
637	#542	C₂×D₄₃	1	2	yes	complemented
638	#540	—	43	2	no	—
639	#538	—	86	2	no	—
640	#532	—	2	1	no	—
641	#532	—	43	1	no	—
642	#532	C₂×D₄₃	1	1	yes	characteristic, complemented
643	#529	—	2	1	no	—
644	#529	C₂×D₄₃	1	1	yes	characteristic
645	#525	—	86	1	no	—
646	C₂×#121	—	86	1	no	—
647	#520	C₂×D₄₃	1	2	yes	complemented
648	#518	—	43	2	no	—
649	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
650	C₂×C₄×D₄	—	43	1	no	—
651	#501	—	43	2	no	—
652	#500	—	43	1	no	—
653	#496	—	43	2	no	—
654	#493	—	43	1	no	—
655	#488	—	43	2	no	—
656	#486	—	43	1	no	—
657	#486	—	43	2	no	—
658	#486	—	43	1	no	—
659	#485	—	43	2	no	—
660	#482	—	43	2	no	—
661	#481	—	43	2	no	—
662	#481	—	43	2	no	—
663	#480	—	43	2	no	—
664	#480	—	43	2	no	—
665	#479	—	43	2	no	—
666	#478	—	43	2	no	—
667	#477	—	43	1	no	—
668	#477	—	43	1	no	—
669	#476	—	43	2	no	—
670	#476	—	43	1	no	—
671	#476	—	43	1	no	—
672	#474	—	43	2	no	—
673	#469	—	43	2	no	—
674	#468	—	43	2	no	—
675	#466	—	43	2	no	—
676	#466	—	43	2	no	—
677	#466	—	43	2	no	—
678	#465	—	43	2	no	—
679	#463	—	43	2	no	—
680	#463	—	43	2	no	—
681	#460	—	43	1	no	—
682	#460	—	43	2	no	—
683	#460	—	43	1	no	—
684	#459	—	43	1	no	—
685	#459	—	43	1	no	—
686	#459	—	43	2	no	—
687	#450	—	43	2	no	—
688	#449	—	43	2	no	—
689	#449	—	43	2	no	—
690	#448	—	43	2	no	—
691	#447	—	43	2	no	—
692	#447	—	43	2	no	—
693	#446	—	43	1	no	—
694	C₈×Q₈	—	43	1	no	—
695	#442	—	43	2	no	—
696	#442	—	43	2	no	—
697	#442	—	43	2	no	—
698	#440	—	43	2	no	—
699	#440	—	43	2	no	—
700	#440	—	43	2	no	—
701	C₄×SD₁₆	—	43	1	no	—
702	C₄×SD₁₆	—	43	1	no	—
703	C₄×SD₁₆	—	43	1	no	—
704	C₄×SD₁₆	—	43	2	no	—
705	C₄×SD₁₆	—	43	1	no	—
706	C₄×SD₁₆	—	43	1	no	—
707	C₄×SD₁₆	—	43	1	no	—
708	C₄×SD₁₆	—	43	1	no	—
709	C₄×SD₁₆	—	43	1	no	—
710	C₄×D₈	—	43	2	no	—
711	C₄×D₈	—	43	2	no	—
712	C₄×D₈	—	43	2	no	—
713	#436	—	43	1	no	—
714	#435	—	43	2	no	—
715	C₈×D₄	—	43	2	no	—
716	C₈×D₄	—	43	1	no	—
717	#433	—	43	2	no	—
718	#432	—	43	1	no	—
719	#428	—	43	2	no	—
720	C₂×#106	—	43	1	no	—
721	#416	—	43	2	no	—
722	C₂×#103	—	43	1	no	—
723	C₂×#102	—	43	1	no	—
724	C₂×#102	—	43	2	no	—
725	#405	—	43	2	no	—
726	C₂×C₄×C₈	—	43	1	no	—
727	C₄₃	#61498	1	1	yes	characteristic, complemented, Sylow
728	C₂×#41	—	2	2	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	—	86	1	no	—
731	C₂×#41	—	86	1	no	—
732	C₂×#41	C₂²×D₄₃	1	2	yes	—
733	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
734	C₂²×D₄	—	43	1	no	—
735	C₂²×D₄	—	43	2	no	—
736	C₂²×D₄	—	86	2	no	—
737	C₂²×D₄	—	86	1	no	—
738	C₂³×C₄	—	86	1	no	—
739	AGL(1,ℤ/8)	—	86	8	no	—
740	C₂×SD₁₆	—	43	1	no	—
741	C₂×SD₁₆	—	43	1	no	—
742	C₂×SD₁₆	—	43	1	no	—
743	C₂×SD₁₆	—	43	1	no	—
744	C₂×SD₁₆	—	43	2	no	—
745	C₂×SD₁₆	—	43	2	no	—
746	C₂×SD₁₆	—	86	4	no	—
747	C₂×D₈	—	43	2	no	—
748	C₂×D₈	—	43	2	no	—
749	C₂×D₈	—	43	2	no	—
750	C₂×D₈	—	43	2	no	—
751	C₂×M₁₆	—	43	2	no	—
752	C₂²×C₈	—	43	1	no	—
753	C₂²×C₈	—	43	1	no	—
754	C₂²×C₈	—	43	2	no	—
755	C₄⋊Q₈	—	2	1	no	—
756	C₄⋊Q₈	—	2	2	no	—
757	C₄⋊Q₈	—	43	1	no	—
758	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
759	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
760	#127	—	2	1	no	—
761	#127	—	43	1	no	—
762	#127	—	43	2	no	—
763	#127	C₂²×D₄₃	1	1	yes	characteristic
764	#126	—	2	2	no	—
765	#126	—	86	2	no	—
766	#126	C₂²⋊D₄₃	1	2	yes	—
767	#125	—	2	1	no	—
768	#125	—	43	2	no	—
769	#125	C₂²⋊D₄₃	1	1	yes	characteristic
770	#124	—	2	1	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	1	no	—
774	#124	—	86	2	no	—
775	#124	—	86	1	no	—
776	#124	C₂²⋊D₄₃	1	1	yes	characteristic
777	#124	C₂²×D₄₃	1	2	yes	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	86	2	no	—
783	#123	—	86	2	no	—
784	#123	—	86	2	no	—
785	#123	C₂²⋊D₄₃	1	2	yes	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	86	1	no	—
791	C₂²⋊Q₈	—	86	2	no	—
792	C₂²⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
794	#121	—	2	2	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	43	2	no	—
798	#121	—	43	2	no	—
799	#121	—	43	2	no	—
800	#121	—	86	2	no	—
801	#121	—	86	1	no	—
802	#121	—	86	1	no	—
803	#121	—	86	1	no	—
804	#121	—	86	1	no	—
805	#121	—	86	2	no	—
806	#121	—	86	2	no	—
807	#121	—	86	2	no	—
808	#121	—	86	2	no	—
809	#121	C₂²⋊D₄₃	1	1	yes	characteristic
810	#121	C₂²×D₄₃	1	2	yes	—
811	#121	C₂²×D₄₃	1	2	yes	—
812	#120	—	86	2	no	—
813	#120	—	86	2	no	—
814	#120	—	86	2	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
819	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
820	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
821	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
822	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
823	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	43	1	no	—
832	C₄×D₄	—	43	1	no	—
833	C₄×D₄	—	43	1	no	—
834	C₄×D₄	—	43	1	no	—
835	C₄×D₄	—	43	2	no	—
836	C₄×D₄	—	43	2	no	—
837	C₄×D₄	—	43	2	no	—
838	C₄×D₄	—	86	2	no	—
839	C₄×D₄	—	86	2	no	—
840	C₄×D₄	—	86	2	no	—
841	C₄×D₄	—	86	1	no	—
842	C₄×D₄	—	86	1	no	—
843	C₄×D₄	—	86	1	no	—
844	C₄×D₄	C₂²×D₄₃	1	2	yes	—
845	C₄×D₄	C₂²×D₄₃	1	2	yes	—
846	C₄×D₄	C₂²×D₄₃	1	2	yes	—
847	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
848	#117	—	2	2	no	—
849	#117	—	43	2	no	—
850	#117	—	86	1	no	—
851	#117	C₂²×D₄₃	1	2	yes	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	2	no	—
854	C₂×C₄⋊C₄	—	43	1	no	—
855	C₂×C₄⋊C₄	—	86	1	no	—
856	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
857	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
858	C₂×C₂²⋊C₄	—	86	1	no	—
859	C₂×C₂²⋊C₄	—	86	2	no	—
860	C₂×C₂²⋊C₄	—	86	2	no	—
861	C₂×C₄²	—	2	1	no	—
862	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
863	#107	—	43	2	no	—
864	#107	—	43	2	no	—
865	#107	—	43	2	no	—
866	#107	—	43	2	no	—
867	#106	—	43	1	no	—
868	#106	—	43	1	no	—
869	#106	—	43	1	no	—
870	#106	—	43	1	no	—
871	#106	—	43	2	no	—
872	#106	—	43	2	no	—
873	C₄⋊C₈	—	43	1	no	—
874	C₄⋊C₈	—	43	1	no	—
875	C₄⋊C₈	—	43	2	no	—
876	C₄⋊C₈	—	43	2	no	—
877	#103	—	43	1	no	—
878	#103	—	43	1	no	—
879	#103	—	43	1	no	—
880	#103	—	43	1	no	—
881	#103	—	43	2	no	—
882	#103	—	43	2	no	—
883	#102	—	43	2	no	—
884	#102	—	43	2	no	—
885	#102	—	43	2	no	—
886	#102	—	43	2	no	—
887	#102	—	43	1	no	—
888	#102	—	43	2	no	—
889	#102	—	43	1	no	—
890	#102	—	43	1	no	—
891	#102	—	43	1	no	—
892	#102	—	43	2	no	—
893	#102	—	43	2	no	—
894	#102	—	43	2	no	—
895	#102	—	43	2	no	—
896	#102	—	43	2	no	—
897	C₂²⋊C₈	—	43	2	no	—
898	C₂²⋊C₈	—	43	2	no	—
899	C₂²⋊C₈	—	43	2	no	—
900	#97	—	43	2	no	—
901	#97	—	43	2	no	—
902	C₄×C₈	—	43	1	no	—
903	C₄×C₈	—	43	1	no	—
904	C₄×C₈	—	43	1	no	—
905	C₄×C₈	—	43	1	no	—
906	C₄×C₈	—	43	2	no	—
907	C₂⁴	—	86	2	no	—
908	C₂⁴	—	86	1	no	—
909	#41	—	2	4	no	—
910	#41	—	4	2	no	—
911	#41	—	8	2	no	—
912	#41	—	8	4	no	—
913	#41	—	344	2	no	—
914	#41	—	344	2	no	—
915	C₂×Q₈	—	2	1	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	2	1	no	—
918	C₂×Q₈	—	2	2	no	—
919	C₂×Q₈	—	4	1	no	—
920	C₂×Q₈	—	86	1	no	—
921	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
922	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
923	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	43	1	no	—
930	C₂×D₄	—	43	2	no	—
931	C₂×D₄	—	43	1	no	—
932	C₂×D₄	—	86	2	no	—
933	C₂×D₄	—	86	4	no	—
934	C₂×D₄	—	86	2	no	—
935	C₂×D₄	—	86	2	no	—
936	C₂×D₄	—	86	2	no	—
937	C₂×D₄	—	86	2	no	—
938	C₂×D₄	—	86	1	no	—
939	C₂×D₄	—	86	2	no	—
940	C₂×D₄	—	86	2	no	—
941	C₂×D₄	—	86	1	no	—
942	C₂×D₄	—	86	1	no	—
943	C₂×D₄	—	344	4	no	—
944	C₂×D₄	—	344	2	no	—
945	C₂×D₄	—	172	1	no	—
946	C₂×D₄	—	172	2	no	—
947	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
948	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
949	C₂×D₄	C₂³×D₄₃	1	2	yes	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	86	1	no	—
957	C₂²×C₄	—	86	1	no	—
958	C₂²×C₄	—	86	2	no	—
959	C₂²×C₄	—	86	2	no	—
960	C₂²×C₄	—	86	2	no	—
961	C₂²×C₄	—	86	1	no	—
962	C₂²×C₄	—	86	1	no	—
963	C₂²×C₄	—	86	1	no	—
964	C₂²×C₄	—	344	2	no	—
965	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
966	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
967	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
968	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
969	SD₁₆	—	43	4	no	—
970	SD₁₆	—	86	2	no	—
971	SD₁₆	—	86	2	no	—
972	SD₁₆	—	86	2	no	—
973	SD₁₆	—	86	4	no	—
974	SD₁₆	—	172	2	no	—
975	D₈	—	86	4	no	—
976	D₈	—	86	4	no	—
977	D₈	—	172	2	no	—
978	D₈	—	172	2	no	—
979	M₁₆	—	86	4	no	—
980	C₂×C₈	—	43	1	no	—
981	C₂×C₈	—	43	1	no	—
982	C₂×C₈	—	43	1	no	—
983	C₂×C₈	—	43	1	no	—
984	C₂×C₈	—	43	2	no	—
985	C₂×C₈	—	43	2	no	—
986	C₂×C₈	—	86	2	no	—
987	C₂×C₈	—	172	1	no	—
988	C₂×C₈	—	172	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	43	1	no	—
1000	C₄⋊C₄	—	43	1	no	—
1001	C₄⋊C₄	—	43	2	no	—
1002	C₄⋊C₄	—	86	1	no	—
1003	C₄⋊C₄	—	86	1	no	—
1004	C₄⋊C₄	—	86	2	no	—
1005	C₄⋊C₄	—	86	2	no	—
1006	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1007	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1008	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
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	2	yes	—
1014	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	86	2	no	—
1023	C₂²⋊C₄	—	86	1	no	—
1024	C₂²⋊C₄	—	86	2	no	—
1025	C₂²⋊C₄	—	86	1	no	—
1026	C₂²⋊C₄	—	86	2	no	—
1027	C₂²⋊C₄	—	86	1	no	—
1028	C₂²⋊C₄	—	86	2	no	—
1029	C₂²⋊C₄	—	86	1	no	—
1030	C₂²⋊C₄	—	86	2	no	—
1031	C₂²⋊C₄	—	86	2	no	—
1032	C₂²⋊C₄	—	86	2	no	—
1033	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1034	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1035	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1036	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1037	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	86	2	no	—
1044	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1045	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1046	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1047	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1048	C₄²	C₂³×D₄₃	1	2	yes	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	86	1	no	—
1051	C₂³	—	86	2	no	—
1052	C₂³	—	86	1	no	—
1053	C₂³	—	344	1	no	—
1054	C₂³	—	344	2	no	—
1055	C₂³	—	344	2	no	—
1056	C₂³	—	172	2	no	—
1057	C₂³	—	172	4	no	—
1058	C₂³	—	172	2	no	—
1059	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
1060	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	1	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	—	4	2	no	—
1066	Q₈	—	8	1	no	—
1067	Q₈	—	8	2	no	—
1068	Q₈	—	344	1	no	—
1069	Q₈	#41×D₄₃	1	2	yes	—
1070	D₄	—	2	4	no	—
1071	D₄	—	2	2	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	4	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	43	2	no	—
1080	D₄	—	86	2	no	—
1081	D₄	—	86	1	no	—
1082	D₄	—	86	1	no	—
1083	D₄	—	86	1	no	—
1084	D₄	—	86	2	no	—
1085	D₄	—	344	2	no	—
1086	D₄	—	344	1	no	—
1087	D₄	—	344	2	no	—
1088	D₄	—	344	2	no	—
1089	D₄	—	344	2	no	—
1090	D₄	—	172	4	no	—
1091	D₄	—	172	2	no	—
1092	D₄	—	172	4	no	—
1093	D₄	—	172	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	4	4	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	8	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	86	1	no	—
1112	C₂×C₄	—	86	2	no	—
1113	C₂×C₄	—	86	1	no	—
1114	C₂×C₄	—	344	1	no	—
1115	C₂×C₄	—	344	1	no	—
1116	C₂×C₄	—	344	2	no	—
1117	C₂×C₄	—	344	2	no	—
1118	C₂×C₄	—	344	2	no	—
1119	C₂×C₄	—	344	1	no	—
1120	C₂×C₄	—	172	2	no	—
1121	C₂×C₄	—	172	2	no	—
1122	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1123	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
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	1	yes	characteristic
1130	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1131	C₈	—	43	2	no	—
1132	C₈	—	86	1	no	—
1133	C₈	—	86	2	no	—
1134	C₈	—	86	1	no	—
1135	C₈	—	86	1	no	—
1136	C₈	—	86	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	86	2	no	—
1146	C₂²	—	344	4	no	—
1147	C₂²	—	172	2	no	—
1148	C₂²	—	172	1	no	—
1149	C₂²	—	172	1	no	—
1150	C₂²	—	172	2	no	—
1151	C₂²	—	172	1	no	—
1152	C₂²	—	172	2	no	—
1153	C₂²	—	172	1	no	—
1154	C₂²	—	172	1	no	—
1155	C₂²	—	688	4	no	—
1156	C₂²	#14583702	1	2	yes	—
1157	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	172	2	no	—
1171	C₄	—	172	1	no	—
1172	C₄	—	172	1	no	—
1173	C₄	#14583707	1	2	yes	—
1174	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1175	C₄	#14583735	1	1	yes	characteristic
1176	C₂	—	2	2	no	—
1177	C₂	—	4	2	no	—
1178	C₂	—	8	2	no	—
1179	C₂	—	344	1	no	—
1180	C₂	—	344	2	no	—
1181	C₂	—	172	2	no	—
1182	C₂	#41×C₂²⋊D₄₃	1	1	yes	characteristic
1183	C₂	C₂×#14583702	1	1	yes	characteristic
1184	C₂	C₂×#14583707	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×#3522	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3522	D₄₃
hypocenter	C₄₃	#61498
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #529 ◁ #3522

Complements

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

N	H ≅ G/N	type
1. #19148629	C₂	semidirect
2. #19147633	C₂	semidirect
3. #19147501	C₂	semidirect
4. #19147266	C₂	semidirect
5. #19147251	C₂	semidirect
6. #19147221	C₂	semidirect
7. #19147065	C₂	semidirect
8. #19146545	C₂	semidirect
9. #19146497	C₂	semidirect
10. #19146413	C₂	semidirect
11. #19146402	C₂	semidirect
12. #19146215	C₂	semidirect
13. #19146091	C₂	semidirect
14. #19145272	C₂	semidirect
15. #19145170	C₂	semidirect
16. #19144794	C₂	semidirect
17. #19144773	C₂	semidirect
18. #19144717	C₂	semidirect
19. #19144682	C₂	semidirect
20. #19143571	C₂	semidirect
21. #19143423	C₂	semidirect
22. C₂×C₄×#10621884	C₂	semidirect
23. C₄₃×#3522	C₂	semidirect
42. #14583305	C₂²	semidirect
43. #14583302	C₂²	semidirect
44. #14583289	C₂²	semidirect
45. #14583275	C₂²	semidirect
46. #14583253	C₂²	semidirect
47. #14583247	C₂²	semidirect
48. #14583247	C₂²	semidirect
49. #14583245	C₂²	semidirect
50. #14583237	C₂²	semidirect
51. #14583220	C₂²	semidirect
52. #14583217	C₂²	semidirect
53. #14583215	C₂²	semidirect
54. #14583212	C₂²	semidirect
55. #14583212	C₂²	semidirect
56. #14583206	C₂²	semidirect
57. #14583199	C₂²	semidirect
58. #14583194	C₂²	semidirect
59. #14583194	C₂²	semidirect
61. #14583186	C₂²	semidirect
62. #14583186	C₂²	semidirect
64. #14583150	C₂²	semidirect
65. #14583147	C₂²	semidirect
66. #14583133	C₂²	semidirect
67. #14583133	C₂²	semidirect
68. #14583133	C₂²	semidirect
69. #14583130	C₂²	semidirect
71. #14583111	C₂²	semidirect
72. #14583099	C₂²	semidirect
73. #14583099	C₂²	semidirect
74. #14583099	C₂²	semidirect
75. #14583094	C₂²	semidirect
77. #14583091	C₂²	semidirect
79. #14583044	C₂²	semidirect
80. #14583044	C₂²	semidirect
81. #14583038	C₂²	semidirect
84. #14583030	C₂²	semidirect
85. Q₈×C₄₃⋊C₈	C₂²	semidirect
87. #14583009	C₂²	semidirect
88. #14583009	C₂²	semidirect
90. #14582997	C₂²	semidirect
91. #14582997	C₂²	semidirect
96. C₄×#10621884	C₂²	semidirect
97. C₄×#10621884	C₂²	semidirect
98. C₄×#10621884	C₂²	semidirect
99. C₄×#10621884	C₂²	semidirect
100. C₄×#10621884	C₂²	semidirect
102. C₄×#10621882	C₂²	semidirect
103. C₄×#10621882	C₂²	semidirect
104. #14582977	C₂²	semidirect
105. #14582971	C₂²	semidirect
106. D₄×C₄₃⋊C₈	C₂²	semidirect
107. D₄×C₄₃⋊C₈	C₂²	semidirect
108. #14582960	C₂²	semidirect
109. #14582956	C₂²	semidirect
110. #14582939	C₂²	semidirect
111. C₂×#13063256	C₂²	semidirect
112. #14582895	C₂²	semidirect
113. C₂×#13063249	C₂²	semidirect
116. #14582855	C₂²	semidirect
117. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
119. C₄₃×#559	C₂²	semidirect
120. Q₈²×C₄₃	C₂²	semidirect
122. C₄₃×#554	C₂²	semidirect
123. C₄₃×#550	C₂²	semidirect
124. C₄₃×#548	C₂²	semidirect
126. C₄₃×#547	C₂²	semidirect
128. C₄₃×#542	C₂²	semidirect
130. C₄₃×#532	C₂²	semidirect
133. C₄₃×#520	C₂²	semidirect
134. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
423. #10621884	#41	semidirect
584. #3522	D₄₃	semidirect
619. #559	C₂×D₄₃	semidirect
620. Q₈²	C₂×D₄₃	semidirect
624. #554	C₂×D₄₃	semidirect
628. #550	C₂×D₄₃	semidirect
629. #548	C₂×D₄₃	semidirect
631. #547	C₂×D₄₃	semidirect
637. #542	C₂×D₄₃	semidirect
642. #532	C₂×D₄₃	semidirect
647. #520	C₂×D₄₃	semidirect
649. C₂×C₄×Q₈	C₂×D₄₃	semidirect
727. C₄₃	#61498	semidirect

Maximal subgroups

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

subgroup	index
#19148629	2
#19147633	2
#19147501	2
#19147266	2
#19147251	2
#19147221	2
#19147065	2
#19146545	2
#19146497	2
#19146413	2
#19146402	2
#19146215	2
#19146091	2
#19145272	2
#19145170	2
#19144794	2
#19144773	2
#19144717	2
#19144682	2
#19143571	2
#19143423	2
C₂×C₄×#10621884	2
C₄₃×#3522	2
#61498	43