Subgroups — #25989811

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148558	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148153	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147589	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147581	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147253	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147242	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146891	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146866	C₂	1	2	yes	maximal, complemented
9	#19146839	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146814	C₂	1	2	yes	maximal, complemented
11	#19146242	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146230	C₂	1	2	yes	maximal, complemented
13	#19146206	C₂	1	2	yes	maximal, complemented
14	#19146196	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145995	C₂	1	2	yes	maximal, complemented
16	#19145968	C₂	1	1	yes	maximal, characteristic, complemented
17	#19145558	C₂	1	2	yes	maximal, complemented
18	#19145553	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144618	C₂	1	2	yes	maximal, complemented
20	#19144084	C₂	1	2	yes	maximal, complemented
21	#19144059	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143724	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063354	C₂²	1	2	yes	complemented
25	C₂×#13063351	C₂²	1	2	yes	complemented
26	C₂×#13063349	C₂²	1	2	yes	—
27	#14583634	C₂²	1	1	yes	characteristic, complemented
28	#14583619	C₂²	1	1	yes	characteristic, complemented
29	#14583619	C₂²	1	1	yes	characteristic, complemented
30	#14583614	—	2	1	no	—
31	#14583614	C₂²	1	1	yes	characteristic
32	#14583606	C₂²	1	1	yes	characteristic, complemented
33	#14583595	—	2	1	no	—
34	#14583589	—	2	1	no	—
35	#14583584	C₂²	1	2	yes	complemented
36	#14583575	—	2	2	no	—
37	#14583574	—	2	2	no	—
38	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
39	#14583559	C₂²	1	2	yes	—
40	#14583553	C₂²	1	1	yes	characteristic
41	#14583546	C₂²	1	2	yes	—
42	#14583545	—	2	1	no	—
43	#14583543	C₂²	1	2	yes	complemented
44	D₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
45	#14583520	—	2	1	no	—
46	#14583485	—	2	2	no	—
47	#14583456	C₂²	1	1	yes	characteristic, complemented
48	#14583449	C₂²	1	1	yes	characteristic
49	#14583434	C₂²	1	2	yes	complemented
50	#14583431	C₂²	1	2	yes	complemented
51	#14583429	—	2	2	no	—
52	#124×D₄₃	C₂²	1	2	yes	complemented
53	#14583410	—	2	1	no	—
54	#14583373	—	2	1	no	—
55	C₄×#10621898	C₂²	1	1	yes	characteristic
56	C₄×#10621900	C₂²	1	2	yes	complemented
57	C₂×#13063284	—	2	1	no	—
58	#14583282	C₂²	1	2	yes	—
59	#14583280	C₂²	1	2	yes	complemented
60	#14583279	C₂²	1	1	yes	characteristic, complemented
61	#14583272	C₂²	1	1	yes	characteristic, complemented
62	#14583255	C₂²	1	2	yes	complemented
63	#14583252	C₂²	1	2	yes	complemented
64	#14583250	C₂²	1	1	yes	characteristic, complemented
65	#14583246	C₂²	1	1	yes	characteristic, complemented
66	#14583243	C₂²	1	2	yes	complemented
67	#14583226	C₂²	1	2	yes	complemented
68	#14583205	C₂²	1	2	yes	complemented
69	#14583203	C₂²	1	2	yes	complemented
70	#14583198	C₂²	1	2	yes	complemented
71	#14583194	C₂²	1	1	yes	characteristic, complemented
72	#14583189	C₂²	1	1	yes	characteristic, complemented
73	#14583158	C₂²	1	2	yes	complemented
74	#14583155	C₂²	1	2	yes	complemented
75	#14583151	C₂²	1	2	yes	—
76	#14583146	C₂²	1	2	yes	complemented
77	#14583144	C₂²	1	2	yes	complemented
78	#14583143	C₂²	1	2	yes	—
79	#14583124	C₂²	1	2	yes	complemented
80	#14583122	C₂²	1	2	yes	complemented
81	#14583122	C₂²	1	2	yes	complemented
82	#14583120	C₂²	1	2	yes	complemented
83	#14583120	C₂²	1	2	yes	complemented
84	#14583118	C₂²	1	2	yes	complemented
85	#14583116	C₂²	1	2	yes	complemented
86	#14583114	C₂²	1	2	yes	complemented
87	#14583114	C₂²	1	2	yes	complemented
88	#14583113	C₂²	1	2	yes	complemented
89	#14583112	C₂²	1	2	yes	—
90	#14583109	C₂²	1	1	yes	characteristic, complemented
91	#14583104	C₂²	1	1	yes	characteristic, complemented
92	#14583104	C₂²	1	1	yes	characteristic, complemented
93	#14583104	C₂²	1	1	yes	characteristic, complemented
94	#14583094	C₂²	1	1	yes	characteristic
95	#14583094	C₂²	1	1	yes	characteristic
96	#14583063	C₂²	1	2	yes	complemented
97	#14583063	C₂²	1	2	yes	complemented
98	#14583062	C₂²	1	2	yes	complemented
99	#14583056	C₂²	1	2	yes	complemented
100	#14583051	C₂²	1	2	yes	complemented
101	#14583045	C₂²	1	2	yes	—
102	#14583036	C₂²	1	2	yes	complemented
103	#14583031	C₂²	1	2	yes	—
104	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
105	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
106	#14582993	C₂²	1	2	yes	complemented
107	#14582990	C₂²	1	2	yes	complemented
108	#14582986	C₂²	1	2	yes	complemented
109	#14582979	C₂²	1	2	yes	complemented
110	#14582978	C₂²	1	1	yes	characteristic, complemented
111	#14582978	C₂²	1	1	yes	characteristic, complemented
112	#14582974	C₂²	1	2	yes	complemented
113	#14582974	C₂²	1	2	yes	complemented
114	#14582951	C₂²	1	2	yes	complemented
115	#14582923	C₂²	1	1	yes	characteristic, complemented
116	#14582921	C₂²	1	2	yes	complemented
117	#14582906	C₂²	1	2	yes	complemented
118	#14582902	C₂²	1	2	yes	complemented
119	#14582898	C₂²	1	2	yes	complemented
120	C₄₃×#529	C₂²	1	1	yes	characteristic
121	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#484	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#481	C₂²	1	1	yes	characteristic
124	C₄₃×#478	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#463	C₂²	1	1	yes	characteristic
127	C₄₃×#463	C₂²	1	1	yes	characteristic
128	C₄₃×#450	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#447	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
131	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
133	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
134	C₄₃×#431	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621898	D₄	1	1	yes	characteristic
136	C₂×#10621898	C₂³	1	2	yes	—
137	C₂×#10621900	C₂³	1	2	yes	—
138	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
139	C₂²×D₁₇₂	—	2	1	no	—
140	C₂×D₄×D₄₃	C₂³	1	2	yes	—
141	#13063354	—	4	4	no	—
142	#13063351	—	4	4	no	—
143	#13063349	—	4	4	no	—
144	C₂×Dic₁₇₂	C₂³	1	2	yes	—
145	C₂×Dic₁₇₂	C₂³	1	2	yes	—
146	C₂×#10621885	C₂³	1	2	yes	—
147	C₂×#10621873	C₂³	1	2	yes	—
148	C₂×#10621873	C₂³	1	2	yes	—
149	C₂×#10621883	C₂³	1	2	yes	—
150	C₂×#10621883	C₂³	1	2	yes	—
151	C₂×#10621883	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	C₂×#10621872	C₂³	1	2	yes	—
156	C₂×#10621872	C₂³	1	2	yes	—
157	#13063325	—	2	1	no	—
158	#13063325	C₂³	1	1	yes	characteristic
159	#13063325	C₂³	1	1	yes	characteristic
160	#13063325	C₂³	1	1	yes	characteristic
161	#13063322	C₂³	1	1	yes	characteristic
162	#13063320	—	2	2	no	—
163	#13063320	—	2	2	no	—
164	#13063318	—	2	2	no	—
165	#13063318	—	2	2	no	—
166	#13063318	—	2	2	no	—
167	#13063317	—	2	1	no	—
168	#13063316	C₂³	1	2	yes	—
169	#13063315	—	2	2	no	—
170	#13063314	C₂³	1	2	yes	—
171	#13063313	—	2	1	no	—
172	#13063313	C₂³	1	2	yes	—
173	#13063312	C₂³	1	2	yes	—
174	#13063312	C₂³	1	2	yes	—
175	#13063311	—	2	2	no	—
176	#13063311	—	2	2	no	—
177	#13063311	—	2	2	no	—
178	#13063311	—	2	2	no	—
179	#13063310	—	2	2	no	—
180	#13063310	—	2	2	no	—
181	#13063309	—	2	2	no	—
182	#13063308	—	2	2	no	—
183	#13063307	—	2	2	no	—
184	#13063307	—	2	2	no	—
185	#13063306	—	2	2	no	—
186	#13063305	—	2	2	no	—
187	#13063305	C₂³	1	2	yes	—
188	#13063305	C₂³	1	2	yes	—
189	#13063304	—	2	1	no	—
190	#13063304	—	2	1	no	—
191	#13063304	—	2	1	no	—
192	#13063304	—	2	1	no	—
193	#13063304	C₂³	1	2	yes	—
194	#13063303	—	2	2	no	—
195	#13063302	—	2	2	no	—
196	#13063300	C₂³	1	2	yes	—
197	#13063299	—	2	1	no	—
198	#13063299	—	2	1	no	—
199	#13063299	—	2	1	no	—
200	#13063299	—	2	1	no	—
201	#13063299	—	2	1	no	—
202	#13063298	—	2	2	no	—
203	#13063297	—	2	2	no	—
204	#13063296	—	2	2	no	—
205	#13063296	C₂³	1	2	yes	—
206	#13063295	—	2	2	no	—
207	#13063294	—	2	2	no	—
208	#13063293	—	2	2	no	—
209	C₄×Dic₈₆	—	2	1	no	—
210	C₄×Dic₈₆	D₄	1	1	yes	characteristic
211	C₄×Dic₈₆	C₂³	1	2	yes	—
212	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
213	#13063290	C₂³	1	2	yes	—
214	#13063290	C₂³	1	2	yes	—
215	C₄×D₁₇₂	—	2	1	no	—
216	C₄×D₁₇₂	—	2	1	no	—
217	C₄×D₁₇₂	—	2	1	no	—
218	C₄×D₁₇₂	—	2	1	no	—
219	C₄×D₁₇₂	D₄	1	1	yes	characteristic
220	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
221	D₄×Dic₄₃	C₂³	1	2	yes	—
222	#13063287	—	2	2	no	—
223	#13063287	—	2	2	no	—
224	#13063287	C₂³	1	2	yes	—
225	C₄×C₂²⋊D₄₃	—	2	2	no	—
226	C₄×C₂²⋊D₄₃	—	2	2	no	—
227	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
228	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
229	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
230	#13063284	—	2	1	no	—
231	#13063284	—	2	2	no	—
232	#13063284	—	2	1	no	—
233	#13063284	—	2	1	no	—
234	#13063284	—	2	1	no	—
235	#13063284	—	2	2	no	—
236	#13063284	D₄	1	1	yes	characteristic
237	#13063283	—	2	2	no	—
238	#13063283	C₂³	1	2	yes	—
239	#13063282	D₄	1	2	yes	—
240	#13063281	—	2	2	no	—
241	C₂×C₄⋊Dic₄₃	—	2	1	no	—
242	C₂×C₄⋊Dic₄₃	—	2	1	no	—
243	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
244	C₂²⋊C₄×D₄₃	—	2	2	no	—
245	C₂²⋊C₄×D₄₃	—	2	2	no	—
246	C₂²⋊C₄×D₄₃	—	2	2	no	—
247	C₂×C₄×Dic₄₃	—	2	2	no	—
248	C₄²×D₄₃	C₂³	1	2	yes	—
249	#13063258	C₂³	1	2	yes	—
250	#13063256	C₂³	1	2	yes	—
251	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
252	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
253	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
254	Dic₄₃⋊C₈	C₂³	1	2	yes	—
255	Dic₄₃⋊C₈	C₂³	1	2	yes	—
256	#13063250	C₂³	1	2	yes	—
257	#13063250	C₂³	1	2	yes	—
258	#13063249	C₂³	1	2	yes	—
259	#13063248	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063248	C₂³	1	2	yes	—
263	#13063247	C₂³	1	2	yes	—
264	#13063247	C₂³	1	2	yes	—
265	#13063246	C₂³	1	2	yes	—
266	#13063245	C₂³	1	2	yes	—
267	#13063245	C₂³	1	2	yes	—
268	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
270	C₈×Dic₄₃	C₂³	1	2	yes	—
271	C₈×Dic₄₃	C₂³	1	2	yes	—
272	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
273	C₂³×C₄×C₄₃	—	2	1	no	—
274	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
278	#126×C₄₃	—	2	1	no	—
279	#125×C₄₃	C₂³	1	1	yes	characteristic
280	#124×C₄₃	C₂³	1	1	yes	characteristic
281	#123×C₄₃	—	2	1	no	—
282	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	#121×C₄₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₄₃	—	2	1	no	—
286	C₄×D₄×C₄₃	—	2	1	no	—
287	C₄×D₄×C₄₃	—	2	1	no	—
288	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
293	#117×C₄₃	—	2	1	no	—
294	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
296	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
297	#107×C₄₃	C₂³	1	1	yes	characteristic
298	#107×C₄₃	C₂³	1	1	yes	characteristic
299	#106×C₄₃	C₂³	1	1	yes	characteristic
300	#106×C₄₃	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
303	#103×C₄₃	C₂³	1	1	yes	characteristic
304	#103×C₄₃	C₂³	1	1	yes	characteristic
305	#102×C₄₃	C₂³	1	1	yes	characteristic
306	#102×C₄₃	C₂³	1	1	yes	characteristic
307	#102×C₄₃	C₂³	1	1	yes	characteristic
308	#102×C₄₃	C₂³	1	1	yes	characteristic
309	#102×C₄₃	C₂³	1	1	yes	characteristic
310	#102×C₄₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
315	C₂⁴×C₄₃	—	2	1	no	—
316	C₂³×D₄₃	—	2	2	no	—
317	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₄₃	—	2	1	no	—
319	C₂×D₄×C₄₃	—	2	1	no	—
320	C₂×D₄×C₄₃	—	2	2	no	—
321	C₂×D₄×C₄₃	—	4	1	no	—
322	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₃	—	2	1	no	—
326	C₂²×C₄×C₄₃	—	2	1	no	—
327	C₂²×C₄×C₄₃	—	2	1	no	—
328	C₂²×C₄×C₄₃	—	2	1	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	—	4	4	no	—
332	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
335	C₂×C₂²⋊D₄₃	—	2	2	no	—
336	C₂×C₂²⋊D₄₃	—	2	2	no	—
337	C₂×C₂²⋊D₄₃	—	2	2	no	—
338	C₂×C₂²⋊D₄₃	—	2	2	no	—
339	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
340	C₂²×Dic₄₃	—	2	2	no	—
341	C₂²×Dic₄₃	—	2	2	no	—
342	Q₈×D₄₃	—	4	2	no	—
343	Q₈×D₄₃	—	4	2	no	—
344	#10621900	—	2	4	no	—
345	#10621900	—	4	2	no	—
346	D₄×D₄₃	—	4	2	no	—
347	D₄×D₄₃	—	4	2	no	—
348	#10621898	—	4	2	no	—
349	#10621898	—	4	2	no	—
350	#10621898	—	4	2	no	—
351	C₂×D₁₇₂	—	2	1	no	—
352	C₂×D₁₇₂	—	2	1	no	—
353	C₂×D₁₇₂	—	2	2	no	—
354	C₂×D₁₇₂	—	4	4	no	—
355	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
356	C₂×D₁₇₂	C₂⁴	1	2	yes	—
357	C₂×C₄×D₄₃	—	2	2	no	—
358	C₂×C₄×D₄₃	—	2	2	no	—
359	C₂×C₄×D₄₃	—	2	2	no	—
360	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
361	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
362	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
363	C₂×Dic₈₆	—	2	1	no	—
364	C₂×Dic₈₆	—	2	2	no	—
365	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
366	C₂×Dic₈₆	C₂⁴	1	2	yes	—
367	C₂×Dic₈₆	C₂⁴	1	2	yes	—
368	SD₁₆×C₄₃	—	2	2	no	—
369	SD₁₆×C₄₃	—	4	1	no	—
370	D₈×C₄₃	—	2	2	no	—
371	D₈×C₄₃	—	4	1	no	—
372	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₄₃	—	2	1	no	—
377	C₄⋊C₄×C₄₃	—	2	1	no	—
378	C₄⋊C₄×C₄₃	—	2	1	no	—
379	C₄⋊C₄×C₄₃	—	2	1	no	—
380	C₄⋊C₄×C₄₃	—	2	1	no	—
381	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
385	C₂²⋊C₄×C₄₃	—	2	1	no	—
386	C₂²⋊C₄×C₄₃	—	2	1	no	—
387	C₂²⋊C₄×C₄₃	—	2	1	no	—
388	C₂²⋊C₄×C₄₃	—	2	1	no	—
389	C₂²⋊C₄×C₄₃	—	2	1	no	—
390	C₂²⋊C₄×C₄₃	—	2	1	no	—
391	C₂²⋊C₄×C₄₃	—	2	1	no	—
392	C₂²⋊C₄×C₄₃	—	2	1	no	—
393	C₂²⋊C₄×C₄₃	—	2	1	no	—
394	C₄²×C₄₃	—	2	1	no	—
395	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
398	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
399	C₂²⋊Dic₄₃	—	2	2	no	—
400	C₂²⋊Dic₄₃	—	2	2	no	—
401	C₂²⋊Dic₄₃	—	2	2	no	—
402	C₂²⋊Dic₄₃	—	2	2	no	—
403	C₂²⋊Dic₄₃	—	2	2	no	—
404	C₂²⋊Dic₄₃	—	2	2	no	—
405	C₂²⋊Dic₄₃	—	2	2	no	—
406	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
407	#10621885	—	4	2	no	—
408	#10621883	—	2	4	no	—
409	#10621883	—	4	2	no	—
410	#10621883	—	4	2	no	—
411	#10621882	—	2	4	no	—
412	#10621882	—	4	2	no	—
413	(C₂×D₄₃)⋊C₄	—	2	2	no	—
414	(C₂×D₄₃)⋊C₄	—	2	2	no	—
415	(C₂×D₄₃)⋊C₄	—	2	2	no	—
416	(C₂×D₄₃)⋊C₄	—	2	2	no	—
417	(C₂×D₄₃)⋊C₄	—	2	2	no	—
418	(C₂×D₄₃)⋊C₄	—	2	2	no	—
419	(C₂×D₄₃)⋊C₄	—	2	2	no	—
420	(C₂×D₄₃)⋊C₄	—	2	2	no	—
421	(C₂×D₄₃)⋊C₄	—	2	2	no	—
422	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
423	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
424	C₄⋊Dic₄₃	—	2	1	no	—
425	C₄⋊Dic₄₃	—	2	1	no	—
426	C₄⋊Dic₄₃	—	2	1	no	—
427	C₄⋊Dic₄₃	—	2	1	no	—
428	C₄⋊Dic₄₃	—	2	1	no	—
429	C₄⋊Dic₄₃	—	2	2	no	—
430	C₄⋊Dic₄₃	—	2	2	no	—
431	C₄⋊Dic₄₃	—	2	2	no	—
432	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
433	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
434	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
435	Dic₄₃⋊C₄	—	2	2	no	—
436	Dic₄₃⋊C₄	—	2	2	no	—
437	Dic₄₃⋊C₄	—	2	2	no	—
438	Dic₄₃⋊C₄	—	2	2	no	—
439	Dic₄₃⋊C₄	—	2	2	no	—
440	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
441	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
442	C₄×Dic₄₃	—	2	2	no	—
443	C₄×Dic₄₃	—	2	2	no	—
444	C₄×Dic₄₃	—	2	2	no	—
445	C₄×Dic₄₃	—	2	2	no	—
446	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
447	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
448	C₄×Dic₄₃	C₂⁴	1	2	yes	—
449	#10621877	—	4	2	no	—
450	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
451	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
452	Dic₁₇₂	—	4	2	no	—
453	Dic₁₇₂	—	4	2	no	—
454	#10621873	—	4	2	no	—
455	#10621873	—	4	2	no	—
456	#10621872	—	4	2	no	—
457	#10621872	—	4	2	no	—
458	C₂³×C₄₃	—	2	1	no	—
459	C₂³×C₄₃	—	2	1	no	—
460	C₂³×C₄₃	—	2	1	no	—
461	C₂³×C₄₃	—	4	2	no	—
462	C₂³×C₄₃	—	4	2	no	—
463	C₂³×C₄₃	—	8	1	no	—
464	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
465	C₂²×D₄₃	—	2	2	no	—
466	C₂²×D₄₃	—	4	4	no	—
467	C₂²×D₄₃	—	8	2	no	—
468	C₂²×D₄₃	—	8	2	no	—
469	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
470	Q₈×C₄₃	—	2	1	no	—
471	Q₈×C₄₃	—	2	1	no	—
472	D₄×C₄₃	—	2	1	no	—
473	D₄×C₄₃	—	2	1	no	—
474	D₄×C₄₃	—	2	1	no	—
475	D₄×C₄₃	—	2	1	no	—
476	D₄×C₄₃	—	2	1	no	—
477	D₄×C₄₃	—	4	2	no	—
478	D₄×C₄₃	—	8	1	no	—
479	D₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
480	C₂×C₄×C₄₃	—	2	2	no	—
481	C₂×C₄×C₄₃	—	2	1	no	—
482	C₂×C₄×C₄₃	—	2	1	no	—
483	C₂×C₄×C₄₃	—	2	1	no	—
484	C₂×C₄×C₄₃	—	2	1	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	—	4	1	no	—
489	C₂×C₄×C₄₃	—	4	2	no	—
490	C₂×C₄×C₄₃	—	4	2	no	—
491	C₂×C₄×C₄₃	—	4	2	no	—
492	C₂×C₄×C₄₃	—	4	2	no	—
493	C₂×C₄×C₄₃	—	4	2	no	—
494	C₂×C₄×C₄₃	—	4	2	no	—
495	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
501	C₂²⋊D₄₃	—	4	2	no	—
502	C₂²⋊D₄₃	—	4	4	no	—
503	C₂²⋊D₄₃	—	8	2	no	—
504	C₂²⋊D₄₃	—	8	2	no	—
505	C₂²⋊D₄₃	—	8	2	no	—
506	C₂×Dic₄₃	—	2	2	no	—
507	C₂×Dic₄₃	—	2	2	no	—
508	C₂×Dic₄₃	—	2	2	no	—
509	C₂×Dic₄₃	—	4	4	no	—
510	C₂×Dic₄₃	—	8	2	no	—
511	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
512	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
513	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
514	D₁₇₂	—	2	2	no	—
515	D₁₇₂	—	2	2	no	—
516	D₁₇₂	—	2	2	no	—
517	D₁₇₂	—	4	4	no	—
518	D₁₇₂	—	4	2	no	—
519	D₁₇₂	—	8	1	no	—
520	C₄×D₄₃	—	2	2	no	—
521	C₄×D₄₃	—	2	2	no	—
522	C₄×D₄₃	—	4	2	no	—
523	C₄×D₄₃	—	4	2	no	—
524	C₄×D₄₃	—	8	2	no	—
525	C₄×D₄₃	—	8	2	no	—
526	C₄×D₄₃	—	8	2	no	—
527	Dic₈₆	—	2	2	no	—
528	Dic₈₆	—	2	2	no	—
529	Dic₈₆	—	2	2	no	—
530	Dic₈₆	—	2	2	no	—
531	Dic₈₆	—	2	2	no	—
532	Dic₈₆	—	8	2	no	—
533	Dic₈₆	—	8	1	no	—
534	C₈×C₄₃	—	2	1	no	—
535	C₈×C₄₃	—	2	1	no	—
536	C₈×C₄₃	—	2	1	no	—
537	C₈×C₄₃	—	2	1	no	—
538	C₄₃⋊C₈	—	2	2	no	—
539	C₄₃⋊C₈	—	2	2	no	—
540	#62004	—	43	1	no	maximal, Sylow
541	C₂²×C₄₃	—	2	1	no	—
542	C₂²×C₄₃	—	2	2	no	—
543	C₂²×C₄₃	—	2	1	no	—
544	C₂²×C₄₃	—	2	1	no	—
545	C₂²×C₄₃	—	4	1	no	—
546	C₂²×C₄₃	—	4	1	no	—
547	C₂²×C₄₃	—	4	1	no	—
548	C₂²×C₄₃	—	4	1	no	—
549	C₂²×C₄₃	—	4	1	no	—
550	C₂²×C₄₃	—	4	1	no	—
551	C₂²×C₄₃	—	4	1	no	—
552	C₂²×C₄₃	—	4	1	no	—
553	C₂²×C₄₃	—	8	4	no	—
554	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
555	C₂×D₄₃	—	2	2	no	—
556	C₂×D₄₃	—	2	2	no	—
557	C₂×D₄₃	—	2	2	no	—
558	C₂×D₄₃	—	4	2	no	—
559	C₂×D₄₃	—	4	2	no	—
560	C₂×D₄₃	—	4	2	no	—
561	C₂×D₄₃	—	16	4	no	—
562	C₄×C₄₃	—	2	1	no	—
563	C₄×C₄₃	—	2	1	no	—
564	C₄×C₄₃	—	2	1	no	—
565	C₄×C₄₃	—	2	1	no	—
566	C₄×C₄₃	—	4	1	no	—
567	C₄×C₄₃	—	4	1	no	—
568	C₄×C₄₃	—	4	1	no	—
569	C₄×C₄₃	—	4	1	no	—
570	C₄×C₄₃	—	4	1	no	—
571	C₄×C₄₃	#575	1	2	yes	—
572	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₄×C₄₃	#585	1	1	yes	characteristic
574	Dic₄₃	—	2	2	no	—
575	Dic₄₃	—	2	2	no	—
576	Dic₄₃	—	2	2	no	—
577	Dic₄₃	—	4	2	no	—
578	Dic₄₃	—	4	2	no	—
579	Dic₄₃	—	4	2	no	—
580	#3514	—	43	1	no	—
581	#3475	—	43	1	no	—
582	#3394	—	43	1	no	—
583	#3393	—	43	1	no	—
584	#3361	—	43	1	no	—
585	#3360	—	43	1	no	—
586	#3329	—	43	1	no	—
587	#3327	—	43	2	no	—
588	#3325	—	43	1	no	—
589	#3323	—	43	2	no	—
590	#3276	—	43	1	no	—
591	#3275	—	43	2	no	—
592	#3273	—	43	2	no	—
593	#3272	—	43	1	no	—
594	#3256	—	43	2	no	—
595	#3252	—	43	1	no	—
596	#3211	—	43	2	no	—
597	#3210	—	43	1	no	—
598	#3105	D₄₃	1	1	yes	characteristic, complemented
599	#3102	—	43	2	no	—
600	#3040	—	43	2	no	—
601	#3036	—	43	1	no	—
602	#2991	—	43	1	no	—
603	C₂×C₄₃	—	4	1	no	—
604	C₂×C₄₃	—	4	2	no	—
605	C₂×C₄₃	—	8	1	no	—
606	C₂×C₄₃	—	8	1	no	—
607	C₂×C₄₃	#3488	1	1	yes	characteristic
608	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
609	C₂×C₄₃	#3584	1	1	yes	characteristic
610	D₄₃	—	4	2	no	—
611	D₄₃	—	8	2	no	—
612	C₂×#137	—	43	2	no	—
613	C₂×AGL(1,ℤ/8)	—	43	2	no	—
614	C₂×AGL(1,ℤ/8)	—	43	2	no	—
615	#559	—	43	1	no	—
616	#556	—	43	1	no	—
617	#556	—	43	1	no	—
618	#555	—	43	1	no	—
619	#555	—	86	1	no	—
620	#554	—	43	1	no	—
621	#553	—	86	1	no	—
622	#552	—	43	2	no	—
623	#552	—	86	1	no	—
624	#551	—	86	2	no	—
625	#551	—	86	2	no	—
626	D₄×Q₈	—	43	1	no	—
627	#548	—	43	2	no	—
628	#547	—	43	1	no	—
629	#546	—	43	2	no	—
630	#546	—	43	2	no	—
631	#546	—	86	1	no	—
632	D₄²	—	43	1	no	—
633	#542	—	86	1	no	—
634	#538	—	86	2	no	—
635	#533	—	43	1	no	—
636	#532	—	43	1	no	—
637	#529	—	43	2	no	—
638	#529	—	43	2	no	—
639	#529	—	86	2	no	—
640	#529	C₂×D₄₃	1	1	yes	characteristic
641	C₂×#124	—	43	2	no	—
642	#525	—	86	1	no	—
643	#518	—	86	1	no	—
644	C₄×#41	—	43	1	no	—
645	C₄×#41	—	43	2	no	—
646	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
647	C₂×#117	—	86	1	no	—
648	#495	—	43	2	no	—
649	#495	—	43	2	no	—
650	#494	—	43	1	no	—
651	#492	—	43	1	no	—
652	#488	—	43	2	no	—
653	#488	—	43	2	no	—
654	#487	—	43	1	no	—
655	#486	—	43	1	no	—
656	#485	—	43	2	no	—
657	#484	C₂×D₄₃	1	1	yes	characteristic, complemented
658	#482	—	43	2	no	—
659	#481	C₂×D₄₃	1	1	yes	characteristic
660	#479	—	43	2	no	—
661	#479	—	43	2	no	—
662	#478	—	43	2	no	—
663	#478	C₂×D₄₃	1	1	yes	characteristic, complemented
664	#478	C₂×D₄₃	1	1	yes	characteristic, complemented
665	#477	—	43	1	no	—
666	#476	—	43	1	no	—
667	#470	—	43	2	no	—
668	#470	—	43	2	no	—
669	#469	—	43	2	no	—
670	#468	—	43	2	no	—
671	#468	—	43	2	no	—
672	#468	—	43	2	no	—
673	#464	—	43	2	no	—
674	#464	—	43	2	no	—
675	#464	—	43	2	no	—
676	#464	—	43	2	no	—
677	#464	—	43	2	no	—
678	#464	—	43	2	no	—
679	#463	—	43	2	no	—
680	#463	—	43	2	no	—
681	#463	—	43	2	no	—
682	#463	—	43	2	no	—
683	#463	—	43	2	no	—
684	#463	C₂×D₄₃	1	1	yes	characteristic
685	#463	C₂×D₄₃	1	1	yes	characteristic
686	#462	—	43	1	no	—
687	#461	—	43	1	no	—
688	#461	—	43	1	no	—
689	#461	—	43	1	no	—
690	#459	—	43	1	no	—
691	#459	—	43	1	no	—
692	#452	—	43	2	no	—
693	#452	—	43	2	no	—
694	#452	—	43	2	no	—
695	#451	—	43	2	no	—
696	#450	—	43	2	no	—
697	#450	C₂×D₄₃	1	1	yes	characteristic, complemented
698	#449	—	43	2	no	—
699	#448	—	43	2	no	—
700	#447	—	43	2	no	—
701	#447	C₂×D₄₃	1	1	yes	characteristic
702	C₈×Q₈	—	43	1	no	—
703	C₈×Q₈	—	43	1	no	—
704	C₄×Q₁₆	—	43	2	no	—
705	C₄×SD₁₆	—	43	2	no	—
706	C₄×SD₁₆	—	43	2	no	—
707	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
709	C₄×D₈	—	43	2	no	—
710	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
711	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
712	#436	—	43	2	no	—
713	#436	—	43	2	no	—
714	#436	—	43	1	no	—
715	#436	—	43	1	no	—
716	#431	—	43	2	no	—
717	#431	C₂×D₄₃	1	1	yes	characteristic, complemented
718	#423	—	43	1	no	—
719	#423	—	43	2	no	—
720	#419	—	43	2	no	—
721	#418	—	43	2	no	—
722	#417	—	43	2	no	—
723	C₄₃	#62004	1	1	yes	characteristic, complemented, Sylow
724	C₂×#41	—	43	1	no	—
725	C₂×#41	—	43	2	no	—
726	C₂×#41	—	43	2	no	—
727	C₂²×Q₈	—	43	2	no	—
728	C₂²×D₄	—	43	2	no	—
729	C₂²×D₄	—	86	1	no	—
730	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
731	C₂³×C₄	—	2	1	no	—
732	#137	—	172	4	no	—
733	AGL(1,ℤ/8)	—	172	4	no	—
734	AGL(1,ℤ/8)	—	172	4	no	—
735	C₂×Q₁₆	—	43	2	no	—
736	C₂×Q₁₆	—	43	2	no	—
737	C₂×Q₁₆	—	43	2	no	—
738	C₂×SD₁₆	—	43	2	no	—
739	C₂×SD₁₆	—	43	2	no	—
740	C₂×SD₁₆	—	43	2	no	—
741	C₂×SD₁₆	—	43	2	no	—
742	C₂×SD₁₆	—	43	2	no	—
743	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
744	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
745	C₂×D₈	—	43	2	no	—
746	C₂×D₈	—	43	2	no	—
747	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
748	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
749	C₂×M₁₆	—	43	2	no	—
750	C₂×M₁₆	—	43	2	no	—
751	C₂×M₁₆	—	43	2	no	—
752	C₄⋊Q₈	—	43	1	no	—
753	C₄⋊Q₈	—	43	1	no	—
754	C₄⋊Q₈	—	43	1	no	—
755	C₄⋊Q₈	—	86	1	no	—
756	#127	—	43	1	no	—
757	#126	—	2	1	no	—
758	#126	—	86	2	no	—
759	#126	—	86	2	no	—
760	#126	—	86	2	no	—
761	#126	—	86	2	no	—
762	#126	—	86	2	no	—
763	#125	—	43	2	no	—
764	#125	—	86	2	no	—
765	#125	—	86	1	no	—
766	#125	C₂²×D₄₃	1	1	yes	characteristic
767	#124	—	43	2	no	—
768	#124	—	43	2	no	—
769	#124	—	43	2	no	—
770	#124	—	43	2	no	—
771	#124	—	86	1	no	—
772	#124	—	86	2	no	—
773	#124	—	86	2	no	—
774	#124	—	86	2	no	—
775	#124	—	86	2	no	—
776	#124	C₂²×D₄₃	1	1	yes	characteristic
777	#123	—	2	1	no	—
778	#123	—	86	2	no	—
779	#123	—	86	2	no	—
780	#123	—	86	2	no	—
781	#123	—	86	2	no	—
782	#123	—	86	2	no	—
783	#123	—	86	2	no	—
784	#123	—	86	2	no	—
785	C₂²⋊Q₈	—	43	2	no	—
786	C₂²⋊Q₈	—	43	2	no	—
787	C₂²⋊Q₈	—	43	2	no	—
788	C₂²⋊Q₈	—	86	2	no	—
789	C₂²⋊Q₈	—	86	2	no	—
790	C₂²⋊Q₈	—	86	2	no	—
791	C₂²⋊Q₈	—	86	1	no	—
792	C₂²⋊Q₈	—	86	1	no	—
793	C₂²⋊Q₈	—	86	1	no	—
794	C₂²⋊Q₈	—	86	1	no	—
795	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
796	#121	—	43	2	no	—
797	#121	—	43	2	no	—
798	#121	—	86	2	no	—
799	#121	—	86	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	1	no	—
806	#121	C₂²×D₄₃	1	1	yes	characteristic
807	#120	—	86	2	no	—
808	#120	—	86	2	no	—
809	#120	—	86	2	no	—
810	C₄×Q₈	—	43	1	no	—
811	C₄×Q₈	—	43	1	no	—
812	C₄×Q₈	—	43	2	no	—
813	C₄×Q₈	—	43	2	no	—
814	C₄×Q₈	—	43	2	no	—
815	C₄×Q₈	—	86	1	no	—
816	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	43	2	no	—
821	C₄×D₄	—	43	2	no	—
822	C₄×D₄	—	43	2	no	—
823	C₄×D₄	—	43	2	no	—
824	C₄×D₄	—	43	1	no	—
825	C₄×D₄	—	43	1	no	—
826	C₄×D₄	—	86	1	no	—
827	C₄×D₄	—	86	1	no	—
828	C₄×D₄	—	86	2	no	—
829	C₄×D₄	—	86	2	no	—
830	C₄×D₄	—	86	2	no	—
831	C₄×D₄	—	86	2	no	—
832	C₄×D₄	—	86	2	no	—
833	C₄×D₄	—	86	1	no	—
834	C₄×D₄	—	86	1	no	—
835	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
836	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
837	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
838	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
839	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
840	#117	—	2	1	no	—
841	#117	—	43	1	no	—
842	#117	—	43	2	no	—
843	#117	—	43	2	no	—
844	#117	—	86	2	no	—
845	#117	—	86	2	no	—
846	#117	—	86	2	no	—
847	#117	—	86	2	no	—
848	#117	—	86	1	no	—
849	#117	—	86	1	no	—
850	#117	—	86	1	no	—
851	#117	—	86	1	no	—
852	C₂×C₄⋊C₄	—	86	1	no	—
853	C₂×C₄⋊C₄	—	86	1	no	—
854	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	86	2	no	—
857	C₂×C₂²⋊C₄	—	86	2	no	—
858	C₂×C₂²⋊C₄	—	86	2	no	—
859	C₂×C₂²⋊C₄	—	86	2	no	—
860	C₂×C₄²	—	43	2	no	—
861	C₂×C₄²	—	86	2	no	—
862	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
863	#107	—	43	2	no	—
864	#107	C₂²×D₄₃	1	1	yes	characteristic
865	#107	C₂²×D₄₃	1	1	yes	characteristic
866	#106	—	43	2	no	—
867	#106	C₂²×D₄₃	1	1	yes	characteristic
868	#106	C₂²×D₄₃	1	1	yes	characteristic
869	C₄⋊C₈	—	43	2	no	—
870	C₄⋊C₈	—	43	2	no	—
871	C₄⋊C₈	—	43	2	no	—
872	C₄⋊C₈	—	43	1	no	—
873	C₄⋊C₈	—	43	1	no	—
874	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
875	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
876	#103	—	43	2	no	—
877	#103	—	43	2	no	—
878	#103	—	43	2	no	—
879	#103	—	43	2	no	—
880	#103	—	43	2	no	—
881	#103	—	43	2	no	—
882	#103	—	43	2	no	—
883	#103	C₂²×D₄₃	1	1	yes	characteristic
884	#103	C₂²×D₄₃	1	1	yes	characteristic
885	#102	—	43	2	no	—
886	#102	—	43	2	no	—
887	#102	—	43	2	no	—
888	#102	—	43	2	no	—
889	#102	—	43	2	no	—
890	#102	C₂²×D₄₃	1	1	yes	characteristic
891	#102	C₂²×D₄₃	1	1	yes	characteristic
892	#102	C₂²×D₄₃	1	1	yes	characteristic
893	#102	C₂²×D₄₃	1	1	yes	characteristic
894	#102	C₂²×D₄₃	1	1	yes	characteristic
895	#102	C₂²×D₄₃	1	1	yes	characteristic
896	C₂²⋊C₈	—	43	2	no	—
897	C₂²⋊C₈	—	43	2	no	—
898	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
899	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
900	C₄×C₈	—	43	2	no	—
901	C₄×C₈	—	43	2	no	—
902	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
903	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
904	C₂⁴	—	2	1	no	—
905	C₂⁴	—	86	2	no	—
906	#41	—	86	4	no	—
907	#41	—	172	2	no	—
908	#41	—	172	2	no	—
909	#41	—	172	2	no	—
910	#41	—	172	2	no	—
911	C₂×Q₈	—	43	1	no	—
912	C₂×Q₈	—	43	2	no	—
913	C₂×Q₈	—	43	2	no	—
914	C₂×Q₈	—	86	2	no	—
915	C₂×Q₈	—	86	1	no	—
916	C₂×Q₈	—	172	2	no	—
917	C₂×Q₈	—	172	2	no	—
918	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	4	1	no	—
923	C₂×D₄	—	43	2	no	—
924	C₂×D₄	—	43	1	no	—
925	C₂×D₄	—	43	2	no	—
926	C₂×D₄	—	86	2	no	—
927	C₂×D₄	—	86	2	no	—
928	C₂×D₄	—	86	2	no	—
929	C₂×D₄	—	86	2	no	—
930	C₂×D₄	—	86	2	no	—
931	C₂×D₄	—	86	1	no	—
932	C₂×D₄	—	86	1	no	—
933	C₂×D₄	—	172	4	no	—
934	C₂×D₄	—	172	2	no	—
935	C₂×D₄	—	172	2	no	—
936	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
937	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
938	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	4	4	no	—
946	C₂²×C₄	—	43	2	no	—
947	C₂²×C₄	—	43	2	no	—
948	C₂²×C₄	—	43	2	no	—
949	C₂²×C₄	—	86	2	no	—
950	C₂²×C₄	—	86	2	no	—
951	C₂²×C₄	—	86	2	no	—
952	C₂²×C₄	—	86	2	no	—
953	C₂²×C₄	—	86	2	no	—
954	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
955	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
956	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
957	Q₁₆	—	172	2	no	—
958	Q₁₆	—	172	2	no	—
959	Q₁₆	—	172	2	no	—
960	SD₁₆	—	2	2	no	—
961	SD₁₆	—	4	1	no	—
962	SD₁₆	—	86	4	no	—
963	SD₁₆	—	172	2	no	—
964	SD₁₆	—	172	2	no	—
965	SD₁₆	—	172	2	no	—
966	SD₁₆	—	172	2	no	—
967	D₈	—	2	2	no	—
968	D₈	—	4	1	no	—
969	D₈	—	86	4	no	—
970	D₈	—	172	2	no	—
971	M₁₆	—	172	2	no	—
972	M₁₆	—	172	2	no	—
973	M₁₆	—	172	2	no	—
974	C₂×C₈	—	43	2	no	—
975	C₂×C₈	—	43	2	no	—
976	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
977	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
978	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
979	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	43	1	no	—
986	C₄⋊C₄	—	43	1	no	—
987	C₄⋊C₄	—	43	2	no	—
988	C₄⋊C₄	—	43	2	no	—
989	C₄⋊C₄	—	43	2	no	—
990	C₄⋊C₄	—	86	2	no	—
991	C₄⋊C₄	—	86	2	no	—
992	C₄⋊C₄	—	86	2	no	—
993	C₄⋊C₄	—	86	2	no	—
994	C₄⋊C₄	—	86	2	no	—
995	C₄⋊C₄	—	86	2	no	—
996	C₄⋊C₄	—	86	1	no	—
997	C₄⋊C₄	—	86	1	no	—
998	C₄⋊C₄	—	86	1	no	—
999	C₄⋊C₄	—	86	2	no	—
1000	C₄⋊C₄	—	86	1	no	—
1001	C₄⋊C₄	—	86	2	no	—
1002	C₄⋊C₄	—	86	1	no	—
1003	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	43	2	no	—
1017	C₂²⋊C₄	—	43	2	no	—
1018	C₂²⋊C₄	—	43	2	no	—
1019	C₂²⋊C₄	—	86	2	no	—
1020	C₂²⋊C₄	—	86	2	no	—
1021	C₂²⋊C₄	—	86	2	no	—
1022	C₂²⋊C₄	—	86	2	no	—
1023	C₂²⋊C₄	—	86	2	no	—
1024	C₂²⋊C₄	—	86	2	no	—
1025	C₂²⋊C₄	—	86	2	no	—
1026	C₂²⋊C₄	—	86	2	no	—
1027	C₂²⋊C₄	—	86	2	no	—
1028	C₂²⋊C₄	—	86	2	no	—
1029	C₂²⋊C₄	—	86	2	no	—
1030	C₂²⋊C₄	—	86	2	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	C₄²	—	2	1	no	—
1036	C₄²	—	43	2	no	—
1037	C₄²	—	43	2	no	—
1038	C₄²	—	43	2	no	—
1039	C₄²	—	86	2	no	—
1040	C₄²	—	86	2	no	—
1041	C₄²	—	86	2	no	—
1042	C₄²	—	86	2	no	—
1043	C₄²	D₄×D₄₃	1	1	yes	characteristic
1044	C₄²	D₄×D₄₃	1	1	yes	characteristic
1045	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1046	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	—	43	2	no	—
1054	C₂³	—	86	2	no	—
1055	C₂³	—	344	2	no	—
1056	C₂³	—	344	2	no	—
1057	C₂³	—	172	4	no	—
1058	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1059	Q₈	—	2	1	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	86	2	no	—
1062	Q₈	—	86	2	no	—
1063	Q₈	—	86	2	no	—
1064	Q₈	—	86	2	no	—
1065	Q₈	—	86	2	no	—
1066	Q₈	—	344	1	no	—
1067	Q₈	—	344	2	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	1	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	86	2	no	—
1076	D₄	—	86	2	no	—
1077	D₄	—	86	2	no	—
1078	D₄	—	344	1	no	—
1079	D₄	—	344	2	no	—
1080	D₄	—	344	2	no	—
1081	D₄	—	344	2	no	—
1082	D₄	—	172	4	no	—
1083	D₄	—	172	2	no	—
1084	D₄	—	172	4	no	—
1085	D₄	—	172	2	no	—
1086	D₄	#13063371	1	2	yes	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	43	2	no	—
1103	C₂×C₄	—	43	2	no	—
1104	C₂×C₄	—	43	2	no	—
1105	C₂×C₄	—	86	2	no	—
1106	C₂×C₄	—	86	2	no	—
1107	C₂×C₄	—	86	2	no	—
1108	C₂×C₄	—	86	2	no	—
1109	C₂×C₄	—	86	2	no	—
1110	C₂×C₄	—	344	2	no	—
1111	C₂×C₄	—	344	2	no	—
1112	C₂×C₄	—	344	2	no	—
1113	C₂×C₄	—	344	2	no	—
1114	C₂×C₄	—	172	2	no	—
1115	C₂×C₄	—	172	2	no	—
1116	C₂×C₄	—	172	4	no	—
1117	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1118	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1119	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1120	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1121	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1122	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1123	C₈	—	2	1	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	86	2	no	—
1128	C₈	—	86	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	8	4	no	—
1142	C₂²	—	86	2	no	—
1143	C₂²	—	86	2	no	—
1144	C₂²	—	86	2	no	—
1145	C₂²	—	172	2	no	—
1146	C₂²	—	172	2	no	—
1147	C₂²	—	172	2	no	—
1148	C₂²	—	688	4	no	—
1149	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	86	2	no	—
1160	C₄	—	86	2	no	—
1161	C₄	—	86	2	no	—
1162	C₄	—	172	2	no	—
1163	C₄	—	172	2	no	—
1164	C₄	—	172	2	no	—
1165	C₄	#14583695	1	2	yes	—
1166	C₄	C₂×#13063371	1	1	yes	characteristic
1167	C₄	#14583735	1	1	yes	characteristic
1168	C₂	—	4	1	no	—
1169	C₂	—	4	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	—	8	1	no	—
1172	C₂	—	344	2	no	—
1173	C₂	—	172	2	no	—
1174	C₂	#19148256	1	1	yes	characteristic
1175	C₂	C₂×#14583695	1	1	yes	characteristic
1176	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3105	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3105	D₄₃
hypocenter	C₄₃	#62004
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #19148558	C₂	semidirect
2. #19148153	C₂	semidirect
3. #19147589	C₂	semidirect
4. #19147581	C₂	semidirect
5. #19147253	C₂	semidirect
6. #19147242	C₂	semidirect
7. #19146891	C₂	semidirect
8. #19146866	C₂	semidirect
9. #19146839	C₂	semidirect
10. #19146814	C₂	semidirect
11. #19146242	C₂	semidirect
12. #19146230	C₂	semidirect
13. #19146206	C₂	semidirect
14. #19146196	C₂	semidirect
15. #19145995	C₂	semidirect
16. #19145968	C₂	semidirect
17. #19145558	C₂	semidirect
18. #19145553	C₂	semidirect
19. #19144618	C₂	semidirect
20. #19144084	C₂	semidirect
21. #19144059	C₂	semidirect
22. #19143724	C₂	semidirect
23. C₄₃×#3105	C₂	semidirect
24. C₂×#13063354	C₂²	semidirect
25. C₂×#13063351	C₂²	semidirect
27. #14583634	C₂²	semidirect
28. #14583619	C₂²	semidirect
29. #14583619	C₂²	semidirect
32. #14583606	C₂²	semidirect
35. #14583584	C₂²	semidirect
38. Q₈×D₁₇₂	C₂²	semidirect
43. #14583543	C₂²	semidirect
44. D₄×D₁₇₂	C₂²	semidirect
47. #14583456	C₂²	semidirect
49. #14583434	C₂²	semidirect
50. #14583431	C₂²	semidirect
52. #124×D₄₃	C₂²	semidirect
56. C₄×#10621900	C₂²	semidirect
59. #14583280	C₂²	semidirect
60. #14583279	C₂²	semidirect
61. #14583272	C₂²	semidirect
62. #14583255	C₂²	semidirect
63. #14583252	C₂²	semidirect
64. #14583250	C₂²	semidirect
65. #14583246	C₂²	semidirect
66. #14583243	C₂²	semidirect
67. #14583226	C₂²	semidirect
68. #14583205	C₂²	semidirect
69. #14583203	C₂²	semidirect
70. #14583198	C₂²	semidirect
71. #14583194	C₂²	semidirect
72. #14583189	C₂²	semidirect
73. #14583158	C₂²	semidirect
74. #14583155	C₂²	semidirect
76. #14583146	C₂²	semidirect
77. #14583144	C₂²	semidirect
79. #14583124	C₂²	semidirect
80. #14583122	C₂²	semidirect
81. #14583122	C₂²	semidirect
82. #14583120	C₂²	semidirect
83. #14583120	C₂²	semidirect
84. #14583118	C₂²	semidirect
85. #14583116	C₂²	semidirect
86. #14583114	C₂²	semidirect
87. #14583114	C₂²	semidirect
88. #14583113	C₂²	semidirect
90. #14583109	C₂²	semidirect
91. #14583104	C₂²	semidirect
92. #14583104	C₂²	semidirect
93. #14583104	C₂²	semidirect
96. #14583063	C₂²	semidirect
97. #14583063	C₂²	semidirect
98. #14583062	C₂²	semidirect
99. #14583056	C₂²	semidirect
100. #14583051	C₂²	semidirect
102. #14583036	C₂²	semidirect
104. C₈×Dic₈₆	C₂²	semidirect
105. C₈×Dic₈₆	C₂²	semidirect
106. #14582993	C₂²	semidirect
107. #14582990	C₂²	semidirect
108. #14582986	C₂²	semidirect
109. #14582979	C₂²	semidirect
110. #14582978	C₂²	semidirect
111. #14582978	C₂²	semidirect
112. #14582974	C₂²	semidirect
113. #14582974	C₂²	semidirect
114. #14582951	C₂²	semidirect
115. #14582923	C₂²	semidirect
116. #14582921	C₂²	semidirect
117. #14582906	C₂²	semidirect
118. #14582902	C₂²	semidirect
119. #14582898	C₂²	semidirect
121. C₂×C₄×D₄×C₄₃	C₂²	semidirect
122. C₄₃×#484	C₂²	semidirect
124. C₄₃×#478	C₂²	semidirect
125. C₄₃×#478	C₂²	semidirect
128. C₄₃×#450	C₂²	semidirect
130. C₄×SD₁₆×C₄₃	C₂²	semidirect
131. C₄×SD₁₆×C₄₃	C₂²	semidirect
134. C₄₃×#431	C₂²	semidirect
598. #3105	D₄₃	semidirect
646. C₂×C₄×D₄	C₂×D₄₃	semidirect
657. #484	C₂×D₄₃	semidirect
663. #478	C₂×D₄₃	semidirect
664. #478	C₂×D₄₃	semidirect
697. #450	C₂×D₄₃	semidirect
707. C₄×SD₁₆	C₂×D₄₃	semidirect
708. C₄×SD₁₆	C₂×D₄₃	semidirect
717. #431	C₂×D₄₃	semidirect
723. C₄₃	#62004	semidirect

Maximal subgroups

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

subgroup	index
#19148558	2
#19148153	2
#19147589	2
#19147581	2
#19147253	2
#19147242	2
#19146891	2
#19146866	2
#19146839	2
#19146814	2
#19146242	2
#19146230	2
#19146206	2
#19146196	2
#19145995	2
#19145968	2
#19145558	2
#19145553	2
#19144618	2
#19144084	2
#19144059	2
#19143724	2
C₄₃×#3105	2
#62004	43