Subgroups — #25965206

Order 11008.

2068 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148011	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13063372	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144883	C₂	1	2	yes	maximal, complemented
4	#19144868	C₂	1	2	yes	maximal, complemented
5	#19144830	C₂	1	2	yes	maximal, complemented
6	#19144790	C₂	1	2	yes	maximal, complemented
7	#19144679	C₂	1	2	yes	maximal, complemented
8	#19144651	C₂	1	2	yes	maximal, complemented
9	#19144624	C₂	1	2	yes	maximal, complemented
10	#19144617	C₂	1	2	yes	maximal, complemented
11	#19144582	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144556	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144455	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144440	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144132	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144119	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143906	C₂	1	1	yes	maximal, characteristic, complemented
18	#19143884	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13063355	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13063350	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×#10621873	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143237	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063372	C₂²	1	1	yes	characteristic
25	C₂×#13063355	C₂²	1	1	yes	characteristic
26	C₂×#13063350	C₂²	1	1	yes	characteristic
27	C₂²×#10621873	C₂²	1	1	yes	characteristic
28	#14583527	C₂²	1	1	yes	characteristic
29	#14583521	C₂²	1	2	yes	—
30	#14583520	—	2	1	no	—
31	#14583504	—	2	1	no	—
32	#14583500	C₂²	1	2	yes	—
33	#14583482	—	2	2	no	—
34	#14583477	C₂²	1	1	yes	characteristic
35	#14583468	C₂²	1	1	yes	characteristic
36	#14583463	C₂²	1	1	yes	characteristic
37	#14583449	—	2	1	no	—
38	#14583446	C₂²	1	2	yes	—
39	#14583436	C₂²	1	2	yes	—
40	#14583433	—	2	1	no	—
41	#14583408	—	2	2	no	—
42	#14583382	C₂²	1	1	yes	characteristic
43	#14583379	—	2	1	no	—
44	#14583379	C₂²	1	1	yes	characteristic
45	#14583378	—	2	2	no	—
46	#14583378	C₂²	1	2	yes	complemented
47	#14583376	—	2	1	no	—
48	#14583376	C₂²	1	1	yes	characteristic
49	#14583375	C₂²	1	2	yes	complemented
50	C₄×#10621898	—	2	1	no	—
51	C₄×#10621898	C₂²	1	1	yes	characteristic
52	C₄×#10621900	—	2	2	no	—
53	C₄×#10621900	C₂²	1	2	yes	complemented
54	C₂×C₄×Dic₈₆	—	2	1	no	—
55	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
56	C₄×Q₈×D₄₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
58	#14583238	C₂²	1	2	yes	complemented
59	#14583228	C₂²	1	2	yes	complemented
60	#14583226	C₂²	1	2	yes	—
61	#14583225	C₂²	1	2	yes	—
62	#14583222	C₂²	1	2	yes	complemented
63	#14583219	C₂²	1	2	yes	—
64	#14583216	C₂²	1	2	yes	complemented
65	#14583214	C₂²	1	2	yes	—
66	#14583209	C₂²	1	2	yes	complemented
67	#14583205	C₂²	1	2	yes	complemented
68	#14583204	C₂²	1	2	yes	complemented
69	#14583201	C₂²	1	2	yes	complemented
70	#14583193	C₂²	1	2	yes	complemented
71	#14583187	C₂²	1	2	yes	complemented
72	#14583183	C₂²	1	2	yes	complemented
73	#14583182	C₂²	1	2	yes	complemented
74	#14583124	C₂²	1	2	yes	—
75	#14583124	C₂²	1	2	yes	—
76	#14583123	C₂²	1	2	yes	—
77	#14583116	C₂²	1	2	yes	—
78	#14583098	C₂²	1	2	yes	—
79	#14583098	C₂²	1	2	yes	—
80	#14583097	C₂²	1	2	yes	—
81	#14583092	C₂²	1	2	yes	—
82	#14583058	C₂²	1	2	yes	complemented
83	#14583053	C₂²	1	2	yes	complemented
84	#14583045	C₂²	1	2	yes	—
85	#14583045	C₂²	1	2	yes	—
86	#14583041	C₂²	1	2	yes	complemented
87	#14583039	C₂²	1	2	yes	—
88	#14583039	C₂²	1	2	yes	—
89	#14583036	C₂²	1	2	yes	complemented
90	#14583009	C₂²	1	2	yes	—
91	#14583004	C₂²	1	2	yes	complemented
92	#14582999	C₂²	1	2	yes	complemented
93	#14582997	C₂²	1	2	yes	—
94	C₄×#10621885	C₂²	1	2	yes	complemented
95	C₄×#10621873	C₂²	1	2	yes	—
96	C₄×#10621873	C₂²	1	2	yes	—
97	C₄×#10621873	C₂²	1	2	yes	—
98	C₄×#10621873	C₂²	1	2	yes	—
99	C₄×#10621884	C₂²	1	2	yes	—
100	C₄×#10621883	C₂²	1	2	yes	complemented
101	C₄×#10621882	C₂²	1	2	yes	—
102	#14582958	C₂²	1	2	yes	complemented
103	#14582958	C₂²	1	2	yes	complemented
104	#14582950	C₂²	1	2	yes	complemented
105	#14582950	C₂²	1	2	yes	complemented
106	#14582942	C₂²	1	1	yes	characteristic
107	#14582942	C₂²	1	1	yes	characteristic
108	C₂×#13063257	C₂²	1	1	yes	characteristic
109	#14582925	C₂²	1	1	yes	characteristic
110	#14582925	C₂²	1	1	yes	characteristic
111	#14582907	C₂²	1	1	yes	characteristic
112	#14582903	C₂²	1	1	yes	characteristic
113	#14582900	C₂²	1	1	yes	characteristic
114	#14582900	C₂²	1	1	yes	characteristic
115	C₂×#13063250	C₂²	1	1	yes	characteristic
116	C₂×#13063247	C₂²	1	1	yes	characteristic
117	#14582865	C₂²	1	1	yes	characteristic
118	#14582865	C₂²	1	1	yes	characteristic
119	C₄×#10621877	C₂²	1	1	yes	characteristic
120	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
123	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
124	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
127	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#427	C₂²	1	1	yes	characteristic
132	C₄₃×#416	C₂²	1	1	yes	characteristic
133	C₄₃×#416	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
135	#13063372	—	2	4	no	—
136	#13063372	—	2	4	no	—
137	C₂×#10621898	—	2	1	no	—
138	C₂×#10621898	—	2	2	no	—
139	C₂×#10621898	C₂³	1	1	yes	characteristic
140	C₂×#10621900	—	2	2	no	—
141	C₂×#10621900	C₂³	1	2	yes	—
142	C₂²×Dic₈₆	—	2	1	no	—
143	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
144	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
145	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
146	C₂²×C₄×D₄₃	—	2	1	no	—
147	#13063355	—	2	4	no	—
148	#13063350	—	2	4	no	—
149	C₂×#10621885	C₂³	1	2	yes	—
150	C₂×#10621873	—	2	4	no	—
151	C₂×#10621873	C₂³	1	2	yes	—
152	C₂×#10621873	C₂³	1	2	yes	—
153	C₂×#10621883	C₂³	1	2	yes	—
154	C₂×#10621884	C₂³	1	2	yes	—
155	C₂×#10621882	C₂³	1	2	yes	—
156	C₂×#10621877	C₂³	1	1	yes	characteristic
157	C₂×#10621877	C₂³	1	1	yes	characteristic
158	#13063325	—	2	1	no	—
159	#13063324	C₂³	1	2	yes	—
160	#13063322	—	2	1	no	—
161	#13063321	C₂³	1	2	yes	—
162	#13063320	—	2	2	no	—
163	#13063319	—	2	2	no	—
164	#13063317	—	2	1	no	—
165	#13063316	C₂³	1	2	yes	—
166	#13063314	C₂³	1	2	yes	—
167	#13063313	—	2	1	no	—
168	#13063313	—	2	2	no	—
169	#13063311	—	2	2	no	—
170	#13063310	—	2	2	no	—
171	#13063310	—	2	2	no	—
172	#13063308	—	2	2	no	—
173	#13063307	—	2	2	no	—
174	#13063304	—	2	1	no	—
175	#13063303	—	2	2	no	—
176	#13063302	—	2	2	no	—
177	#13063301	C₂³	1	2	yes	—
178	#13063300	C₂³	1	2	yes	—
179	#13063300	C₂³	1	2	yes	—
180	#13063299	—	2	1	no	—
181	#13063299	—	2	2	no	—
182	#13063299	—	2	1	no	—
183	#13063299	—	2	1	no	—
184	#13063298	—	2	2	no	—
185	#13063298	—	2	2	no	—
186	#13063297	—	2	2	no	—
187	#13063296	C₂³	1	2	yes	—
188	#13063295	—	2	2	no	—
189	#13063293	—	2	2	no	—
190	Q₈×Dic₄₃	C₂³	1	2	yes	—
191	C₄×Dic₈₆	—	2	1	no	—
192	C₄×Dic₈₆	—	2	1	no	—
193	C₄×Dic₈₆	—	2	1	no	—
194	C₄×Dic₈₆	—	2	1	no	—
195	C₄×Dic₈₆	—	2	1	no	—
196	C₄×Dic₈₆	—	2	2	no	—
197	C₄×Dic₈₆	—	2	2	no	—
198	C₄×Dic₈₆	D₄	1	1	yes	characteristic
199	C₄×Dic₈₆	D₄	1	1	yes	characteristic
200	C₄×Dic₈₆	C₂³	1	2	yes	—
201	C₄×Dic₈₆	C₂³	1	2	yes	—
202	#13063290	—	2	2	no	—
203	#13063290	—	2	2	no	—
204	#13063290	C₂³	1	2	yes	—
205	#13063290	C₂³	1	2	yes	—
206	C₄×D₁₇₂	—	2	1	no	—
207	C₄×D₁₇₂	—	2	2	no	—
208	C₄×D₁₇₂	—	2	1	no	—
209	C₄×D₁₇₂	—	2	1	no	—
210	C₄×D₁₇₂	D₄	1	1	yes	characteristic
211	C₄×D₁₇₂	D₄	1	1	yes	characteristic
212	C₄×D₁₇₂	C₂³	1	2	yes	—
213	C₄×D₁₇₂	C₂³	1	2	yes	—
214	D₄×Dic₄₃	—	2	2	no	—
215	D₄×Dic₄₃	C₂³	1	2	yes	—
216	C₄×C₂²⋊D₄₃	—	2	2	no	—
217	C₄×C₂²⋊D₄₃	—	2	2	no	—
218	C₄×C₂²⋊D₄₃	—	2	2	no	—
219	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
220	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
221	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
222	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
223	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
224	#13063284	—	2	1	no	—
225	#13063284	C₂³	1	1	yes	characteristic
226	#13063283	—	2	2	no	—
227	#13063283	C₂³	1	2	yes	—
228	#13063282	—	2	2	no	—
229	#13063282	—	2	2	no	—
230	#13063282	C₂³	1	2	yes	—
231	#13063281	—	2	2	no	—
232	#13063281	—	2	2	no	—
233	#13063281	—	2	2	no	—
234	C₂×C₄⋊Dic₄₃	—	2	1	no	—
235	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
237	C₂×Dic₄₃⋊C₄	—	2	1	no	—
238	C₂×Dic₄₃⋊C₄	—	2	2	no	—
239	C₄⋊C₄×D₄₃	—	2	2	no	—
240	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
241	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
242	C₂×C₄×Dic₄₃	—	2	1	no	—
243	C₂×C₄×Dic₄₃	—	2	2	no	—
244	C₄²×D₄₃	—	2	2	no	—
245	C₄²×D₄₃	C₂³	1	2	yes	—
246	#13063258	C₂³	1	2	yes	—
247	#13063258	C₂³	1	2	yes	—
248	#13063257	C₂³	1	2	yes	—
249	#13063257	C₂³	1	2	yes	—
250	#13063256	C₂³	1	2	yes	—
251	#13063256	C₂³	1	2	yes	—
252	Dic₄₃⋊C₈	C₂³	1	2	yes	—
253	Dic₄₃⋊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	#13063249	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063247	C₂³	1	2	yes	—
263	#13063247	C₂³	1	2	yes	—
264	#13063246	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	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
271	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
272	#13063236	C₂³	1	2	yes	—
273	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
274	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
276	#135×C₄₃	—	2	4	no	—
277	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
278	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
279	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
280	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
281	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₃	—	2	1	no	—
288	C₄×D₄×C₄₃	—	2	1	no	—
289	C₄×D₄×C₄₃	—	2	1	no	—
290	C₄×D₄×C₄₃	—	2	1	no	—
291	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
295	#117×C₄₃	—	2	1	no	—
296	#117×C₄₃	—	2	1	no	—
297	#117×C₄₃	C₂³	1	1	yes	characteristic
298	#117×C₄₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₄₃	—	2	1	no	—
300	C₂×C₄²×C₄₃	—	2	1	no	—
301	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
302	#107×C₄₃	C₂³	1	1	yes	characteristic
303	#107×C₄₃	C₂³	1	1	yes	characteristic
304	#106×C₄₃	C₂³	1	1	yes	characteristic
305	#106×C₄₃	C₂³	1	1	yes	characteristic
306	#103×C₄₃	C₂³	1	1	yes	characteristic
307	#103×C₄₃	C₂³	1	1	yes	characteristic
308	#103×C₄₃	C₂³	1	1	yes	characteristic
309	#103×C₄₃	C₂³	1	1	yes	characteristic
310	#102×C₄₃	C₂³	1	1	yes	characteristic
311	#102×C₄₃	C₂³	1	1	yes	characteristic
312	#102×C₄₃	C₂³	1	1	yes	characteristic
313	#102×C₄₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
318	C₂³×D₄₃	—	2	1	no	—
319	#41×C₄₃	—	2	2	no	—
320	#41×C₄₃	—	2	2	no	—
321	#41×C₄₃	—	2	2	no	—
322	#41×C₄₃	#41	1	4	yes	complemented
323	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₃	—	2	1	no	—
326	C₂×D₄×C₄₃	—	2	1	no	—
327	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂×C₂²⋊D₄₃	—	2	2	no	—
339	C₂×C₂²⋊D₄₃	—	2	2	no	—
340	C₂×C₂²⋊D₄₃	—	2	2	no	—
341	C₂×C₂²⋊D₄₃	—	2	2	no	—
342	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
343	C₂²×Dic₄₃	—	2	2	no	—
344	C₂²×Dic₄₃	—	2	2	no	—
345	C₂²×Dic₄₃	—	2	1	no	—
346	C₂²×Dic₄₃	—	2	1	no	—
347	C₂²×Dic₄₃	—	2	1	no	—
348	Q₈×D₄₃	—	2	4	no	—
349	Q₈×D₄₃	—	2	4	no	—
350	#10621900	—	2	16	no	—
351	#10621900	—	2	4	no	—
352	#10621900	—	2	4	no	—
353	#10621898	—	2	8	no	—
354	#10621898	—	2	2	no	—
355	#10621898	—	2	2	no	—
356	#10621898	—	8	4	no	—
357	C₂×D₁₇₂	—	2	1	no	—
358	C₂×D₁₇₂	—	2	2	no	—
359	C₂×D₁₇₂	—	2	2	no	—
360	C₂×D₁₇₂	—	2	2	no	—
361	C₂×D₁₇₂	—	2	2	no	—
362	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
363	C₂×D₁₇₂	C₂⁴	1	2	yes	—
364	C₂×C₄×D₄₃	—	2	2	no	—
365	C₂×C₄×D₄₃	—	2	2	no	—
366	C₂×C₄×D₄₃	—	2	2	no	—
367	C₂×C₄×D₄₃	—	2	2	no	—
368	C₂×C₄×D₄₃	—	8	2	no	—
369	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
370	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
371	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
372	C₂×Dic₈₆	—	2	8	no	—
373	C₂×Dic₈₆	—	2	1	no	—
374	C₂×Dic₈₆	—	2	2	no	—
375	C₂×Dic₈₆	—	2	2	no	—
376	C₂×Dic₈₆	—	2	2	no	—
377	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
378	C₂×Dic₈₆	#41	1	4	yes	complemented
379	C₂×Dic₈₆	C₂⁴	1	2	yes	—
380	Q₁₆×C₄₃	—	2	2	no	—
381	SD₁₆×C₄₃	—	2	2	no	—
382	SD₁₆×C₄₃	—	2	2	no	—
383	D₈×C₄₃	—	2	2	no	—
384	C₂×C₈×C₄₃	—	2	2	no	—
385	C₂×C₈×C₄₃	—	2	2	no	—
386	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄×C₄₃	—	2	1	no	—
391	C₄⋊C₄×C₄₃	—	2	1	no	—
392	C₄⋊C₄×C₄₃	—	2	1	no	—
393	C₄⋊C₄×C₄₃	—	2	1	no	—
394	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
398	C₂²⋊C₄×C₄₃	—	2	1	no	—
399	C₂²⋊C₄×C₄₃	—	2	1	no	—
400	C₂²⋊C₄×C₄₃	—	2	1	no	—
401	C₂²⋊C₄×C₄₃	—	2	1	no	—
402	C₂²⋊C₄×C₄₃	—	2	1	no	—
403	C₂²⋊C₄×C₄₃	—	2	1	no	—
404	C₄²×C₄₃	—	2	1	no	—
405	C₄²×C₄₃	—	2	1	no	—
406	C₄²×C₄₃	—	2	1	no	—
407	C₄²×C₄₃	—	2	1	no	—
408	C₄²×C₄₃	—	2	1	no	—
409	C₄²×C₄₃	—	2	1	no	—
410	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
411	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
412	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
413	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
414	C₂²⋊Dic₄₃	—	2	2	no	—
415	C₂²⋊Dic₄₃	—	2	2	no	—
416	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
417	#10621885	—	2	4	no	—
418	#10621884	—	2	4	no	—
419	#10621883	—	2	4	no	—
420	#10621882	—	2	4	no	—
421	(C₂×D₄₃)⋊C₄	—	2	2	no	—
422	(C₂×D₄₃)⋊C₄	—	2	2	no	—
423	(C₂×D₄₃)⋊C₄	—	2	2	no	—
424	(C₂×D₄₃)⋊C₄	—	2	2	no	—
425	(C₂×D₄₃)⋊C₄	—	2	2	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	2	no	—
428	(C₂×D₄₃)⋊C₄	—	2	2	no	—
429	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
430	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
431	C₄⋊Dic₄₃	—	2	1	no	—
432	C₄⋊Dic₄₃	—	2	1	no	—
433	C₄⋊Dic₄₃	—	2	2	no	—
434	C₄⋊Dic₄₃	—	2	2	no	—
435	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
437	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
438	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
439	Dic₄₃⋊C₄	—	2	2	no	—
440	Dic₄₃⋊C₄	—	2	2	no	—
441	Dic₄₃⋊C₄	—	2	2	no	—
442	Dic₄₃⋊C₄	—	2	2	no	—
443	Dic₄₃⋊C₄	—	2	2	no	—
444	Dic₄₃⋊C₄	—	2	2	no	—
445	Dic₄₃⋊C₄	—	2	2	no	—
446	Dic₄₃⋊C₄	—	2	2	no	—
447	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
448	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
449	C₄×Dic₄₃	—	2	2	no	—
450	C₄×Dic₄₃	—	2	2	no	—
451	C₄×Dic₄₃	—	2	2	no	—
452	C₄×Dic₄₃	—	2	2	no	—
453	C₄×Dic₄₃	—	2	2	no	—
454	C₄×Dic₄₃	—	2	2	no	—
455	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
456	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
457	C₄×Dic₄₃	C₂⁴	1	2	yes	—
458	#10621877	—	2	2	no	—
459	#10621877	—	2	2	no	—
460	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
461	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
462	#10621873	—	2	4	no	—
463	#10621873	—	2	4	no	—
464	C₂³×C₄₃	—	2	1	no	—
465	C₂³×C₄₃	—	2	1	no	—
466	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂²×D₄₃	—	2	2	no	—
468	C₂²×D₄₃	—	4	2	no	—
469	C₂²×D₄₃	—	8	1	no	—
470	C₂²×D₄₃	—	8	1	no	—
471	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
472	Q₈×C₄₃	—	2	1	no	—
473	Q₈×C₄₃	—	2	1	no	—
474	Q₈×C₄₃	—	2	1	no	—
475	Q₈×C₄₃	C₂×#41	1	2	yes	—
476	D₄×C₄₃	—	2	4	no	—
477	D₄×C₄₃	—	2	1	no	—
478	D₄×C₄₃	—	2	1	no	—
479	D₄×C₄₃	—	2	1	no	—
480	D₄×C₄₃	—	4	2	no	—
481	D₄×C₄₃	C₂×#41	1	2	yes	—
482	C₂×C₄×C₄₃	—	2	1	no	—
483	C₂×C₄×C₄₃	—	2	4	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	1	no	—
489	C₂×C₄×C₄₃	—	2	1	no	—
490	C₂×C₄×C₄₃	—	4	1	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	—	8	1	no	—
495	C₂×C₄×C₄₃	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
502	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
503	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
504	C₂²⋊D₄₃	—	2	8	no	—
505	C₂²⋊D₄₃	—	2	4	no	—
506	C₂²⋊D₄₃	—	8	2	no	—
507	C₂²⋊D₄₃	—	8	2	no	—
508	C₂²⋊D₄₃	—	8	2	no	—
509	C₂×Dic₄₃	—	2	8	no	—
510	C₂×Dic₄₃	—	2	4	no	—
511	C₂×Dic₄₃	—	2	2	no	—
512	C₂×Dic₄₃	—	2	2	no	—
513	C₂×Dic₄₃	—	2	2	no	—
514	C₂×Dic₄₃	—	8	2	no	—
515	C₂×Dic₄₃	—	8	1	no	—
516	C₂×Dic₄₃	—	8	1	no	—
517	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
518	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
519	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
520	D₁₇₂	—	2	2	no	—
521	D₁₇₂	—	2	2	no	—
522	D₁₇₂	—	2	2	no	—
523	D₁₇₂	—	4	2	no	—
524	D₁₇₂	—	8	2	no	—
525	D₁₇₂	—	8	2	no	—
526	C₄×D₄₃	—	2	8	no	—
527	C₄×D₄₃	—	2	4	no	—
528	C₄×D₄₃	—	2	2	no	—
529	C₄×D₄₃	—	2	2	no	—
530	C₄×D₄₃	—	4	2	no	—
531	C₄×D₄₃	—	4	4	no	—
532	C₄×D₄₃	—	8	2	no	—
533	C₄×D₄₃	—	8	2	no	—
534	Dic₈₆	—	2	8	no	—
535	Dic₈₆	—	2	2	no	—
536	Dic₈₆	—	2	4	no	—
537	Dic₈₆	—	2	2	no	—
538	Dic₈₆	—	8	2	no	—
539	Dic₈₆	C₂×#41	1	4	yes	—
540	C₈×C₄₃	—	2	1	no	—
541	C₈×C₄₃	—	2	1	no	—
542	C₈×C₄₃	—	2	1	no	—
543	C₈×C₄₃	—	2	1	no	—
544	C₄₃⋊C₈	—	2	2	no	—
545	C₄₃⋊C₈	—	2	2	no	—
546	#60572	—	43	1	no	maximal, Sylow
547	C₂²×C₄₃	—	2	1	no	—
548	C₂²×C₄₃	—	2	1	no	—
549	C₂²×C₄₃	—	2	2	no	—
550	C₂²×C₄₃	—	4	1	no	—
551	C₂²×C₄₃	—	4	1	no	—
552	C₂²×C₄₃	—	4	1	no	—
553	C₂²×C₄₃	—	4	1	no	—
554	C₂²×C₄₃	—	4	1	no	—
555	C₂²×C₄₃	#525	1	2	yes	—
556	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
557	C₂×D₄₃	—	2	2	no	—
558	C₂×D₄₃	—	2	2	no	—
559	C₂×D₄₃	—	2	2	no	—
560	C₂×D₄₃	—	4	2	no	—
561	C₂×D₄₃	—	4	2	no	—
562	C₂×D₄₃	—	4	2	no	—
563	C₂×D₄₃	—	8	4	no	—
564	C₄×C₄₃	—	2	1	no	—
565	C₄×C₄₃	—	2	1	no	—
566	C₄×C₄₃	—	2	2	no	—
567	C₄×C₄₃	—	2	1	no	—
568	C₄×C₄₃	—	4	1	no	—
569	C₄×C₄₃	—	4	1	no	—
570	C₄×C₄₃	—	4	1	no	—
571	C₄×C₄₃	—	4	1	no	—
572	C₄×C₄₃	—	4	1	no	—
573	C₄×C₄₃	#525	1	2	yes	—
574	C₄×C₄₃	#577	1	2	yes	—
575	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
576	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
577	Dic₄₃	—	2	2	no	—
578	Dic₄₃	—	2	2	no	—
579	Dic₄₃	—	2	4	no	—
580	Dic₄₃	—	2	2	no	—
581	Dic₄₃	—	4	2	no	—
582	Dic₄₃	—	4	2	no	—
583	#3460	—	43	1	no	—
584	C₄×2₋¹⁺⁴	—	43	1	no	—
585	#3126	—	43	2	no	—
586	#3125	—	43	2	no	—
587	#3121	—	43	2	no	—
588	#3119	—	43	2	no	—
589	#3108	—	43	2	no	—
590	#3106	—	43	2	no	—
591	#3103	—	43	2	no	—
592	#3102	—	43	2	no	—
593	#3099	—	43	1	no	—
594	#3096	—	43	1	no	—
595	#3084	—	43	1	no	—
596	#3082	—	43	1	no	—
597	#3045	—	43	1	no	—
598	#3043	—	43	1	no	—
599	#3013	—	43	1	no	—
600	#3010	—	43	1	no	—
601	C₄×#137	—	43	1	no	—
602	C₄×AGL(1,ℤ/8)	—	43	1	no	—
603	C₄×#135	D₄₃	1	1	yes	characteristic, complemented
604	C₂×C₄×SD₁₆	—	43	1	no	—
605	#2922	—	43	1	no	—
606	C₂×C₄₃	—	2	2	no	—
607	C₂×C₄₃	—	4	2	no	—
608	C₂×C₄₃	—	8	1	no	—
609	C₂×C₄₃	C₂×#525	1	1	yes	characteristic
610	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
611	C₂×C₄₃	#3584	1	1	yes	characteristic
612	D₄₃	—	4	2	no	—
613	D₄₃	—	8	2	no	—
614	C₂×2₋¹⁺⁴	—	43	1	no	—
615	C₂×#137	—	43	1	no	—
616	C₂×AGL(1,ℤ/8)	—	43	1	no	—
617	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
618	C₂²×SD₁₆	—	43	1	no	—
619	#544	—	43	1	no	—
620	#542	—	43	2	no	—
621	#542	—	86	1	no	—
622	#540	—	43	2	no	—
623	#540	—	86	1	no	—
624	#538	—	86	2	no	—
625	#537	—	43	1	no	—
626	#535	—	43	1	no	—
627	#535	—	43	1	no	—
628	#532	—	43	2	no	—
629	#532	—	86	1	no	—
630	#529	—	43	2	no	—
631	#529	—	86	1	no	—
632	#525	—	86	2	no	—
633	#520	—	43	1	no	—
634	#520	—	43	1	no	—
635	#520	—	43	2	no	—
636	#520	—	86	1	no	—
637	#520	—	86	2	no	—
638	#519	—	43	2	no	—
639	#519	—	43	1	no	—
640	#519	—	86	1	no	—
641	C₄×#41	—	43	1	no	—
642	C₄×#41	—	43	2	no	—
643	C₄×#41	—	86	1	no	—
644	C₄×#41	—	86	2	no	—
645	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
646	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
647	C₂×C₄×Q₈	—	43	2	no	—
648	C₂×C₄×Q₈	—	43	1	no	—
649	C₂×C₄×Q₈	—	86	1	no	—
650	C₂×C₄×D₄	—	43	1	no	—
651	#485	—	43	2	no	—
652	#483	—	43	2	no	—
653	#482	—	43	2	no	—
654	#482	—	43	2	no	—
655	#482	—	43	2	no	—
656	#481	—	43	2	no	—
657	#481	—	43	2	no	—
658	#480	—	43	2	no	—
659	#479	—	43	2	no	—
660	#479	—	43	2	no	—
661	#479	—	43	2	no	—
662	#478	—	43	2	no	—
663	#477	—	43	2	no	—
664	#476	—	43	2	no	—
665	#475	—	43	2	no	—
666	#475	—	43	2	no	—
667	#464	—	43	2	no	—
668	#464	—	43	2	no	—
669	#464	—	43	2	no	—
670	#463	—	43	2	no	—
671	#460	—	43	2	no	—
672	#460	—	43	2	no	—
673	#460	—	43	2	no	—
674	#459	—	43	2	no	—
675	#452	—	43	2	no	—
676	#451	—	43	2	no	—
677	#449	—	43	2	no	—
678	#449	—	43	2	no	—
679	#449	—	43	2	no	—
680	#448	—	43	2	no	—
681	#448	—	43	2	no	—
682	#448	—	43	2	no	—
683	#442	—	43	2	no	—
684	#441	—	43	2	no	—
685	#440	—	43	2	no	—
686	#440	—	43	2	no	—
687	C₄×Q₁₆	—	43	2	no	—
688	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
689	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	—	43	2	no	—
691	C₄×SD₁₆	—	43	2	no	—
692	C₄×SD₁₆	—	43	2	no	—
693	C₄×SD₁₆	—	43	2	no	—
694	C₄×SD₁₆	—	43	2	no	—
695	C₄×SD₁₆	—	43	2	no	—
696	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
697	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
700	C₄×D₈	—	43	2	no	—
701	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
702	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
703	#433	—	43	2	no	—
704	#433	—	43	2	no	—
705	#431	—	43	2	no	—
706	#431	—	43	2	no	—
707	#428	—	43	1	no	—
708	#428	—	43	1	no	—
709	#427	C₂×D₄₃	1	1	yes	characteristic
710	C₂×#106	—	43	1	no	—
711	#424	—	43	1	no	—
712	#424	—	43	1	no	—
713	#419	—	43	1	no	—
714	#418	—	43	1	no	—
715	#417	—	43	1	no	—
716	#417	—	43	1	no	—
717	#416	C₂×D₄₃	1	1	yes	characteristic
718	#416	C₂×D₄₃	1	1	yes	characteristic
719	C₂×#103	—	43	1	no	—
720	C₂×#102	—	43	1	no	—
721	#408	—	43	1	no	—
722	#408	—	43	1	no	—
723	C₄×M₁₆	—	43	1	no	—
724	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
725	C₄₃	#60572	1	1	yes	characteristic, complemented, Sylow
726	2₋¹⁺⁴	—	86	4	no	—
727	2₋¹⁺⁴	—	86	4	no	—
728	C₂×#41	—	43	1	no	—
729	C₂×#41	—	43	2	no	—
730	C₂×#41	—	86	2	no	—
731	C₂×#41	—	86	1	no	—
732	C₂×#41	—	86	2	no	—
733	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
734	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
735	C₂²×Q₈	—	43	2	no	—
736	C₂²×Q₈	—	43	1	no	—
737	C₂²×Q₈	—	86	1	no	—
738	C₂²×D₄	—	43	1	no	—
739	C₂³×C₄	—	86	1	no	—
740	#137	—	86	4	no	—
741	AGL(1,ℤ/8)	—	86	4	no	—
742	#135	—	2	4	no	—
743	C₂×Q₁₆	—	43	2	no	—
744	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
745	C₂×SD₁₆	—	43	2	no	—
746	C₂×SD₁₆	—	43	2	no	—
747	C₂×SD₁₆	—	43	2	no	—
748	C₂×SD₁₆	—	43	2	no	—
749	C₂×SD₁₆	—	86	4	no	—
750	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
751	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
752	C₂×D₈	—	43	2	no	—
753	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
754	C₂×M₁₆	—	43	1	no	—
755	C₂×M₁₆	—	43	1	no	—
756	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
757	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
758	C₄⋊Q₈	—	43	2	no	—
759	C₄⋊Q₈	—	86	1	no	—
760	#127	—	43	2	no	—
761	#127	—	86	1	no	—
762	#126	—	86	2	no	—
763	#126	—	86	2	no	—
764	#125	—	43	2	no	—
765	#125	—	86	1	no	—
766	#124	—	43	2	no	—
767	#124	—	86	2	no	—
768	#124	—	86	1	no	—
769	#124	—	86	2	no	—
770	#123	—	86	2	no	—
771	#123	—	86	2	no	—
772	#123	—	86	2	no	—
773	#123	—	86	2	no	—
774	C₂²⋊Q₈	—	43	2	no	—
775	C₂²⋊Q₈	—	86	2	no	—
776	C₂²⋊Q₈	—	86	2	no	—
777	C₂²⋊Q₈	—	86	1	no	—
778	#121	—	43	2	no	—
779	#121	—	43	2	no	—
780	#121	—	43	2	no	—
781	#121	—	86	2	no	—
782	#121	—	86	2	no	—
783	#121	—	86	2	no	—
784	#121	—	86	1	no	—
785	#121	—	86	1	no	—
786	#121	—	86	1	no	—
787	#121	—	86	2	no	—
788	#120	—	86	2	no	—
789	#120	—	86	2	no	—
790	C₄×Q₈	—	43	1	no	—
791	C₄×Q₈	—	43	1	no	—
792	C₄×Q₈	—	43	2	no	—
793	C₄×Q₈	—	43	2	no	—
794	C₄×Q₈	—	43	2	no	—
795	C₄×Q₈	—	43	2	no	—
796	C₄×Q₈	—	43	2	no	—
797	C₄×Q₈	—	86	2	no	—
798	C₄×Q₈	—	86	1	no	—
799	C₄×Q₈	—	86	2	no	—
800	C₄×Q₈	—	86	1	no	—
801	C₄×Q₈	—	86	1	no	—
802	C₄×Q₈	—	86	2	no	—
803	C₄×Q₈	—	86	2	no	—
804	C₄×Q₈	—	86	1	no	—
805	C₄×Q₈	—	86	1	no	—
806	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
807	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
808	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
809	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	43	2	no	—
815	C₄×D₄	—	43	2	no	—
816	C₄×D₄	—	43	2	no	—
817	C₄×D₄	—	43	1	no	—
818	C₄×D₄	—	43	1	no	—
819	C₄×D₄	—	43	2	no	—
820	C₄×D₄	—	43	2	no	—
821	C₄×D₄	—	86	2	no	—
822	C₄×D₄	—	86	1	no	—
823	C₄×D₄	—	86	2	no	—
824	C₄×D₄	—	86	2	no	—
825	C₄×D₄	—	86	2	no	—
826	C₄×D₄	—	86	2	no	—
827	C₄×D₄	—	86	2	no	—
828	C₄×D₄	—	86	2	no	—
829	C₄×D₄	—	86	2	no	—
830	C₄×D₄	—	86	1	no	—
831	C₄×D₄	—	86	1	no	—
832	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
833	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
834	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
835	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
836	#117	—	2	1	no	—
837	#117	—	2	1	no	—
838	#117	—	43	1	no	—
839	#117	—	43	2	no	—
840	#117	—	43	2	no	—
841	#117	—	86	2	no	—
842	#117	—	86	2	no	—
843	#117	—	86	2	no	—
844	#117	—	86	2	no	—
845	#117	—	86	2	no	—
846	#117	—	86	2	no	—
847	#117	—	86	1	no	—
848	#117	C₂²×D₄₃	1	1	yes	characteristic
849	#117	C₂²×D₄₃	1	1	yes	characteristic
850	C₂×C₄⋊C₄	—	43	1	no	—
851	C₂×C₄⋊C₄	—	43	1	no	—
852	C₂×C₄⋊C₄	—	43	2	no	—
853	C₂×C₄⋊C₄	—	86	2	no	—
854	C₂×C₄⋊C₄	—	86	2	no	—
855	C₂×C₄⋊C₄	—	86	1	no	—
856	C₂×C₄⋊C₄	—	86	1	no	—
857	C₂×C₂²⋊C₄	—	86	1	no	—
858	C₂×C₄²	—	2	1	no	—
859	C₂×C₄²	—	2	1	no	—
860	C₂×C₄²	—	43	2	no	—
861	C₂×C₄²	—	86	2	no	—
862	C₂×C₄²	—	86	2	no	—
863	C₂×C₄²	—	86	1	no	—
864	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
865	#107	—	43	2	no	—
866	#107	—	43	2	no	—
867	#107	C₂²×D₄₃	1	1	yes	characteristic
868	#107	C₂²×D₄₃	1	1	yes	characteristic
869	#106	—	43	2	no	—
870	#106	—	43	2	no	—
871	#106	—	43	2	no	—
872	#106	—	43	2	no	—
873	#106	C₂²×D₄₃	1	1	yes	characteristic
874	#106	C₂²×D₄₃	1	1	yes	characteristic
875	C₄⋊C₈	—	43	2	no	—
876	C₄⋊C₈	—	43	2	no	—
877	C₄⋊C₈	—	43	2	no	—
878	C₄⋊C₈	—	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	—	43	2	no	—
884	#103	—	43	2	no	—
885	#103	C₂²×D₄₃	1	1	yes	characteristic
886	#103	C₂²×D₄₃	1	1	yes	characteristic
887	#103	C₂²×D₄₃	1	1	yes	characteristic
888	#103	C₂²×D₄₃	1	1	yes	characteristic
889	#102	—	43	2	no	—
890	#102	—	43	2	no	—
891	#102	—	43	2	no	—
892	#102	—	43	2	no	—
893	#102	—	43	2	no	—
894	#102	—	43	2	no	—
895	#102	C₂²×D₄₃	1	1	yes	characteristic
896	#102	C₂²×D₄₃	1	1	yes	characteristic
897	#102	C₂²×D₄₃	1	1	yes	characteristic
898	#102	C₂²×D₄₃	1	1	yes	characteristic
899	C₂²⋊C₈	—	43	2	no	—
900	C₂²⋊C₈	—	43	2	no	—
901	C₂²⋊C₈	—	43	2	no	—
902	C₂²⋊C₈	—	43	2	no	—
903	#97	—	43	2	no	—
904	C₄×C₈	—	43	2	no	—
905	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
906	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
907	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
908	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
909	C₂⁴	—	86	1	no	—
910	#41	—	2	2	no	—
911	#41	—	2	2	no	—
912	#41	—	2	2	no	—
913	#41	—	86	8	no	—
914	#41	—	86	4	no	—
915	#41	—	86	16	no	—
916	#41	—	86	4	no	—
917	#41	—	86	2	no	—
918	#41	—	86	2	no	—
919	#41	—	344	4	no	—
920	#41	#10621898	1	4	yes	complemented
921	C₂×Q₈	—	43	1	no	—
922	C₂×Q₈	—	43	4	no	—
923	C₂×Q₈	—	43	2	no	—
924	C₂×Q₈	—	86	2	no	—
925	C₂×Q₈	—	86	2	no	—
926	C₂×Q₈	—	86	8	no	—
927	C₂×Q₈	—	86	4	no	—
928	C₂×Q₈	—	86	4	no	—
929	C₂×Q₈	—	86	1	no	—
930	C₂×Q₈	—	86	2	no	—
931	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
932	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	43	2	no	—
936	C₂×D₄	—	43	1	no	—
937	C₂×D₄	—	43	2	no	—
938	C₂×D₄	—	86	2	no	—
939	C₂×D₄	—	86	2	no	—
940	C₂×D₄	—	86	2	no	—
941	C₂×D₄	—	86	2	no	—
942	C₂×D₄	—	86	2	no	—
943	C₂×D₄	—	86	2	no	—
944	C₂×D₄	—	86	1	no	—
945	C₂×D₄	—	86	2	no	—
946	C₂×D₄	—	86	2	no	—
947	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
948	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	43	2	no	—
956	C₂²×C₄	—	43	2	no	—
957	C₂²×C₄	—	43	2	no	—
958	C₂²×C₄	—	86	2	no	—
959	C₂²×C₄	—	86	2	no	—
960	C₂²×C₄	—	86	2	no	—
961	C₂²×C₄	—	86	2	no	—
962	C₂²×C₄	—	86	1	no	—
963	C₂²×C₄	—	86	1	no	—
964	C₂²×C₄	—	86	1	no	—
965	C₂²×C₄	—	86	2	no	—
966	C₂²×C₄	—	86	2	no	—
967	C₂²×C₄	—	344	2	no	—
968	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
969	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
970	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
971	Q₁₆	—	2	2	no	—
972	Q₁₆	—	86	4	no	—
973	SD₁₆	—	2	2	no	—
974	SD₁₆	—	2	2	no	—
975	SD₁₆	—	86	4	no	—
976	SD₁₆	—	86	4	no	—
977	SD₁₆	—	86	4	no	—
978	SD₁₆	—	86	4	no	—
979	D₈	—	2	2	no	—
980	D₈	—	86	4	no	—
981	M₁₆	—	86	2	no	—
982	M₁₆	—	86	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	—	2	2	no	—
985	C₂×C₈	—	43	2	no	—
986	C₂×C₈	—	43	2	no	—
987	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
988	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
989	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
990	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	43	1	no	—
996	C₄⋊C₄	—	43	2	no	—
997	C₄⋊C₄	—	43	1	no	—
998	C₄⋊C₄	—	43	2	no	—
999	C₄⋊C₄	—	43	2	no	—
1000	C₄⋊C₄	—	43	2	no	—
1001	C₄⋊C₄	—	86	2	no	—
1002	C₄⋊C₄	—	86	2	no	—
1003	C₄⋊C₄	—	86	2	no	—
1004	C₄⋊C₄	—	86	2	no	—
1005	C₄⋊C₄	—	86	2	no	—
1006	C₄⋊C₄	—	86	2	no	—
1007	C₄⋊C₄	—	86	2	no	—
1008	C₄⋊C₄	—	86	2	no	—
1009	C₄⋊C₄	—	86	1	no	—
1010	C₄⋊C₄	—	86	1	no	—
1011	C₄⋊C₄	—	86	2	no	—
1012	C₄⋊C₄	—	86	2	no	—
1013	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1014	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1015	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1016	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	43	2	no	—
1024	C₂²⋊C₄	—	43	2	no	—
1025	C₂²⋊C₄	—	43	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	C₂²⋊C₄	—	86	2	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	43	2	no	—
1043	C₄²	—	43	2	no	—
1044	C₄²	—	43	2	no	—
1045	C₄²	—	86	2	no	—
1046	C₄²	—	86	2	no	—
1047	C₄²	—	86	2	no	—
1048	C₄²	—	86	2	no	—
1049	C₄²	—	86	2	no	—
1050	C₄²	—	86	2	no	—
1051	C₄²	D₄×D₄₃	1	1	yes	characteristic
1052	C₄²	D₄×D₄₃	1	1	yes	characteristic
1053	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1054	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	43	2	no	—
1058	C₂³	—	86	2	no	—
1059	C₂³	—	344	1	no	—
1060	C₂³	—	344	1	no	—
1061	C₂³	—	172	2	no	—
1062	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	43	4	no	—
1067	Q₈	—	86	8	no	—
1068	Q₈	—	86	2	no	—
1069	Q₈	—	86	4	no	—
1070	Q₈	—	86	2	no	—
1071	Q₈	—	344	2	no	—
1072	Q₈	C₂×#10621898	1	2	yes	—
1073	D₄	—	2	4	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	86	8	no	—
1079	D₄	—	86	4	no	—
1080	D₄	—	86	2	no	—
1081	D₄	—	86	2	no	—
1082	D₄	—	86	2	no	—
1083	D₄	—	344	2	no	—
1084	D₄	—	344	2	no	—
1085	D₄	—	344	2	no	—
1086	D₄	—	344	2	no	—
1087	D₄	—	344	2	no	—
1088	D₄	—	172	2	no	—
1089	D₄	C₂×#10621898	1	2	yes	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	4	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	1	no	—
1104	C₂×C₄	—	43	2	no	—
1105	C₂×C₄	—	43	2	no	—
1106	C₂×C₄	—	43	2	no	—
1107	C₂×C₄	—	86	8	no	—
1108	C₂×C₄	—	86	8	no	—
1109	C₂×C₄	—	86	4	no	—
1110	C₂×C₄	—	86	2	no	—
1111	C₂×C₄	—	86	4	no	—
1112	C₂×C₄	—	86	2	no	—
1113	C₂×C₄	—	86	2	no	—
1114	C₂×C₄	—	86	2	no	—
1115	C₂×C₄	—	86	2	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	—	344	1	no	—
1121	C₂×C₄	—	172	2	no	—
1122	C₂×C₄	—	172	4	no	—
1123	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1124	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1125	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1126	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1127	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1128	C₂×C₄	#41×D₄₃	1	2	yes	—
1129	C₂×C₄	C₂×#10621898	1	2	yes	—
1130	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	86	2	no	—
1136	C₈	—	86	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	86	2	no	—
1146	C₂²	—	86	2	no	—
1147	C₂²	—	86	2	no	—
1148	C₂²	—	344	4	no	—
1149	C₂²	—	172	2	no	—
1150	C₂²	—	172	2	no	—
1151	C₂²	—	172	2	no	—
1152	C₂²	#14583408	1	2	yes	—
1153	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	86	2	no	—
1164	C₄	—	86	2	no	—
1165	C₄	—	86	2	no	—
1166	C₄	—	86	4	no	—
1167	C₄	—	172	2	no	—
1168	C₄	—	172	2	no	—
1169	C₄	#14583408	1	2	yes	—
1170	C₄	#14583706	1	2	yes	—
1171	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1172	C₄	C₂²×#10621898	1	1	yes	characteristic
1173	C₂	—	2	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	8	1	no	—
1176	C₂	—	344	2	no	—
1177	C₂	—	172	2	no	—
1178	C₂	C₂×#14583408	1	1	yes	characteristic
1179	C₂	C₂×#14583706	1	1	yes	characteristic
1180	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₄×#135	D₄₃
hypocenter	C₄₃	#60572
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #19148011	C₂	semidirect
2. C₄×#13063372	C₂	semidirect
3. #19144883	C₂	semidirect
4. #19144868	C₂	semidirect
5. #19144830	C₂	semidirect
6. #19144790	C₂	semidirect
7. #19144679	C₂	semidirect
8. #19144651	C₂	semidirect
9. #19144624	C₂	semidirect
10. #19144617	C₂	semidirect
11. #19144582	C₂	semidirect
12. #19144556	C₂	semidirect
13. #19144455	C₂	semidirect
14. #19144440	C₂	semidirect
15. #19144132	C₂	semidirect
16. #19144119	C₂	semidirect
17. #19143906	C₂	semidirect
18. #19143884	C₂	semidirect
19. C₄×#13063355	C₂	semidirect
20. C₄×#13063350	C₂	semidirect
21. C₂×C₄×#10621873	C₂	semidirect
22. #19143237	C₂	semidirect
23. C₄×#135×C₄₃	C₂	semidirect
46. #14583378	C₂²	semidirect
49. #14583375	C₂²	semidirect
53. C₄×#10621900	C₂²	semidirect
56. C₄×Q₈×D₄₃	C₂²	semidirect
58. #14583238	C₂²	semidirect
59. #14583228	C₂²	semidirect
62. #14583222	C₂²	semidirect
64. #14583216	C₂²	semidirect
66. #14583209	C₂²	semidirect
67. #14583205	C₂²	semidirect
68. #14583204	C₂²	semidirect
69. #14583201	C₂²	semidirect
70. #14583193	C₂²	semidirect
71. #14583187	C₂²	semidirect
72. #14583183	C₂²	semidirect
73. #14583182	C₂²	semidirect
82. #14583058	C₂²	semidirect
83. #14583053	C₂²	semidirect
86. #14583041	C₂²	semidirect
89. #14583036	C₂²	semidirect
91. #14583004	C₂²	semidirect
92. #14582999	C₂²	semidirect
94. C₄×#10621885	C₂²	semidirect
100. C₄×#10621883	C₂²	semidirect
102. #14582958	C₂²	semidirect
103. #14582958	C₂²	semidirect
104. #14582950	C₂²	semidirect
105. #14582950	C₂²	semidirect
123. C₄×Q₁₆×C₄₃	C₂²	semidirect
124. C₄×Q₁₆×C₄₃	C₂²	semidirect
125. C₄×SD₁₆×C₄₃	C₂²	semidirect
126. C₄×SD₁₆×C₄₃	C₂²	semidirect
127. C₄×SD₁₆×C₄₃	C₂²	semidirect
128. C₄×SD₁₆×C₄₃	C₂²	semidirect
129. C₄×D₈×C₄₃	C₂²	semidirect
130. C₄×D₈×C₄₃	C₂²	semidirect
322. #41×C₄₃	#41	semidirect
378. C₂×Dic₈₆	#41	semidirect
603. C₄×#135	D₄₃	semidirect
688. C₄×Q₁₆	C₂×D₄₃	semidirect
689. C₄×Q₁₆	C₂×D₄₃	semidirect
696. C₄×SD₁₆	C₂×D₄₃	semidirect
697. C₄×SD₁₆	C₂×D₄₃	semidirect
698. C₄×SD₁₆	C₂×D₄₃	semidirect
699. C₄×SD₁₆	C₂×D₄₃	semidirect
701. C₄×D₈	C₂×D₄₃	semidirect
702. C₄×D₈	C₂×D₄₃	semidirect
725. C₄₃	#60572	semidirect
920. #41	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148011	2
C₄×#13063372	2
#19144883	2
#19144868	2
#19144830	2
#19144790	2
#19144679	2
#19144651	2
#19144624	2
#19144617	2
#19144582	2
#19144556	2
#19144455	2
#19144440	2
#19144132	2
#19144119	2
#19143906	2
#19143884	2
C₄×#13063355	2
C₄×#13063350	2
C₂×C₄×#10621873	2
#19143237	2
C₄×#135×C₄₃	2
#60572	43