Finite Group Databasebeta

← #19146636

Subgroups — #19146636

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583622C211yesmaximal, characteristic, complemented
2#14583544C211yesmaximal, characteristic
3#14583259C211yesmaximal, characteristic, complemented
4#14583242C211yesmaximal, characteristic, complemented
5#14583226C211yesmaximal, characteristic, complemented
6#14583189C211yesmaximal, characteristic, complemented
7#14583156C211yesmaximal, characteristic, complemented
8#14583131C211yesmaximal, characteristic, complemented
9#14583121C211yesmaximal, characteristic, complemented
10#14583058C211yesmaximal, characteristic, complemented
11#14583048C211yesmaximal, characteristic, complemented
12#14582972C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C43×#440C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621885C2211yescharacteristic, complemented
19C2×#10621884C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic, complemented
22#13063325C2211yescharacteristic, complemented
23#13063320—21no—
24#13063320—21no—
25#13063313—21no—
26#13063313C2211yescharacteristic
27#13063309—21no—
28#13063305C2211yescharacteristic
29#13063301C2211yescharacteristic
30#13063301C2211yescharacteristic, complemented
31#13063300C2211yescharacteristic
32#13063299—21no—
33#13063295—21no—
34C4×Dic86—21no—
35C4×D172C2211yescharacteristic
36#13063283C2211yescharacteristic
37#13063283C2211yescharacteristic, complemented
38C2×(C2×D43)⋊C4—21no—
39#13063256C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic, complemented
54C4×D4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C22×Dic43—21no—
66#10621900—22no—
67#10621900—41no—
68D4×D43—22no—
69D4×D43—41no—
70C2×D172—21no—
71C2×D172D411yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43C2311yescharacteristic
74C2×C4×D43C2311yescharacteristic
75C2×Dic86—21no—
76C2×Dic86C2311yescharacteristic
77SD16×C43—22no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C42×C43—21no—
85C42×C43C2311yescharacteristic
86#10621885—41no—
87#10621884—41no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4D411yescharacteristic
97(C2×D43)⋊C4D411yescharacteristic
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43D411yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109#10621872—41no—
110C8×D43—41no—
111C23×C43—21no—
112C22×D43—21no—
113C22×D43—42no—
114C22×D43—42no—
115C22×D43—81no—
116C22×D43C2×D411yescharacteristic
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—21no—
121D4×C43#4112yes—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—81no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—42no—
130C22⋊D43—42no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—21no—
138D172—21no—
139D172—41no—
140D172—81no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—21no—
145Dic86—21no—
146Dic86—21no—
147Dic86—42no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—22no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—84no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3311—431nomaximal, Sylow
179C2×C43—42no—
180C2×C43#54611yescharacteristic
181C2×C43#57511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—41no—
184D43—41no—
185D43—81no—
186#556—431no—
187#546—431no—
188#489—431no—
189#485—431no—
190#482—431no—
191#476—431no—
192#470—431no—
193#465—431no—
194#464—431no—
195#452—431no—
196#450—431no—
197#440D4311yescharacteristic, complemented
198#435—431no—
199#418—431no—
200#416—431no—
201C43#331111yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C22×D4—431no—
204C2×Q16—431no—
205C2×SD16—431no—
206C2×SD16C2×D4311yescharacteristic
207C2×M16—431no—
208C22×C8—431no—
209C4⋊Q8—431no—
210#126—861no—
211#126—861no—
212#124—431no—
213#124—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8—861no—
222C4×Q8C2×D4311yescharacteristic, complemented
223C4×D4—431no—
224C4×D4C2×D4311yescharacteristic
225#117—431no—
226#117—431no—
227C2×C22⋊C4—861no—
228#107C2×D4311yescharacteristic, complemented
229#106—431no—
230#106—431no—
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103C2×D4311yescharacteristic, complemented
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102C2×D4311yescharacteristic
242C22⋊C8—431no—
243C22⋊C8—431no—
244#97C2×D4311yescharacteristic, complemented
245C24—861no—
246#41—862no—
247#41—1721no—
248C2×Q8—431no—
249C2×Q8—861no—
250C2×Q8C22×D4311yescharacteristic
251C2×D4—431no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4—862no—
256C2×D4—861no—
257C2×D4—1721no—
258C2×D4C22×D4311yescharacteristic
259C22×C4—21no—
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—861no—
263Q16—1721no—
264SD16—22no—
265SD16—1721no—
266M16—1721no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—1721no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4C22×D4311yescharacteristic
281C4⋊C4C22×D4311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—431no—
284C22⋊C4—431no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C42—21no—
294C42—861no—
295C42—861no—
296C42C22×D4311yescharacteristic
297C23—21no—
298C23—431no—
299C23—431no—
300C23—861no—
301C23—3441no—
302C23—1722no—
303C23—1722no—
304Q8—21no—
305Q8—21no—
306Q8—861no—
307Q8—861no—
308Q8—1722no—
309D4—21no—
310D4—861no—
311D4—861no—
312D4—3441no—
313D4—1721no—
314D4—1722no—
315D4—1722no—
316D4#1062189812yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—1722no—
331C2×C4D4×D4311yescharacteristic
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—861no—
342C22—861no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—3444no—
348C22—1721no—
349C22—1721no—
350C22—1721no—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—861no—
358C4—861no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C4C2×#1062189811yescharacteristic
363C4#1306337111yescharacteristic
364C2—42no—
365C2—3441no—
366C2—1721no—
367C2—1721no—
368C2#1458354511yescharacteristic
369C2#1458369811yescharacteristic
370C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#440C2
socleC22×C43C22×D4
hypercenter#440D43
hypocenterC43#3311
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14583622C2semidirect
3. #14583259C2semidirect
4. #14583242C2semidirect
5. #14583226C2semidirect
6. #14583189C2semidirect
7. #14583156C2semidirect
8. #14583131C2semidirect
9. #14583121C2semidirect
10. #14583058C2semidirect
11. #14583048C2semidirect
12. #14582972C2semidirect
13. #14582902C2semidirect
14. #14582892C2semidirect
15. C43×#440C2semidirect
18. C2×#10621885C22semidirect
21. C2×C8×D43C22semidirect
22. #13063325C22semidirect
30. #13063301C22semidirect
37. #13063283C22semidirect
39. #13063256C22semidirect
40. #13063256C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063250C22semidirect
43. #13063250C22semidirect
44. #13063248C22semidirect
51. (C2×D43)⋊C8C22semidirect
53. C4×Q8×C43C22semidirect
55. #107×C43C22semidirect
56. #103×C43C22semidirect
58. #97×C43C22semidirect
197. #440D43semidirect
201. C43#3311semidirect
222. C4×Q8C2×D43semidirect
228. #107C2×D43semidirect
235. #103C2×D43semidirect
244. #97C2×D43semidirect