Finite Group Databasebeta

← #19146748

Subgroups — #19146748

Order 5504.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583615C211yesmaximal, characteristic, complemented
2#14583544C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic, complemented
4#14583242C211yesmaximal, characteristic, complemented
5#14583226C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583136C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583045C211yesmaximal, characteristic, complemented
10#14583034C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C43×#474C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621873C2211yescharacteristic, complemented
19C2×D344C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621872C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic, complemented
23#13063314—21no—
24#13063314—21no—
25#13063313C2211yescharacteristic
26#13063309—21no—
27#13063305C2211yescharacteristic
28#13063300—21no—
29#13063300C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic, complemented
32#13063299—21no—
33#13063295—21no—
34C4×D172C2211yescharacteristic
35C4×D172C2211yescharacteristic, complemented
36#13063283—21no—
37#13063283C2211yescharacteristic
38#13063283C2211yescharacteristic, complemented
39C2×(C2×D43)⋊C4—21no—
40#13063256C2211yescharacteristic, complemented
41#13063250C2211yescharacteristic, complemented
42#13063248C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic, complemented
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51#13063236C2211yescharacteristic, complemented
52C4⋊Q8×C43C2211yescharacteristic, complemented
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#107×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43—21no—
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×D172—21no—
72C2×D172—21no—
73C2×D172D411yescharacteristic
74C2×D172C2311yescharacteristic
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×C4×D43C2311yescharacteristic
79C2×Dic86C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C42×C43C2311yescharacteristic
88#10621882—22no—
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)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4D411yescharacteristic
99(C2×D43)⋊C4D411yescharacteristic
100C4⋊Dic43—21no—
101C4⋊Dic43D411yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103C4×Dic43—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107D344—41no—
108#10621873—41no—
109#10621872—41no—
110C8×D43—41no—
111C23×C43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—81no—
117C22×D43C2×D411yescharacteristic
118C22×D43C2×D411yescharacteristic
119Q8×C43—81no—
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—42no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136D172—21no—
137D172—21no—
138D172—21no—
139D172—21no—
140D172—41no—
141D172—81no—
142D172—81no—
143D172—81no—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—42no—
149Dic86—21no—
150Dic86—21no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—22no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43C22×D411yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—84no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43C2×#4111yescharacteristic
178C4×C43H(5,𝔽2)11yescharacteristic
179Dic43—21no—
180Dic43—21no—
181Dic43—41no—
182Dic43—41no—
183#3319—431nomaximal, Sylow
184C2×C43—42no—
185C2×C43#54611yescharacteristic
186C2×C43#57511yescharacteristic
187C2×C43#57611yescharacteristic
188D43—41no—
189D43—41no—
190D43—81no—
191D43—81no—
192#555—431no—
193#546—431no—
194#489—431no—
195#485—431no—
196#482—431no—
197#474D4311yescharacteristic, complemented
198#468—431no—
199#466—431no—
200#463—431no—
201#449—431no—
202#447—431no—
203#442—431no—
204#435—431no—
205#418—431no—
206#416—431no—
207C43#331911yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4—431no—
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8—431no—
213C2×M16—431no—
214C22×C8—431no—
215C4⋊Q8C2×D4311yescharacteristic, complemented
216#124—431no—
217#124—861no—
218#124—861no—
219#123—861no—
220C22⋊Q8—431no—
221#121—431no—
222#121—431no—
223#121—431no—
224#121—861no—
225#121—861no—
226#120—861no—
227C4×D4—431no—
228C4×D4—431no—
229C4×D4C2×D4311yescharacteristic
230#117—431no—
231#117—431no—
232#117—861no—
233C2×C22⋊C4—861no—
234#107C2×D4311yescharacteristic, complemented
235#107C2×D4311yescharacteristic, complemented
236#106—431no—
237C4⋊C8C2×D4311yescharacteristic, complemented
238#103—431no—
239#103—431no—
240#103—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102C2×D4311yescharacteristic
247#102C2×D4311yescharacteristic
248C22⋊C8—431no—
249C22⋊C8—431no—
250#97—431no—
251C24—861no—
252#41—862no—
253#41—1721no—
254C2×Q8—21no—
255C2×Q8—431no—
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—862no—
264C2×D4—861no—
265C2×D4—1721no—
266C2×D4C22×D4311yescharacteristic
267C22×C4—21no—
268C22×C4—431no—
269C22×C4—431no—
270C22×C4—861no—
271C22×C4—861no—
272SD16—1721no—
273D8—862no—
274D8—1721no—
275M16—1721no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—1721no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—861no—
285C4⋊C4C22×D4311yescharacteristic
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—431no—
290C22⋊C4—431no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C42—861no—
301C42—861no—
302C42C22×D4311yescharacteristic
303C23—21no—
304C23—431no—
305C23—431no—
306C23—861no—
307C23—861no—
308C23—3441no—
309C23—1722no—
310C23—1722no—
311Q8—81no—
312Q8—861no—
313Q8—861no—
314D4—21no—
315D4—861no—
316D4—861no—
317D4—861no—
318D4—861no—
319D4—3441no—
320D4—3441no—
321D4—3441no—
322D4—1721no—
323D4—1722no—
324D4—1722no—
325D4#1062190212yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—431no—
331C2×C4—431no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4D4×D4311yescharacteristic
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—861no—
351C22—861no—
352C22—861no—
353C22—861no—
354C22—861no—
355C22—861no—
356C22—3444no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22C2×D4×D4311yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—861no—
370C4—861no—
371C4—1721no—
372C4—1721no—
373C4C2×#1062190211yescharacteristic
374C4#1306337111yescharacteristic
375C2—42no—
376C2—3441no—
377C2—3441no—
378C2—1721no—
379C2—1721no—
380C2#1458354011yescharacteristic
381C2#1458369811yescharacteristic
382C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#474C2
socleC22×C43C22×D4
hypercenter#474D43
hypocenterC43#3319
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14583615C2semidirect
2. #14583544C2semidirect
3. #14583261C2semidirect
4. #14583242C2semidirect
5. #14583226C2semidirect
6. #14583146C2semidirect
7. #14583136C2semidirect
8. #14583115C2semidirect
9. #14583045C2semidirect
10. #14583034C2semidirect
11. #14583009C2semidirect
12. #14582969C2semidirect
13. #14582902C2semidirect
14. #14582892C2semidirect
15. C43×#474C2semidirect
18. C2×#10621873C22semidirect
22. C2×C8×D43C22semidirect
31. #13063300C22semidirect
35. C4×D172C22semidirect
38. #13063283C22semidirect
40. #13063256C22semidirect
41. #13063250C22semidirect
42. #13063248C22semidirect
43. #13063248C22semidirect
48. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. #13063236C22semidirect
52. C4⋊Q8×C43C22semidirect
54. #107×C43C22semidirect
55. #107×C43C22semidirect
56. C4⋊C8×C43C22semidirect
197. #474D43semidirect
207. C43#3319semidirect
215. C4⋊Q8C2×D43semidirect
234. #107C2×D43semidirect
235. #107C2×D43semidirect
237. C4⋊C8C2×D43semidirect