Finite Group Databasebeta

← #19146141

Subgroups — #19146141

Order 5504.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063349C211yesmaximal, characteristic, complemented
2C2×#13063344C211yesmaximal, characteristic, complemented
3#14583569C211yesmaximal, characteristic, complemented
4#14583544C211yesmaximal, characteristic, complemented
5#14583286C211yesmaximal, characteristic, complemented
6#14583144C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583062C211yesmaximal, characteristic, complemented
10#14583045C211yesmaximal, characteristic, complemented
11#14583041C211yesmaximal, characteristic, complemented
12#14583031C211yesmaximal, characteristic, complemented
13#14582999C211yesmaximal, characteristic, complemented
14#14582969C211yesmaximal, characteristic, complemented
15C43×#459C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621900C2211yescharacteristic, complemented
19C2×D4×D43C2211yescharacteristic
20#13063349—24no—
21#13063344—24no—
22C2×Dic172C2211yescharacteristic, complemented
23C2×#10621873C2211yescharacteristic
24C2×#10621883C2211yescharacteristic
25C2×#10621883C2211yescharacteristic, complemented
26C2×#10621883C2211yescharacteristic, complemented
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C2×#10621872C2211yescharacteristic
30C2×C8×D43C2211yescharacteristic, complemented
31#13063321—21no—
32#13063313C2211yescharacteristic
33#13063309—21no—
34#13063305C2211yescharacteristic
35#13063300C2211yescharacteristic
36#13063299—21no—
37#13063297—21no—
38#13063297—21no—
39#13063296C2211yescharacteristic
40#13063296C2211yescharacteristic, complemented
41#13063295—21no—
42C4×Dic86C2211yescharacteristic, complemented
43C4×D172C2211yescharacteristic
44D4×Dic43—21no—
45C2×(C2×D43)⋊C4—21no—
46#13063258C2211yescharacteristic, complemented
47#13063250C2211yescharacteristic, complemented
48#13063248C2211yescharacteristic, complemented
49#13063247C2211yescharacteristic
50#13063246C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52(C2×D43)⋊C8C2211yescharacteristic, complemented
53#13063236C2211yescharacteristic, complemented
54C2×D8×C43C2211yescharacteristic
55C2×D8×C43C2211yescharacteristic
56#127×C43C2211yescharacteristic, complemented
57C4×D4×C43C2211yescharacteristic
58C4⋊C8×C43C2211yescharacteristic, complemented
59#102×C43C2211yescharacteristic, complemented
60#102×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77#10621900—22no—
78#10621900—22no—
79#10621900—22no—
80#10621900—41no—
81#10621900—41no—
82#10621900—41no—
83D4×D43—22no—
84D4×D43—41no—
85C2×D172—21no—
86C2×D172D411yescharacteristic
87C2×D172C2311yescharacteristic
88C2×C4×D43C2311yescharacteristic
89C2×C4×D43C2311yescharacteristic
90C2×Dic86C2311yescharacteristic
91C2×Dic86C2311yescharacteristic
92D8×C43—22no—
93D8×C43—22no—
94C2×C8×C43C2311yescharacteristic
95C2×C8×C43C2311yescharacteristic
96C4⋊C4×C43C2311yescharacteristic
97C22⋊C4×C43—21no—
98C42×C43C2311yescharacteristic
99C22⋊Dic43—21no—
100C22⋊Dic43—21no—
101#10621883—22no—
102#10621883—41no—
103#10621883D414yescomplemented
104#10621882—22no—
105#10621882—41no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4D411yescharacteristic
111(C2×D43)⋊C4D411yescharacteristic
112C4⋊Dic43—21no—
113C4⋊Dic43D411yescharacteristic
114C4⋊Dic43C2311yescharacteristic
115Dic43⋊C4—21no—
116C4×Dic43—21no—
117C2×C43⋊C8C2311yescharacteristic
118C2×C43⋊C8C2311yescharacteristic
119Dic172—22no—
120#10621873—22no—
121#10621872—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—81no—
130C22×D43C2×D411yescharacteristic
131C22×D43C2×D411yescharacteristic
132D4×C43—21no—
133D4×C43—21no—
134D4×C43—21no—
135D4×C43—21no—
136D4×C43—21no—
137D4×C43—42no—
138D4×C43—81no—
139D4×C43C2×D412yes—
140C2×C4×C43—21no—
141C2×C4×C43—81no—
142C2×C4×C43C2×D411yescharacteristic
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2411yescharacteristic
145C22⋊D43—42no—
146C22⋊D43—42no—
147C22⋊D43—42no—
148C22⋊D43—42no—
149C22⋊D43—81no—
150C22⋊D43—81no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43C2×D411yescharacteristic
158C2×Dic43C2×D411yescharacteristic
159D172—21no—
160D172—21no—
161D172—41no—
162D172—81no—
163C4×D43—21no—
164C4×D43—21no—
165C4×D43—21no—
166C4×D43—21no—
167Dic86—21no—
168Dic86—21no—
169Dic86—21no—
170Dic86C2×D412yes—
171C8×C43—21no—
172C8×C43—21no—
173C43⋊C8—21no—
174C43⋊C8C2×D412yes—
175C22×C43—22no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43C22×D411yescharacteristic
185C2×D43—21no—
186C2×D43—21no—
187C2×D43—21no—
188C2×D43—21no—
189C2×D43—21no—
190C2×D43—21no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—84no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—41no—
198C4×C43C22×D411yescharacteristic
199C4×C43H(5,𝔽2)11yescharacteristic
200Dic43—22no—
201Dic43—21no—
202Dic43—21no—
203Dic43—41no—
204Dic43—41no—
205#3268—431nomaximal, Sylow
206C2×C43—42no—
207C2×C43—81no—
208C2×C43—81no—
209C2×C43D4211yescharacteristic
210C2×C43#57511yescharacteristic
211C2×C43#57611yescharacteristic
212D43—41no—
213D43—41no—
214D43—81no—
215C2×AGL(1,ℤ/8)—431no—
216C2×#135—431no—
217#550—431no—
218#546—431no—
219#496—431no—
220#468—431no—
221#466—431no—
222#464—431no—
223#459D4311yescharacteristic, complemented
224#452—431no—
225#449—431no—
226#449—431no—
227#447—431no—
228#440—431no—
229#435—431no—
230C43#326811yescharacteristic, complemented, Sylow
231C2×#41—431no—
232C2×#41—431no—
233C2×#41—431no—
234C22×D4—431no—
235AGL(1,ℤ/8)—864no—
236#135—864no—
237C2×Q16—431no—
238C2×SD16—431no—
239C2×SD16—431no—
240C2×SD16—431no—
241C2×SD16—431no—
242C2×D8—431no—
243C2×D8—431no—
244C2×D8C2×D4311yescharacteristic
245C2×D8C2×D4311yescharacteristic
246C2×M16—431no—
247C22×C8—431no—
248#127—861no—
249#127C2×D4311yescharacteristic, complemented
250#124—431no—
251#123—861no—
252C22⋊Q8—431no—
253#121—431no—
254#121—431no—
255#121—431no—
256#121—861no—
257#121—861no—
258#121—861no—
259#120—861no—
260C4×Q8—431no—
261C4×D4—431no—
262C4×D4—861no—
263C4×D4C2×D4311yescharacteristic
264C2×C22⋊C4—861no—
265#107—431no—
266C4⋊C8C2×D4311yescharacteristic, complemented
267#103—431no—
268#103—431no—
269#102—431no—
270#102—431no—
271#102C2×D4311yescharacteristic, complemented
272#102C2×D4311yescharacteristic, complemented
273C22⋊C8—431no—
274C22⋊C8—431no—
275#97—431no—
276C24—861no—
277#41—862no—
278#41—862no—
279#41—862no—
280#41—1721no—
281#41—1721no—
282#41—1721no—
283C2×Q8—431no—
284C2×Q8—431no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—431no—
288C2×D4—431no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—862no—
292C2×D4—861no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—1721no—
298C2×D4C22×D4311yescharacteristic
299C2×D4C22×D4311yescharacteristic
300C2×D4C22×D4311yescharacteristic
301C22×C4—21no—
302C22×C4—431no—
303C22×C4—431no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307Q16—862no—
308SD16—434no—
309SD16—862no—
310SD16—862no—
311SD16—1721no—
312D8—22no—
313D8—22no—
314D8—862no—
315D8—1721no—
316M16—862no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—862no—
320C2×C8C22×D4311yescharacteristic
321C2×C8C22×D4311yescharacteristic
322C4⋊C4—431no—
323C4⋊C4—431no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4C22×D4311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—431no—
329C22⋊C4—431no—
330C22⋊C4—861no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C42—861no—
337C42C22×D4311yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—431no—
342C23—431no—
343C23—861no—
344C23—3441no—
345C23—1722no—
346C23—1722no—
347Q8—432no—
348Q8—861no—
349Q8—861no—
350Q8—861no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—861no—
359D4—861no—
360D4—3441no—
361D4—3441no—
362D4—3441no—
363D4—1721no—
364D4—1722no—
365D4—1722no—
366D4—1722no—
367D4—1722no—
368D4D4×D4312yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—431no—
372C2×C4—431no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4D4×D4311yescharacteristic
384C2×C4D4×D4311yescharacteristic
385C2×C4C23×D4311yescharacteristic
386C8—21no—
387C8—21no—
388C8—432no—
389C8—861no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—861no—
400C22—861no—
401C22—861no—
402C22—861no—
403C22—861no—
404C22—861no—
405C22—3444no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22C2×D4×D4311yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—861no—
414C4—861no—
415C4—862no—
416C4—1721no—
417C4—1721no—
418C4C2×D4×D4311yescharacteristic
419C4#1306337111yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—3441no—
424C2—1721no—
425C2—1721no—
426C2#1458353311yescharacteristic
427C2#1458369511yescharacteristic
428C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. C2×#13063344C2semidirect
3. #14583569C2semidirect
4. #14583544C2semidirect
5. #14583286C2semidirect
6. #14583144C2semidirect
7. #14583134C2semidirect
8. #14583122C2semidirect
9. #14583062C2semidirect
10. #14583045C2semidirect
11. #14583041C2semidirect
12. #14583031C2semidirect
13. #14582999C2semidirect
14. #14582969C2semidirect
15. C43×#459C2semidirect
18. C2×#10621900C22semidirect
22. C2×Dic172C22semidirect
25. C2×#10621883C22semidirect
26. C2×#10621883C22semidirect
30. C2×C8×D43C22semidirect
40. #13063296C22semidirect
42. C4×Dic86C22semidirect
46. #13063258C22semidirect
47. #13063250C22semidirect
48. #13063248C22semidirect
52. (C2×D43)⋊C8C22semidirect
53. #13063236C22semidirect
56. #127×C43C22semidirect
58. C4⋊C8×C43C22semidirect
59. #102×C43C22semidirect
60. #102×C43C22semidirect
103. #10621883D4semidirect
223. #459D43semidirect
230. C43#3268semidirect
249. #127C2×D43semidirect
266. C4⋊C8C2×D43semidirect
271. #102C2×D43semidirect
272. #102C2×D43semidirect