Finite Group Databasebeta

← #19146133

Subgroups — #19146133

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×#13063351C211yesmaximal, characteristic, complemented
2C2×#13063344C211yesmaximal, characteristic, complemented
3#14583567C211yesmaximal, characteristic, complemented
4#14583543C211yesmaximal, characteristic, complemented
5#14583287C211yesmaximal, characteristic, complemented
6#14583143C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583120C211yesmaximal, characteristic, complemented
9#14583092C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14583045C211yesmaximal, characteristic, complemented
12#14583041C211yesmaximal, characteristic, complemented
13#14582996C211yesmaximal, characteristic, complemented
14#14582973C211yesmaximal, characteristic, complemented
15C43×#447C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621900C2211yescharacteristic, complemented
19#13063351—24no—
20#13063344—24no—
21C2×Dic172C2211yescharacteristic, complemented
22C2×#10621873C2211yescharacteristic, complemented
23C2×#10621883C2211yescharacteristic
24C2×#10621883C2211yescharacteristic
25C2×#10621883C2211yescharacteristic, complemented
26C2×#10621882C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621877C2211yescharacteristic
29C2×C8×D43C2211yescharacteristic, complemented
30#13063321—21no—
31#13063321C2211yescharacteristic, complemented
32#13063312C2211yescharacteristic
33#13063306—21no—
34#13063304C2211yescharacteristic
35#13063300C2211yescharacteristic, complemented
36#13063298—21no—
37#13063297—21no—
38#13063297—21no—
39#13063296C2211yescharacteristic
40#13063294—21no—
41#13063290C2211yescharacteristic, complemented
42D4×Dic43C2211yescharacteristic
43C4×C22⋊D43C2211yescharacteristic
44(C22⋊D43)⋊C4—21no—
45C2×C22⋊Dic43—21no—
46#13063258C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063248C2211yescharacteristic, complemented
50#13063247C2211yescharacteristic, complemented
51#13063246C2211yescharacteristic, complemented
52(C2×D43)⋊C8C2211yescharacteristic, complemented
53#13063235C2211yescharacteristic, complemented
54C22×D4×C43C2211yescharacteristic
55C2×D8×C43C2211yescharacteristic
56C2×D8×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59#102×C43C2211yescharacteristic
60C22⋊C8×C43C2211yescharacteristic
61C24×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43—22no—
65C2×D4×C43—41no—
66C2×D4×C43C2311yescharacteristic
67C2×D4×C43C2311yescharacteristic
68C2×D4×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C2×C22⋊D43D411yescharacteristic
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80#10621900—22no—
81#10621900—22no—
82#10621900—41no—
83#10621900—41no—
84#10621898—22no—
85#10621898—41no—
86C2×D172—21no—
87C2×D172C2311yescharacteristic
88C2×C4×D43—21no—
89C2×C4×D43C2311yescharacteristic
90C2×Dic86C2311yescharacteristic
91C2×Dic86C2311yescharacteristic
92D8×C43—22no—
93D8×C43—41no—
94C2×C8×C43C2311yescharacteristic
95C2×C8×C43C2311yescharacteristic
96C4⋊C4×C43C2311yescharacteristic
97C22⋊C4×C43—21no—
98C22⋊Dic43—21no—
99C22⋊Dic43—21no—
100C22⋊Dic43—21no—
101C22⋊Dic43—21no—
102C22⋊Dic43—21no—
103C22⋊Dic43D411yescharacteristic
104#10621883—22no—
105#10621883—22no—
106#10621883D414yescomplemented
107#10621882—22no—
108#10621882—22no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4D411yescharacteristic
111C4⋊Dic43C2311yescharacteristic
112Dic43⋊C4—21no—
113Dic43⋊C4—21no—
114Dic43⋊C4D411yescharacteristic
115C4×Dic43—21no—
116C4×Dic43C2311yescharacteristic
117#10621877—22no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120Dic172—22no—
121#10621873—41no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—42no—
127C23×C43—42no—
128C23×C43—81no—
129C23×C43C2×D411yescharacteristic
130C22×D43—21no—
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—21no—
142C2×C4×C43—21no—
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2411yescharacteristic
145C22⋊D43—41no—
146C22⋊D43—42no—
147C22⋊D43—42no—
148C22⋊D43—42no—
149C22⋊D43—42no—
150C22⋊D43—81no—
151C22⋊D43—81no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—81no—
158C2×Dic43C2×D411yescharacteristic
159C2×Dic43C2×D411yescharacteristic
160C2×Dic43C2×D411yescharacteristic
161D172—21no—
162D172—21no—
163D172—81no—
164C4×D43—21no—
165C4×D43—21no—
166C4×D43—42no—
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—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—84no—
188C22×C43C22×D411yescharacteristic
189C2×D43—21no—
190C2×D43—21no—
191C2×D43—21no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C4×C43—21no—
196C4×C43—41no—
197C4×C43C22×D411yescharacteristic
198C4×C43H(5,𝔽2)11yescharacteristic
199Dic43—22no—
200Dic43—21no—
201Dic43—21no—
202Dic43—21no—
203Dic43—41no—
204Dic43—41no—
205#3268—431nomaximal, Sylow
206C2×C43—41no—
207C2×C43—42no—
208C2×C43—81no—
209C2×C43—81no—
210C2×C43D4211yescharacteristic
211C2×C43#57511yescharacteristic
212C2×C43#57611yescharacteristic
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#459—431no—
224#452—431no—
225#449—431no—
226#449—431no—
227#447D4311yescharacteristic, complemented
228#440—431no—
229#435—431no—
230C43#326811yescharacteristic, complemented, Sylow
231C2×#41—431no—
232C2×#41—431no—
233C2×#41—431no—
234C22×D4C2×D4311yescharacteristic
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—431no—
249#127—861no—
250#124—431no—
251#123—861no—
252C22⋊Q8—431no—
253#121—431no—
254#121—431no—
255#121—861no—
256#121—861no—
257#121—861no—
258#121C2×D4311yescharacteristic
259#120—861no—
260C4×Q8—431no—
261C4×D4—431no—
262C4×D4—431no—
263C4×D4—861no—
264C2×C22⋊C4—861no—
265#107—431no—
266C4⋊C8—431no—
267#103—431no—
268#103—431no—
269#102—431no—
270#102—431no—
271#102C2×D4311yescharacteristic
272#102C2×D4311yescharacteristic
273C22⋊C8—431no—
274C22⋊C8C2×D4311yescharacteristic
275#97—431no—
276C24—21no—
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—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—431no—
290C2×D4—431no—
291C2×D4—861no—
292C2×D4—861no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4C22×D4311yescharacteristic
299C2×D4C22×D4311yescharacteristic
300C2×D4C22×D4311yescharacteristic
301C22×C4—431no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4C22×D4311yescharacteristic
307Q16—862no—
308SD16—434no—
309SD16—862no—
310SD16—862no—
311SD16—1721no—
312D8—22no—
313D8—41no—
314D8—862no—
315D8—862no—
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—431no—
337C42—861no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—431no—
345C23—861no—
346C23D4×D4311yescharacteristic
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—21no—
371C2×C4—21no—
372C2×C4—431no—
373C2×C4—431no—
374C2×C4—431no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—3441no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4D4×D4311yescharacteristic
385C2×C4C23×D4311yescharacteristic
386C8—21no—
387C8—21no—
388C8—432no—
389C8—861no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—861no—
404C22—861no—
405C22—861no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22C2×D4×D4311yescharacteristic
410C4—21no—
411C4—41no—
412C4—861no—
413C4—861no—
414C4—861no—
415C4—862no—
416C4—1721no—
417C4—1721no—
418C4C2×D4×D4311yescharacteristic
419C4#1306337011yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—81no—
424C2—3441no—
425C2—1721no—
426C2#1458353111yescharacteristic
427C2#1458369511yescharacteristic
428C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#447C2
socleC22×C43C22×D4
hypercenter#447D43
hypocenterC43#3268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#13063351C2semidirect
2. C2×#13063344C2semidirect
3. #14583567C2semidirect
4. #14583543C2semidirect
5. #14583287C2semidirect
6. #14583143C2semidirect
7. #14583134C2semidirect
8. #14583120C2semidirect
9. #14583092C2semidirect
10. #14583063C2semidirect
11. #14583045C2semidirect
12. #14583041C2semidirect
13. #14582996C2semidirect
14. #14582973C2semidirect
15. C43×#447C2semidirect
18. C2×#10621900C22semidirect
21. C2×Dic172C22semidirect
22. C2×#10621873C22semidirect
25. C2×#10621883C22semidirect
29. C2×C8×D43C22semidirect
31. #13063321C22semidirect
35. #13063300C22semidirect
41. #13063290C22semidirect
46. #13063258C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063250C22semidirect
49. #13063248C22semidirect
50. #13063247C22semidirect
51. #13063246C22semidirect
52. (C2×D43)⋊C8C22semidirect
53. #13063235C22semidirect
106. #10621883D4semidirect
227. #447D43semidirect
230. C43#3268semidirect