Finite Group Databasebeta

← C2×#19133892 #25077736

Subgroups — C2×#19133892 #25077736

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583653C211yesmaximal, characteristic, complemented
2C2×#14583286C211yesmaximal, characteristic
3C2×#14583263C211yesmaximal, characteristic, complemented
4#19133892C218yesmaximal, direct product factor
5C2×#14582641C211yesmaximal, characteristic, complemented
6C2×#14582640C211yesmaximal, characteristic, complemented
7C2×#14582638C211yesmaximal, characteristic, complemented
8C2×C43×#490C211yesmaximal, characteristic, complemented
9C22×#10621883—21no—
10C22×#10621882—21no—
11#14583653—22no—
12#14583653—22no—
13#14583653—22no—
14#14583653C2214yescomplemented
15C2×#13063324—21no—
16C2×#13063320—21no—
17C2×#13063320—21no—
18C2×#13063317C2211yescharacteristic
19C2×#13063313C2211yescharacteristic
20C2×#13063310—21no—
21C2×#13063305—21no—
22C2×#13063303—21no—
23#14583286—22no—
24#14583286C2214yes—
25#14583263—22no—
26#14583263C2214yescomplemented
27C2×#13063246—21no—
28C2×#13063246—21no—
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31#14582641C2214yescomplemented
32#14582640C2214yescomplemented
33#14582638C2214yescomplemented
34C2×#127×C43C2211yescharacteristic
35C2×#125×C43C2211yescharacteristic
36C43×#490—22no—
37C43×#490C2214yescomplemented
38C2×#102×C43—21no—
39C2×#102×C43—21no—
40C2×#97×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D411yescharacteristic
43C22×D172D411yescharacteristic
44C22×C4×D43—21no—
45C2×#10621883—24no—
46C2×#10621883—44no—
47C2×#10621882—24no—
48C2×#10621882—44no—
49C22×C43⋊C8—21no—
50C22×C43⋊C8—21no—
51#13063324—24no—
52#13063324—24no—
53#13063320—24no—
54#13063320—24no—
55#13063320—24no—
56#13063320—24no—
57#13063317—21no—
58#13063317—21no—
59#13063317D412yes—
60#13063317C2312yes—
61#13063313—21no—
62#13063313—21no—
63#13063313D412yes—
64#13063313C2312yes—
65#13063310—24no—
66#13063310—24no—
67#13063305—24no—
68#13063305—24no—
69#13063303—24no—
70#13063303—24no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43D411yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83#13063246—24no—
84#13063246—24no—
85#13063236—21no—
86#13063236—21no—
87#13063236C2312yes—
88#13063236C2312yes—
89C22×D4×C43—21no—
90C22×D4×C43—21no—
91C22×D4×C43—21no—
92C22×C8×C43—21no—
93#127×C43—21no—
94#127×C43—21no—
95#127×C43—21no—
96#127×C43C2312yes—
97#125×C43—21no—
98#125×C43—21no—
99#125×C43D412yes—
100#125×C43C2312yes—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C42×C43C2311yescharacteristic
106#102×C43—24no—
107#102×C43—24no—
108#97×C43—21no—
109#97×C43C2312yes—
110C24×C43—41no—
111C23×D43—21no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—41no—
116C2×D4×C43—41no—
117C2×D4×C43—41no—
118C2×D4×C43—44no—
119C2×D4×C43—44no—
120C2×D4×C43—42no—
121C2×D4×C43—42no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C2×D172—21no—
131C2×D172—42no—
132C2×D172C2×D412yes—
133C2×C4×D43—24no—
134C2×C4×D43—82no—
135C2×Dic86—24no—
136C2×Dic86—21no—
137C2×Dic86—42no—
138C2×Dic86—82no—
139C2×Dic86C2×D412yes—
140C2×C8×C43—22no—
141C2×C8×C43—42no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43C2×D412yes—
149C4⋊C4×C43C2×D412yes—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2411yescharacteristic
154#10621883—48no—
155#10621882—48no—
156(C2×D43)⋊C4—24no—
157(C2×D43)⋊C4—24no—
158(C2×D43)⋊C4—24no—
159(C2×D43)⋊C4—22no—
160(C2×D43)⋊C4—22no—
161(C2×D43)⋊C4—22no—
162(C2×D43)⋊C4—22no—
163C4⋊Dic43—24no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43C2×D412yes—
167C4⋊Dic43C2×D412yes—
168Dic43⋊C4—24no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
171Dic43⋊C4—22no—
172Dic43⋊C4—22no—
173C4×Dic43—24no—
174C2×C43⋊C8—24no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—42no—
178C23×C43—42no—
179C23×C43—82no—
180C23×C43—82no—
181C23×C43—82no—
182C23×C43#12011yescharacteristic
183C22×D43—22no—
184C22×D43—42no—
185C22×D43—42no—
186C22×D43—42no—
187D4×C43—42no—
188D4×C43—42no—
189D4×C43—44no—
190D4×C43—44no—
191D4×C43—82no—
192D4×C43—82no—
193D4×C43—82no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43#12011yescharacteristic
202C2×C4×C43#12011yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C2×Dic43—22no—
208C2×Dic43—22no—
209C2×Dic43—22no—
210C2×Dic43—42no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213D172—42no—
214D172—81no—
215C4×D43—84no—
216Dic86—42no—
217Dic86—81no—
218Dic86—84no—
219C8×C43—42no—
220C43⋊C8—24no—
221C43⋊C8—42no—
222C2×#1657—431nomaximal, Sylow
223C22×C43—82no—
224C22×C43—82no—
225C22×C43—82no—
226C22×C43—164no—
227C22×C43#45312yes—
228C22×C43#45412yes—
229C22×C43#45412yes—
230C22×C43C2×#12011yescharacteristic
231C2×D43—42no—
232C2×D43—42no—
233C2×D43—42no—
234C2×D43—84no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—42no—
242C4×C43—42no—
243Dic43—42no—
244Dic43—42no—
245Dic43—42no—
246C2×#563—431no—
247C2×#496—431no—
248C2×#490—431no—
249C2×#490D4311yescharacteristic, complemented
250#1657—438no—
251C2×#330—431no—
252C2×#330—431no—
253C2×#329—431no—
254C2×C43—162no—
255C2×C43#165714yescomplemented
256C2×C43C2×#45311yescharacteristic
257C2×C43C2×#45411yescharacteristic
258C2×C43C2×#45411yescharacteristic
259D43—82no—
260C22×SD16—861no—
261C22×D8—861no—
262#563—434no—
263#563—862no—
264#563—862no—
265#563—862no—
266C2×C4⋊Q8—861no—
267C2×#127C2×D4311yescharacteristic
268C2×#126—861no—
269C2×#126—861no—
270C2×#125—431no—
271C2×#125C2×D4311yescharacteristic
272C2×#124—431no—
273C2×#123—861no—
274C2×C22⋊Q8—861no—
275C2×C22⋊Q8—861no—
276#496—434no—
277#496—862no—
278#490—22no—
279#490—434no—
280#490—862no—
281#490C2×D4314yescomplemented
282C2×#102—21no—
283C2×#102—21no—
284C2×#102—861no—
285C2×#102—861no—
286C2×#97—431no—
287C2×#97—431no—
288C2×#97C2×D4311yescharacteristic
289#330—434no—
290#330—434no—
291#329—434no—
292C43C2×#165711yescharacteristic, complemented, Sylow
293C22×Q8—431no—
294C22×Q8—861no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—431no—
299C23×C4—861no—
300C2×SD16—864no—
301C2×SD16—1724no—
302C2×D8—864no—
303C2×D8—1724no—
304C22×C8—21no—
305C22×C8—861no—
306C22×C8—861no—
307C4⋊Q8—864no—
308C4⋊Q8—864no—
309#127—21no—
310#127—21no—
311#127—21no—
312#127C22×D4312yes—
313#126—864no—
314#126—864no—
315#126—864no—
316#126—864no—
317#125—21no—
318#125—21no—
319#125—432no—
320#125—432no—
321#125—861no—
322#125—861no—
323#125C22⋊D4312yes—
324#125C22×D4312yes—
325#124—432no—
326#124—432no—
327#124—861no—
328#124—861no—
329#123—864no—
330#123—864no—
331C22⋊Q8—864no—
332C22⋊Q8—864no—
333C22⋊Q8—864no—
334C22⋊Q8—864no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—431no—
338C2×C4⋊C4—431no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4C22⋊D4311yescharacteristic
344C2×C4⋊C4C22⋊D4311yescharacteristic
345C2×C22⋊C4—861no—
346C2×C22⋊C4—861no—
347C2×C22⋊C4—861no—
348C2×C22⋊C4—861no—
349C2×C22⋊C4—861no—
350C2×C42—861no—
351C2×C42C22×D4311yescharacteristic
352#102—24no—
353#102—24no—
354#102—864no—
355#102—864no—
356#97—21no—
357#97—432no—
358#97—432no—
359#97—861no—
360#97—861no—
361#97C22×D4312yes—
362C24—41no—
363C24—861no—
364C2×Q8—432no—
365C2×Q8—864no—
366C2×Q8—861no—
367C2×Q8—3442no—
368C2×Q8—1722no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—44no—
375C2×D4—44no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—432no—
380C2×D4—861no—
381C2×D4—1722no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—864no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—3442no—
389C22×C4D4×D4311yescharacteristic
390C22×C4D4×D4311yescharacteristic
391C22×C4C2×C22⋊D4311yescharacteristic
392SD16—1728no—
393D8—1728no—
394C2×C8—22no—
395C2×C8—42no—
396C2×C8—864no—
397C2×C8—862no—
398C2×C8—862no—
399C2×C8—1722no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—432no—
407C4⋊C4—432no—
408C4⋊C4—864no—
409C4⋊C4—864no—
410C4⋊C4—861no—
411C4⋊C4—861no—
412C4⋊C4—862no—
413C4⋊C4—862no—
414C4⋊C4—862no—
415C4⋊C4—862no—
416C4⋊C4C2×C22⋊D4312yes—
417C4⋊C4C2×C22⋊D4312yes—
418C22⋊C4—864no—
419C22⋊C4—864no—
420C22⋊C4—864no—
421C22⋊C4—862no—
422C22⋊C4—862no—
423C22⋊C4—862no—
424C22⋊C4—862no—
425C42—864no—
426C42D4×D4311yescharacteristic
427C42D4×D4311yescharacteristic
428C42C2×C22⋊D4311yescharacteristic
429C42C23×D4311yescharacteristic
430C23—42no—
431C23—82no—
432C23—82no—
433C23—82no—
434C23—862no—
435C23—1722no—
436C23—1722no—
437C23—1722no—
438C23#1306329311yescharacteristic
439Q8—3441no—
440Q8—3444no—
441Q8—1722no—
442D4—42no—
443D4—42no—
444D4—44no—
445D4—44no—
446D4—82no—
447D4—82no—
448D4—82no—
449D4—3441no—
450D4—1722no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—862no—
459C2×C4—862no—
460C2×C4—862no—
461C2×C4—3444no—
462C2×C4—1722no—
463C2×C4—1722no—
464C2×C4—1722no—
465C2×C4#1306329311yescharacteristic
466C2×C4#1306329311yescharacteristic
467C2×C4#1306329311yescharacteristic
468C2×C4C2×D4×D4311yescharacteristic
469C2×C4C2×D4×D4311yescharacteristic
470C2×C4C22×C22⋊D4311yescharacteristic
471C8—42no—
472C8—864no—
473C8—1722no—
474C22—82no—
475C22—82no—
476C22—82no—
477C22—164no—
478C22—3444no—
479C22—1722no—
480C22—1722no—
481C22—1722no—
482C22#1458306512yes—
483C22#1458307012yes—
484C22#1458307112yes—
485C22C2×#1306329311yescharacteristic
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—42no—
494C4—1722no—
495C4—1722no—
496C4—1722no—
497C2—162no—
498C2—3442no—
499C2#1913389214yesdirect product factor
500C2C2×#1458306511yescharacteristic
501C2C2×#1458307011yescharacteristic
502C2C2×#1458307111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#490C2
socleC23×C43#120
prime radicalC2×#14583286C2
hypercenterC2×#490D43
hypocenterC43C2×#1657
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#14583653C2semidirect
3. C2×#14583263C2semidirect
4. #19133892C2direct (N × H)
5. C2×#14582641C2semidirect
6. C2×#14582640C2semidirect
7. C2×#14582638C2semidirect
8. C2×C43×#490C2semidirect
14. #14583653C22semidirect
26. #14583263C22semidirect
31. #14582641C22semidirect
32. #14582640C22semidirect
33. #14582638C22semidirect
37. C43×#490C22semidirect
249. C2×#490D43semidirect
255. C2×C43#1657semidirect
281. #490C2×D43semidirect
292. C43C2×#1657semidirect
499. C2#19133892direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836532
C2×#145832862
C2×#145832632
#191338922
C2×#145826412
C2×#145826402
C2×#145826382
C2×C43×#4902
C2×#165743