Finite Group Databasebeta

← C2×#19133917 #25077758

Subgroups — C2×#19133917 #25077758

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583643C211yesmaximal, characteristic
2C2×#14583267C211yesmaximal, characteristic, complemented
3C2×#14583261C211yesmaximal, characteristic, complemented
4#19133917C218yesmaximal, direct product factor
5C2×#14582640C211yesmaximal, characteristic, complemented
6C2×#14582639C211yesmaximal, characteristic, complemented
7C2×#14582638C211yesmaximal, characteristic, complemented
8C2×C43×#489C211yesmaximal, characteristic, complemented
9#14583643—22no—
10#14583643—22no—
11#14583643—22no—
12#14583643C2214yes—
13C2×#13063317C2211yescharacteristic
14C2×#13063313C2211yescharacteristic
15C2×#13063309—21no—
16C2×#13063307—21no—
17C2×#13063302—21no—
18C2×#13063301—21no—
19C2×#13063298—21no—
20C2×#13063297—21no—
21#14583267—22no—
22#14583267C2214yescomplemented
23#14583261—22no—
24#14583261C2214yescomplemented
25C2×#13063249—21no—
26C2×#13063249—21no—
27C2×#13063248—21no—
28C2×#13063245—21no—
29C2×#13063236C2211yescharacteristic
30C2×#13063236C2211yescharacteristic
31#14582640C2214yescomplemented
32#14582639C2214yescomplemented
33#14582638C2214yescomplemented
34C2×C4⋊Q8×C43C2211yescharacteristic
35C2×#124×C43C2211yescharacteristic
36C43×#489—22no—
37C43×#489C2214yescomplemented
38C2×#103×C43—21no—
39C2×#102×C43—21no—
40C2×#97×C43C2211yescharacteristic
41C22×Dic86D411yescharacteristic
42C22×D172D411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C22⋊D43—21no—
45C23×Dic43—21no—
46C22×C4×D43—21no—
47C22×C43⋊C8—21no—
48C22×C43⋊C8—21no—
49#13063317—21no—
50#13063317—21no—
51#13063317D412yes—
52#13063317C2312yes—
53#13063313—21no—
54#13063313—21no—
55#13063313D412yes—
56#13063313C2312yes—
57#13063309—24no—
58#13063309—24no—
59#13063307—24no—
60#13063307—24no—
61#13063302—24no—
62#13063302—24no—
63#13063301—24no—
64#13063301—24no—
65#13063298—24no—
66#13063298—24no—
67#13063297—24no—
68#13063297—24no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43D411yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79#13063249—24no—
80#13063249—24no—
81#13063248—24no—
82#13063245—24no—
83#13063236—21no—
84#13063236—21no—
85#13063236C2312yes—
86#13063236C2312yes—
87C22×Q8×C43—21no—
88C22×Q8×C43D411yescharacteristic
89C22×D4×C43D411yescharacteristic
90C22×C8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43—21no—
94C4⋊Q8×C43C2312yes—
95#124×C43—21no—
96#124×C43—21no—
97#124×C43D412yes—
98#124×C43C2312yes—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#103×C43—24no—
105#102×C43—24no—
106#97×C43—21no—
107#97×C43C2312yes—
108C24×C43—21no—
109C23×D43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—42no—
113C2×Q8×C43—44no—
114C2×Q8×C43—41no—
115C2×Q8×C43C2×D412yes—
116C2×D4×C43—21no—
117C2×D4×C43—42no—
118C2×D4×C43C2×D412yes—
119C22×C4×C43—21no—
120C22×C4×C43—41no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C2×C22⋊D43—24no—
125C2×C22⋊D43—24no—
126C2×C22⋊D43—82no—
127C2×C22⋊D43—82no—
128C22×Dic43—24no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43—82no—
133C2×D172—21no—
134C2×D172—42no—
135C2×D172C2×D412yes—
136C2×C4×D43—24no—
137C2×C4×D43—82no—
138C2×Dic86—21no—
139C2×Dic86—42no—
140C2×Dic86C2×D412yes—
141C2×C8×C43—22no—
142C2×C8×C43—42no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43—41no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—22no—
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43C2411yescharacteristic
155C22⋊Dic43—24no—
156(C2×D43)⋊C4—24no—
157(C2×D43)⋊C4—22no—
158(C2×D43)⋊C4—22no—
159(C2×D43)⋊C4—22no—
160(C2×D43)⋊C4—22no—
161C4⋊Dic43—24no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43C2×D412yes—
165C4⋊Dic43C2×D412yes—
166Dic43⋊C4—24no—
167Dic43⋊C4—22no—
168Dic43⋊C4—22no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—42no—
174C2×C43⋊C8—42no—
175C23×C43—22no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43#12011yescharacteristic
180C22×D43—22no—
181C22×D43—42no—
182C22×D43—42no—
183C22×D43—42no—
184Q8×C43—42no—
185Q8×C43—44no—
186Q8×C43—81no—
187Q8×C43—82no—
188D4×C43—42no—
189D4×C43—81no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—82no—
197C2×C4×C43#12011yescharacteristic
198C2×C4×C43#12011yescharacteristic
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C22⋊D43—84no—
204C22⋊D43—84no—
205C2×Dic43—22no—
206C2×Dic43—22no—
207C2×Dic43—22no—
208C2×Dic43—42no—
209C2×Dic43—42no—
210C2×Dic43—42no—
211C2×Dic43—84no—
212D172—42no—
213D172—81no—
214C4×D43—84no—
215Dic86—42no—
216Dic86—81no—
217C8×C43—42no—
218C43⋊C8—42no—
219C43⋊C8—42no—
220C2×#1662—431nomaximal, Sylow
221C22×C43—42no—
222C22×C43—42no—
223C22×C43—42no—
224C22×C43—84no—
225C22×C43#45412yes—
226C22×C43#45512yes—
227C22×C43#45512yes—
228C22×C43C2×#12011yescharacteristic
229C2×D43—42no—
230C2×D43—42no—
231C2×D43—42no—
232C2×D43—84no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—42no—
240C4×C43—82no—
241Dic43—42no—
242Dic43—42no—
243Dic43—42no—
244C2×#562—431no—
245C2×#491—431no—
246C2×#489—431no—
247C2×#489D4311yescharacteristic, complemented
248#1662—438no—
249C2×#330—431no—
250C2×#329—431no—
251C2×#329—431no—
252C2×C43—82no—
253C2×C43#166214yescomplemented
254C2×C43C2×#45511yescharacteristic
255C2×C43C2×#45511yescharacteristic
256C2×C43C2×#45411yescharacteristic
257D43—82no—
258#562—434no—
259#562—862no—
260#562—862no—
261#562—862no—
262C2×C4⋊Q8C2×D4311yescharacteristic
263C2×#125—431no—
264C2×#124—431no—
265C2×#124C2×D4311yescharacteristic
266C2×#123—861no—
267C2×#123—861no—
268C2×C22⋊Q8—861no—
269C2×C22⋊Q8—861no—
270C2×#121—861no—
271C2×#121—861no—
272#491—434no—
273#491—862no—
274#489—22no—
275#489—434no—
276#489—862no—
277#489C2×D4314yescomplemented
278C2×#103—21no—
279C2×#103—861no—
280C2×#103—861no—
281C2×#103—861no—
282C2×#102—21no—
283C2×#102—861no—
284C2×#97—431no—
285C2×#97—431no—
286C2×#97C2×D4311yescharacteristic
287#330—434no—
288#329—434no—
289#329—434no—
290C43C2×#166211yescharacteristic, complemented, Sylow
291C22×Q8—21no—
292C22×Q8—431no—
293C22×Q8C22⋊D4311yescharacteristic
294C22×D4—431no—
295C22×D4—861no—
296C22×D4—861no—
297C22×D4C22⋊D4311yescharacteristic
298C23×C4—861no—
299C23×C4—861no—
300C22×C8—21no—
301C22×C8—861no—
302C22×C8—861no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C22×D4312yes—
307#125—432no—
308#125—432no—
309#125—861no—
310#125—861no—
311#124—21no—
312#124—21no—
313#124—432no—
314#124—432no—
315#124—861no—
316#124—861no—
317#124C22⋊D4312yes—
318#124C22×D4312yes—
319#123—864no—
320#123—864no—
321#123—864no—
322#123—864no—
323C22⋊Q8—864no—
324C22⋊Q8—864no—
325C22⋊Q8—864no—
326C22⋊Q8—864no—
327#121—864no—
328#121—864no—
329#121—864no—
330#121—864no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—431no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4—861no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4—861no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—861no—
342C2×C22⋊C4—861no—
343C2×C22⋊C4—861no—
344C2×C22⋊C4—861no—
345C2×C42C22×D4311yescharacteristic
346#103—24no—
347#103—864no—
348#103—864no—
349#103—864no—
350#102—24no—
351#102—864no—
352#97—21no—
353#97—432no—
354#97—432no—
355#97—861no—
356#97—861no—
357#97C22×D4312yes—
358C24—21no—
359C24—861no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—42no—
363C2×Q8—44no—
364C2×Q8—41no—
365C2×Q8—432no—
366C2×Q8—861no—
367C2×Q8—1722no—
368C2×Q8C2×C22⋊D4312yes—
369C2×D4—21no—
370C2×D4—42no—
371C2×D4—432no—
372C2×D4—864no—
373C2×D4—864no—
374C2×D4—861no—
375C2×D4—3442no—
376C2×D4—3442no—
377C2×D4—1722no—
378C2×D4C2×C22⋊D4312yes—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—864no—
382C22×C4—864no—
383C22×C4—861no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—3442no—
387C22×C4—3442no—
388C22×C4D4×D4311yescharacteristic
389C22×C4D4×D4311yescharacteristic
390C22×C4C2×C22⋊D4311yescharacteristic
391C2×C8—22no—
392C2×C8—42no—
393C2×C8—862no—
394C2×C8—862no—
395C2×C8—1722no—
396C2×C8—1722no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—432no—
402C4⋊C4—432no—
403C4⋊C4—864no—
404C4⋊C4—864no—
405C4⋊C4—861no—
406C4⋊C4—861no—
407C4⋊C4—862no—
408C4⋊C4—862no—
409C4⋊C4—862no—
410C4⋊C4—862no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—864no—
416C22⋊C4—864no—
417C22⋊C4—862no—
418C22⋊C4—862no—
419C22⋊C4—862no—
420C22⋊C4—862no—
421C42D4×D4311yescharacteristic
422C42D4×D4311yescharacteristic
423C42C2×C22⋊D4311yescharacteristic
424C42C23×D4311yescharacteristic
425C23—22no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—862no—
430C23—1722no—
431C23—1722no—
432C23—1722no—
433C23#1306329311yescharacteristic
434Q8—42no—
435Q8—44no—
436Q8—81no—
437Q8—82no—
438Q8—3441no—
439Q8—1722no—
440D4—42no—
441D4—81no—
442D4—3441no—
443D4—3444no—
444D4—3444no—
445D4—1722no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—82no—
453C2×C4—862no—
454C2×C4—862no—
455C2×C4—862no—
456C2×C4—3444no—
457C2×C4—3444no—
458C2×C4—1722no—
459C2×C4—1722no—
460C2×C4—1722no—
461C2×C4#1306329311yescharacteristic
462C2×C4#1306329311yescharacteristic
463C2×C4#1306329311yescharacteristic
464C2×C4C2×D4×D4311yescharacteristic
465C2×C4C2×D4×D4311yescharacteristic
466C2×C4C22×C22⋊D4311yescharacteristic
467C8—42no—
468C8—1722no—
469C8—1722no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—84no—
474C22—3444no—
475C22—1722no—
476C22—1722no—
477C22—1722no—
478C22#1458307012yes—
479C22#1458307512yes—
480C22#1458307612yes—
481C22C2×#1306329311yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—82no—
490C4—1722no—
491C4—1722no—
492C4—1722no—
493C2—82no—
494C2—3442no—
495C2#1913391714yesdirect product factor
496C2C2×#1458307511yescharacteristic
497C2C2×#1458307611yescharacteristic
498C2C2×#1458307011yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#489C2
socleC23×C43#120
prime radicalC2×#14583643C2
hypercenterC2×#489D43
hypocenterC43C2×#1662
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
2. C2×#14583267C2semidirect
3. C2×#14583261C2semidirect
4. #19133917C2direct (N × H)
5. C2×#14582640C2semidirect
6. C2×#14582639C2semidirect
7. C2×#14582638C2semidirect
8. C2×C43×#489C2semidirect
22. #14583267C22semidirect
24. #14583261C22semidirect
31. #14582640C22semidirect
32. #14582639C22semidirect
33. #14582638C22semidirect
37. C43×#489C22semidirect
247. C2×#489D43semidirect
253. C2×C43#1662semidirect
277. #489C2×D43semidirect
290. C43C2×#1662semidirect
495. C2#19133917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836432
C2×#145832672
C2×#145832612
#191339172
C2×#145826402
C2×#145826392
C2×#145826382
C2×C43×#4892
C2×#166243