Finite Group Databasebeta

← C2×#19133556 #25068692

Subgroups — C2×#19133556 #25068692

Order 11008.

1232 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583496C211yesmaximal, characteristic
2C2×#14583055C211yesmaximal, characteristic, complemented
3C2×#14583038C211yesmaximal, characteristic
4#19133556C218yesmaximal, direct product factor
5C2×#14582635C211yesmaximal, characteristic, complemented
6C2×#14582632C211yesmaximal, characteristic
7C2×#14582625C211yesmaximal, characteristic, complemented
8C2×C43×#395C211yesmaximal, characteristic, complemented
9C22×#10621885—21no—
10C22×#10621884—21no—
11#14583496—22no—
12#14583496—22no—
13#14583496—22no—
14#14583496C2214yes—
15C2×#13063320—21no—
16C2×#13063315—21no—
17C2×#13063310—21no—
18C2×#13063308—21no—
19C2×#13063304C2211yescharacteristic
20C2×#13063303—21no—
21C2×#13063299C2211yescharacteristic
22C2×C4×C22⋊D43—21no—
23#14583055—22no—
24#14583055C2214yescomplemented
25#14583038—22no—
26#14583038C2214yes—
27C2×#13063249—21no—
28C2×#13063249—21no—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582635C2214yescomplemented
32#14582632C2214yes—
33#14582625C2214yescomplemented
34C23×Q8×C43C2211yescharacteristic
35C22×C4⋊C4×C43—21no—
36C22×C4⋊C4×C43C2211yescharacteristic
37C43×#395—22no—
38C43×#395C2214yescomplemented
39C2×#95×C43—21no—
40C2×#95×C43C2211yescharacteristic
41C22×Dic86D411yescharacteristic
42C22×D172D411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C4×D43—21no—
45C2×#10621885—24no—
46C2×#10621885—44no—
47C2×#10621884—24no—
48C2×#10621884—44no—
49C22×C43⋊C8—21no—
50C22×C43⋊C8—21no—
51#13063320—24no—
52#13063320—24no—
53#13063315—24no—
54#13063315—24no—
55#13063310—24no—
56#13063310—24no—
57#13063308—24no—
58#13063308—24no—
59#13063304—21no—
60#13063304—21no—
61#13063304D412yes—
62#13063304C2312yes—
63#13063303—24no—
64#13063303—24no—
65#13063299—21no—
66#13063299—21no—
67#13063299D412yes—
68#13063299C2312yes—
69C4×C22⋊D43—24no—
70C4×C22⋊D43—24no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43D411yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—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#13063249—24no—
84#13063249—24no—
85C22⋊(C43⋊C8)—21no—
86C22⋊(C43⋊C8)—21no—
87C22⋊(C43⋊C8)C2312yes—
88C22⋊(C43⋊C8)C2312yes—
89C22×Q8×C43—21no—
90C22×Q8×C43—21no—
91C22×Q8×C43—21no—
92C22×Q8×C43—21no—
93C22×Q8×C43—21no—
94C22×Q8×C43—44no—
95C22×Q8×C43C2312yes—
96C23×C4×C43—21no—
97C23×C4×C43—21no—
98C23×C4×C43D411yescharacteristic
99C23×C4×C43D411yescharacteristic
100C23×C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—24no—
106C2×C4⋊C4×C43—44no—
107C2×C4⋊C4×C43D412yes—
108C2×C4⋊C4×C43C2312yes—
109#95×C43—24no—
110#95×C43—21no—
111#95×C43C2312yes—
112C24×C43C2×D411yescharacteristic
113C23×D43—21no—
114C2×Q8×C43—24no—
115C2×Q8×C43—24no—
116C2×Q8×C43—22no—
117C2×Q8×C43—22no—
118C2×Q8×C43—44no—
119C2×Q8×C43—42no—
120C2×Q8×C43—42no—
121C2×Q8×C43—44no—
122C2×Q8×C43—44no—
123C2×Q8×C43—44no—
124C2×Q8×C43—41no—
125C2×Q8×C43—41no—
126C22×C4×C43—24no—
127C22×C4×C43—24no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43—41no—
141C22×C4×C43—41no—
142C22×C4×C43—42no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
153C2×C22⋊D43—42no—
154C2×C22⋊D43—42no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C2×D172—21no—
159C2×D172—42no—
160C2×D172C2×D412yes—
161C2×C4×D43—24no—
162C2×C4×D43—82no—
163C2×Dic86—21no—
164C2×Dic86—42no—
165C2×Dic86C2×D412yes—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—48no—
171C22⋊Dic43—22no—
172C22⋊Dic43—22no—
173#10621885—48no—
174#10621884—48no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—22no—
179(C2×D43)⋊C4—22no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43C2×D412yes—
183C4⋊Dic43C2×D412yes—
184Dic43⋊C4—24no—
185Dic43⋊C4—24no—
186Dic43⋊C4—24no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189C4×Dic43—24no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—42no—
193C2×C43⋊C8—42no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43#12011yescharacteristic
197C23×C43#12011yescharacteristic
198C23×C43#13512yes—
199C23×C43#13712yes—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205Q8×C43—24no—
206Q8×C43—24no—
207Q8×C43—42no—
208Q8×C43—42no—
209Q8×C43—44no—
210Q8×C43—44no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—48no—
225C2×C4×C43—44no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—44no—
233C2×C4×C43—42no—
234C2×C4×C43—81no—
235C2×C4×C43#12011yescharacteristic
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C22⋊D43—42no—
240C22⋊D43—42no—
241C22⋊D43—44no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248D172—42no—
249D172—81no—
250C4×D43—84no—
251Dic86—42no—
252Dic86—81no—
253C43⋊C8—42no—
254C43⋊C8—42no—
255C2×#1603—431nomaximal, Sylow
256C22×C43—24no—
257C22×C43—24no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43#45212yes—
263C22×C43#45212yes—
264C22×C43#45612yes—
265C22×C43B(4,𝔽2)12yes—
266C22×C43C2×#12011yescharacteristic
267C22×C43C2×#13511yescharacteristic
268C22×C43C2×#13711yescharacteristic
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—84no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—44no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43—44no—
281Dic43—42no—
282Dic43—42no—
283Dic43—42no—
284C2×#539—431no—
285C2×#451—431no—
286C2×#448—431no—
287C2×#395D4311yescharacteristic, complemented
288#1603—438no—
289C2×#328—431no—
290C2×#327—431no—
291C2×#324—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—22no—
295C2×C43#160314yescomplemented
296C2×C43C2×#45211yescharacteristic
297C2×C43C2×#45611yescharacteristic
298C2×C43C2×B(4,𝔽2)11yescharacteristic
299D43—82no—
300C23×Q8C2×D4311yescharacteristic
301C22×Q16—861no—
302C22×SD16—861no—
303#539—434no—
304#539—862no—
305#539—862no—
306#539—862no—
307C2×#126—861no—
308C2×#125—861no—
309C2×#123—861no—
310C2×#123—861no—
311C2×C22⋊Q8—431no—
312C2×C22⋊Q8—861no—
313C2×#121—431no—
314C2×C4×D4—861no—
315C22×C4⋊C4—21no—
316C22×C4⋊C4C2×D4311yescharacteristic
317#451—434no—
318#451—862no—
319#448—434no—
320#448—862no—
321C2×#103—861no—
322C2×#103—861no—
323C2×C22⋊C8—431no—
324C2×C22⋊C8—431no—
325#395—22no—
326#395C2×D4314yescomplemented
327C2×#95—21no—
328C2×#95C2×D4311yescharacteristic
329#328—434no—
330#327—434no—
331#324—434no—
332C43C2×#160311yescharacteristic, complemented, Sylow
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—21no—
338C22×Q8—44no—
339C22×Q8—431no—
340C22×Q8C22×D4312yes—
341C22×D4—431no—
342C22×D4—861no—
343C23×C4—21no—
344C23×C4—21no—
345C23×C4—861no—
346C23×C4C22⋊D4311yescharacteristic
347C23×C4C22⋊D4311yescharacteristic
348C23×C4C22×D4311yescharacteristic
349C2×Q16—864no—
350C2×Q16—1724no—
351C2×SD16—864no—
352C2×SD16—1724no—
353C22×C8—861no—
354C22×C8—861no—
355#126—864no—
356#126—864no—
357#125—864no—
358#125—864no—
359#123—864no—
360#123—864no—
361#123—864no—
362#123—864no—
363C22⋊Q8—432no—
364C22⋊Q8—432no—
365C22⋊Q8—864no—
366C22⋊Q8—864no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369#121—432no—
370#121—432no—
371#121—861no—
372#121—861no—
373C4×D4—864no—
374C4×D4—864no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4C22⋊D4312yes—
388C2×C4⋊C4C22×D4312yes—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C42—861no—
395#103—864no—
396#103—864no—
397C22⋊C8—432no—
398C22⋊C8—432no—
399C22⋊C8—861no—
400C22⋊C8—861no—
401#95—24no—
402#95—21no—
403#95C22×D4312yes—
404C24—861no—
405C24C2×C22⋊D4311yescharacteristic
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—44no—
411C2×Q8—42no—
412C2×Q8—42no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—432no—
419C2×Q8—861no—
420C2×Q8—1722no—
421C2×D4—432no—
422C2×D4—862no—
423C2×D4—862no—
424C2×D4—861no—
425C2×D4—1722no—
426C2×D4—1722no—
427C2×D4—1722no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—864no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—3442no—
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4C2×C22⋊D4312yes—
455C22×C4C2×C22⋊D4312yes—
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458Q16—1728no—
459SD16—1728no—
460C2×C8—862no—
461C2×C8—862no—
462C2×C8—1722no—
463C2×C8—1722no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—48no—
469C4⋊C4—432no—
470C4⋊C4—432no—
471C4⋊C4—864no—
472C4⋊C4—864no—
473C4⋊C4—864no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C22⋊C4—864no—
479C22⋊C4—864no—
480C22⋊C4—864no—
481C22⋊C4—862no—
482C22⋊C4—862no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C42—864no—
486C23—22no—
487C23—22no—
488C23—862no—
489C23—1722no—
490C23—1722no—
491C23—1722no—
492C23#1306329311yescharacteristic
493C23#1306329311yescharacteristic
494C23#1306334512yes—
495C23#1306335612yes—
496C23C22×C22⋊D4311yescharacteristic
497Q8—24no—
498Q8—24no—
499Q8—42no—
500Q8—42no—
501Q8—44no—
502Q8—44no—
503Q8—3441no—
504Q8—1722no—
505D4—3441no—
506D4—1722no—
507D4—1724no—
508D4—1722no—
509D4—1722no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—3444no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4#1306329311yescharacteristic
542C2×C4#1306329311yescharacteristic
543C2×C4C2×D4×D4311yescharacteristic
544C2×C4C2×D4×D4311yescharacteristic
545C8—1722no—
546C8—1722no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—24no—
552C22—24no—
553C22—3444no—
554C22—1722no—
555C22—1722no—
556C22—1722no—
557C22#1458305912yes—
558C22#1458305912yes—
559C22#1458308112yes—
560C22#1458308512yes—
561C22C2×#1306329311yescharacteristic
562C22C2×#1306334511yescharacteristic
563C22C2×#1306335611yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—44no—
569C4—44no—
570C4—42no—
571C4—42no—
572C4—1722no—
573C4—1722no—
574C4—1722no—
575C2—21no—
576C2—22no—
577C2—21no—
578C2—3442no—
579C2#1913355614yesdirect product factor
580C2C2×#1458305911yescharacteristic
581C2C2×#1458308111yescharacteristic
582C2C2×#1458308511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#395C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenterC2×#395D43
hypocenterC43C2×#1603
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
2. C2×#14583055C2semidirect
4. #19133556C2direct (N × H)
5. C2×#14582635C2semidirect
7. C2×#14582625C2semidirect
8. C2×C43×#395C2semidirect
24. #14583055C22semidirect
31. #14582635C22semidirect
33. #14582625C22semidirect
38. C43×#395C22semidirect
287. C2×#395D43semidirect
295. C2×C43#1603semidirect
326. #395C2×D43semidirect
332. C43C2×#1603semidirect
579. C2#19133556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834962
C2×#145830552
C2×#145830382
#191335562
C2×#145826352
C2×#145826322
C2×#145826252
C2×C43×#3952
C2×#160343