Finite Group Databasebeta

← C2×#19133559 #25068695

Subgroups — C2×#19133559 #25068695

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×#14583494C211yesmaximal, characteristic
2C2×#14583057C211yesmaximal, characteristic, complemented
3C2×#14583037C211yesmaximal, characteristic
4C2×#14582820C211yesmaximal, characteristic, complemented
5#19133559C218yesmaximal, direct product factor
6C2×#14582635C211yesmaximal, characteristic, complemented
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#327C211yesmaximal, characteristic
9C23×Dic86C2211yescharacteristic
10C22×Dic172—21no—
11C22×#10621883—21no—
12#14583494—22no—
13#14583494—22no—
14#14583494—22no—
15#14583494C2214yes—
16C2×#13063318—21no—
17C2×#13063315—21no—
18C2×#13063306—21no—
19C2×#13063306—21no—
20C2×#13063304C2211yescharacteristic
21C2×#13063302—21no—
22C2×D4×Dic43—21no—
23C22×C4⋊Dic43—21no—
24C22×Dic43⋊C4C2211yescharacteristic
25#14583057—22no—
26#14583057C2214yescomplemented
27#14583037—22no—
28#14583037C2214yes—
29C2×#13063250—21no—
30C2×#13063248—21no—
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32#14582820—22no—
33#14582820C2214yescomplemented
34C2×C43⋊#95—21no—
35#14582635C2214yescomplemented
36#14582624C2214yescomplemented
37C2×#121×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C43×#327C2214yes—
41C22×Dic86—21no—
42C22×Dic86—21no—
43C22×Dic86—21no—
44C22×Dic86—21no—
45C22×Dic86—21no—
46C22×Dic86—44no—
47C22×Dic86D411yescharacteristic
48C22×Dic86C2312yes—
49C23×Dic43—21no—
50C23×Dic43—21no—
51C23×Dic43D411yescharacteristic
52C23×Dic43D411yescharacteristic
53C2×Dic172—24no—
54C2×Dic172—44no—
55C2×#10621883—24no—
56C2×#10621883—44no—
57C22×C43⋊C8—21no—
58#13063318—24no—
59#13063318—24no—
60#13063315—24no—
61#13063315—24no—
62#13063306—24no—
63#13063306—24no—
64#13063306—24no—
65#13063306—24no—
66#13063304—21no—
67#13063304—21no—
68#13063304D412yes—
69#13063304C2312yes—
70#13063302—24no—
71#13063302—24no—
72D4×Dic43—24no—
73D4×Dic43—24no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—24no—
76C2×C4⋊Dic43—44no—
77C2×C4⋊Dic43D411yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D412yes—
86C2×Dic43⋊C4C2312yes—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92#13063250—24no—
93#13063248—24no—
94C22⋊(C43⋊C8)—21no—
95C22⋊(C43⋊C8)C2312yes—
96C43⋊#95—24no—
97C22×D4×C43—21no—
98C22×D4×C43D411yescharacteristic
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101C22×C8×C43—21no—
102#121×C43—21no—
103#121×C43—21no—
104#121×C43D412yes—
105#121×C43C2312yes—
106C2×C4⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43—21no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43C2312yes—
110#95×C43—21no—
111#95×C43C2312yes—
112C24×C43—21no—
113C24×C43C2×D411yescharacteristic
114C2×D4×C43—21no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43—42no—
118C2×D4×C43—42no—
119C2×D4×C43—42no—
120C2×D4×C43C2×D412yes—
121C22×C4×C43—24no—
122C22×C4×C43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—24no—
134C22×Dic43—24no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43—41no—
147C22×Dic43—41no—
148C22×Dic43—82no—
149C22×Dic43C2×D412yes—
150C22×Dic43C2×D412yes—
151C2×Dic86—24no—
152C2×Dic86—24no—
153C2×Dic86—22no—
154C2×Dic86—22no—
155C2×Dic86—21no—
156C2×Dic86—44no—
157C2×Dic86—44no—
158C2×Dic86—44no—
159C2×Dic86—44no—
160C2×Dic86—42no—
161C2×Dic86—42no—
162C2×Dic86—41no—
163C2×Dic86—41no—
164C2×Dic86—42no—
165C2×Dic86C2×D412yes—
166C2×C8×C43—22no—
167C2×C8×C43—42no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C2×D412yes—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊Dic43—24no—
173C22⋊Dic43—24no—
174C22⋊Dic43—24no—
175C22⋊Dic43—22no—
176C22⋊Dic43—22no—
177#10621883—48no—
178C4⋊Dic43—24no—
179C4⋊Dic43—21no—
180C4⋊Dic43—48no—
181C4⋊Dic43C2×D412yes—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190C4×Dic43—24no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—42no—
193Dic172—48no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43#12011yescharacteristic
201C23×C43#12011yescharacteristic
202C23×C43#13512yes—
203C23×C43#13712yes—
204C23×C43C22×D411yescharacteristic
205D4×C43—42no—
206D4×C43—42no—
207D4×C43—42no—
208D4×C43—44no—
209D4×C43—81no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—22no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—48no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12011yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×Dic43—24no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—44no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—44no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—81no—
244C2×Dic43—84no—
245Dic86—24no—
246Dic86—24no—
247Dic86—42no—
248Dic86—42no—
249Dic86—44no—
250Dic86—44no—
251Dic86—42no—
252Dic86—81no—
253C8×C43—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—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—84no—
266C22×C43#45212yes—
267C22×C43#45212yes—
268C22×C43#45612yes—
269C22×C43B(4,𝔽2)12yes—
270C22×C43C2×#12011yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43C2×#13711yescharacteristic
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—44no—
278C4×C43—42no—
279Dic43—42no—
280Dic43—42no—
281Dic43—44no—
282Dic43—42no—
283Dic43—42no—
284C2×#539—431no—
285C2×#451—431no—
286C2×#448—431no—
287C2×#395—431no—
288#1603—438no—
289C2×#328—431no—
290C2×#327D4311yescharacteristic
291C2×#324—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—22no—
295C2×C43—82no—
296C2×C43#160314yescomplemented
297C2×C43C2×#45211yescharacteristic
298C2×C43C2×#45611yescharacteristic
299C2×C43C2×B(4,𝔽2)11yescharacteristic
300C23×Q8—431no—
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×#121C2×D4311yescharacteristic
314C2×C4×D4—861no—
315C22×C4⋊C4—431no—
316C22×C4⋊C4—861no—
317#451—434no—
318#451—862no—
319#448—434no—
320#448—862no—
321C2×#103—861no—
322C2×#103—861no—
323C2×C22⋊C8—431no—
324C2×C22⋊C8C2×D4311yescharacteristic
325#395—434no—
326#395—862no—
327C2×#95—861no—
328C2×#95C2×D4311yescharacteristic
329#328—434no—
330#327C2×D4314yes—
331#324—434no—
332C43C2×#160311yescharacteristic, complemented, Sylow
333C22×Q8—431no—
334C22×Q8—432no—
335C22×Q8—861no—
336C22×Q8—861no—
337C22×Q8—861no—
338C22×Q8—861no—
339C22×Q8—861no—
340C22×Q8—1724no—
341C22×D4—21no—
342C22×D4D17211yescharacteristic
343C23×C4—21no—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—861no—
347C23×C4—861no—
348C23×C4C22×D4311yescharacteristic
349C2×Q16—864no—
350C2×Q16—1724no—
351C2×SD16—864no—
352C2×SD16—1724no—
353C22×C8—21no—
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—21no—
370#121—21no—
371#121D17212yes—
372#121C22×D4312yes—
373C4×D4—864no—
374C4×D4—864no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—432no—
377C2×C4⋊C4—432no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—1724no—
388C2×C4⋊C4D17211yescharacteristic
389C2×C22⋊C4—21no—
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—21no—
398C22⋊C8—432no—
399C22⋊C8—861no—
400C22⋊C8C22×D4312yes—
401#95—21no—
402#95—864no—
403#95C22×D4312yes—
404C24—21no—
405C24D4×D4311yescharacteristic
406C2×Q8—432no—
407C2×Q8—864no—
408C2×Q8—864no—
409C2×Q8—861no—
410C2×Q8—862no—
411C2×Q8—862no—
412C2×Q8—1722no—
413C2×Q8—1722no—
414C2×Q8—1722no—
415C2×Q8—1724no—
416C2×Q8—1724no—
417C2×Q8—1724no—
418C2×Q8—1724no—
419C2×Q8—1721no—
420C2×Q8—1721no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C2×D17212yes—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—432no—
435C22×C4—432no—
436C22×C4—864no—
437C22×C4—861no—
438C22×C4—864no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—3442no—
448C22×C4—1722no—
449C22×C4—1722no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4C2×D17211yescharacteristic
453C22×C4C2×D17211yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458Q16—1728no—
459SD16—1728no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—862no—
463C2×C8—1722no—
464C4⋊C4—21no—
465C4⋊C4—432no—
466C4⋊C4—864no—
467C4⋊C4—864no—
468C4⋊C4—864no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C4⋊C4—861no—
472C4⋊C4—862no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—1728no—
477C4⋊C4C2×D17212yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—864no—
481C22⋊C4—864no—
482C22⋊C4—864no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C42—864no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23#1306329511yescharacteristic
493C23#1306329511yescharacteristic
494C23#1306334412yes—
495C23#1306335412yes—
496C23C2×D4×D4311yescharacteristic
497Q8—864no—
498Q8—864no—
499Q8—3441no—
500Q8—1722no—
501Q8—1722no—
502Q8—1722no—
503Q8—1724no—
504Q8—1724no—
505D4—42no—
506D4—44no—
507D4—42no—
508D4—42no—
509D4—81no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—48no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—864no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—3441no—
530C2×C4—3444no—
531C2×C4—1722no—
532C2×C4—1724no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1724no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4#1306329511yescharacteristic
542C2×C4#1306329511yescharacteristic
543C2×C4C2×D4×D4311yescharacteristic
544C2×C4C22×D17211yescharacteristic
545C8—42no—
546C8—1722no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—24no—
552C22—24no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—84no—
557C22#1458306212yes—
558C22#1458306212yes—
559C22#1458308312yes—
560C22#1458308712yes—
561C22C2×#1306329511yescharacteristic
562C22C2×#1306334411yescharacteristic
563C22C2×#1306335411yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—44no—
569C4—42no—
570C4—1722no—
571C4—1722no—
572C4—1722no—
573C4—1724no—
574C4—1722no—
575C2—21no—
576C2—22no—
577C2—21no—
578C2—82no—
579C2#1913355914yesdirect product factor
580C2C2×#1458306211yescharacteristic
581C2C2×#1458308311yescharacteristic
582C2C2×#1458308711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#327C2
socleC23×C43#120
prime radicalC2×#121×C43C22
hypercenterC2×#327D43
hypocenterC43C2×#1603
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#14583057C2semidirect
4. C2×#14582820C2semidirect
5. #19133559C2direct (N × H)
6. C2×#14582635C2semidirect
7. C2×#14582624C2semidirect
26. #14583057C22semidirect
33. #14582820C22semidirect
35. #14582635C22semidirect
36. #14582624C22semidirect
296. C2×C43#1603semidirect
332. C43C2×#1603semidirect
579. C2#19133559direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834942
C2×#145830572
C2×#145830372
C2×#145828202
#191335592
C2×#145826352
C2×#145826242
C2×C43×#3272
C2×#160343