Finite Group Databasebeta

← C2×#19133640 #25068844

Subgroups — C2×#19133640 #25068844

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583486C211yesmaximal, characteristic
2C2×#14583234C211yesmaximal, characteristic, complemented
3C2×#14582834C211yesmaximal, characteristic, complemented
4#19133640C218yesmaximal, direct product factor
5C2×#14582637C211yesmaximal, characteristic, complemented
6C2×#14582633C211yesmaximal, characteristic, complemented
7C2×#14582622C211yesmaximal, characteristic, complemented
8C2×C43×#481C211yesmaximal, characteristic, complemented
9#14583486—22no—
10#14583486—22no—
11#14583486—22no—
12#14583486C2214yes—
13C2×#13063320—21no—
14C2×#13063311—21no—
15C2×#13063309—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063297—21no—
18C2×#13063293—21no—
19C2×D4×Dic43—21no—
20C22×Dic43⋊C4—21no—
21C22×(C2×D43)⋊C4—21no—
22C22×(C2×D43)⋊C4C2211yescharacteristic
23#14583234—22no—
24#14583234C2214yescomplemented
25C2×#13063258—21no—
26C2×#13063248—21no—
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28#14582834—22no—
29#14582834C2214yescomplemented
30C2×C43⋊#95C2211yescharacteristic
31#14582637C2214yescomplemented
32#14582633C2214yescomplemented
33#14582622C2214yescomplemented
34C2×#121×C43C2211yescharacteristic
35C22×C4⋊C4×C43C2211yescharacteristic
36C43×#481—22no—
37C43×#481C2214yescomplemented
38C2×#106×C43—21no—
39C2×#102×C43—21no—
40C2×C22⋊C8×C43C2211yescharacteristic
41C24×D43D411yescharacteristic
42C22×Dic86D411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C22⋊D43—21no—
45C23×Dic43—21no—
46C23×Dic43—21no—
47C23×Dic43D411yescharacteristic
48C22×C43⋊C8—21no—
49#13063320—24no—
50#13063320—24no—
51#13063311—24no—
52#13063311—24no—
53#13063309—24no—
54#13063309—24no—
55#13063304—21no—
56#13063304—21no—
57#13063304D412yes—
58#13063304C2312yes—
59#13063297—24no—
60#13063297—24no—
61#13063293—24no—
62#13063293—24no—
63D4×Dic43—24no—
64D4×Dic43—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43D411yescharacteristic
67C2×Dic43⋊C4—21no—
68C2×Dic43⋊C4—24no—
69C2×Dic43⋊C4—44no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—44no—
80C2×(C2×D43)⋊C4D412yes—
81C2×(C2×D43)⋊C4C2312yes—
82C2×C4×Dic43—21no—
83#13063258—24no—
84#13063248—24no—
85C22⋊(C43⋊C8)—21no—
86C22⋊(C43⋊C8)C2312yes—
87C43⋊#95—21no—
88C43⋊#95C2312yes—
89C22×D4×C43—21no—
90C22×D4×C43D411yescharacteristic
91C23×C4×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C22×C8×C43—21no—
94#121×C43—21no—
95#121×C43—21no—
96#121×C43D412yes—
97#121×C43C2312yes—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43C2312yes—
105C2×C22⋊C4×C43—21no—
106#106×C43—24no—
107#102×C43—24no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43C2312yes—
110C24×C43—21no—
111C24×C43C2×D411yescharacteristic
112C23×D43—21no—
113C23×D43—22no—
114C23×D43—21no—
115C23×D43—22no—
116C23×D43—42no—
117C23×D43—42no—
118C23×D43C2×D412yes—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43C2×D412yes—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—41no—
132C22×C4×C43—41no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—24no—
140C2×C22⋊D43—24no—
141C2×C22⋊D43—82no—
142C2×C22⋊D43—82no—
143C22×Dic43—24no—
144C22×Dic43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—22no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—82no—
154C22×Dic43C2×D412yes—
155C2×Dic86—21no—
156C2×Dic86—42no—
157C2×Dic86C2×D412yes—
158C2×C8×C43—22no—
159C2×C8×C43—42no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—41no—
164C4⋊C4×C43—41no—
165C4⋊C4×C43C2×D412yes—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊Dic43—24no—
169C22⋊Dic43—22no—
170C22⋊Dic43—22no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—22no—
175(C2×D43)⋊C4—22no—
176(C2×D43)⋊C4—22no—
177(C2×D43)⋊C4—48no—
178C4⋊Dic43—24no—
179C4⋊Dic43—21no—
180C4⋊Dic43C2×D412yes—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4—48no—
184C4×Dic43—24no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—42no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43#12011yescharacteristic
194C23×C43#12011yescharacteristic
195C23×C43#13512yes—
196C23×C43#13712yes—
197C23×C43C22×D411yescharacteristic
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—48no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—81no—
209C22×D43—81no—
210C22×D43—84no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—44no—
215D4×C43—81no—
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—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—82no—
228C2×C4×C43—82no—
229C2×C4×C43#12011yescharacteristic
230C2×C4×C43#12011yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C22⋊D43—84no—
234C22⋊D43—84no—
235C2×Dic43—24no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—48no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—81no—
247C2×Dic43—84no—
248Dic86—42no—
249Dic86—81no—
250C8×C43—42no—
251C43⋊C8—42no—
252C2×#1618—431nomaximal, Sylow
253C22×C43—24no—
254C22×C43—24no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—84no—
263C22×C43#45212yes—
264C22×C43#45212yes—
265C22×C43#45312yes—
266C22×C43#45812yes—
267C22×C43C2×#12011yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43C2×#13711yescharacteristic
270C2×D43—44no—
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—84no—
275C2×D43—84no—
276C2×D43—82no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—42no—
282C4×C43—82no—
283Dic43—44no—
284Dic43—42no—
285Dic43—42no—
286Dic43—42no—
287C2×#538—431no—
288C2×#484—431no—
289C2×#481D4311yescharacteristic, complemented
290C2×#399—431no—
291#1618—438no—
292C2×#328—431no—
293C2×#327—431no—
294C2×#323—431no—
295C2×C43—21no—
296C2×C43—21no—
297C2×C43—22no—
298C2×C43—82no—
299C2×C43#161814yescomplemented
300C2×C43C2×#45211yescharacteristic
301C2×C43C2×#45311yescharacteristic
302C2×C43C2×#45811yescharacteristic
303D43—82no—
304#538—434no—
305#538—862no—
306#538—862no—
307#538—862no—
308C2×#126—861no—
309C2×#124—861no—
310C2×#123—861no—
311C2×C22⋊Q8—431no—
312C2×#121—861no—
313C2×#121C2×D4311yescharacteristic
314C2×#120—861no—
315C2×C4×D4—861no—
316C22×C4⋊C4—861no—
317C22×C4⋊C4C2×D4311yescharacteristic
318C22×C22⋊C4—431no—
319C22×C22⋊C4—861no—
320#484—434no—
321#484—862no—
322#481—22no—
323#481C2×D4314yescomplemented
324C2×#107—861no—
325C2×#106—21no—
326C2×#103—861no—
327C2×#102—21no—
328C2×C22⋊C8—431no—
329C2×C22⋊C8C2×D4311yescharacteristic
330#399—434no—
331#399—862no—
332C2×#95—431no—
333#328—434no—
334#327—434no—
335#323—434no—
336C43C2×#161811yescharacteristic, complemented, Sylow
337C25—431no—
338C22×Q8—431no—
339C22×D4—21no—
340C22×D4—861no—
341C22×D4—861no—
342C22×D4C22⋊D4311yescharacteristic
343C23×C4—21no—
344C23×C4—431no—
345C23×C4—861no—
346C23×C4—861no—
347C23×C4C22×D4311yescharacteristic
348C22×C8—21no—
349C22×C8—861no—
350#126—864no—
351#126—864no—
352#124—864no—
353#124—864no—
354#123—864no—
355#123—864no—
356C22⋊Q8—432no—
357C22⋊Q8—432no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360#121—21no—
361#121—21no—
362#121—864no—
363#121—864no—
364#121C22⋊D4312yes—
365#121C22×D4312yes—
366#120—864no—
367#120—864no—
368C4×D4—864no—
369C4×D4—864no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—864no—
379C2×C4⋊C4—1724no—
380C2×C4⋊C4C22⋊D4311yescharacteristic
381C2×C4⋊C4C22×D4312yes—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—432no—
384C2×C22⋊C4—432no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—864no—
394C2×C22⋊C4—1724no—
395C2×C42—861no—
396#107—864no—
397#106—24no—
398#103—864no—
399#102—24no—
400C22⋊C8—21no—
401C22⋊C8—432no—
402C22⋊C8—861no—
403C22⋊C8C22×D4312yes—
404#95—432no—
405#95—861no—
406C24—21no—
407C24—432no—
408C24—861no—
409C24—862no—
410C24—861no—
411C24—862no—
412C24—1722no—
413C24—1722no—
414C24D4×D4311yescharacteristic
415C2×Q8—432no—
416C2×Q8—861no—
417C2×Q8—1722no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—864no—
425C2×D4—864no—
426C2×D4—3442no—
427C2×D4—3442no—
428C2×D4C2×C22⋊D4312yes—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—432no—
437C22×C4—864no—
438C22×C4—861no—
439C22×C4—864no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—862no—
444C22×C4—3442no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C23×D4311yescharacteristic
454C2×C8—22no—
455C2×C8—42no—
456C2×C8—862no—
457C2×C8—1722no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—432no—
464C4⋊C4—864no—
465C4⋊C4—861no—
466C4⋊C4—862no—
467C4⋊C4—862no—
468C4⋊C4—1728no—
469C4⋊C4C2×C22⋊D4312yes—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—864no—
473C22⋊C4—864no—
474C22⋊C4—864no—
475C22⋊C4—862no—
476C22⋊C4—862no—
477C22⋊C4—862no—
478C22⋊C4—862no—
479C22⋊C4—862no—
480C22⋊C4—862no—
481C22⋊C4—1728no—
482C42—864no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—862no—
490C23—862no—
491C23—862no—
492C23—3444no—
493C23—3441no—
494C23—3441no—
495C23—1728no—
496C23—1722no—
497C23—1722no—
498C23—1722no—
499C23—1722no—
500C23—1722no—
501C23—1722no—
502C23#1306329311yescharacteristic
503C23#1306329311yescharacteristic
504C23#1306334612yes—
505C23#1306335412yes—
506C23C2×D4×D4311yescharacteristic
507Q8—3441no—
508Q8—1722no—
509D4—42no—
510D4—44no—
511D4—42no—
512D4—42no—
513D4—81no—
514D4—3444no—
515D4—3444no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—864no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—862no—
533C2×C4—3441no—
534C2×C4—3444no—
535C2×C4—1722no—
536C2×C4—1728no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1722no—
542C2×C4#1306329311yescharacteristic
543C2×C4#1306329311yescharacteristic
544C2×C4C2×D4×D4311yescharacteristic
545C2×C4C22×C22⋊D4311yescharacteristic
546C8—42no—
547C8—1722no—
548C22—21no—
549C22—21no—
550C22—24no—
551C22—24no—
552C22—21no—
553C22—21no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—84no—
558C22—3442no—
559C22—3444no—
560C22—3444no—
561C22—1724no—
562C22—1722no—
563C22—1722no—
564C22—1722no—
565C22#1458305812yes—
566C22#1458305812yes—
567C22#1458306512yes—
568C22#1458308812yes—
569C22C2×#1306329311yescharacteristic
570C22C2×#1306334611yescharacteristic
571C22C2×#1306335411yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—42no—
577C4—82no—
578C4—1724no—
579C4—1722no—
580C4—1722no—
581C4—1722no—
582C2—21no—
583C2—22no—
584C2—21no—
585C2—82no—
586C2—3442no—
587C2#1913364014yesdirect product factor
588C2C2×#1458305811yescharacteristic
589C2C2×#1458306511yescharacteristic
590C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#481C2
socleC23×C43#120
prime radicalC2×#14583486C2
hypercenterC2×#481D43
hypocenterC43C2×#1618
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. C2×#14583234C2semidirect
3. C2×#14582834C2semidirect
4. #19133640C2direct (N × H)
5. C2×#14582637C2semidirect
6. C2×#14582633C2semidirect
7. C2×#14582622C2semidirect
8. C2×C43×#481C2semidirect
24. #14583234C22semidirect
29. #14582834C22semidirect
31. #14582637C22semidirect
32. #14582633C22semidirect
33. #14582622C22semidirect
37. C43×#481C22semidirect
289. C2×#481D43semidirect
299. C2×C43#1618semidirect
323. #481C2×D43semidirect
336. C43C2×#1618semidirect
587. C2#19133640direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834862
C2×#145832342
C2×#145828342
#191336402
C2×#145826372
C2×#145826332
C2×#145826222
C2×C43×#4812
C2×#161843