Finite Group Databasebeta

← C2×#20243739 #26217605

Subgroups — C2×#20243739 #26217605

Order 12032.

2470 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625334C211yesmaximal, characteristic
2C22×C4×D188C211yesmaximal, characteristic, complemented
3C22×#13093945C211yesmaximal, characteristic, complemented
4C22×#13093944C211yesmaximal, characteristic, complemented
5#20243739C218yesmaximal, direct product factor
6C2×#15688885C211yesmaximal, characteristic, complemented
7C2×#15688878C211yesmaximal, characteristic, complemented
8C2×C47×#390C211yesmaximal, characteristic, complemented
9C23×D188C2211yescharacteristic
10C23×C4×D47—21no—
11C22×#10625334—24no—
12C22×#10625334—24no—
13C22×#10625334C418yescomplemented
14C22×#10625334C2214yes—
15C23×C47⋊C8C2211yescharacteristic
16C23×C47⋊C8C2211yescharacteristic
17C2×C4×D188—24no—
18C2×C4×D188—24no—
19C2×C4×D188—22no—
20C2×C4×D188C2214yescomplemented
21C22×C4⋊Dic47C2211yescharacteristic
22C22×(C2×D47)⋊C4—21no—
23C2×#13093945—24no—
24C2×#13093945C2214yescomplemented
25C2×#13093944—24no—
26C2×#13093944C2214yescomplemented
27#15688885C2214yescomplemented
28#15688878C2214yescomplemented
29C23×D4×C47C2211yescharacteristic
30C22×C4⋊C4×C47C2211yescharacteristic
31C22×C22⋊C4×C47—21no—
32C22×C22⋊C4×C47—21no—
33C22×C42×C47C2211yescharacteristic
34C47×#390—22no—
35C47×#390C2214yescomplemented
36C24×D47—21no—
37C22×D188—21no—
38C22×D188—22no—
39C22×D188—22no—
40C22×D188—22no—
41C22×D188C2×C414yes—
42C22×D188D414yes—
43C22×D188D414yes—
44C22×D188C2312yes—
45C23×Dic47—21no—
46C22×C4×D47—28no—
47C22×C4×D47—24no—
48C22×C4×D47—44no—
49C22×C4×D47—44no—
50C2×#10625334—232no—
51C2×#10625334—28no—
52C2×#10625334—28no—
53C2×#10625334C2×C4116yescomplemented
54C22×C47⋊C8—22no—
55C22×C47⋊C8—22no—
56C22×C47⋊C8—22no—
57C22×C47⋊C8—22no—
58C22×C47⋊C8—22no—
59C22×C47⋊C8C2×C414yescomplemented
60C22×C47⋊C8C2312yes—
61C22×C47⋊C8C2312yes—
62C4×D188—216no—
63C4×D188—28no—
64C4×D188—28no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47D414yes—
68C2×C4⋊Dic47C2312yes—
69C2×(C2×D47)⋊C4—28no—
70C2×(C2×D47)⋊C4—24no—
71#13093945—28no—
72#13093944—28no—
73C25×C47—21no—
74C22×D4×C47—22no—
75C22×D4×C47—22no—
76C22×D4×C47—22no—
77C22×D4×C47—21no—
78C22×D4×C47—22no—
79C22×D4×C47—22no—
80C22×D4×C47C2×C414yescomplemented
81C22×D4×C47C2312yes—
82C23×C4×C47—21no—
83C23×C4×C47D411yescharacteristic
84C23×C4×C47D411yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47—22no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47C2312yes—
90C2×C22⋊C4×C47—24no—
91C2×C22⋊C4×C47—24no—
92C2×C22⋊C4×C47—44no—
93C2×C22⋊C4×C47—44no—
94C2×C42×C47—22no—
95C2×C42×C47—22no—
96C2×C42×C47D412yes—
97C2×C42×C47C2312yes—
98C24×C47—24no—
99C24×C47—22no—
100C24×C47—42no—
101C24×C47—42no—
102C24×C47—42no—
103C24×C47—42no—
104C24×C47—42no—
105C24×C47—42no—
106C24×C47C2×D411yescharacteristic
107C23×D47—24no—
108C23×D47—24no—
109C23×D47—24no—
110C23×D47—22no—
111C23×D47—42no—
112C23×D47—42no—
113C23×D47—42no—
114C23×D47—42no—
115C2×D4×C47—28no—
116C2×D4×C47—28no—
117C2×D4×C47—24no—
118C2×D4×C47—22no—
119C2×D4×C47—22no—
120C2×D4×C47—22no—
121C2×D4×C47—22no—
122C2×D4×C47—22no—
123C2×D4×C47—42no—
124C2×D4×C47—42no—
125C2×D4×C47—44no—
126C2×D4×C47—44no—
127C2×D4×C47C22×C414yescomplemented
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—42no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47D814yescomplemented
138C22×C4×C47C22×C412yes—
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×D412yes—
141C22×C4×C47C2×D412yes—
142C22×C4×C47C2×D412yes—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D412yes—
145C22×C4×C47#4112yes—
146C22×C4×C47#4112yes—
147C22×C4×C47C2411yescharacteristic
148C22×Dic47—24no—
149C22×Dic47—22no—
150C22×Dic47—42no—
151C22×Dic47—42no—
152C2×D188—28no—
153C2×D188—24no—
154C2×D188—24no—
155C2×D188—28no—
156C2×D188—24no—
157C2×D188—28no—
158C2×D188—22no—
159C2×D188—22no—
160C2×D188—22no—
161C2×D188C22⋊C4116yescomplemented
162C2×D188C22×C414yes—
163C2×D188C2×D414yes—
164C2×D188C2×D414yes—
165C2×C4×D47—216no—
166C2×C4×D47—48no—
167C2×C4×D47—432no—
168C2×C4×D47—48no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—42no—
172C22⋊C4×C47—48no—
173C22⋊C4×C47—48no—
174C42×C47—24no—
175C42×C47—22no—
176C42×C47—22no—
177#10625334—232no—
178(C2×D47)⋊C4—216no—
179C4⋊Dic47—24no—
180C4⋊Dic47—22no—
181C4⋊Dic47C2×D414yes—
182C2×C47⋊C8—28no—
183C2×C47⋊C8—22no—
184C2×C47⋊C8—22no—
185C2×C47⋊C8—22no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—44no—
189C2×C47⋊C8C22×C414yescomplemented
190C23×C47—24no—
191C23×C47—42no—
192C23×C47—42no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—42no—
196C23×C47—42no—
197C23×C47—48no—
198C23×C47—48no—
199C23×C47—48no—
200C23×C47—84no—
201C23×C47—84no—
202C23×C47—84no—
203C23×C47—84no—
204C23×C47C4×D412yes—
205C23×C47#12012yes—
206C23×C47#12112yes—
207C23×C47C2×D812yes—
208C23×C47#13512yes—
209C23×C47AGL(1,ℤ/8)12yes—
210C23×C47AGL(1,ℤ/8)12yes—
211C23×C47C22×D411yescharacteristic
212C22×D47—24no—
213C22×D47—24no—
214C22×D47—24no—
215C22×D47—216no—
216C22×D47—42no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47—42no—
220C22×D47—48no—
221C22×D47—48no—
222C22×D47—48no—
223C22×D47—48no—
224C22×D47—48no—
225C22×D47—48no—
226D4×C47—24no—
227D4×C47—24no—
228D4×C47—42no—
229D4×C47—42no—
230D4×C47—48no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—28no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—44no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47—84no—
242C2×C4×C47C2×C22⋊C414yes—
243C2×C4×C47C4×D414yes—
244C2×C4×C47C4×D412yes—
245C2×C4×C47#12012yes—
246C2×C4×C47#12112yes—
247C2×C4×C47#12114yes—
248C2×C4×C47#12314yes—
249C2×C4×C47C2×D814yescomplemented
250C2×C4×C47C23×C411yescharacteristic
251C2×C4×C47C22×D411yescharacteristic
252C2×C4×C47C22×D411yescharacteristic
253C2×C4×C47C22×D411yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C2×Dic47—24no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—48no—
260D188—24no—
261D188—24no—
262D188—24no—
263D188—216no—
264D188C2×C22⋊C418yescomplemented
265C4×D47—432no—
266C47⋊C8—24no—
267C47⋊C8—42no—
268C2×#1879—471nomaximal, Sylow
269C22×C47—44no—
270C22×C47—44no—
271C22×C47—44no—
272C22×C47—816no—
273C22×C47—82no—
274C22×C47—82no—
275C22×C47—82no—
276C22×C47—82no—
277C22×C47#38614yes—
278C22×C47C4×D814yes—
279C22×C47#44214yes—
280C22×C47#44714yes—
281C22×C47#44914yes—
282C22×C47#45914yes—
283C22×C47#46314yes—
284C22×C47C2×C4×D411yescharacteristic
285C22×C47C2×#12011yescharacteristic
286C22×C47C2×#12111yescharacteristic
287C22×C47C22×D811yescharacteristic
288C22×C47C2×#13511yescharacteristic
289C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
291C2×D47—28no—
292C2×D47—432no—
293C2×D47—44no—
294C2×D47—44no—
295C2×D47—44no—
296C2×D47—44no—
297C2×D47—44no—
298C2×D47—44no—
299C4×C47—24no—
300C4×C47—42no—
301C4×C47—82no—
302C4×C47#38614yes—
303C4×C47C22×C22⋊C411yescharacteristic
304C4×C47C2×C4×D411yescharacteristic
305C4×C47C2×#12111yescharacteristic
306C4×C47C2×#12311yescharacteristic
307Dic47—44no—
308C23×D8—471no—
309C22×C4×D4—471no—
310C22×#102—471no—
311C22×#102—471no—
312C2×#390D4711yescharacteristic, complemented
313#1879—478no—
314C2×#340—471no—
315C2×#336—471no—
316C2×C47—84no—
317C2×C47#187918yescomplemented
318C2×C47C2×#38611yescharacteristic
319C2×C47C2×C4×D811yescharacteristic
320C2×C47C2×#44211yescharacteristic
321C2×C47C2×#44711yescharacteristic
322C2×C47C2×#44911yescharacteristic
323C2×C47C2×#45911yescharacteristic
324C2×C47C2×#46311yescharacteristic
325D47—48no—
326C23×D4—471no—
327C23×D4C2×D4711yescharacteristic
328C24×C4—941no—
329C22×D8—478no—
330C22×D8—474no—
331C22×D8—944no—
332C22×D8—944no—
333C23×C8—471no—
334C23×C8—471no—
335C2×C4×D4—474no—
336C2×C4×D4—944no—
337C2×C4×D4—944no—
338C2×C4×D4—942no—
339C22×C4⋊C4—471no—
340C22×C4⋊C4C2×D4711yescharacteristic
341C22×C22⋊C4—21no—
342C22×C22⋊C4—21no—
343C22×C22⋊C4—941no—
344C22×C42C2×D4711yescharacteristic
345C2×#102—474no—
346C2×#102—474no—
347C2×#102—944no—
348C2×#102—944no—
349#390—22no—
350#390C2×D4714yescomplemented
351#340—474no—
352#336—474no—
353C47C2×#187911yescharacteristic, complemented, Sylow
354C25—21no—
355C25—941no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—21no—
362C22×D4—474no—
363C22×D4—474no—
364C22×D4—474no—
365C22×D4—472no—
366C22×D4—942no—
367C22×D4—942no—
368C22×D4—942no—
369C22×D4—941no—
370C22×D4C4×D4714yescomplemented
371C22×D4C22×D4712yes—
372C23×C4—21no—
373C23×C4—948no—
374C23×C4—941no—
375C23×C4—944no—
376C23×C4—1884no—
377C23×C4—1884no—
378C23×C4C22⋊D4711yescharacteristic
379C23×C4C22⋊D4711yescharacteristic
380C23×C4C22×D4711yescharacteristic
381C2×D8—4716no—
382C2×D8—9432no—
383C2×D8—948no—
384C2×D8—948no—
385C22×C8—474no—
386C22×C8—472no—
387C22×C8—472no—
388C22×C8—942no—
389C22×C8—942no—
390C22×C8—942no—
391C22×C8—942no—
392C22×C8—942no—
393C4×D4—948no—
394C4×D4—948no—
395C4×D4—9416no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—474no—
400C2×C4⋊C4—472no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4C22×D4712yes—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—948no—
409C2×C22⋊C4—944no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42C22⋊D4712yes—
413C2×C42C22×D4712yes—
414#102—948no—
415#102—948no—
416C24—24no—
417C24—22no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—944no—
425C24—944no—
426C24—944no—
427C24—942no—
428C24—1882no—
429C24—1882no—
430C24—1882no—
431C24—1882no—
432C24C2×C22⋊D4711yescharacteristic
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—24no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—4716no—
446C2×D4—474no—
447C2×D4—474no—
448C2×D4—474no—
449C2×D4—948no—
450C2×D4—944no—
451C2×D4—944no—
452C2×D4—944no—
453C2×D4—948no—
454C2×D4—948no—
455C2×D4—942no—
456C2×D4—942no—
457C2×D4—942no—
458C2×D4C2×C4×D4714yescomplemented
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—9416no—
469C22×C4—944no—
470C22×C4—942no—
471C22×C4—18832no—
472C22×C4—1888no—
473C22×C4—1882no—
474C22×C4—1882no—
475C22×C4—1888no—
476C22×C4#1062533414yescomplemented
477C22×C4C2×C4×D4712yes—
478C22×C4#1062535012yes—
479C22×C4D4×D4712yes—
480C22×C4D4×D4712yes—
481C22×C4D4×D4712yes—
482C22×C4#1062535212yes—
483C22×C4C2×C22⋊D4712yes—
484C22×C4C2×C22⋊D4712yes—
485C22×C4C2×C22⋊D4711yescharacteristic
486C22×C4C23×D4711yescharacteristic
487D8—9432no—
488C2×C8—474no—
489C2×C8—948no—
490C2×C8—942no—
491C2×C8—942no—
492C2×C8—942no—
493C2×C8—942no—
494C2×C8—942no—
495C2×C8—1884no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—42no—
499C4⋊C4—474no—
500C4⋊C4—944no—
501C4⋊C4—942no—
502C22⋊C4—48no—
503C22⋊C4—48no—
504C22⋊C4—9416no—
505C42—24no—
506C42—22no—
507C42—22no—
508C23—24no—
509C23—48no—
510C23—48no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—48no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23—9416no—
523C23—944no—
524C23—944no—
525C23—944no—
526C23—1888no—
527C23—1888no—
528C23—1888no—
529C23—1888no—
530C23—1888no—
531C23—1882no—
532C23—1882no—
533C23—1882no—
534C23—1882no—
535C23—1888no—
536C23C4×C22⋊D4712yes—
537C23#1309399212yes—
538C23#1309399512yes—
539C23C2×#1062533412yes—
540C23#1309404412yes—
541C23#1309404912yes—
542C23#1309405012yes—
543C23C22×C22⋊D4711yescharacteristic
544D4—24no—
545D4—24no—
546D4—48no—
547D4—42no—
548D4—42no—
549D4—478no—
550D4—9416no—
551D4—944no—
552D4—944no—
553D4—944no—
554C2×C4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—84no—
565C2×C4—944no—
566C2×C4—18832no—
567C2×C4—1888no—
568C2×C4—1882no—
569C2×C4—1882no—
570C2×C4C22⋊C4×D4714yes—
571C2×C4(C22⋊D47)⋊C414yes—
572C2×C4C4×C22⋊D4712yes—
573C2×C4#1309399212yes—
574C2×C4#1309399512yes—
575C2×C4#1309399714yes—
576C2×C4#1309400614yes—
577C2×C4C2×#1062533414yescomplemented
578C2×C4C22×C4×D4711yescharacteristic
579C2×C4C2×D4×D4711yescharacteristic
580C2×C4C2×D4×D4711yescharacteristic
581C2×C4C2×D4×D4711yescharacteristic
582C2×C4C2×#1062535211yescharacteristic
583C2×C4C2×#1062535011yescharacteristic
584C8—944no—
585C8—1882no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—816no—
590C22—82no—
591C22—82no—
592C22—82no—
593C22—82no—
594C22—948no—
595C22—1884no—
596C22—18832no—
597C22—1884no—
598C22—1884no—
599C22—1884no—
600C22—1884no—
601C22—1884no—
602C22#1568899914yes—
603C22C4×#1062533414yes—
604C22#1568923314yes—
605C22#1568925614yes—
606C22#1568926614yes—
607C22#1568931514yes—
608C22#1568933514yes—
609C22C2×C4×C22⋊D4711yescharacteristic
610C22C2×#1309399211yescharacteristic
611C22C2×#1309399511yescharacteristic
612C22C22×#1062533411yescharacteristic
613C22C2×#1309404411yescharacteristic
614C22C2×#1309404911yescharacteristic
615C22C2×#1309405011yescharacteristic
616C4—24no—
617C4—42no—
618C4—82no—
619C4—1884no—
620C4#1568899914yes—
621C4C2×C22⋊C4×D4711yescharacteristic
622C4C2×(C22⋊D47)⋊C411yescharacteristic
623C4C2×#1309399711yescharacteristic
624C4C2×#1309400611yescharacteristic
625C2—84no—
626C2—1888no—
627C2#2024373918yesdirect product factor
628C2C2×#1568899911yescharacteristic
629C2C2×C4×#1062533411yescharacteristic
630C2C2×#1568923311yescharacteristic
631C2C2×#1568925611yescharacteristic
632C2C2×#1568926611yescharacteristic
633C2C2×#1568931511yescharacteristic
634C2C2×#1568933511yescharacteristic
subgroupG/H
centerC24C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#390C2
socleC24×C47C2×D4
prime radicalC23×#10625334C2
cosocleC22×C4×C47C24
hypercenterC2×#390D47
hypocenterC47C2×#1879
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×C4×D188C2semidirect
3. C22×#13093945C2semidirect
4. C22×#13093944C2semidirect
5. #20243739C2direct (N × H)
6. C2×#15688885C2semidirect
7. C2×#15688878C2semidirect
8. C2×C47×#390C2semidirect
13. C22×#10625334C4semidirect
20. C2×C4×D188C22semidirect
24. C2×#13093945C22semidirect
26. C2×#13093944C22semidirect
27. #15688885C22semidirect
28. #15688878C22semidirect
35. C47×#390C22semidirect
53. C2×#10625334C2×C4semidirect
59. C22×C47⋊C8C2×C4semidirect
80. C22×D4×C47C2×C4semidirect
127. C2×D4×C47C22×C4semidirect
137. C22×C4×C47D8semidirect
161. C2×D188C22⋊C4semidirect
189. C2×C47⋊C8C22×C4semidirect
249. C2×C4×C47C2×D8semidirect
264. D188C2×C22⋊C4semidirect
312. C2×#390D47semidirect
317. C2×C47#1879semidirect
350. #390C2×D47semidirect
353. C47C2×#1879semidirect
370. C22×D4C4×D47semidirect
458. C2×D4C2×C4×D47semidirect
476. C22×C4#10625334semidirect
577. C2×C4C2×#10625334semidirect
627. C2#20243739direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106253342
C22×C4×D1882
C22×#130939452
C22×#130939442
#202437392
C2×#156888852
C2×#156888782
C2×C47×#3902
C2×#187947