Finite Group Databasebeta

← C2×#20243813 #26217944

Subgroups — C2×#20243813 #26217944

Order 12032.

2438 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C8×D47C211yesmaximal, characteristic, complemented
2C22×#13093995C211yesmaximal, characteristic
3C22×#13093945C211yesmaximal, characteristic, complemented
4C2×#15688980C211yesmaximal, characteristic, complemented
5#20243813C218yesmaximal, direct product factor
6C2×#15688886C211yesmaximal, characteristic, complemented
7C2×#15688885C211yesmaximal, characteristic, complemented
8C22×#102×C47C211yesmaximal, characteristic, complemented
9C23×C22⋊D47—21no—
10C23×C4×D47C2211yescharacteristic
11C23×C47⋊C8C2211yescharacteristic
12C22×C8×D47—24no—
13C22×C8×D47—24no—
14C22×C8×D47—24no—
15C22×C8×D47C2214yescomplemented
16C2×#13093995—24no—
17C2×#13093995—22no—
18C2×#13093995C418yescomplemented
19C2×#13093995C2214yes—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C22⋊Dic47—21no—
23C22×(C2×D47)⋊C4—21no—
24C2×#13093945—24no—
25C2×#13093945C2214yescomplemented
26#15688980—22no—
27#15688980C2214yescomplemented
28C2×C47⋊#95—21no—
29#15688886C2214yescomplemented
30#15688885C2214yescomplemented
31C23×D4×C47C2211yescharacteristic
32C23×C8×C47C2211yescharacteristic
33C22×C4⋊C4×C47C2211yescharacteristic
34C2×#102×C47—24no—
35C2×#102×C47C2214yescomplemented
36C24×D47D411yescharacteristic
37C22×C22⋊D47—28no—
38C22×C22⋊D47—24no—
39C22×C22⋊D47—44no—
40C22×C22⋊D47—44no—
41C23×Dic47—21no—
42C23×Dic47—21no—
43C23×Dic47D411yescharacteristic
44C22×C4×D47—22no—
45C22×C4×D47—22no—
46C22×C4×D47—22no—
47C22×C4×D47—22no—
48C22×C4×D47C2×C414yes—
49C22×C4×D47D412yes—
50C22×C4×D47D414yes—
51C22×C4×D47C2312yes—
52C22×C47⋊C8—22no—
53C22×C47⋊C8—22no—
54C22×C47⋊C8D414yescomplemented
55C22×C47⋊C8C2312yes—
56C2×C8×D47—232no—
57C2×C8×D47—28no—
58C2×C8×D47—28no—
59C2×C8×D47—28no—
60#13093995—216no—
61#13093995—28no—
62#13093995C2×C4116yescomplemented
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47C2×C414yes—
69C2×C4⋊Dic47C2312yes—
70C2×C4⋊Dic47C2312yes—
71C2×C22⋊Dic47—28no—
72C2×C22⋊Dic47—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—44no—
75#13093945—28no—
76C47⋊#95—24no—
77C25×C47—21no—
78C22×D4×C47—22no—
79C22×D4×C47—22no—
80C22×D4×C47—21no—
81C22×D4×C47—22no—
82C22×D4×C47—22no—
83C22×D4×C47—22no—
84C22×D4×C47C2×C414yes—
85C22×D4×C47C2312yes—
86C23×C4×C47—21no—
87C23×C4×C47C2311yescharacteristic
88C22×C8×C47—22no—
89C22×C8×C47—22no—
90C22×C8×C47D414yescomplemented
91C22×C8×C47C2312yes—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47C2312yes—
96#102×C47—28no—
97C24×C47—24no—
98C24×C47—22no—
99C24×C47—42no—
100C24×C47—42no—
101C24×C47—42no—
102C24×C47—42no—
103C24×C47—42no—
104C24×C47—42no—
105C24×C47C2×D411yescharacteristic
106C23×D47—22no—
107C23×D47—22no—
108C23×D47—22no—
109C23×D47—22no—
110C23×D47C22⋊C414yes—
111C23×D47D814yes—
112C23×D47SD1614yes—
113C23×D47C2×D412yes—
114C2×D4×C47—24no—
115C2×D4×C47—28no—
116C2×D4×C47—28no—
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47—22no—
120C2×D4×C47—22no—
121C2×D4×C47—22no—
122C2×D4×C47—44no—
123C2×D4×C47—42no—
124C2×D4×C47—42no—
125C2×D4×C47—44no—
126C2×D4×C47C22×C414yes—
127C22×C4×C47—22no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47—42no—
131C22×C4×C47C22×C412yes—
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47#4112yes—
137C22×C4×C47#4112yes—
138C22×C4×C47C2411yescharacteristic
139C2×C22⋊D47—216no—
140C2×C22⋊D47—432no—
141C2×C22⋊D47—48no—
142C2×C22⋊D47—48no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—24no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—42no—
149C22×Dic47—42no—
150C22×Dic47—42no—
151C22×Dic47—42no—
152C22×Dic47—42no—
153C22×Dic47C22⋊C414yes—
154C22×Dic47C2×D412yes—
155C2×C4×D47—28no—
156C2×C4×D47—28no—
157C2×C4×D47—28no—
158C2×C4×D47—24no—
159C2×C4×D47—24no—
160C2×C4×D47—28no—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47C22⋊C418yes—
166C2×C4×D47C22×C414yes—
167C2×C4×D47C2×D414yes—
168C2×C8×C47—28no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47C2×D414yescomplemented
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—42no—
175C22⋊Dic47—216no—
176(C2×D47)⋊C4—48no—
177C4⋊Dic47—24no—
178C4⋊Dic47—22no—
179C4⋊Dic47—22no—
180C4⋊Dic47—22no—
181C4⋊Dic47—42no—
182C4⋊Dic47C22×C414yes—
183C2×C47⋊C8—28no—
184C2×C47⋊C8—22no—
185C2×C47⋊C8—22no—
186C2×C47⋊C8C2×D414yescomplemented
187C8×D47—232no—
188C23×C47—24no—
189C23×C47—42no—
190C23×C47—42no—
191C23×C47—42no—
192C23×C47—42no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—48no—
196C23×C47—48no—
197C23×C47—48no—
198C23×C47—84no—
199C23×C47—84no—
200C23×C47—84no—
201C23×C47—84no—
202C23×C47C2×C22⋊C412yes—
203C23×C47#12112yes—
204C23×C47#12112yes—
205C23×C47C2×D812yes—
206C23×C47C2×SD1612yes—
207C23×C47#13512yes—
208C23×C47#13512yes—
209C23×C47C22×D411yescharacteristic
210C22×D47—22no—
211C22×D47—22no—
212C22×D47—22no—
213C22×D47—22no—
214C22×D47—28no—
215C22×D47—28no—
216C22×D47—28no—
217C22×D47—28no—
218C22×D47—28no—
219C22×D47—28no—
220C22×D47#102116yescomplemented
221C22×D47C2×C22⋊C414yes—
222C22×D47C2×D814yes—
223C22×D47C2×SD1614yes—
224D4×C47—24no—
225D4×C47—24no—
226D4×C47—42no—
227D4×C47—42no—
228D4×C47—48no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47—84no—
233C2×C4×C47C2×C22⋊C412yes—
234C2×C4×C47C4×D414yes—
235C2×C4×C47C4×D414yes—
236C2×C4×C47#12014yes—
237C2×C4×C47#12112yes—
238C2×C4×C47#12112yes—
239C2×C4×C47#12314yes—
240C2×C4×C47C23×C411yescharacteristic
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C22⋊D47—432no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—28no—
250C2×Dic47—24no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—48no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—84no—
258C2×Dic47C2×C22⋊C414yes—
259C4×D47—24no—
260C4×D47—24no—
261C4×D47—24no—
262C4×D47—24no—
263C4×D47—216no—
264C8×C47—24no—
265C47⋊C8—24no—
266C2×#1893—471nomaximal, Sylow
267C22×C47—44no—
268C22×C47—44no—
269C22×C47—44no—
270C22×C47—816no—
271C22×C47—82no—
272C22×C47—82no—
273C22×C47—82no—
274C22×C47—82no—
275C22×C47#38614yes—
276C22×C47C2×#10214yes—
277C22×C47#41614yes—
278C22×C47#46514yes—
279C22×C47#46514yes—
280C22×C47#46614yes—
281C22×C47#46614yes—
282C22×C47C22×C22⋊C411yescharacteristic
283C22×C47C2×#12111yescharacteristic
284C22×C47C2×#12111yescharacteristic
285C22×C47C22×D811yescharacteristic
286C22×C47C22×SD1611yescharacteristic
287C22×C47C2×#13511yescharacteristic
288C22×C47C2×#13511yescharacteristic
289C2×D47—24no—
290C2×D47—232no—
291C2×D47—24no—
292C2×D47—24no—
293C2×D47—24no—
294C2×D47—24no—
295C2×D47—24no—
296C2×D47C2×#10218yescomplemented
297C4×C47—82no—
298C4×C47#38614yes—
299C4×C47C2×C4×D411yescharacteristic
300C4×C47C2×C4×D411yescharacteristic
301C4×C47C2×#12011yescharacteristic
302C4×C47C2×#12311yescharacteristic
303Dic47—24no—
304Dic47—44no—
305Dic47—82no—
306C24×C8—471no—
307C22×#121—471no—
308C22×#102—471no—
309C22×#102D4711yescharacteristic, complemented
310C2×#380—471no—
311#1893—478no—
312C2×#340—471no—
313C2×#340—471no—
314C2×C47—84no—
315C2×C47#189318yescomplemented
316C2×C47C2×#38611yescharacteristic
317C2×C47C22×#10211yescharacteristic
318C2×C47C2×#41611yescharacteristic
319C2×C47C2×#46511yescharacteristic
320C2×C47C2×#46511yescharacteristic
321C2×C47C2×#46611yescharacteristic
322C2×C47C2×#46611yescharacteristic
323D47—28no—
324C23×D4—941no—
325C23×D4C2×D4711yescharacteristic
326C24×C4—471no—
327C23×C8—471no—
328C23×C8—474no—
329C23×C8—944no—
330C23×C8—944no—
331C23×C8—944no—
332C23×C8C2×D4711yescharacteristic
333C2×#121—478no—
334C2×#121—474no—
335C2×#121—944no—
336C2×#121—942no—
337C22×C4⋊C4—471no—
338C22×C4⋊C4—471no—
339C22×C4⋊C4C2×D4711yescharacteristic
340C22×C22⋊C4—941no—
341C22×C22⋊C4—941no—
342C2×#102—24no—
343C2×#102—474no—
344C2×#102—944no—
345C2×#102C2×D4714yescomplemented
346#380—474no—
347#380—942no—
348C2×#95—941no—
349#340—474no—
350#340—474no—
351C47C2×#189311yescharacteristic, complemented, Sylow
352C25—21no—
353C25—471no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—948no—
361C22×D4—944no—
362C22×D4—1884no—
363C22×D4—1884no—
364C22×D4C4×D4714yes—
365C22×D4C22×D4712yes—
366C23×C4—21no—
367C23×C4—471no—
368C23×C4—474no—
369C23×C4—474no—
370C23×C4—472no—
371C23×C4—472no—
372C23×C4—942no—
373C23×C4—942no—
374C23×C4—942no—
375C23×C4—942no—
376C23×C4—941no—
377C23×C4—941no—
378C23×C4C22×D4711yescharacteristic
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—474no—
382C22×C8—472no—
383C22×C8—948no—
384C22×C8—948no—
385C22×C8—9432no—
386C22×C8—942no—
387C22×C8—942no—
388C22×C8—948no—
389C22×C8C22⋊D4714yescomplemented
390C22×C8C22×D4712yes—
391#121—4716no—
392#121—9416no—
393#121—948no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—474no—
398C2×C4⋊C4—472no—
399C2×C4⋊C4—472no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4C22×D4712yes—
406C2×C22⋊C4—948no—
407C2×C22⋊C4—944no—
408C2×C22⋊C4—944no—
409C2×C22⋊C4—1884no—
410#102—28no—
411#102—948no—
412#95—944no—
413C24—24no—
414C24—22no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—474no—
422C24—474no—
423C24—474no—
424C24—472no—
425C24—942no—
426C24—942no—
427C24—942no—
428C24—942no—
429C24D4×D4711yescharacteristic
430C2×D4—24no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—44no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—9416no—
443C2×D4—18832no—
444C2×D4—1888no—
445C2×D4—1888no—
446C2×D4C2×C4×D4714yes—
447C22×C4—22no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—474no—
452C22×C4—472no—
453C22×C4—478no—
454C22×C4—474no—
455C22×C4—474no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—948no—
459C22×C4—948no—
460C22×C4—948no—
461C22×C4—944no—
462C22×C4—944no—
463C22×C4—948no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—944no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—1882no—
472C22×C4—1882no—
473C22×C4—1882no—
474C22×C4—1882no—
475C22×C4—1882no—
476C22×C4C2×C4×D4712yes—
477C22×C4#1062535012yes—
478C22×C4D4×D4711yescharacteristic
479C22×C4D4×D4712yes—
480C22×C4D4×D4712yes—
481C22×C4#1062535212yes—
482C22×C4C2×C22⋊D4712yes—
483C22×C4C23×D4711yescharacteristic
484C2×C8—28no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—474no—
488C2×C8—9432no—
489C2×C8—948no—
490C2×C8—942no—
491C2×C8—942no—
492C2×C8C2×C22⋊D4714yescomplemented
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—42no—
496C4⋊C4—474no—
497C4⋊C4—944no—
498C4⋊C4—942no—
499C4⋊C4—942no—
500C4⋊C4—942no—
501C4⋊C4—1882no—
502C22⋊C4—9416no—
503C22⋊C4—1888no—
504C23—24no—
505C23—48no—
506C23—42no—
507C23—42no—
508C23—48no—
509C23—48no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23—84no—
518C23—474no—
519C23—4716no—
520C23—474no—
521C23—474no—
522C23—948no—
523C23—948no—
524C23—948no—
525C23—948no—
526C23—942no—
527C23—948no—
528C23—942no—
529C23—948no—
530C23—942no—
531C23—942no—
532C23C22⋊C4×D4712yes—
533C23#1309399512yes—
534C23#1309399712yes—
535C23D8×D4712yes—
536C23SD16×D4712yes—
537C23#1309404312yes—
538C23#1309404512yes—
539C23C2×D4×D4711yescharacteristic
540D4—24no—
541D4—24no—
542D4—48no—
543D4—42no—
544D4—42no—
545D4—18832no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—84no—
550C2×C4—474no—
551C2×C4—948no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—9416no—
555C2×C4—944no—
556C2×C4—944no—
557C2×C4—944no—
558C2×C4—944no—
559C2×C4—944no—
560C2×C4—3764no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4—1888no—
565C2×C4—1882no—
566C2×C4—1882no—
567C2×C4C22⋊C4×D4712yes—
568C2×C4(C22⋊D47)⋊C414yes—
569C2×C4C4×C22⋊D4714yes—
570C2×C4#1309399214yes—
571C2×C4#1309399512yes—
572C2×C4#1309399712yes—
573C2×C4#1309400614yes—
574C2×C4C22×C4×D4711yescharacteristic
575C2×C4C2×D4×D4711yescharacteristic
576C2×C4C2×D4×D4711yescharacteristic
577C2×C4C22×C22⋊D4711yescharacteristic
578C2×C4C2×#1062535211yescharacteristic
579C2×C4C2×#1062535011yescharacteristic
580C8—24no—
581C8—944no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—816no—
590C22—478no—
591C22—944no—
592C22—944no—
593C22—944no—
594C22—944no—
595C22—944no—
596C22—9432no—
597C22—944no—
598C22#1568899914yes—
599C22#102×D4714yes—
600C22#1568911614yes—
601C22#1568934914yes—
602C22#1568935114yes—
603C22#1568935614yes—
604C22#1568935814yes—
605C22C2×C22⋊C4×D4711yescharacteristic
606C22C2×#1309399511yescharacteristic
607C22C2×#1309399711yescharacteristic
608C22C2×D8×D4711yescharacteristic
609C22C2×SD16×D4711yescharacteristic
610C22C2×#1309404311yescharacteristic
611C22C2×#1309404511yescharacteristic
612C4—82no—
613C4—944no—
614C4—3762no—
615C4—1884no—
616C4#1568899914yes—
617C4C2×(C22⋊D47)⋊C411yescharacteristic
618C4C2×C4×C22⋊D4711yescharacteristic
619C4C2×#1309399211yescharacteristic
620C4C2×#1309400611yescharacteristic
621C2—84no—
622C2—948no—
623C2#2024381318yesdirect product factor
624C2C2×#1568899911yescharacteristic
625C2C2×#102×D4711yescharacteristic
626C2C2×#1568911611yescharacteristic
627C2C2×#1568934911yescharacteristic
628C2C2×#1568935111yescharacteristic
629C2C2×#1568935611yescharacteristic
630C2C2×#1568935811yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#102×C47C2
socleC24×C47C2×D4
prime radicalC22×#13093995C2
cosocleC22×C4×C47C24
hypercenterC22×#102D47
hypocenterC47C2×#1893
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C23×C8×D47C2semidirect
3. C22×#13093945C2semidirect
4. C2×#15688980C2semidirect
5. #20243813C2direct (N × H)
6. C2×#15688886C2semidirect
7. C2×#15688885C2semidirect
8. C22×#102×C47C2semidirect
15. C22×C8×D47C22semidirect
18. C2×#13093995C4semidirect
25. C2×#13093945C22semidirect
27. #15688980C22semidirect
29. #15688886C22semidirect
30. #15688885C22semidirect
35. C2×#102×C47C22semidirect
54. C22×C47⋊C8D4semidirect
62. #13093995C2×C4semidirect
90. C22×C8×C47D4semidirect
171. C2×C8×C47C2×D4semidirect
186. C2×C47⋊C8C2×D4semidirect
220. C22×D47#102semidirect
296. C2×D47C2×#102semidirect
309. C22×#102D47semidirect
315. C2×C47#1893semidirect
345. C2×#102C2×D47semidirect
351. C47C2×#1893semidirect
389. C22×C8C22⋊D47semidirect
492. C2×C8C2×C22⋊D47semidirect
623. C2#20243813direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C8×D472
C22×#130939952
C22×#130939452
C2×#156889802
#202438132
C2×#156888862
C2×#156888852
C22×#102×C472
C2×#189347