Finite Group Databasebeta

← C2×#20249103 #26382607

Subgroups — C2×#20249103 #26382607

Order 12032.

7946 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C22⋊D47C211yesmaximal, characteristic, complemented
2C22×#13094008C211yesmaximal, characteristic, complemented
3C22×#13093994C211yesmaximal, characteristic, complemented
4C22×#13093993C211yesmaximal, characteristic, complemented
5#20249103C2116yesmaximal, direct product factor
6C2×#15689039C214yesmaximal, complemented
7C2×#15689032C214yesmaximal, complemented
8C2×#15688984C211yesmaximal, characteristic, complemented
9C2×#15688978C211yesmaximal, characteristic, complemented
10C2×C47×#379C211yesmaximal, characteristic, complemented
11C25×D47C2211yescharacteristic
12C23×D188C2212yescomplemented
13C23×C22⋊D47—28no—
14C23×C22⋊D47—28no—
15C23×C22⋊D47—28no—
16C23×C22⋊D47C2214yes—
17C23×C22⋊D47C2211yescharacteristic
18C23×C22⋊D47C2218yescomplemented
19C23×C22⋊D47C2212yescomplemented
20C24×Dic47C2211yescharacteristic
21C2×#13094008—28no—
22C2×#13094008C2218yescomplemented
23C2×#13093994—28no—
24C2×#13093994C2218yescomplemented
25C2×#13093993—28no—
26C2×#13093993C2218yescomplemented
27C22×C4⋊Dic47C2212yescomplemented
28C22×C22⋊Dic47C2211yescharacteristic
29C22×C22⋊Dic47C2212yescomplemented
30C22×(C2×D47)⋊C4C2212yescomplemented
31C22×(C2×D47)⋊C4C2212yescomplemented
32C22×(C2×D47)⋊C4C2214yescomplemented
33#15689039C22132yescomplemented
34#15689032C22132yescomplemented
35#15688984C2218yescomplemented
36#15688978C2218yescomplemented
37C2×C47⋊#95C2214yescomplemented
38C26×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C22×C22⋊C4×C47C2211yescharacteristic
41C22×C22⋊C4×C47C2214yescomplemented
42C47×#379C2218yescomplemented
43C24×D47—24no—
44C24×D47—24no—
45C24×D47—48no—
46C24×D47D418yescomplemented
47C24×D47C2311yescharacteristic
48C24×D47C2312yes—
49C24×D47C2314yes—
50C22×D188—28no—
51C22×D188—48no—
52C22×D188C2318yescomplemented
53C22×C22⋊D47—2128no—
54C22×C22⋊D47—216no—
55C22×C22⋊D47—232no—
56C22×C22⋊D47—216no—
57C22×C22⋊D47—232no—
58C22×C22⋊D47—24no—
59C22×C22⋊D47—28no—
60C22×C22⋊D47—24no—
61C22×C22⋊D47—24no—
62C22×C22⋊D47—216no—
63C22×C22⋊D47—232no—
64C22×C22⋊D47—48no—
65C22×C22⋊D47C23116yes—
66C22×C22⋊D47C2314yes—
67C22×C22⋊D47C2318yescomplemented
68C23×Dic47—24no—
69C23×Dic47—24no—
70C23×Dic47D418yescomplemented
71C23×Dic47C2312yes—
72C23×Dic47C2311yescharacteristic
73C23×Dic47C2312yes—
74C23×Dic47C2314yes—
75#13094008—232no—
76#13093994—232no—
77#13093993—232no—
78C2×C4⋊Dic47—28no—
79C2×C4⋊Dic47C2318yescomplemented
80C2×C22⋊Dic47—24no—
81C2×C22⋊Dic47—28no—
82C2×C22⋊Dic47C2314yes—
83C2×C22⋊Dic47C2318yescomplemented
84C2×(C2×D47)⋊C4—28no—
85C2×(C2×D47)⋊C4—28no—
86C2×(C2×D47)⋊C4—48no—
87C2×(C2×D47)⋊C4C2318yescomplemented
88C2×(C2×D47)⋊C4C2318yescomplemented
89C2×(C2×D47)⋊C4C23116yescomplemented
90C47⋊#95C23116yescomplemented
91C25×C47—24no—
92C25×C47—24no—
93C25×C47—48no—
94C25×C47D418yescomplemented
95C25×C47C2312yes—
96C25×C47C2311yescharacteristic
97C25×C47C2314yes—
98C23×C4×C47C2312yes—
99C23×C4×C47C2312yes—
100C2×C22⋊C4×C47—24no—
101C2×C22⋊C4×C47—24no—
102C2×C22⋊C4×C47—48no—
103C2×C22⋊C4×C47C2314yes—
104C2×C22⋊C4×C47C2314yes—
105C2×C22⋊C4×C47C23116yescomplemented
106C24×C47—28no—
107C24×C47—232no—
108C24×C47—24no—
109C24×C47—24no—
110C24×C47—28no—
111C24×C47—28no—
112C24×C47—28no—
113C24×C47—28no—
114C24×C47—432no—
115C24×C47—416no—
116C24×C47—432no—
117C24×C47—432no—
118C24×C47C2×D418yes—
119C24×C47C2×D414yes—
120C24×C47C2×D414yes—
121C24×C47C2×D414yes—
122C24×C47C2×D4116yescomplemented
123C24×C47C2414yes—
124C24×C47C2412yes—
125C24×C47C2411yescharacteristic
126C23×D47—232no—
127C23×D47—24no—
128C23×D47—24no—
129C23×D47—28no—
130C23×D47—28no—
131C23×D47—28no—
132C23×D47—28no—
133C23×D47—22no—
134C23×D47—22no—
135C23×D47—22no—
136C23×D47—28no—
137C23×D47—432no—
138C23×D47—416no—
139C23×D47—432no—
140C23×D47—432no—
141C23×D47C2×D418yes—
142C23×D47C2×D4116yescomplemented
143C23×D47C2412yes—
144C23×D47C2414yes—
145C22×C4×C47—24no—
146C22×C4×C47—24no—
147C22×C4×C47—28no—
148C22×C4×C47—28no—
149C22×C4×C47C2414yes—
150C22×C4×C47C2414yes—
151C2×C22⋊D47—2128no—
152C2×C22⋊D47—2256no—
153C2×C22⋊D47—232no—
154C2×C22⋊D47—232no—
155C2×C22⋊D47—28no—
156C2×C22⋊D47—216no—
157C2×C22⋊D47—28no—
158C2×C22⋊D47—28no—
159C2×C22⋊D47—232no—
160C2×C22⋊D47—416no—
161C2×C22⋊D47—432no—
162C2×C22⋊D47—416no—
163C22×Dic47—232no—
164C22×Dic47—24no—
165C22×Dic47—24no—
166C22×Dic47—28no—
167C22×Dic47—28no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—24no—
171C22×Dic47—22no—
172C22×Dic47—28no—
173C22×Dic47C2×D418yes—
174C22×Dic47C2×D4116yescomplemented
175C22×Dic47C2414yes—
176C22×Dic47C2412yes—
177C22×Dic47C2414yes—
178C2×D188—216no—
179C2×D188—416no—
180C2×D188—432no—
181C22⋊C4×C47—28no—
182C22⋊C4×C47—28no—
183C22⋊C4×C47—416no—
184C22⋊Dic47—28no—
185C22⋊Dic47—216no—
186(C2×D47)⋊C4—216no—
187(C2×D47)⋊C4—216no—
188(C2×D47)⋊C4—416no—
189C4⋊Dic47—216no—
190C23×C47—216no—
191C23×C47—216no—
192C23×C47—216no—
193C23×C47—28no—
194C23×C47—216no—
195C23×C47—232no—
196C23×C47—216no—
197C23×C47—216no—
198C23×C47—24no—
199C23×C47—24no—
200C23×C47—28no—
201C23×C47—28no—
202C23×C47—432no—
203C23×C47—4128no—
204C23×C47—432no—
205C23×C47—432no—
206C23×C47—416no—
207C23×C47—416no—
208C23×C47#120116yes—
209C23×C47C22×D414yes—
210C23×C47C22×D414yes—
211C23×C47C22×D412yes—
212C23×C47C22×D412yes—
213C23×C47C22×D418yes—
214C23×C47C22×D414yes—
215C23×C47C22×D412yes—
216C23×C47H(5,𝔽2)18yes—
217C23×C47C2511yescharacteristic
218C22×D47—216no—
219C22×D47—232no—
220C22×D47—216no—
221C22×D47—216no—
222C22×D47—24no—
223C22×D47—24no—
224C22×D47—28no—
225C22×D47—28no—
226C22×D47—22no—
227C22×D47—22no—
228C22×D47—22no—
229C22×D47—28no—
230C22×D47—432no—
231C22×D47—4128no—
232C22×D47—432no—
233C22×D47—432no—
234C22×D47—416no—
235C22×D47—416no—
236C22×D47—44no—
237C22×D47—48no—
238C22×D47—48no—
239C22×D47—48no—
240C22×D47C22×D418yes—
241C2×C4×C47—24no—
242C2×C4×C47—24no—
243C2×C4×C47—28no—
244C2×C4×C47—28no—
245C2×C4×C47—48no—
246C2×C4×C47—48no—
247C22⋊D47—2128no—
248C22⋊D47—432no—
249C22⋊D47—416no—
250C2×Dic47—216no—
251C2×Dic47—232no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—22no—
257C2×Dic47—24no—
258C2×Dic47—28no—
259C2×Dic47—44no—
260C2×Dic47—48no—
261C2×Dic47C22×D418yes—
262D188—432no—
263C2×#2613—471nomaximal, Sylow
264C22×C47—232no—
265C22×C47—28no—
266C22×C47—28no—
267C22×C47—28no—
268C22×C47—28no—
269C22×C47—28no—
270C22×C47—28no—
271C22×C47—464no—
272C22×C47—432no—
273C22×C47—48no—
274C22×C47—48no—
275C22×C47C2×#12018yes—
276C22×C47C2×#12014yes—
277C22×C47#53418yes—
278C22×C47#53418yes—
279C22×C47#53518yes—
280C22×C47C23×D411yescharacteristic
281C22×C47C23×D411yescharacteristic
282C22×C47C23×D411yescharacteristic
283C22×C47C2×H(5,𝔽2)14yes—
284C2×D47—28no—
285C2×D47—28no—
286C2×D47—28no—
287C2×D47—464no—
288C2×D47—432no—
289C2×D47—48no—
290C2×D47—48no—
291C2×D47—42no—
292C2×D47—44no—
293C2×D47—44no—
294C2×D47—44no—
295C2×D47—88no—
296C4×C47—44no—
297C4×C47—44no—
298Dic47—28no—
299Dic47—42no—
300Dic47—44no—
301C24×D4—471no—
302C22×#123—471no—
303C22×#120—471no—
304C22×#120—471no—
305#2613—4716no—
306C2×#394—474no—
307C2×#392—474no—
308C2×#381—471no—
309C2×#379—471no—
310C2×#379D4711yescharacteristic, complemented
311C2×C47—28no—
312C2×C47—48no—
313C2×C47#261318yescomplemented
314C2×C47C22×#12011yescharacteristic
315C2×C47C2×#53412yes—
316C2×C47C2×#53412yes—
317C2×C47C2×#53512yes—
318D47—48no—
319D47—82no—
320C26—471no—
321C26C2×D4711yescharacteristic
322C23×D4—478no—
323C23×D4—474no—
324C23×D4—471no—
325C23×D4—472no—
326C23×D4—472no—
327C23×D4—948no—
328C23×D4—948no—
329C23×D4—948no—
330C24×C4—471no—
331C2×#123—478no—
332C2×#123—948no—
333C2×#120—478no—
334C2×#120—478no—
335C2×#120—948no—
336C2×#120—948no—
337C22×C4⋊C4—472no—
338C22×C22⋊C4—472no—
339C22×C22⋊C4—471no—
340C22×C22⋊C4—472no—
341C22×C22⋊C4—472no—
342C22×C22⋊C4—474no—
343C22×C22⋊C4C2×D4711yescharacteristic
344C22×C22⋊C4C2×D4711yescharacteristic
345C22×C22⋊C4C2×D4714yescomplemented
346#394—4732no—
347#392—4732no—
348#381—478no—
349#379—478no—
350#379C2×D4718yescomplemented
351C2×#95—474no—
352C47C2×#261311yescharacteristic, complemented, Sylow
353C25—24no—
354C25—24no—
355C25—48no—
356C25—472no—
357C25—478no—
358C25—474no—
359C25—471no—
360C25—944no—
361C25—944no—
362C25—1888no—
363C25D18818yescomplemented
364C25C22×D4712yes—
365C25C22×D4711yescharacteristic
366C25C22×D4714yes—
367C22×D4—474no—
368C22×D4—4716no—
369C22×D4—478no—
370C22×D4—478no—
371C22×D4—948no—
372C22×D4—9416no—
373C22×D4—9432no—
374C22×D4—9416no—
375C22×D4—9432no—
376C22×D4—94128no—
377C22×D4—9416no—
378C22×D4—9432no—
379C22×D4—948no—
380C22×D4—944no—
381C22×D4—944no—
382C22×D4—944no—
383C22×D4—1888no—
384C22×D4—1888no—
385C23×C4—478no—
386C23×C4—474no—
387C23×C4—472no—
388C23×C4—471no—
389C23×C4—472no—
390C23×C4—944no—
391C23×C4—944no—
392C23×C4C22×D4712yes—
393C23×C4C22×D4712yes—
394#123—9432no—
395#120—9432no—
396#120—9432no—
397C2×C4⋊C4—478no—
398C2×C4⋊C4—948no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—48no—
402C2×C22⋊C4—474no—
403C2×C22⋊C4—478no—
404C2×C22⋊C4—478no—
405C2×C22⋊C4—478no—
406C2×C22⋊C4—4716no—
407C2×C22⋊C4—948no—
408C2×C22⋊C4—948no—
409C2×C22⋊C4—948no—
410C2×C22⋊C4—944no—
411C2×C22⋊C4—1888no—
412C2×C22⋊C4C22×D4714yes—
413C2×C22⋊C4C22×D4714yes—
414C2×C22⋊C4C22×D47116yescomplemented
415#95—4716no—
416C24—28no—
417C24—232no—
418C24—24no—
419C24—24no—
420C24—28no—
421C24—28no—
422C24—28no—
423C24—28no—
424C24—432no—
425C24—416no—
426C24—432no—
427C24—432no—
428C24—478no—
429C24—474no—
430C24—4716no—
431C24—472no—
432C24—9432no—
433C24—948no—
434C24—944no—
435C24—948no—
436C24—944no—
437C24—948no—
438C24—948no—
439C24—942no—
440C24—942no—
441C24—942no—
442C24—948no—
443C24—18832no—
444C24—18816no—
445C24—18832no—
446C24—18832no—
447C24C2×D18818yes—
448C24C2×D18814yes—
449C24C2×D188116yescomplemented
450C24D4×D4714yes—
451C24D4×D4714yes—
452C24C23×D4714yes—
453C24C23×D4712yes—
454C24C23×D4711yescharacteristic
455C2×D4—9416no—
456C2×D4—9432no—
457C2×D4—9432no—
458C2×D4—94128no—
459C2×D4—94256no—
460C2×D4—9432no—
461C2×D4—948no—
462C2×D4—948no—
463C2×D4—9416no—
464C2×D4—948no—
465C2×D4—18816no—
466C2×D4—18832no—
467C2×D4—18816no—
468C2×D4—18832no—
469C2×D4—18816no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—478no—
475C22×C4—4716no—
476C22×C4—474no—
477C22×C4—474no—
478C22×C4—472no—
479C22×C4—9432no—
480C22×C4—948no—
481C22×C4—944no—
482C22×C4—948no—
483C22×C4—944no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—944no—
488C22×C4—948no—
489C22×C4C23×D4714yes—
490C22×C4C23×D4714yes—
491C4⋊C4—9416no—
492C22⋊C4—28no—
493C22⋊C4—28no—
494C22⋊C4—416no—
495C22⋊C4—9416no—
496C22⋊C4—9416no—
497C22⋊C4—9416no—
498C22⋊C4—948no—
499C22⋊C4—18816no—
500C23—216no—
501C23—216no—
502C23—216no—
503C23—28no—
504C23—216no—
505C23—232no—
506C23—216no—
507C23—216no—
508C23—24no—
509C23—24no—
510C23—28no—
511C23—28no—
512C23—432no—
513C23—4128no—
514C23—432no—
515C23—432no—
516C23—416no—
517C23—416no—
518C23—478no—
519C23—9432no—
520C23—9416no—
521C23—9416no—
522C23—9416no—
523C23—944no—
524C23—944no—
525C23—948no—
526C23—948no—
527C23—942no—
528C23—942no—
529C23—942no—
530C23—948no—
531C23—18832no—
532C23—188128no—
533C23—18832no—
534C23—18832no—
535C23—1884no—
536C23—1888no—
537C23—1888no—
538C23—1888no—
539C23—18816no—
540C23—18816no—
541C23#13093994116yes—
542C23C2×D4×D4714yes—
543C23C2×D4×D4714yes—
544C23C2×D4×D4712yes—
545C23C2×D4×D4712yes—
546C23C22×D18818yes—
547C23C22×D18814yes—
548C23C22×D18812yes—
549C23#1309406918yes—
550C23C24×D4711yescharacteristic
551D4—94128no—
552D4—18832no—
553D4—18832no—
554D4—18816no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—28no—
558C2×C4—28no—
559C2×C4—48no—
560C2×C4—48no—
561C2×C4—478no—
562C2×C4—9432no—
563C2×C4—9416no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—942no—
569C2×C4—944no—
570C2×C4—948no—
571C2×C4—1884no—
572C2×C4—1888no—
573C22—232no—
574C22—28no—
575C22—28no—
576C22—28no—
577C22—28no—
578C22—28no—
579C22—28no—
580C22—464no—
581C22—432no—
582C22—48no—
583C22—48no—
584C22—948no—
585C22—948no—
586C22—948no—
587C22—3768no—
588C22—18864no—
589C22—1882no—
590C22—1884no—
591C22—1884no—
592C22—1884no—
593C22—18832no—
594C22—1888no—
595C22—1888no—
596C22C2×#1309399418yes—
597C22C2×#1309399414yes—
598C22#1568968318yes—
599C22#1568968518yes—
600C22#1568968818yes—
601C22C22×D4×D4711yescharacteristic
602C22C22×D4×D4711yescharacteristic
603C22C23×D18811yescharacteristic
604C22C2×#1309406914yes—
605C4—44no—
606C4—44no—
607C4—948no—
608C4—1882no—
609C4—1884no—
610C2—28no—
611C2—48no—
612C2—3762no—
613C2—1888no—
614C2#2024910318yesdirect product factor
615C2C22×#1309399411yescharacteristic
616C2C2×#1568968312yes—
617C2C2×#1568968512yes—
618C2C2×#1568968812yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#379C2
socleC24×C47C24
hypercenterC2×#379D47
hypocenterC47C2×#2613
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C24×C22⋊D47C2semidirect
2. C22×#13094008C2semidirect
3. C22×#13093994C2semidirect
4. C22×#13093993C2semidirect
5. #20249103C2direct (N × H)
6. C2×#15689039C2semidirect
7. C2×#15689032C2semidirect
8. C2×#15688984C2semidirect
9. C2×#15688978C2semidirect
10. C2×C47×#379C2semidirect
12. C23×D188C22semidirect
18. C23×C22⋊D47C22semidirect
19. C23×C22⋊D47C22semidirect
22. C2×#13094008C22semidirect
24. C2×#13093994C22semidirect
26. C2×#13093993C22semidirect
27. C22×C4⋊Dic47C22semidirect
29. C22×C22⋊Dic47C22semidirect
30. C22×(C2×D47)⋊C4C22semidirect
31. C22×(C2×D47)⋊C4C22semidirect
32. C22×(C2×D47)⋊C4C22semidirect
33. #15689039C22semidirect
34. #15689032C22semidirect
35. #15688984C22semidirect
36. #15688978C22semidirect
37. C2×C47⋊#95C22semidirect
41. C22×C22⋊C4×C47C22semidirect
42. C47×#379C22semidirect
46. C24×D47D4semidirect
52. C22×D188C23semidirect
67. C22×C22⋊D47C23semidirect
70. C23×Dic47D4semidirect
79. C2×C4⋊Dic47C23semidirect
83. C2×C22⋊Dic47C23semidirect
87. C2×(C2×D47)⋊C4C23semidirect
88. C2×(C2×D47)⋊C4C23semidirect
89. C2×(C2×D47)⋊C4C23semidirect
90. C47⋊#95C23semidirect
94. C25×C47D4semidirect
105. C2×C22⋊C4×C47C23semidirect
122. C24×C47C2×D4semidirect
142. C23×D47C2×D4semidirect
174. C22×Dic47C2×D4semidirect
310. C2×#379D47semidirect
313. C2×C47#2613semidirect
345. C22×C22⋊C4C2×D47semidirect
350. #379C2×D47semidirect
352. C47C2×#2613semidirect
363. C25D188semidirect
414. C2×C22⋊C4C22×D47semidirect
449. C24C2×D188semidirect
614. C2#20249103direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C22⋊D472
C22×#130940082
C22×#130939942
C22×#130939932
#202491032
C2×#156890392
C2×#156890322
C2×#156889842
C2×#156889782
C2×C47×#3792
C2×#261347