Finite Group Databasebeta

← #26123844

Subgroups — #26123844

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689171C211yesmaximal, characteristic, complemented
2C2×#15689141C211yesmaximal, characteristic
3C22×#13093950C211yesmaximal, characteristic
4C2×#15689105C211yesmaximal, characteristic
5C2×#15688882C211yesmaximal, characteristic, complemented
6#20243081C211yesmaximal, characteristic, complemented
7C2×C47×#344C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×C4×Dic47C2211yescharacteristic
12#15689171—22no—
13#15689171—22no—
14C2×#13093959—22no—
15#15689141—22no—
16#15689141—22no—
17C2×#13093952—22no—
18C2×#13093950—22no—
19C2×#13093950—22no—
20C2×#13093950—22no—
21#15689105—22no—
22#15689105—22no—
23C2×#13093942C412yescomplemented
24C2×#13093940C412yescomplemented
25#15688882—22no—
26#15688877—22no—
27C22×M16×C47C2211yescharacteristic
28C22×M16×C47C2211yescharacteristic
29C2×#117×C47C2211yescharacteristic
30C47×#344—22no—
31C2×#10625350—21no—
32C2×#10625350—21no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350D412yes—
42C2×#10625350Q812yes—
43C22×Dic94C2×C411yescharacteristic
44C22×D188C2×C411yescharacteristic
45C22×C22⋊D47—21no—
46C23×Dic47—21no—
47C22×C4×D47—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329C2×C412yes—
57C2×#10625329D412yes—
58C2×#10625329D412yes—
59C2×#10625329D412yes—
60C22×C47⋊C8—21no—
61C22×C47⋊C8—21no—
62C2×C4×Dic47—21no—
63C2×C4×Dic47—21no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47—21no—
67C2×C4×Dic47D412yes—
68#13093959—28no—
69#13093952—28no—
70#13093950—28no—
71#13093942—24no—
72#13093940—24no—
73C23×C4×C47C2311yescharacteristic
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47—21no—
82C2×M16×C47—21no—
83C2×M16×C47—21no—
84C2×M16×C47C2×C412yes—
85C2×M16×C47D412yes—
86C22×C8×C47—21no—
87C22×C8×C47—21no—
88#117×C47—21no—
89#117×C47—21no—
90#117×C47—21no—
91#117×C47D412yes—
92C2×C4⋊C4×C47—21no—
93C2×C22⋊C4×C47—21no—
94C2×C42×C47—21no—
95C24×C47#4111yescharacteristic
96C23×D47—21no—
97C22×C4×C47—41no—
98C22×C4×C47C22×C411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×Q811yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C2×C22⋊D47—22no—
113C2×C22⋊D47—22no—
114C2×C22⋊D47—41no—
115C2×C22⋊D47—41no—
116C2×C22⋊D47—41no—
117C2×C22⋊D47—41no—
118C22×Dic47—21no—
119C22×Dic47—22no—
120C22×Dic47—44no—
121C22×Dic47—41no—
122C22×Dic47—41no—
123#10625350—22no—
124#10625350—22no—
125#10625350—22no—
126#10625350—22no—
127#10625350—22no—
128#10625350—22no—
129#10625350—22no—
130#10625350—22no—
131#10625350—41no—
132#10625350—41no—
133#10625350—41no—
134#10625350—41no—
135#10625350—41no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188C4⋊C412yes—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—41no—
148C2×C4×D47—41no—
149C2×C4×D47—41no—
150C2×C4×D47—41no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94C4⋊C412yes—
157M16×C47—22no—
158M16×C47—22no—
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—41no—
162M16×C47—41no—
163M16×C47—41no—
164M16×C47—41no—
165C2×C8×C47—22no—
166C2×C8×C47—22no—
167C2×C8×C47—41no—
168C2×C8×C47—41no—
169C2×C8×C47—41no—
170C2×C8×C47—41no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—41no—
173C22⋊C4×C47—22no—
174C22⋊C4×C47—41no—
175C42×C47—22no—
176C42×C47—41no—
177C4×Dic47—22no—
178C4×Dic47—22no—
179C4×Dic47—41no—
180C4×Dic47—41no—
181#10625329—22no—
182#10625329—22no—
183#10625329—22no—
184#10625329—22no—
185#10625329—22no—
186#10625329—41no—
187#10625329—41no—
188#10625329C22⋊C414yes—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C2×C47⋊C8—41no—
194C2×C47⋊C8—41no—
195C23×C47—42no—
196C23×C47#11711yescharacteristic
197C23×C47#12111yescharacteristic
198C23×C47C22⋊Q811yescharacteristic
199C23×C47#12311yescharacteristic
200C23×C47#12311yescharacteristic
201C23×C47#12411yescharacteristic
202C23×C47#12411yescharacteristic
203C22×D47—22no—
204C22×D47—41no—
205C22×D47—41no—
206C22×D47—82no—
207C2×C4×C47—42no—
208C2×C4×C47—82no—
209C2×C4×C47C2×C22⋊C411yescharacteristic
210C2×C4×C47C2×C4⋊C411yescharacteristic
211C2×C4×C47C4×D411yescharacteristic
212C2×C4×C47C4×D411yescharacteristic
213C2×C4×C47C4×D411yescharacteristic
214C2×C4×C47C4×D411yescharacteristic
215C2×C4×C47#12011yescharacteristic
216C2×C4×C47#12011yescharacteristic
217C2×C4×C47#12011yescharacteristic
218C2×C4×C47#12111yescharacteristic
219C2×C4×C47#12111yescharacteristic
220C2×C4×C47#12111yescharacteristic
221C2×C4×C47#12111yescharacteristic
222C2×C4×C47#12111yescharacteristic
223C2×C4×C47#12111yescharacteristic
224C2×C4×C47#12111yescharacteristic
225C2×C4×C47C22⋊Q811yescharacteristic
226C2×C4×C47C22⋊Q811yescharacteristic
227C2×C4×C47C22⋊Q811yescharacteristic
228C2×C4×C47C22⋊Q811yescharacteristic
229C2×C4×C47C22⋊Q811yescharacteristic
230C2×C4×C47#12311yescharacteristic
231C2×C4×C47#12311yescharacteristic
232C2×C4×C47#12311yescharacteristic
233C2×C4×C47#12411yescharacteristic
234C2×C4×C47#12611yescharacteristic
235C2×C4×C47#12611yescharacteristic
236C2×C4×C47#12711yescharacteristic
237C22⋊D47—42no—
238C22⋊D47—42no—
239C22⋊D47—42no—
240C22⋊D47—42no—
241C2×Dic47—24no—
242C2×Dic47—22no—
243C2×Dic47—42no—
244C2×Dic47—44no—
245C2×Dic47—44no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—42no—
249D188—22no—
250D188—22no—
251D188—41no—
252D188—41no—
253C4×D47—42no—
254C4×D47—42no—
255C4×D47—42no—
256C4×D47—42no—
257Dic94—22no—
258Dic94—22no—
259Dic94—41no—
260Dic94—41no—
261C8×C47—42no—
262C8×C47—42no—
263C47⋊C8—24no—
264C47⋊C8—42no—
265#11146—471nomaximal, Sylow
266C22×C47—22no—
267C22×C47—22no—
268C22×C47—22no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47#38011yescharacteristic
274C22×C47#38811yescharacteristic
275C22×C47#38811yescharacteristic
276C22×C47#39311yescharacteristic
277C22×C47#39411yescharacteristic
278C22×C47#39411yescharacteristic
279C22×C47#39911yescharacteristic
280C2×D47—42no—
281C2×D47—82no—
282C2×D47—82no—
283C2×D47—82no—
284C4×C47—82no—
285C4×C47#38511yescharacteristic
286C4×C47#38511yescharacteristic
287C4×C47#38611yescharacteristic
288C4×C47#39011yescharacteristic
289C4×C47#39211yescharacteristic
290C4×C47#39611yescharacteristic
291C4×C47#39611yescharacteristic
292C4×C47#39711yescharacteristic
293Dic47—44no—
294Dic47—42no—
295C2×#430—471no—
296C2×#421—471no—
297C22×#104—471no—
298C2×#413—471no—
299C2×#344D4711yescharacteristic, complemented
300C2×#339—471no—
301#1728—471no—
302C2×C47—21no—
303C2×C47—21no—
304C2×C47—21no—
305C2×C47—21no—
306C2×C47—21no—
307C2×C47—21no—
308C2×C47#143911yescharacteristic
309C2×C47#193212yes—
310D47—82no—
311C22×#41—471no—
312C22×M16—471no—
313C22×M16—471no—
314C22×M16C2×D4711yescharacteristic
315C22×M16C2×D4711yescharacteristic
316C2×#117C2×D4711yescharacteristic
317C22×C42—471no—
318#430—942no—
319#430—942no—
320C2×#108—942no—
321#421—942no—
322#421—942no—
323C2×#104—942no—
324C2×#104—942no—
325C2×#104—942no—
326C2×#104—942no—
327#413—942no—
328#413—942no—
329C2×#101—472no—
330C2×#100—472no—
331#344—22no—
332#339—942no—
333#336—942no—
334C47#1114611yescharacteristic, complemented, Sylow
335C2×#41—472no—
336C2×#41—472no—
337C2×#41—941no—
338C2×#41—941no—
339C2×#41—941no—
340C2×#41—941no—
341C2×#41—941no—
342C2×#41—941no—
343C2×#41—941no—
344C2×#41—941no—
345C2×#41—941no—
346C2×#41—941no—
347C22×Q8—471no—
348C22×D4—471no—
349C22×D4—941no—
350C23×C4—941no—
351C23×C4—941no—
352C23×C4C22×D4711yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—472no—
364C2×M16—472no—
365C2×M16—472no—
366C2×M16—472no—
367C2×M16—941no—
368C2×M16—941no—
369C2×M16—941no—
370C2×M16—941no—
371C2×M16—941no—
372C2×M16—941no—
373C2×M16—941no—
374C2×M16—941no—
375C2×M16C4×D4712yes—
376C2×M16D18812yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—941no—
380C22×C8—941no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117C22⋊D4712yes—
385C2×C4⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—21no—
388C2×C42—472no—
389C2×C42—941no—
390C2×C42—941no—
391C2×C42—941no—
392C2×C42—941no—
393C2×C42—941no—
394#108—948no—
395#104—948no—
396#104—948no—
397#101—944no—
398#100—944no—
399C24—941no—
400C24#1062535011yescharacteristic
401#41—942no—
402#41—942no—
403#41—942no—
404#41—942no—
405#41—942no—
406#41—942no—
407#41—942no—
408#41—942no—
409#41—1881no—
410#41—1881no—
411#41—1881no—
412#41—1881no—
413#41—1881no—
414#41—1881no—
415#41—1881no—
416#41—1881no—
417C2×Q8—472no—
418C2×Q8—941no—
419C2×Q8—941no—
420C2×Q8—941no—
421C2×Q8—941no—
422C2×Q8—941no—
423C2×D4—472no—
424C2×D4—942no—
425C2×D4—942no—
426C2×D4—941no—
427C2×D4—941no—
428C2×D4—941no—
429C2×D4—941no—
430C2×D4—941no—
431C2×D4—1881no—
432C2×D4—1881no—
433C2×D4—1881no—
434C2×D4—1881no—
435C22×C4—41no—
436C22×C4—941no—
437C22×C4—942no—
438C22×C4—942no—
439C22×C4—942no—
440C22×C4—1884no—
441C22×C4—1881no—
442C22×C4—1881no—
443C22×C4—1881no—
444C22×C4—1881no—
445C22×C4—1881no—
446C22×C4—1881no—
447C22×C4C2×C4×D4711yescharacteristic
448C22×C4C2×D18811yescharacteristic
449C22×C4#1062535011yescharacteristic
450C22×C4#1062535011yescharacteristic
451C22×C4#1062535011yescharacteristic
452C22×C4D4×D4711yescharacteristic
453C22×C4D4×D4711yescharacteristic
454C22×C4D4×D4711yescharacteristic
455C22×C4D4×D4711yescharacteristic
456C22×C4D4×D4711yescharacteristic
457C22×C4#1062535211yescharacteristic
458C22×C4Q8×D4711yescharacteristic
459C22×C4#1062535411yescharacteristic
460C22×C4C2×C22⋊D4711yescharacteristic
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—474no—
470M16—942no—
471M16—942no—
472M16—942no—
473M16—942no—
474M16—942no—
475M16—1881no—
476M16—1881no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—942no—
484C2×C8—942no—
485C2×C8—942no—
486C2×C8—942no—
487C2×C8—1881no—
488C2×C8—1881no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C22⋊C4—22no—
492C22⋊C4—41no—
493C42—22no—
494C42—41no—
495C42—942no—
496C42—942no—
497C42—1881no—
498C42—1881no—
499C23—42no—
500C23—942no—
501C23—3762no—
502C23—1881no—
503C23—1881no—
504C23#1309398111yescharacteristic
505C23#1309399711yescharacteristic
506C23#1309400211yescharacteristic
507C23#1309400711yescharacteristic
508C23#1309400911yescharacteristic
509C23#1309401011yescharacteristic
510C23#1309401211yescharacteristic
511Q8—942no—
512Q8—942no—
513Q8—1881no—
514Q8—1881no—
515D4—942no—
516D4—942no—
517D4—1882no—
518D4—1882no—
519D4—1882no—
520D4—1882no—
521D4—1881no—
522D4—1881no—
523C2×C4—42no—
524C2×C4—82no—
525C2×C4—944no—
526C2×C4—942no—
527C2×C4—1882no—
528C2×C4—1884no—
529C2×C4—1884no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1882no—
533C2×C4—1882no—
534C2×C4—1882no—
535C2×C4—1882no—
536C2×C4—1882no—
537C2×C4C22⋊C4×D4711yescharacteristic
538C2×C4C4⋊C4×D4711yescharacteristic
539C2×C4(C22⋊D47)⋊C411yescharacteristic
540C2×C4C4×C22⋊D4711yescharacteristic
541C2×C4#1309398611yescharacteristic
542C2×C4C4×D18811yescharacteristic
543C2×C4#1309399211yescharacteristic
544C2×C4#1309399411yescharacteristic
545C2×C4#1309399411yescharacteristic
546C2×C4#1309399611yescharacteristic
547C2×C4#1309399711yescharacteristic
548C2×C4#1309399711yescharacteristic
549C2×C4#1309399711yescharacteristic
550C2×C4#1309399711yescharacteristic
551C2×C4#1309399811yescharacteristic
552C2×C4#1309399911yescharacteristic
553C2×C4#1309400011yescharacteristic
554C2×C4#1309400211yescharacteristic
555C2×C4#1309400211yescharacteristic
556C2×C4#1309400211yescharacteristic
557C2×C4#1309400411yescharacteristic
558C2×C4#1309400611yescharacteristic
559C2×C4#1309400911yescharacteristic
560C2×C4#1309400911yescharacteristic
561C2×C4#1309401011yescharacteristic
562C2×C4#1309401811yescharacteristic
563C2×C4#1309401911yescharacteristic
564C2×C4#1309402011yescharacteristic
565C8—42no—
566C8—42no—
567C8—944no—
568C8—1882no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—3762no—
577C22—3762no—
578C22—3762no—
579C22—1882no—
580C22#1568898211yescharacteristic
581C22#1568901211yescharacteristic
582C22#1568901411yescharacteristic
583C22#1568903611yescharacteristic
584C22#1568903811yescharacteristic
585C22#1568904111yescharacteristic
586C22#1568905811yescharacteristic
587C4—82no—
588C4—1884no—
589C4—1882no—
590C4#1568899411yescharacteristic
591C4#1568899711yescharacteristic
592C4#1568900111yescharacteristic
593C4#1568902311yescharacteristic
594C4#1568903211yescharacteristic
595C4#1568904511yescharacteristic
596C4#1568904711yescharacteristic
597C4#1568905211yescharacteristic
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—3762no—
605C2#2024163211yescharacteristic
606C2#2024405512yes—
subgroupG/H
centerC2×C4#13093997
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#344C2
socleC22×C47#388
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#344D47
hypocenterC47#11146
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#15689171C2semidirect
5. C2×#15688882C2semidirect
6. #20243081C2semidirect
7. C2×C47×#344C2semidirect
23. C2×#13093942C4semidirect
24. C2×#13093940C4semidirect
299. C2×#344D47semidirect
334. C47#11146semidirect

Maximal subgroups

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

subgroupindex
C2×#156891712
C2×#156891412
C22×#130939502
C2×#156891052
C2×#156888822
#202430812
C2×C47×#3442
#1114647