Finite Group Databasebeta

← #26123559

Subgroups — #26123559

Order 12032.

836 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689171C211yesmaximal, characteristic, complemented
2C2×#15689105C211yesmaximal, characteristic
3C2×#15689105C211yesmaximal, characteristic
4#20251832C211yesmaximal, characteristic
5#20243114C211yesmaximal, characteristic, complemented
6C2×C47⋊#338C211yesmaximal, characteristic, complemented
7C47×#1738C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12#15689171—22no—
13#15689171—22no—
14C2×#13093959—22no—
15#15689105—22no—
16#15689105—22no—
17#15689105—22no—
18#15689105—22no—
19C2×#13093942—21no—
20C2×#13093942—21no—
21C2×#13093940—21no—
22C2×#13093940—21no—
23#15689091—22no—
24#15689089—22no—
25#15689086C414yes—
26#15688887—22no—
27C47⋊#338—22no—
28C22×M16×C47C2211yescharacteristic
29C22×M16×C47C2211yescharacteristic
30C22×M16×C47C2211yescharacteristic
31C47×#341—22no—
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×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C22×Dic94D411yescharacteristic
45C22×D188D411yescharacteristic
46C22×C22⋊D47Q812yes—
47C22×C4×D47C2×C412yes—
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×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329C2×C412yes—
63C2×#10625329D412yes—
64C2×#10625329D412yes—
65C2×#10625329D412yes—
66C22×C47⋊C8—21no—
67C22×C47⋊C8—21no—
68C22×C47⋊C8D412yes—
69#13093959—28no—
70#13093942—24no—
71#13093942—24no—
72#13093940—24no—
73#13093940—24no—
74(C2×D47)⋊C8—28no—
75C23×C4×C47C2311yescharacteristic
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×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47C2×C412yes—
92C2×M16×C47D412yes—
93C2×M16×C47D412yes—
94C22×C8×C47—21no—
95C22×C8×C47—21no—
96C22×C8×C47—21no—
97C24×C47C2×Q811yescharacteristic
98C23×D47C4⋊C412yes—
99C22×C4×C47C22×C411yescharacteristic
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×D411yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C2×C22⋊D47—22no—
114C2×C22⋊D47—22no—
115C2×C22⋊D47—22no—
116C2×C22⋊D47—22no—
117C2×C22⋊D47—22no—
118C2×C22⋊D47—22no—
119C22×Dic47C4⋊C412yes—
120#10625350—41no—
121#10625350—41no—
122#10625350—41no—
123#10625350—41no—
124#10625350—41no—
125#10625350—41no—
126#10625350—41no—
127#10625350—41no—
128#10625350—41no—
129#10625350—41no—
130#10625350—41no—
131#10625350—41no—
132#10625350—41no—
133#10625350—41no—
134#10625350—41no—
135#10625350—41no—
136C2×D188—21no—
137C2×D188—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×C4×D47—22no—
143C2×C4×D47—22no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×Dic94—21no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154M16×C47—22no—
155M16×C47—22no—
156M16×C47—22no—
157M16×C47—22no—
158M16×C47—22no—
159M16×C47—22no—
160M16×C47—41no—
161M16×C47—41no—
162M16×C47—41no—
163M16×C47—41no—
164M16×C47—41no—
165M16×C47—41no—
166C2×C8×C47—22no—
167C2×C8×C47—22no—
168C2×C8×C47—22no—
169C2×C8×C47—41no—
170C2×C8×C47—41no—
171C2×C8×C47—41no—
172C2×C8×C47—41no—
173C2×C8×C47—41no—
174C2×C8×C47—41no—
175#10625329—22no—
176#10625329—22no—
177#10625329—22no—
178#10625329—22no—
179#10625329—22no—
180#10625329—22no—
181#10625329—22no—
182#10625329—22no—
183#10625329—41no—
184#10625329—41no—
185#10625329—41no—
186#10625329—41no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—41no—
192C2×C47⋊C8—41no—
193C2×C47⋊C8—41no—
194C2×C47⋊C8—41no—
195C2×C47⋊C8C22⋊C414yes—
196C23×C47—81no—
197C23×C47C2×C4⋊C411yescharacteristic
198C23×C47C22⋊Q811yescharacteristic
199C23×C47C22⋊Q811yescharacteristic
200C23×C47C22⋊Q811yescharacteristic
201C23×C47C22⋊Q811yescharacteristic
202C23×C47C22⋊Q811yescharacteristic
203C23×C47C22⋊Q811yescharacteristic
204C22×D47—22no—
205C22×D47—22no—
206C22×D47—22no—
207C22×D47—82no—
208C2×C4×C47C2×C22⋊C411yescharacteristic
209C2×C4×C47#11711yescharacteristic
210C2×C4×C47C4×D411yescharacteristic
211C2×C4×C47C4×D411yescharacteristic
212C2×C4×C47C4×D411yescharacteristic
213C2×C4×C47C4×D411yescharacteristic
214C2×C4×C47#12011yescharacteristic
215C2×C4×C47#12011yescharacteristic
216C2×C4×C47#12011yescharacteristic
217C2×C4×C47#12111yescharacteristic
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×C47#12311yescharacteristic
226C2×C4×C47#12311yescharacteristic
227C2×C4×C47#12311yescharacteristic
228C2×C4×C47#12311yescharacteristic
229C2×C4×C47#12311yescharacteristic
230C2×C4×C47#12411yescharacteristic
231C2×C4×C47#12411yescharacteristic
232C2×C4×C47#12411yescharacteristic
233C2×C4×C47#12611yescharacteristic
234C2×C4×C47#12611yescharacteristic
235C2×C4×C47#12711yescharacteristic
236C22⋊D47—42no—
237C22⋊D47—42no—
238C22⋊D47—42no—
239C22⋊D47—42no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243D188—41no—
244D188—41no—
245D188—41no—
246D188—41no—
247C4×D47—42no—
248C4×D47—42no—
249C4×D47—42no—
250C4×D47—42no—
251Dic94—41no—
252Dic94—41no—
253Dic94—41no—
254Dic94—41no—
255C8×C47—42no—
256C8×C47—42no—
257C8×C47—42no—
258C47⋊C8—24no—
259C47⋊C8—42no—
260C47⋊C8—42no—
261#11103—471nomaximal, Sylow
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47—41no—
268C22×C47—41no—
269C22×C47#38011yescharacteristic
270C22×C47#38511yescharacteristic
271C22×C47#38511yescharacteristic
272C22×C47#39311yescharacteristic
273C22×C47#39611yescharacteristic
274C22×C47#39611yescharacteristic
275C22×C47#39911yescharacteristic
276C2×D47—44no—
277C2×D47—42no—
278C2×D47—82no—
279C2×D47—82no—
280C4×C47#38611yescharacteristic
281C4×C47#38811yescharacteristic
282C4×C47#38811yescharacteristic
283C4×C47#39011yescharacteristic
284C4×C47#39211yescharacteristic
285C4×C47#39411yescharacteristic
286C4×C47#39411yescharacteristic
287C4×C47#39711yescharacteristic
288Dic47—42no—
289C2×#430—471no—
290C2×#413—471no—
291C2×#413—471no—
292#2879—471no—
293#1738—471no—
294#1738D4711yescharacteristic, complemented
295C2×#338—471no—
296C2×C47—21no—
297C2×C47—21no—
298C2×C47—21no—
299C2×C47—21no—
300C2×C47—21no—
301C2×C47—21no—
302C2×C47—21no—
303C2×C47#143911yescharacteristic
304D47—82no—
305C22×#41—471no—
306C22×M16—471no—
307C22×M16—471no—
308C22×M16—471no—
309C22×M16C2×D4711yescharacteristic
310C22×M16C2×D4711yescharacteristic
311C22×M16C2×D4711yescharacteristic
312#430—942no—
313#430—942no—
314C2×#108—942no—
315#413—942no—
316#413—942no—
317#413—942no—
318#413—942no—
319C2×#101—941no—
320C2×#101—941no—
321C2×#100—941no—
322C2×#100—941no—
323#408—942no—
324#408—942no—
325#407—474no—
326#341—22no—
327#341—942no—
328#338—942no—
329C47#1110311yescharacteristic, complemented, Sylow
330C2×#41—941no—
331C2×#41—941no—
332C2×#41—941no—
333C2×#41—941no—
334C2×#41—941no—
335C2×#41—941no—
336C2×#41—941no—
337C2×#41—941no—
338C2×#41—941no—
339C2×#41—941no—
340C2×#41—941no—
341C2×#41—941no—
342C22×Q8—471no—
343C22×D4—472no—
344C22×D4—471no—
345C23×C4—472no—
346C23×C4C22×D4711yescharacteristic
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
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—472no—
363C2×M16—472no—
364C2×M16—472no—
365C2×M16—472no—
366C2×M16—941no—
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×M16—941no—
376C2×M16—941no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—941no—
380C2×M16C4×D4712yes—
381C2×M16D18812yes—
382C2×M16C22⋊D4712yes—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—472no—
387C22×C8—941no—
388C22×C8—941no—
389#108—948no—
390#101—944no—
391#101—944no—
392#100—944no—
393#100—944no—
394C22⋊C8—948no—
395C24—472no—
396C24Q8×D4711yescharacteristic
397#41—1881no—
398#41—1881no—
399#41—1881no—
400#41—1881no—
401#41—1881no—
402#41—1881no—
403#41—1881no—
404#41—1881no—
405#41—1881no—
406#41—1881no—
407#41—1881no—
408#41—1881no—
409#41—1881no—
410#41—1881no—
411#41—1881no—
412#41—1881no—
413C2×Q8—941no—
414C2×Q8—941no—
415C2×Q8—941no—
416C2×Q8—941no—
417C2×Q8—941no—
418C2×Q8—941no—
419C2×D4—942no—
420C2×D4—942no—
421C2×D4—942no—
422C2×D4—942no—
423C2×D4—942no—
424C2×D4—942no—
425C2×D4—941no—
426C2×D4—941no—
427C2×D4—941no—
428C2×D4—941no—
429C2×D4—941no—
430C2×D4—941no—
431C22×C4—472no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4C2×C4×D4711yescharacteristic
439C22×C4C2×D18811yescharacteristic
440C22×C4#1062535011yescharacteristic
441C22×C4#1062535011yescharacteristic
442C22×C4#1062535011yescharacteristic
443C22×C4#1062535011yescharacteristic
444C22×C4D4×D4711yescharacteristic
445C22×C4D4×D4711yescharacteristic
446C22×C4D4×D4711yescharacteristic
447C22×C4D4×D4711yescharacteristic
448C22×C4D4×D4711yescharacteristic
449C22×C4#1062535211yescharacteristic
450C22×C4#1062535411yescharacteristic
451C22×C4C2×C22⋊D4711yescharacteristic
452M16—22no—
453M16—22no—
454M16—22no—
455M16—22no—
456M16—22no—
457M16—22no—
458M16—41no—
459M16—41no—
460M16—41no—
461M16—41no—
462M16—41no—
463M16—41no—
464M16—942no—
465M16—942no—
466M16—942no—
467M16—942no—
468M16—942no—
469M16—942no—
470M16—942no—
471M16—942no—
472M16—1881no—
473M16—1881no—
474M16—1881no—
475M16—1881no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—474no—
486C2×C8—942no—
487C2×C8—942no—
488C2×C8—942no—
489C2×C8—942no—
490C2×C8—1881no—
491C2×C8—1881no—
492C2×C8—1881no—
493C2×C8—1881no—
494C23—81no—
495C23—942no—
496C23—942no—
497C23—942no—
498C23—3762no—
499C23C4⋊C4×D4711yescharacteristic
500C23#1309400011yescharacteristic
501C23#1309400211yescharacteristic
502C23#1309400211yescharacteristic
503C23#1309400211yescharacteristic
504C23#1309400211yescharacteristic
505C23#1309400411yescharacteristic
506Q8—1881no—
507Q8—1881no—
508Q8—1881no—
509Q8—1881no—
510D4—1882no—
511D4—1882no—
512D4—1882no—
513D4—1882no—
514D4—1881no—
515D4—1881no—
516D4—1881no—
517D4—1881no—
518C2×C4—942no—
519C2×C4—942no—
520C2×C4—942no—
521C2×C4—1882no—
522C2×C4—1882no—
523C2×C4—1882no—
524C2×C4—1882no—
525C2×C4C22⋊C4×D4711yescharacteristic
526C2×C4#1309398111yescharacteristic
527C2×C4(C22⋊D47)⋊C411yescharacteristic
528C2×C4C4×C22⋊D4711yescharacteristic
529C2×C4#1309398611yescharacteristic
530C2×C4C4×D18811yescharacteristic
531C2×C4#1309399211yescharacteristic
532C2×C4#1309399411yescharacteristic
533C2×C4#1309399411yescharacteristic
534C2×C4#1309399611yescharacteristic
535C2×C4#1309399711yescharacteristic
536C2×C4#1309399711yescharacteristic
537C2×C4#1309399711yescharacteristic
538C2×C4#1309399711yescharacteristic
539C2×C4#1309399711yescharacteristic
540C2×C4#1309399811yescharacteristic
541C2×C4#1309399911yescharacteristic
542C2×C4#1309400611yescharacteristic
543C2×C4#1309400711yescharacteristic
544C2×C4#1309400911yescharacteristic
545C2×C4#1309400911yescharacteristic
546C2×C4#1309400911yescharacteristic
547C2×C4#1309401011yescharacteristic
548C2×C4#1309401011yescharacteristic
549C2×C4#1309401211yescharacteristic
550C2×C4#1309401811yescharacteristic
551C2×C4#1309401911yescharacteristic
552C2×C4#1309402011yescharacteristic
553C8—42no—
554C8—42no—
555C8—42no—
556C8—944no—
557C8—1882no—
558C8—1882no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—3762no—
567C22—3762no—
568C22—1884no—
569C22—1882no—
570C22#1568898211yescharacteristic
571C22#1568899411yescharacteristic
572C22#1568899711yescharacteristic
573C22#1568903611yescharacteristic
574C22#1568904511yescharacteristic
575C22#1568904711yescharacteristic
576C22#1568905811yescharacteristic
577C4—1882no—
578C4#1568900111yescharacteristic
579C4#1568901211yescharacteristic
580C4#1568901411yescharacteristic
581C4#1568902311yescharacteristic
582C4#1568903211yescharacteristic
583C4#1568903811yescharacteristic
584C4#1568904111yescharacteristic
585C4#1568905211yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—3762no—
594C2#2024163211yescharacteristic
subgroupG/H
centerC4#15689023
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1738C2
socleC2×C47#1439
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1738D47
hypocenterC47#11103
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
1. C2×#15689171C2semidirect
5. #20243114C2semidirect
6. C2×C47⋊#338C2semidirect
7. C47×#1738C2semidirect
294. #1738D47semidirect
329. C47#11103semidirect

Maximal subgroups

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

subgroupindex
C2×#156891712
C2×#156891052
#202518322
#202431142
C2×C47⋊#3382
C47×#17382
#1110347