Finite Group Databasebeta

← #26123474

Subgroups — #26123474

Order 12032.

882 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×#15689149C211yesmaximal, characteristic, complemented
2C2×#15689096C211yesmaximal, characteristic
3#20251832C211yesmaximal, characteristic
4C2×#15689089C211yesmaximal, characteristic
5C2×#15688894C211yesmaximal, characteristic, complemented
6C2×#15688893C211yesmaximal, characteristic, complemented
7C47×#1729C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689149—22no—
13#15689149—22no—
14C2×Dic47⋊C8—22no—
15#15689096—22no—
16#15689096—22no—
17C2×#13093938C414yes—
18#15689091—22no—
19#15689089—22no—
20#15689089—22no—
21#15689089—22no—
22#15689086—22no—
23C2×(C2×D47)⋊C8—22no—
24#15688894—22no—
25#15688893—22no—
26C22×M16×C47C2211yescharacteristic
27C23×C8×C47C2211yescharacteristic
28C2×#117×C47C2211yescharacteristic
29C47×#336—22no—
30C2×#10625350—21no—
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×#10625350—21no—
42C22×Dic94Q811yescharacteristic
43C22×D188Q811yescharacteristic
44C22×C22⋊D47C2×C412yes—
45C22×C4×D47D412yes—
46C2×#10625329—21no—
47C2×#10625329—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×#10625329—21no—
57C2×#10625329D412yes—
58C22×C47⋊C8—21no—
59C22×C47⋊C8D412yes—
60#13093983—21no—
61#13093983—21no—
62#13093983D412yes—
63#13093983D412yes—
64C2×C4⋊Dic47—21no—
65C2×C22⋊Dic47C2×C412yes—
66C2×C4×Dic47—21no—
67Dic47⋊C8—28no—
68#13093938—28no—
69(C2×D47)⋊C8—28no—
70(C2×D47)⋊C8—28no—
71C23×C4×C47C2311yescharacteristic
72C2×M16×C47—21no—
73C2×M16×C47—21no—
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C22×C8×C47—21no—
79C22×C8×C47—21no—
80C22×C8×C47—21no—
81C22×C8×C47—21no—
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47D412yes—
85C22×C8×C47D412yes—
86#117×C47—21no—
87#117×C47—21no—
88#117×C47—21no—
89#117×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C22⋊C4×C47C2×C412yes—
92C2×C42×C47—21no—
93C24×C47C22×C411yescharacteristic
94C23×D47C4⋊C412yes—
95C22×C4×C47—22no—
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×Q811yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C22×C4×C47#4111yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C2×C22⋊D47—22no—
111C2×C22⋊D47—22no—
112C2×C22⋊D47—22no—
113C2×C22⋊D47—22no—
114C2×C22⋊D47—22no—
115C2×C22⋊D47—22no—
116C22×Dic47—22no—
117C22×Dic47C4⋊C412yes—
118#10625350—41no—
119#10625350—41no—
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—
134C2×D188—21no—
135C2×D188—21no—
136C2×D188—21no—
137C2×D188—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×C4×D47—22no—
141C2×C4×D47—22no—
142C2×C4×D47—22no—
143C2×C4×D47—22no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×Dic94—21no—
147C2×Dic94—21no—
148C2×Dic94—21no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152M16×C47—41no—
153M16×C47—41no—
154M16×C47—41no—
155M16×C47—41no—
156C2×C8×C47—22no—
157C2×C8×C47—22no—
158C2×C8×C47—22no—
159C2×C8×C47—22no—
160C2×C8×C47—22no—
161C2×C8×C47—22no—
162C2×C8×C47—41no—
163C2×C8×C47—41no—
164C2×C8×C47—41no—
165C2×C8×C47—41no—
166C4⋊C4×C47—41no—
167C4⋊C4×C47—41no—
168C22⋊C4×C47—22no—
169C22⋊C4×C47—22no—
170C42×C47—41no—
171C42×C47—41no—
172C22⋊Dic47—22no—
173C22⋊Dic47C22⋊C414yes—
174C4⋊Dic47—22no—
175C4⋊Dic47—22no—
176C4×Dic47—22no—
177C4×Dic47—22no—
178#10625329—22no—
179#10625329—22no—
180#10625329—41no—
181#10625329—41no—
182#10625329—41no—
183#10625329—41no—
184#10625329—41no—
185#10625329—41no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—41no—
191C2×C47⋊C8—41no—
192C23×C47—42no—
193C23×C47C2×C22⋊C411yescharacteristic
194C23×C47C2×C4⋊C411yescharacteristic
195C23×C47#11711yescharacteristic
196C23×C47C4×D411yescharacteristic
197C23×C47C4×D411yescharacteristic
198C23×C47C4×D411yescharacteristic
199C23×C47C4×D411yescharacteristic
200C22×D47—22no—
201C22×D47—22no—
202C22×D47—22no—
203C22×D47—44no—
204C2×C4×C47—44no—
205C2×C4×C47—42no—
206C2×C4×C47#12011yescharacteristic
207C2×C4×C47#12011yescharacteristic
208C2×C4×C47#12011yescharacteristic
209C2×C4×C47#12111yescharacteristic
210C2×C4×C47#12111yescharacteristic
211C2×C4×C47#12111yescharacteristic
212C2×C4×C47#12111yescharacteristic
213C2×C4×C47#12111yescharacteristic
214C2×C4×C47#12111yescharacteristic
215C2×C4×C47#12111yescharacteristic
216C2×C4×C47#12111yescharacteristic
217C2×C4×C47C22⋊Q811yescharacteristic
218C2×C4×C47C22⋊Q811yescharacteristic
219C2×C4×C47C22⋊Q811yescharacteristic
220C2×C4×C47C22⋊Q811yescharacteristic
221C2×C4×C47C22⋊Q811yescharacteristic
222C2×C4×C47C22⋊Q811yescharacteristic
223C2×C4×C47#12311yescharacteristic
224C2×C4×C47#12311yescharacteristic
225C2×C4×C47#12311yescharacteristic
226C2×C4×C47#12311yescharacteristic
227C2×C4×C47#12311yescharacteristic
228C2×C4×C47#12411yescharacteristic
229C2×C4×C47#12411yescharacteristic
230C2×C4×C47#12411yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×C4×C47#12611yescharacteristic
233C2×C4×C47#12711yescharacteristic
234C22⋊D47—42no—
235C22⋊D47—42no—
236C22⋊D47—42no—
237C22⋊D47—42no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—24no—
242C2×Dic47—44no—
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—
257C47⋊C8—42no—
258C47⋊C8—42no—
259#11088—471nomaximal, Sylow
260C22×C47—22no—
261C22×C47—22no—
262C22×C47—22no—
263C22×C47—41no—
264C22×C47—41no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47#38011yescharacteristic
268C22×C47#38511yescharacteristic
269C22×C47#38511yescharacteristic
270C22×C47#38611yescharacteristic
271C22×C47#38811yescharacteristic
272C22×C47#38811yescharacteristic
273C22×C47#39011yescharacteristic
274C2×D47—44no—
275C2×D47—44no—
276C2×D47—42no—
277C2×D47—82no—
278C4×C47—82no—
279C4×C47#39211yescharacteristic
280C4×C47#39311yescharacteristic
281C4×C47#39411yescharacteristic
282C4×C47#39411yescharacteristic
283C4×C47#39611yescharacteristic
284C4×C47#39611yescharacteristic
285C4×C47#39711yescharacteristic
286C4×C47#39911yescharacteristic
287Dic47—44no—
288Dic47—42no—
289C2×#424—471no—
290C2×#410—471no—
291#2879—471no—
292C2×#408—471no—
293C2×#344—471no—
294C2×#344—471no—
295#1729D4711yescharacteristic, complemented
296C2×C47—21no—
297C2×C47—21no—
298C2×C47—21no—
299C2×C47—21no—
300C2×C47—21no—
301C2×C47—21no—
302C2×C47#143911yescharacteristic
303C2×C47#186812yes—
304D47—82no—
305C22×#41—471no—
306C22×M16—471no—
307C22×M16—471no—
308C22×M16C2×D4711yescharacteristic
309C23×C8C2×D4711yescharacteristic
310C2×#117—471no—
311C2×#117C2×D4711yescharacteristic
312#424—942no—
313#424—942no—
314C2×C4⋊C8—942no—
315#410—942no—
316#410—942no—
317C2×#99—474no—
318#408—942no—
319#408—942no—
320#408—942no—
321#408—942no—
322#407—942no—
323C2×C22⋊C8—942no—
324#344—942no—
325#344—942no—
326#336—22no—
327C47#1108811yescharacteristic, complemented, Sylow
328C2×#41—941no—
329C2×#41—941no—
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—
340C22×Q8—471no—
341C22×D4—472no—
342C22×D4—471no—
343C23×C4—472no—
344C23×C4C22×D4711yescharacteristic
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—472no—
352C2×M16—941no—
353C2×M16—941no—
354C2×M16—941no—
355C2×M16—941no—
356C2×M16—941no—
357C2×M16—941no—
358C2×M16—941no—
359C2×M16—941no—
360C2×M16—941no—
361C2×M16—941no—
362C2×M16—941no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—472no—
370C22×C8—941no—
371C22×C8D18812yes—
372C22×C8C22⋊D4712yes—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—472no—
378#117—472no—
379#117—941no—
380#117—941no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—941no—
383C2×C22⋊C4—472no—
384C2×C22⋊C4C4×D4712yes—
385C2×C42—21no—
386C2×C42—941no—
387C4⋊C8—948no—
388#99—948no—
389C22⋊C8—948no—
390C22⋊C8—948no—
391C24—472no—
392C24C2×C4×D4711yescharacteristic
393#41—1881no—
394#41—1881no—
395#41—1881no—
396#41—1881no—
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—
409C2×Q8—941no—
410C2×Q8—941no—
411C2×Q8—941no—
412C2×Q8—941no—
413C2×Q8—941no—
414C2×Q8—941no—
415C2×D4—942no—
416C2×D4—942no—
417C2×D4—942no—
418C2×D4—942no—
419C2×D4—942no—
420C2×D4—942no—
421C2×D4—941no—
422C2×D4—941no—
423C2×D4—941no—
424C2×D4—941no—
425C2×D4—941no—
426C2×D4—941no—
427C22×C4—22no—
428C22×C4—472no—
429C22×C4—942no—
430C22×C4—942no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4C2×D18811yescharacteristic
437C22×C4#1062535011yescharacteristic
438C22×C4#1062535011yescharacteristic
439C22×C4#1062535011yescharacteristic
440C22×C4#1062535011yescharacteristic
441C22×C4D4×D4711yescharacteristic
442C22×C4D4×D4711yescharacteristic
443C22×C4D4×D4711yescharacteristic
444C22×C4D4×D4711yescharacteristic
445C22×C4D4×D4711yescharacteristic
446C22×C4#1062535211yescharacteristic
447C22×C4Q8×D4711yescharacteristic
448C22×C4#1062535411yescharacteristic
449C22×C4C2×C22⋊D4711yescharacteristic
450M16—41no—
451M16—41no—
452M16—41no—
453M16—41no—
454M16—942no—
455M16—942no—
456M16—1881no—
457M16—1881no—
458M16—1881no—
459M16—1881no—
460M16—1881no—
461M16—1881no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—942no—
473C2×C8—942no—
474C2×C8—942no—
475C2×C8—942no—
476C2×C8—1881no—
477C2×C8—1881no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—942no—
481C4⋊C4—942no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—474no—
485C22⋊C4—942no—
486C42—41no—
487C42—41no—
488C42—942no—
489C42—942no—
490C23—42no—
491C23—942no—
492C23—942no—
493C23—942no—
494C23—1884no—
495C23C22⋊C4×D4711yescharacteristic
496C23C4⋊C4×D4711yescharacteristic
497C23#1309398111yescharacteristic
498C23(C22⋊D47)⋊C411yescharacteristic
499C23C4×C22⋊D4711yescharacteristic
500C23#1309398611yescharacteristic
501C23C4×D18811yescharacteristic
502Q8—1881no—
503Q8—1881no—
504Q8—1881no—
505Q8—1881no—
506D4—1882no—
507D4—1882no—
508D4—1882no—
509D4—1882no—
510D4—1881no—
511D4—1881no—
512D4—1881no—
513D4—1881no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—942no—
517C2×C4—942no—
518C2×C4—942no—
519C2×C4—944no—
520C2×C4—1884no—
521C2×C4—1882no—
522C2×C4—1882no—
523C2×C4—1882no—
524C2×C4—1882no—
525C2×C4#1309399211yescharacteristic
526C2×C4#1309399411yescharacteristic
527C2×C4#1309399411yescharacteristic
528C2×C4#1309399611yescharacteristic
529C2×C4#1309399711yescharacteristic
530C2×C4#1309399711yescharacteristic
531C2×C4#1309399711yescharacteristic
532C2×C4#1309399711yescharacteristic
533C2×C4#1309399711yescharacteristic
534C2×C4#1309399811yescharacteristic
535C2×C4#1309399911yescharacteristic
536C2×C4#1309400011yescharacteristic
537C2×C4#1309400211yescharacteristic
538C2×C4#1309400211yescharacteristic
539C2×C4#1309400211yescharacteristic
540C2×C4#1309400211yescharacteristic
541C2×C4#1309400411yescharacteristic
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—1882no—
556C8—1882no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—3762no—
565C22—1884no—
566C22—1884no—
567C22—1882no—
568C22#1568898211yescharacteristic
569C22#1568899411yescharacteristic
570C22#1568899711yescharacteristic
571C22#1568900111yescharacteristic
572C22#1568901211yescharacteristic
573C22#1568901411yescharacteristic
574C22#1568902311yescharacteristic
575C4—82no—
576C4—1884no—
577C4—1882no—
578C4#1568903211yescharacteristic
579C4#1568903611yescharacteristic
580C4#1568903811yescharacteristic
581C4#1568904111yescharacteristic
582C4#1568904511yescharacteristic
583C4#1568904711yescharacteristic
584C4#1568905211yescharacteristic
585C4#1568905811yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—3762no—
593C2#2024163211yescharacteristic
594C2#2024367212yes—
subgroupG/H
centerC2×C4#13093992
commutatorC24×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1729C2
socleC22×C47#385
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1729D47
hypocenterC47#11088
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1729

Complements

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

NH ≅ G/Ntype
1. C2×#15689149C2semidirect
5. C2×#15688894C2semidirect
6. C2×#15688893C2semidirect
7. C47×#1729C2semidirect
295. #1729D47semidirect
327. C47#11088semidirect

Maximal subgroups

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

subgroupindex
C2×#156891492
C2×#156890962
#202518322
C2×#156890892
C2×#156888942
C2×#156888932
C47×#17292
#1108847