Finite Group Databasebeta

← #26266396

Subgroups — #26266396

Order 12032.

958 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689188C211yesmaximal, characteristic, complemented
2#20248562C211yesmaximal, characteristic, complemented
3#20248301C211yesmaximal, characteristic
4#20244822C212yesmaximal, complemented
5#20244576C212yesmaximal, complemented
6#20244350C211yesmaximal, characteristic, complemented
7#20244152C211yesmaximal, characteristic, complemented
8#20243813C212yesmaximal, complemented
9#20243410C212yesmaximal, complemented
10C4×#13093945C211yesmaximal, characteristic, complemented
11C2×C47×#476C211yesmaximal, characteristic, complemented
12C22×C8×D47C2212yes—
13C2×#13093998—21no—
14C2×#13093995C2212yes—
15C2×C4×D188C2211yescharacteristic
16#15689188—24no—
17C2×#13093956C2212yes—
18C2×#13093945C2211yescharacteristic
19C2×#13093945C2211yescharacteristic
20C2×(C2×D47)⋊C8C2212yes—
21C2×C4×C47⋊C8C2211yescharacteristic
22#15689039—22no—
23#15689034—22no—
24#15689024—21no—
25#15688993C2211yescharacteristic
26#15688988—21no—
27#15688983—21no—
28#15688980C2212yes—
29#15688980C2212yes—
30#15688980C2212yes—
31C4×C4⋊Dic47C2211yescharacteristic
32#15688886C2212yes—
33#15688885C2211yescharacteristic
34#15688885C2211yescharacteristic
35#15688885C2212yes—
36#15688885C2212yes—
37C2×C4⋊Q8×C47C2211yescharacteristic
38C2×C4×D4×C47C2211yescharacteristic
39C47×#476—24no—
40C2×#106×C47C2212yes—
41C2×C4⋊C8×C47C2211yescharacteristic
42C2×#102×C47C2212yes—
43C22×D188D411yescharacteristic
44C22×C22⋊D47—22no—
45C22×C4×D47C2312yes—
46C22×C47⋊C8C2311yescharacteristic
47C22×C47⋊C8C2311yescharacteristic
48C2×C8×D47—24no—
49C2×C8×D47—24no—
50C2×C8×D47—42no—
51#13093998—44no—
52#13093995—24no—
53#13093995—42no—
54C4×D188—22no—
55C4×D188—22no—
56C2×C4⋊Dic47—21no—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47D411yescharacteristic
59C2×C4⋊Dic47C2311yescharacteristic
60C2×C4⋊Dic47C2311yescharacteristic
61C2×C4⋊Dic47C2312yes—
62C2×C22⋊Dic47—22no—
63C2×(C2×D47)⋊C4—22no—
64C2×(C2×D47)⋊C4—22no—
65C2×(C2×D47)⋊C4—22no—
66C2×(C2×D47)⋊C4D412yes—
67C2×C4×Dic47—21no—
68#13093956—42no—
69#13093945—22no—
70#13093945—22no—
71(C2×D47)⋊C8—24no—
72C4×C47⋊C8—22no—
73C47⋊#95—21no—
74C47⋊#95—22no—
75C47⋊#95—22no—
76C47⋊#95—22no—
77C22×Q8×C47—21no—
78C22×D4×C47C2311yescharacteristic
79C23×C4×C47—21no—
80C22×C8×C47C2312yes—
81C4⋊Q8×C47—22no—
82C4⋊Q8×C47—22no—
83C4×D4×C47—22no—
84C4×D4×C47—22no—
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47C2312yes—
88C2×C22⋊C4×C47—21no—
89C2×C42×C47C2311yescharacteristic
90#106×C47—24no—
91C4⋊C8×C47D414yescomplemented
92#102×C47—24no—
93C24×C47—21no—
94C23×D47C2×D412yes—
95C2×Q8×C47—42no—
96C2×Q8×C47—81no—
97C2×Q8×C47—81no—
98C2×D4×C47—21no—
99C2×D4×C47—21no—
100C2×D4×C47—21no—
101C2×D4×C47—21no—
102C2×D4×C47—21no—
103C2×D4×C47#4112yes—
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—42no—
107C22×C4×C47—42no—
108C22×C4×C47—42no—
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2411yescharacteristic
112C2×C22⋊D47—44no—
113C2×C22⋊D47—44no—
114C2×C22⋊D47—82no—
115C22×Dic47—21no—
116C22×Dic47—21no—
117C22×Dic47—22no—
118C22×Dic47C2×D412yes—
119C2×D188—22no—
120C2×D188—22no—
121C2×D188SD1614yes—
122C2×C4×D47—22no—
123C2×C4×D47—22no—
124C2×C4×D47—22no—
125C2×C4×D47—22no—
126C2×C4×D47—22no—
127C2×C4×D47—22no—
128C2×C8×C47—22no—
129C2×C8×C47—22no—
130C2×C8×C47C2×D414yes—
131C4⋊C4×C47—21no—
132C4⋊C4×C47—22no—
133C4⋊C4×C47—21no—
134C4⋊C4×C47—22no—
135C4⋊C4×C47—42no—
136C22⋊C4×C47—42no—
137C42×C47C2×D412yes—
138C42×C47#4112yes—
139C22⋊Dic47—44no—
140(C2×D47)⋊C4—24no—
141(C2×D47)⋊C4—44no—
142(C2×D47)⋊C4—82no—
143(C2×D47)⋊C4—82no—
144C4⋊Dic47—22no—
145C4⋊Dic47—21no—
146C4⋊Dic47—21no—
147C4⋊Dic47—22no—
148C4⋊Dic47—21no—
149C4⋊Dic47—22no—
150C4⋊Dic47—21no—
151C4⋊Dic47—42no—
152C4⋊Dic47—81no—
153C4×Dic47—42no—
154C2×C47⋊C8—21no—
155C2×C47⋊C8—21no—
156C2×C47⋊C8—21no—
157C2×C47⋊C8—21no—
158C2×C47⋊C8—21no—
159C2×C47⋊C8#4112yes—
160C8×D47—48no—
161C23×C47—22no—
162C23×C47—41no—
163C23×C47—41no—
164C23×C47—41no—
165C23×C47—41no—
166C23×C47—41no—
167C23×C47—41no—
168C23×C47C22×D411yescharacteristic
169C22×D47—22no—
170C22×D47—22no—
171C22×D47—22no—
172C22×D47—22no—
173C22×D47—22no—
174C22×D47—22no—
175C22×D47C2×SD1614yes—
176Q8×C47—84no—
177D4×C47—22no—
178D4×C47—22no—
179D4×C47—41no—
180D4×C47—41no—
181C2×C4×C47—21no—
182C2×C4×C47—21no—
183C2×C4×C47—41no—
184C2×C4×C47—42no—
185C2×C4×C47—41no—
186C2×C4×C47—41no—
187C2×C4×C47—42no—
188C2×C4×C47—42no—
189C2×C4×C47—84no—
190C2×C4×C47#12112yes—
191C2×C4×C47#12112yes—
192C2×C4×C47C2×SD1612yes—
193C2×C4×C47#13512yes—
194C2×C4×C47C22×D411yescharacteristic
195C2×C4×C47C2×#4111yescharacteristic
196C2×C4×C47C2×#4111yescharacteristic
197C2×C4×C47C2×#4111yescharacteristic
198C2×C4×C47H(5,𝔽2)11yescharacteristic
199C2×C4×C472−1+411yescharacteristic
200C22⋊D47—88no—
201C2×Dic47—22no—
202C2×Dic47—22no—
203C2×Dic47—22no—
204C2×Dic47—42no—
205C2×Dic47—41no—
206C2×Dic47—41no—
207C2×Dic47—42no—
208C2×Dic47—41no—
209C2×Dic47—41no—
210C2×Dic47—42no—
211C2×Dic47—41no—
212C2×Dic47—41no—
213D188—28no—
214C4×D47—42no—
215C4×D47—42no—
216C4×D47—42no—
217C4×D47—42no—
218C8×C47—24no—
219C47⋊C8—22no—
220C47⋊C8—41no—
221#25339—471nomaximal, Sylow
222C22×C47—42no—
223C22×C47—42no—
224C22×C47—42no—
225C22×C47—81no—
226C22×C47—81no—
227C22×C47—81no—
228C22×C47—81no—
229C22×C47C2×#12111yescharacteristic
230C22×C47#54611yescharacteristic
231C22×C47#54711yescharacteristic
232C22×C47C22×SD1611yescharacteristic
233C22×C47C2×#13511yescharacteristic
234C22×C47#57611yescharacteristic
235C22×C47#57711yescharacteristic
236C2×D47—24no—
237C2×D47—24no—
238C2×D47—24no—
239C2×D47—42no—
240C2×D47—42no—
241C2×D47—42no—
242C2×D47—42no—
243C4×C47—22no—
244C4×C47—81no—
245C4×C47—82no—
246C4×C47#46514yes—
247C4×C47#52911yescharacteristic
248C4×C47#54211yescharacteristic
249C4×C47#54611yescharacteristic
250C4×C47#54811yescharacteristic
251Dic47—42no—
252Dic47—81no—
253Dic47—82no—
254Dic47—81no—
255C2×#476D4711yescharacteristic, complemented
256C2×C8×D4—471no—
257#2563—471no—
258#2537—471no—
259#2077—472no—
260#2034—472no—
261#1990—471no—
262#1948—471no—
263#1893—472no—
264#1807—472no—
265C4×#102—471no—
266C2×C47—82no—
267C2×C47#242711yescharacteristic
268C2×C47C2×#46511yescharacteristic
269C2×C47#306211yescharacteristic
270C2×C47#329511yescharacteristic
271C2×C47#330311yescharacteristic
272C2×C47#333511yescharacteristic
273C2×C47#334111yescharacteristic
274D47—44no—
275C23×C8—472no—
276C2×C4⋊Q8C2×D4711yescharacteristic
277C2×#121—472no—
278C2×#121—941no—
279C2×C4×D4—471no—
280C2×C4×D4C2×D4711yescharacteristic
281#476—24no—
282C8×D4—944no—
283C2×#106—472no—
284C2×#106C2×D4712yes—
285C2×C4⋊C8C2×D4711yescharacteristic
286C2×#102—471no—
287C2×#102—471no—
288C2×#102C2×D4712yes—
289C2×C22⋊C8—472no—
290C2×C4×C8—471no—
291#394—942no—
292#393—942no—
293#390—941no—
294#384—471no—
295#382—941no—
296#380—472no—
297#380—472no—
298#380—472no—
299#380—941no—
300C4×C4⋊C4—471no—
301#340—472no—
302#340—471no—
303#340—472no—
304#340—471no—
305#340—472no—
306C47#2533911yescharacteristic, complemented, Sylow
307C22×Q8—21no—
308C22×D4—471no—
309C22×D4—942no—
310C22×D4C22×D4711yescharacteristic
311C23×C4—21no—
312C23×C4—472no—
313C22×C8—471no—
314C22×C8—471no—
315C22×C8—944no—
316C22×C8—944no—
317C22×C8—1882no—
318C22×C8C22×D4712yes—
319C4⋊Q8—22no—
320C4⋊Q8—22no—
321#121—944no—
322#121—1882no—
323#121—1884no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—942no—
327C4×D4—942no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—471no—
330C2×C4⋊C4—472no—
331C2×C4⋊C4—471no—
332C2×C4⋊C4—471no—
333C2×C4⋊C4—941no—
334C2×C4⋊C4—941no—
335C2×C4⋊C4C22×D4711yescharacteristic
336C2×C4⋊C4C22×D4712yes—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—472no—
339C2×C22⋊C4—942no—
340C2×C22⋊C4—942no—
341C2×C22⋊C4—942no—
342C2×C22⋊C4—942no—
343C2×C42—941no—
344C2×C42C22×D4711yescharacteristic
345#106—24no—
346#106—1882no—
347C4⋊C8C22⋊D4714yescomplemented
348#102—24no—
349#102—942no—
350#102—942no—
351C22⋊C8—944no—
352C4×C8—942no—
353#95—942no—
354#95—942no—
355#95—942no—
356#95—941no—
357C24—21no—
358C24—472no—
359C2×Q8—42no—
360C2×Q8—81no—
361C2×Q8—81no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—474no—
368C2×D4—942no—
369C2×D4—942no—
370C2×D4—3762no—
371C2×D4—1884no—
372C2×D4—1884no—
373C2×D4#1062535412yes—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—472no—
380C22×C4—942no—
381C22×C4—942no—
382C22×C4—942no—
383C22×C4—942no—
384C22×C4—942no—
385C22×C4—942no—
386C22×C4—941no—
387C22×C4—941no—
388C22×C4—942no—
389C22×C4D4×D4711yescharacteristic
390C22×C4D4×D4711yescharacteristic
391C22×C4C23×D4711yescharacteristic
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—472no—
395C2×C8—941no—
396C2×C8—941no—
397C2×C8—941no—
398C2×C8—941no—
399C2×C8—941no—
400C2×C8—1888no—
401C2×C8C2×C22⋊D4714yes—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—42no—
407C4⋊C4—942no—
408C4⋊C4—941no—
409C4⋊C4—941no—
410C4⋊C4—942no—
411C4⋊C4—941no—
412C4⋊C4—942no—
413C4⋊C4—941no—
414C4⋊C4—3761no—
415C4⋊C4—1882no—
416C22⋊C4—42no—
417C22⋊C4—944no—
418C22⋊C4—3762no—
419C22⋊C4—3762no—
420C22⋊C4—1884no—
421C22⋊C4—1884no—
422C42—1882no—
423C42#1062535212yes—
424C42C2×C22⋊D4712yes—
425C23—22no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—474no—
433C23—942no—
434C23—942no—
435C23—942no—
436C23—942no—
437C23—942no—
438C23—942no—
439C23C2×D4×D4711yescharacteristic
440Q8—84no—
441D4—22no—
442D4—22no—
443D4—41no—
444D4—41no—
445D4—948no—
446D4—3768no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—84no—
456C2×C4—942no—
457C2×C4—942no—
458C2×C4—942no—
459C2×C4—1882no—
460C2×C4—1881no—
461C2×C4—1881no—
462C2×C4—1882no—
463C2×C4—1881no—
464C2×C4—1881no—
465C2×C4—1881no—
466C2×C4—1882no—
467C2×C4—1881no—
468C2×C4—1882no—
469C2×C4—1882no—
470C2×C4—1882no—
471C2×C4—1882no—
472C2×C4#1309399512yes—
473C2×C4#1309399512yes—
474C2×C4SD16×D4712yes—
475C2×C4#1309404512yes—
476C2×C4C22×C22⋊D4711yescharacteristic
477C2×C4#41×D4711yescharacteristic
478C2×C4C2×#1062535211yescharacteristic
479C2×C4C2×#1062535411yescharacteristic
480C2×C4#1309407011yescharacteristic
481C2×C4#1309407211yescharacteristic
482C8—24no—
483C8—942no—
484C8—1881no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—944no—
493C22—944no—
494C22—944no—
495C22—1882no—
496C22—1882no—
497C22—1882no—
498C22—1882no—
499C22C2×#1309399511yescharacteristic
500C22#1568976411yescharacteristic
501C22#1568977511yescharacteristic
502C22C2×SD16×D4711yescharacteristic
503C22C2×#1309404511yescharacteristic
504C22#1568992711yescharacteristic
505C22#1568993311yescharacteristic
506C4—22no—
507C4—81no—
508C4—82no—
509C4—3761no—
510C4—3761no—
511C4—3762no—
512C4—1882no—
513C4#1568934914yes—
514C4#1568965911yescharacteristic
515C4#1568974611yescharacteristic
516C4#1568976111yescharacteristic
517C4#1568978411yescharacteristic
518C2—82no—
519C2—1884no—
520C2#2024696111yescharacteristic
521C2C2×#1568934911yescharacteristic
522C2#2025306211yescharacteristic
523C2#2025520911yescharacteristic
524C2#2025531311yescharacteristic
525C2#2025574211yescharacteristic
526C2#2025580911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#476C2
socleC23×C47C22×D4
prime radical#20248301C2
hypercenterC2×#476D47
hypocenterC47#25339
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#15689188C2semidirect
2. #20248562C2semidirect
4. #20244822C2semidirect
5. #20244576C2semidirect
6. #20244350C2semidirect
7. #20244152C2semidirect
8. #20243813C2semidirect
9. #20243410C2semidirect
10. C4×#13093945C2semidirect
11. C2×C47×#476C2semidirect
91. C4⋊C8×C47D4semidirect
255. C2×#476D47semidirect
306. C47#25339semidirect
347. C4⋊C8C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891882
#202485622
#202483012
#202448222
#202445762
#202443502
#202441522
#202438132
#202434102
C4×#130939452
C2×C47×#4762
#2533947