Finite Group Databasebeta

← #26111621

Subgroups — #26111621

Order 12032.

694 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689174C211yesmaximal, characteristic, complemented
2C4×#13093995C211yesmaximal, characteristic
3#20243365C211yesmaximal, characteristic, complemented
4C2×D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
5#20241228C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C2×C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#13093995C411yescharacteristic
9C2×C4×C22⋊D47—21no—
10C2×C42×D47C2211yescharacteristic
11#15689174—22no—
12#15689174—22no—
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×Dic47⋊C8—21no—
15C2×(C2×D47)⋊C8—21no—
16C2×(C2×D47)⋊C8—21no—
17C2×C4×C47⋊C8C2211yescharacteristic
18#15689026C411yescharacteristic
19#15689019C411yescharacteristic
20#15689011—21no—
21#15688999—21no—
22#15688980C411yescharacteristic
23C4×C4⋊Dic47C2211yescharacteristic
24C4×C22⋊Dic47—21no—
25#15688877—21no—
26D4⋊(C47⋊C8)—22no—
27C2×C4×D4×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4×C8×C47C2211yescharacteristic
30C47×D4⋊C8—22no—
31C22×C22⋊D47—21no—
32C22×C4×D47C2×C411yescharacteristic
33C22×C4×D47D411yescharacteristic
34C22×C4×D47D411yescharacteristic
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37#13093995—22no—
38#13093995C814yescomplemented
39C4×C22⋊D47—42no—
40C4×C22⋊D47—42no—
41C2×C4⋊Dic47C2×C411yescharacteristic
42C2×C4⋊Dic47C2×C411yescharacteristic
43C2×Dic47⋊C4—21no—
44C2×C22⋊Dic47—21no—
45C2×C22⋊Dic47—21no—
46C2×C22⋊Dic47—21no—
47C2×(C2×D47)⋊C4—21no—
48C2×C4×Dic47—21no—
49C2×C4×Dic47C2×C411yescharacteristic
50C2×C4×Dic47D411yescharacteristic
51C2×C4×Dic47D411yescharacteristic
52C42×D47—21no—
53C42×D47—21no—
54C42×D47—21no—
55C42×D47—21no—
56C4⋊(C47⋊C8)—21no—
57C4⋊(C47⋊C8)—21no—
58Dic47⋊C8—24no—
59(C2×D47)⋊C8—24no—
60(C2×D47)⋊C8—42no—
61C4×C47⋊C8—21no—
62C4×C47⋊C8D412yescomplemented
63C47⋊#95—21no—
64C47⋊#95—21no—
65C47⋊#95—21no—
66C22×D4×C47C2×C411yescharacteristic
67C23×C4×C47—21no—
68C22×C8×C47—21no—
69C22×C8×C47—21no—
70C4×D4×C47—21no—
71C4×D4×C47—21no—
72C4×D4×C47—21no—
73C4×D4×C47—21no—
74C2×C4⋊C4×C47C2×C411yescharacteristic
75C2×C22⋊C4×C47—21no—
76C2×C42×C47C2311yescharacteristic
77C4⋊C8×C47—21no—
78C4⋊C8×C47—21no—
79C4×C8×C47—21no—
80C4×C8×C47D412yescomplemented
81C24×C47—21no—
82C23×D47C22⋊C411yescharacteristic
83C2×D4×C47—21no—
84C2×D4×C47—21no—
85C2×D4×C47—21no—
86C2×D4×C47—21no—
87C2×D4×C47—21no—
88C2×D4×C47C2×C812yes—
89C22×C4×C47—21no—
90C22×C4×C47—41no—
91C22×C4×C47—41no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47C22×C411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C2×C22⋊D47—24no—
100C2×C22⋊D47—42no—
101C2×C22⋊D47—42no—
102C22×Dic47—21no—
103C22×Dic47—21no—
104C22×Dic47C22⋊C411yescharacteristic
105C22×Dic47C22⋊C411yescharacteristic
106C22×Dic47C22⋊C411yescharacteristic
107C2×C4×D47—21no—
108C2×C4×D47—21no—
109C2×C4×D47—21no—
110C2×C4×D47—21no—
111C2×C4×D47—21no—
112C2×C4×D47—21no—
113C2×C4×D47—21no—
114C2×C4×D47—21no—
115C2×C4×D47—21no—
116C2×C4×D47—21no—
117C2×C4×D47—21no—
118C2×C4×D47—21no—
119C2×C4×D47—41no—
120C2×C4×D47—41no—
121C2×C4×D47C2×C812yes—
122C2×C4×D47M1612yes—
123C2×C8×C47—22no—
124C2×C8×C47—41no—
125C2×C8×C47—41no—
126C2×C8×C47—41no—
127C2×C8×C47—41no—
128C2×C8×C47—41no—
129C4⋊C4×C47—21no—
130C4⋊C4×C47—21no—
131C22⋊C4×C47—41no—
132C22⋊C4×C47—41no—
133C42×C47C2×D411yescharacteristic
134C42×C47C2×D411yescharacteristic
135C42×C47#4111yescharacteristic
136C42×C47#4111yescharacteristic
137C22⋊Dic47—24no—
138C22⋊Dic47—42no—
139C22⋊Dic47—42no—
140(C2×D47)⋊C4—42no—
141C4⋊Dic47—21no—
142C4⋊Dic47—21no—
143C4⋊Dic47—21no—
144C4⋊Dic47C2×C812yes—
145Dic47⋊C4—42no—
146C4×Dic47—21no—
147C4×Dic47—21no—
148C4×Dic47—21no—
149C4×Dic47—21no—
150C4×Dic47—21no—
151C4×Dic47—21no—
152C4×Dic47—41no—
153C4×Dic47—41no—
154C2×C47⋊C8—22no—
155C2×C47⋊C8—41no—
156C2×C47⋊C8—41no—
157C2×C47⋊C8—41no—
158C2×C47⋊C8—41no—
159C2×C47⋊C8—41no—
160C23×C47—22no—
161C23×C47—41no—
162C23×C47—41no—
163C23×C47—41no—
164C23×C47—41no—
165C23×C47—41no—
166C23×C47—41no—
167C23×C47C2×C22⋊C411yescharacteristic
168C22×D47—21no—
169C22×D47—21no—
170C22×D47—21no—
171C22×D47—21no—
172C22×D47—21no—
173C22×D47—21no—
174C22×D47C22⋊C812yes—
175D4×C47—22no—
176D4×C47—22no—
177D4×C47—41no—
178D4×C47—41no—
179C2×C4×C47—21no—
180C2×C4×C47—21no—
181C2×C4×C47—41no—
182C2×C4×C47—41no—
183C2×C4×C47—41no—
184C2×C4×C47—81no—
185C2×C4×C47—81no—
186C2×C4×C47—81no—
187C2×C4×C47—81no—
188C2×C4×C47C4×D411yescharacteristic
189C2×C4×C47C4×D411yescharacteristic
190C2×C4×C47#12011yescharacteristic
191C2×C4×C47#12111yescharacteristic
192C2×C4×C47#12111yescharacteristic
193C2×C4×C47#12311yescharacteristic
194C2×C4×C47C22×C811yescharacteristic
195C2×C4×C47C2×M1611yescharacteristic
196C2×C4×C47#13111yescharacteristic
197C2×C4×C47#13111yescharacteristic
198C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C47#13711yescharacteristic
202C22⋊D47—48no—
203C2×Dic47—21no—
204C2×Dic47—21no—
205C2×Dic47—21no—
206C2×Dic47—21no—
207C2×Dic47—22no—
208C2×Dic47—21no—
209C2×Dic47—21no—
210C2×Dic47—21no—
211C2×Dic47—21no—
212C2×Dic47—41no—
213C2×Dic47—41no—
214C2×Dic47—41no—
215C2×Dic47—41no—
216C2×Dic47—41no—
217C2×Dic47C22⋊C812yes—
218C4×D47—22no—
219C4×D47—22no—
220C4×D47—22no—
221C4×D47—22no—
222C4×D47—42no—
223C4×D47—42no—
224C4×D47—41no—
225C4×D47—41no—
226C4×D47—41no—
227C4×D47—41no—
228C8×C47—42no—
229C8×C47—81no—
230C47⋊C8—42no—
231C47⋊C8—81no—
232#9074—471nomaximal, Sylow
233C22×C47—42no—
234C22×C47—42no—
235C22×C47—42no—
236C22×C47—81no—
237C22×C47—81no—
238C22×C47—81no—
239C22×C47—81no—
240C22×C47#38611yescharacteristic
241C22×C47C2×C22⋊C811yescharacteristic
242C22×C47#40811yescharacteristic
243C22×C47#41711yescharacteristic
244C22×C47#41811yescharacteristic
245C22×C47#42111yescharacteristic
246C22×C47#42111yescharacteristic
247C2×D47—22no—
248C2×D47—22no—
249C2×D47—22no—
250C2×D47—41no—
251C2×D47—41no—
252C2×D47—41no—
253C2×D47—41no—
254C4×C47—21no—
255C4×C47—21no—
256C4×C47—81no—
257C4×C47C8×D411yescharacteristic
258C4×C47C8×D411yescharacteristic
259C4×C47#43511yescharacteristic
260C4×C47#43511yescharacteristic
261C4×C47#46811yescharacteristic
262C4×C47#46811yescharacteristic
263C4×C47#46911yescharacteristic
264C4×C47#46911yescharacteristic
265Dic47—22no—
266Dic47—41no—
267Dic47—41no—
268Dic47—42no—
269Dic47—81no—
270C2×#431—471no—
271C4×#121—471no—
272#1797—471no—
273C2×D4⋊C8—471no—
274C2×D4⋊C8D4711yescharacteristic, complemented
275#1279—471no—
276#1279—471no—
277C2×C47—82no—
278C2×C47#147711yescharacteristic
279C2×C47#147811yescharacteristic
280C2×C47#149511yescharacteristic
281C2×C47#149611yescharacteristic
282C2×C47#186911yescharacteristic
283C2×C47#189511yescharacteristic
284C2×C47#189711yescharacteristic
285D47—42no—
286C2×#121—471no—
287C2×C4×D4—941no—
288C2×C4×D4C2×D4711yescharacteristic
289C22×C42—471no—
290#431—942no—
291#431—942no—
292C2×C4⋊C8—471no—
293C2×C4⋊C8—941no—
294C2×C4⋊C8C2×D4711yescharacteristic
295C2×C22⋊C8—941no—
296C2×C22⋊C8—941no—
297C2×C4×C8—471no—
298C2×C4×C8C2×D4711yescharacteristic
299#390—471no—
300#389—471no—
301#388—941no—
302#386—941no—
303#380—471no—
304C4×C4⋊C4—471no—
305C4×C22⋊C4—941no—
306#336—941no—
307D4⋊C8—22no—
308D4⋊C8—942no—
309C47#907411yescharacteristic, complemented, Sylow
310C22×D4—941no—
311C22×D4C4×D4711yescharacteristic
312C23×C4—21no—
313C23×C4—471no—
314C23×C4—471no—
315C23×C4—471no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—941no—
319C22×C8—941no—
320#121—474no—
321#121—942no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—1882no—
327C4×D4—1882no—
328C2×C4⋊C4—471no—
329C2×C4⋊C4—471no—
330C2×C4⋊C4—941no—
331C2×C4⋊C4C4×D4711yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—941no—
334C2×C22⋊C4—941no—
335C2×C22⋊C4—941no—
336C2×C22⋊C4—941no—
337C2×C42—471no—
338C2×C42—471no—
339C2×C42—471no—
340C2×C42—941no—
341C2×C42—941no—
342C2×C42—941no—
343C2×C42—941no—
344C2×C42—941no—
345C2×C42C22×D4711yescharacteristic
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—944no—
349C4⋊C8—941no—
350C4⋊C8—941no—
351C22⋊C8—944no—
352C22⋊C8—1882no—
353C4×C8—21no—
354C4×C8—472no—
355C4×C8—941no—
356C4×C8C22⋊D4712yescomplemented
357#95—941no—
358#95—941no—
359#95—941no—
360C24—21no—
361C24—471no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—944no—
368C2×D4—1882no—
369C2×D4—1882no—
370C2×D4C8×D4712yes—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—471no—
379C22×C4—472no—
380C22×C4—472no—
381C22×C4—471no—
382C22×C4—471no—
383C22×C4—941no—
384C22×C4—941no—
385C22×C4—941no—
386C22×C4—941no—
387C22×C4—941no—
388C22×C4—941no—
389C22×C4—941no—
390C22×C4—941no—
391C22×C4—941no—
392C22×C4—941no—
393C22×C4—941no—
394C22×C4—941no—
395C22×C4—941no—
396C22×C4—941no—
397C22×C4—1881no—
398C22×C4—1881no—
399C22×C4C2×C4×D4711yescharacteristic
400C22×C4D4×D4711yescharacteristic
401C22×C4D4×D4711yescharacteristic
402C2×C8—22no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—942no—
409C2×C8—1881no—
410C2×C8—1881no—
411C2×C8—1881no—
412C2×C8—1881no—
413C2×C8—1881no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—472no—
417C4⋊C4—941no—
418C4⋊C4—941no—
419C4⋊C4—941no—
420C4⋊C4—1882no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—944no—
424C22⋊C4—1882no—
425C22⋊C4—1882no—
426C22⋊C4—1882no—
427C42—941no—
428C42—941no—
429C42—941no—
430C42—941no—
431C42—941no—
432C42—941no—
433C42—1881no—
434C42—1881no—
435C42#1062535011yescharacteristic
436C42D4×D4711yescharacteristic
437C42#1062535211yescharacteristic
438C42C2×C22⋊D4711yescharacteristic
439C23—22no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23—472no—
447C23—941no—
448C23—941no—
449C23—941no—
450C23—941no—
451C23—941no—
452C23—941no—
453C23C22⋊C4×D4711yescharacteristic
454D4—22no—
455D4—22no—
456D4—41no—
457D4—41no—
458D4—1888no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—472no—
469C2×C4—941no—
470C2×C4—941no—
471C2×C4—942no—
472C2×C4—942no—
473C2×C4—942no—
474C2×C4—942no—
475C2×C4—941no—
476C2×C4—941no—
477C2×C4—942no—
478C2×C4—941no—
479C2×C4—941no—
480C2×C4—941no—
481C2×C4—941no—
482C2×C4—1882no—
483C2×C4—1882no—
484C2×C4—1881no—
485C2×C4—1881no—
486C2×C4—1881no—
487C2×C4—1881no—
488C2×C4—1881no—
489C2×C4—1881no—
490C2×C4—1881no—
491C2×C4—1881no—
492C2×C4—1881no—
493C2×C4(C22⋊D47)⋊C411yescharacteristic
494C2×C4C4×C22⋊D4711yescharacteristic
495C2×C4#1309399211yescharacteristic
496C2×C4#1309399511yescharacteristic
497C2×C4#1309399711yescharacteristic
498C2×C4#1309400611yescharacteristic
499C2×C4C2×C8×D4711yescharacteristic
500C2×C4M16×D4711yescharacteristic
501C2×C4#1309403011yescharacteristic
502C2×C4#1309403211yescharacteristic
503C2×C4#1309404811yescharacteristic
504C2×C4#1309404811yescharacteristic
505C2×C4#1309405111yescharacteristic
506C2×C4#1309405311yescharacteristic
507C8—42no—
508C8—81no—
509C8—3761no—
510C8—1882no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—942no—
519C22—942no—
520C22—942no—
521C22—1881no—
522C22—1881no—
523C22—1881no—
524C22—1881no—
525C22#1568899911yescharacteristic
526C22C22⋊C8×D4711yescharacteristic
527C22#1568908811yescharacteristic
528C22#1568912111yescharacteristic
529C22#1568912611yescharacteristic
530C22#1568913811yescharacteristic
531C22#1568913811yescharacteristic
532C4—21no—
533C4—21no—
534C4—81no—
535C4—942no—
536C4—3761no—
537C4—1881no—
538C4—1882no—
539C4—1881no—
540C4(C22⋊D47)⋊C811yescharacteristic
541C4C8×C22⋊D4711yescharacteristic
542C4#1568919211yescharacteristic
543C4#1568919711yescharacteristic
544C4#1568936611yescharacteristic
545C4#1568936811yescharacteristic
546C4#1568937311yescharacteristic
547C4#1568937511yescharacteristic
548C2—82no—
549C2—1882no—
550C2#2024177211yescharacteristic
551C2#2024177711yescharacteristic
552C2#2024185011yescharacteristic
553C2#2024185511yescharacteristic
554C2#2024367711yescharacteristic
555C2#2024382311yescharacteristic
556C2#2024383311yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×D4⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093995C4
cosocleC2×C42×C47C23
hypercenterC2×D4⋊C8D47
hypocenterC47#9074
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#15689174C2semidirect
3. #20243365C2semidirect
4. C2×D4⋊(C47⋊C8)C2semidirect
5. #20241228C2semidirect
6. #20241227C2semidirect
7. C2×C47×D4⋊C8C2semidirect
38. #13093995C8semidirect
62. C4×C47⋊C8D4semidirect
80. C4×C8×C47D4semidirect
274. C2×D4⋊C8D47semidirect
309. C47#9074semidirect
356. C4×C8C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891742
C4×#130939952
#202433652
C2×D4⋊(C47⋊C8)2
#202412282
#202412272
C2×C47×D4⋊C82
#907447