Finite Group Databasebeta

← #26111657

Subgroups — #26111657

Order 12032.

964 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic
2C2×#15688996C211yesmaximal, characteristic
3C2×#15688848C212yesmaximal, complemented
4#20241230C212yesmaximal, complemented
5C47×#1779C211yesmaximal, characteristic
6C23×C47⋊C8—21no—
7C22×Dic47⋊C4C411yescharacteristic
8C22×Dic47⋊C4C2211yescharacteristic
9C22×C22⋊Dic47C411yescharacteristic
10C22×C22⋊Dic47C411yescharacteristic
11C2×C22⋊(C47⋊C8)—24no—
12C2×C22⋊(C47⋊C8)—21no—
13C2×C22⋊(C47⋊C8)C2212yes—
14#15688996—21no—
15#15688996—21no—
16#15688996—21no—
17#15688996—21no—
18C2×C47⋊#95C411yescharacteristic
19C2×C47⋊#95C2211yescharacteristic
20#15688848—24no—
21C24×C4×C47C2211yescharacteristic
22C2×C22⋊C8×C47—21no—
23C2×C22⋊C8×C47—21no—
24C2×C22⋊C8×C47C2212yes—
25C23×Dic47C2×C411yescharacteristic
26C23×Dic47C2×C411yescharacteristic
27C23×Dic47C2×C411yescharacteristic
28C23×Dic47C2×C411yescharacteristic
29C22×C47⋊C8—24no—
30C22×C47⋊C8—22no—
31C22×C47⋊C8—42no—
32C22×C47⋊C8—42no—
33C2×Dic47⋊C4—21no—
34C2×Dic47⋊C4—21no—
35C2×Dic47⋊C4—21no—
36C2×Dic47⋊C4—21no—
37C2×Dic47⋊C4—22no—
38C2×Dic47⋊C4—22no—
39C2×Dic47⋊C4—42no—
40C2×C22⋊Dic47—21no—
41C2×C22⋊Dic47—21no—
42C2×C22⋊Dic47—22no—
43C2×C22⋊Dic47—21no—
44C2×C22⋊Dic47—21no—
45C2×C22⋊Dic47—42no—
46C2×C22⋊Dic47C814yescomplemented
47C22⋊(C47⋊C8)—24no—
48C22⋊(C47⋊C8)—22no—
49C22⋊(C47⋊C8)D414yes—
50C47⋊#95—21no—
51C47⋊#95—21no—
52C47⋊#95—21no—
53C47⋊#95—21no—
54C25×C47C2×C411yescharacteristic
55C23×C4×C47—22no—
56C23×C4×C47—22no—
57C23×C4×C47—42no—
58C23×C4×C47—42no—
59C23×C4×C47C2×C411yescharacteristic
60C23×C4×C47D411yescharacteristic
61C23×C4×C47D411yescharacteristic
62C23×C4×C47D411yescharacteristic
63C23×C4×C47D411yescharacteristic
64C23×C4×C47C2311yescharacteristic
65C22×C8×C47—22no—
66C22⋊C8×C47—22no—
67C22⋊C8×C47—22no—
68C22⋊C8×C47—42no—
69C22⋊C8×C47—42no—
70C24×C47—22no—
71C24×C47—22no—
72C24×C47—22no—
73C24×C47—22no—
74C24×C47—41no—
75C24×C47—41no—
76C24×C47C22⋊C411yescharacteristic
77C24×C47C22⋊C411yescharacteristic
78C24×C47C2×C812yes—
79C24×C47M1612yes—
80C24×C47C22×C411yescharacteristic
81C22×C4×C47—22no—
82C22×C4×C47—22no—
83C22×C4×C47—21no—
84C22×C4×C47—21no—
85C22×C4×C47—22no—
86C22×C4×C47—22no—
87C22×C4×C47—22no—
88C22×C4×C47—22no—
89C22×C4×C47—21no—
90C22×C4×C47—22no—
91C22×C4×C47—22no—
92C22×C4×C47—21no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47—41no—
99C22×C4×C47—41no—
100C22×C4×C47—48no—
101C22×C4×C47—48no—
102C22×C4×C47C22⋊C411yescharacteristic
103C22×C4×C47C22⋊C411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D412yes—
107C22×C4×C47#4112yes—
108C22×Dic47—21no—
109C22×Dic47—21no—
110C22×Dic47—22no—
111C22×Dic47—21no—
112C22×Dic47—21no—
113C22×Dic47—22no—
114C22×Dic47—21no—
115C22×Dic47—21no—
116C22×Dic47—22no—
117C22×Dic47—22no—
118C22×Dic47—41no—
119C22×Dic47—41no—
120C22×Dic47—41no—
121C22×Dic47—41no—
122C22×Dic47—41no—
123C22×Dic47—41no—
124C22×Dic47C2×C812yescomplemented
125C22×Dic47C2×C812yescomplemented
126C2×C8×C47—42no—
127C2×C8×C47—42no—
128C2×C8×C47—42no—
129C22⋊Dic47—24no—
130C22⋊Dic47—24no—
131C22⋊Dic47—42no—
132C22⋊Dic47—42no—
133Dic47⋊C4—42no—
134Dic47⋊C4—42no—
135Dic47⋊C4—41no—
136Dic47⋊C4—42no—
137Dic47⋊C4—41no—
138C2×C47⋊C8—24no—
139C2×C47⋊C8—48no—
140C2×C47⋊C8—42no—
141C2×C47⋊C8—42no—
142C23×C47—21no—
143C23×C47—21no—
144C23×C47—21no—
145C23×C47—21no—
146C23×C47—21no—
147C23×C47—21no—
148C23×C47—21no—
149C23×C47—21no—
150C23×C47—24no—
151C23×C47—24no—
152C23×C47—21no—
153C23×C47—21no—
154C23×C47—21no—
155C23×C47—21no—
156C23×C47—21no—
157C23×C47—21no—
158C23×C47—24no—
159C23×C47—24no—
160C23×C47—42no—
161C23×C47—42no—
162C23×C47—44no—
163C23×C47—44no—
164C23×C47—44no—
165C23×C47—44no—
166C23×C47C22⋊C812yes—
167C23×C47C22⋊C812yes—
168C23×C47#9912yes—
169C23×C47#10112yes—
170C23×C47C2×C22⋊C411yescharacteristic
171C23×C47C4×D412yes—
172C23×C47C22×C811yescharacteristic
173C23×C47C2×M1611yescharacteristic
174C23×C47#13112yes—
175C2×C4×C47—24no—
176C2×C4×C47—24no—
177C2×C4×C47—21no—
178C2×C4×C47—21no—
179C2×C4×C47—21no—
180C2×C4×C47—21no—
181C2×C4×C47—21no—
182C2×C4×C47—21no—
183C2×C4×C47—21no—
184C2×C4×C47—21no—
185C2×C4×C47—21no—
186C2×C4×C47—42no—
187C2×C4×C47—42no—
188C2×C4×C47—44no—
189C2×C4×C47—44no—
190C2×C4×C47—44no—
191C2×C4×C47—42no—
192C2×C4×C47—42no—
193C2×C4×C47#9912yes—
194C2×C4×C47#12011yescharacteristic
195C2×C4×C47#12112yes—
196C2×C4×C47#12311yescharacteristic
197C2×Dic47—22no—
198C2×Dic47—22no—
199C2×Dic47—24no—
200C2×Dic47—42no—
201C2×Dic47—41no—
202C2×Dic47—41no—
203C2×Dic47—41no—
204C2×Dic47—41no—
205C2×Dic47—42no—
206C2×Dic47—42no—
207C2×Dic47—41no—
208C2×Dic47—41no—
209C2×Dic47—41no—
210C2×Dic47—41no—
211C2×Dic47—41no—
212C2×Dic47—41no—
213C2×Dic47—82no—
214C2×Dic47—82no—
215C8×C47—82no—
216C47⋊C8—44no—
217#9081—471nomaximal, Sylow
218C22×C47—22no—
219C22×C47—22no—
220C22×C47—22no—
221C22×C47—22no—
222C22×C47—22no—
223C22×C47—21no—
224C22×C47—21no—
225C22×C47—21no—
226C22×C47—21no—
227C22×C47—22no—
228C22×C47—22no—
229C22×C47—22no—
230C22×C47—22no—
231C22×C47—22no—
232C22×C47—22no—
233C22×C47—22no—
234C22×C47—22no—
235C22×C47—48no—
236C22×C47—48no—
237C22×C47—41no—
238C22×C47—41no—
239C22×C47—41no—
240C22×C47—41no—
241C22×C47#32414yescomplemented
242C22×C47#38611yescharacteristic
243C22×C47C2×C22⋊C811yescharacteristic
244C22×C47#40811yescharacteristic
245C22×C47C2×#9911yescharacteristic
246C22×C47C2×#9911yescharacteristic
247C22×C47C2×#10111yescharacteristic
248C22×C47#41311yescharacteristic
249C22×C47C8×D412yes—
250C22×C47#43512yes—
251C4×C47—21no—
252C4×C47—22no—
253C4×C47—22no—
254C4×C47—21no—
255C4×C47—41no—
256Dic47—42no—
257Dic47—42no—
258Dic47—81no—
259Dic47—81no—
260C22×C22⋊C8—471no—
261C2×#385—471no—
262#1779D4711yescharacteristic
263C2×#324—472no—
264#1280—472no—
265C2×C47—24no—
266C2×C47—22no—
267C2×C47—22no—
268C2×C47—42no—
269C2×C47C2×#32411yescharacteristic
270C2×C47#145911yescharacteristic
271C2×C47#146811yescharacteristic
272C2×C47#147211yescharacteristic
273C2×C47#186911yescharacteristic
274C2×C47#189811yescharacteristic
275C2×C47#190111yescharacteristic
276C24×C4C2×D4711yescharacteristic
277C23×C8—941no—
278C22×C4⋊C4—471no—
279C22×C4⋊C4—471no—
280C22×C22⋊C4—471no—
281C22×C22⋊C4—471no—
282C2×C22⋊C8—21no—
283C2×C22⋊C8—21no—
284C2×C22⋊C8—472no—
285C2×C22⋊C8—944no—
286C2×C22⋊C8—941no—
287C2×C22⋊C8C2×D4712yes—
288#385—941no—
289#385—941no—
290#385—941no—
291#385—941no—
292C2×#95—471no—
293C2×#95—471no—
294#324—944no—
295C47#908111yescharacteristic, complemented, Sylow
296C25C4×D4711yescharacteristic
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—471no—
302C23×C4—471no—
303C23×C4—471no—
304C23×C4—471no—
305C23×C4C4×D4711yescharacteristic
306C23×C4D18811yescharacteristic
307C23×C4D18811yescharacteristic
308C23×C4C22⋊D4711yescharacteristic
309C23×C4C22⋊D4711yescharacteristic
310C23×C4C22×D4711yescharacteristic
311C22×C8—22no—
312C22×C8—944no—
313C22×C8—942no—
314C22×C8—1882no—
315C22×C8—1882no—
316C2×C4⋊C4—941no—
317C2×C4⋊C4—941no—
318C2×C4⋊C4—941no—
319C2×C4⋊C4—942no—
320C2×C4⋊C4—942no—
321C2×C4⋊C4—941no—
322C2×C4⋊C4—1882no—
323C2×C22⋊C4—474no—
324C2×C22⋊C4—942no—
325C2×C22⋊C4—941no—
326C2×C22⋊C4—941no—
327C2×C22⋊C4—941no—
328C2×C22⋊C4—941no—
329C2×C22⋊C4—1882no—
330C22⋊C8—22no—
331C22⋊C8—22no—
332C22⋊C8—42no—
333C22⋊C8—42no—
334C22⋊C8—474no—
335C22⋊C8—944no—
336C22⋊C8—942no—
337#95—941no—
338#95—941no—
339#95—941no—
340#95—941no—
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—41no—
346C24—41no—
347C24C8×D4712yes—
348C24#1062532412yes—
349C24(C2×D47)⋊C411yescharacteristic
350C24(C2×D47)⋊C411yescharacteristic
351C24C2×C4×D4711yescharacteristic
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—48no—
372C22×C4—48no—
373C22×C4—472no—
374C22×C4—472no—
375C22×C4—941no—
376C22×C4—941no—
377C22×C4—942no—
378C22×C4—941no—
379C22×C4—941no—
380C22×C4—942no—
381C22×C4—942no—
382C22×C4—942no—
383C22×C4—941no—
384C22×C4—941no—
385C22×C4—1881no—
386C22×C4—1881no—
387C22×C4—1881no—
388C22×C4—1881no—
389C22×C4—1881no—
390C22×C4—1881no—
391C22×C4(C2×D47)⋊C411yescharacteristic
392C22×C4(C2×D47)⋊C411yescharacteristic
393C22×C4C2×D18811yescharacteristic
394C22×C4D4×D4712yes—
395C22×C4#1062535212yes—
396C22×C4C2×C22⋊D4711yescharacteristic
397C2×C8—42no—
398C2×C8—42no—
399C2×C8—42no—
400C2×C8—944no—
401C2×C8—1888no—
402C2×C8—1882no—
403C2×C8—1882no—
404C4⋊C4—1882no—
405C4⋊C4—1882no—
406C4⋊C4—1881no—
407C4⋊C4—1882no—
408C4⋊C4—1881no—
409C22⋊C4—944no—
410C22⋊C4—944no—
411C22⋊C4—1882no—
412C22⋊C4—1882no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—24no—
427C23—24no—
428C23—21no—
429C23—24no—
430C23—24no—
431C23—42no—
432C23—42no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23(C2×D47)⋊C812yes—
438C23(C2×D47)⋊C812yes—
439C23#1309393812yes—
440C23#1309394212yes—
441C23C2×(C2×D47)⋊C411yescharacteristic
442C23(C22⋊D47)⋊C412yes—
443C23C2×C8×D4711yescharacteristic
444C23C2×#1062532411yescharacteristic
445C23#1309403212yes—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—942no—
465C2×C4—942no—
466C2×C4—944no—
467C2×C4—3762no—
468C2×C4—3762no—
469C2×C4—1881no—
470C2×C4—1881no—
471C2×C4—1881no—
472C2×C4—1881no—
473C2×C4—1881no—
474C2×C4—1881no—
475C2×C4—1882no—
476C2×C4—1881no—
477C2×C4—1881no—
478C2×C4—1881no—
479C2×C4—1881no—
480C2×C4—1882no—
481C2×C4—1882no—
482C2×C4#1309393812yes—
483C2×C4#1309399411yescharacteristic
484C2×C4#1309399612yes—
485C2×C4#1309400811yescharacteristic
486C8—82no—
487C8—1884no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—48no—
506C22—48no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22#1568884814yescomplemented
512C22#1568900011yescharacteristic
513C22C2×(C2×D47)⋊C811yescharacteristic
514C22#1568909111yescharacteristic
515C22C2×#1309393811yescharacteristic
516C22C2×#1309393811yescharacteristic
517C22C2×#1309394211yescharacteristic
518C22#1568910511yescharacteristic
519C22(C22⋊D47)⋊C812yes—
520C22#1568919112yes—
521C4—22no—
522C4—21no—
523C4—22no—
524C4—21no—
525C4—41no—
526C4—3761no—
527C4—3761no—
528C4—1882no—
529C4—1882no—
530C2—24no—
531C2—22no—
532C2—22no—
533C2—42no—
534C2C2×#1568884811yescharacteristic
535C2#2024170411yescharacteristic
536C2#2024173711yescharacteristic
537C2#2024175311yescharacteristic
538C2#2024367811yescharacteristic
539C2#2024383911yescharacteristic
540C2#2024385411yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC23×C47C22×C8
FrattiniC23×C4C22×D47
FittingC47×#1779C2
socleC23×C47C2×C22⋊C4
prime radicalC25×C47C2×C4
cosocleC23×C4×C47C23
hypercenter#1779D47
hypocenterC47#9081
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#15688848C2semidirect
4. #20241230C2semidirect
46. C2×C22⋊Dic47C8semidirect
124. C22×Dic47C2×C8semidirect
125. C22×Dic47C2×C8semidirect
241. C22×C47#324semidirect
295. C47#9081semidirect
511. C22#15688848semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊(C47⋊C8)2
C2×#156889962
C2×#156888482
#202412302
C47×#17792
#908147