Finite Group Databasebeta

← #26119650

Subgroups — #26119650

Order 12032.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248387C211yesmaximal, characteristic
2#20244193C211yesmaximal, characteristic
3#20244149C211yesmaximal, characteristic, complemented
4C2×#15688866C211yesmaximal, characteristic
5C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#20241227C211yesmaximal, characteristic, complemented
7C47×#1803C211yesmaximal, characteristic, complemented
8C2×#13094021C2211yescharacteristic
9C2×#13094013—21no—
10C2×#13093955—21no—
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×#13093944—22no—
13C2×C4×C47⋊C8C2211yescharacteristic
14#15689040—22no—
15#15689025—21no—
16#15689025—21no—
17#15689024—21no—
18C4×C4⋊Dic47C2211yescharacteristic
19#15688885—21no—
20#15688866—22no—
21Q8⋊(C47⋊C8)—22no—
22C2×C4×Q8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×#103×C47—21no—
25C47×#384C2211yescharacteristic
26C47×#340—21no—
27C22×D188—21no—
28C22×D188—21no—
29C22×D188D412yes—
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32#13094021—21no—
33#13094021—21no—
34#13094021—21no—
35#13094021—21no—
36#13094013—42no—
37#13094013—42no—
38C2×C4⋊Dic47D411yescharacteristic
39C2×C4⋊Dic47D411yescharacteristic
40C2×(C2×D47)⋊C4—22no—
41C2×(C2×D47)⋊C4—22no—
42C2×(C2×D47)⋊C4—22no—
43C2×(C2×D47)⋊C4—22no—
44C2×C4×Dic47—21no—
45#13093955—42no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)D412yes—
48#13093944—44no—
49C4×C47⋊C8—21no—
50C4×C47⋊C8—21no—
51C47⋊#95—21no—
52C22×Q8×C47D411yescharacteristic
53C22×C8×C47—21no—
54C4×Q8×C47—21no—
55C4×Q8×C47—21no—
56C4×Q8×C47—21no—
57C4×Q8×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47D411yescharacteristic
63C2×C42×C47—21no—
64C2×C42×C47C2311yescharacteristic
65C4⋊C8×C47—21no—
66C4⋊C8×C47—21no—
67#103×C47—42no—
68C23×D47—22no—
69C2×Q8×C47—21no—
70C2×Q8×C47—21no—
71C2×Q8×C47—21no—
72C2×Q8×C47—21no—
73C2×Q8×C47—21no—
74C2×Q8×C47SD1612yes—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47—41no—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47C2×D411yescharacteristic
81C22×Dic47—21no—
82C22×Dic47—21no—
83C2×D188—22no—
84C2×D188—22no—
85C2×D188—42no—
86C2×D188—42no—
87C2×D188—41no—
88C2×D188—41no—
89C2×D188—41no—
90C2×D188—41no—
91C2×D188—41no—
92C2×D188—41no—
93C2×D188—41no—
94C2×D188—41no—
95C2×D188—41no—
96C2×D188—41no—
97C2×D188—41no—
98C2×D188—41no—
99C2×C8×C47—41no—
100C2×C8×C47—41no—
101C2×C8×C47—41no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—42no—
105C4⋊C4×C47—41no—
106C4⋊C4×C47—41no—
107C4⋊C4×C47—41no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47—41no—
110C4⋊C4×C47—41no—
111C42×C47—41no—
112C42×C47—41no—
113C42×C47C2×D411yescharacteristic
114C42×C47#4111yescharacteristic
115C42×C47#4111yescharacteristic
116C42×C47#4111yescharacteristic
117(C2×D47)⋊C4—44no—
118(C2×D47)⋊C4—44no—
119(C2×D47)⋊C4—82no—
120(C2×D47)⋊C4—82no—
121C4⋊Dic47—21no—
122C4⋊Dic47—21no—
123C4⋊Dic47—21no—
124C4⋊Dic47—21no—
125C4×Dic47—41no—
126C4×Dic47—41no—
127C2×C47⋊C8—22no—
128C2×C47⋊C8—22no—
129C2×C47⋊C8—41no—
130C2×C47⋊C8—41no—
131C2×C47⋊C8—41no—
132C2×C47⋊C8—41no—
133C23×C47#12011yescharacteristic
134C22×D47—42no—
135C22×D47—42no—
136C22×D47—42no—
137C22×D47—42no—
138C22×D47—42no—
139C22×D47—42no—
140C22×D47—42no—
141Q8×C47—22no—
142Q8×C47—22no—
143Q8×C47—41no—
144Q8×C47—41no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—22no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—81no—
154C2×C4×C47—81no—
155C2×C4×C47—81no—
156C2×C4×C47#12111yescharacteristic
157C2×C4×C47#12111yescharacteristic
158C2×C4×C47#12111yescharacteristic
159C2×C4×C47#12311yescharacteristic
160C2×C4×C47#12311yescharacteristic
161C2×C4×C47#12411yescharacteristic
162C2×C4×C47C2×SD1611yescharacteristic
163C2×C4×C47#13511yescharacteristic
164C2×C4×C47#13511yescharacteristic
165C2×C4×C47#13511yescharacteristic
166C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C47#13711yescharacteristic
170C2×Dic47—41no—
171C2×Dic47—41no—
172C2×Dic47—41no—
173C2×Dic47—41no—
174C2×Dic47—41no—
175C2×Dic47—41no—
176D188—44no—
177D188—82no—
178D188—81no—
179D188—81no—
180D188—81no—
181D188—81no—
182D188—81no—
183D188—81no—
184D188—81no—
185D188—81no—
186C8×C47—81no—
187C47⋊C8—42no—
188C47⋊C8—42no—
189#10410—471nomaximal, Sylow
190C22×C47#39411yescharacteristic
191C22×C47#44911yescharacteristic
192C22×C47#44911yescharacteristic
193C22×C47#45011yescharacteristic
194C22×C47#45211yescharacteristic
195C22×C47#45311yescharacteristic
196C22×C47#45511yescharacteristic
197C2×D47—82no—
198C2×D47—82no—
199C2×D47—82no—
200C2×D47—82no—
201C2×D47—82no—
202C2×D47—82no—
203C2×D47—82no—
204C4×C47—21no—
205C4×C47—21no—
206C4×C47—42no—
207C4×C47—81no—
208C4×C47—161no—
209C4×C47#46311yescharacteristic
210C4×C47#46411yescharacteristic
211C4×C47#46511yescharacteristic
212C4×C47#46911yescharacteristic
213C4×C47#48111yescharacteristic
214C4×C47#48211yescharacteristic
215C4×C47#48811yescharacteristic
216C4×C47#48911yescharacteristic
217Dic47—81no—
218Dic47—81no—
219#2548—471no—
220#1957—471no—
221#1948—471no—
222#1803D4711yescharacteristic, complemented
223C2×#331—471no—
224C2×Q8⋊C8—471no—
225#1279—471no—
226C2×C47#162011yescharacteristic
227C2×C47#163111yescharacteristic
228C2×C47#164011yescharacteristic
229C2×C47#164211yescharacteristic
230C2×C47#203411yescharacteristic
231C2×C47#203711yescharacteristic
232C2×C47#204211yescharacteristic
233D47—162no—
234C2×#127—471no—
235C2×#124—941no—
236C2×C4×Q8C2×D4711yescharacteristic
237C2×#106—941no—
238C2×C4⋊C8—471no—
239C2×C4⋊C8C2×D4711yescharacteristic
240C2×#103—21no—
241C2×#102—942no—
242C2×C4×C8—471no—
243#394—942no—
244#390—941no—
245#390—941no—
246#390—941no—
247#384C2×D4711yescharacteristic
248C4×C4⋊C4—471no—
249#340—21no—
250#340—941no—
251#331—942no—
252Q8⋊C8—942no—
253C47#1041011yescharacteristic, complemented, Sylow
254C22×Q8C22⋊D4711yescharacteristic
255C22×D4—472no—
256C22×D4—941no—
257C22×D4—941no—
258C22×C8—21no—
259C22×C8—941no—
260C22×C8—941no—
261#127—941no—
262#127—941no—
263#127—941no—
264#127—941no—
265#124—1882no—
266#124—1882no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—471no—
276C2×C4⋊C4—471no—
277C2×C4⋊C4C22⋊D4711yescharacteristic
278C2×C22⋊C4—942no—
279C2×C22⋊C4—942no—
280C2×C22⋊C4—942no—
281C2×C22⋊C4—942no—
282C2×C42—21no—
283C2×C42—941no—
284C2×C42C22×D4711yescharacteristic
285#106—1882no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—472no—
289C4⋊C8—941no—
290#103—42no—
291#102—1884no—
292C4×C8—941no—
293C4×C8—941no—
294#95—941no—
295C24—942no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8#1062533612yes—
302C2×D4—942no—
303C2×D4—942no—
304C2×D4—1882no—
305C2×D4—1882no—
306C2×D4—1881no—
307C2×D4—1881no—
308C2×D4—1881no—
309C2×D4—1881no—
310C2×D4—1881no—
311C2×D4—1881no—
312C2×D4—1881no—
313C2×D4—1881no—
314C2×D4—1881no—
315C2×D4—1881no—
316C2×D4—1881no—
317C2×D4—1881no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—941no—
322C22×C4—941no—
323C22×C4D4×D4711yescharacteristic
324C22×C4D4×D4711yescharacteristic
325C22×C4C2×C22⋊D4711yescharacteristic
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—942no—
330C2×C8—942no—
331C2×C8—1881no—
332C2×C8—1881no—
333C2×C8—1881no—
334C2×C8—1881no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—42no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—941no—
345C4⋊C4—941no—
346C4⋊C4—941no—
347C4⋊C4—941no—
348C22⋊C4—3762no—
349C22⋊C4—3762no—
350C22⋊C4—1884no—
351C22⋊C4—1884no—
352C42—41no—
353C42—41no—
354C42—1881no—
355C42—1881no—
356C42#1062535011yescharacteristic
357C42#1062535011yescharacteristic
358C42D4×D4711yescharacteristic
359C42#1062535211yescharacteristic
360C23—1882no—
361C23—1882no—
362C23—1882no—
363C23—1882no—
364C23—1882no—
365C23—1882no—
366C23—1882no—
367C23#1309399211yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372D4—3762no—
373D4—3761no—
374D4—3761no—
375D4—3761no—
376D4—3761no—
377D4—3761no—
378D4—3761no—
379D4—3761no—
380D4—3761no—
381D4—1884no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—1881no—
394C2×C4—1881no—
395C2×C4—1881no—
396C2×C4—1881no—
397C2×C4—1881no—
398C2×C4—1881no—
399C2×C4#1309399611yescharacteristic
400C2×C4#1309399711yescharacteristic
401C2×C4#1309399711yescharacteristic
402C2×C4#1309400611yescharacteristic
403C2×C4#1309400711yescharacteristic
404C2×C4#1309401011yescharacteristic
405C2×C4C2×#1062533611yescharacteristic
406C2×C4#1309404411yescharacteristic
407C2×C4#1309404511yescharacteristic
408C2×C4#1309404711yescharacteristic
409C2×C4#1309404911yescharacteristic
410C2×C4#1309405011yescharacteristic
411C2×C4#1309405111yescharacteristic
412C2×C4#1309405611yescharacteristic
413C8—81no—
414C8—1882no—
415C8—1882no—
416C22—3762no—
417C22—3762no—
418C22—3762no—
419C22—3762no—
420C22—3762no—
421C22—3762no—
422C22—3762no—
423C22#1568903811yescharacteristic
424C22#1568926611yescharacteristic
425C22#1568926711yescharacteristic
426C22#1568927311yescharacteristic
427C22#1568928411yescharacteristic
428C22#1568928911yescharacteristic
429C22#1568929911yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—161no—
435C4—3761no—
436C4—3761no—
437C4#1568934111yescharacteristic
438C4#1568934811yescharacteristic
439C4#1568935411yescharacteristic
440C4#1568937411yescharacteristic
441C4#1568944111yescharacteristic
442C4#1568944711yescharacteristic
443C4#1568947911yescharacteristic
444C4#1568948411yescharacteristic
445C2—7522no—
446C2#2024244611yescharacteristic
447C2#2024251311yescharacteristic
448C2#2024257211yescharacteristic
449C2#2024258711yescharacteristic
450C2#2024457711yescharacteristic
451C2#2024459611yescharacteristic
452C2#2024462511yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1803C2
socleC23×C47#120
prime radicalC2×#13094021C22
hypercenter#1803D47
hypocenterC47#10410
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
3. #20244149C2semidirect
5. C2×Q8⋊(C47⋊C8)C2semidirect
6. #20241227C2semidirect
7. C47×#1803C2semidirect
222. #1803D47semidirect
253. C47#10410semidirect

Maximal subgroups

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

subgroupindex
#202483872
#202441932
#202441492
C2×#156888662
C2×Q8⋊(C47⋊C8)2
#202412272
C47×#18032
#1041047