Finite Group Databasebeta

← #26119722

Subgroups — #26119722

Order 12032.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248337C211yesmaximal, characteristic
2#20244348C211yesmaximal, characteristic, complemented
3#20243385C211yesmaximal, characteristic
4C2×#15688870C211yesmaximal, characteristic, complemented
5C2×#15688850C211yesmaximal, characteristic
6#20241229C211yesmaximal, characteristic, complemented
7C47×#1948C211yesmaximal, characteristic, complemented
8C2×#13094024C2211yescharacteristic
9C2×#13094004—21no—
10C2×#13094004—21no—
11C2×C4×D188C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093944—21no—
14C2×C4×C47⋊C8C2211yescharacteristic
15#15689060—22no—
16#15689025—21no—
17#15688993—21no—
18#15688885—22no—
19#15688885—21no—
20#15688870—22no—
21#15688850—22no—
22C2×#106×C47—21no—
23C2×C4⋊C8×C47C2211yescharacteristic
24C47×#384C2211yescharacteristic
25C4×C4⋊C4×C47C2211yescharacteristic
26C47×#340—21no—
27C22×Dic94—21no—
28C22×D188D411yescharacteristic
29C22×C4×D47—21no—
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32#13094024—21no—
33#13094024—21no—
34#13094024—21no—
35#13094024—21no—
36#13094004—42no—
37#13094004—42no—
38#13094004—42no—
39#13094004—42no—
40C4×D188—21no—
41C4×D188—21no—
42C4×D188—21no—
43C4×D188—21no—
44C2×C4⋊Dic47—22no—
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47D411yescharacteristic
48C2×C4⋊Dic47D412yes—
49C2×(C2×D47)⋊C4—22no—
50C2×(C2×D47)⋊C4—22no—
51C2×(C2×D47)⋊C4—21no—
52C4⋊(C47⋊C8)—21no—
53C4⋊(C47⋊C8)—21no—
54#13093944—42no—
55C4×C47⋊C8—21no—
56C4×C47⋊C8—21no—
57C22×C8×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47D411yescharacteristic
62C2×C4⋊C4×C47D411yescharacteristic
63C2×C42×C47—21no—
64C2×C42×C47C2311yescharacteristic
65#106×C47—42no—
66C4⋊C8×C47—21no—
67C4⋊C8×C47D412yes—
68#95×C47—21no—
69C23×D47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—41no—
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×Dic47—22no—
77C22×Dic47—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188SD1612yes—
84C2×C4×D47—41no—
85C2×C4×D47—41no—
86C2×C4×D47—41no—
87C2×C4×D47—41no—
88C2×C4×D47—41no—
89C2×C4×D47—41no—
90C2×Dic94—41no—
91C2×Dic94—41no—
92C2×Dic94—41no—
93C2×Dic94—41no—
94C2×Dic94—41no—
95C2×Dic94—41no—
96C2×C8×C47—22no—
97C2×C8×C47—41no—
98C2×C8×C47—41no—
99C4⋊C4×C47—21no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—42no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—41no—
106C4⋊C4×C47D812yes—
107C4⋊C4×C47SD1612yes—
108C42×C47—41no—
109C42×C47—41no—
110C42×C47C2×D411yescharacteristic
111C42×C47#4111yescharacteristic
112C42×C47#4111yescharacteristic
113C42×C47#4111yescharacteristic
114(C2×D47)⋊C4—44no—
115(C2×D47)⋊C4—44no—
116(C2×D47)⋊C4—41no—
117(C2×D47)⋊C4—41no—
118C4⋊Dic47—21no—
119C4⋊Dic47—22no—
120C4⋊Dic47—21no—
121C4⋊Dic47—22no—
122C4⋊Dic47—44no—
123C4⋊Dic47—44no—
124C4⋊Dic47—41no—
125C4⋊Dic47—41no—
126C2×C47⋊C8—22no—
127C2×C47⋊C8—41no—
128C2×C47⋊C8—41no—
129C2×C47⋊C8—41no—
130C2×C47⋊C8—41no—
131C2×C47⋊C8—41no—
132C23×C47#12011yescharacteristic
133C22×D47—22no—
134C22×D47—41no—
135C22×D47—41no—
136C22×D47—41no—
137C22×D47—41no—
138C22×D47—41no—
139C22×D47—41no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—22no—
143C2×C4×C47—22no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—41no—
147C2×C4×C47—41no—
148C2×C4×C47—81no—
149C2×C4×C47—81no—
150C2×C4×C47—81no—
151C2×C4×C47#12111yescharacteristic
152C2×C4×C47#12111yescharacteristic
153C2×C4×C47#12111yescharacteristic
154C2×C4×C47#12311yescharacteristic
155C2×C4×C47#12311yescharacteristic
156C2×C4×C47#12411yescharacteristic
157C2×C4×C47C2×D811yescharacteristic
158C2×C4×C47C2×SD1611yescharacteristic
159C2×C4×C47C2×SD1611yescharacteristic
160C2×C4×C47#13511yescharacteristic
161C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C47#13711yescharacteristic
164C2×C4×C47#13711yescharacteristic
165C2×Dic47—42no—
166C2×Dic47—41no—
167C2×Dic47—41no—
168C2×Dic47—42no—
169C2×Dic47—41no—
170C2×Dic47—42no—
171D188—22no—
172D188—22no—
173D188—41no—
174D188—41no—
175C4×D47—81no—
176C4×D47—81no—
177C4×D47—81no—
178C4×D47—81no—
179Dic94—81no—
180Dic94—81no—
181Dic94—81no—
182Dic94—81no—
183C8×C47—42no—
184C47⋊C8—42no—
185C47⋊C8—81no—
186#10420—471nomaximal, Sylow
187C22×C47#39411yescharacteristic
188C22×C47#44711yescharacteristic
189C22×C47#44811yescharacteristic
190C22×C47#45011yescharacteristic
191C22×C47#45211yescharacteristic
192C22×C47#45411yescharacteristic
193C22×C47#45611yescharacteristic
194C2×D47—42no—
195C2×D47—42no—
196C2×D47—42no—
197C2×D47—81no—
198C2×D47—81no—
199C2×D47—81no—
200C2×D47—81no—
201C4×C47—21no—
202C4×C47—21no—
203C4×C47—42no—
204C4×C47—42no—
205C4×C47—161no—
206C4×C47#45911yescharacteristic
207C4×C47#46011yescharacteristic
208C4×C47#46511yescharacteristic
209C4×C47#47011yescharacteristic
210C4×C47#48311yescharacteristic
211C4×C47#48511yescharacteristic
212C4×C47#48611yescharacteristic
213C4×C47#49011yescharacteristic
214Dic47—82no—
215Dic47—81no—
216#2542—471no—
217#1990—471no—
218#1948D4711yescharacteristic, complemented
219#1802—471no—
220C2×#332—471no—
221C2×D4⋊C8—471no—
222#1279—471no—
223C2×C47#162711yescharacteristic
224C2×C47#163511yescharacteristic
225C2×C47#164711yescharacteristic
226C2×C47#165111yescharacteristic
227C2×C47#203511yescharacteristic
228C2×C47#203811yescharacteristic
229C2×C47#204111yescharacteristic
230D47—82no—
231C2×C4⋊Q8—471no—
232C2×C22⋊Q8—941no—
233C2×C22⋊Q8—941no—
234C2×C4×D4—471no—
235C2×#106—21no—
236C2×C4⋊C8—471no—
237C2×C4⋊C8C2×D4711yescharacteristic
238C2×#102—941no—
239C2×C4×C8—471no—
240#399—942no—
241#390—941no—
242#384—941no—
243#384C2×D4711yescharacteristic
244C4×C4⋊C4C2×D4711yescharacteristic
245#340—21no—
246#340—941no—
247#340—942no—
248#332—942no—
249D4⋊C8—942no—
250C47#1042011yescharacteristic, complemented, Sylow
251C22×Q8—941no—
252C22×D4—471no—
253C23×C4—941no—
254C22×C8—21no—
255C22×C8—941no—
256C22×C8—941no—
257C4⋊Q8—941no—
258C4⋊Q8—941no—
259C4⋊Q8—941no—
260C4⋊Q8—941no—
261C22⋊Q8—1882no—
262C22⋊Q8—1882no—
263C22⋊Q8—1882no—
264C22⋊Q8—1882no—
265C4×D4—941no—
266C4×D4—941no—
267C4×D4—941no—
268C4×D4—941no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—471no—
273C2×C4⋊C4—472no—
274C2×C4⋊C4—942no—
275C2×C4⋊C4—942no—
276C2×C4⋊C4—941no—
277C2×C4⋊C4C22⋊D4711yescharacteristic
278C2×C4⋊C4C22⋊D4711yescharacteristic
279C2×C22⋊C4—942no—
280C2×C22⋊C4—942no—
281C2×C22⋊C4—941no—
282C2×C42—21no—
283C2×C42C22×D4711yescharacteristic
284#106—42no—
285C4⋊C8—21no—
286C4⋊C8—941no—
287C4⋊C8—941no—
288C4⋊C8D18812yes—
289#102—1882no—
290C4×C8—941no—
291C4×C8—941no—
292#95—21no—
293C24—941no—
294C2×Q8—1881no—
295C2×Q8—1881no—
296C2×Q8—1881no—
297C2×Q8—1881no—
298C2×Q8—1881no—
299C2×Q8—1881no—
300C2×D4—472no—
301C2×D4—941no—
302C2×D4—941no—
303C2×D4—941no—
304C2×D4—941no—
305C2×D4—941no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—942no—
310C22×C4—941no—
311C22×C4—1881no—
312C22×C4—1881no—
313C22×C4—1881no—
314C22×C4—1881no—
315C22×C4—1881no—
316C22×C4—1881no—
317C22×C4D4×D4711yescharacteristic
318C22×C4D4×D4711yescharacteristic
319C22×C4C2×C22⋊D4711yescharacteristic
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—942no—
324C2×C8—1881no—
325C2×C8—1881no—
326C2×C8—1881no—
327C2×C8—1881no—
328C2×C8—1881no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—941no—
337C4⋊C4—942no—
338C4⋊C4—941no—
339C4⋊C4—942no—
340C4⋊C4—1884no—
341C4⋊C4—1884no—
342C4⋊C4—1881no—
343C4⋊C4—1881no—
344C4⋊C4#1062533412yes—
345C4⋊C4#1062533612yes—
346C22⋊C4—1884no—
347C22⋊C4—1884no—
348C22⋊C4—1881no—
349C22⋊C4—1881no—
350C42—41no—
351C42—41no—
352C42C2×D18811yescharacteristic
353C42#1062535011yescharacteristic
354C42#1062535411yescharacteristic
355C42#1062535411yescharacteristic
356C23—942no—
357C23—1881no—
358C23—1881no—
359C23—1881no—
360C23—1881no—
361C23—1881no—
362C23—1881no—
363C23#1309399211yescharacteristic
364Q8—3761no—
365Q8—3761no—
366Q8—3761no—
367Q8—3761no—
368D4—942no—
369D4—942no—
370D4—1881no—
371D4—1881no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—3761no—
384C2×C4—3761no—
385C2×C4—3761no—
386C2×C4—3761no—
387C2×C4—1882no—
388C2×C4—1881no—
389C2×C4—1882no—
390C2×C4—1881no—
391C2×C4—1881no—
392C2×C4—1882no—
393C2×C4#1309399811yescharacteristic
394C2×C4#1309399911yescharacteristic
395C2×C4#1309399911yescharacteristic
396C2×C4#1309400911yescharacteristic
397C2×C4#1309400911yescharacteristic
398C2×C4#1309401311yescharacteristic
399C2×C4C2×#1062533411yescharacteristic
400C2×C4SD16×D4711yescharacteristic
401C2×C4C2×#1062533611yescharacteristic
402C2×C4#1309404511yescharacteristic
403C2×C4#1309404911yescharacteristic
404C2×C4#1309404911yescharacteristic
405C2×C4#1309405311yescharacteristic
406C2×C4#1309405311yescharacteristic
407C8—42no—
408C8—3761no—
409C8—1882no—
410C22—3761no—
411C22—3761no—
412C22—3761no—
413C22—3761no—
414C22—1882no—
415C22—1882no—
416C22—1882no—
417C22#1568904011yescharacteristic
418C22#1568925611yescharacteristic
419C22#1568926011yescharacteristic
420C22#1568927311yescharacteristic
421C22#1568928211yescharacteristic
422C22#1568929411yescharacteristic
423C22#1568930411yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—161no—
429C4—3761no—
430C4—3762no—
431C4#1568931811yescharacteristic
432C4#1568932311yescharacteristic
433C4#1568935311yescharacteristic
434C4#1568938211yescharacteristic
435C4#1568945511yescharacteristic
436C4#1568946711yescharacteristic
437C4#1568947111yescharacteristic
438C4#1568948911yescharacteristic
439C2—3762no—
440C2#2024248911yescharacteristic
441C2#2024253711yescharacteristic
442C2#2024262111yescharacteristic
443C2#2024265011yescharacteristic
444C2#2024458611yescharacteristic
445C2#2024460711yescharacteristic
446C2#2024462211yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1948C2
socleC23×C47#120
prime radicalC22×D188D4
hypercenter#1948D47
hypocenterC47#10420
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #20244348C2semidirect
4. C2×#15688870C2semidirect
6. #20241229C2semidirect
7. C47×#1948C2semidirect
218. #1948D47semidirect
250. C47#10420semidirect

Maximal subgroups

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

subgroupindex
#202483372
#202443482
#202433852
C2×#156888702
C2×#156888502
#202412292
C47×#19482
#1042047