Finite Group Databasebeta

← #26135433

Subgroups — #26135433

Order 12032.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689359C211yesmaximal, characteristic
2C2×#15688948C211yesmaximal, characteristic, complemented
3C2×#15688923C211yesmaximal, characteristic, complemented
4C2×#15688923C211yesmaximal, characteristic, complemented
5C2×C22⋊(C47⋊C16)C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1808C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C2×#13093998—21no—
10C22×C47⋊C16C2211yescharacteristic
11C22×C47⋊C16C2211yescharacteristic
12#15689359—22no—
13#15689359—22no—
14C2×#13093958C2211yescharacteristic
15C2×#13093946—21no—
16#15688948—22no—
17#15688923—22no—
18#15688923—22no—
19C22⋊(C47⋊C16)—22no—
20C23×C8×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C47×#380—21no—
24C47×#340—21no—
25C22×D188—21no—
26C22×C22⋊D47—41no—
27C2×D376—21no—
28C2×D376—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376D412yes—
33#13093998—24no—
34#13093998—42no—
35C2×C4⋊Dic47—21no—
36C2×(C2×D47)⋊C4—41no—
37C2×C47⋊C16—21no—
38C2×C47⋊C16—21no—
39C2×C47⋊C16—21no—
40C2×C47⋊C16—21no—
41C2×C47⋊C16—21no—
42C2×C47⋊C16D412yescomplemented
43#13093958—21no—
44#13093958D412yes—
45#13093946—24no—
46C23×C4×C47D411yescharacteristic
47C22×C8×C47—21no—
48C22×C8×C47—21no—
49C22×C8×C47—21no—
50C22×C8×C47—21no—
51C22×C8×C47—21no—
52C22×C8×C47—21no—
53C22×C8×C47D411yescharacteristic
54C22×C8×C47C2311yescharacteristic
55C2×C4⋊C4×C47—21no—
56C2×C4⋊C4×C47—21no—
57C2×C22⋊C4×C47—41no—
58#107×C47—21no—
59#107×C47—21no—
60#107×C47—21no—
61#107×C47—21no—
62#95×C47—41no—
63C24×C47D811yescharacteristic
64C23×D47—41no—
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47D811yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C2×C22⋊D47—44no—
76C2×C22⋊D47—82no—
77C2×C22⋊D47—82no—
78C22×Dic47—41no—
79C2×D188—22no—
80C2×D188—41no—
81C2×D188—41no—
82C2×D188—41no—
83C2×D188—41no—
84C2×D188—41no—
85C2×C8×C47—21no—
86C2×C8×C47—21no—
87C2×C8×C47—21no—
88C2×C8×C47—41no—
89C2×C8×C47—41no—
90C2×C8×C47—41no—
91C2×C8×C47—41no—
92C2×C8×C47C2×D411yescharacteristic
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47#4111yescharacteristic
96C2×C8×C47#4111yescharacteristic
97C2×C8×C47#4111yescharacteristic
98C4⋊C4×C47—41no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C22⋊C4×C47—82no—
103(C2×D47)⋊C4—44no—
104C4⋊Dic47—22no—
105C4⋊Dic47—41no—
106D376—22no—
107D376—22no—
108D376—41no—
109D376—41no—
110C47⋊C16—22no—
111C47⋊C16—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47D1612yes—
119C23×C47C2×D811yescharacteristic
120C22×D47—42no—
121C22×D47—81no—
122C22×D47—81no—
123C22×D47—81no—
124C22×D47—81no—
125C22×D47—81no—
126C22×D47—81no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—81no—
135C2×C4×C47—81no—
136C2×C4×C47—81no—
137C2×C4×C47—81no—
138C2×C4×C47—81no—
139C2×C4×C47—81no—
140C2×C4×C47#12011yescharacteristic
141C2×C4×C47#12111yescharacteristic
142C2×C4×C47#12311yescharacteristic
143C2×C4×C47#13511yescharacteristic
144C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C47#13711yescharacteristic
146C22⋊D47—88no—
147C2×Dic47—42no—
148C2×Dic47—81no—
149C2×Dic47—81no—
150D188—42no—
151D188—42no—
152D188—81no—
153D188—81no—
154C8×C47—41no—
155C8×C47#12111yescharacteristic
156C8×C47#12111yescharacteristic
157C8×C47#12311yescharacteristic
158C8×C47#12411yescharacteristic
159#13380—471nomaximal, Sylow
160C22×C47—22no—
161C22×C47—22no—
162C22×C47—22no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47#44711yescharacteristic
168C22×C47#46611yescharacteristic
169C22×C47#48011yescharacteristic
170C22×C47C2×D1611yescharacteristic
171C22×C47#50811yescharacteristic
172C22×C47#50911yescharacteristic
173C22×C47#51011yescharacteristic
174C2×D47—82no—
175C2×D47—82no—
176C2×D47—82no—
177C2×D47—161no—
178C2×D47—161no—
179C2×D47—161no—
180C2×D47—161no—
181C4×C47—41no—
182C4×C47—161no—
183C4×C47—161no—
184C4×C47#39411yescharacteristic
185C4×C47#45211yescharacteristic
186C4×C47#46811yescharacteristic
187C4×C47#48211yescharacteristic
188Dic47—82no—
189C2×#466—471no—
190C2×#366—471no—
191C2×#357—471no—
192C2×#357—471no—
193C2×C22⋊C16—471no—
194#1808D4711yescharacteristic, complemented
195#1380—471no—
196C2×C47—42no—
197C2×C47#203311yescharacteristic
198C2×C47#218411yescharacteristic
199C2×C47#218911yescharacteristic
200C2×C47#221511yescharacteristic
201C2×C47#222011yescharacteristic
202C2×C47#223211yescharacteristic
203C2×C47#223411yescharacteristic
204D47—162no—
205C22×D8—471no—
206C23×C8C2×D4711yescharacteristic
207C2×#121—941no—
208C22×C16—471no—
209C22×C16—471no—
210#466—942no—
211#466—942no—
212C2×#107—471no—
213C2×#107C2×D4711yescharacteristic
214C2×#107C2×D4711yescharacteristic
215C2×#102—941no—
216#380—21no—
217#366—942no—
218#357—942no—
219#357—942no—
220C22⋊C16—942no—
221#340—21no—
222C47#1338011yescharacteristic, complemented, Sylow
223C22×D4—941no—
224C22×D4—1881no—
225C23×C4C22⋊D4711yescharacteristic
226C2×D8—472no—
227C2×D8—941no—
228C2×D8—941no—
229C2×D8—941no—
230C2×D8—941no—
231C2×D8—941no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8C22⋊D4711yescharacteristic
239C22×C8C22×D4711yescharacteristic
240#121—944no—
241#121—1882no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—941no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—1881no—
247C2×C16—472no—
248C2×C16—941no—
249C2×C16—941no—
250C2×C16—941no—
251C2×C16—941no—
252C2×C16—941no—
253#107—21no—
254#107—21no—
255#107—21no—
256#107—21no—
257#107—472no—
258#107—941no—
259#102—944no—
260#95—41no—
261C24—1881no—
262C24#1062533411yescharacteristic
263C2×D4—942no—
264C2×D4—3762no—
265C2×D4—3762no—
266C2×D4—1884no—
267C2×D4—1881no—
268C2×D4—1881no—
269C2×D4—1881no—
270C2×D4—1881no—
271C2×D4—1881no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—1881no—
281C22×C4#1062533411yescharacteristic
282C22×C4C2×C22⋊D4711yescharacteristic
283D8—942no—
284D8—942no—
285D8—1881no—
286D8—1881no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8#1062535011yescharacteristic
295C2×C8#1062535011yescharacteristic
296C2×C8D4×D4711yescharacteristic
297C2×C8D4×D4711yescharacteristic
298C2×C8D4×D4711yescharacteristic
299C2×C8#1062535211yescharacteristic
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—942no—
305C4⋊C4—1881no—
306C22⋊C4—82no—
307C22⋊C4—1884no—
308C16—942no—
309C16—1881no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—3761no—
317C23—3761no—
318C23—3761no—
319C23—3761no—
320C23—3761no—
321C23—3761no—
322C23—1882no—
323C23#1309396512yes—
324C23C2×#1062533411yescharacteristic
325D4—3768no—
326D4—3761no—
327D4—3761no—
328D4—1882no—
329D4—1882no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—3761no—
344C2×C4—3761no—
345C2×C4—1882no—
346C2×C4#1309399211yescharacteristic
347C2×C4#1309399611yescharacteristic
348C2×C4#1309400711yescharacteristic
349C2×C4#1309404411yescharacteristic
350C2×C4#1309404911yescharacteristic
351C2×C4#1309405511yescharacteristic
352C8—41no—
353C8#1309399711yescharacteristic
354C8#1309399711yescharacteristic
355C8#1309400611yescharacteristic
356C8#1309401011yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—3762no—
365C22—3762no—
366C22—3762no—
367C22—7521no—
368C22—7521no—
369C22—7521no—
370C22—7521no—
371C22#1568925611yescharacteristic
372C22#1568935711yescharacteristic
373C22#1568943611yescharacteristic
374C22C2×#1309396511yescharacteristic
375C22#1568955311yescharacteristic
376C22#1568955811yescharacteristic
377C22#1568956411yescharacteristic
378C4—41no—
379C4—161no—
380C4—161no—
381C4—3762no—
382C4#1568903811yescharacteristic
383C4#1568928311yescharacteristic
384C4#1568937111yescharacteristic
385C4#1568944711yescharacteristic
386C2—42no—
387C2—7522no—
388C2#2024457011yescharacteristic
389C2#2024529911yescharacteristic
390C2#2024532611yescharacteristic
391C2#2024547211yescharacteristic
392C2#2024550311yescharacteristic
393C2#2024556811yescharacteristic
394C2#2024557911yescharacteristic
subgroupG/H
centerC23C2×#10625334
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC47×#1808C2
socleC23×C47C2×D8
prime radicalC2×#15689359C2
hypercenter#1808D47
hypocenterC47#13380
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C2×#15688948C2semidirect
3. C2×#15688923C2semidirect
4. C2×#15688923C2semidirect
5. C2×C22⋊(C47⋊C16)C2semidirect
6. #20241479C2semidirect
7. C47×#1808C2semidirect
42. C2×C47⋊C16D4semidirect
194. #1808D47semidirect
222. C47#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#156893592
C2×#156889482
C2×#156889232
C2×C22⋊(C47⋊C16)2
#202414792
C47×#18082
#1338047