Finite Group Databasebeta

← #26133639

Subgroups — #26133639

Order 12032.

578 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C16×D47C211yesmaximal, characteristic, complemented
2C2×#15689360C211yesmaximal, characteristic
3C2×#15688925C211yesmaximal, characteristic, complemented
4C2×#15688923C211yesmaximal, characteristic, complemented
5#20243414C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C47×#1380C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C22×C8×D47C2211yescharacteristic
10C2×#13093999—21no—
11C22×C47⋊C16C2211yescharacteristic
12C2×C16×D47—22no—
13C2×C16×D47—22no—
14C2×C16×D47—22no—
15#15689360—22no—
16#15689360C414yescomplemented
17C2×#13093958C2211yescharacteristic
18C2×#13093944—21no—
19#15688980—21no—
20#15688925—22no—
21#15688923—22no—
22#15688885—21no—
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C2×#107×C47C2211yescharacteristic
26C22×D188—21no—
27C22×D188—41no—
28C22×C4×D47D411yescharacteristic
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376—21no—
34C2×D376C2×C412yes—
35C22×C47⋊C8D411yescharacteristic
36C2×C8×D47—21no—
37C2×C8×D47—21no—
38C2×C8×D47—21no—
39C2×C8×D47—21no—
40C2×C8×D47C2×C412yes—
41C2×C8×D47D412yes—
42#13093999—24no—
43#13093999—42no—
44C2×C4⋊Dic47—21no—
45C2×(C2×D47)⋊C4—41no—
46C2×(C2×D47)⋊C4—41no—
47C2×C47⋊C16—21no—
48C2×C47⋊C16—21no—
49C2×C47⋊C16D412yescomplemented
50C16×D47—28no—
51#13093958—21no—
52#13093958—21no—
53#13093944—24no—
54C47⋊#95—41no—
55C22×C8×C47C2311yescharacteristic
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C16×C47—21no—
59C2×C16×C47—21no—
60C2×C16×C47D412yescomplemented
61#107×C47—21no—
62#107×C47—21no—
63#107×C47—21no—
64#107×C47C2×C412yes—
65C23×D47—41no—
66C23×D47D811yescharacteristic
67C22×C4×C47—41no—
68C22×C4×C47—41no—
69C22×C4×C47C2×D411yescharacteristic
70C22×Dic47—41no—
71C22×Dic47D811yescharacteristic
72C2×D188—22no—
73C2×D188—41no—
74C2×D188—41no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188—44no—
78C2×D188—41no—
79C2×D188—82no—
80C2×D188—82no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47C22⋊C412yes—
86C2×C4×D47SD1612yes—
87C2×C8×C47C22×C411yescharacteristic
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47C2×D411yescharacteristic
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C4⋊C4×C47—22no—
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96C4⋊C4×C47—41no—
97(C2×D47)⋊C4—44no—
98(C2×D47)⋊C4—82no—
99C4⋊Dic47—41no—
100C4⋊Dic47—41no—
101C2×C47⋊C8—21no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8C22⋊C412yes—
104D376—22no—
105D376—22no—
106D376—41no—
107D376—41no—
108C8×D47—22no—
109C8×D47—22no—
110C8×D47—22no—
111C8×D47—22no—
112C16×C47—22no—
113C47⋊C16—22no—
114C23×C47C2×D811yescharacteristic
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47—81no—
123C22×D47—81no—
124C22×D47—81no—
125C22×D47—81no—
126C22×D47#10212yes—
127C22×D47D1612yes—
128C22×D47SD3212yes—
129C2×C4×C47—42no—
130C2×C4×C47—81no—
131C2×C4×C47—81no—
132C2×C4×C47—81no—
133C2×C4×C47—81no—
134C2×C4×C47—81no—
135C2×C4×C47C2×C22⋊C411yescharacteristic
136C2×C4×C47#12111yescharacteristic
137C2×C4×C47#12111yescharacteristic
138C2×C4×C47C2×SD1611yescharacteristic
139C2×C4×C47#13511yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—81no—
144C2×Dic47—81no—
145C2×Dic47—81no—
146C2×Dic47#10212yes—
147D188—42no—
148D188—42no—
149D188—88no—
150D188—81no—
151D188—81no—
152C4×D47—22no—
153C4×D47—22no—
154C4×D47—22no—
155C4×D47—22no—
156C8×C47C4×D411yescharacteristic
157C8×C47C4×D411yescharacteristic
158C8×C47#12011yescharacteristic
159C8×C47#12311yescharacteristic
160C47⋊C8—22no—
161#13059—471nomaximal, Sylow
162C22×C47C2×#10211yescharacteristic
163C22×C47#46611yescharacteristic
164C22×C47#46611yescharacteristic
165C22×C47C2×D1611yescharacteristic
166C22×C47C2×SD3211yescharacteristic
167C22×C47#50811yescharacteristic
168C22×C47#50811yescharacteristic
169C2×D47—22no—
170C2×D47—22no—
171C2×D47—22no—
172C2×D47—22no—
173C2×D47—22no—
174C2×D47—22no—
175C2×D47—82no—
176C2×D47—82no—
177C2×D47—82no—
178C2×D47—161no—
179C2×D47—161no—
180C2×D47—161no—
181C2×D47—161no—
182C2×D47#35714yescomplemented
183C4×C47—82no—
184C4×C47—161no—
185C4×C47#38611yescharacteristic
186C4×C47#41611yescharacteristic
187C4×C47#46511yescharacteristic
188C4×C47#46511yescharacteristic
189Dic47—22no—
190Dic47—161no—
191C23×C16—471no—
192C2×#466—471no—
193C2×#357—471no—
194C2×#357—471no—
195#1808—471no—
196#1380—471no—
197#1380D4711yescharacteristic, complemented
198C2×C47#189311yescharacteristic
199C2×C47C2×#35711yescharacteristic
200C2×C47#213811yescharacteristic
201C2×C47#221511yescharacteristic
202C2×C47#221511yescharacteristic
203C2×C47#221711yescharacteristic
204C2×C47#221711yescharacteristic
205D47—24no—
206D47—162no—
207C22×D8—471no—
208C23×C8—471no—
209C2×#121—941no—
210C22×C16—471no—
211C22×C16—942no—
212C22×C16—942no—
213C22×C16—942no—
214C22×C16C2×D4711yescharacteristic
215#466—474no—
216#466—942no—
217C2×#107—471no—
218C2×#107C2×D4711yescharacteristic
219C2×#107C2×D4711yescharacteristic
220C2×#102—941no—
221#380—941no—
222#357—942no—
223#357—942no—
224#340—941no—
225C47#1305911yescharacteristic, complemented, Sylow
226C22×D4—941no—
227C22×D4—1881no—
228C23×C4—471no—
229C2×D8—472no—
230C2×D8—941no—
231C2×D8—941no—
232C2×D8—941no—
233C2×D8—941no—
234C2×D8—941no—
235C22×C8—471no—
236C22×C8—472no—
237C22×C8—472no—
238C22×C8—941no—
239C22×C8—941no—
240C22×C8—941no—
241C22×C8—941no—
242C22×C8C22×D4711yescharacteristic
243#121—944no—
244#121—1882no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—941no—
248C2×C22⋊C4—1881no—
249C2×C22⋊C4—1881no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16—472no—
253C2×C16—948no—
254C2×C16—941no—
255C2×C16—941no—
256C2×C16D18812yescomplemented
257#107—21no—
258#107—21no—
259#107—21no—
260#107—941no—
261#107—941no—
262#107C4×D4712yes—
263#102—944no—
264#95—1881no—
265C24—471no—
266C24—1881no—
267C2×D4—942no—
268C2×D4—3762no—
269C2×D4—3762no—
270C2×D4—1884no—
271C2×D4—1881no—
272C2×D4—1881no—
273C2×D4—1881no—
274C2×D4—1881no—
275C2×D4—1881no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—471no—
279C22×C4—472no—
280C22×C4—472no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4—941no—
285C22×C4—1881no—
286C22×C4D4×D4711yescharacteristic
287D8—942no—
288D8—942no—
289D8—1881no—
290D8—1881no—
291C2×C8—472no—
292C2×C8—941no—
293C2×C8—941no—
294C2×C8—942no—
295C2×C8—942no—
296C2×C8—942no—
297C2×C8—942no—
298C2×C8C2×C4×D4711yescharacteristic
299C2×C8C2×D18811yescharacteristic
300C2×C8#1062535011yescharacteristic
301C2×C8D4×D4711yescharacteristic
302C2×C8D4×D4711yescharacteristic
303C2×C8#1062535411yescharacteristic
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—1881no—
309C4⋊C4—1881no—
310C22⋊C4—3762no—
311C22⋊C4—1884no—
312C16—22no—
313C16—942no—
314C23—472no—
315C23—472no—
316C23—472no—
317C23—941no—
318C23—941no—
319C23—941no—
320C23—941no—
321C23—3761no—
322C23—3761no—
323C23—3761no—
324C23—3761no—
325C23—3761no—
326C23—3761no—
327C23—1882no—
328C23D8×D4711yescharacteristic
329D4—3768no—
330D4—3761no—
331D4—3761no—
332D4—1882no—
333D4—1882no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—472no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—942no—
344C2×C4—942no—
345C2×C4—942no—
346C2×C4—942no—
347C2×C4—3761no—
348C2×C4—3761no—
349C2×C4—3761no—
350C2×C4C22⋊C4×D4711yescharacteristic
351C2×C4#1309399711yescharacteristic
352C2×C4#1309399911yescharacteristic
353C2×C4SD16×D4711yescharacteristic
354C2×C4#1309404511yescharacteristic
355C2×C4#1309404711yescharacteristic
356C8—942no—
357C8#1309398611yescharacteristic
358C8C4×D18811yescharacteristic
359C8#1309399411yescharacteristic
360C8#1309400911yescharacteristic
361C22—474no—
362C22—942no—
363C22—942no—
364C22—942no—
365C22—942no—
366C22—942no—
367C22—942no—
368C22—3762no—
369C22—3762no—
370C22—3762no—
371C22—7521no—
372C22—7521no—
373C22—7521no—
374C22—7521no—
375C22#102×D4711yescharacteristic
376C22#1568935811yescharacteristic
377C22#1568936011yescharacteristic
378C22D16×D4711yescharacteristic
379C22SD32×D4711yescharacteristic
380C22#1568955411yescharacteristic
381C22#1568955611yescharacteristic
382C4—82no—
383C4—161no—
384C4—942no—
385C4—7521no—
386C4#1568900111yescharacteristic
387C4#1568911811yescharacteristic
388C4#1568935311yescharacteristic
389C4#1568935511yescharacteristic
390C2—944no—
391C2—7522no—
392C2#2024381511yescharacteristic
393C2#357×D4711yescharacteristic
394C2#2024509411yescharacteristic
395C2#2024547311yescharacteristic
396C2#2024547511yescharacteristic
397C2#2024548511yescharacteristic
398C2#2024548711yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1380C2
socleC23×C47C2×D8
prime radicalC2×#15689360C2
cosocleC22×C8×C47C23
hypercenter#1380D47
hypocenterC47#13059
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C22×C16×D47C2semidirect
3. C2×#15688925C2semidirect
4. C2×#15688923C2semidirect
5. #20243414C2semidirect
6. #20241479C2semidirect
7. C47×#1380C2semidirect
16. #15689360C4semidirect
49. C2×C47⋊C16D4semidirect
60. C2×C16×C47D4semidirect
182. C2×D47#357semidirect
197. #1380D47semidirect
225. C47#13059semidirect
256. C2×C16D188semidirect

Maximal subgroups

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

subgroupindex
C22×C16×D472
C2×#156893602
C2×#156889252
C2×#156889232
#202434142
#202414792
C47×#13802
#1305947