Finite Group Databasebeta

← #26133637

Subgroups — #26133637

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×#15689356C211yesmaximal, characteristic
3C2×#15688924C211yesmaximal, characteristic, complemented
4#20243414C211yesmaximal, characteristic, complemented
5#20241480C211yesmaximal, characteristic, complemented
6#20241479C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13093995—21no—
10C22×C47⋊C16C2211yescharacteristic
11C2×C16×D47—22no—
12C2×C16×D47—22no—
13C2×C16×D47—22no—
14#15689356—22no—
15#15689356C414yescomplemented
16C2×#13093958C2211yescharacteristic
17C2×#13093958C2211yescharacteristic
18C2×#13093945—21no—
19#15688980—21no—
20#15688924—22no—
21#15688885—21no—
22C22×D8×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C47×#357—22no—
26C22×C22⋊D47—41no—
27C22×C4×D47D411yescharacteristic
28C22×C47⋊C8D411yescharacteristic
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47—21no—
33C2×C8×D47C2×C412yes—
34C2×C8×D47D412yes—
35#13093995—24no—
36#13093995—42no—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47—21no—
39C2×C22⋊Dic47—41no—
40C2×(C2×D47)⋊C4—41no—
41C2×C47⋊C16—21no—
42C2×C47⋊C16—21no—
43C2×C47⋊C16D412yescomplemented
44C16×D47—28no—
45#13093958—21no—
46#13093958—21no—
47#13093958—21no—
48#13093958C2×C412yes—
49#13093945—24no—
50C47⋊#95—41no—
51C22×D4×C47—21no—
52C2×D8×C47—21no—
53C2×D8×C47—21no—
54C2×D8×C47—21no—
55C2×D8×C47—21no—
56C2×D8×C47—21no—
57C2×D8×C47C2×C412yes—
58C22×C8×C47C2311yescharacteristic
59C2×C4⋊C4×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47D412yescomplemented
63#107×C47—21no—
64#107×C47—21no—
65C24×C47—41no—
66C23×D47D811yescharacteristic
67C2×D4×C47—22no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C2×D4×C47—41no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47C2×D411yescharacteristic
75C2×C22⋊D47—44no—
76C2×C22⋊D47—82no—
77C2×C22⋊D47—82no—
78C22×Dic47—41no—
79C22×Dic47—41no—
80C22×Dic47D811yescharacteristic
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47C22⋊C412yes—
86C2×C4×D47SD1612yes—
87D8×C47—22no—
88D8×C47—22no—
89D8×C47—41no—
90D8×C47—41no—
91C2×C8×C47C22×C411yescharacteristic
92C2×C8×C47C2×D411yescharacteristic
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47#4111yescharacteristic
96C2×C8×C47#4111yescharacteristic
97C4⋊C4×C47—41no—
98C4⋊C4×C47—41no—
99C22⋊Dic47—44no—
100(C2×D47)⋊C4—82no—
101C4⋊Dic47—22no—
102C4⋊Dic47—41no—
103C4⋊Dic47—41no—
104C4⋊Dic47—41no—
105C2×C47⋊C8—21no—
106C2×C47⋊C8—21no—
107C2×C47⋊C8C22⋊C412yes—
108C8×D47—22no—
109C8×D47—22no—
110C8×D47—22no—
111C8×D47—22no—
112C16×C47—22no—
113C47⋊C16—22no—
114C23×C47—42no—
115C23×C47—81no—
116C23×C47—81no—
117C23×C47—81no—
118C23×C47—81no—
119C23×C47—81no—
120C23×C47—81no—
121C23×C47C2×D811yescharacteristic
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47#10212yes—
127C22×D47D1612yes—
128C22×D47SD3212yes—
129D4×C47—42no—
130D4×C47—42no—
131D4×C47—81no—
132D4×C47—81no—
133C2×C4×C47—81no—
134C2×C4×C47—81no—
135C2×C4×C47—81no—
136C2×C4×C47C2×C22⋊C411yescharacteristic
137C2×C4×C47#12111yescharacteristic
138C2×C4×C47#12111yescharacteristic
139C2×C4×C47C2×SD1611yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×C4×C47#13511yescharacteristic
142C22⋊D47—88no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—42no—
146C2×Dic47—81no—
147C2×Dic47—81no—
148C2×Dic47—81no—
149C2×Dic47—81no—
150C2×Dic47—81no—
151C2×Dic47#10212yes—
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×C47—82no—
163C22×C47—82no—
164C22×C47—82no—
165C22×C47—161no—
166C22×C47—161no—
167C22×C47—161no—
168C22×C47—161no—
169C22×C47C2×#10211yescharacteristic
170C22×C47#46611yescharacteristic
171C22×C47#46611yescharacteristic
172C22×C47C2×D1611yescharacteristic
173C22×C47C2×SD3211yescharacteristic
174C22×C47#50811yescharacteristic
175C22×C47#50811yescharacteristic
176C2×D47—22no—
177C2×D47—22no—
178C2×D47—22no—
179C2×D47—22no—
180C2×D47—22no—
181C2×D47—22no—
182C2×D47#35714yescomplemented
183C4×C47—161no—
184C4×C47#38611yescharacteristic
185C4×C47#41611yescharacteristic
186C4×C47#46511yescharacteristic
187C4×C47#46511yescharacteristic
188Dic47—22no—
189Dic47—82no—
190Dic47—161no—
191C23×C16—471no—
192C2×#466—471no—
193C2×#357—471no—
194C2×#357D4711yescharacteristic, complemented
195#1808—471no—
196#1380—471no—
197#1380—471no—
198C2×C47—162no—
199C2×C47#189311yescharacteristic
200C2×C47C2×#35711yescharacteristic
201C2×C47#213811yescharacteristic
202C2×C47#221511yescharacteristic
203C2×C47#221511yescharacteristic
204C2×C47#221711yescharacteristic
205C2×C47#221711yescharacteristic
206D47—24no—
207C22×D8C2×D4711yescharacteristic
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×#107—471no—
219C2×#107C2×D4711yescharacteristic
220C2×#102—941no—
221#380—941no—
222#357—22no—
223#357—942no—
224#340—941no—
225C47#1305911yescharacteristic, complemented, Sylow
226C22×D4—21no—
227C22×D4—1881no—
228C23×C4—471no—
229C2×D8—21no—
230C2×D8—21no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8C4×D4712yes—
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—941no—
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×C16C22⋊D4712yescomplemented
257#107—21no—
258#107—21no—
259#107—472no—
260#107—941no—
261#107—941no—
262#107—941no—
263#102—944no—
264#95—1881no—
265C24—41no—
266C24—471no—
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—3762no—
274C2×D4—3762no—
275C2×D4—1884no—
276C22×C4—41no—
277C22×C4—471no—
278C22×C4—472no—
279C22×C4—472no—
280C22×C4—941no—
281C22×C4—941no—
282C22×C4—941no—
283C22×C4—941no—
284C22×C4—1881no—
285C22×C4—1881no—
286C22×C4D4×D4711yescharacteristic
287D8—22no—
288D8—22no—
289D8—41no—
290D8—41no—
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×C8#1062535011yescharacteristic
300C2×C8D4×D4711yescharacteristic
301C2×C8D4×D4711yescharacteristic
302C2×C8#1062535211yescharacteristic
303C2×C8C2×C22⋊D4711yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—942no—
307C4⋊C4—1881no—
308C4⋊C4—1881no—
309C4⋊C4—1881no—
310C22⋊C4—3762no—
311C22⋊C4—1884no—
312C16—22no—
313C16—942no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—472no—
322C23—472no—
323C23—472no—
324C23—941no—
325C23—941no—
326C23—941no—
327C23—941no—
328C23D8×D4711yescharacteristic
329D4—42no—
330D4—42no—
331D4—81no—
332D4—81no—
333D4—3768no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—472no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—942no—
341C2×C4—942no—
342C2×C4—942no—
343C2×C4—942no—
344C2×C4—3761no—
345C2×C4—3761no—
346C2×C4—3761no—
347C2×C4—3761no—
348C2×C4—3761no—
349C2×C4—1882no—
350C2×C4C22⋊C4×D4711yescharacteristic
351C2×C4#1309399511yescharacteristic
352C2×C4#1309399711yescharacteristic
353C2×C4SD16×D4711yescharacteristic
354C2×C4#1309404311yescharacteristic
355C2×C4#1309404511yescharacteristic
356C8—942no—
357C8(C22⋊D47)⋊C411yescharacteristic
358C8C4×C22⋊D4711yescharacteristic
359C8#1309399211yescharacteristic
360C8#1309400611yescharacteristic
361C22—82no—
362C22—82no—
363C22—82no—
364C22—161no—
365C22—161no—
366C22—161no—
367C22—161no—
368C22—474no—
369C22—942no—
370C22—942no—
371C22—942no—
372C22—942no—
373C22—942no—
374C22—942no—
375C22#102×D4711yescharacteristic
376C22#1568935611yescharacteristic
377C22#1568935811yescharacteristic
378C22D16×D4711yescharacteristic
379C22SD32×D4711yescharacteristic
380C22#1568955211yescharacteristic
381C22#1568955411yescharacteristic
382C4—161no—
383C4—942no—
384C4—3762no—
385C4—7521no—
386C4#1568899911yescharacteristic
387C4#1568911611yescharacteristic
388C4#1568934911yescharacteristic
389C4#1568935111yescharacteristic
390C2—162no—
391C2—944no—
392C2#2024381311yescharacteristic
393C2#357×D4711yescharacteristic
394C2#2024509211yescharacteristic
395C2#2024547111yescharacteristic
396C2#2024547311yescharacteristic
397C2#2024548111yescharacteristic
398C2#2024548311yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC2×#15689356C2
cosocleC22×C8×C47C23
hypercenterC2×#357D47
hypocenterC47#13059
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. C22×C16×D47C2semidirect
3. C2×#15688924C2semidirect
4. #20243414C2semidirect
5. #20241480C2semidirect
6. #20241479C2semidirect
7. C2×C47×#357C2semidirect
15. #15689356C4semidirect
43. C2×C47⋊C16D4semidirect
62. C2×C16×C47D4semidirect
182. C2×D47#357semidirect
194. C2×#357D47semidirect
225. C47#13059semidirect
256. C2×C16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C22×C16×D472
C2×#156893562
C2×#156889242
#202434142
#202414802
#202414792
C2×C47×#3572
#1305947