Finite Group Databasebeta

← #26115608

Subgroups — #26115608

Order 12032.

510 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689471C211yesmaximal, characteristic
2#20244315C211yesmaximal, characteristic
3#20243257C211yesmaximal, characteristic, complemented
4C2×#15688875C211yesmaximal, characteristic, complemented
5C2×#15688872C211yesmaximal, characteristic, complemented
6C2×#15688866C211yesmaximal, characteristic
7C47×#1987C211yesmaximal, characteristic, complemented
8C2×#13094021C2211yescharacteristic
9#15689471—22no—
10#15689471C414yescomplemented
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093944—21no—
14C2×#13093944—21no—
15C2×#13093944—22no—
16C2×#13093935—21no—
17C2×C4×C47⋊C8C2211yescharacteristic
18#15688878—21no—
19#15688875—22no—
20#15688872—22no—
21#15688866—22no—
22C2×C4⋊Q8×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C4×C4⋊C4×C47C2211yescharacteristic
25C47×#340—22no—
26C22×D188—21no—
27C22×D188—21no—
28C22×D188—21no—
29C22×C47⋊C8—21no—
30C22×C47⋊C8—21no—
31C22×C47⋊C8D411yescharacteristic
32C22×C47⋊C8D411yescharacteristic
33#13094021—21no—
34#13094021—21no—
35#13094021—21no—
36#13094021C2×C412yes—
37C4⋊(C47⋊C8)—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)D412yes—
41#13093944—24no—
42#13093944—24no—
43#13093944—44no—
44#13093935—42no—
45C4×C47⋊C8C2×C412yes—
46C4×C47⋊C8D412yes—
47C22×Q8×C47—21no—
48C22×C8×C47—21no—
49C4⋊Q8×C47—21no—
50C4⋊Q8×C47—21no—
51C4⋊Q8×C47—21no—
52C4⋊Q8×C47C2×C412yes—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47D412yes—
56C2×C42×C47—21no—
57C2×C42×C47C2311yescharacteristic
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60#95×C47—21no—
61C23×D47—41no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47—82no—
65C22×C4×C47—22no—
66C22×C4×C47—41no—
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47#4111yescharacteristic
70C2×D188—22no—
71C2×D188—22no—
72C2×D188—22no—
73C2×D188—41no—
74C2×D188—41no—
75C2×D188—42no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—42no—
79C2×D188—41no—
80C2×D188—41no—
81C2×D188—41no—
82C2×D188—82no—
83C2×C8×C47—41no—
84C2×C8×C47—42no—
85C4⋊C4×C47—22no—
86C4⋊C4×C47—22no—
87C4⋊C4×C47—22no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C42×C47—41no—
92C42×C47—41no—
93C42×C47C22×C411yescharacteristic
94C42×C47C2×D411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47#4111yescharacteristic
97C2×C47⋊C8—21no—
98C2×C47⋊C8—21no—
99C2×C47⋊C8—21no—
100C2×C47⋊C8—21no—
101C2×C47⋊C8—22no—
102C2×C47⋊C8—41no—
103C2×C47⋊C8—41no—
104C2×C47⋊C8—41no—
105C2×C47⋊C8—42no—
106C2×C47⋊C8C22⋊C412yes—
107C2×C47⋊C8C22⋊C412yes—
108C23×C47#12111yescharacteristic
109C22×D47—42no—
110C22×D47—81no—
111C22×D47—81no—
112C22×D47—82no—
113C22×D47—82no—
114Q8×C47—82no—
115Q8×C47—82no—
116C2×C4×C47—22no—
117C2×C4×C47—42no—
118C2×C4×C47—42no—
119C2×C4×C47—42no—
120C2×C4×C47—42no—
121C2×C4×C47—82no—
122C2×C4×C47C2×C22⋊C411yescharacteristic
123C2×C4×C47C4×D411yescharacteristic
124C2×C4×C47C4×D411yescharacteristic
125C2×C4×C47#12111yescharacteristic
126C2×C4×C47#12411yescharacteristic
127C2×C4×C47#12711yescharacteristic
128C2×C4×C47#13511yescharacteristic
129C2×C4×C47#13511yescharacteristic
130C2×C4×C47AGL(1,ℤ/8)12yes—
131C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C47#13712yes—
133C2×C4×C47#13711yescharacteristic
134D188—42no—
135D188—42no—
136D188—44no—
137D188—82no—
138D188—82no—
139D188—81no—
140D188—81no—
141D188—81no—
142D188—81no—
143C8×C47—81no—
144C47⋊C8—22no—
145C47⋊C8—22no—
146C47⋊C8—42no—
147C47⋊C8—81no—
148#9747—471nomaximal, Sylow
149C22×C47#39011yescharacteristic
150C22×C47#46311yescharacteristic
151C22×C47#46411yescharacteristic
152C22×C47#46812yes—
153C22×C47#47212yes—
154C2×D47—82no—
155C2×D47—82no—
156C2×D47—82no—
157C2×D47—162no—
158C2×D47—162no—
159C4×C47—21no—
160C4×C47—21no—
161C4×C47—82no—
162C4×C47—82no—
163C4×C47#41611yescharacteristic
164C4×C47#41711yescharacteristic
165C4×C47#44012yes—
166C4×C47#46311yescharacteristic
167C4×C47#46411yescharacteristic
168C4×C47#49611yescharacteristic
169C4×C47#49711yescharacteristic
170C2×#486—471no—
171#1987D4711yescharacteristic, complemented
172#1982—471no—
173#1770—471no—
174C2×#335—471no—
175C2×#333—471no—
176C2×#331—471no—
177C2×C47#169712yes—
178C2×C47#169812yes—
179C2×C47#197311yescharacteristic
180C2×C47#197811yescharacteristic
181C2×C47#198311yescharacteristic
182D47—162no—
183C2×C4⋊Q8C2×D4711yescharacteristic
184C2×#127—471no—
185#486—474no—
186#486—942no—
187C2×C4⋊C8—471no—
188C2×C4⋊C8—471no—
189C2×C4⋊C8C2×D4711yescharacteristic
190C2×#102—941no—
191C2×#102—941no—
192C2×#102—942no—
193C2×#97—941no—
194C2×C4×C8—471no—
195C4×C4⋊C4C2×D4711yescharacteristic
196#340—22no—
197#336—941no—
198#335—942no—
199#333—942no—
200#331—942no—
201C47#974711yescharacteristic, complemented, Sylow
202C22×Q8—21no—
203C22×D4—941no—
204C22×D4—941no—
205C22×D4—941no—
206C22×C8—21no—
207C22×C8—471no—
208C22×C8—471no—
209C22×C8—941no—
210C22×C8—941no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8C4×D4712yes—
215#127—472no—
216#127—941no—
217#127—941no—
218#127—941no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C22⋊D4712yes—
222C2×C42—21no—
223C2×C42C22×D4711yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—472no—
227C4⋊C8—941no—
228C4⋊C8—941no—
229C4⋊C8—941no—
230#102—944no—
231#102—944no—
232#102—1884no—
233#97—1882no—
234C4×C8—472no—
235C4×C8—472no—
236#95—21no—
237C24—1881no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—82no—
241C2×D4—942no—
242C2×D4—942no—
243C2×D4—942no—
244C2×D4—3762no—
245C2×D4—1881no—
246C2×D4—1881no—
247C2×D4—1881no—
248C2×D4—1881no—
249C2×D4—1881no—
250C2×D4—1882no—
251C2×D4—1881no—
252C2×D4—1882no—
253C2×D4—1881no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4D4×D4711yescharacteristic
257C22×C4#1062535211yescharacteristic
258C22×C4C2×C22⋊D4711yescharacteristic
259C2×C8—41no—
260C2×C8—42no—
261C2×C8—472no—
262C2×C8—472no—
263C2×C8—941no—
264C2×C8—941no—
265C2×C8—941no—
266C2×C8—941no—
267C2×C8—942no—
268C2×C8—1881no—
269C2×C8—1882no—
270C2×C8—1881no—
271C2×C8—1881no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C42—41no—
279C42—41no—
280C42C2×C4×D4711yescharacteristic
281C42#1062535011yescharacteristic
282C42D4×D4711yescharacteristic
283C42D4×D4711yescharacteristic
284C23—3761no—
285C23—3761no—
286C23—3762no—
287C23—3762no—
288C23—1882no—
289C23#1309399611yescharacteristic
290Q8—82no—
291Q8—82no—
292D4—3762no—
293D4—3762no—
294D4—3761no—
295D4—3761no—
296D4—3761no—
297D4—3761no—
298D4—1884no—
299D4—1882no—
300D4—1882no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—82no—
307C2×C4C22⋊C4×D4711yescharacteristic
308C2×C4(C22⋊D47)⋊C411yescharacteristic
309C2×C4C4×C22⋊D4711yescharacteristic
310C2×C4#1309399711yescharacteristic
311C2×C4#1309401011yescharacteristic
312C2×C4#1309402011yescharacteristic
313C2×C4#1309404511yescharacteristic
314C2×C4#1309404711yescharacteristic
315C2×C4#1309404912yes—
316C2×C4#1309405111yescharacteristic
317C2×C4#1309405512yes—
318C2×C4#1309405611yescharacteristic
319C8—81no—
320C8—942no—
321C8—942no—
322C8—3761no—
323C8—1882no—
324C22—3762no—
325C22—3762no—
326C22—3762no—
327C22—7522no—
328C22—7522no—
329C22#1568902311yescharacteristic
330C22#1568934011yescharacteristic
331C22#1568934711yescharacteristic
332C22#1568937112yes—
333C22#1568939112yes—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—82no—
338C4#1568911811yescharacteristic
339C4#1568912311yescharacteristic
340C4#1568922112yes—
341C4#1568934111yescharacteristic
342C4#1568934811yescharacteristic
343C4#1568951311yescharacteristic
344C4#1568951511yescharacteristic
345C2—7522no—
346C2#2024292312yes—
347C2#2024293012yes—
348C2#2024427211yescharacteristic
349C2#2024429711yescharacteristic
350C2#2024431711yescharacteristic
subgroupG/H
centerC23#13093996
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1987C2
socleC23×C47#121
prime radicalC2×#13094021C22
cosocleC2×C42×C47C23
hypercenter#1987D47
hypocenterC47#9747
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
3. #20243257C2semidirect
4. C2×#15688875C2semidirect
5. C2×#15688872C2semidirect
7. C47×#1987C2semidirect
10. #15689471C4semidirect
171. #1987D47semidirect
201. C47#9747semidirect

Maximal subgroups

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

subgroupindex
C2×#156894712
#202443152
#202432572
C2×#156888752
C2×#156888722
C2×#156888662
C47×#19872
#974747