Finite Group Databasebeta

← #26132831

Subgroups — #26132831

Order 12032.

420 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#108×D47C211yesmaximal, characteristic
2C2×#15688947C211yesmaximal, characteristic, complemented
3C2×#15688946C211yesmaximal, characteristic, complemented
4#20244998C211yesmaximal, characteristic
5#20243410C211yesmaximal, characteristic
6#20241486C211yesmaximal, characteristic, complemented
7C47×#1383C211yesmaximal, characteristic, complemented
8C2×M16×D47—21no—
9C22×C8×D47C2211yescharacteristic
10C2×#13093964C2211yescharacteristic
11C2×#13093960C2211yescharacteristic
12C2×#13093959—21no—
13#108×D47—22no—
14#108×D47—22no—
15C2×#13093956C2211yescharacteristic
16#15688980—21no—
17#15688947—22no—
18#15688946—22no—
19(C2×D47)⋊C16C412yescomplemented
20(C2×D47)⋊C16C412yescomplemented
21#15688885—21no—
22C2×M32×C47C2211yescharacteristic
23C2×#108×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C22×C4×D47D411yescharacteristic
26C2×#10625329—21no—
27C2×#10625324—41no—
28M16×D47—24no—
29M16×D47—42no—
30C22×C47⋊C8D411yescharacteristic
31C2×C8×D47—21no—
32C2×C8×D47—21no—
33C2×C8×D47—21no—
34C2×C8×D47—21no—
35C2×C8×D47—41no—
36C2×C8×D47C2×C411yescharacteristic
37C2×C8×D47C2×C411yescharacteristic
38C2×C8×D47Q811yescharacteristic
39C2×C8×D47Q811yescharacteristic
40C2×C4⋊Dic47—21no—
41C2×(C2×D47)⋊C4—41no—
42#13093964—21no—
43#13093964—21no—
44C2×C47⋊C16C2×C412yes—
45#13093960—21no—
46#13093960D412yes—
47#13093959—24no—
48#13093956—21no—
49#13093956—21no—
50C47⋊#95—41no—
51C2×M16×C47—21no—
52C22×C8×C47C2311yescharacteristic
53C2×C4⋊C4×C47—21no—
54M32×C47—21no—
55M32×C47—21no—
56C2×C16×C47C2×C412yes—
57#108×C47—21no—
58#108×C47D412yes—
59#106×C47—21no—
60#106×C47—21no—
61C23×D47SD1611yescharacteristic
62C22×C4×C47—41no—
63C22×C4×C47C2×D411yescharacteristic
64C22×Dic47—41no—
65C22×Dic47SD1611yescharacteristic
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47C4⋊C411yescharacteristic
71C2×C4×D47C4⋊C411yescharacteristic
72C2×C4×D47SD1611yescharacteristic
73C2×C4×D47SD1611yescharacteristic
74M16×C47—22no—
75M16×C47—41no—
76C2×C8×C47—41no—
77C2×C8×C47C22×C411yescharacteristic
78C2×C8×C47C2×D411yescharacteristic
79C2×C8×C47C2×D411yescharacteristic
80C2×C8×C47C2×Q811yescharacteristic
81C2×C8×C47#4111yescharacteristic
82C2×C8×C47#4111yescharacteristic
83C4⋊C4×C47—41no—
84C4⋊C4×C47—41no—
85(C2×D47)⋊C4—82no—
86C4⋊Dic47—41no—
87C4⋊Dic47—41no—
88#10625329—22no—
89#10625329—41no—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—21no—
92C2×C47⋊C8—41no—
93C2×C47⋊C8C4⋊C411yescharacteristic
94C2×C47⋊C8C4⋊C411yescharacteristic
95#10625324—44no—
96C8×D47—21no—
97C8×D47—21no—
98C8×D47—21no—
99C8×D47—21no—
100C8×D47—21no—
101C8×D47—21no—
102C8×D47—21no—
103C8×D47—21no—
104C8×D47—44no—
105C16×C47—22no—
106C47⋊C16—22no—
107C23×C47C2×SD1611yescharacteristic
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—22no—
111C22×D47—41no—
112C22×D47#10611yescharacteristic
113C22×D47#10611yescharacteristic
114C2×C4×C47—81no—
115C2×C4×C47—81no—
116C2×C4×C47—81no—
117C2×C4×C47C2×C4⋊C411yescharacteristic
118C2×C4×C47#12011yescharacteristic
119C2×C4×C47#12311yescharacteristic
120C2×C4×C47C2×SD1611yescharacteristic
121C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C47#13711yescharacteristic
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—81no—
126C2×Dic47—81no—
127C2×Dic47—81no—
128C2×Dic47#10611yescharacteristic
129C2×Dic47#10611yescharacteristic
130C4×D47—21no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—21no—
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—21no—
138C8×C47—42no—
139C8×C47C4×D411yescharacteristic
140C8×C47C4×D411yescharacteristic
141C8×C47C22⋊Q811yescharacteristic
142C8×C47C22⋊Q811yescharacteristic
143C47⋊C8—21no—
144C47⋊C8—21no—
145C47⋊C8—42no—
146#12928—471nomaximal, Sylow
147C22×C47—21no—
148C22×C47—21no—
149C22×C47C2×#10611yescharacteristic
150C22×C47#44811yescharacteristic
151C22×C47#48111yescharacteristic
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—21no—
155C2×D47—21no—
156C2×D47—21no—
157C2×D47—42no—
158C2×D47—42no—
159C2×D47#36512yescomplemented
160C4×C47—161no—
161C4×C47#38511yescharacteristic
162C4×C47#42811yescharacteristic
163C4×C47#45011yescharacteristic
164C4×C47#48311yescharacteristic
165Dic47—21no—
166Dic47—21no—
167Dic47—161no—
168C22×#108—471no—
169C2×#365—471no—
170C2×#365—471no—
171#2112—471no—
172#1807—471no—
173#1383—471no—
174#1383D4711yescharacteristic, complemented
175C2×C47—21no—
176C2×C47—21no—
177C2×C47#185311yescharacteristic
178C2×C47C2×#36511yescharacteristic
179C2×C47#215511yescharacteristic
180D47—22no—
181D47—41no—
182C22×M16—941no—
183C23×C8—471no—
184C2×M32—471no—
185C2×M32C2×D4711yescharacteristic
186C2×#108—471no—
187C2×#108—942no—
188C2×#108—941no—
189C2×#108—942no—
190C2×#108C2×D4711yescharacteristic
191C2×#106—471no—
192C2×#106C2×D4711yescharacteristic
193#380—941no—
194#365—942no—
195#365—942no—
196C22⋊C16—472no—
197C22⋊C16—472no—
198#340—941no—
199C47#1292811yescharacteristic, complemented, Sylow
200C23×C4—471no—
201C2×M16—21no—
202C2×M16—944no—
203C2×M16—941no—
204C2×M16—1881no—
205C2×M16—1882no—
206C22×C8—471no—
207C22×C8—471no—
208C22×C8—471no—
209C22×C8—471no—
210C22×C8—471no—
211C22×C8—941no—
212C22×C8—941no—
213C22×C8—941no—
214C22×C8—941no—
215C22×C8—1881no—
216C22×C8C22×D4711yescharacteristic
217C2×C4⋊C4—21no—
218C2×C4⋊C4—941no—
219C2×C22⋊C4—1881no—
220M32—21no—
221M32—21no—
222M32—941no—
223M32—941no—
224C2×C16—472no—
225C2×C16C4×D4712yes—
226#108—21no—
227#108—472no—
228#108—944no—
229#108—941no—
230#108D18812yes—
231#106—21no—
232#106—21no—
233#106—941no—
234#106—941no—
235#95—1881no—
236C24—471no—
237C22×C4—41no—
238C22×C4—471no—
239C22×C4—471no—
240C22×C4—471no—
241C22×C4—471no—
242C22×C4—471no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—1881no—
248C22×C4D4×D4711yescharacteristic
249M16—22no—
250M16—41no—
251M16—942no—
252M16—1884no—
253M16—1881no—
254C2×C8—41no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8—941no—
258C2×C8—941no—
259C2×C8—941no—
260C2×C8—941no—
261C2×C8—941no—
262C2×C8—941no—
263C2×C8—941no—
264C2×C8—941no—
265C2×C8—941no—
266C2×C8—941no—
267C2×C8—1884no—
268C2×C8—1881no—
269C2×C8C2×C4×D4711yescharacteristic
270C2×C8C2×D18811yescharacteristic
271C2×C8#1062535011yescharacteristic
272C2×C8D4×D4711yescharacteristic
273C2×C8#1062535211yescharacteristic
274C2×C8Q8×D4711yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—1881no—
278C4⋊C4—1881no—
279C22⋊C4—3762no—
280C16—22no—
281C16—942no—
282C23—471no—
283C23—471no—
284C23—942no—
285C23—941no—
286C23—941no—
287C23—1881no—
288C23SD16×D4711yescharacteristic
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—471no—
293C2×C4—471no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—941no—
299C2×C4—941no—
300C2×C4—941no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—3761no—
305C2×C4—3761no—
306C2×C4—3761no—
307C2×C4C4⋊C4×D4711yescharacteristic
308C2×C4#1309399411yescharacteristic
309C2×C4#1309400611yescharacteristic
310C2×C4SD16×D4711yescharacteristic
311C2×C4#1309404811yescharacteristic
312C2×C4#1309405611yescharacteristic
313C8—42no—
314C8—941no—
315C8—941no—
316C8—1882no—
317C8(C22⋊D47)⋊C411yescharacteristic
318C8C4×D18811yescharacteristic
319C8#1309400211yescharacteristic
320C8#1309400411yescharacteristic
321C22—21no—
322C22—21no—
323C22—472no—
324C22—941no—
325C22—941no—
326C22—941no—
327C22—941no—
328C22—941no—
329C22—1882no—
330C22—1882no—
331C22#106×D4711yescharacteristic
332C22#1568926311yescharacteristic
333C22#1568944011yescharacteristic
334C4—161no—
335C4—941no—
336C4—941no—
337C4—7521no—
338C4#1568899711yescharacteristic
339C4#1568916411yescharacteristic
340C4#1568927511yescharacteristic
341C4#1568945211yescharacteristic
342C2—21no—
343C2—21no—
344C2—942no—
345C2—1881no—
346C2#2024358211yescharacteristic
347C2#365×D4711yescharacteristic
348C2#2024515911yescharacteristic
subgroupG/H
centerC22#106×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#1383C2
socleC22×C47C2×#106
prime radicalC23×D47SD16
cosocleC22×C8×C47C23
hypercenter#1383D47
hypocenterC47#12928
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1383

Complements

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

NH ≅ G/Ntype
2. C2×#15688947C2semidirect
3. C2×#15688946C2semidirect
6. #20241486C2semidirect
7. C47×#1383C2semidirect
19. (C2×D47)⋊C16C4semidirect
20. (C2×D47)⋊C16C4semidirect
159. C2×D47#365semidirect
174. #1383D47semidirect
199. C47#12928semidirect

Maximal subgroups

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

subgroupindex
C2×#108×D472
C2×#156889472
C2×#156889462
#202449982
#202434102
#202414862
C47×#13832
#1292847