Finite Group Databasebeta

← #26132428

Subgroups — #26132428

Order 12032.

396 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D47C211yesmaximal, characteristic
2C2×#15688947C211yesmaximal, characteristic, complemented
3C2×#15688945C211yesmaximal, characteristic, complemented
4#20243423C211yesmaximal, characteristic
5#20243410C211yesmaximal, characteristic
6#20241487C211yesmaximal, characteristic, complemented
7C47×#1383C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9C2×#13093964C2211yescharacteristic
10C2×#13093963C412yescomplemented
11M32×D47—22no—
12M32×D47—22no—
13C2×C16×D47C412yescomplemented
14C2×#13093960C2211yescharacteristic
15C2×#13093956C2211yescharacteristic
16#15689086—21no—
17#15688980—21no—
18#15688947—22no—
19#15688945—22no—
20#15688887—21no—
21#15688885—21no—
22C2×M32×C47C2211yescharacteristic
23C2×#108×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C22×C4×D47D411yescharacteristic
26C2×#10625329—21no—
27C22×C47⋊C8D411yescharacteristic
28C2×C8×D47—21no—
29C2×C8×D47—21no—
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47C2×C411yescharacteristic
33C2×C8×D47C2×C411yescharacteristic
34C2×C8×D47Q811yescharacteristic
35C2×C8×D47Q811yescharacteristic
36C2×C4⋊Dic47—21no—
37C2×(C2×D47)⋊C4—41no—
38#13093964D412yes—
39#13093964D412yes—
40#13093963—24no—
41C2×C47⋊C16C2×C412yes—
42C16×D47—24no—
43#13093960—21no—
44#13093960—21no—
45#13093956—21no—
46#13093956—21no—
47(C2×D47)⋊C8—41no—
48(C2×D47)⋊C8—41no—
49C47⋊#95—41no—
50C2×M16×C47—21no—
51C22×C8×C47C2311yescharacteristic
52C2×C4⋊C4×C47—21no—
53M32×C47—21no—
54M32×C47—21no—
55C2×C16×C47C2×C412yes—
56#108×C47—21no—
57#108×C47—21no—
58#106×C47—21no—
59#106×C47—21no—
60C23×D47SD1611yescharacteristic
61C22×C4×C47—41no—
62C22×C4×C47C2×D411yescharacteristic
63C22×Dic47—41no—
64C22×Dic47SD1611yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C4⋊C411yescharacteristic
70C2×C4×D47C4⋊C411yescharacteristic
71C2×C4×D47SD1611yescharacteristic
72C2×C4×D47SD1611yescharacteristic
73M16×C47—41no—
74M16×C47—41no—
75C2×C8×C47—41no—
76C2×C8×C47C22×C411yescharacteristic
77C2×C8×C47C2×D411yescharacteristic
78C2×C8×C47C2×D411yescharacteristic
79C2×C8×C47C2×Q811yescharacteristic
80C2×C8×C47#4111yescharacteristic
81C2×C8×C47#4111yescharacteristic
82C4⋊C4×C47—41no—
83C4⋊C4×C47—41no—
84(C2×D47)⋊C4—82no—
85C4⋊Dic47—41no—
86C4⋊Dic47—41no—
87#10625329—41no—
88#10625329—41no—
89C2×C47⋊C8—21no—
90C2×C47⋊C8—21no—
91C2×C47⋊C8—41no—
92C2×C47⋊C8C4⋊C411yescharacteristic
93C2×C47⋊C8C4⋊C411yescharacteristic
94C8×D47—21no—
95C8×D47—21no—
96C8×D47—21no—
97C8×D47—21no—
98C8×D47—21no—
99C8×D47—21no—
100C8×D47—21no—
101C8×D47—21no—
102C16×C47—22no—
103C47⋊C16C22⋊C414yescomplemented
104C23×C47C2×SD1611yescharacteristic
105C22×D47—21no—
106C22×D47—21no—
107C22×D47—22no—
108C22×D47—41no—
109C22×D47#10611yescharacteristic
110C22×D47#10611yescharacteristic
111C2×C4×C47—81no—
112C2×C4×C47—81no—
113C2×C4×C47—81no—
114C2×C4×C47C2×C4⋊C411yescharacteristic
115C2×C4×C47#12111yescharacteristic
116C2×C4×C47#12111yescharacteristic
117C2×C4×C47C2×SD1611yescharacteristic
118C2×C4×C47#13511yescharacteristic
119C2×C4×C47#13511yescharacteristic
120C2×Dic47—21no—
121C2×Dic47—21no—
122C2×Dic47—81no—
123C2×Dic47—81no—
124C2×Dic47—81no—
125C2×Dic47#10611yescharacteristic
126C2×Dic47#10611yescharacteristic
127C4×D47—21no—
128C4×D47—21no—
129C4×D47—21no—
130C4×D47—21no—
131C4×D47—21no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—21no—
135C8×C47—81no—
136C8×C47C2×C22⋊C411yescharacteristic
137C8×C47#11711yescharacteristic
138C8×C47C22⋊Q811yescharacteristic
139C8×C47C22⋊Q811yescharacteristic
140C47⋊C8—21no—
141C47⋊C8—21no—
142C47⋊C8—81no—
143#12831—471nomaximal, Sylow
144C22×C47—21no—
145C22×C47—21no—
146C22×C47C2×#10611yescharacteristic
147C22×C47#46511yescharacteristic
148C22×C47#46511yescharacteristic
149C2×D47—21no—
150C2×D47—21no—
151C2×D47—21no—
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—42no—
155C2×D47—42no—
156C2×D47#36512yescomplemented
157C4×C47—161no—
158C4×C47#38011yescharacteristic
159C4×C47#42711yescharacteristic
160C4×C47#46511yescharacteristic
161C4×C47#46511yescharacteristic
162Dic47—21no—
163Dic47—21no—
164Dic47—161no—
165C22×M32—471no—
166C2×#365—471no—
167C2×#365—471no—
168#1810—471no—
169#1807—471no—
170#1383—471no—
171#1383D4711yescharacteristic, complemented
172C2×C47—21no—
173C2×C47—21no—
174C2×C47#180711yescharacteristic
175C2×C47C2×#36511yescharacteristic
176C2×C47#215511yescharacteristic
177D47—22no—
178D47—41no—
179C23×C8—471no—
180C2×M32—471no—
181C2×M32—472no—
182C2×M32—942no—
183C2×M32—942no—
184C2×M32C2×D4711yescharacteristic
185C22×C16—472no—
186C2×#108—471no—
187C2×#108C2×D4711yescharacteristic
188C2×#106—471no—
189C2×#106C2×D4711yescharacteristic
190#407—941no—
191#380—941no—
192#365—942no—
193#365—942no—
194#341—941no—
195#340—941no—
196C47#1283111yescharacteristic, complemented, Sylow
197C23×C4—471no—
198C2×M16—21no—
199C2×M16—941no—
200C22×C8—471no—
201C22×C8—471no—
202C22×C8—471no—
203C22×C8—471no—
204C22×C8—471no—
205C22×C8—941no—
206C22×C8—941no—
207C22×C8—941no—
208C22×C8—941no—
209C22×C8C22×D4711yescharacteristic
210C2×C4⋊C4—21no—
211C2×C4⋊C4—941no—
212C2×C22⋊C4—1881no—
213M32—21no—
214M32—21no—
215M32—472no—
216M32—472no—
217M32—944no—
218C2×C16—472no—
219C2×C16—944no—
220C2×C16C4×D4712yes—
221#108—21no—
222#108—21no—
223#108—941no—
224#108—941no—
225#106—21no—
226#106—21no—
227#106—941no—
228#106—941no—
229C22⋊C8—1881no—
230C22⋊C8—1881no—
231#95—1881no—
232C24—471no—
233C22×C4—41no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—1881no—
244C22×C4D4×D4711yescharacteristic
245M16—41no—
246M16—41no—
247M16—1881no—
248M16—1881no—
249C2×C8—41no—
250C2×C8—471no—
251C2×C8—471no—
252C2×C8—941no—
253C2×C8—941no—
254C2×C8—941no—
255C2×C8—941no—
256C2×C8—941no—
257C2×C8—941no—
258C2×C8—941no—
259C2×C8—941no—
260C2×C8—941no—
261C2×C8—941no—
262C2×C8—1881no—
263C2×C8C2×C4×D4711yescharacteristic
264C2×C8#1062535011yescharacteristic
265C2×C8#1062535011yescharacteristic
266C2×C8D4×D4711yescharacteristic
267C2×C8D4×D4711yescharacteristic
268C2×C8Q8×D4711yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—1881no—
272C4⋊C4—1881no—
273C22⋊C4—3762no—
274C16—22no—
275C16—474no—
276C23—471no—
277C23—471no—
278C23—942no—
279C23—941no—
280C23—941no—
281C23—1881no—
282C23SD16×D4711yescharacteristic
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—471no—
287C2×C4—471no—
288C2×C4—941no—
289C2×C4—941no—
290C2×C4—941no—
291C2×C4—941no—
292C2×C4—941no—
293C2×C4—941no—
294C2×C4—941no—
295C2×C4—941no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—3761no—
299C2×C4—3761no—
300C2×C4—3761no—
301C2×C4C4⋊C4×D4711yescharacteristic
302C2×C4#1309399711yescharacteristic
303C2×C4#1309399711yescharacteristic
304C2×C4SD16×D4711yescharacteristic
305C2×C4#1309404311yescharacteristic
306C2×C4#1309404711yescharacteristic
307C8—81no—
308C8—941no—
309C8—941no—
310C8—3761no—
311C8C22⋊C4×D4711yescharacteristic
312C8#1309398111yescharacteristic
313C8#1309400211yescharacteristic
314C8#1309400211yescharacteristic
315C22—21no—
316C22—21no—
317C22—472no—
318C22—941no—
319C22—941no—
320C22—941no—
321C22—941no—
322C22—941no—
323C22—1882no—
324C22—1882no—
325C22#106×D4711yescharacteristic
326C22#1568935111yescharacteristic
327C22#1568935511yescharacteristic
328C4—161no—
329C4—941no—
330C4—941no—
331C4—7521no—
332C4#1568898211yescharacteristic
333C4#1568916011yescharacteristic
334C4#1568935111yescharacteristic
335C4#1568935511yescharacteristic
336C2—21no—
337C2—21no—
338C2—942no—
339C2—1881no—
340C2#2024341211yescharacteristic
341C2#365×D4711yescharacteristic
342C2#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#12831
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×#15688945C2semidirect
6. #20241487C2semidirect
7. C47×#1383C2semidirect
10. C2×#13093963C4semidirect
13. C2×C16×D47C4semidirect
103. C47⋊C16C22⋊C4semidirect
156. C2×D47#365semidirect
171. #1383D47semidirect
196. C47#12831semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D472
C2×#156889472
C2×#156889452
#202434232
#202434102
#202414872
C47×#13832
#1283147