Finite Group Databasebeta

← #26134500

Subgroups — #26134500

Order 12032.

514 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689508C211yesmaximal, characteristic
2C2×#15688927C211yesmaximal, characteristic, complemented
3C2×#15688925C211yesmaximal, characteristic
4C2×#15688923C211yesmaximal, characteristic
5C2×C16×Dic47C211yesmaximal, characteristic, complemented
6#20243551C211yesmaximal, characteristic, complemented
7C2×C47×#358C211yesmaximal, characteristic, complemented
8C22×#10625336—21no—
9C22×D376C2211yescharacteristic
10C2×#13094013—21no—
11C22×C47⋊C16C2211yescharacteristic
12#15689508—22no—
13#15689508C414yescomplemented
14C2×#13093958C2211yescharacteristic
15C2×#13093955—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15688988—21no—
18#15688927—22no—
19#15688925—22no—
20#15688923—22no—
21C16×Dic47—22no—
22C22×Q16×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C47×#358—22no—
26C22×D188—21no—
27C2×#10625336—24no—
28C2×#10625336—42no—
29C2×#10625336—42no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376—21no—
34C2×D376—21no—
35C2×D376C2×C412yes—
36C22×C47⋊C8D411yescharacteristic
37#13094013—24no—
38#13094013—42no—
39C2×C4⋊Dic47—21no—
40C2×(C2×D47)⋊C4—42no—
41C2×C4×Dic47D411yescharacteristic
42C2×C47⋊C16—21no—
43C2×C47⋊C16—21no—
44C2×C47⋊C16D412yes—
45#13093958—21no—
46#13093958—21no—
47#13093955—42no—
48C8×Dic47C2×C412yes—
49C8×Dic47D412yes—
50C47⋊#95—42no—
51C22×Q8×C47—21no—
52C2×Q16×C47—21no—
53C2×Q16×C47—21no—
54C2×Q16×C47—21no—
55C2×Q16×C47—21no—
56C2×Q16×C47—21no—
57C2×Q16×C47C2×C412yes—
58C22×C8×C47C2311yescharacteristic
59C2×C4⋊C4×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47D412yes—
63#107×C47—21no—
64#107×C47—21no—
65C23×D47—41no—
66C2×Q8×C47—22no—
67C2×Q8×C47—41no—
68C2×Q8×C47—41no—
69C2×Q8×C47—41no—
70C2×Q8×C47—41no—
71C2×Q8×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47C2×D411yescharacteristic
75C22×Dic47—41no—
76C22×Dic47D812yes—
77C2×D188—22no—
78C2×D188—41no—
79C2×D188—41no—
80C2×D188—41no—
81C2×D188—41no—
82C2×D188—41no—
83Q16×C47—22no—
84Q16×C47—22no—
85Q16×C47—41no—
86Q16×C47—41no—
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—41no—
94C4⋊C4×C47—41no—
95#10625336—48no—
96(C2×D47)⋊C4—48no—
97C4⋊Dic47—41no—
98C4⋊Dic47—41no—
99C4×Dic47C22⋊C412yes—
100C4×Dic47SD1612yes—
101C2×C47⋊C8C22⋊C412yes—
102C2×C47⋊C8D812yes—
103C2×C47⋊C8SD1612yes—
104D376—22no—
105D376—22no—
106D376—41no—
107D376—41no—
108C16×C47—22no—
109C47⋊C16—22no—
110C23×C47C2×D811yescharacteristic
111C22×D47—42no—
112C22×D47—81no—
113C22×D47—81no—
114C22×D47—82no—
115C22×D47—82no—
116Q8×C47—42no—
117Q8×C47—42no—
118Q8×C47—81no—
119Q8×C47—81no—
120C2×C4×C47—42no—
121C2×C4×C47—81no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47—82no—
125C2×C4×C47C2×C22⋊C411yescharacteristic
126C2×C4×C47#12411yescharacteristic
127C2×C4×C47#12711yescharacteristic
128C2×C4×C47C2×D811yescharacteristic
129C2×C4×C47C2×SD1611yescharacteristic
130C2×C4×C47C2×SD1611yescharacteristic
131C2×Dic47—22no—
132C2×Dic47—22no—
133C2×Dic47—81no—
134C2×Dic47—82no—
135C2×Dic47#10214yes—
136D188—42no—
137D188—42no—
138D188—81no—
139D188—81no—
140C8×C47C4×D411yescharacteristic
141C8×C47C4×D411yescharacteristic
142C8×C47#12111yescharacteristic
143C8×C47#12111yescharacteristic
144C47⋊C8#10214yes—
145#13204—471nomaximal, Sylow
146C22×C47C2×#10211yescharacteristic
147C22×C47#48611yescharacteristic
148C22×C47#49311yescharacteristic
149C22×C47#50812yes—
150C22×C47#50812yes—
151C2×D47—84no—
152C2×D47—82no—
153C2×D47—162no—
154C2×D47—161no—
155C2×D47—161no—
156C4×C47—82no—
157C4×C47—161no—
158C4×C47#39011yescharacteristic
159C4×C47C2×#10211yescharacteristic
160C4×C47#48611yescharacteristic
161C4×C47#49211yescharacteristic
162Dic47—24no—
163Dic47—161no—
164C2×#495—471no—
165C2×#358—471no—
166C2×#358D4711yescharacteristic, complemented
167C2×#357—471no—
168C2×#357—471no—
169C2×C4×C16—471no—
170#1846—471no—
171C2×C47#195711yescharacteristic
172C2×C47#213812yes—
173C2×C47#224212yes—
174C2×C47#224911yescharacteristic
175C2×C47#224911yescharacteristic
176D47—162no—
177C22×Q16C2×D4711yescharacteristic
178C22×SD16—941no—
179C22×D8—471no—
180C2×#124—941no—
181C22×C16—471no—
182C22×C16C2×D4711yescharacteristic
183#495—474no—
184#495—942no—
185C2×#107—471no—
186C2×#107C2×D4711yescharacteristic
187C2×#106—941no—
188C2×C4×C8—471no—
189#382—941no—
190#358—22no—
191#358—942no—
192#357—942no—
193#357—942no—
194C4×C16—942no—
195C47#1320411yescharacteristic, complemented, Sylow
196C22×Q8—21no—
197C22×D4—941no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16C4×D4712yes—
204C2×SD16—944no—
205C2×SD16—1882no—
206C2×SD16—1882no—
207C2×D8—472no—
208C2×D8—941no—
209C2×D8—941no—
210C2×D8—941no—
211C2×D8—941no—
212C2×D8—941no—
213C22×C8—471no—
214C22×C8C22×D4711yescharacteristic
215#124—944no—
216#124—1882no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—941no—
219C2×C22⋊C4—1882no—
220C2×C42—471no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—472no—
224C2×C16—941no—
225C2×C16—941no—
226C2×C16C22⋊D4712yes—
227#107—21no—
228#107—21no—
229#107—941no—
230#107—941no—
231#106—1882no—
232C4×C8—472no—
233C4×C8—472no—
234#95—1882no—
235C24—1881no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×D4—942no—
243C2×D4—1881no—
244C2×D4—1881no—
245C2×D4—1881no—
246C2×D4—1881no—
247C2×D4—1881no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—472no—
251C22×C4—1881no—
252C22×C4D4×D4711yescharacteristic
253Q16—22no—
254Q16—22no—
255Q16—41no—
256Q16—41no—
257SD16—1888no—
258D8—942no—
259D8—942no—
260D8—1881no—
261D8—1881no—
262C2×C8—472no—
263C2×C8—472no—
264C2×C8—472no—
265C2×C8C2×C4×D4711yescharacteristic
266C2×C8#1062535011yescharacteristic
267C2×C8D4×D4711yescharacteristic
268C2×C8D4×D4711yescharacteristic
269C2×C8#1062535211yescharacteristic
270C2×C8C2×C22⋊D4711yescharacteristic
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—1881no—
274C4⋊C4—1881no—
275C22⋊C4—1888no—
276C42—472no—
277C42—472no—
278C16—22no—
279C16—942no—
280C23—3761no—
281C23—3762no—
282C23—3762no—
283C23—3761no—
284C23—1882no—
285C23D8×D4711yescharacteristic
286Q8—42no—
287Q8—42no—
288Q8—81no—
289Q8—81no—
290D4—3761no—
291D4—3761no—
292D4—1882no—
293D4—1882no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4—474no—
300C2×C4—942no—
301C2×C4—942no—
302C2×C4—3761no—
303C2×C4—3762no—
304C2×C4C22⋊C4×D4711yescharacteristic
305C2×C4#1309401011yescharacteristic
306C2×C4#1309402011yescharacteristic
307C2×C4D8×D4711yescharacteristic
308C2×C4SD16×D4711yescharacteristic
309C2×C4SD16×D4711yescharacteristic
310C8—474no—
311C8(C22⋊D47)⋊C411yescharacteristic
312C8C4×C22⋊D4711yescharacteristic
313C8#1309399611yescharacteristic
314C8#1309399711yescharacteristic
315C22—3764no—
316C22—3762no—
317C22—7522no—
318C22—7521no—
319C22—7521no—
320C22#102×D4711yescharacteristic
321C22#1568946811yescharacteristic
322C22#1568949811yescharacteristic
323C22#1568955412yes—
324C22#1568955612yes—
325C4—82no—
326C4—161no—
327C4—944no—
328C4—7521no—
329C4#1568902311yescharacteristic
330C4#102×D4711yescharacteristic
331C4#1568946811yescharacteristic
332C4#1568949411yescharacteristic
333C2—7522no—
334C2#2024419211yescharacteristic
335C2#2024509412yes—
336C2#2024562112yes—
337C2#2024564811yescharacteristic
338C2#2024565011yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#358C2
socleC23×C47C2×D8
prime radicalC22×D376C22
cosocleC22×C8×C47C23
hypercenterC2×#358D47
hypocenterC47#13204
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#15688927C2semidirect
5. C2×C16×Dic47C2semidirect
6. #20243551C2semidirect
7. C2×C47×#358C2semidirect
13. #15689508C4semidirect
166. C2×#358D47semidirect
195. C47#13204semidirect

Maximal subgroups

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

subgroupindex
C2×#156895082
C2×#156889272
C2×#156889252
C2×#156889232
C2×C16×Dic472
#202435512
C2×C47×#3582
#1320447