Finite Group Databasebeta

← #26133214

Subgroups — #26133214

Order 12032.

626 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689359C211yesmaximal, characteristic
2C22×#13093958C211yesmaximal, characteristic, complemented
3C2×#15688925C212yesmaximal, complemented
4#20241480C212yesmaximal, complemented
5C2×C47×C22⋊C16C211yesmaximal, characteristic, complemented
6C22×D376C2211yescharacteristic
7C2×#13093998—21no—
8C22×C4⋊Dic47—21no—
9#15689359—22no—
10#15689359C414yescomplemented
11C2×#13093958—24no—
12C2×#13093958—21no—
13C2×#13093958C2211yescharacteristic
14C2×#13093958C2212yes—
15C2×#13093946—21no—
16#15688925—24no—
17C23×C8×C47C2211yescharacteristic
18C22×C16×C47C2212yes—
19C47×C22⋊C16—22no—
20C22×D188—21no—
21C22×C22⋊D47—41no—
22C23×Dic47—41no—
23C2×D376—22no—
24C2×D376—22no—
25C2×D376—21no—
26C2×D376C2×C412yescomplemented
27#13093998—24no—
28#13093998—42no—
29C2×C4⋊Dic47—24no—
30C2×C4⋊Dic47—22no—
31C2×C4⋊Dic47—21no—
32C2×C4⋊Dic47—42no—
33C2×C4⋊Dic47—41no—
34C2×(C2×D47)⋊C4—41no—
35#13093958—24no—
36#13093958—21no—
37#13093958—22no—
38#13093958C2×C412yescomplemented
39#13093958D414yescomplemented
40#13093946—24no—
41C23×C4×C47D411yescharacteristic
42C22×C8×C47—22no—
43C22×C8×C47—22no—
44C22×C8×C47C2×C412yes—
45C22×C8×C47D411yescharacteristic
46C22×C8×C47D412yes—
47C22×C8×C47C2311yescharacteristic
48C2×C16×C47—22no—
49C2×C16×C47—22no—
50C2×C16×C47—22no—
51C24×C47D811yescharacteristic
52C23×D47—41no—
53C22×C4×C47—21no—
54C22×C4×C47—21no—
55C22×C4×C47—21no—
56C22×C4×C47—21no—
57C22×C4×C47C22⋊C412yes—
58C22×C4×C47D811yescharacteristic
59C22×C4×C47SD1612yes—
60C22×C4×C47C2×D411yescharacteristic
61C2×C22⋊D47—44no—
62C2×C22⋊D47—82no—
63C2×C22⋊D47—82no—
64C22×Dic47—44no—
65C22×Dic47—41no—
66C22×Dic47—42no—
67C22×Dic47—82no—
68C22×Dic47—82no—
69C2×D188—22no—
70C2×D188—41no—
71C2×D188—41no—
72C2×D188—41no—
73C2×D188—41no—
74C2×D188—41no—
75C2×C8×C47—21no—
76C2×C8×C47—21no—
77C2×C8×C47—24no—
78C2×C8×C47—24no—
79C2×C8×C47C22⋊C412yes—
80C2×C8×C47C22×C411yescharacteristic
81C2×C8×C47C2×D412yes—
82C2×C8×C47C2×D411yescharacteristic
83C2×C8×C47#4112yes—
84(C2×D47)⋊C4—44no—
85C4⋊Dic47—22no—
86C4⋊Dic47—24no—
87C4⋊Dic47—44no—
88C4⋊Dic47—41no—
89C4⋊Dic47—42no—
90D376—24no—
91D376—42no—
92C16×C47—42no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47#10212yes—
98C23×C47D1612yes—
99C23×C47SD3212yes—
100C23×C47C2×D811yescharacteristic
101C22×D47—42no—
102C22×D47—81no—
103C22×D47—81no—
104C22×D47—81no—
105C22×D47—81no—
106C22×D47—81no—
107C22×D47—81no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—22no—
111C2×C4×C47—22no—
112C2×C4×C47—22no—
113C2×C4×C47—22no—
114C2×C4×C47#10212yes—
115C2×C4×C47C2×C22⋊C411yescharacteristic
116C2×C4×C47#12011yescharacteristic
117C2×C4×C47#12311yescharacteristic
118C2×C4×C47C2×SD1611yescharacteristic
119C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C47#13711yescharacteristic
121C22⋊D47—88no—
122C2×Dic47—42no—
123C2×Dic47—44no—
124C2×Dic47—88no—
125C2×Dic47—82no—
126C2×Dic47—81no—
127C2×Dic47—81no—
128C2×Dic47—82no—
129D188—42no—
130D188—42no—
131D188—81no—
132D188—81no—
133C8×C47—22no—
134C8×C47C4×D412yes—
135C8×C47#12112yes—
136#12991—471nomaximal, Sylow
137C22×C47—22no—
138C22×C47—22no—
139C22×C47—22no—
140C22×C47—22no—
141C22×C47—22no—
142C22×C47—22no—
143C22×C47#35714yescomplemented
144C22×C47C2×#10211yescharacteristic
145C22×C47#44711yescharacteristic
146C22×C47#48011yescharacteristic
147C22×C47C2×D1611yescharacteristic
148C22×C47C2×SD3211yescharacteristic
149C22×C47#50911yescharacteristic
150C22×C47#51011yescharacteristic
151C2×D47—82no—
152C2×D47—82no—
153C2×D47—82no—
154C2×D47—161no—
155C2×D47—161no—
156C2×D47—161no—
157C2×D47—161no—
158C4×C47—22no—
159C4×C47#38611yescharacteristic
160C4×C47#41711yescharacteristic
161C4×C47#44811yescharacteristic
162C4×C47#48111yescharacteristic
163Dic47—82no—
164Dic47—84no—
165C2×#466—471no—
166C22×#107—471no—
167C2×#357—472no—
168C2×C22⋊C16D4711yescharacteristic, complemented
169#1380—472no—
170C2×C47—24no—
171C2×C47#187411yescharacteristic
172C2×C47C2×#35711yescharacteristic
173C2×C47#213911yescharacteristic
174C2×C47#218411yescharacteristic
175C2×C47#218511yescharacteristic
176C2×C47#223211yescharacteristic
177C2×C47#223311yescharacteristic
178D47—162no—
179C22×D8—471no—
180C23×C8C2×D4711yescharacteristic
181C2×#121—941no—
182C22×C4⋊C4—941no—
183C22×C16C2×D4712yes—
184#466—474no—
185#466—942no—
186C2×#107—472no—
187C2×#107—471no—
188C2×#107—944no—
189C2×#107—941no—
190C2×#102—941no—
191#357—944no—
192C22⋊C16—22no—
193C47#1299111yescharacteristic, complemented, Sylow
194C22×D4—941no—
195C22×D4—1881no—
196C23×C4—1881no—
197C23×C4D18811yescharacteristic
198C2×D8—472no—
199C2×D8—942no—
200C2×D8—942no—
201C2×D8—941no—
202C22×C8—22no—
203C22×C8—22no—
204C22×C8C4×D4712yes—
205C22×C8D18811yescharacteristic
206C22×C8C22⋊D4712yes—
207C22×C8C22×D4711yescharacteristic
208#121—944no—
209#121—1882no—
210C2×C4⋊C4—944no—
211C2×C4⋊C4—942no—
212C2×C4⋊C4—941no—
213C2×C4⋊C4—1882no—
214C2×C4⋊C4—1881no—
215C2×C22⋊C4—1881no—
216C2×C16—22no—
217C2×C16—22no—
218C2×C16—22no—
219#107—472no—
220#107—474no—
221#107—944no—
222#107—942no—
223#107—941no—
224#102—944no—
225C24—1881no—
226C24D37611yescharacteristic
227C2×D4—942no—
228C2×D4—3762no—
229C2×D4—3762no—
230C2×D4—1884no—
231C2×D4—1881no—
232C2×D4—1881no—
233C2×D4—1881no—
234C2×D4—1881no—
235C2×D4—1881no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—3762no—
241C22×C4—3762no—
242C22×C4—1884no—
243C22×C4—1881no—
244C22×C4—1882no—
245C22×C4#1062532512yes—
246C22×C4D37611yescharacteristic
247C22×C4(C2×D47)⋊C412yes—
248C22×C4C2×D18811yescharacteristic
249D8—944no—
250D8—1882no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—24no—
254C2×C8—24no—
255C2×C8(C2×D47)⋊C412yes—
256C2×C8C2×C4×D4711yescharacteristic
257C2×C8D4×D4712yes—
258C2×C8#1062535212yes—
259C2×C8C2×C22⋊D4711yescharacteristic
260C4⋊C4—942no—
261C4⋊C4—944no—
262C4⋊C4—1884no—
263C4⋊C4—1881no—
264C4⋊C4—1882no—
265C22⋊C4—1884no—
266C16—42no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—3761no—
272C23—3761no—
273C23—3761no—
274C23—3761no—
275C23—3761no—
276C23—3761no—
277C23—1882no—
278C23#1309394612yes—
279C23D75212yes—
280C23#1309396912yes—
281C23C2×D37611yescharacteristic
282D4—3768no—
283D4—3761no—
284D4—3761no—
285D4—1882no—
286D4—1882no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—3768no—
294C2×C4—3762no—
295C2×C4—3761no—
296C2×C4—3761no—
297C2×C4—3762no—
298C2×C4—1884no—
299C2×C4—1882no—
300C2×C4#1309394612yes—
301C2×C4C2×(C2×D47)⋊C411yescharacteristic
302C2×C4#1309399411yescharacteristic
303C2×C4#1309400811yescharacteristic
304C2×C4C2×#1062532511yescharacteristic
305C2×C4#1309405211yescharacteristic
306C2×C4#1309405711yescharacteristic
307C8—22no—
308C8(C22⋊D47)⋊C412yes—
309C8#1309399612yes—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—3762no—
317C22—3762no—
318C22—3762no—
319C22—7521no—
320C22—7521no—
321C22—7521no—
322C22—7521no—
323C22#1568892514yescomplemented
324C22C2×#1309394611yescharacteristic
325C22#1568925911yescharacteristic
326C22#1568943711yescharacteristic
327C22C2×D75211yescharacteristic
328C22C2×#1309396911yescharacteristic
329C22#1568956111yescharacteristic
330C22#1568956611yescharacteristic
331C4—22no—
332C4—3764no—
333C4—3762no—
334C4#1568900011yescharacteristic
335C4#1568912511yescharacteristic
336C4#1568926411yescharacteristic
337C4#1568944211yescharacteristic
338C2—24no—
339C2—7522no—
340C2#2024370311yescharacteristic
341C2C2×#1568892511yescharacteristic
342C2#2024510111yescharacteristic
343C2#2024530211yescharacteristic
344C2#2024530711yescharacteristic
345C2#2024556911yescharacteristic
346C2#2024557411yescharacteristic
subgroupG/H
centerC23C2×D376
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×C22⋊C16C2
socleC23×C47C2×D8
prime radicalC2×#15689359C2
cosocleC22×C8×C47C23
hypercenterC2×C22⋊C16D47
hypocenterC47#12991
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C22×#13093958C2semidirect
3. C2×#15688925C2semidirect
4. #20241480C2semidirect
5. C2×C47×C22⋊C16C2semidirect
10. #15689359C4semidirect
26. C2×D376C2×C4semidirect
38. #13093958C2×C4semidirect
39. #13093958D4semidirect
143. C22×C47#357semidirect
168. C2×C22⋊C16D47semidirect
193. C47#12991semidirect
323. C22#15688925semidirect

Maximal subgroups

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

subgroupindex
C2×#156893592
C22×#130939582
C2×#156889252
#202414802
C2×C47×C22⋊C162
#1299147