Finite Group Databasebeta

← #26134508

Subgroups — #26134508

Order 12032.

590 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689498C211yesmaximal, characteristic
2C2×#15688925C211yesmaximal, characteristic, complemented
3C2×#15688924C211yesmaximal, characteristic, complemented
4C2×#15688923C211yesmaximal, characteristic, complemented
5C2×#15688898C211yesmaximal, characteristic, complemented
6#20243551C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9C22×#10625334—21no—
10C2×#13094020—21no—
11C22×C47⋊C16C2211yescharacteristic
12#15689498—22no—
13#15689498C414yescomplemented
14C2×#13093958C2211yescharacteristic
15C2×#13093955—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15688988—21no—
18#15688925—22no—
19#15688924—22no—
20#15688923—22no—
21#15688898—22no—
22C22×D8×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C47×#357—22no—
26C22×D188—21no—
27C22×C22⋊D47—42no—
28C2×D376—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376C2×C412yes—
34C2×#10625334—24no—
35C2×#10625334—42no—
36C2×#10625334—42no—
37C22×C47⋊C8D411yescharacteristic
38#13094020—24no—
39#13094020—42no—
40C2×C4⋊Dic47—21no—
41C2×C4×Dic47D411yescharacteristic
42C2×C47⋊C16—21no—
43C2×C47⋊C16—21no—
44C2×C47⋊C16D412yescomplemented
45#13093958—21no—
46#13093958—21no—
47#13093955—42no—
48C8×Dic47C2×C412yes—
49C8×Dic47D412yes—
50C47⋊#95—42no—
51C22×D4×C47—21no—
52C2×D8×C47—21no—
53C2×D8×C47—21no—
54C2×D8×C47—21no—
55C2×D8×C47—21no—
56C2×D8×C47—21no—
57C2×D8×C47C2×C412yes—
58C22×C8×C47C2311yescharacteristic
59C2×C4⋊C4×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47D412yescomplemented
63#107×C47—21no—
64#107×C47—21no—
65C24×C47—41no—
66C23×D47—41no—
67C2×D4×C47—22no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C2×D4×C47—41no—
71C2×D4×C47—41no—
72C2×D4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47C2×D411yescharacteristic
75C2×C22⋊D47—48no—
76C2×C22⋊D47—84no—
77C2×C22⋊D47—84no—
78C22×Dic47—41no—
79C22×Dic47D812yes—
80C2×D188—22no—
81C2×D188—41no—
82C2×D188—41no—
83C2×D188—41no—
84C2×D188—41no—
85C2×D188—41no—
86D8×C47—22no—
87D8×C47—22no—
88D8×C47—41no—
89D8×C47—41no—
90C2×C8×C47C22×C411yescharacteristic
91C2×C8×C47C2×D411yescharacteristic
92C2×C8×C47C2×D411yescharacteristic
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47#4111yescharacteristic
95C2×C8×C47#4111yescharacteristic
96C4⋊C4×C47—41no—
97C4⋊C4×C47—41no—
98#10625334—48no—
99C4⋊Dic47—41no—
100C4⋊Dic47—41no—
101C4×Dic47C22⋊C412yes—
102C4×Dic47SD1612yes—
103C2×C47⋊C8C22⋊C412yes—
104C2×C47⋊C8D812yes—
105C2×C47⋊C8SD1612yes—
106D376—22no—
107D376—22no—
108D376—41no—
109D376—41no—
110C16×C47—22no—
111C47⋊C16—22no—
112C23×C47—42no—
113C23×C47—81no—
114C23×C47—81no—
115C23×C47—82no—
116C23×C47—82no—
117C23×C47C2×D811yescharacteristic
118C22×D47—42no—
119C22×D47—81no—
120C22×D47—81no—
121C22×D47—82no—
122C22×D47—82no—
123D4×C47—42no—
124D4×C47—42no—
125D4×C47—81no—
126D4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47—82no—
129C2×C4×C47C2×C22⋊C411yescharacteristic
130C2×C4×C47#12411yescharacteristic
131C2×C4×C47#12711yescharacteristic
132C2×C4×C47C2×D811yescharacteristic
133C2×C4×C47C2×SD1611yescharacteristic
134C2×C4×C47C2×SD1611yescharacteristic
135C22⋊D47—816no—
136C2×Dic47—22no—
137C2×Dic47—22no—
138C2×Dic47—81no—
139C2×Dic47—82no—
140C2×Dic47#10214yes—
141D188—42no—
142D188—42no—
143D188—81no—
144D188—81no—
145C8×C47C4×D411yescharacteristic
146C8×C47C4×D411yescharacteristic
147C8×C47#12111yescharacteristic
148C8×C47#12111yescharacteristic
149C47⋊C8#10214yes—
150#13206—471nomaximal, Sylow
151C22×C47—84no—
152C22×C47—82no—
153C22×C47—162no—
154C22×C47—161no—
155C22×C47—161no—
156C22×C47C2×#10211yescharacteristic
157C22×C47#48611yescharacteristic
158C22×C47#49311yescharacteristic
159C22×C47#50912yes—
160C22×C47#50912yes—
161C2×D47—84no—
162C2×D47—82no—
163C2×D47—162no—
164C2×D47—161no—
165C2×D47—161no—
166C4×C47—161no—
167C4×C47#39011yescharacteristic
168C4×C47C2×#10211yescharacteristic
169C4×C47#48611yescharacteristic
170C4×C47#49211yescharacteristic
171Dic47—24no—
172Dic47—161no—
173C2×#493—471no—
174C2×#357—471no—
175C2×#357—471no—
176C2×#357—471no—
177C2×#357D4711yescharacteristic, complemented
178C2×#346—471no—
179#1846—471no—
180C2×C47—162no—
181C2×C47#195711yescharacteristic
182C2×C47#214012yes—
183C2×C47#224412yes—
184C2×C47#225011yescharacteristic
185C2×C47#225011yescharacteristic
186D47—162no—
187C22×D8—471no—
188C22×D8—941no—
189C22×D8C2×D4711yescharacteristic
190C2×#127—941no—
191C22×C16—471no—
192C22×C16C2×D4711yescharacteristic
193#493—474no—
194#493—942no—
195C2×#107—471no—
196C2×#107C2×D4711yescharacteristic
197C2×#106—941no—
198C2×C4×C8—471no—
199#382—941no—
200#357—22no—
201#357—942no—
202#357—942no—
203#357—942no—
204#346—942no—
205C47#1320611yescharacteristic, complemented, Sylow
206C22×D4—21no—
207C22×D4—941no—
208C22×D4—1882no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8—21no—
213C2×D8—21no—
214C2×D8—472no—
215C2×D8—944no—
216C2×D8—941no—
217C2×D8—941no—
218C2×D8—941no—
219C2×D8—941no—
220C2×D8—941no—
221C2×D8—1882no—
222C2×D8—1882no—
223C2×D8C4×D4712yes—
224C22×C8—471no—
225C22×C8C22×D4711yescharacteristic
226#127—944no—
227#127—1882no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—941no—
230C2×C42—471no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—472no—
234C2×C16—941no—
235C2×C16—941no—
236C2×C16C22⋊D4712yescomplemented
237#107—21no—
238#107—21no—
239#107—941no—
240#107—941no—
241#106—1882no—
242C4×C8—472no—
243C4×C8—472no—
244#95—1882no—
245C24—41no—
246C24—1881no—
247C2×D4—22no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—942no—
254C2×D4—3764no—
255C2×D4—3764no—
256C2×D4—1888no—
257C2×D4—1881no—
258C2×D4—1881no—
259C2×D4—1881no—
260C2×D4—1881no—
261C2×D4—1881no—
262C22×C4—41no—
263C22×C4—472no—
264C22×C4—1881no—
265C22×C4D4×D4711yescharacteristic
266D8—22no—
267D8—22no—
268D8—41no—
269D8—41no—
270D8—942no—
271D8—942no—
272D8—1888no—
273D8—1881no—
274D8—1881no—
275C2×C8—472no—
276C2×C8—472no—
277C2×C8—472no—
278C2×C8C2×C4×D4711yescharacteristic
279C2×C8#1062535011yescharacteristic
280C2×C8D4×D4711yescharacteristic
281C2×C8D4×D4711yescharacteristic
282C2×C8#1062535211yescharacteristic
283C2×C8C2×C22⋊D4711yescharacteristic
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—1881no—
287C4⋊C4—1881no—
288C42—472no—
289C42—472no—
290C16—22no—
291C16—942no—
292C23—42no—
293C23—81no—
294C23—82no—
295C23—82no—
296C23—81no—
297C23—3761no—
298C23—3762no—
299C23—3762no—
300C23—3761no—
301C23—1882no—
302C23D8×D4711yescharacteristic
303D4—42no—
304D4—42no—
305D4—81no—
306D4—81no—
307D4—37616no—
308D4—3761no—
309D4—3761no—
310D4—1882no—
311D4—1882no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4—474no—
315C2×C4—942no—
316C2×C4—942no—
317C2×C4—3761no—
318C2×C4—3762no—
319C2×C4C22⋊C4×D4711yescharacteristic
320C2×C4#1309401011yescharacteristic
321C2×C4#1309402011yescharacteristic
322C2×C4D8×D4711yescharacteristic
323C2×C4SD16×D4711yescharacteristic
324C2×C4SD16×D4711yescharacteristic
325C8—474no—
326C8(C22⋊D47)⋊C411yescharacteristic
327C8C4×C22⋊D4711yescharacteristic
328C8#1309399611yescharacteristic
329C8#1309399711yescharacteristic
330C22—84no—
331C22—82no—
332C22—162no—
333C22—161no—
334C22—161no—
335C22—3764no—
336C22—3762no—
337C22—7522no—
338C22—7521no—
339C22—7521no—
340C22#102×D4711yescharacteristic
341C22#1568946811yescharacteristic
342C22#1568949811yescharacteristic
343C22#1568955712yes—
344C22#1568956012yes—
345C4—161no—
346C4—944no—
347C4—7521no—
348C4#1568902311yescharacteristic
349C4#102×D4711yescharacteristic
350C4#1568946811yescharacteristic
351C4#1568949411yescharacteristic
352C2—162no—
353C2—7522no—
354C2#2024419211yescharacteristic
355C2#2024510212yes—
356C2#2024562812yes—
357C2#2024565111yescharacteristic
358C2#2024565311yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC2×#15689498C2
cosocleC22×C8×C47C23
hypercenterC2×#357D47
hypocenterC47#13206
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#15688925C2semidirect
3. C2×#15688924C2semidirect
4. C2×#15688923C2semidirect
5. C2×#15688898C2semidirect
6. #20243551C2semidirect
7. C2×C47×#357C2semidirect
13. #15689498C4semidirect
44. C2×C47⋊C16D4semidirect
62. C2×C16×C47D4semidirect
177. C2×#357D47semidirect
205. C47#13206semidirect
236. C2×C16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156894982
C2×#156889252
C2×#156889242
C2×#156889232
C2×#156888982
#202435512
C2×C47×#3572
#1320647