Finite Group Databasebeta

← #26134498

Subgroups — #26134498

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×#15689506C211yesmaximal, characteristic
2C2×#15688928C211yesmaximal, characteristic, complemented
3C2×#15688926C211yesmaximal, characteristic, complemented
4C2×#15688924C211yesmaximal, characteristic
5C2×C16×Dic47C211yesmaximal, characteristic, complemented
6#20243551C211yesmaximal, characteristic, complemented
7C2×C47×#357C211yesmaximal, characteristic
8C22×Dic188C2211yescharacteristic
9C22×#10625335—21no—
10C2×#13094011—21no—
11C22×C47⋊C16C2211yescharacteristic
12#15689506—22no—
13#15689506C414yescomplemented
14C2×#13093958C2211yescharacteristic
15C2×#13093955—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15688988—21no—
18#15688928—22no—
19#15688926—22no—
20#15688924—22no—
21C16×Dic47—22no—
22C22×D8×C47C2211yescharacteristic
23C22×C16×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C47×#357—22no—
26C22×Dic94—21no—
27C2×Dic188—21no—
28C2×Dic188—21no—
29C2×Dic188—21no—
30C2×Dic188—21no—
31C2×Dic188—21no—
32C2×Dic188C2×C412yes—
33C2×#10625335—24no—
34C2×#10625335—42no—
35C2×#10625335—42no—
36C22×C47⋊C8D411yescharacteristic
37#13094011—24no—
38#13094011—42no—
39C2×C4⋊Dic47—21no—
40C2×C22⋊Dic47—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×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×C47D412yes—
63#107×C47—21no—
64#107×C47—21no—
65C24×C47—41no—
66C2×D4×C47—22no—
67C2×D4×C47—41no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C2×D4×C47—41no—
71C2×D4×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—41no—
75C22×Dic47—41no—
76C22×Dic47D812yes—
77C2×Dic94—22no—
78C2×Dic94—41no—
79C2×Dic94—41no—
80C2×Dic94—41no—
81C2×Dic94—41no—
82C2×Dic94—41no—
83D8×C47—22no—
84D8×C47—22no—
85D8×C47—41no—
86D8×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—
95C22⋊Dic47—48no—
96#10625335—48no—
97C4⋊Dic47—41no—
98C4⋊Dic47—41no—
99C4×Dic47C22⋊C412yes—
100C4×Dic47SD1612yes—
101C2×C47⋊C8C22⋊C412yes—
102C2×C47⋊C8D812yes—
103C2×C47⋊C8SD1612yes—
104Dic188—22no—
105Dic188—22no—
106Dic188—41no—
107Dic188—41no—
108C16×C47—22no—
109C47⋊C16—22no—
110C23×C47—42no—
111C23×C47—81no—
112C23×C47—81no—
113C23×C47—82no—
114C23×C47—82no—
115C23×C47C2×D811yescharacteristic
116D4×C47—42no—
117D4×C47—42no—
118D4×C47—81no—
119D4×C47—81no—
120C2×C4×C47—81no—
121C2×C4×C47—82no—
122C2×C4×C47C2×C22⋊C411yescharacteristic
123C2×C4×C47#12411yescharacteristic
124C2×C4×C47#12711yescharacteristic
125C2×C4×C47C2×D811yescharacteristic
126C2×C4×C47C2×SD1611yescharacteristic
127C2×C4×C47C2×SD1611yescharacteristic
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—42no—
131C2×Dic47—81no—
132C2×Dic47—81no—
133C2×Dic47—81no—
134C2×Dic47—82no—
135C2×Dic47#10214yes—
136Dic94—42no—
137Dic94—42no—
138Dic94—81no—
139Dic94—81no—
140C8×C47C4×D411yescharacteristic
141C8×C47C4×D411yescharacteristic
142C8×C47#12111yescharacteristic
143C8×C47#12111yescharacteristic
144C47⋊C8#10214yes—
145#13204—471nomaximal, Sylow
146C22×C47—84no—
147C22×C47—82no—
148C22×C47—162no—
149C22×C47—161no—
150C22×C47—161no—
151C22×C47C2×#10211yescharacteristic
152C22×C47#48611yescharacteristic
153C22×C47#49311yescharacteristic
154C22×C47#50812yes—
155C22×C47#50812yes—
156C4×C47—161no—
157C4×C47#39011yescharacteristic
158C4×C47C2×#10211yescharacteristic
159C4×C47#48611yescharacteristic
160C4×C47#49211yescharacteristic
161Dic47—24no—
162Dic47—82no—
163Dic47—161no—
164C2×#495—471no—
165C2×#358—471no—
166C2×#358—471no—
167C2×#357—471no—
168C2×#357D4711yescharacteristic
169C2×C4×C16—471no—
170#1846—471no—
171C2×C47—162no—
172C2×C47#195711yescharacteristic
173C2×C47#213812yes—
174C2×C47#224212yes—
175C2×C47#224911yescharacteristic
176C2×C47#224911yescharacteristic
177C22×Q16—471no—
178C22×SD16—941no—
179C22×D8C2×D4711yescharacteristic
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—942no—
191#358—942no—
192#357—22no—
193#357—942no—
194C4×C16—942no—
195C47#1320411yescharacteristic, complemented, Sylow
196C22×Q8—941no—
197C22×D4—21no—
198C2×Q16—472no—
199C2×Q16—941no—
200C2×Q16—941no—
201C2×Q16—941no—
202C2×Q16—941no—
203C2×Q16—941no—
204C2×SD16—944no—
205C2×SD16—1882no—
206C2×SD16—1882no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8C4×D4712yes—
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—41no—
236C2×Q8—942no—
237C2×Q8—1881no—
238C2×Q8—1881no—
239C2×Q8—1881no—
240C2×Q8—1881no—
241C2×Q8—1881no—
242C2×D4—22no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—472no—
250C22×C4—1881no—
251C22×C4—1881no—
252C22×C4D4×D4711yescharacteristic
253Q16—942no—
254Q16—942no—
255Q16—1881no—
256Q16—1881no—
257SD16—1888no—
258D8—22no—
259D8—22no—
260D8—41no—
261D8—41no—
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—42no—
281C23—81no—
282C23—82no—
283C23—82no—
284C23—81no—
285C23D8×D4711yescharacteristic
286Q8—3761no—
287Q8—3761no—
288Q8—1882no—
289Q8—1882no—
290D4—42no—
291D4—42no—
292D4—81no—
293D4—81no—
294C2×C4—81no—
295C2×C4—82no—
296C2×C4—474no—
297C2×C4—942no—
298C2×C4—942no—
299C2×C4—3761no—
300C2×C4—3761no—
301C2×C4—3761no—
302C2×C4—3762no—
303C2×C4—1882no—
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—84no—
316C22—82no—
317C22—162no—
318C22—161no—
319C22—161no—
320C22#102×D4711yescharacteristic
321C22#1568946811yescharacteristic
322C22#1568949811yescharacteristic
323C22#1568955212yes—
324C22#1568955412yes—
325C4—161no—
326C4—944no—
327C4—3762no—
328C4—7521no—
329C4#1568902311yescharacteristic
330C4#102×D4711yescharacteristic
331C4#1568946811yescharacteristic
332C4#1568949411yescharacteristic
333C2—162no—
334C2#2024419211yescharacteristic
335C2#2024509212yes—
336C2#2024561812yes—
337C2#2024564611yescharacteristic
338C2#2024564811yescharacteristic
subgroupG/H
centerC23D8×D47
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#357C2
socleC23×C47C2×D8
prime radicalC22×D8×C47C22
cosocleC22×C8×C47C23
hypercenterC2×#357D47
hypocenterC47#13204
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×#15688928C2semidirect
3. C2×#15688926C2semidirect
5. C2×C16×Dic47C2semidirect
6. #20243551C2semidirect
13. #15689506C4semidirect
195. C47#13204semidirect

Maximal subgroups

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

subgroupindex
C2×#156895062
C2×#156889282
C2×#156889262
C2×#156889242
C2×C16×Dic472
#202435512
C2×C47×#3572
#1320447