Finite Group Databasebeta

← #26134490

Subgroups — #26134490

Order 12032.

614 conjugacy classes of subgroups.

The subgroup lattice has 362 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×C16×Dic47C211yesmaximal, characteristic, complemented
6#20243546C211yesmaximal, 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×#13093957—21no—
16C2×C8×Dic47C2211yescharacteristic
17#15688992—21no—
18#15688925—22no—
19#15688924—22no—
20#15688923—22no—
21C16×Dic47—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×Dic47⋊C4—42no—
42C2×C4×Dic47D411yescharacteristic
43C2×C47⋊C16—21no—
44C2×C47⋊C16—21no—
45C2×C47⋊C16D412yescomplemented
46#13093958—21no—
47#13093958—21no—
48#13093957—42no—
49C8×Dic47C2×C412yes—
50C8×Dic47D412yes—
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—
101Dic47⋊C4—84no—
102C4×Dic47C22⋊C412yes—
103C4×Dic47SD1612yes—
104C2×C47⋊C8C22⋊C412yes—
105C2×C47⋊C8D812yes—
106C2×C47⋊C8SD1612yes—
107D376—22no—
108D376—22no—
109D376—41no—
110D376—41no—
111C16×C47—22no—
112C47⋊C16—22no—
113C23×C47—42no—
114C23×C47—81no—
115C23×C47—81no—
116C23×C47—82no—
117C23×C47—82no—
118C23×C47C2×D811yescharacteristic
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47—82no—
123C22×D47—82no—
124D4×C47—42no—
125D4×C47—42no—
126D4×C47—81no—
127D4×C47—81no—
128C2×C4×C47—81no—
129C2×C4×C47—82no—
130C2×C4×C47C2×C22⋊C411yescharacteristic
131C2×C4×C47#12411yescharacteristic
132C2×C4×C47#12711yescharacteristic
133C2×C4×C47C2×D811yescharacteristic
134C2×C4×C47C2×SD1611yescharacteristic
135C2×C4×C47C2×SD1611yescharacteristic
136C22⋊D47—816no—
137C2×Dic47—81no—
138C2×Dic47—82no—
139C2×Dic47#10214yes—
140C2×Dic47D1614yes—
141C2×Dic47SD3214yes—
142D188—42no—
143D188—42no—
144D188—81no—
145D188—81no—
146C8×C47C4×D411yescharacteristic
147C8×C47C4×D411yescharacteristic
148C8×C47#12111yescharacteristic
149C8×C47#12111yescharacteristic
150C47⋊C8#10214yes—
151#13202—471nomaximal, Sylow
152C22×C47—84no—
153C22×C47—82no—
154C22×C47—162no—
155C22×C47—161no—
156C22×C47—161no—
157C22×C47C2×#10211yescharacteristic
158C22×C47#48611yescharacteristic
159C22×C47#49311yescharacteristic
160C22×C47C2×D1612yes—
161C22×C47C2×SD3212yes—
162C2×D47—84no—
163C2×D47—82no—
164C2×D47—162no—
165C2×D47—161no—
166C2×D47—161no—
167C4×C47—161no—
168C4×C47#39011yescharacteristic
169C4×C47C2×#10211yescharacteristic
170C4×C47#48611yescharacteristic
171C4×C47#49211yescharacteristic
172Dic47—161no—
173Dic47#35718yescomplemented
174C2×#493—471no—
175C2×#357—471no—
176C2×#357—471no—
177C2×#357—471no—
178C2×#357D4711yescharacteristic, complemented
179C2×C4×C16—471no—
180#1845—471no—
181C2×C47—162no—
182C2×C47#195711yescharacteristic
183C2×C47C2×#35712yes—
184C2×C47#224012yes—
185C2×C47#224611yescharacteristic
186C2×C47#224811yescharacteristic
187D47—162no—
188C22×D8—471no—
189C22×D8—941no—
190C22×D8C2×D4711yescharacteristic
191C2×#127—941no—
192C22×C16—471no—
193C22×C16C2×D4711yescharacteristic
194#493—474no—
195#493—942no—
196C2×#107—471no—
197C2×#107—941no—
198C2×#107C2×D4711yescharacteristic
199C2×C4×C8—471no—
200#384—941no—
201#357—22no—
202#357—942no—
203#357—942no—
204#357—942no—
205C4×C16—942no—
206C47#1320211yescharacteristic, complemented, Sylow
207C22×D4—21no—
208C22×D4—941no—
209C22×D4—1882no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—472no—
216C2×D8—944no—
217C2×D8—941no—
218C2×D8—941no—
219C2×D8—941no—
220C2×D8—941no—
221C2×D8—941no—
222C2×D8—1882no—
223C2×D8—1882no—
224C2×D8C4×D4712yes—
225C22×C8—471no—
226C22×C8C22×D4711yescharacteristic
227#127—944no—
228#127—1882no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—941no—
231C2×C4⋊C4—1882no—
232C2×C42—471no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—472no—
236C2×C16—941no—
237C2×C16—941no—
238C2×C16C22⋊D4712yescomplemented
239#107—21no—
240#107—21no—
241#107—941no—
242#107—941no—
243#107—1882no—
244C4×C8—472no—
245C4×C8—472no—
246C24—41no—
247C24—1881no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—942no—
255C2×D4—3764no—
256C2×D4—3764no—
257C2×D4—1888no—
258C2×D4—1881no—
259C2×D4—1881no—
260C2×D4—1881no—
261C2×D4—1881no—
262C2×D4—1881no—
263C22×C4—41no—
264C22×C4—472no—
265C22×C4—1881no—
266C22×C4D4×D4711yescharacteristic
267D8—22no—
268D8—22no—
269D8—41no—
270D8—41no—
271D8—942no—
272D8—942no—
273D8—1888no—
274D8—1881no—
275D8—1881no—
276C2×C8—472no—
277C2×C8—472no—
278C2×C8—472no—
279C2×C8C2×C4×D4711yescharacteristic
280C2×C8#1062535011yescharacteristic
281C2×C8D4×D4711yescharacteristic
282C2×C8D4×D4711yescharacteristic
283C2×C8#1062535211yescharacteristic
284C2×C8C2×C22⋊D4711yescharacteristic
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—3764no—
288C4⋊C4—1881no—
289C4⋊C4—1881no—
290C42—472no—
291C42—472no—
292C16—22no—
293C16—942no—
294C23—42no—
295C23—81no—
296C23—82no—
297C23—82no—
298C23—81no—
299C23—3761no—
300C23—3762no—
301C23—3762no—
302C23—3761no—
303C23—1882no—
304C23D8×D4711yescharacteristic
305D4—42no—
306D4—42no—
307D4—81no—
308D4—81no—
309D4—37616no—
310D4—3761no—
311D4—3761no—
312D4—1882no—
313D4—1882no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—474no—
317C2×C4—474no—
318C2×C4—474no—
319C2×C4—3761no—
320C2×C4—3762no—
321C2×C4C22⋊C4×D4711yescharacteristic
322C2×C4#1309401011yescharacteristic
323C2×C4#1309402011yescharacteristic
324C2×C4D8×D4711yescharacteristic
325C2×C4SD16×D4711yescharacteristic
326C2×C4SD16×D4711yescharacteristic
327C8—474no—
328C8(C22⋊D47)⋊C411yescharacteristic
329C8C4×C22⋊D4711yescharacteristic
330C8#1309399611yescharacteristic
331C8#1309399711yescharacteristic
332C22—84no—
333C22—82no—
334C22—162no—
335C22—161no—
336C22—161no—
337C22—3764no—
338C22—3762no—
339C22—7522no—
340C22—7521no—
341C22—7521no—
342C22#102×D4711yescharacteristic
343C22#1568946811yescharacteristic
344C22#1568949811yescharacteristic
345C22D16×D4712yes—
346C22SD32×D4712yes—
347C4—161no—
348C4—478no—
349C4—7521no—
350C4#1568902311yescharacteristic
351C4#102×D4711yescharacteristic
352C4#1568946811yescharacteristic
353C4#1568949411yescharacteristic
354C2—162no—
355C2—7522no—
356C2#2024419211yescharacteristic
357C2#357×D4712yes—
358C2#2024561012yes—
359C2#2024563611yescharacteristic
360C2#2024564211yescharacteristic
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#13202
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×C16×Dic47C2semidirect
6. #20243546C2semidirect
7. C2×C47×#357C2semidirect
13. #15689498C4semidirect
45. C2×C47⋊C16D4semidirect
62. C2×C16×C47D4semidirect
173. Dic47#357semidirect
178. C2×#357D47semidirect
206. C47#13202semidirect
238. 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×C16×Dic472
#202435462
C2×C47×#3572
#1320247