Finite Group Databasebeta

← #26374422

Subgroups — #26374422

Order 12032.

466 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689555C211yesmaximal, characteristic, complemented
2#20245706C212yesmaximal, complemented
3#20245705C212yesmaximal, complemented
4#20245701C212yesmaximal, complemented
5#20245700C212yesmaximal, complemented
6#20245695C214yesmaximal, complemented
7C2×#15688957C211yesmaximal, characteristic, complemented
8C2×C47×#508C211yesmaximal, characteristic, complemented
9C2×#13094046—21no—
10#15689555—21no—
11#15689555—21no—
12#15689555C2212yes—
13#15689555C2212yescomplemented
14C2×Dic376C2211yescharacteristic, complemented
15C2×#13093969—21no—
16C2×D752C2211yescharacteristic, complemented
17#15688963C2214yescomplemented
18#15688961C2214yescomplemented
19#15688960C2214yescomplemented
20#15688958C2214yescomplemented
21#15688957C2212yescomplemented
22#15688957C2212yescomplemented
23C2×C47⋊C32C2212yescomplemented
24C2×#135×C47—21no—
25C47×#508—21no—
26C47×#508—21no—
27C47×#508C2212yes—
28C47×#508C2212yescomplemented
29C2×Q32×C47C2211yescharacteristic, complemented
30C2×SD32×C47—21no—
31C2×D16×C47C2211yescharacteristic, complemented
32C22×C16×C47C2211yescharacteristic
33C2×#10625350—41no—
34#13094046—22no—
35#13094046—22no—
36#13094046—41no—
37#13094046—41no—
38C2×Dic188—21no—
39C2×#10625325—41no—
40C2×D376—21no—
41Dic376—21no—
42Dic376C2312yes—
43#13093969—22no—
44#13093969—22no—
45D752—21no—
46D752C2312yes—
47C47⋊C32C2314yes—
48C2×#41×C47—41no—
49#135×C47—22no—
50#135×C47—22no—
51#135×C47—41no—
52#135×C47—41no—
53C2×Q16×C47—21no—
54C2×SD16×C47—41no—
55C2×D8×C47—21no—
56C22×C8×C47D411yescharacteristic
57Q32×C47—21no—
58Q32×C47C2312yes—
59SD32×C47—22no—
60SD32×C47—22no—
61D16×C47—21no—
62D16×C47C2312yes—
63C2×C16×C47D411yescharacteristic
64C2×C16×C47D411yescharacteristic
65C2×C16×C47D411yescharacteristic
66C2×C16×C47C2311yescharacteristic
67C2×C16×C47C2311yescharacteristic
68C2×C16×C47C2311yescharacteristic
69#41×C47—42no—
70#41×C47—42no—
71#41×C47—81no—
72#41×C47—81no—
73C2×Q8×C47—41no—
74C2×D4×C47—41no—
75C2×D4×C47—81no—
76C22×C4×C47—81no—
77C22×C4×C47D811yescharacteristic
78C2×C22⋊D47—81no—
79#10625350—42no—
80#10625350—42no—
81#10625350—81no—
82#10625350—81no—
83C2×D188—41no—
84C2×C4×D47—81no—
85C2×Dic94—41no—
86Q16×C47—22no—
87Q16×C47—41no—
88SD16×C47—42no—
89SD16×C47—42no—
90D8×C47—22no—
91D8×C47—41no—
92C2×C8×C47D811yescharacteristic
93C2×C8×C47D811yescharacteristic
94C2×C8×C47D811yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47C2×D411yescharacteristic
98Dic188—22no—
99Dic188—41no—
100D376—22no—
101D376—41no—
102#10625325—42no—
103#10625325—42no—
104C16×C47C2×D411yescharacteristic
105C16×C47C2×D411yescharacteristic
106C16×C47C2×D411yescharacteristic
107C16×C47C2411yescharacteristic
108C23×C47—81no—
109C23×C47D1611yescharacteristic
110C22×D47—81no—
111Q8×C47—42no—
112Q8×C47—81no—
113D4×C47—42no—
114D4×C47—82no—
115D4×C47—82no—
116D4×C47—81no—
117C2×C4×C47—81no—
118C2×C4×C47—82no—
119C2×C4×C47—82no—
120C2×C4×C47D1611yescharacteristic
121C2×C4×C47D1611yescharacteristic
122C2×C4×C47D1611yescharacteristic
123C2×C4×C47C2×D811yescharacteristic
124C2×C4×C47C2×D811yescharacteristic
125C2×C4×C47C2×D811yescharacteristic
126C22⋊D47—82no—
127C22⋊D47—82no—
128C2×Dic47—81no—
129D188—42no—
130D188—81no—
131C4×D47—82no—
132C4×D47—82no—
133Dic94—42no—
134Dic94—81no—
135C8×C47C2×D811yescharacteristic
136C8×C47C2×D811yescharacteristic
137C8×C47C2×D811yescharacteristic
138C8×C47C22×D411yescharacteristic
139#33981—471nomaximal, Sylow
140C22×C47—41no—
141C22×C47—82no—
142C22×C47—162no—
143C22×C47C2×D1611yescharacteristic
144C22×C47C2×D1611yescharacteristic
145C22×C47C2×D1611yescharacteristic
146C2×D47—82no—
147C2×D47—162no—
148C4×C47—82no—
149C4×C47C2×D1611yescharacteristic
150C4×C47C2×D1611yescharacteristic
151C4×C47C2×D1611yescharacteristic
152C4×C47C22×D811yescharacteristic
153Dic47—82no—
154C2×#508—471no—
155C2×#508D4711yescharacteristic, complemented
156#2264—472no—
157#2264—472no—
158#2263—472no—
159#2263—472no—
160#2262—474no—
161C2×M64—471no—
162C2×C47—21no—
163C2×C47—21no—
164C2×C47—21no—
165C2×C47—162no—
166C2×C47C22×D1611yescharacteristic
167D47—162no—
168C2×#135—21no—
169C2×#135—941no—
170#508—21no—
171#508—21no—
172#508—472no—
173#508—472no—
174#508—941no—
175#508—941no—
176#508C2×D4712yes—
177#508C2×D4712yescomplemented
178C2×Q32—471no—
179C2×Q32C2×D4711yescharacteristic, complemented
180C2×SD32—21no—
181C2×SD32—941no—
182C2×D16—471no—
183C2×D16C2×D4711yescharacteristic, complemented
184C22×C16C2×D4711yescharacteristic
185Q64—474no—
186SD64—474no—
187SD64—474no—
188D32—474no—
189M64—472no—
190M64—472no—
191C2×C32—472no—
192C47#3398111yescharacteristic, complemented, Sylow
193C2×#41—41no—
194C2×#41—1881no—
195#135—22no—
196#135—22no—
197#135—41no—
198#135—41no—
199#135—942no—
200#135—942no—
201#135—1881no—
202#135—1881no—
203C2×Q16—21no—
204C2×Q16—941no—
205C2×SD16—41no—
206C2×SD16—1881no—
207C2×D8—21no—
208C2×D8—941no—
209C22×C8C22⋊D4711yescharacteristic
210Q32—21no—
211Q32—472no—
212Q32—941no—
213Q32C22×D4712yes—
214SD32—22no—
215SD32—22no—
216SD32—942no—
217SD32—942no—
218D16—21no—
219D16—472no—
220D16—941no—
221D16C22×D4712yes—
222C2×C16C22⋊D4711yescharacteristic
223C2×C16C22⋊D4711yescharacteristic
224C2×C16C22⋊D4711yescharacteristic
225C2×C16C22×D4711yescharacteristic
226C2×C16C22×D4711yescharacteristic
227C2×C16C22×D4711yescharacteristic
228C32—474no—
229#41—42no—
230#41—42no—
231#41—81no—
232#41—81no—
233#41—3761no—
234#41—3761no—
235#41—1882no—
236#41—1882no—
237C2×Q8—41no—
238C2×Q8—1881no—
239C2×D4—41no—
240C2×D4—81no—
241C2×D4—3761no—
242C2×D4—1881no—
243C22×C4—81no—
244C22×C4—3761no—
245C22×C4#1062533411yescharacteristic
246Q16—22no—
247Q16—41no—
248Q16—942no—
249Q16—1881no—
250SD16—42no—
251SD16—42no—
252SD16—1882no—
253SD16—1882no—
254D8—22no—
255D8—41no—
256D8—942no—
257D8—1881no—
258C2×C8#1062533411yescharacteristic
259C2×C8#1062533411yescharacteristic
260C2×C8#1062533411yescharacteristic
261C2×C8C2×C22⋊D4711yescharacteristic
262C2×C8C2×C22⋊D4711yescharacteristic
263C2×C8C2×C22⋊D4711yescharacteristic
264C16C2×C22⋊D4711yescharacteristic
265C16C2×C22⋊D4711yescharacteristic
266C16C2×C22⋊D4711yescharacteristic
267C16C23×D4711yescharacteristic
268C23—81no—
269C23—3761no—
270C23#1309396511yescharacteristic
271Q8—42no—
272Q8—81no—
273Q8—3761no—
274Q8—1882no—
275D4—42no—
276D4—82no—
277D4—82no—
278D4—81no—
279D4—3762no—
280D4—3762no—
281D4—3761no—
282D4—1882no—
283C2×C4—81no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—3761no—
287C2×C4—3762no—
288C2×C4—3762no—
289C2×C4#1309396511yescharacteristic
290C2×C4#1309396511yescharacteristic
291C2×C4#1309396511yescharacteristic
292C2×C4C2×#1062533411yescharacteristic
293C2×C4C2×#1062533411yescharacteristic
294C2×C4C2×#1062533411yescharacteristic
295C8C2×#1062533411yescharacteristic
296C8C2×#1062533411yescharacteristic
297C8C2×#1062533411yescharacteristic
298C8C22×C22⋊D4711yescharacteristic
299C22—41no—
300C22—82no—
301C22—162no—
302C22—3762no—
303C22—7522no—
304C22C2×#1309396511yescharacteristic
305C22C2×#1309396511yescharacteristic
306C22C2×#1309396511yescharacteristic
307C4—82no—
308C4—3762no—
309C4C2×#1309396511yescharacteristic
310C4C2×#1309396511yescharacteristic
311C4C2×#1309396511yescharacteristic
312C4C22×#1062533411yescharacteristic
313C2—21no—
314C2—21no—
315C2—21no—
316C2—162no—
317C2—7522no—
318C2C22×#1309396511yescharacteristic
subgroupG/H
centerC4C2×#13093965
commutator, cosocleC16×C47C24
FrattiniC16C23×D47
FittingC2×C47×#508C2
socleC2×C47C22×D16
hypercenterC2×#508D47
hypocenterC47#33981
LCSG ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#15689555C2semidirect
2. #20245706C2semidirect
3. #20245705C2semidirect
4. #20245701C2semidirect
5. #20245700C2semidirect
6. #20245695C2semidirect
7. C2×#15688957C2semidirect
8. C2×C47×#508C2semidirect
13. #15689555C22semidirect
14. C2×Dic376C22semidirect
16. C2×D752C22semidirect
17. #15688963C22semidirect
18. #15688961C22semidirect
19. #15688960C22semidirect
20. #15688958C22semidirect
21. #15688957C22semidirect
22. #15688957C22semidirect
23. C2×C47⋊C32C22semidirect
28. C47×#508C22semidirect
29. C2×Q32×C47C22semidirect
31. C2×D16×C47C22semidirect
155. C2×#508D47semidirect
177. #508C2×D47semidirect
179. C2×Q32C2×D47semidirect
183. C2×D16C2×D47semidirect
192. C47#33981semidirect

Maximal subgroups

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

subgroupindex
C2×#156895552
#202457062
#202457052
#202457012
#202457002
#202456952
C2×#156889572
C2×C47×#5082
#3398147