Finite Group Databasebeta

← #26371852

Subgroups — #26371852

Order 12032.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253967C211yesmaximal, characteristic, complemented
2#20245675C211yesmaximal, characteristic, complemented
3#20245655C211yesmaximal, characteristic, complemented
4#20245631C211yesmaximal, characteristic, complemented
5#20245624C211yesmaximal, characteristic, complemented
6#20245503C212yesmaximal, complemented
7#20245489C212yesmaximal, complemented
8C4×#13093967C212yesmaximal, complemented
9C4×#13093965C212yesmaximal, complemented
10C4×#13093964C211yesmaximal, characteristic, complemented
11C47×#3168C211yesmaximal, characteristic, complemented
12#15689673—21no—
13C2×#13093967C2212yes—
14C2×#13093965C2212yes—
15C2×#13093964C2212yes—
16#15689528C2211yescharacteristic
17#15689500C2211yescharacteristic
18#15689470—21no—
19#15689359—21no—
20#15689359C2212yes—
21C4×D376—21no—
22C4×D376C2212yes—
23#15688950C2212yes—
24#15688948C2212yes—
25#15688927C2212yes—
26#15688924C2212yes—
27#15688923C2212yes—
28#15688923C2212yes—
29#15688899C2211yescharacteristic
30#15688899C2211yescharacteristic
31C4×C47⋊C16C2212yes—
32C47×#529—21no—
33C47×#499C2211yescharacteristic
34C47×#495C2211yescharacteristic
35C47×#488—21no—
36C47×#467C2211yescharacteristic
37C47×#466C2211yescharacteristic
38C47×#465—21no—
39C4×Q16×C47C2211yescharacteristic
40C4×SD16×C47—21no—
41C4×D8×C47C2211yescharacteristic
42C2×C4×C8×C47C2211yescharacteristic
43C2×#10625350—41no—
44C2×D376—21no—
45C2×D376C2312yes—
46#13094024—21no—
47#13094021—21no—
48#13094012—41no—
49#13093998—22no—
50#13093998—41no—
51C4×D188—22no—
52C4×D188—41no—
53#13093967—24no—
54#13093965—24no—
55#13093964—24no—
56C2×C47⋊C16C2312yes—
57C2×C47⋊C16C2312yes—
58#13093958—21no—
59#13093958C2312yes—
60#13093946—22no—
61#13093946—22no—
62C2×Q16×C47C2311yescharacteristic
63C2×SD16×C47—21no—
64C2×D8×C47C2311yescharacteristic
65C22×C8×C47D411yescharacteristic
66C22×C8×C47C2311yescharacteristic
67#126×C47—41no—
68#125×C47—21no—
69#124×C47—21no—
70#123×C47—41no—
71C22⋊Q8×C47—21no—
72#121×C47—21no—
73C4×Q8×C47—21no—
74C4×D4×C47—21no—
75C4×D4×C47—41no—
76#117×C47—41no—
77C2×C42×C47D411yescharacteristic
78#107×C47C2311yescharacteristic
79#107×C47C2311yescharacteristic
80#106×C47—21no—
81#103×C47—21no—
82#103×C47—21no—
83#102×C47—21no—
84#102×C47—21no—
85C4×C8×C47D411yescharacteristic
86C4×C8×C47D411yescharacteristic
87C4×C8×C47C2311yescharacteristic
88C4×C8×C47C2311yescharacteristic
89C2×Q8×C47—21no—
90C2×D4×C47—21no—
91C2×D4×C47—41no—
92C22×C4×C47—41no—
93C22×C4×C47D811yescharacteristic
94C22×C4×C47D811yescharacteristic
95C22×C4×C47C2×D411yescharacteristic
96C2×C22⋊D47—42no—
97#10625350—84no—
98C2×D188—22no—
99C2×D188—41no—
100C2×D188—41no—
101C2×C4×D47—42no—
102C2×Dic94—41no—
103Q16×C47—22no—
104SD16×C47—42no—
105D8×C47—22no—
106C2×C8×C47—22no—
107C2×C8×C47—22no—
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47C2×D411yescharacteristic
110C2×C8×C47C2×D411yescharacteristic
111C2×C8×C47C2411yescharacteristic
112C4⋊C4×C47—21no—
113C4⋊C4×C47—21no—
114C4⋊C4×C47—41no—
115C4⋊C4×C47—41no—
116C4⋊C4×C47—41no—
117C4⋊C4×C47—41no—
118C22⋊C4×C47—41no—
119C22⋊C4×C47—41no—
120C22⋊C4×C47—41no—
121C22⋊C4×C47—41no—
122C22⋊C4×C47—41no—
123C42×C47—41no—
124C42×C47D811yescharacteristic
125C42×C47D811yescharacteristic
126C42×C47C2×D411yescharacteristic
127C42×C47C2×D411yescharacteristic
128(C2×D47)⋊C4—42no—
129(C2×D47)⋊C4—42no—
130C4⋊Dic47—22no—
131C4⋊Dic47—41no—
132D376—22no—
133D376—22no—
134D376—42no—
135C47⋊C16—22no—
136C47⋊C16#4114yescomplemented
137C23×C47—41no—
138C23×C47C2×D811yescharacteristic
139C22×D47—42no—
140Q8×C47—41no—
141Q8×C47—41no—
142D4×C47—41no—
143D4×C47—41no—
144D4×C47—82no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—22no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—82no—
153C2×C4×C47C2×D811yescharacteristic
154C2×C4×C47C2×D811yescharacteristic
155C2×C4×C47C2×D811yescharacteristic
156C2×C4×C47C2×D811yescharacteristic
157C2×C4×C47C2×D811yescharacteristic
158C2×C4×C47C22×D411yescharacteristic
159C22⋊D47—84no—
160C2×Dic47—42no—
161D188—42no—
162D188—42no—
163D188—82no—
164D188—82no—
165C4×D47—84no—
166Dic94—82no—
167C8×C47—21no—
168C8×C47—21no—
169C8×C47#13512yes—
170C8×C47C2×#4112yes—
171#33737—471nomaximal, Sylow
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—81no—
176C22×C47—81no—
177C22×C47—81no—
178C22×C47C22×D811yescharacteristic
179C2×D47—82no—
180C2×D47—82no—
181C2×D47—82no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—81no—
187C4×C47—81no—
188C4×C47—81no—
189C4×C47#50912yes—
190C4×C47#53211yescharacteristic
191C4×C47C2×#13511yescharacteristic
192Dic47—82no—
193#3169—471no—
194#3168D4711yescharacteristic, complemented
195#2255—471no—
196#2250—471no—
197#2244—471no—
198#2243—471no—
199#2220—472no—
200#2218—472no—
201C4×SD32—472no—
202C4×D16—472no—
203C4×M32—471no—
204C2×C47—41no—
205C2×C47—161no—
206C2×C47#316911yescharacteristic
207C2×C47C2×#50911yescharacteristic
208C2×C47#341411yescharacteristic
209D47—162no—
210#532—941no—
211#529—21no—
212C2×SD32—472no—
213C2×D16—472no—
214C2×M32—472no—
215#500—471no—
216#499C2×D4711yescharacteristic
217#495C2×D4711yescharacteristic
218#493—471no—
219#488—21no—
220#486—941no—
221#467C2×D4711yescharacteristic
222#466—472no—
223#466—941no—
224#466C2×D4711yescharacteristic
225#465—21no—
226C4×Q16C2×D4711yescharacteristic
227C4×SD16—21no—
228C4×D8—472no—
229C4×D8—941no—
230C4×D8C2×D4711yescharacteristic
231C2×C4×C8C2×D4711yescharacteristic
232#367—472no—
233#366—472no—
234#358—472no—
235#357—472no—
236#357—472no—
237#357—472no—
238#346—471no—
239#346—471no—
240C4×C16—472no—
241C47#3373711yescharacteristic, complemented, Sylow
242C2×#41—1881no—
243C2×Q16C22×D4711yescharacteristic
244C2×SD16—21no—
245C2×D8—472no—
246C2×D8—941no—
247C2×D8C22×D4711yescharacteristic
248C22×C8C22⋊D4711yescharacteristic
249C22×C8C22×D4711yescharacteristic
250C4⋊Q8—941no—
251#127—941no—
252#126—41no—
253#125—21no—
254#124—21no—
255#124—1881no—
256#123—41no—
257C22⋊Q8—21no—
258#121—21no—
259#121—942no—
260#121—1881no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—41no—
264C4×D4—942no—
265C4×D4—1881no—
266#117—41no—
267C2×C42C22⋊D4711yescharacteristic
268SD32—944no—
269D16—944no—
270M32—944no—
271C2×C16—472no—
272C2×C16—472no—
273#107—472no—
274#107—941no—
275#107C22×D4711yescharacteristic
276#107C22×D4711yescharacteristic
277#106—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282#102—942no—
283#102—942no—
284C4×C8C22⋊D4711yescharacteristic
285C4×C8C22⋊D4711yescharacteristic
286C4×C8C22×D4711yescharacteristic
287C4×C8C22×D4711yescharacteristic
288#41—3764no—
289C2×Q8—21no—
290C2×Q8—1881no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—942no—
294C2×D4—1882no—
295C2×D4—1881no—
296C2×D4—1881no—
297C22×C4—41no—
298C22×C4—1882no—
299C22×C4#1062533411yescharacteristic
300C22×C4#1062533411yescharacteristic
301C22×C4C2×C22⋊D4711yescharacteristic
302Q16—22no—
303SD16—42no—
304D8—22no—
305D8—942no—
306D8—942no—
307D8—1882no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8C2×C22⋊D4711yescharacteristic
311C2×C8C2×C22⋊D4711yescharacteristic
312C2×C8C2×C22⋊D4711yescharacteristic
313C2×C8C23×D4711yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—942no—
321C4⋊C4—1881no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—1882no—
328C22⋊C4—1882no—
329C42—41no—
330C42#1062533411yescharacteristic
331C42#1062533411yescharacteristic
332C42C2×C22⋊D4711yescharacteristic
333C42C2×C22⋊D4711yescharacteristic
334C16—474no—
335C16—942no—
336C23—41no—
337C23—1882no—
338C23C2×#1062533411yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—3762no—
342D4—41no—
343D4—41no—
344D4—82no—
345D4—3762no—
346D4—3762no—
347D4—3764no—
348D4—1882no—
349D4—1882no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—3764no—
359C2×C4—1882no—
360C2×C4C2×#1062533411yescharacteristic
361C2×C4C2×#1062533411yescharacteristic
362C2×C4C2×#1062533411yescharacteristic
363C2×C4C2×#1062533411yescharacteristic
364C2×C4C2×#1062533411yescharacteristic
365C2×C4C22×C22⋊D4711yescharacteristic
366C8—21no—
367C8—21no—
368C8#1309404412yes—
369C8#41×D4712yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—3762no—
377C22—3762no—
378C22—3762no—
379C22C22×#1062533411yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—3762no—
388C4#1568955812yes—
389C4#1568966911yescharacteristic
390C4C2×#1309404411yescharacteristic
391C2—41no—
392C2—161no—
393C2—7522no—
394C2#2025396311yescharacteristic
395C2C2×#1568955811yescharacteristic
396C2#2025652211yescharacteristic
subgroupG/H
centerC2×C4C2×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3168C2
socleC22×C47C22×D8
hypercenter#3168D47
hypocenterC47#33737
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #20253967C2semidirect
2. #20245675C2semidirect
3. #20245655C2semidirect
4. #20245631C2semidirect
5. #20245624C2semidirect
6. #20245503C2semidirect
7. #20245489C2semidirect
8. C4×#13093967C2semidirect
9. C4×#13093965C2semidirect
10. C4×#13093964C2semidirect
11. C47×#3168C2semidirect
136. C47⋊C16#41semidirect
194. #3168D47semidirect
241. C47#33737semidirect

Maximal subgroups

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

subgroupindex
#202539672
#202456752
#202456552
#202456312
#202456242
#202455032
#202454892
C4×#130939672
C4×#130939652
C4×#130939642
C47×#31682
#3373747