Finite Group Databasebeta

← #26186414

Subgroups — #26186414

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253396C211yesmaximal, characteristic
2#20252485C211yesmaximal, characteristic, complemented
3#20252412C211yesmaximal, characteristic
4#20242242C212yesmaximal, complemented
5#20242221C212yesmaximal, complemented
6#20242197C212yesmaximal, complemented
7#20242191C212yesmaximal, complemented
8#20242169C211yesmaximal, characteristic, complemented
9#20241810C211yesmaximal, characteristic, complemented
10#20241685C211yesmaximal, characteristic, complemented
11C47×#1490C211yesmaximal, characteristic
12#15689680C2211yescharacteristic
13#15689453C412yes—
14#15689413C412yes—
15#15689328C412yes—
16#15689274C412yes—
17#15689251—22no—
18#15689250C2212yescomplemented
19#15689247C2212yescomplemented
20C4×#10625335C2212yes—
21C4×#10625335C2212yes—
22D4×C47⋊C8—22no—
23D4×C47⋊C8C2212yes—
24D4×C47⋊C8C2212yes—
25#15689181—22no—
26#15689176C2211yescharacteristic
27#15689176C2211yescharacteristic
28#15689176C2211yescharacteristic
29C2×C22⋊(C47⋊C8)—22no—
30#15688875C2212yescomplemented
31#15688873C2212yescomplemented
32#15688855C2212yescomplemented
33#15688855C2212yescomplemented
34#15688845C2211yescharacteristic, complemented
35#15688845C2211yescharacteristic, complemented
36#15688844C2211yescharacteristic, complemented
37C8×C47⋊C8C2211yescharacteristic, complemented
38C2×C4×D4×C47C2211yescharacteristic
39C47×#432C2211yescharacteristic
40C4×M16×C47C2211yescharacteristic
41C47×D4⋊C8C2212yes—
42C47×D4⋊C8C2212yes—
43C2×#10625335C2×C412yes—
44C2×#10625335C2×C412yes—
45C22×C47⋊C8—22no—
46C22×C47⋊C8—22no—
47#13094024C2×C411yescharacteristic
48#13094024C2×C411yescharacteristic
49#13094016—21no—
50#13094003—21no—
51#13094003C2×C412yes—
52C4×Dic94—21no—
53C4×Dic94C2312yes—
54#13093983—21no—
55#13093955C2×C412yes—
56#13093955C2×C412yes—
57C4⋊(C47⋊C8)C2×C412yes—
58C4⋊(C47⋊C8)D412yes—
59C4⋊(C47⋊C8)C2312yes—
60Dic47⋊C8—22no—
61Dic47⋊C8—22no—
62#13093947C2×C412yes—
63#13093947C2×C412yes—
64#13093945C2×C412yes—
65#13093945C2×C412yes—
66C22⋊(C47⋊C8)—21no—
67C22⋊(C47⋊C8)—22no—
68C22⋊(C47⋊C8)—22no—
69C22⋊(C47⋊C8)C2×C412yes—
70C22⋊(C47⋊C8)D412yes—
71#13093934—22no—
72C4×C47⋊C8—21no—
73C4×C47⋊C8C2311yescharacteristic
74C4×C47⋊C8C2311yescharacteristic
75C4×C47⋊C8C2311yescharacteristic
76C4×C47⋊C8C2311yescharacteristic
77C8×Dic47—22no—
78C22×D4×C47C2×C411yescharacteristic
79C23×C4×C47—21no—
80C2×M16×C47—21no—
81C4×D4×C47—21no—
82C4×D4×C47—21no—
83C4×D4×C47C2×C412yes—
84C4×D4×C47C2312yes—
85C2×C4⋊C4×C47C2×C411yescharacteristic
86C2×C22⋊C4×C47—21no—
87C2×C42×C47C2311yescharacteristic
88C4⋊C8×C47C2312yes—
89C22⋊C8×C47—21no—
90#97×C47—21no—
91#97×C47—21no—
92C4×C8×C47C2311yescharacteristic
93C4×C8×C47C2311yescharacteristic
94C24×C47—21no—
95C2×D4×C47—24no—
96C2×D4×C47—21no—
97C2×D4×C47C22×C412yes—
98C22×C4×C47—21no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—82no—
102C22×C4×C47C22×C411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C2×Dic94—21no—
106C2×Dic94C22×C412yes—
107M16×C47—42no—
108C2×C8×C47—21no—
109C2×C8×C47—22no—
110C2×C8×C47—21no—
111C4⋊C4×C47—21no—
112C4⋊C4×C47C22×C412yes—
113C22⋊C4×C47—22no—
114C22⋊C4×C47—22no—
115C42×C47C22×C411yescharacteristic
116C42×C47C2×D411yescharacteristic
117C42×C47#4111yescharacteristic
118C42×C47C2411yescharacteristic
119C22⋊Dic47—22no—
120#10625335—24no—
121#10625335—24no—
122C4⋊Dic47—21no—
123C4⋊Dic47—21no—
124C4⋊Dic47—21no—
125C4⋊Dic47C22×C412yes—
126Dic47⋊C4—22no—
127Dic47⋊C4—22no—
128C4×Dic47—22no—
129C2×C47⋊C8—22no—
130C2×C47⋊C8—82no—
131C2×C47⋊C8—82no—
132C2×C47⋊C8C22×C412yes—
133C2×C47⋊C8C22×C412yes—
134C2×C47⋊C8C2×D412yes—
135C2×C47⋊C8C2×D412yes—
136C23×C47—24no—
137C23×C47—22no—
138C23×C47—81no—
139C23×C47—81no—
140C23×C47C4×D411yescharacteristic
141D4×C47—24no—
142D4×C47—22no—
143D4×C47#13114yes—
144C2×C4×C47—22no—
145C2×C4×C47—22no—
146C2×C4×C47—22no—
147C2×C4×C47—41no—
148C2×C4×C47—42no—
149C2×C4×C47—42no—
150C2×C4×C47—82no—
151C2×C4×C47—81no—
152C2×C4×C47C4×D411yescharacteristic
153C2×C4×C47C4×D411yescharacteristic
154C2×C4×C47C4×D411yescharacteristic
155C2×C4×C47C23×C411yescharacteristic
156C2×C4×C47C22×D411yescharacteristic
157C2×C4×C47C2×#4111yescharacteristic
158C2×Dic47—22no—
159C2×Dic47—22no—
160Dic94—22no—
161Dic94—22no—
162Dic94—81no—
163C8×C47—22no—
164C8×C47—41no—
165C8×C47—42no—
166C47⋊C8—22no—
167C47⋊C8—22no—
168C47⋊C8—22no—
169C47⋊C8—22no—
170C47⋊C8—42no—
171#17924—471nomaximal, Sylow
172C22×C47—21no—
173C22×C47—24no—
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—42no—
177C22×C47—42no—
178C22×C47—84no—
179C22×C47C2×C4×D411yescharacteristic
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—42no—
185C4×C47C2×#13112yes—
186C4×C47#57712yes—
187Dic47—42no—
188Dic47—42no—
189#3101—471no—
190#2985—471no—
191#2972—471no—
192#1585—472no—
193#1582—472no—
194SD16⋊C8—472no—
195C8×SD16—472no—
196#1572—471no—
197#1490D4711yescharacteristic
198#1485—471no—
199#1453—471no—
200C2×C47—41no—
201C2×C47—44no—
202C2×C47#292911yescharacteristic
203C2×C47#294911yescharacteristic
204C2×C47#295611yescharacteristic
205#533—471no—
206C2×C4×D4C2×D4711yescharacteristic
207#483—472no—
208#476—472no—
209#461—472no—
210#450—472no—
211#446—472no—
212#446—942no—
213C8×Q8—472no—
214C4×SD16—472no—
215C4×SD16—472no—
216C8×D4—472no—
217C8×D4—472no—
218C8×D4—942no—
219#433—942no—
220#432C2×D4711yescharacteristic
221#431—471no—
222#431—471no—
223#431—471no—
224C2×C22⋊C8—942no—
225C4×M16C2×D4711yescharacteristic
226#335—472no—
227#334—472no—
228Q8⋊C8—472no—
229Q8⋊C8—472no—
230D4⋊C8C2×D4712yes—
231D4⋊C8C2×D4712yes—
232#322—471no—
233#322—471no—
234#322—471no—
235C82—471no—
236C47#1792411yescharacteristic, complemented, Sylow
237C22×D4C4×D4711yescharacteristic
238C23×C4—21no—
239C2×SD16—472no—
240C2×SD16—472no—
241C2×M16—21no—
242C22×C8—942no—
243C22×C8—942no—
244C4⋊Q8—471no—
245C4⋊Q8—471no—
246#125—941no—
247C22⋊Q8—472no—
248C22⋊Q8—941no—
249C4×Q8—472no—
250C4×Q8—941no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4C4×D4712yes—
254C4×D4C22×D4712yes—
255#117—941no—
256C2×C4⋊C4C4×D4711yescharacteristic
257C2×C22⋊C4—21no—
258C2×C42C22×D4711yescharacteristic
259#106—472no—
260#106—472no—
261C4⋊C8—472no—
262C4⋊C8—472no—
263C4⋊C8—472no—
264C4⋊C8—942no—
265C4⋊C8—942no—
266C4⋊C8C22×D4712yes—
267#103—472no—
268#103—472no—
269#102—472no—
270#102—472no—
271C22⋊C8—21no—
272C22⋊C8—472no—
273C22⋊C8—472no—
274C22⋊C8—942no—
275C22⋊C8—942no—
276C22⋊C8—941no—
277#97—21no—
278#97—21no—
279#97—942no—
280C4×C8—471no—
281C4×C8—471no—
282C4×C8—471no—
283C4×C8—471no—
284C4×C8—942no—
285C4×C8—941no—
286C4×C8C22×D4711yescharacteristic
287C4×C8C22×D4711yescharacteristic
288C24—21no—
289C2×Q8—472no—
290C2×Q8—941no—
291C2×D4—24no—
292C2×D4—21no—
293C2×D4C2×C4×D4712yes—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—82no—
298C22×C4C2×C4×D4711yescharacteristic
299C22×C4D4×D4711yescharacteristic
300C22×C4#1062535211yescharacteristic
301SD16—944no—
302SD16—944no—
303M16—42no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—21no—
307C2×C8—472no—
308C2×C8—472no—
309C2×C8—472no—
310C2×C8—472no—
311C2×C8—942no—
312C2×C8—3762no—
313C2×C8—3762no—
314C4⋊C4—21no—
315C4⋊C4—472no—
316C4⋊C4—942no—
317C4⋊C4—941no—
318C4⋊C4—941no—
319C4⋊C4—941no—
320C4⋊C4—942no—
321C4⋊C4C2×C4×D4712yes—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—942no—
325C42—942no—
326C42C2×C4×D4711yescharacteristic
327C42D4×D4711yescharacteristic
328C42#1062535211yescharacteristic
329C42C23×D4711yescharacteristic
330C23—24no—
331C23—22no—
332C23—81no—
333C23—81no—
334C23(C22⋊D47)⋊C411yescharacteristic
335Q8—942no—
336Q8—942no—
337Q8—3761no—
338D4—24no—
339D4—22no—
340D4#1309403214yes—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—942no—
350C2×C4—942no—
351C2×C4(C22⋊D47)⋊C411yescharacteristic
352C2×C4(C22⋊D47)⋊C411yescharacteristic
353C2×C4(C22⋊D47)⋊C411yescharacteristic
354C2×C4C22×C4×D4711yescharacteristic
355C2×C4C2×D4×D4711yescharacteristic
356C2×C4C2×#1062535211yescharacteristic
357C8—22no—
358C8—41no—
359C8—42no—
360C8—942no—
361C8—942no—
362C8—942no—
363C8—942no—
364C8—1882no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—24no—
369C22—42no—
370C22—42no—
371C22—84no—
372C22C2×(C22⋊D47)⋊C411yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—1882no—
379C4—1882no—
380C4C2×#1309403212yes—
381C4#1568993312yes—
382C2—41no—
383C2—44no—
384C2#2025207811yescharacteristic
385C2#2025225011yescharacteristic
386C2#2025229411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1490C2
socleC22×C47C2×C4×D4
prime radicalC22×D4×C47C2×C4
cosocleC42×C47C24
hypercenter#1490D47
hypocenterC47#17924
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #20252485C2semidirect
4. #20242242C2semidirect
5. #20242221C2semidirect
6. #20242197C2semidirect
7. #20242191C2semidirect
8. #20242169C2semidirect
9. #20241810C2semidirect
10. #20241685C2semidirect
18. #15689250C22semidirect
19. #15689247C22semidirect
30. #15688875C22semidirect
31. #15688873C22semidirect
32. #15688855C22semidirect
33. #15688855C22semidirect
34. #15688845C22semidirect
35. #15688845C22semidirect
36. #15688844C22semidirect
37. C8×C47⋊C8C22semidirect
236. C47#17924semidirect

Maximal subgroups

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

subgroupindex
#202533962
#202524852
#202524122
#202422422
#202422212
#202421972
#202421912
#202421692
#202418102
#202416852
C47×#14902
#1792447