Finite Group Databasebeta

← #26112545

Subgroups — #26112545

Order 12032.

724 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Dic47C211yesmaximal, characteristic, complemented
2#20244217C211yesmaximal, characteristic, complemented
3#20241883C211yesmaximal, characteristic, complemented
4#20241813C211yesmaximal, characteristic, complemented
5#20241290C211yesmaximal, characteristic, complemented
6#20241220C211yesmaximal, characteristic, complemented
7C47×#3100C211yesmaximal, characteristic
8C2×D4×Dic47—21no—
9C22×C4×Dic47—21no—
10#15689176C2211yescharacteristic
11#15689147C2211yescharacteristic
12C2×#13093951—21no—
13C2×#13093951—21no—
14C4⋊C4×Dic47—21no—
15C4×C4⋊Dic47C2211yescharacteristic
16C22⋊C4×Dic47—22no—
17C4×C22⋊Dic47—21no—
18C42×Dic47C2211yescharacteristic
19#15688857—22no—
20D4⋊(C47⋊C8)—22no—
21C47×#532C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C47×#480—21no—
24C47×#474C412yescomplemented
25C47×#459C412yescomplemented
26C47×#447—21no—
27C4×D8×C47—22no—
28C47×#431C2211yescharacteristic
29C23×Dic47—22no—
30C2×#10625329—21no—
31D4×Dic47—28no—
32C2×C4⋊Dic47—21no—
33C2×C22⋊Dic47—22no—
34C2×C4×Dic47—21no—
35C2×C4×Dic47—22no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47—42no—
39C2×C4×Dic47—42no—
40C2×C4×Dic47D411yescharacteristic
41C2×C4×Dic47D411yescharacteristic
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45#13093951—42no—
46#13093951—42no—
47C22⋊(C47⋊C8)—21no—
48C4×C47⋊C8—21no—
49C47⋊#95—22no—
50C47⋊#95D412yes—
51C2×#41×C47—21no—
52C22×D4×C47D411yescharacteristic
53C23×C4×C47—21no—
54C2×D8×C47—22no—
55C4⋊Q8×C47C2×C411yescharacteristic, complemented
56#127×C47C2×C411yescharacteristic, complemented
57#124×C47—21no—
58#121×C47—21no—
59#121×C47—21no—
60C4×D4×C47—21no—
61C4×D4×C47—21no—
62C4×D4×C47—21no—
63C4×D4×C47—21no—
64C4×D4×C47C2×C412yes—
65C4×D4×C47D412yes—
66C2×C4⋊C4×C47D411yescharacteristic
67C2×C22⋊C4×C47—21no—
68C2×C42×C47C2311yescharacteristic
69#107×C47—22no—
70C4⋊C8×C47C2×C412yescomplemented
71#102×C47—22no—
72#102×C47—22no—
73C22⋊C8×C47—21no—
74C4×C8×C47—21no—
75C24×C47—21no—
76#41×C47—41no—
77#41×C47—41no—
78#41×C47—41no—
79#41×C47—41no—
80C2×Q8×C47—21no—
81C2×D4×C47—24no—
82C2×D4×C47—21no—
83C2×D4×C47—21no—
84C2×D4×C47—21no—
85C2×D4×C47—21no—
86C2×D4×C47—41no—
87C2×D4×C47C22⋊C412yes—
88C22×C4×C47—21no—
89C22×C4×C47—22no—
90C22×C4×C47—22no—
91C22×C4×C47—41no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×Dic47—21no—
100C22×Dic47—28no—
101C22×Dic47—21no—
102C22×Dic47—22no—
103C22×Dic47—44no—
104C22×Dic47—44no—
105D8×C47—44no—
106C2×C8×C47—22no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—21no—
110C4⋊C4×C47C22⋊C412yes—
111C22⋊C4×C47—22no—
112C22⋊C4×C47—22no—
113C22⋊C4×C47—41no—
114C22⋊C4×C47—41no—
115C42×C47C22×C411yescharacteristic
116C42×C47C2×D411yescharacteristic
117C42×C47#4111yescharacteristic
118C42×C47#4111yescharacteristic
119C22⋊Dic47—28no—
120C4⋊Dic47—24no—
121C4×Dic47—24no—
122C4×Dic47—21no—
123C4×Dic47—21no—
124C4×Dic47—21no—
125C4×Dic47—42no—
126C4×Dic47—44no—
127C4×Dic47—41no—
128C4×Dic47—41no—
129C4×Dic47D812yescomplemented
130#10625329—41no—
131#10625329—41no—
132C2×C47⋊C8—41no—
133C2×C47⋊C8—41no—
134C23×C47—24no—
135C23×C47—22no—
136C23×C47—42no—
137C23×C47—41no—
138C23×C47—41no—
139C23×C47—41no—
140C23×C47#12011yescharacteristic
141Q8×C47—41no—
142Q8×C47—41no—
143D4×C47—24no—
144D4×C47—22no—
145D4×C47—42no—
146D4×C47—41no—
147D4×C47—41no—
148D4×C47—81no—
149D4×C47—81no—
150D4×C47—81no—
151D4×C47#10414yescomplemented
152C2×C4×C47—22no—
153C2×C4×C47—22no—
154C2×C4×C47—41no—
155C2×C4×C47—41no—
156C2×C4×C47—41no—
157C2×C4×C47—42no—
158C2×C4×C47—42no—
159C2×C4×C47—42no—
160C2×C4×C47—42no—
161C2×C4×C47—41no—
162C2×C4×C47—81no—
163C2×C4×C47—81no—
164C2×C4×C47C2×C22⋊C411yescharacteristic
165C2×C4×C47C4×D411yescharacteristic
166C2×C4×C47C4×D411yescharacteristic
167C2×C4×C47#12111yescharacteristic
168C2×C4×C47#12111yescharacteristic
169C2×C4×C47#12311yescharacteristic
170C2×C4×C47C2×D811yescharacteristic
171C2×C4×C47#13511yescharacteristic
172C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
174C2×Dic47—22no—
175C2×Dic47—22no—
176C2×Dic47—22no—
177C2×Dic47—22no—
178C2×Dic47—24no—
179C2×Dic47—416no—
180C2×Dic47—41no—
181C2×Dic47—42no—
182C2×Dic47—42no—
183C2×Dic47—41no—
184C8×C47—42no—
185C47⋊C8—81no—
186C47⋊C8—81no—
187#9233—471nomaximal, Sylow
188C22×C47—21no—
189C22×C47—21no—
190C22×C47—24no—
191C22×C47—44no—
192C22×C47—44no—
193C22×C47—42no—
194C22×C47—42no—
195C22×C47—81no—
196C22×C47—81no—
197C22×C47—81no—
198C22×C47#38611yescharacteristic
199C22×C47#44711yescharacteristic
200C22×C47#44911yescharacteristic
201C4×C47—21no—
202C4×C47—21no—
203C4×C47—21no—
204C4×C47—42no—
205C4×C47—81no—
206C4×C47C2×#10412yes—
207C4×C47C4×D811yescharacteristic
208C4×C47#44211yescharacteristic
209C4×C47#45911yescharacteristic
210C4×C47#46311yescharacteristic
211Dic47—24no—
212Dic47—42no—
213Dic47—44no—
214#3100D4711yescharacteristic
215C42×D4—471no—
216#1962—471no—
217#1502—471no—
218#1486—471no—
219#1303—471no—
220#1276—471no—
221C2×C47—21no—
222C2×C47—21no—
223C2×C47—44no—
224C2×C47—161no—
225C2×C47#187911yescharacteristic
226C2×C47#189611yescharacteristic
227C2×C47#190611yescharacteristic
228#532C2×D4711yescharacteristic
229C2×C4×D4—941no—
230C2×C4×D4C2×D4711yescharacteristic
231C22×C42—941no—
232#480—21no—
233#474Dic4712yescomplemented
234#459Dic4712yescomplemented
235#447—21no—
236C4×D8—22no—
237#431—471no—
238#431C2×D4711yescharacteristic
239#423—471no—
240C2×#104—941no—
241C2×#104—941no—
242C4×C4⋊C4—471no—
243C4×C4⋊C4—941no—
244C4×C22⋊C4—942no—
245C4×C22⋊C4—941no—
246C43—471no—
247#327—942no—
248D4⋊C8—942no—
249C47#923311yescharacteristic, complemented, Sylow
250C2×#41—21no—
251C22×D4C22⋊D4711yescharacteristic
252C23×C4—21no—
253C23×C4—942no—
254C2×D8—22no—
255C2×M16—941no—
256C4⋊Q8C2×Dic4711yescharacteristic, complemented
257#127C2×Dic4711yescharacteristic, complemented
258#124—21no—
259#121—21no—
260#121—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—948no—
266C4×D4C2×Dic4712yes—
267C4×D4C22⋊D4712yes—
268C2×C4⋊C4—941no—
269C2×C4⋊C4C22⋊D4711yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—942no—
272C2×C42—471no—
273C2×C42—471no—
274C2×C42—941no—
275C2×C42—942no—
276C2×C42—941no—
277C2×C42—941no—
278C2×C42—1882no—
279C2×C42—1882no—
280C2×C42C22×D4711yescharacteristic
281#107—22no—
282C4⋊C8—941no—
283C4⋊C8—941no—
284C4⋊C8—941no—
285C4⋊C8C2×Dic4712yescomplemented
286#104—1882no—
287#104—1882no—
288#102—22no—
289#102—22no—
290C22⋊C8—21no—
291C22⋊C8—941no—
292C4×C8—21no—
293C4×C8—941no—
294#95—472no—
295#95—942no—
296C24—21no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301C2×Q8—21no—
302C2×D4—24no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4C22⋊Dic4712yes—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—941no—
318C22×C4—948no—
319C22×C4—942no—
320C22×C4—941no—
321C22×C4—1884no—
322C22×C4—1884no—
323C22×C4D4×D4711yescharacteristic
324C22×C4D4×D4711yescharacteristic
325C22×C4C2×C22⋊D4711yescharacteristic
326D8—44no—
327M16—1881no—
328M16—1881no—
329C2×C8—22no—
330C2×C8—1881no—
331C2×C8—1881no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—944no—
336C4⋊C4C22⋊Dic4712yes—
337C22⋊C4—22no—
338C22⋊C4—22no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—948no—
342C42—472no—
343C42—944no—
344C42—941no—
345C42—941no—
346C42—941no—
347C42—1882no—
348C42—1884no—
349C42—1881no—
350C42—1881no—
351C42#1062535211yescharacteristic
352C42#1062535211yescharacteristic
353C42C22×Dic4711yescharacteristic
354C42C2×C22⋊D4711yescharacteristic
355C23—24no—
356C23—22no—
357C23—42no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23#1309399211yescharacteristic
362Q8—41no—
363Q8—41no—
364D4—24no—
365D4—22no—
366D4—41no—
367D4—42no—
368D4—41no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4#1309395114yescomplemented
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—942no—
386C2×C4—942no—
387C2×C4—942no—
388C2×C4—942no—
389C2×C4—944no—
390C2×C4—18816no—
391C2×C4—1881no—
392C2×C4—1882no—
393C2×C4—1882no—
394C2×C4—1881no—
395C2×C4C2×C22⋊Dic4711yescharacteristic
396C2×C4D4×Dic4711yescharacteristic
397C2×C4D4×Dic4711yescharacteristic
398C2×C4#1309399611yescharacteristic
399C2×C4#1309399611yescharacteristic
400C2×C4#1309400511yescharacteristic
401C2×C4D8×D4711yescharacteristic
402C2×C4#1309404311yescharacteristic
403C2×C4#1309404811yescharacteristic
404C2×C4#1309404811yescharacteristic
405C8—42no—
406C8—3761no—
407C8—3761no—
408C22—21no—
409C22—21no—
410C22—24no—
411C22—44no—
412C22—44no—
413C22—42no—
414C22—42no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22#1568900311yescharacteristic
419C22#1568925511yescharacteristic
420C22#1568926511yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—944no—
427C4—1884no—
428C4—1882no—
429C4C2×#1309395112yes—
430C4D8×Dic4711yescharacteristic
431C4#1568923511yescharacteristic
432C4#1568931611yescharacteristic
433C4#1568933611yescharacteristic
434C2—21no—
435C2—21no—
436C2—44no—
437C2—161no—
438C2#2024373811yescharacteristic
439C2#2024383211yescharacteristic
440C2#2024389111yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3100C2
socleC22×C47#386
cosocleC2×C42×C47C23
hypercenter#3100D47
hypocenterC47#9233
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. C4×D4×Dic47C2semidirect
2. #20244217C2semidirect
3. #20241883C2semidirect
4. #20241813C2semidirect
5. #20241290C2semidirect
6. #20241220C2semidirect
24. C47×#474C4semidirect
25. C47×#459C4semidirect
55. C4⋊Q8×C47C2×C4semidirect
56. #127×C47C2×C4semidirect
70. C4⋊C8×C47C2×C4semidirect
129. C4×Dic47D8semidirect
151. D4×C47#104semidirect
233. #474Dic47semidirect
234. #459Dic47semidirect
249. C47#9233semidirect
256. C4⋊Q8C2×Dic47semidirect
257. #127C2×Dic47semidirect
285. C4⋊C8C2×Dic47semidirect
372. D4#13093951semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Dic472
#202442172
#202418832
#202418132
#202412902
#202412202
C47×#31002
#923347