Finite Group Databasebeta

← #26112531

Subgroups — #26112531

Order 12032.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×Dic47C211yesmaximal, characteristic
2#20244366C211yesmaximal, characteristic, complemented
3#20241887C211yesmaximal, characteristic, complemented
4#20241813C211yesmaximal, characteristic
5#20241290C211yesmaximal, characteristic, complemented
6#20241220C211yesmaximal, characteristic, complemented
7C47×#3101C211yesmaximal, characteristic
8C2×D4×Dic47—21no—
9C22×C4×Dic47—21no—
10#15689176C2211yescharacteristic
11#15689147C2211yescharacteristic
12C4⋊C4×Dic47—21no—
13C4×C4⋊Dic47C2211yescharacteristic
14C22⋊C4×Dic47—22no—
15C4×C22⋊Dic47—21no—
16C42×Dic47C2211yescharacteristic
17#15688882—21no—
18#15688882—21no—
19#15688860—22no—
20D4⋊(C47⋊C8)—22no—
21C47×#533C2211yescharacteristic
22C2×C4×D4×C47C2211yescharacteristic
23C47×#483—21no—
24C47×#476C412yescomplemented
25C47×#461C412yescomplemented
26C47×#450—21no—
27C4×SD16×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—
45C22⋊(C47⋊C8)—21no—
46C4×C47⋊C8—21no—
47C47⋊#95—22no—
48C47⋊#95D412yes—
49C22×D4×C47D411yescharacteristic
50C23×C4×C47—21no—
51C2×SD16×C47—22no—
52C4⋊Q8×C47C2×C411yescharacteristic, complemented
53C4⋊Q8×C47C2×C411yescharacteristic, complemented
54#125×C47—21no—
55C22⋊Q8×C47—21no—
56C22⋊Q8×C47—21no—
57C4×Q8×C47—21no—
58C4×Q8×C47—21no—
59C4×D4×C47—21no—
60C4×D4×C47—21no—
61C4×D4×C47C2×C412yes—
62C4×D4×C47D412yes—
63#117×C47—21no—
64C2×C4⋊C4×C47D411yescharacteristic
65C2×C22⋊C4×C47—21no—
66C2×C42×C47C2311yescharacteristic
67#106×C47—22no—
68C4⋊C8×C47C2×C412yescomplemented
69#103×C47—22no—
70#102×C47—22no—
71C22⋊C8×C47—21no—
72C4×C8×C47—21no—
73C24×C47—21no—
74C2×Q8×C47—21no—
75C2×Q8×C47—21no—
76C2×D4×C47—24no—
77C2×D4×C47—21no—
78C2×D4×C47C22⋊C412yes—
79C22×C4×C47—21no—
80C22×C4×C47—22no—
81C22×C4×C47—22no—
82C22×C4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47—41no—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×Dic47—21no—
90C22×Dic47—28no—
91C22×Dic47—21no—
92C22×Dic47—22no—
93C22×Dic47—44no—
94C22×Dic47—44no—
95SD16×C47—44no—
96C2×C8×C47—22no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—21no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—21no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47C22⋊C412yes—
105C22⋊C4×C47—22no—
106C22⋊C4×C47—22no—
107C22⋊C4×C47—41no—
108C42×C47—41no—
109C42×C47C22×C411yescharacteristic
110C42×C47C2×D411yescharacteristic
111C42×C47#4111yescharacteristic
112C42×C47#4111yescharacteristic
113C22⋊Dic47—28no—
114C4⋊Dic47—24no—
115C4×Dic47—24no—
116C4×Dic47—21no—
117C4×Dic47—21no—
118C4×Dic47—21no—
119C4×Dic47—42no—
120C4×Dic47—44no—
121C4×Dic47—41no—
122C4×Dic47—41no—
123C4×Dic47SD1612yescomplemented
124#10625329—41no—
125#10625329—41no—
126C2×C47⋊C8—41no—
127C2×C47⋊C8—41no—
128C23×C47—24no—
129C23×C47—22no—
130C23×C47—42no—
131C23×C47—41no—
132C23×C47—41no—
133C23×C47#12011yescharacteristic
134Q8×C47—42no—
135Q8×C47—81no—
136D4×C47—24no—
137D4×C47—22no—
138D4×C47#10414yes—
139C2×C4×C47—22no—
140C2×C4×C47—22no—
141C2×C4×C47—41no—
142C2×C4×C47—41no—
143C2×C4×C47—41no—
144C2×C4×C47—42no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—42no—
148C2×C4×C47—41no—
149C2×C4×C47—41no—
150C2×C4×C47C2×C22⋊C411yescharacteristic
151C2×C4×C47C4×D411yescharacteristic
152C2×C4×C47C4×D411yescharacteristic
153C2×C4×C47#12111yescharacteristic
154C2×C4×C47#12111yescharacteristic
155C2×C4×C47#12311yescharacteristic
156C2×C4×C47C2×SD1611yescharacteristic
157C2×C4×C47#13511yescharacteristic
158C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C47#13711yescharacteristic
160C2×Dic47—22no—
161C2×Dic47—22no—
162C2×Dic47—22no—
163C2×Dic47—22no—
164C2×Dic47—24no—
165C2×Dic47—416no—
166C2×Dic47—41no—
167C2×Dic47—42no—
168C2×Dic47—42no—
169C2×Dic47—41no—
170C8×C47—42no—
171C47⋊C8—81no—
172C47⋊C8—81no—
173#9231—471nomaximal, Sylow
174C22×C47—21no—
175C22×C47—21no—
176C22×C47—24no—
177C22×C47—44no—
178C22×C47—44no—
179C22×C47—42no—
180C22×C47—42no—
181C22×C47#38611yescharacteristic
182C22×C47#45011yescharacteristic
183C22×C47#45211yescharacteristic
184C4×C47—21no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—42no—
188C4×C47—81no—
189C4×C47—81no—
190C4×C47C2×#10412yes—
191C4×C47C4×SD1611yescharacteristic
192C4×C47#44011yescharacteristic
193C4×C47#46111yescharacteristic
194C4×C47#46311yescharacteristic
195Dic47—24no—
196Dic47—42no—
197Dic47—44no—
198#3101D4711yescharacteristic
199C42×D4—471no—
200#1994—471no—
201#1503—471no—
202#1486—471no—
203#1303—471no—
204#1276—471no—
205C2×C47—21no—
206C2×C47—21no—
207C2×C47—44no—
208C2×C47#187711yescharacteristic
209C2×C47#189611yescharacteristic
210C2×C47#190611yescharacteristic
211#533C2×D4711yescharacteristic
212C2×C4×D4—941no—
213C2×C4×D4C2×D4711yescharacteristic
214C22×C42—941no—
215#483—21no—
216#476Dic4712yescomplemented
217#461Dic4712yescomplemented
218#450—21no—
219C4×SD16—22no—
220#431—471no—
221#431C2×D4711yescharacteristic
222#423—471no—
223C4×C4⋊C4—471no—
224C4×C4⋊C4—941no—
225C4×C22⋊C4—942no—
226C4×C22⋊C4—941no—
227C43—471no—
228#339—941no—
229#339—941no—
230#328—942no—
231D4⋊C8—942no—
232C47#923111yescharacteristic, complemented, Sylow
233C22×D4C22⋊D4711yescharacteristic
234C23×C4—21no—
235C23×C4—942no—
236C2×SD16—22no—
237C2×M16—941no—
238C4⋊Q8C2×Dic4711yescharacteristic, complemented
239C4⋊Q8C2×Dic4711yescharacteristic, complemented
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×D4—21no—
246C4×D4—21no—
247C4×D4—948no—
248C4×D4C2×Dic4712yes—
249C4×D4C22⋊D4712yes—
250#117—21no—
251C2×C4⋊C4—941no—
252C2×C4⋊C4C22⋊D4711yescharacteristic
253C2×C22⋊C4—21no—
254C2×C22⋊C4—942no—
255C2×C42—471no—
256C2×C42—471no—
257C2×C42—941no—
258C2×C42—942no—
259C2×C42—941no—
260C2×C42—941no—
261C2×C42—1882no—
262C2×C42—1882no—
263C2×C42C22×D4711yescharacteristic
264#106—22no—
265C4⋊C8—941no—
266C4⋊C8—941no—
267C4⋊C8—941no—
268C4⋊C8C2×Dic4712yescomplemented
269#103—22no—
270#102—22no—
271C22⋊C8—21no—
272C22⋊C8—941no—
273C4×C8—21no—
274C4×C8—941no—
275#95—472no—
276#95—942no—
277C24—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×D4—24no—
281C2×D4—21no—
282C2×D4C22⋊Dic4712yes—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—941no—
291C22×C4—948no—
292C22×C4—942no—
293C22×C4—941no—
294C22×C4—1884no—
295C22×C4—1884no—
296C22×C4D4×D4711yescharacteristic
297C22×C4D4×D4711yescharacteristic
298C22×C4C2×C22⋊D4711yescharacteristic
299SD16—44no—
300M16—1881no—
301M16—1881no—
302C2×C8—22no—
303C2×C8—1881no—
304C2×C8—1881no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—944no—
313C4⋊C4C22⋊Dic4712yes—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—41no—
317C22⋊C4—948no—
318C42—41no—
319C42—472no—
320C42—944no—
321C42—941no—
322C42—941no—
323C42—941no—
324C42—1882no—
325C42—1884no—
326C42—1881no—
327C42—1881no—
328C42#1062535211yescharacteristic
329C42#1062535211yescharacteristic
330C42C22×Dic4711yescharacteristic
331C42C2×C22⋊D4711yescharacteristic
332C23—24no—
333C23—22no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23#1309399211yescharacteristic
338Q8—42no—
339Q8—81no—
340D4—24no—
341D4—22no—
342D4#1309395114yes—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—942no—
355C2×C4—942no—
356C2×C4—942no—
357C2×C4—942no—
358C2×C4—944no—
359C2×C4—18816no—
360C2×C4—1881no—
361C2×C4—1882no—
362C2×C4—1882no—
363C2×C4—1881no—
364C2×C4C2×C22⋊Dic4711yescharacteristic
365C2×C4D4×Dic4711yescharacteristic
366C2×C4D4×Dic4711yescharacteristic
367C2×C4#1309399611yescharacteristic
368C2×C4#1309399611yescharacteristic
369C2×C4#1309400511yescharacteristic
370C2×C4SD16×D4711yescharacteristic
371C2×C4#1309404511yescharacteristic
372C2×C4#1309405111yescharacteristic
373C2×C4#1309405311yescharacteristic
374C8—42no—
375C8—3761no—
376C8—3761no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22#1568900311yescharacteristic
385C22#1568927211yescharacteristic
386C22#1568928211yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—81no—
392C4—81no—
393C4—944no—
394C4—1884no—
395C4—1882no—
396C4C2×#1309395112yes—
397C4SD16×Dic4711yescharacteristic
398C4#1568922411yescharacteristic
399C4#1568932611yescharacteristic
400C4#1568934011yescharacteristic
401C2—21no—
402C2—21no—
403C2—44no—
404C2#2024372411yescharacteristic
405C2#2024383211yescharacteristic
406C2#2024389111yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#3101C2
socleC22×C47#386
prime radicalC22×D4×C47D4
cosocleC2×C42×C47C23
hypercenter#3101D47
hypocenterC47#9231
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
2. #20244366C2semidirect
3. #20241887C2semidirect
5. #20241290C2semidirect
6. #20241220C2semidirect
24. C47×#476C4semidirect
25. C47×#461C4semidirect
52. C4⋊Q8×C47C2×C4semidirect
53. C4⋊Q8×C47C2×C4semidirect
68. C4⋊C8×C47C2×C4semidirect
123. C4×Dic47SD16semidirect
216. #476Dic47semidirect
217. #461Dic47semidirect
232. C47#9231semidirect
238. C4⋊Q8C2×Dic47semidirect
239. C4⋊Q8C2×Dic47semidirect
268. C4⋊C8C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C4×D4×Dic472
#202443662
#202418872
#202418132
#202412902
#202412202
C47×#31012
#923147