Finite Group Databasebeta

← #26112529

Subgroups — #26112529

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
1#20253396C211yesmaximal, characteristic
2#20244365C211yesmaximal, characteristic, complemented
3#20241886C211yesmaximal, characteristic, complemented
4#20241813C211yesmaximal, characteristic
5#20241291C211yesmaximal, characteristic, complemented
6#20241221C211yesmaximal, characteristic, complemented
7C42×D4×C47C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689453—21no—
10#15689413C412yescomplemented
11#15689328C412yescomplemented
12#15689274—21no—
13C4×#10625335—22no—
14#15689176C2211yescharacteristic
15#15689176C2211yescharacteristic
16#15689147C2211yescharacteristic
17#15688883—21no—
18#15688883—21no—
19#15688859—22no—
20D4⋊(C47⋊C8)—22no—
21C2×C4×D4×C47—21no—
22C2×C4×D4×C47C2211yescharacteristic
23C22×C42×C47—21no—
24C4×C4⋊C4×C47—21no—
25C4×C4⋊C4×C47C2211yescharacteristic
26C4×C22⋊C4×C47—22no—
27C4×C22⋊C4×C47—21no—
28C43×C47C2211yescharacteristic
29C2×#10625335—22no—
30C2×#10625329—21no—
31#13094024C2×C411yescharacteristic, complemented
32#13094024C2×C411yescharacteristic, complemented
33#13094016—21no—
34#13094003—21no—
35#13094003—21no—
36C4×Dic94—21no—
37C4×Dic94—21no—
38#13093983—21no—
39#13093955—22no—
40C4⋊(C47⋊C8)—21no—
41C4⋊(C47⋊C8)—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)C2×C412yescomplemented
44#13093947—22no—
45#13093945—22no—
46C22⋊(C47⋊C8)—21no—
47C22⋊(C47⋊C8)—21no—
48C4×C47⋊C8—21no—
49C4×C47⋊C8—21no—
50C22×D4×C47D411yescharacteristic
51C23×C4×C47—22no—
52C23×C4×C47—21no—
53C4×D4×C47—28no—
54C4×D4×C47—21no—
55C4×D4×C47—21no—
56C4×D4×C47C2×C412yes—
57C4×D4×C47D412yes—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47D411yescharacteristic
60C2×C22⋊C4×C47—22no—
61C2×C22⋊C4×C47—21no—
62C2×C42×C47—21no—
63C2×C42×C47—22no—
64C2×C42×C47—21no—
65C2×C42×C47—21no—
66C2×C42×C47—42no—
67C2×C42×C47—42no—
68C2×C42×C47D411yescharacteristic
69C2×C42×C47D411yescharacteristic
70C2×C42×C47C2311yescharacteristic
71#95×C47—22no—
72#95×C47D412yes—
73C24×C47—21no—
74C2×D4×C47—24no—
75C2×D4×C47—21no—
76C2×D4×C47C22⋊C412yes—
77C22×C4×C47—21no—
78C22×C4×C47—28no—
79C22×C4×C47—21no—
80C22×C4×C47—22no—
81C22×C4×C47—21no—
82C22×C4×C47—22no—
83C22×C4×C47—22no—
84C22×C4×C47—44no—
85C22×C4×C47—44no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47—41no—
89C22×C4×C47—41no—
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47C2×D411yescharacteristic
92C22×C4×C47C2×D411yescharacteristic
93C2×Dic94—21no—
94C2×Dic94—21no—
95C4⋊C4×C47—24no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47C22⋊C412yes—
98C22⋊C4×C47—28no—
99C22⋊C4×C47—22no—
100C22⋊C4×C47—22no—
101C42×C47—24no—
102C42×C47—21no—
103C42×C47—21no—
104C42×C47—21no—
105C42×C47—42no—
106C42×C47—44no—
107C42×C47—41no—
108C42×C47—41no—
109C42×C47SD1612yescomplemented
110C42×C47C22×C411yescharacteristic
111C42×C47C2×D411yescharacteristic
112C42×C47#4111yescharacteristic
113C42×C47#4111yescharacteristic
114C22⋊Dic47—41no—
115#10625335—44no—
116C4⋊Dic47—21no—
117C4⋊Dic47—21no—
118C4⋊Dic47—21no—
119C4⋊Dic47—21no—
120Dic47⋊C4—41no—
121Dic47⋊C4—41no—
122C4×Dic47—41no—
123#10625329—41no—
124#10625329—41no—
125C2×C47⋊C8—22no—
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
134D4×C47—24no—
135D4×C47—22no—
136D4×C47#10414yes—
137C2×C4×C47—22no—
138C2×C4×C47—22no—
139C2×C4×C47—22no—
140C2×C4×C47—22no—
141C2×C4×C47—22no—
142C2×C4×C47—24no—
143C2×C4×C47—22no—
144C2×C4×C47—41no—
145C2×C4×C47—416no—
146C2×C4×C47—41no—
147C2×C4×C47—42no—
148C2×C4×C47—42no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—42no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47—42no—
156C2×C4×C47C2×C22⋊C411yescharacteristic
157C2×C4×C47C4×D411yescharacteristic
158C2×C4×C47C4×D411yescharacteristic
159C2×C4×C47#12111yescharacteristic
160C2×C4×C47#12111yescharacteristic
161C2×C4×C47#12311yescharacteristic
162C2×C4×C47C2×SD1611yescharacteristic
163C2×C4×C47#13511yescharacteristic
164C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C47#13711yescharacteristic
166C2×Dic47—41no—
167C2×Dic47—41no—
168Dic94—42no—
169Dic94—81no—
170C47⋊C8—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—24no—
185C4×C47—21no—
186C4×C47—21no—
187C4×C47—21no—
188C4×C47—42no—
189C4×C47—44no—
190C4×C47—42no—
191C4×C47C2×#10412yes—
192C4×C47C4×SD1611yescharacteristic
193C4×C47#44011yescharacteristic
194C4×C47#46111yescharacteristic
195C4×C47#46311yescharacteristic
196Dic47—81no—
197Dic47—81no—
198#3101—471no—
199C42×D4D4711yescharacteristic
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#533—471no—
212C2×C4×D4—21no—
213C2×C4×D4C2×D4711yescharacteristic
214C22×C42—21no—
215#483—941no—
216#476—472no—
217#461—472no—
218#450—941no—
219C4×SD16—942no—
220#431—471no—
221#431—471no—
222#423—471no—
223C4×C4⋊C4—21no—
224C4×C4⋊C4C2×D4711yescharacteristic
225C4×C22⋊C4—21no—
226C4×C22⋊C4—22no—
227C43C2×D4711yescharacteristic
228#339—941no—
229#339—941no—
230#328—942no—
231D4⋊C8—942no—
232C47#923111yescharacteristic, complemented, Sylow
233C22×D4C22⋊D4711yescharacteristic
234C23×C4—22no—
235C23×C4—21no—
236C2×SD16—942no—
237C2×M16—941no—
238C4⋊Q8—471no—
239C4⋊Q8—471no—
240#125—941no—
241C22⋊Q8—941no—
242C22⋊Q8—941no—
243C4×Q8—941no—
244C4×Q8—941no—
245C4×D4—28no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4C4×D4712yes—
249C4×D4D18812yes—
250#117—941no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C22⋊D4711yescharacteristic
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42—22no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—42no—
260C2×C42—42no—
261C2×C42C22⋊D4711yescharacteristic
262C2×C42C22⋊D4711yescharacteristic
263C2×C42C22×D4711yescharacteristic
264#106—942no—
265C4⋊C8—472no—
266C4⋊C8—941no—
267C4⋊C8—941no—
268C4⋊C8—941no—
269#103—942no—
270#102—942no—
271C22⋊C8—941no—
272C22⋊C8—941no—
273C4×C8—941no—
274C4×C8—941no—
275#95—22no—
276#95C22⋊D4712yes—
277C24—21no—
278C2×Q8—941no—
279C2×Q8—941no—
280C2×D4—24no—
281C2×D4—21no—
282C2×D4(C2×D47)⋊C412yes—
283C22×C4—21no—
284C22×C4—28no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4C2×C22⋊D4711yescharacteristic
297C22×C4C2×C22⋊D4711yescharacteristic
298C22×C4C2×C22⋊D4711yescharacteristic
299SD16—1884no—
300M16—1881no—
301M16—1881no—
302C2×C8—942no—
303C2×C8—1881no—
304C2×C8—1881no—
305C4⋊C4—24no—
306C4⋊C4—21no—
307C4⋊C4—941no—
308C4⋊C4—941no—
309C4⋊C4—941no—
310C4⋊C4—941no—
311C4⋊C4—1881no—
312C4⋊C4—1881no—
313C4⋊C4(C2×D47)⋊C412yes—
314C22⋊C4—28no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—1881no—
318C42—24no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42—42no—
323C42—44no—
324C42—41no—
325C42—41no—
326C42—1881no—
327C42#1062533512yescomplemented
328C42C2×C4×D4711yescharacteristic
329C42C2×D18811yescharacteristic
330C42#1062535011yescharacteristic
331C42#1062535011yescharacteristic
332C23—24no—
333C23—22no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23#1309399311yescharacteristic
338Q8—3761no—
339Q8—1882no—
340D4—24no—
341D4—22no—
342D4#1309395214yes—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—416no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—1881no—
363C2×C4—1881no—
364C2×C4C2×(C2×D47)⋊C411yescharacteristic
365C2×C4C4×C22⋊D4711yescharacteristic
366C2×C4C4×C22⋊D4711yescharacteristic
367C2×C4#1309399811yescharacteristic
368C2×C4#1309399811yescharacteristic
369C2×C4#1309400711yescharacteristic
370C2×C4C2×#1062533511yescharacteristic
371C2×C4#1309404411yescharacteristic
372C2×C4#1309405011yescharacteristic
373C2×C4#1309405411yescharacteristic
374C8—3761no—
375C8—3761no—
376C8—1882no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22#1568900211yescharacteristic
385C22#1568927411yescharacteristic
386C22#1568928511yescharacteristic
387C4—24no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—42no—
393C4—42no—
394C4—3761no—
395C4—3761no—
396C4C2×#1309395212yes—
397C4C4×#1062533511yescharacteristic
398C4#1568922311yescharacteristic
399C4#1568932811yescharacteristic
400C4#1568933811yescharacteristic
401C2—21no—
402C2—21no—
403C2—44no—
404C2#2024372211yescharacteristic
405C2#2024383111yescharacteristic
406C2#2024388911yescharacteristic
subgroupG/H
centerC2×C4#13093998
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC42×D4×C47C2
socleC22×C47#386
prime radicalC22×D4×C47D4
cosocleC2×C42×C47C23
hypercenterC42×D4D47
hypocenterC47#9231
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. #20244365C2semidirect
3. #20241886C2semidirect
5. #20241291C2semidirect
6. #20241221C2semidirect
10. #15689413C4semidirect
11. #15689328C4semidirect
31. #13094024C2×C4semidirect
32. #13094024C2×C4semidirect
43. C4⋊(C47⋊C8)C2×C4semidirect
109. C42×C47SD16semidirect
232. C47#9231semidirect
327. C42#10625335semidirect

Maximal subgroups

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

subgroupindex
#202533962
#202443652
#202418862
#202418132
#202412912
#202412212
C42×D4×C472
#923147