Finite Group Databasebeta

← #26112977

Subgroups — #26112977

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20254329C211yesmaximal, characteristic
2#20244369C211yesmaximal, characteristic, complemented
3#20242056C211yesmaximal, characteristic
4#20241951C211yesmaximal, characteristic, complemented
5#20241246C211yesmaximal, characteristic, complemented
6#20241217C211yesmaximal, characteristic, complemented
7C47×#2328C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689495C412yescomplemented
10#15689469C412yescomplemented
11#15689320—22no—
12#15689274—22no—
13#15689176C2211yescharacteristic
14#15689176C2211yescharacteristic
15#15689147C2211yescharacteristic
16#15688883—21no—
17#15688883—21no—
18#15688867—22no—
19#15688859—22no—
20C2×#127×C47C2211yescharacteristic
21C2×C4×D4×C47—21no—
22C47×#390—21no—
23C47×#386—22no—
24C47×#386—22no—
25C47×#382C2211yescharacteristic
26C47×#376C2211yescharacteristic
27C2×#10625335—24no—
28C2×#10625329—21no—
29#13094024C2×C411yescharacteristic, complemented
30#13094024C2×C411yescharacteristic, complemented
31#13094016—21no—
32#13094003—21no—
33#13094003—21no—
34C4×Dic94—21no—
35C4×Dic94—21no—
36#13093983—21no—
37C4⋊(C47⋊C8)—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—21no—
41#13093945—24no—
42C22⋊(C47⋊C8)—21no—
43C22⋊(C47⋊C8)—21no—
44C4×C47⋊C8—21no—
45C4×C47⋊C8C2×C412yescomplemented
46C22×D4×C47—21no—
47C22×D4×C47—21no—
48C22×D4×C47D412yes—
49C23×C4×C47—22no—
50#127×C47—21no—
51#127×C47—21no—
52#127×C47C2×C412yes—
53#127×C47D412yes—
54C4×D4×C47—42no—
55C4×D4×C47—42no—
56C2×C4⋊C4×C47—21no—
57C2×C22⋊C4×C47—22no—
58C2×C22⋊C4×C47—22no—
59C2×C22⋊C4×C47—22no—
60C2×C42×C47D411yescharacteristic
61C2×C42×C47D411yescharacteristic
62C2×C42×C47C2311yescharacteristic
63#95×C47—21no—
64#95×C47—21no—
65#95×C47—21no—
66#95×C47D412yes—
67C24×C47—22no—
68C2×D4×C47—22no—
69C2×D4×C47—22no—
70C2×D4×C47—22no—
71C2×D4×C47—22no—
72C2×D4×C47—22no—
73C2×D4×C47—41no—
74C2×D4×C47—41no—
75C2×D4×C47—41no—
76C2×D4×C47—41no—
77C2×D4×C47—82no—
78C2×D4×C47—82no—
79C2×D4×C47C22⋊C414yes—
80C22×C4×C47—21no—
81C22×C4×C47—21no—
82C22×C4×C47—22no—
83C22×C4×C47—44no—
84C22×C4×C47—82no—
85C22×C4×C47—82no—
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C2×Dic94—21no—
90C2×Dic94—21no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—41no—
93C22⋊C4×C47—44no—
94C22⋊C4×C47—82no—
95C22⋊C4×C47—82no—
96C42×C47—21no—
97C42×C47—21no—
98C42×C47—21no—
99C42×C47SD1612yescomplemented
100C42×C47C22×C411yescharacteristic
101C42×C47C2×D411yescharacteristic
102C42×C47#4111yescharacteristic
103C42×C47#4111yescharacteristic
104C22⋊Dic47—41no—
105#10625335—84no—
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47—21no—
109C4⋊Dic47—21no—
110Dic47⋊C4—41no—
111Dic47⋊C4—41no—
112C4×Dic47—41no—
113#10625329—41no—
114#10625329—41no—
115C2×C47⋊C8—22no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C23×C47—24no—
119C23×C47—42no—
120C23×C47—42no—
121C23×C47—42no—
122C23×C47—42no—
123C23×C47—42no—
124C23×C47—42no—
125C23×C47#12011yescharacteristic
126D4×C47—44no—
127D4×C47—42no—
128D4×C47—42no—
129D4×C47—42no—
130D4×C47—42no—
131D4×C47—82no—
132D4×C47—82no—
133D4×C47—82no—
134C2×C4×C47—22no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—41no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47—42no—
144C2×C4×C47—41no—
145C2×C4×C47—88no—
146C2×C4×C47C2×C22⋊C411yescharacteristic
147C2×C4×C47C4×D411yescharacteristic
148C2×C4×C47C4×D411yescharacteristic
149C2×C4×C47#12111yescharacteristic
150C2×C4×C47#12111yescharacteristic
151C2×C4×C47#12311yescharacteristic
152C2×C4×C47C2×SD1611yescharacteristic
153C2×C4×C47#13511yescharacteristic
154C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C47#13711yescharacteristic
156C2×Dic47—41no—
157C2×Dic47—41no—
158Dic94—42no—
159Dic94—81no—
160C47⋊C8—42no—
161C47⋊C8—81no—
162C47⋊C8—81no—
163#9295—471nomaximal, Sylow
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—44no—
167C22×C47—44no—
168C22×C47—44no—
169C22×C47—82no—
170C22×C47—82no—
171C22×C47—82no—
172C22×C47—82no—
173C22×C47#38611yescharacteristic
174C22×C47#45011yescharacteristic
175C22×C47#45211yescharacteristic
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—42no—
181C4×C47—81no—
182C4×C47—82no—
183C4×C47C4×SD1611yescharacteristic
184C4×C47#44011yescharacteristic
185C4×C47#46111yescharacteristic
186C4×C47#46311yescharacteristic
187Dic47—81no—
188Dic47—81no—
189#3208—471no—
190#2328D4711yescharacteristic
191#1995—471no—
192#1545—471no—
193#1518—471no—
194#1286—471no—
195#1274—471no—
196C2×C47—21no—
197C2×C47—21no—
198C2×C47—84no—
199C2×C47#187711yescharacteristic
200C2×C47#190411yescharacteristic
201C2×C47#191111yescharacteristic
202#533—471no—
203C2×#127C2×D4711yescharacteristic
204C2×C4×D4—21no—
205#492—472no—
206#486—472no—
207#460—942no—
208#450—942no—
209#431—471no—
210#431—471no—
211#423—471no—
212#390—21no—
213#386—22no—
214#386—22no—
215#382C2×D4711yescharacteristic
216#376C2×D4711yescharacteristic
217#339—941no—
218#339—941no—
219#331—942no—
220#328—942no—
221C47#929511yescharacteristic, complemented, Sylow
222C22×D4—21no—
223C22×D4—21no—
224C22×D4C22⋊D4712yes—
225C23×C4—22no—
226C2×SD16—944no—
227C2×M16—941no—
228C4⋊Q8—471no—
229C4⋊Q8—471no—
230#127—21no—
231#127—21no—
232#127C4×D4712yes—
233#127D18812yes—
234#125—941no—
235C22⋊Q8—941no—
236C22⋊Q8—941no—
237C4×Q8—941no—
238C4×Q8—941no—
239C4×D4—42no—
240C4×D4—42no—
241#117—941no—
242C2×C4⋊C4—21no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C42C22⋊D4711yescharacteristic
247C2×C42C22⋊D4711yescharacteristic
248C2×C42C22×D4711yescharacteristic
249C4⋊C8—941no—
250C4⋊C8—941no—
251C4⋊C8—941no—
252C4⋊C8—941no—
253#102—944no—
254C22⋊C8—941no—
255C22⋊C8—941no—
256C4×C8—472no—
257C4×C8—941no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95C22⋊D4712yes—
262C24—22no—
263C2×Q8—941no—
264C2×Q8—941no—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—82no—
275C2×D4—82no—
276C2×D4(C2×D47)⋊C414yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—44no—
281C22×C4—82no—
282C22×C4—82no—
283C22×C4C2×C22⋊D4711yescharacteristic
284C22×C4C2×C22⋊D4711yescharacteristic
285C22×C4C2×C22⋊D4711yescharacteristic
286SD16—3764no—
287M16—1881no—
288M16—1881no—
289C2×C8—942no—
290C2×C8—1881no—
291C2×C8—1881no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—941no—
295C4⋊C4—941no—
296C4⋊C4—941no—
297C4⋊C4—941no—
298C4⋊C4—1881no—
299C4⋊C4—1881no—
300C22⋊C4—44no—
301C22⋊C4—82no—
302C22⋊C4—82no—
303C22⋊C4—1881no—
304C42—21no—
305C42—21no—
306C42—21no—
307C42—1881no—
308C42#1062533512yescomplemented
309C42C2×C4×D4711yescharacteristic
310C42C2×D18811yescharacteristic
311C42#1062535011yescharacteristic
312C42#1062535011yescharacteristic
313C23—24no—
314C23—42no—
315C23—42no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23#1309399311yescharacteristic
321Q8—3761no—
322Q8—1882no—
323D4—44no—
324D4—42no—
325D4—42no—
326D4—42no—
327D4—42no—
328D4—82no—
329D4—82no—
330D4—82no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—88no—
343C2×C4—1881no—
344C2×C4—1881no—
345C2×C4C2×(C2×D47)⋊C411yescharacteristic
346C2×C4C4×C22⋊D4711yescharacteristic
347C2×C4C4×C22⋊D4711yescharacteristic
348C2×C4#1309399811yescharacteristic
349C2×C4#1309399811yescharacteristic
350C2×C4#1309400711yescharacteristic
351C2×C4C2×#1062533511yescharacteristic
352C2×C4#1309404411yescharacteristic
353C2×C4#1309405011yescharacteristic
354C2×C4#1309405411yescharacteristic
355C8—3761no—
356C8—3761no—
357C8—1882no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—44no—
362C22—44no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22#1568900211yescharacteristic
368C22#1568927411yescharacteristic
369C22#1568928511yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—82no—
376C4—81no—
377C4—3761no—
378C4—3761no—
379C4C4×#1062533511yescharacteristic
380C4#1568922311yescharacteristic
381C4#1568932811yescharacteristic
382C4#1568933811yescharacteristic
383C2—21no—
384C2—21no—
385C2—84no—
386C2#2024372211yescharacteristic
387C2#2024387511yescharacteristic
388C2#2024392011yescharacteristic
subgroupG/H
centerC22#15689002
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2328C2
socleC22×C47#386
prime radicalC2×#127×C47C22
cosocleC2×C42×C47C23
hypercenter#2328D47
hypocenterC47#9295
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #20244369C2semidirect
4. #20241951C2semidirect
5. #20241246C2semidirect
6. #20241217C2semidirect
9. #15689495C4semidirect
10. #15689469C4semidirect
29. #13094024C2×C4semidirect
30. #13094024C2×C4semidirect
45. C4×C47⋊C8C2×C4semidirect
99. C42×C47SD16semidirect
221. C47#9295semidirect
308. C42#10625335semidirect

Maximal subgroups

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

subgroupindex
#202543292
#202443692
#202420562
#202419512
#202412462
#202412172
C47×#23282
#929547