Finite Group Databasebeta

← #26120848

Subgroups — #26120848

Order 12032.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20244315C211yesmaximal, characteristic
2#20244193C211yesmaximal, characteristic
3#20244107C211yesmaximal, characteristic, complemented
4C2×#15688873C211yesmaximal, characteristic, complemented
5C2×#15688866C211yesmaximal, characteristic
6#20241271C211yesmaximal, characteristic, complemented
7C47×#1948C211yesmaximal, characteristic, complemented
8C2×#13094021C2211yescharacteristic
9C2×C4⋊(C47⋊C8)—21no—
10C2×C4⋊(C47⋊C8)C2211yescharacteristic
11C2×C4⋊(C47⋊C8)C2211yescharacteristic
12C2×#13093944—21no—
13C2×#13093944—21no—
14C2×#13093944—21no—
15C2×#13093944—21no—
16C2×C4×C47⋊C8C2211yescharacteristic
17#15688878—21no—
18#15688873—22no—
19#15688866—22no—
20C2×#106×C47—21no—
21C2×C4⋊C8×C47C2211yescharacteristic
22C47×#384C2211yescharacteristic
23C4×C4⋊C4×C47C2211yescharacteristic
24C47×#340—21no—
25C22×D188—21no—
26C22×D188—21no—
27C22×D188—21no—
28C22×C47⋊C8—21no—
29C22×C47⋊C8—21no—
30C22×C47⋊C8D411yescharacteristic
31C22×C47⋊C8D411yescharacteristic
32#13094021—21no—
33#13094021—21no—
34#13094021—21no—
35#13094021Q812yes—
36C4⋊(C47⋊C8)—21no—
37C4⋊(C47⋊C8)—21no—
38C4⋊(C47⋊C8)—21no—
39C4⋊(C47⋊C8)—21no—
40C4⋊(C47⋊C8)—42no—
41#13093944—42no—
42#13093944—42no—
43#13093944—42no—
44#13093944—42no—
45C4×C47⋊C8—21no—
46C4×C47⋊C8—21no—
47C22×C8×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47D411yescharacteristic
52C2×C4⋊C4×C47D411yescharacteristic
53C2×C42×C47—21no—
54C2×C42×C47C2311yescharacteristic
55#106×C47—42no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47D412yes—
58#95×C47—21no—
59C23×D47—41no—
60C22×C4×C47—21no—
61C22×C4×C47—21no—
62C22×C4×C47—41no—
63C22×C4×C47C2×D411yescharacteristic
64C22×C4×C47C2×D411yescharacteristic
65C22×C4×C47#4111yescharacteristic
66C2×D188—22no—
67C2×D188—22no—
68C2×D188—22no—
69C2×D188—41no—
70C2×D188—41no—
71C2×D188—41no—
72C2×D188—41no—
73C2×D188—41no—
74C2×D188—41no—
75C2×D188—41no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—41no—
79C2×D188—41no—
80C2×D188—81no—
81C2×D188—81no—
82C2×C8×C47—22no—
83C2×C8×C47—41no—
84C2×C8×C47—41no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47—41no—
89C4⋊C4×C47—41no—
90C4⋊C4×C47—41no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—81no—
93C4⋊C4×C47SD1612yes—
94C42×C47—41no—
95C42×C47—41no—
96C42×C47C2×D411yescharacteristic
97C42×C47C2×Q811yescharacteristic
98C42×C47#4111yescharacteristic
99C42×C47#4111yescharacteristic
100C2×C47⋊C8—21no—
101C2×C47⋊C8—21no—
102C2×C47⋊C8—21no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8—41no—
108C2×C47⋊C8—41no—
109C2×C47⋊C8—41no—
110C2×C47⋊C8—41no—
111C2×C47⋊C8SD1612yes—
112C23×C47#12111yescharacteristic
113C22×D47—42no—
114C22×D47—81no—
115C22×D47—81no—
116C22×D47—81no—
117C22×D47—81no—
118C22×D47—81no—
119C22×D47—81no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—22no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—81no—
129C2×C4×C47—81no—
130C2×C4×C47—81no—
131C2×C4×C47#12111yescharacteristic
132C2×C4×C47#12111yescharacteristic
133C2×C4×C47C22⋊Q811yescharacteristic
134C2×C4×C47C22⋊Q811yescharacteristic
135C2×C4×C47C22⋊Q811yescharacteristic
136C2×C4×C47#12611yescharacteristic
137C2×C4×C47C2×SD1611yescharacteristic
138C2×C4×C47C2×SD1611yescharacteristic
139C2×C4×C47#13511yescharacteristic
140C2×C4×C47#13511yescharacteristic
141C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
145D188—42no—
146D188—42no—
147D188—42no—
148D188—42no—
149D188—82no—
150D188—82no—
151D188—81no—
152D188—81no—
153D188—81no—
154D188—81no—
155C8×C47—42no—
156C47⋊C8—22no—
157C47⋊C8—41no—
158C47⋊C8—81no—
159C47⋊C8—81no—
160#10595—471nomaximal, Sylow
161C22×C47#39611yescharacteristic
162C22×C47#46011yescharacteristic
163C22×C47#46311yescharacteristic
164C22×C47#46511yescharacteristic
165C22×C47#46911yescharacteristic
166C22×C47#47111yescharacteristic
167C22×C47#47211yescharacteristic
168C2×D47—82no—
169C2×D47—82no—
170C2×D47—82no—
171C2×D47—161no—
172C2×D47—161no—
173C2×D47—161no—
174C2×D47—161no—
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—42no—
178C4×C47—81no—
179C4×C47—161no—
180C4×C47#46011yescharacteristic
181C4×C47#46311yescharacteristic
182C4×C47#46511yescharacteristic
183C4×C47#46911yescharacteristic
184C4×C47#47611yescharacteristic
185C4×C47#47611yescharacteristic
186C4×C47#47811yescharacteristic
187C4×C47#47811yescharacteristic
188#1982—471no—
189#1957—471no—
190#1948D4711yescharacteristic, complemented
191#1939—471no—
192C2×#334—471no—
193C2×#331—471no—
194#1296—471no—
195C2×C47#166611yescharacteristic
196C2×C47#167711yescharacteristic
197C2×C47#168811yescharacteristic
198C2×C47#170111yescharacteristic
199C2×C47#206311yescharacteristic
200C2×C47#206511yescharacteristic
201C2×C47#206511yescharacteristic
202D47—162no—
203C2×#127—471no—
204C2×#106—21no—
205C2×C4⋊C8—471no—
206C2×C4⋊C8—471no—
207C2×C4⋊C8—941no—
208C2×C4⋊C8C2×D4711yescharacteristic
209C2×#102—941no—
210C2×#102—941no—
211C2×#102—941no—
212C2×#102—941no—
213C2×C4×C8—471no—
214#384C2×D4711yescharacteristic
215C4×C4⋊C4C2×D4711yescharacteristic
216#340—21no—
217#336—941no—
218#334—942no—
219#331—942no—
220C47#1059511yescharacteristic, complemented, Sylow
221C22×D4—941no—
222C22×D4—941no—
223C22×D4—941no—
224C22×C8—21no—
225C22×C8—471no—
226C22×C8—471no—
227C22×C8—941no—
228C22×C8—941no—
229#127—472no—
230#127—941no—
231#127—941no—
232#127—941no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C22⋊D4711yescharacteristic
237C2×C4⋊C4C22⋊D4711yescharacteristic
238C2×C42—21no—
239C2×C42C22×D4711yescharacteristic
240#106—42no—
241C4⋊C8—21no—
242C4⋊C8—941no—
243C4⋊C8—941no—
244C4⋊C8—941no—
245C4⋊C8—941no—
246C4⋊C8—1882no—
247C4⋊C8D18812yes—
248#102—1882no—
249#102—1882no—
250#102—1882no—
251#102—1882no—
252C4×C8—941no—
253C4×C8—941no—
254#95—21no—
255C24—1881no—
256C2×D4—942no—
257C2×D4—942no—
258C2×D4—942no—
259C2×D4—3761no—
260C2×D4—3761no—
261C2×D4—1881no—
262C2×D4—1881no—
263C2×D4—1881no—
264C2×D4—1881no—
265C2×D4—1881no—
266C2×D4—1881no—
267C2×D4—1881no—
268C2×D4—1881no—
269C2×D4—1881no—
270C2×D4—1881no—
271C2×D4—1881no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4D4×D4711yescharacteristic
276C22×C4#1062535211yescharacteristic
277C22×C4C2×C22⋊D4711yescharacteristic
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—472no—
282C2×C8—941no—
283C2×C8—941no—
284C2×C8—941no—
285C2×C8—941no—
286C2×C8—941no—
287C2×C8—1881no—
288C2×C8—1881no—
289C2×C8—1881no—
290C2×C8—1881no—
291C2×C8—1881no—
292C2×C8—1881no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—81no—
301C4⋊C4#1062533612yes—
302C42—41no—
303C42—41no—
304C42C2×D18811yescharacteristic
305C42#1062535011yescharacteristic
306C42Q8×D4711yescharacteristic
307C42#1062535411yescharacteristic
308C23—3761no—
309C23—3761no—
310C23—3761no—
311C23—3761no—
312C23—3761no—
313C23—3761no—
314C23—1882no—
315C23#1309399611yescharacteristic
316D4—3762no—
317D4—3762no—
318D4—3761no—
319D4—3761no—
320D4—3761no—
321D4—3761no—
322D4—1882no—
323D4—1882no—
324D4—1882no—
325D4—1882no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#1309399811yescharacteristic
338C2×C4#1309399911yescharacteristic
339C2×C4#1309400011yescharacteristic
340C2×C4#1309400211yescharacteristic
341C2×C4#1309400411yescharacteristic
342C2×C4#1309401911yescharacteristic
343C2×C4SD16×D4711yescharacteristic
344C2×C4C2×#1062533611yescharacteristic
345C2×C4#1309404411yescharacteristic
346C2×C4#1309404511yescharacteristic
347C2×C4#1309404911yescharacteristic
348C2×C4#1309405011yescharacteristic
349C2×C4#1309405111yescharacteristic
350C2×C4#1309405111yescharacteristic
351C8—42no—
352C8—942no—
353C8—3761no—
354C8—3761no—
355C8—1881no—
356C22—3762no—
357C22—3762no—
358C22—3762no—
359C22—7521no—
360C22—7521no—
361C22—7521no—
362C22—7521no—
363C22#1568904511yescharacteristic
364C22#1568932111yescharacteristic
365C22#1568934011yescharacteristic
366C22#1568935411yescharacteristic
367C22#1568937411yescharacteristic
368C22#1568938811yescharacteristic
369C22#1568939111yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#1568932311yescharacteristic
376C4#1568933811yescharacteristic
377C4#1568935311yescharacteristic
378C4#1568937711yescharacteristic
379C4#1568941011yescharacteristic
380C4#1568941211yescharacteristic
381C4#1568942011yescharacteristic
382C4#1568942211yescharacteristic
383C2—7522no—
384C2#2024273811yescharacteristic
385C2#2024279911yescharacteristic
386C2#2024287011yescharacteristic
387C2#2024295111yescharacteristic
388C2#2024474511yescharacteristic
389C2#2024475711yescharacteristic
390C2#2024475911yescharacteristic
subgroupG/H
centerC23#13093996
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1948C2
socleC23×C47#121
prime radicalC2×#13094021C22
hypercenter#1948D47
hypocenterC47#10595
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #20244107C2semidirect
4. C2×#15688873C2semidirect
6. #20241271C2semidirect
7. C47×#1948C2semidirect
190. #1948D47semidirect
220. C47#10595semidirect

Maximal subgroups

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

subgroupindex
#202443152
#202441932
#202441072
C2×#156888732
C2×#156888662
#202412712
C47×#19482
#1059547