Finite Group Databasebeta

← #26112476

Subgroups — #26112476

Order 12032.

546 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689410C211yesmaximal, characteristic
2C2×#15689202C211yesmaximal, characteristic
3#20243385C211yesmaximal, characteristic
4C2×#15688872C211yesmaximal, characteristic, complemented
5#20241271C211yesmaximal, characteristic, complemented
6#20241223C211yesmaximal, characteristic, complemented
7C47×#1990C211yesmaximal, characteristic, complemented
8C22×#10625324—21no—
9C2×C4×D188C2211yescharacteristic
10#15689410—22no—
11#15689410C414yescomplemented
12#15689202—22no—
13#15689202—22no—
14C2×#13093955—21no—
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16C2×C4⋊(C47⋊C8)C2211yescharacteristic
17C2×C4⋊(C47⋊C8)C2211yescharacteristic
18C2×#13093944—21no—
19C2×#13093944—21no—
20C2×(C2×D47)⋊C8—21no—
21#15688885—21no—
22#15688872—22no—
23C2×C4⋊Q8×C47C2211yescharacteristic
24C2×C4×C8×C47C2211yescharacteristic
25C47×#384C2211yescharacteristic
26C47×#340—21no—
27C47×#340—21no—
28C22×D188D411yescharacteristic
29C22×C4×D47—21no—
30C2×#10625324—24no—
31C2×#10625324—42no—
32C2×#10625324—42no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C4×D188—21no—
37C4×D188—21no—
38C4×D188C2×C412yes—
39C4×D188D412yes—
40C2×C4⋊Dic47D411yescharacteristic
41C2×(C2×D47)⋊C4—21no—
42#13093955—24no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)—21no—
46C4⋊(C47⋊C8)—21no—
47C4⋊(C47⋊C8)C2×C412yes—
48C4⋊(C47⋊C8)D412yes—
49#13093944—24no—
50#13093944—42no—
51(C2×D47)⋊C8—24no—
52C22×Q8×C47—21no—
53C22×C8×C47D411yescharacteristic
54C22×C8×C47D411yescharacteristic
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47C2×C412yes—
59C2×C4⋊C4×C47—21no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—21no—
63C2×C4⋊C4×C47—21no—
64C2×C42×C47C2311yescharacteristic
65C4×C8×C47—21no—
66C4×C8×C47—21no—
67C23×D47—21no—
68C2×Q8×C47—22no—
69C2×Q8×C47—41no—
70C2×Q8×C47—81no—
71C2×Q8×C47—81no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47#4111yescharacteristic
77C22×Dic47—21no—
78C2×D188—21no—
79C2×D188—21no—
80C2×D188—21no—
81C2×D188—21no—
82C2×D188—21no—
83C2×D188C22⋊C412yes—
84C2×C4×D47—22no—
85C2×C4×D47—22no—
86C2×C4×D47—41no—
87C2×C4×D47—41no—
88C2×C4×D47—41no—
89C2×C4×D47—41no—
90C2×C8×C47—21no—
91C2×C8×C47—21no—
92C2×C8×C47—21no—
93C2×C8×C47—21no—
94C2×C8×C47—21no—
95C2×C8×C47SD1612yes—
96C4⋊C4×C47—22no—
97C4⋊C4×C47—22no—
98C4⋊C4×C47—41no—
99C4⋊C4×C47—41no—
100C4⋊C4×C47—41no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—81no—
105C42×C47C22×C411yescharacteristic
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47#4111yescharacteristic
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111C4⋊Dic47—21no—
112C4⋊Dic47C22⋊C412yes—
113C2×C47⋊C8—22no—
114C2×C47⋊C8—22no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C2×C47⋊C8—41no—
119C2×C47⋊C8—41no—
120C2×C47⋊C8—41no—
121C2×C47⋊C8—41no—
122#10625324—48no—
123C23×C47#12111yescharacteristic
124C22×D47—22no—
125C22×D47—41no—
126C22×D47—41no—
127C22×D47—41no—
128C22×D47—41no—
129C22×D47—41no—
130C22×D47—41no—
131Q8×C47—82no—
132Q8×C47—82no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—42no—
136C2×C4×C47—81no—
137C2×C4×C47—81no—
138C2×C4×C47—81no—
139C2×C4×C47—81no—
140C2×C4×C47—81no—
141C2×C4×C47C2×C22⋊C411yescharacteristic
142C2×C4×C47C4×D411yescharacteristic
143C2×C4×C47C4×D411yescharacteristic
144C2×C4×C47#12011yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47#12311yescharacteristic
147C2×C4×C47C2×SD1611yescharacteristic
148C2×C4×C47#13511yescharacteristic
149C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C47#13711yescharacteristic
152C2×C4×C47#13711yescharacteristic
153C2×C4×C47#13711yescharacteristic
154C2×C4×C47#13711yescharacteristic
155C2×Dic47—22no—
156C2×Dic47—41no—
157C2×Dic47—41no—
158D188—22no—
159D188—22no—
160D188—41no—
161D188—41no—
162C4×D47—42no—
163C4×D47—42no—
164C4×D47—42no—
165C4×D47—42no—
166C8×C47—22no—
167C8×C47—41no—
168C47⋊C8—42no—
169C47⋊C8—42no—
170C47⋊C8—81no—
171#9223—471nomaximal, Sylow
172C22×C47#38611yescharacteristic
173C22×C47#46111yescharacteristic
174C22×C47#46311yescharacteristic
175C22×C47#46811yescharacteristic
176C22×C47#47011yescharacteristic
177C22×C47#47111yescharacteristic
178C22×C47#47211yescharacteristic
179C2×D47—42no—
180C2×D47—42no—
181C2×D47—42no—
182C2×D47—81no—
183C2×D47—81no—
184C2×D47—81no—
185C2×D47—81no—
186C4×C47—21no—
187C4×C47—21no—
188C4×C47—82no—
189C4×C47—161no—
190C4×C47#41711yescharacteristic
191C4×C47#41911yescharacteristic
192C4×C47C4×SD1611yescharacteristic
193C4×C47#44011yescharacteristic
194C4×C47#45011yescharacteristic
195C4×C47#45211yescharacteristic
196C4×C47#46811yescharacteristic
197C4×C47#47011yescharacteristic
198Dic47—42no—
199C2×#476—471no—
200C2×#436—471no—
201#1990D4711yescharacteristic, complemented
202#1802—471no—
203C2×#333—471no—
204#1296—471no—
205#1277—471no—
206C2×C47#169111yescharacteristic
207C2×C47#169511yescharacteristic
208C2×C47#169711yescharacteristic
209C2×C47#170311yescharacteristic
210C2×C47#187711yescharacteristic
211C2×C47#189411yescharacteristic
212C2×C47#190711yescharacteristic
213D47—82no—
214C22×M16—941no—
215C2×C4⋊Q8C2×D4711yescharacteristic
216C2×C4×D4—471no—
217#476—474no—
218#476—942no—
219#436—942no—
220#436—942no—
221C2×#106—941no—
222C2×C4⋊C8—471no—
223C2×C4⋊C8—471no—
224C2×C4⋊C8—471no—
225C2×#102—941no—
226C2×#102—941no—
227C2×C22⋊C8—941no—
228C2×C4×C8C2×D4711yescharacteristic
229#384C2×D4711yescharacteristic
230#340—21no—
231#340—21no—
232#340—941no—
233#333—942no—
234C47#922311yescharacteristic, complemented, Sylow
235C22×Q8—21no—
236C22×D4—471no—
237C23×C4—941no—
238C2×M16—944no—
239C2×M16—1882no—
240C2×M16—1882no—
241C22×C8—941no—
242C22×C8—941no—
243C22×C8—941no—
244C22×C8C22⋊D4711yescharacteristic
245C22×C8C22⋊D4711yescharacteristic
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8C4×D4712yes—
250C4×D4—472no—
251C4×D4—472no—
252C4×D4—941no—
253C4×D4—941no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—471no—
260C2×C22⋊C4—941no—
261C2×C42C22×D4711yescharacteristic
262#106—944no—
263C4⋊C8—472no—
264C4⋊C8—472no—
265C4⋊C8—941no—
266C4⋊C8—941no—
267C4⋊C8—941no—
268C4⋊C8—941no—
269#102—944no—
270#102—1882no—
271C22⋊C8—944no—
272C4×C8—21no—
273C4×C8—21no—
274C24—941no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—81no—
278C2×Q8—81no—
279C2×D4—472no—
280C2×D4—941no—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—941no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—941no—
288C22×C4—942no—
289C22×C4—942no—
290C22×C4—1881no—
291C22×C4—1881no—
292C22×C4—1881no—
293C22×C4—1881no—
294C22×C4D4×D4711yescharacteristic
295C22×C4#1062535211yescharacteristic
296C22×C4C2×C22⋊D4711yescharacteristic
297M16—1888no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—942no—
304C2×C8—942no—
305C2×C8—1881no—
306C2×C8—1881no—
307C2×C8—1881no—
308C2×C8—1881no—
309C2×C8—1881no—
310C2×C8—1881no—
311C2×C8—1881no—
312C2×C8#1062533612yes—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—81no—
322C4⋊C4—472no—
323C4⋊C4—941no—
324C22⋊C4—942no—
325C22⋊C4—942no—
326C42C2×C4×D4711yescharacteristic
327C42#1062535011yescharacteristic
328C42D4×D4711yescharacteristic
329C42D4×D4711yescharacteristic
330C23—942no—
331C23—1881no—
332C23—1881no—
333C23—1881no—
334C23—1881no—
335C23—1881no—
336C23—1881no—
337C23#1309399511yescharacteristic
338Q8—82no—
339Q8—82no—
340D4—942no—
341D4—942no—
342D4—1881no—
343D4—1881no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—942no—
353C2×C4—1881no—
354C2×C4—1881no—
355C2×C4—1882no—
356C2×C4—1882no—
357C2×C4—1882no—
358C2×C4—1882no—
359C2×C4C22⋊C4×D4711yescharacteristic
360C2×C4(C22⋊D47)⋊C411yescharacteristic
361C2×C4C4×C22⋊D4711yescharacteristic
362C2×C4#1309399211yescharacteristic
363C2×C4#1309399711yescharacteristic
364C2×C4#1309400611yescharacteristic
365C2×C4C2×#1062533611yescharacteristic
366C2×C4#1309404411yescharacteristic
367C2×C4#1309404911yescharacteristic
368C2×C4#1309405111yescharacteristic
369C2×C4#1309405311yescharacteristic
370C2×C4#1309405511yescharacteristic
371C2×C4#1309405611yescharacteristic
372C2×C4#1309405611yescharacteristic
373C8—22no—
374C8—41no—
375C8—3761no—
376C8—1882no—
377C8—1882no—
378C22—3761no—
379C22—3761no—
380C22—3761no—
381C22—3761no—
382C22—1882no—
383C22—1882no—
384C22—1882no—
385C22#1568899911yescharacteristic
386C22#1568932511yescharacteristic
387C22#1568933511yescharacteristic
388C22#1568936611yescharacteristic
389C22#1568937811yescharacteristic
390C22#1568938311yescharacteristic
391C22#1568939011yescharacteristic
392C4—21no—
393C4—21no—
394C4—82no—
395C4—161no—
396C4—1882no—
397C4#1568912311yescharacteristic
398C4#1568913011yescharacteristic
399C4C4×#1062533611yescharacteristic
400C4#1568922111yescharacteristic
401C4#1568927311yescharacteristic
402C4#1568928311yescharacteristic
403C4#1568937211yescharacteristic
404C4#1568938011yescharacteristic
405C2—3762no—
406C2#2024288411yescharacteristic
407C2#2024290811yescharacteristic
408C2#2024291811yescharacteristic
409C2#2024296011yescharacteristic
410C2#2024372511yescharacteristic
411C2#2024381811yescharacteristic
412C2#2024389911yescharacteristic
subgroupG/H
centerC23#13093995
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1990C2
socleC23×C47#121
prime radicalC22×D188D4
cosocleC2×C42×C47C23
hypercenter#1990D47
hypocenterC47#9223
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#15688872C2semidirect
5. #20241271C2semidirect
6. #20241223C2semidirect
7. C47×#1990C2semidirect
11. #15689410C4semidirect
201. #1990D47semidirect
234. C47#9223semidirect

Maximal subgroups

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

subgroupindex
C2×#156894102
C2×#156892022
#202433852
C2×#156888722
#202412712
#202412232
C47×#19902
#922347