Finite Group Databasebeta

← #26115263

Subgroups — #26115263

Order 12032.

668 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251689C211yesmaximal, characteristic
2C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3C2×#15688859C212yesmaximal, complemented
4C2×#15688856C212yesmaximal
5C47×#1434C211yesmaximal, characteristic, complemented
6C2×#13094012C411yescharacteristic, complemented
7C2×#13094003C2211yescharacteristic
8C2×#13093998C2211yescharacteristic
9C2×C22⋊(C47⋊C8)C2212yes—
10C2×C4×C47⋊C8—21no—
11#15689029C411yescharacteristic, complemented
12#15689025C411yescharacteristic, complemented
13#15689014—21no—
14#15689014—21no—
15#15689002—21no—
16#15689002—21no—
17#15688989C411yescharacteristic, complemented
18#15688878—21no—
19#15688859—24no—
20#15688856—24no—
21C22×C42×C47C2211yescharacteristic
22C2×#95×C47—21no—
23C2×#95×C47—21no—
24C2×#95×C47C2212yes—
25C22×Dic94C2×C411yescharacteristic
26C22×D188C2×C411yescharacteristic
27C22×C22⋊D47—21no—
28C22×C47⋊C8—22no—
29#13094012—42no—
30#13094003—22no—
31#13094003—22no—
32#13093998—22no—
33#13093998—22no—
34C2×C4⋊Dic47C2×C411yescharacteristic
35C2×C4⋊Dic47C2×C411yescharacteristic
36C2×Dic47⋊C4—21no—
37C2×C22⋊Dic47—21no—
38C2×(C2×D47)⋊C4—21no—
39C2×(C2×D47)⋊C4—21no—
40C2×(C2×D47)⋊C4—21no—
41C2×(C2×D47)⋊C4—21no—
42C2×(C2×D47)⋊C4—21no—
43C22⋊(C47⋊C8)—22no—
44C22⋊(C47⋊C8)D414yes—
45C4×C47⋊C8—42no—
46C47⋊#95—21no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C23×C4×C47—22no—
51C23×C4×C47D411yescharacteristic
52C23×C4×C47D411yescharacteristic
53C23×C4×C47C2311yescharacteristic
54C2×C42×C47—42no—
55C2×C42×C47C2×C411yescharacteristic
56C2×C42×C47C2×C411yescharacteristic
57C2×C42×C47D411yescharacteristic
58C2×C42×C47D411yescharacteristic
59#95×C47—24no—
60#95×C47—22no—
61#95×C47—22no—
62#95×C47—42no—
63C24×C47C2×D411yescharacteristic
64C23×D47—21no—
65C22×C4×C47—22no—
66C22×C4×C47—22no—
67C22×C4×C47—22no—
68C22×C4×C47—22no—
69C22×C4×C47—24no—
70C22×C4×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47—41no—
74C22×C4×C47—42no—
75C22×C4×C47—42no—
76C22×C4×C47—42no—
77C22×C4×C47—42no—
78C22×C4×C47—42no—
79C22×C4×C47—42no—
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C22⋊C411yescharacteristic
82C22×C4×C47C22⋊C411yescharacteristic
83C22×C4×C47C22⋊C411yescharacteristic
84C22×C4×C47C22×C411yescharacteristic
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47C2×D412yes—
87C22×C4×C47#4112yes—
88C2×C22⋊D47—41no—
89C2×C22⋊D47—41no—
90C2×C22⋊D47—42no—
91C2×C22⋊D47—42no—
92C22×Dic47—21no—
93C22×Dic47—21no—
94C22×Dic47—21no—
95C2×D188—22no—
96C2×D188—41no—
97C2×D188—41no—
98C2×Dic94—22no—
99C2×Dic94—41no—
100C2×Dic94—41no—
101C42×C47—22no—
102C42×C47—22no—
103C42×C47—41no—
104C42×C47—41no—
105C22⋊Dic47—41no—
106C22⋊Dic47—41no—
107(C2×D47)⋊C4—42no—
108(C2×D47)⋊C4—42no—
109(C2×D47)⋊C4—42no—
110(C2×D47)⋊C4—42no—
111(C2×D47)⋊C4—42no—
112C4⋊Dic47—22no—
113C4⋊Dic47—22no—
114Dic47⋊C4—42no—
115C2×C47⋊C8—24no—
116C2×C47⋊C8—42no—
117C2×C47⋊C8—42no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47C2×C22⋊C411yescharacteristic
123C23×C47#12411yescharacteristic
124C23×C47#12711yescharacteristic
125C23×C47#13512yes—
126C23×C47#13512yes—
127C22×D47—41no—
128C22×D47—41no—
129C22×D47—41no—
130C22×D47—41no—
131C22×D47—41no—
132C22×D47—41no—
133C22×D47—41no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
148C2×C4×C47—42no—
149C2×C4×C47—42no—
150C2×C4×C47—44no—
151C2×C4×C47—44no—
152C2×C4×C47—44no—
153C2×C4×C47—44no—
154C2×C4×C47—44no—
155C2×C4×C47—82no—
156C2×C4×C47—82no—
157C2×C4×C47—82no—
158C2×C4×C47—82no—
159C2×C4×C47#9912yes—
160C2×C4×C47#10412yes—
161C2×C4×C47C4×D412yes—
162C2×C4×C47#12112yes—
163C22⋊D47—82no—
164C22⋊D47—82no—
165C2×Dic47—41no—
166C2×Dic47—41no—
167C2×Dic47—41no—
168C2×Dic47—41no—
169C2×Dic47—41no—
170C2×Dic47—41no—
171C2×Dic47—41no—
172C2×Dic47—41no—
173C2×Dic47—41no—
174D188—82no—
175Dic94—82no—
176C47⋊C8—44no—
177#9681—471nomaximal, Sylow
178C22×C47—21no—
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—22no—
183C22×C47—22no—
184C22×C47—22no—
185C22×C47—22no—
186C22×C47#39011yescharacteristic
187C22×C47C2×#9911yescharacteristic
188C22×C47#41011yescharacteristic
189C22×C47#41611yescharacteristic
190C22×C47#41611yescharacteristic
191C22×C47C2×#10411yescharacteristic
192C22×C47#42111yescharacteristic
193C22×C47#48812yes—
194C22×C47#49512yes—
195C2×D47—81no—
196C2×D47—81no—
197C2×D47—81no—
198C2×D47—81no—
199C2×D47—81no—
200C2×D47—81no—
201C2×D47—81no—
202C4×C47—22no—
203C4×C47—22no—
204C4×C47—22no—
205C4×C47—22no—
206C4×C47—41no—
207C4×C47—41no—
208C4×C47—84no—
209Dic47—81no—
210Dic47—81no—
211Dic47—81no—
212#2850—471no—
213C4×C22⋊C8—471no—
214C2×#328—472no—
215C2×#327—472no—
216#1434D4711yescharacteristic, complemented
217C2×C47—22no—
218C2×C47—22no—
219C2×C47#150011yescharacteristic
220C2×C47#150111yescharacteristic
221C2×C47#151611yescharacteristic
222C2×C47#152111yescharacteristic
223C2×C47#195811yescharacteristic
224C2×C47#196411yescharacteristic
225C2×C47#198011yescharacteristic
226D47—161no—
227C2×#124—471no—
228C2×C22⋊Q8—471no—
229C2×#121—471no—
230C22×C42C2×D4711yescharacteristic
231C2×C22⋊C8—472no—
232C2×C4×C8—941no—
233#391—471no—
234#390—471no—
235#388—941no—
236#388—941no—
237#386—941no—
238#386—941no—
239#382—471no—
240C2×#95—21no—
241C2×#95—21no—
242C2×#95C2×D4712yes—
243#336—941no—
244#328—944no—
245#327—944no—
246C47#968111yescharacteristic, complemented, Sylow
247C22×Q8—471no—
248C22×D4—471no—
249C22×D4—941no—
250C23×C4—22no—
251C23×C4C22⋊D4711yescharacteristic
252C23×C4C22⋊D4711yescharacteristic
253C23×C4C22×D4711yescharacteristic
254C22×C8—942no—
255#124—1882no—
256C22⋊Q8—942no—
257C22⋊Q8—942no—
258#121—942no—
259#121—942no—
260C2×C4⋊C4—471no—
261C2×C4⋊C4—471no—
262C2×C4⋊C4—941no—
263C2×C22⋊C4—941no—
264C2×C22⋊C4—941no—
265C2×C22⋊C4—941no—
266C2×C22⋊C4—941no—
267C2×C22⋊C4—941no—
268C2×C22⋊C4—941no—
269C2×C42—42no—
270C2×C42C4×D4711yescharacteristic
271C2×C42C4×D4711yescharacteristic
272C2×C42D18811yescharacteristic
273C2×C42D18811yescharacteristic
274C22⋊C8—474no—
275C22⋊C8—942no—
276C4×C8—1882no—
277#95—24no—
278#95—22no—
279#95—22no—
280#95—42no—
281#95—941no—
282#95—941no—
283#95—941no—
284#95—941no—
285C24—941no—
286C24C2×C22⋊D4711yescharacteristic
287C2×Q8—942no—
288C2×Q8—1881no—
289C2×Q8—1881no—
290C2×D4—942no—
291C2×D4—1881no—
292C2×D4—1881no—
293C2×D4—1881no—
294C2×D4—1881no—
295C2×D4—1882no—
296C2×D4—1882no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—941no—
313C22×C4—941no—
314C22×C4—941no—
315C22×C4(C2×D47)⋊C411yescharacteristic
316C22×C4(C2×D47)⋊C411yescharacteristic
317C22×C4(C2×D47)⋊C411yescharacteristic
318C22×C4(C2×D47)⋊C411yescharacteristic
319C22×C4C2×C4×D4711yescharacteristic
320C22×C4C2×D18811yescharacteristic
321C22×C4D4×D4712yes—
322C22×C4#1062535412yes—
323C2×C8—944no—
324C2×C8—1882no—
325C2×C8—1882no—
326C4⋊C4—942no—
327C4⋊C4—942no—
328C4⋊C4—1882no—
329C22⋊C4—1882no—
330C22⋊C4—1882no—
331C22⋊C4—1881no—
332C22⋊C4—1881no—
333C22⋊C4—1882no—
334C22⋊C4—1882no—
335C22⋊C4—1882no—
336C42—22no—
337C42—22no—
338C42—41no—
339C42—41no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—1881no—
345C23—1881no—
346C23—1881no—
347C23—1881no—
348C23—1881no—
349C23—1881no—
350C23—1881no—
351C23C2×(C2×D47)⋊C411yescharacteristic
352C23#1309401311yescharacteristic
353C23#1309402011yescharacteristic
354C23#1309404412yes—
355C23#1309404412yes—
356Q8—3762no—
357D4—3762no—
358D4—3762no—
359D4—3762no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—82no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—1881no—
386C2×C4—1881no—
387C2×C4—1881no—
388C2×C4—1881no—
389C2×C4—1881no—
390C2×C4—1881no—
391C2×C4—1881no—
392C2×C4—1881no—
393C2×C4—1881no—
394C2×C4#1309393812yes—
395C2×C4#1309395212yes—
396C2×C4#1309398612yes—
397C2×C4#1309399912yes—
398C8—1884no—
399C22—22no—
400C22—22no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—22no—
405C22—21no—
406C22—21no—
407C22—3761no—
408C22—3761no—
409C22—3761no—
410C22—3761no—
411C22—3761no—
412C22—3761no—
413C22—3761no—
414C22#1568902411yescharacteristic
415C22C2×#1309393811yescharacteristic
416C22#1568909611yescharacteristic
417C22#1568911711yescharacteristic
418C22#1568911711yescharacteristic
419C22C2×#1309395211yescharacteristic
420C22#1568914111yescharacteristic
421C22#1568948012yes—
422C22#1568950512yes—
423C4—22no—
424C4—22no—
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—84no—
430C4—3761no—
431C4—3761no—
432C4—3761no—
433C2—22no—
434C2—22no—
435C2—7521no—
436C2#2024187211yescharacteristic
437C2#2024187711yescharacteristic
438C2#2024194211yescharacteristic
439C2#2024196311yescharacteristic
440C2#2024419711yescharacteristic
441C2#2024422311yescharacteristic
442C2#2024430611yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1434C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#13093998C22
cosocleC23×C4×C47C23
hypercenter#1434D47
hypocenterC47#9681
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊(C47⋊C8)C2semidirect
3. C2×#15688859C2semidirect
5. C47×#1434C2semidirect
6. C2×#13094012C4semidirect
11. #15689029C4semidirect
12. #15689025C4semidirect
17. #15688989C4semidirect
216. #1434D47semidirect
246. C47#9681semidirect

Maximal subgroups

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

subgroupindex
#202516892
C4×C22⋊(C47⋊C8)2
C2×#156888592
C2×#156888562
C47×#14342
#968147