Finite Group Databasebeta

← #26134633

Subgroups — #26134633

Order 12032.

448 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245083C211yesmaximal, characteristic, complemented
2#20245080C211yesmaximal, characteristic
3#20245042C211yesmaximal, characteristic, complemented
4#20245038C211yesmaximal, characteristic
5#20243438C211yesmaximal, characteristic, complemented
6#20243188C211yesmaximal, characteristic, complemented
7C47×#3057C211yesmaximal, characteristic
8C2×#13093960—21no—
9#15689107C2211yescharacteristic
10#15689107C2211yescharacteristic
11#15689107C2211yescharacteristic
12#15689097C2211yescharacteristic
13#15689078—21no—
14#15688922—22no—
15#15688920—22no—
16#15688913—22no—
17#15688910—22no—
18#15688894—21no—
19C47⋊#338—21no—
20C22×SD16×C47C411yescharacteristic, complemented
21C2×#131×C47C2211yescharacteristic
22C47×#536C2211yescharacteristic
23C47×#535C2211yescharacteristic
24C47×#468—21no—
25C47×#468—21no—
26C47×#465—21no—
27C47×#465—21no—
28C47×#427C411yescharacteristic, complemented
29C47×#419C411yescharacteristic, complemented
30C47×#418C411yescharacteristic, complemented
31C2×#10625329—21no—
32C2×#10625329—21no—
33C2×#10625329—21no—
34#13093983—21no—
35#13093960—41no—
36#13093960—41no—
37#13093943—21no—
38#13093943—21no—
39#13093943D412yes—
40#13093941—21no—
41#13093941—21no—
42#13093941—21no—
43#13093939—21no—
44#13093939D412yes—
45#13093934—41no—
46C8×Dic47—41no—
47C2×#41×C47C2311yescharacteristic
48C22×Q8×C47C2×C411yescharacteristic
49C22×D4×C47C2×C411yescharacteristic
50C2×SD16×C47—21no—
51C2×SD16×C47—21no—
52C2×SD16×C47—41no—
53C2×SD16×C47—41no—
54#131×C47—41no—
55#131×C47—41no—
56C2×M16×C47C2×C411yescharacteristic
57C2×M16×C47D411yescharacteristic
58C2×M16×C47D411yescharacteristic
59C22×C8×C47C2×C411yescharacteristic
60C22×C8×C47D411yescharacteristic
61C22×C8×C47D411yescharacteristic
62C4⋊Q8×C47—21no—
63#127×C47—21no—
64#124×C47—21no—
65#124×C47—21no—
66#123×C47—21no—
67#123×C47—21no—
68C22⋊Q8×C47—21no—
69C22⋊Q8×C47—21no—
70#121×C47—21no—
71#121×C47—21no—
72#120×C47—21no—
73#120×C47—21no—
74#117×C47C2×C411yescharacteristic
75#117×C47C2×C411yescharacteristic
76#107×C47—21no—
77#106×C47—21no—
78#103×C47—21no—
79#103×C47—21no—
80#102×C47—21no—
81#102×C47—21no—
82C24×C47—21no—
83#41×C47—41no—
84#41×C47—41no—
85C2×Q8×C47—21no—
86C2×Q8×C47—21no—
87C2×Q8×C47—41no—
88C2×Q8×C47—41no—
89C2×Q8×C47C2×D411yescharacteristic
90C2×D4×C47—21no—
91C2×D4×C47—21no—
92C2×D4×C47—41no—
93C2×D4×C47—41no—
94C2×D4×C47—41no—
95C2×D4×C47—41no—
96C2×D4×C47C2×D411yescharacteristic
97C2×D4×C47#4111yescharacteristic
98C2×D4×C47#4111yescharacteristic
99C22×C4×C47—21no—
100C22×C4×C47C22×C411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103SD16×C47—42no—
104SD16×C47—41no—
105SD16×C47—41no—
106M16×C47—41no—
107M16×C47—41no—
108M16×C47—41no—
109C2×C8×C47—21no—
110C2×C8×C47—21no—
111C2×C8×C47—21no—
112C2×C8×C47—21no—
113C2×C8×C47—21no—
114C2×C8×C47—21no—
115C2×C8×C47C22⋊C411yescharacteristic
116C2×C8×C47C22⋊C411yescharacteristic
117C2×C8×C47C22⋊C411yescharacteristic
118C2×C8×C47C22⋊C411yescharacteristic
119C4⋊C4×C47—21no—
120C4⋊C4×C47—21no—
121C4⋊C4×C47—41no—
122C4⋊C4×C47—41no—
123C22⋊C4×C47—21no—
124C22⋊C4×C47—21no—
125C22⋊C4×C47—41no—
126C22⋊C4×C47—41no—
127C22⋊C4×C47—41no—
128C22⋊C4×C47—41no—
129C42×C47—21no—
130C42×C47—21no—
131C22⋊Dic47—22no—
132C4⋊Dic47—41no—
133C4×Dic47—41no—
134#10625329—22no—
135#10625329—41no—
136#10625329—41no—
137#10625329—41no—
138#10625329—41no—
139#10625329—41no—
140C2×C47⋊C8—41no—
141C2×C47⋊C8—41no—
142C2×C47⋊C8—41no—
143C23×C47—41no—
144C23×C47—81no—
145C23×C47—161no—
146C23×C47C4×D411yescharacteristic
147C23×C47#12111yescharacteristic
148C23×C47#12411yescharacteristic
149Q8×C47—41no—
150Q8×C47—41no—
151Q8×C47—41no—
152Q8×C47—81no—
153D4×C47—41no—
154D4×C47—41no—
155D4×C47—41no—
156D4×C47—41no—
157D4×C47—41no—
158D4×C47—81no—
159D4×C47—161no—
160D4×C47—161no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—41no—
168C2×C4×C47—41no—
169C2×C4×C47—41no—
170C2×C4×C47—81no—
171C2×C4×C47C2×C22⋊C411yescharacteristic
172C2×C4×C47C4×D411yescharacteristic
173C2×C4×C47#12111yescharacteristic
174C2×C4×C47#12711yescharacteristic
175C2×Dic47—42no—
176C8×C47—21no—
177C8×C47—21no—
178C8×C47—21no—
179C8×C47#9911yescharacteristic
180C8×C47#9911yescharacteristic
181C47⋊C8—42no—
182C47⋊C8—81no—
183C47⋊C8—81no—
184#13232—471nomaximal, Sylow
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47—41no—
191C22×C47—81no—
192C22×C47—81no—
193C22×C47—81no—
194C22×C47—162no—
195C22×C47#39011yescharacteristic
196C4×C47—21no—
197C4×C47—21no—
198C4×C47—21no—
199C4×C47—81no—
200C4×C47—81no—
201C4×C47—81no—
202C4×C47C2×#9911yescharacteristic
203C4×C47#41011yescharacteristic
204Dic47—82no—
205#3057D4711yescharacteristic
206#2135—471no—
207#2134—471no—
208#2123—471no—
209#2122—471no—
210#1813—471no—
211#1757—471no—
212C2×C47—21no—
213C2×C47—41no—
214C2×C47—41no—
215C2×C47—41no—
216C2×C47—161no—
217C2×C47#196411yescharacteristic
218C22×SD16Dic4711yescharacteristic, complemented
219C2×#131C2×D4711yescharacteristic
220#536C2×D4711yescharacteristic
221#535C2×D4711yescharacteristic
222#468—21no—
223#468—21no—
224#465—21no—
225#465—21no—
226C2×#108—941no—
227#427Dic4711yescharacteristic, complemented
228#419Dic4711yescharacteristic, complemented
229#418Dic4711yescharacteristic, complemented
230#413—471no—
231#413—471no—
232#413—471no—
233#410—471no—
234#405—941no—
235#356—942no—
236#355—942no—
237#352—942no—
238AΣL(1,𝔽16)—942no—
239#344—941no—
240#338—941no—
241C47#1323211yescharacteristic, complemented, Sylow
242C2×#41C22×D4711yescharacteristic
243C22×Q8C2×Dic4711yescharacteristic
244C22×D4C2×Dic4711yescharacteristic
245C2×SD16—21no—
246C2×SD16—21no—
247C2×SD16—41no—
248C2×SD16—41no—
249#131—41no—
250#131—41no—
251C2×M16—941no—
252C2×M16—941no—
253C2×M16—941no—
254C2×M16C2×Dic4711yescharacteristic
255C2×M16C22⋊D4711yescharacteristic
256C2×M16C22⋊D4711yescharacteristic
257C22×C8C2×Dic4711yescharacteristic
258C22×C8C22⋊D4711yescharacteristic
259C22×C8C22⋊D4711yescharacteristic
260C4⋊Q8—21no—
261#127—21no—
262#124—21no—
263#124—21no—
264#123—21no—
265#123—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268#121—21no—
269#121—21no—
270#120—21no—
271#120—21no—
272#117—941no—
273#117C2×Dic4711yescharacteristic
274#117C2×Dic4711yescharacteristic
275#108—1881no—
276#108—1881no—
277#107—21no—
278#106—21no—
279#103—21no—
280#103—21no—
281#102—21no—
282#102—21no—
283#101—472no—
284#101—941no—
285#101—941no—
286#100—941no—
287#100—941no—
288#100—941no—
289#99—472no—
290#99—941no—
291#97—1881no—
292C4×C8—1881no—
293C24—21no—
294#41—41no—
295#41—41no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8D4×D4711yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4D4×D4711yescharacteristic
308C2×D4#1062535211yescharacteristic
309C2×D4#1062535211yescharacteristic
310C22×C4—21no—
311C22×C4C22×Dic4711yescharacteristic
312C22×C4C2×C22⋊D4711yescharacteristic
313C22×C4C2×C22⋊D4711yescharacteristic
314SD16—42no—
315SD16—41no—
316SD16—41no—
317M16—41no—
318M16—41no—
319M16—41no—
320M16—942no—
321M16—1881no—
322M16—1881no—
323M16—1881no—
324M16—1881no—
325M16—1881no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—21no—
332C2×C8—1881no—
333C2×C8—1881no—
334C2×C8—1881no—
335C2×C8C22⋊Dic4711yescharacteristic
336C2×C8C22⋊Dic4711yescharacteristic
337C2×C8C22⋊Dic4711yescharacteristic
338C2×C8C22⋊Dic4711yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—1881no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—942no—
351C42—21no—
352C42—21no—
353C42—1881no—
354C23—41no—
355C23—81no—
356C23—161no—
357C23D4×Dic4711yescharacteristic
358C23#1309399511yescharacteristic
359C23#1309401111yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370D4—161no—
371D4—161no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—1882no—
383C2×C4C2×C22⋊Dic4711yescharacteristic
384C2×C4D4×Dic4711yescharacteristic
385C2×C4#1309399511yescharacteristic
386C2×C4#1309402011yescharacteristic
387C8—21no—
388C8—21no—
389C8—21no—
390C8—3761no—
391C8—3761no—
392C8—1882no—
393C8#1309393911yescharacteristic
394C8#1309393911yescharacteristic
395C22—21no—
396C22—21no—
397C22—21no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—162no—
405C22#1568902611yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—81no—
410C4—81no—
411C4—81no—
412C4—3762no—
413C4C2×#1309393911yescharacteristic
414C4#1568909711yescharacteristic
415C2—21no—
416C2—41no—
417C2—41no—
418C2—41no—
419C2—161no—
420C2#2024422511yescharacteristic
subgroupG/H
centerC2#20244225
commutatorC22×C4×C47C22×C4
FrattiniC2×#41C22×D47
FittingC47×#3057C2
socleC2×C47#1964
prime radicalC47×#535C22
cosocleC2×#41×C47C23
hypercenter#3057D47
hypocenterC47#13232
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #3057

Complements

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

NH ≅ G/Ntype
1. #20245083C2semidirect
3. #20245042C2semidirect
5. #20243438C2semidirect
6. #20243188C2semidirect
20. C22×SD16×C47C4semidirect
28. C47×#427C4semidirect
29. C47×#419C4semidirect
30. C47×#418C4semidirect
218. C22×SD16Dic47semidirect
227. #427Dic47semidirect
228. #419Dic47semidirect
229. #418Dic47semidirect
241. C47#13232semidirect

Maximal subgroups

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

subgroupindex
#202450832
#202450802
#202450422
#202450382
#202434382
#202431882
C47×#30572
#1323247