Finite Group Databasebeta

← #26110892

Subgroups — #26110892

Order 12032.

514 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252496C211yesmaximal, characteristic
2C4×#13094055C211yesmaximal, characteristic
3#20244325C211yesmaximal, characteristic, complemented
4#20241768C211yesmaximal, characteristic
5#20241237C211yesmaximal, characteristic, complemented
6#20241224C211yesmaximal, characteristic, complemented
7C47×#1479C211yesmaximal, characteristic, complemented
8C2×#13094055C411yescharacteristic
9C4×#10625350C2211yescharacteristic
10C8×Dic94—21no—
11#15689228—21no—
12#15689221—21no—
13C4×#10625337—21no—
14C4×#10625336—21no—
15C8×D188—21no—
16(C22⋊D47)⋊C8—22no—
17#15689175—21no—
18#15689163C411yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C4⋊C8×D47—21no—
21#15689132C411yescharacteristic
22#15689122C411yescharacteristic
23C4×#10625329C2211yescharacteristic
24C2×C4×C47⋊C8C2211yescharacteristic
25#15688878—22no—
26#15688853—21no—
27#15688850—21no—
28C2×C4×Q8×C47C2211yescharacteristic
29C47×#431C2211yescharacteristic
30C47×#431C2211yescharacteristic
31C47×Q8⋊C8—21no—
32C47×Q8⋊C8—21no—
33C2×#10625350C2×C411yescharacteristic
34#13094055—22no—
35#13094055C814yescomplemented
36C2×#10625337—21no—
37C2×#10625336—21no—
38C2×#10625329C2×C411yescharacteristic
39C2×#10625329C2×C411yescharacteristic
40C22×C47⋊C8—21no—
41C22×C47⋊C8D412yes—
42C2×C8×D47—22no—
43C4×Dic94D411yescharacteristic
44C4×Dic94D411yescharacteristic
45C4×D188D411yescharacteristic
46C4×D188D411yescharacteristic
47C4×C22⋊D47—21no—
48C4×C22⋊D47—21no—
49#13093983C2×C411yescharacteristic
50#13093981—21no—
51C42×D47—21no—
52#13093957—21no—
53#13093955—21no—
54C4⋊(C47⋊C8)—21no—
55C4⋊(C47⋊C8)—21no—
56Dic47⋊C8—22no—
57#13093948—21no—
58#13093948—21no—
59#13093947—21no—
60#13093944—21no—
61(C2×D47)⋊C8—22no—
62#13093935—21no—
63C4×C47⋊C8—21no—
64C4×C47⋊C8—21no—
65C4×C47⋊C8—21no—
66C8×Dic47—22no—
67C22×Q8×C47C2×C411yescharacteristic
68C4×Q8×C47—21no—
69C4×Q8×C47—21no—
70C4×Q8×C47—21no—
71C4×Q8×C47—21no—
72C2×C4⋊C4×C47—21no—
73C2×C4⋊C4×C47C2×C411yescharacteristic
74C2×C42×C47—21no—
75C2×C42×C47C2311yescharacteristic
76C4⋊C8×C47—21no—
77C4⋊C8×C47D411yescharacteristic
78C4⋊C8×C47D411yescharacteristic
79C22⋊C8×C47—21no—
80C22⋊C8×C47—21no—
81C4×C8×C47—21no—
82C4×C8×C47—21no—
83C2×Q8×C47—21no—
84C2×Q8×C47—21no—
85C2×Q8×C47—21no—
86C2×Q8×C47—21no—
87C2×Q8×C47—21no—
88C2×Q8×C47C2×C812yescomplemented
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47C22×C411yescharacteristic
92C22×C4×C47C2×D411yescharacteristic
93C22×C4×C47#4111yescharacteristic
94C2×C22⋊D47—21no—
95#10625350—21no—
96#10625350—21no—
97#10625350C2×C812yes—
98#10625350M1612yes—
99C2×D188C22⋊C411yescharacteristic
100C2×C4×D47—21no—
101C2×C4×D47—21no—
102C2×C4×D47—21no—
103C2×Dic94C22⋊C411yescharacteristic
104C2×C8×C47—21no—
105C2×C8×C47—21no—
106C2×C8×C47—41no—
107C4⋊C4×C47—21no—
108C4⋊C4×C47—21no—
109C4⋊C4×C47—41no—
110C4⋊C4×C47—41no—
111C42×C47—41no—
112C42×C47—41no—
113C42×C47C2×D411yescharacteristic
114C42×C47C2×D411yescharacteristic
115C42×C47C2×D411yescharacteristic
116C42×C47#4111yescharacteristic
117C22⋊Dic47—21no—
118#10625337—24no—
119#10625336—24no—
120(C2×D47)⋊C4—21no—
121(C2×D47)⋊C4—21no—
122C4⋊Dic47C22⋊C411yescharacteristic
123C4⋊Dic47C22⋊C411yescharacteristic
124Dic47⋊C4—21no—
125Dic47⋊C4—21no—
126C4×Dic47—21no—
127C4×Dic47—21no—
128C4×Dic47—21no—
129#10625329—21no—
130#10625329—21no—
131#10625329—21no—
132#10625329C2×C812yescomplemented
133C2×C47⋊C8—21no—
134C2×C47⋊C8—22no—
135C2×C47⋊C8—21no—
136C2×C47⋊C8—22no—
137C2×C47⋊C8—41no—
138C2×C47⋊C8—41no—
139C2×C47⋊C8—42no—
140C8×D47—82no—
141C23×C47C4×D411yescharacteristic
142C22×D47—21no—
143Q8×C47—22no—
144Q8×C47—22no—
145Q8×C47—41no—
146Q8×C47—41no—
147C2×C4×C47—21no—
148C2×C4×C47—21no—
149C2×C4×C47—22no—
150C2×C4×C47—41no—
151C2×C4×C47—41no—
152C2×C4×C47—41no—
153C2×C4×C47—42no—
154C2×C4×C47—41no—
155C2×C4×C47C2×C22⋊C411yescharacteristic
156C2×C4×C47C4×D411yescharacteristic
157C2×C4×C47#12011yescharacteristic
158C2×C4×C47#12111yescharacteristic
159C2×C4×C47#12111yescharacteristic
160C2×C4×C47#12311yescharacteristic
161C2×C4×C47C22×C811yescharacteristic
162C2×C4×C47C2×M1611yescharacteristic
163C2×C4×C47#13111yescharacteristic
164C2×C4×C47#13111yescharacteristic
165C22⋊D47—22no—
166C22⋊D47—22no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170D188—21no—
171D188C22⋊C812yes—
172C4×D47—22no—
173C4×D47—22no—
174C4×D47—41no—
175C4×D47—41no—
176C4×D47—81no—
177Dic94—21no—
178Dic94C22⋊C812yes—
179C8×C47—41no—
180C8×C47—41no—
181C8×C47—81no—
182C47⋊C8—22no—
183C47⋊C8—42no—
184C47⋊C8—41no—
185C47⋊C8—42no—
186#8953—471nomaximal, Sylow
187C22×C47—21no—
188C22×C47—21no—
189C22×C47#38611yescharacteristic
190C22×C47C8×D411yescharacteristic
191C22×C47#43511yescharacteristic
192C2×D47—22no—
193C2×D47—41no—
194C2×D47—41no—
195C4×C47—21no—
196C4×C47—21no—
197C4×C47—21no—
198C4×C47—42no—
199C4×C47—81no—
200C4×C47C2×C22⋊C811yescharacteristic
201C4×C47#40811yescharacteristic
202C4×C47C8×D411yescharacteristic
203C4×C47#43511yescharacteristic
204C4×C47#45511yescharacteristic
205C4×C47#45611yescharacteristic
206Dic47—22no—
207Dic47—41no—
208Dic47—41no—
209#2988—471no—
210C4×#137—471no—
211#1984—471no—
212#1479D4711yescharacteristic, complemented
213#1476—471no—
214#1283—471no—
215#1278—471no—
216C2×C47—21no—
217C2×C47—21no—
218C2×C47#186911yescharacteristic
219C2×C47#188111yescharacteristic
220C2×C47#188211yescharacteristic
221D47—42no—
222C2×#137—471no—
223C4×#41—471no—
224C2×C4×Q8C2×D4711yescharacteristic
225C8×Q8—941no—
226#441—941no—
227#440—941no—
228C4×Q16—941no—
229C4×SD16—941no—
230C8×D4—941no—
231C8×D4—942no—
232#431—941no—
233#431C2×D4711yescharacteristic
234#431C2×D4711yescharacteristic
235#428—471no—
236C2×C4⋊C8—471no—
237C2×C4⋊C8—941no—
238#419—471no—
239#417—471no—
240C4×M16—471no—
241C2×C4×C8—471no—
242#336—942no—
243Q8⋊C8—21no—
244Q8⋊C8—21no—
245Q8⋊C8—941no—
246D4⋊C8—941no—
247C47#895311yescharacteristic, complemented, Sylow
248C2×#41—471no—
249C22×Q8C4×D4711yescharacteristic
250#137—474no—
251#137—942no—
252C2×Q16—941no—
253C2×SD16—941no—
254C2×M16—471no—
255C2×M16—471no—
256C22×C8—472no—
257C22×C8—942no—
258C22×C8—941no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—471no—
264C4×Q8—471no—
265C4×D4—471no—
266C4×D4—471no—
267C4×D4—941no—
268C4×D4—941no—
269#117—471no—
270#117—941no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4C4×D4711yescharacteristic
273C2×C42—21no—
274C2×C42—941no—
275C2×C42C22×D4711yescharacteristic
276#107—941no—
277#106—941no—
278C4⋊C8—21no—
279C4⋊C8—942no—
280C4⋊C8—941no—
281C4⋊C8—941no—
282C4⋊C8C22⋊D4711yescharacteristic
283C4⋊C8C22⋊D4711yescharacteristic
284#103—941no—
285#103—941no—
286#103—941no—
287#102—941no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—942no—
291#97—941no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—942no—
295C4×C8—941no—
296C4×C8—941no—
297C4×C8—941no—
298#41—472no—
299#41—472no—
300#41—941no—
301#41—941no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—471no—
308C2×Q8C8×D4712yescomplemented
309C2×D4—471no—
310C2×D4—941no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—941no—
314C22×C4—941no—
315C22×C4—941no—
316C22×C4C2×C4×D4711yescharacteristic
317C22×C4D4×D4711yescharacteristic
318C22×C4#1062535211yescharacteristic
319Q16—944no—
320SD16—944no—
321M16—472no—
322M16—941no—
323M16—941no—
324M16—941no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—41no—
328C2×C8—941no—
329C2×C8—942no—
330C2×C8—941no—
331C2×C8—942no—
332C2×C8—3762no—
333C2×C8—1881no—
334C2×C8—1881no—
335C2×C8—1882no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—471no—
341C4⋊C4—471no—
342C4⋊C4—941no—
343C4⋊C4—941no—
344C22⋊C4—941no—
345C22⋊C4—941no—
346C22⋊C4—941no—
347C42—41no—
348C42—41no—
349C42—941no—
350C42—941no—
351C42—941no—
352C42#1062535011yescharacteristic
353C42D4×D4711yescharacteristic
354C42D4×D4711yescharacteristic
355C42C2×C22⋊D4711yescharacteristic
356C23—941no—
357C23(C22⋊D47)⋊C411yescharacteristic
358Q8—22no—
359Q8—22no—
360Q8—41no—
361Q8—41no—
362Q8—472no—
363Q8—941no—
364D4—472no—
365D4—942no—
366D4—942no—
367D4—941no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—941no—
377C2×C4—942no—
378C2×C4—942no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—3761no—
382C2×C4—1881no—
383C2×C4—1881no—
384C2×C4C22⋊C4×D4711yescharacteristic
385C2×C4C4×C22⋊D4711yescharacteristic
386C2×C4#1309399211yescharacteristic
387C2×C4#1309399511yescharacteristic
388C2×C4#1309399711yescharacteristic
389C2×C4#1309400611yescharacteristic
390C2×C4C2×C8×D4711yescharacteristic
391C2×C4M16×D4711yescharacteristic
392C2×C4#1309403011yescharacteristic
393C2×C4#1309403211yescharacteristic
394C8—41no—
395C8—41no—
396C8—81no—
397C8—942no—
398C8—1882no—
399C8—1882no—
400C8—1881no—
401C22—21no—
402C22—21no—
403C22—942no—
404C22—1881no—
405C22—1881no—
406C22#1568899911yescharacteristic
407C22(C22⋊D47)⋊C811yescharacteristic
408C22#1568919711yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—942no—
415C4—1881no—
416C4—1881no—
417C4C22⋊C8×D4711yescharacteristic
418C4#1568908811yescharacteristic
419C4C8×C22⋊D4711yescharacteristic
420C4#1568919211yescharacteristic
421C4#1568929911yescharacteristic
422C4#1568930411yescharacteristic
423C2—21no—
424C2—21no—
425C2—1882no—
426C2#2024367711yescharacteristic
427C2#2024374711yescharacteristic
428C2#2024375411yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1479C2
socleC22×C47#386
prime radicalC2×#10625350C2×C4
cosocleC2×C42×C47C23
hypercenter#1479D47
hypocenterC47#8953
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
3. #20244325C2semidirect
5. #20241237C2semidirect
6. #20241224C2semidirect
7. C47×#1479C2semidirect
35. #13094055C8semidirect
88. C2×Q8×C47C2×C8semidirect
132. #10625329C2×C8semidirect
212. #1479D47semidirect
247. C47#8953semidirect
308. C2×Q8C8×D47semidirect

Maximal subgroups

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

subgroupindex
#202524962
C4×#130940552
#202443252
#202417682
#202412372
#202412242
C47×#14792
#895347