Finite Group Databasebeta

← #26199035

Subgroups — #26199035

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253974C211yesmaximal, characteristic, complemented
2#20253459C212yesmaximal
3#20242942C212yesmaximal, complemented
4#20242935C212yesmaximal, complemented
5#20242906C211yesmaximal, characteristic, complemented
6#20242901C211yesmaximal, characteristic, complemented
7#20242882C211yesmaximal, characteristic, complemented
8#20242877C211yesmaximal, characteristic, complemented
9#20242136C211yesmaximal, characteristic, complemented
10#20242052C212yesmaximal, complemented
11C47×#2965C211yesmaximal, characteristic
12#15689680C2212yes—
13#15689528C2211yescharacteristic
14#15689503C2211yescharacteristic
15#15689474C2212yes—
16#15689464—22no—
17#15689408C2212yes—
18#15689403C2212yes—
19#15689364—21no—
20#15689364—21no—
21#15689333C2212yes—
22#15689328C2212yes—
23#15689285—22no—
24C4×Dic188—21no—
25C4×Dic188—21no—
26C4×#10625337—22no—
27C4×#10625335—22no—
28#15689176C2212yes—
29#15688876C2212yes—
30#15688874C2211yescharacteristic
31#15688874C2211yescharacteristic
32#15688870C2212yes—
33#15688870C2212yes—
34#15688868C2212yes—
35#15688868C2212yes—
36C4×#41×C47C2211yescharacteristic
37C47×#446C2211yescharacteristic
38C47×#446C2211yescharacteristic
39C47×#436C2211yescharacteristic
40C47×#436C2211yescharacteristic
41C47×#435—21no—
42C47×#435—21no—
43C47×#431—21no—
44C47×#431C2211yescharacteristic
45C4×M16×C47—21no—
46C2×C4×C8×C47C2211yescharacteristic
47C2×Dic188—21no—
48C2×Dic188—21no—
49C2×#10625337—22no—
50C2×#10625335—22no—
51#13094024C2312yes—
52#13094024C2312yes—
53#13094016—22no—
54#13094003—22no—
55#13094003—22no—
56C4×Dic94—22no—
57C4×Dic94—22no—
58#13093983—22no—
59#13093958—21no—
60#13093958—21no—
61#13093957—22no—
62#13093955—22no—
63C4⋊(C47⋊C8)C2312yes—
64C4⋊(C47⋊C8)C2312yes—
65#13093949—22no—
66#13093949—22no—
67#13093948—22no—
68#13093947—22no—
69#13093947—22no—
70#13093945—22no—
71C22⋊(C47⋊C8)—22no—
72C4×C47⋊C8—22no—
73C2×#41×C47D411yescharacteristic
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C22×C8×C47D411yescharacteristic
77C22×C8×C47D411yescharacteristic
78C4×Q8×C47D411yescharacteristic
79C4×Q8×C47C2311yescharacteristic
80C4×D4×C47—21no—
81C4×D4×C47—21no—
82C4×D4×C47D411yescharacteristic
83C4×D4×C47C2311yescharacteristic
84#117×C47—21no—
85#117×C47D411yescharacteristic
86C2×C42×C47—21no—
87C2×C42×C47C2311yescharacteristic
88C4⋊C8×C47—21no—
89C4⋊C8×C47—21no—
90C4⋊C8×C47C2311yescharacteristic
91C4⋊C8×C47C2311yescharacteristic
92C22⋊C8×C47—21no—
93C22⋊C8×C47—21no—
94C22⋊C8×C47—21no—
95#97×C47—21no—
96#97×C47—21no—
97C4×C8×C47—21no—
98C4×C8×C47D411yescharacteristic
99C4×C8×C47D411yescharacteristic
100C4×C8×C47C2311yescharacteristic
101C4×C8×C47C2311yescharacteristic
102#41×C47—42no—
103C2×Q8×C47C2×D411yescharacteristic
104C2×D4×C47—21no—
105C2×D4×C47C2×D411yescharacteristic
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C2×Dic94—22no—
113C2×Dic94—22no—
114M16×C47—42no—
115M16×C47—42no—
116C2×C8×C47—22no—
117C2×C8×C47—21no—
118C2×C8×C47—21no—
119C2×C8×C47—41no—
120C2×C8×C47C2×D411yescharacteristic
121C2×C8×C47C2×D411yescharacteristic
122C2×C8×C47C2×D411yescharacteristic
123C2×C8×C47C2×D411yescharacteristic
124C4⋊C4×C47—21no—
125C4⋊C4×C47—21no—
126C4⋊C4×C47C2×D411yescharacteristic
127C4⋊C4×C47C2×D411yescharacteristic
128C22⋊C4×C47—21no—
129C22⋊C4×C47—21no—
130C22⋊C4×C47—21no—
131C42×C47—21no—
132C42×C47—21no—
133C42×C47—21no—
134C42×C47C2×D411yescharacteristic
135C42×C47C2×D411yescharacteristic
136C42×C47#4111yescharacteristic
137C42×C47C2411yescharacteristic
138C22⋊Dic47—42no—
139#10625337—44no—
140#10625335—44no—
141C4⋊Dic47—22no—
142C4⋊Dic47—22no—
143C4⋊Dic47—22no—
144C4⋊Dic47—22no—
145Dic47⋊C4—42no—
146Dic47⋊C4—42no—
147C4×Dic47—42no—
148C2×C47⋊C8—22no—
149C2×C47⋊C8—22no—
150Dic188—42no—
151Dic188—42no—
152C23×C47—21no—
153C23×C47#12111yescharacteristic
154Q8×C47—22no—
155D4×C47—22no—
156D4×C47—42no—
157C2×C4×C47—21no—
158C2×C4×C47—21no—
159C2×C4×C47—22no—
160C2×C4×C47—22no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—42no—
165C2×C4×C47—41no—
166C2×C4×C47—41no—
167C2×C4×C47—42no—
168C2×C4×C47#12111yescharacteristic
169C2×C4×C47#12111yescharacteristic
170C2×C4×C47#12111yescharacteristic
171C2×C4×C47C22×D411yescharacteristic
172C2×C4×C47C22×D411yescharacteristic
173C2×C4×C47C2×#4111yescharacteristic
174C2×Dic47—42no—
175C2×Dic47—42no—
176Dic94—42no—
177Dic94—42no—
178Dic94—42no—
179Dic94—42no—
180C8×C47—21no—
181C8×C47—21no—
182C8×C47—21no—
183C8×C47—41no—
184C8×C47—41no—
185C8×C47#13512yes—
186C47⋊C8—42no—
187C47⋊C8—42no—
188#19161—471nomaximal, Sylow
189C22×C47—21no—
190C22×C47—21no—
191C22×C47—21no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47—41no—
195C22×C47C2×#12111yescharacteristic
196C4×C47—21no—
197C4×C47—21no—
198C4×C47—21no—
199C4×C47—41no—
200C4×C47—41no—
201C4×C47—41no—
202C4×C47#47312yes—
203C4×C47C2×#13511yescharacteristic
204C4×C47#57511yescharacteristic
205C4×C47#57512yes—
206Dic47—82no—
207Dic47—82no—
208#3170—471no—
209#3107—472no—
210#2965D4711yescharacteristic
211#1700—472no—
212#1699—472no—
213#1694—471no—
214#1693—471no—
215#1690—471no—
216#1689—471no—
217#1564—471no—
218#1544—472no—
219C2×C47—41no—
220C2×C47—81no—
221C2×C47#303511yescharacteristic
222C2×C47#305411yescharacteristic
223C2×C47C2×#47311yescharacteristic
224#533—472no—
225C4×#41C2×D4711yescharacteristic
226#500—471no—
227#494—471no—
228#487—472no—
229#485—942no—
230#475—472no—
231#474—472no—
232#467—941no—
233#467—941no—
234#462—472no—
235#461—472no—
236#452—942no—
237#446C2×D4711yescharacteristic
238#446C2×D4711yescharacteristic
239C4×Q16—942no—
240C4×Q16—941no—
241C4×Q16—941no—
242C4×SD16—942no—
243#436C2×D4711yescharacteristic
244#436C2×D4711yescharacteristic
245#435—21no—
246#435—21no—
247#431—21no—
248#431—472no—
249#431C2×D4711yescharacteristic
250C4×M16—21no—
251C2×C4×C8C2×D4711yescharacteristic
252#335—472no—
253#334—471no—
254#334—471no—
255#332—472no—
256#332—472no—
257#332—472no—
258#332—472no—
259C47#1916111yescharacteristic, complemented, Sylow
260C2×#41D18811yescharacteristic
261C2×Q16—942no—
262C2×Q16—941no—
263C2×Q16—941no—
264C2×SD16—942no—
265C2×M16—21no—
266C2×M16—21no—
267C22×C8C22⋊D4711yescharacteristic
268C22×C8C22⋊D4711yescharacteristic
269C4⋊Q8—472no—
270C4⋊Q8—472no—
271#125—942no—
272C22⋊Q8—942no—
273C22⋊Q8—942no—
274C4×Q8—942no—
275C4×Q8—942no—
276C4×Q8D18811yescharacteristic
277C4×Q8C22×D4711yescharacteristic
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D18811yescharacteristic
281C4×D4C22×D4711yescharacteristic
282#117—21no—
283#117—942no—
284#117D18811yescharacteristic
285C2×C42—21no—
286C2×C42C22×D4711yescharacteristic
287#107—941no—
288#107—941no—
289#107—942no—
290#106—942no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—472no—
294C4⋊C8—472no—
295C4⋊C8C22×D4711yescharacteristic
296C4⋊C8C22×D4711yescharacteristic
297#103—942no—
298#103—942no—
299#103—942no—
300#103—942no—
301#103—942no—
302#102—942no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—942no—
307#97—21no—
308#97—21no—
309C4×C8—21no—
310C4×C8—942no—
311C4×C8C22⋊D4711yescharacteristic
312C4×C8C22⋊D4711yescharacteristic
313C4×C8C22×D4711yescharacteristic
314C4×C8C22×D4711yescharacteristic
315#41—42no—
316C2×Q8—942no—
317C2×Q8—942no—
318C2×Q8C2×D18811yescharacteristic
319C2×D4—21no—
320C2×D4C2×D18811yescharacteristic
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4C2×D18811yescharacteristic
325C22×C4#1062535011yescharacteristic
326C22×C4C2×C22⋊D4711yescharacteristic
327Q16—1882no—
328Q16—1884no—
329Q16—1882no—
330SD16—1884no—
331M16—42no—
332M16—42no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—942no—
338C2×C8—942no—
339C2×C8C2×C22⋊D4711yescharacteristic
340C2×C8C2×C22⋊D4711yescharacteristic
341C2×C8C2×C22⋊D4711yescharacteristic
342C2×C8C2×C22⋊D4711yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—942no—
346C4⋊C4—942no—
347C4⋊C4—942no—
348C4⋊C4—942no—
349C4⋊C4—1882no—
350C4⋊C4—1882no—
351C4⋊C4C2×D18811yescharacteristic
352C4⋊C4C2×D18811yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—1882no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—1882no—
361C42C2×D18811yescharacteristic
362C42#1062535011yescharacteristic
363C42C2×C22⋊D4711yescharacteristic
364C42C23×D4711yescharacteristic
365C23—21no—
366C23#1309399811yescharacteristic
367Q8—22no—
368Q8—1882no—
369Q8—1882no—
370Q8—1882no—
371Q8—1882no—
372D4—22no—
373D4—42no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—1882no—
386C2×C4—1882no—
387C2×C4#1309399811yescharacteristic
388C2×C4#1309399811yescharacteristic
389C2×C4#1309399811yescharacteristic
390C2×C4C22×C22⋊D4711yescharacteristic
391C2×C4C22×D18811yescharacteristic
392C2×C4C2×#1062535011yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—41no—
397C8—41no—
398C8—1882no—
399C8—1882no—
400C8#1309404412yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22C2×#1309399811yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—3762no—
415C4—3762no—
416C4#1568939812yes—
417C4C2×#1309404411yescharacteristic
418C4#1568992111yescharacteristic
419C4#1568992312yes—
420C2—41no—
421C2—81no—
422C2#2025284311yescharacteristic
423C2#2025299711yescharacteristic
424C2C2×#1568939811yescharacteristic
subgroupG/H
centerC2×C4#13093998
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC47×#2965C2
socleC22×C47C2×#121
prime radicalC2×#41×C47D4
hypercenter#2965D47
hypocenterC47#19161
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #20253974C2semidirect
3. #20242942C2semidirect
4. #20242935C2semidirect
5. #20242906C2semidirect
6. #20242901C2semidirect
7. #20242882C2semidirect
8. #20242877C2semidirect
9. #20242136C2semidirect
10. #20242052C2semidirect
259. C47#19161semidirect

Maximal subgroups

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

subgroupindex
#202539742
#202534592
#202429422
#202429352
#202429062
#202429012
#202428822
#202428772
#202421362
#202420522
C47×#29652
#1916147