Finite Group Databasebeta

← #26371825

Subgroups — #26371825

Order 12032.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253958C211yesmaximal, characteristic, complemented
2#20245664C211yesmaximal, characteristic, complemented
3#20245647C211yesmaximal, characteristic, complemented
4#20245622C211yesmaximal, characteristic, complemented
5#20245619C211yesmaximal, characteristic, complemented
6#20245486C211yesmaximal, characteristic, complemented
7#20245482C211yesmaximal, characteristic, complemented
8#20245477C211yesmaximal, characteristic, complemented
9#20245472C211yesmaximal, characteristic
10C4×#13093970C211yesmaximal, characteristic, complemented
11C4×#13093967C211yesmaximal, characteristic, complemented
12C4×#13093968C211yesmaximal, characteristic, complemented
13C4×#13093965C211yesmaximal, characteristic, complemented
14C2×C4×C47⋊C16C211yesmaximal, characteristic, complemented
15C47×#3168C211yesmaximal, characteristic, complemented
16#15689657—21no—
17C2×#13093970C2211yescharacteristic
18C2×#13093968C2211yescharacteristic
19C2×#13093967C2211yescharacteristic
20C2×#13093965C2211yescharacteristic
21C22×C47⋊C16C2211yescharacteristic
22C22×C47⋊C16C2211yescharacteristic
23#15689525C2211yescharacteristic
24#15689507C2211yescharacteristic
25#15689478—21no—
26#15689364C2211yescharacteristic
27#15689359C2211yescharacteristic
28#15689352—21no—
29C4×Dic188C2211yescharacteristic
30C4×#10625325—21no—
31C4×D376C2211yescharacteristic
32#15688950C2211yescharacteristic
33#15688950C2211yescharacteristic
34#15688948C2211yescharacteristic
35#15688948C2211yescharacteristic
36#15688927C2211yescharacteristic
37#15688927C2211yescharacteristic
38#15688926C2211yescharacteristic
39#15688926C2211yescharacteristic
40#15688924C2211yescharacteristic
41#15688924C2211yescharacteristic
42#15688923C2211yescharacteristic
43#15688923C2211yescharacteristic
44C4×C47⋊C16C2211yescharacteristic
45C4×C47⋊C16C2211yescharacteristic
46C4×C47⋊C16C2211yescharacteristic
47C4×C47⋊C16C2211yescharacteristic
48C47×#529—21no—
49C47×#499C2211yescharacteristic
50C47×#495C2211yescharacteristic
51C47×#488—21no—
52C47×#467C2211yescharacteristic
53C47×#466C2211yescharacteristic
54C47×#465—21no—
55C4×Q16×C47C2211yescharacteristic
56C4×SD16×C47—21no—
57C4×D8×C47C2211yescharacteristic
58C2×C4×C8×C47C2211yescharacteristic
59C2×Dic188C2311yescharacteristic
60C2×#10625325—21no—
61C2×D376C2311yescharacteristic
62#13094018—41no—
63#13094016—21no—
64#13094012—21no—
65#13094007—41no—
66#13094003—21no—
67#13093998—21no—
68C4×Dic94—21no—
69C4×D188—21no—
70C4×C22⋊D47—41no—
71#13093981—41no—
72#13093970—22no—
73#13093968—22no—
74#13093967—22no—
75#13093965—22no—
76C2×C47⋊C16—22no—
77C2×C47⋊C16—22no—
78C2×C47⋊C16C2311yescharacteristic
79C2×C47⋊C16C2311yescharacteristic
80C2×C47⋊C16C2311yescharacteristic
81C2×C47⋊C16C2311yescharacteristic
82#13093958C2311yescharacteristic
83#13093958C2311yescharacteristic
84#13093956—21no—
85#13093949—21no—
86#13093949—21no—
87#13093946—21no—
88#13093946—21no—
89C2×Q16×C47C2311yescharacteristic
90C2×SD16×C47—21no—
91C2×D8×C47C2311yescharacteristic
92C22×C8×C47D411yescharacteristic
93C22×C8×C47C2311yescharacteristic
94#126×C47—41no—
95#125×C47—21no—
96#124×C47—21no—
97#123×C47—41no—
98C22⋊Q8×C47—21no—
99#121×C47—21no—
100C4×Q8×C47—21no—
101C4×D4×C47—21no—
102C4×D4×C47—41no—
103#117×C47—41no—
104C2×C42×C47D411yescharacteristic
105#107×C47C2311yescharacteristic
106#107×C47C2311yescharacteristic
107#106×C47—21no—
108#103×C47—21no—
109#103×C47—21no—
110#102×C47—21no—
111#102×C47—21no—
112C4×C8×C47D411yescharacteristic
113C4×C8×C47D411yescharacteristic
114C4×C8×C47C2311yescharacteristic
115C4×C8×C47C2311yescharacteristic
116C2×Q8×C47—21no—
117C2×D4×C47—21no—
118C2×D4×C47—41no—
119C22×C4×C47—41no—
120C22×C4×C47D811yescharacteristic
121C22×C4×C47D811yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C2×C22⋊D47—41no—
124C2×D188—21no—
125C2×C4×D47—41no—
126C2×Dic94—21no—
127Q16×C47—21no—
128Q16×C47—21no—
129SD16×C47—42no—
130D8×C47—21no—
131D8×C47—21no—
132C2×C8×C47—22no—
133C2×C8×C47—21no—
134C2×C8×C47—21no—
135C2×C8×C47C2×D411yescharacteristic
136C2×C8×C47C2×D411yescharacteristic
137C2×C8×C47C2×D411yescharacteristic
138C2×C8×C47C2411yescharacteristic
139C4⋊C4×C47—21no—
140C4⋊C4×C47—21no—
141C4⋊C4×C47—41no—
142C4⋊C4×C47—41no—
143C4⋊C4×C47—41no—
144C4⋊C4×C47—41no—
145C22⋊C4×C47—41no—
146C22⋊C4×C47—41no—
147C22⋊C4×C47—41no—
148C22⋊C4×C47—41no—
149C22⋊C4×C47—41no—
150C42×C47—41no—
151C42×C47D811yescharacteristic
152C42×C47D811yescharacteristic
153C42×C47C2×D411yescharacteristic
154C42×C47C2×D411yescharacteristic
155C22⋊Dic47—41no—
156(C2×D47)⋊C4—41no—
157(C2×D47)⋊C4—41no—
158(C2×D47)⋊C4—41no—
159(C2×D47)⋊C4—41no—
160C4⋊Dic47—21no—
161C4⋊Dic47—21no—
162Dic47⋊C4—41no—
163Dic47⋊C4—41no—
164Dic47⋊C4—41no—
165Dic47⋊C4—41no—
166C4×Dic47—41no—
167Dic188—21no—
168Dic188—21no—
169D376—21no—
170D376—21no—
171#10625325—42no—
172C47⋊C16—21no—
173C47⋊C16—21no—
174C47⋊C16#4112yes—
175C47⋊C16#4112yes—
176C23×C47—41no—
177C23×C47C2×D811yescharacteristic
178C22×D47—41no—
179Q8×C47—41no—
180Q8×C47—41no—
181D4×C47—41no—
182D4×C47—41no—
183D4×C47—82no—
184C2×C4×C47—22no—
185C2×C4×C47—21no—
186C2×C4×C47—21no—
187C2×C4×C47—22no—
188C2×C4×C47—41no—
189C2×C4×C47—41no—
190C2×C4×C47—41no—
191C2×C4×C47—82no—
192C2×C4×C47C2×D811yescharacteristic
193C2×C4×C47C2×D811yescharacteristic
194C2×C4×C47C2×D811yescharacteristic
195C2×C4×C47C2×D811yescharacteristic
196C2×C4×C47C2×D811yescharacteristic
197C2×C4×C47C22×D411yescharacteristic
198C22⋊D47—82no—
199C2×Dic47—41no—
200C2×Dic47—41no—
201C2×Dic47—41no—
202D188—41no—
203D188—41no—
204C4×D47—82no—
205Dic94—41no—
206Dic94—41no—
207C8×C47—21no—
208C8×C47—21no—
209C8×C47#13512yes—
210C8×C47C2×#4111yescharacteristic
211C8×C47C2×#4111yescharacteristic
212#33735—471nomaximal, Sylow
213C22×C47—21no—
214C22×C47—21no—
215C22×C47—81no—
216C22×C47—81no—
217C22×C47—81no—
218C22×C47#50812yes—
219C22×C47C22×D811yescharacteristic
220C2×D47—81no—
221C2×D47—81no—
222C2×D47—81no—
223C4×C47—21no—
224C4×C47—21no—
225C4×C47—21no—
226C4×C47—21no—
227C4×C47—81no—
228C4×C47—81no—
229C4×C47—81no—
230C4×C47#50812yes—
231C4×C47#53211yescharacteristic
232C4×C47C2×#13511yescharacteristic
233Dic47—81no—
234Dic47—81no—
235Dic47—81no—
236#3168—471no—
237#3168D4711yescharacteristic, complemented
238#2253—471no—
239#2249—471no—
240#2242—471no—
241#2242—471no—
242#2217—471no—
243#2217—471no—
244#2216—471no—
245#2215—471no—
246C4×Q32—471no—
247C4×SD32—471no—
248C4×SD32—471no—
249C4×D16—471no—
250C2×C4×C16—471no—
251C2×C47—22no—
252C2×C47—161no—
253C2×C47#316911yescharacteristic
254C2×C47C2×#50811yescharacteristic
255C2×C47C2×#50811yescharacteristic
256D47—161no—
257#529—21no—
258#529—941no—
259C2×Q32—471no—
260C2×SD32—471no—
261C2×SD32—471no—
262C2×D16—471no—
263C22×C16—471no—
264C22×C16—471no—
265#499—471no—
266#499C2×D4711yescharacteristic
267#495—471no—
268#495C2×D4711yescharacteristic
269#488—21no—
270#488—941no—
271#467—471no—
272#467C2×D4711yescharacteristic
273#466—471no—
274#466C2×D4711yescharacteristic
275#465—21no—
276#465—941no—
277C4×Q16—471no—
278C4×Q16C2×D4711yescharacteristic
279C4×SD16—21no—
280C4×SD16—941no—
281C4×D8—471no—
282C4×D8C2×D4711yescharacteristic
283C2×C4×C8C2×D4711yescharacteristic
284#367—471no—
285#367—471no—
286#366—471no—
287#366—471no—
288#358—471no—
289#358—471no—
290#358—471no—
291#358—471no—
292#357—471no—
293#357—471no—
294#357—471no—
295#357—471no—
296C4×C16—471no—
297C4×C16—471no—
298C4×C16—471no—
299C4×C16—471no—
300C47#3373511yescharacteristic, complemented, Sylow
301C2×Q16—471no—
302C2×Q16C22×D4711yescharacteristic
303C2×SD16—21no—
304C2×SD16—941no—
305C2×D8—471no—
306C2×D8C22×D4711yescharacteristic
307C22×C8C22⋊D4711yescharacteristic
308C22×C8C22×D4711yescharacteristic
309#126—41no—
310#126—1881no—
311#125—21no—
312#125—941no—
313#124—21no—
314#124—941no—
315#123—41no—
316#123—1881no—
317C22⋊Q8—21no—
318C22⋊Q8—941no—
319#121—21no—
320#121—941no—
321C4×Q8—21no—
322C4×Q8—941no—
323C4×D4—21no—
324C4×D4—41no—
325C4×D4—941no—
326C4×D4—1881no—
327#117—41no—
328#117—1881no—
329C2×C42C22⋊D4711yescharacteristic
330Q32—942no—
331SD32—942no—
332SD32—942no—
333D16—942no—
334C2×C16—471no—
335C2×C16—471no—
336C2×C16—471no—
337C2×C16—471no—
338C2×C16—942no—
339C2×C16—942no—
340#107—471no—
341#107—471no—
342#107C22×D4711yescharacteristic
343#107C22×D4711yescharacteristic
344#106—21no—
345#106—941no—
346#103—21no—
347#103—21no—
348#103—941no—
349#103—941no—
350#102—21no—
351#102—21no—
352#102—941no—
353#102—941no—
354C4×C8C22⋊D4711yescharacteristic
355C4×C8C22⋊D4711yescharacteristic
356C4×C8C22×D4711yescharacteristic
357C4×C8C22×D4711yescharacteristic
358C2×Q8—21no—
359C2×Q8—941no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—941no—
363C2×D4—1881no—
364C22×C4—41no—
365C22×C4—1881no—
366C22×C4#1062533411yescharacteristic
367C22×C4#1062533411yescharacteristic
368C22×C4C2×C22⋊D4711yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—941no—
372Q16—941no—
373SD16—42no—
374SD16—1882no—
375D8—21no—
376D8—21no—
377D8—941no—
378D8—941no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8C2×C22⋊D4711yescharacteristic
383C2×C8C2×C22⋊D4711yescharacteristic
384C2×C8C2×C22⋊D4711yescharacteristic
385C2×C8C23×D4711yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—941no—
393C4⋊C4—941no—
394C4⋊C4—1881no—
395C4⋊C4—1881no—
396C4⋊C4—1881no—
397C4⋊C4—1881no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—1881no—
404C22⋊C4—1881no—
405C22⋊C4—1881no—
406C22⋊C4—1881no—
407C22⋊C4—1881no—
408C42—41no—
409C42—1881no—
410C42#1062533411yescharacteristic
411C42#1062533411yescharacteristic
412C42C2×C22⋊D4711yescharacteristic
413C42C2×C22⋊D4711yescharacteristic
414C16—472no—
415C16—472no—
416C16—941no—
417C16—941no—
418C23—41no—
419C23—1881no—
420C23C2×#1062533411yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—1881no—
424Q8—1881no—
425D4—41no—
426D4—41no—
427D4—82no—
428D4—3762no—
429D4—1881no—
430D4—1881no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—3762no—
440C2×C4—1881no—
441C2×C4—1881no—
442C2×C4—1881no—
443C2×C4C2×#1062533411yescharacteristic
444C2×C4C2×#1062533411yescharacteristic
445C2×C4C2×#1062533411yescharacteristic
446C2×C4C2×#1062533411yescharacteristic
447C2×C4C2×#1062533411yescharacteristic
448C2×C4C22×C22⋊D4711yescharacteristic
449C8—21no—
450C8—21no—
451C8#1309404412yes—
452C8#41×D4711yescharacteristic
453C8#41×D4711yescharacteristic
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—3761no—
460C22—3761no—
461C22—3761no—
462C22#1568955312yes—
463C22C22×#1062533411yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—3761no—
472C4—3761no—
473C4—3761no—
474C4#1568955312yes—
475C4#1568966911yescharacteristic
476C4C2×#1309404411yescharacteristic
477C2—22no—
478C2—161no—
479C2—7521no—
480C2#2025396311yescharacteristic
481C2C2×#1568955311yescharacteristic
482C2C2×#1568955311yescharacteristic
subgroupG/H
centerC2×C4C2×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3168C2
socleC22×C47C22×D8
prime radical#20245472C2
hypercenter#3168D47
hypocenterC47#33735
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #20253958C2semidirect
2. #20245664C2semidirect
3. #20245647C2semidirect
4. #20245622C2semidirect
5. #20245619C2semidirect
6. #20245486C2semidirect
7. #20245482C2semidirect
8. #20245477C2semidirect
10. C4×#13093970C2semidirect
11. C4×#13093967C2semidirect
12. C4×#13093968C2semidirect
13. C4×#13093965C2semidirect
14. C2×C4×C47⋊C16C2semidirect
15. C47×#3168C2semidirect
237. #3168D47semidirect
300. C47#33735semidirect

Maximal subgroups

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

subgroupindex
#202539582
#202456642
#202456472
#202456222
#202456192
#202454862
#202454822
#202454772
#202454722
C4×#130939702
C4×#130939672
C4×#130939682
C4×#130939652
C2×C4×C47⋊C162
C47×#31682
#3373547