Finite Group Databasebeta

← #26111628

Subgroups — #26111628

Order 12032.

606 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689174C211yesmaximal, characteristic
2C4×#13094004C211yesmaximal, characteristic
3#20243365C211yesmaximal, characteristic
4C2×#15688855C211yesmaximal, characteristic, complemented
5C2×#15688853C211yesmaximal, characteristic, complemented
6#20241229C211yesmaximal, characteristic, complemented
7C47×#1279C211yesmaximal, characteristic, complemented
8C2×#13094004C411yescharacteristic
9C2×C4×Dic94C2211yescharacteristic
10C2×C42×D47C2211yescharacteristic
11#15689174—22no—
12#15689174—22no—
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×Dic47⋊C8—21no—
15C2×(C2×D47)⋊C8—21no—
16C2×(C2×D47)⋊C8—21no—
17C2×C4×C47⋊C8C2211yescharacteristic
18#15689028C411yescharacteristic
19#15689022C411yescharacteristic
20#15689008—21no—
21#15688997—21no—
22#15688980C411yescharacteristic
23C4×C4⋊Dic47—21no—
24C4×(C2×D47)⋊C4—21no—
25#15688877—21no—
26#15688855—22no—
27#15688853—22no—
28C2×C4⋊C8×C47C2211yescharacteristic
29C2×C4×C8×C47C2211yescharacteristic
30C4×C4⋊C4×C47C2211yescharacteristic
31C22×Dic94C2×C411yescharacteristic
32C22×C4×D47C2×C411yescharacteristic
33C22×C4×D47D411yescharacteristic
34C22×C4×D47D411yescharacteristic
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37#13094004—22no—
38#13094004—22no—
39C4×Dic94—21no—
40C4×Dic94—21no—
41C4×Dic94—21no—
42C4×Dic94—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47C2×C411yescharacteristic
46C2×Dic47⋊C4—21no—
47C2×(C2×D47)⋊C4—21no—
48C2×(C2×D47)⋊C4—21no—
49C2×C4×Dic47—21no—
50C2×C4×Dic47C2×C411yescharacteristic
51C2×C4×Dic47D411yescharacteristic
52C2×C4×Dic47D411yescharacteristic
53C42×D47—21no—
54C42×D47—21no—
55C42×D47—21no—
56C42×D47—21no—
57C4⋊(C47⋊C8)—21no—
58C4⋊(C47⋊C8)—21no—
59Dic47⋊C8—24no—
60(C2×D47)⋊C8—24no—
61(C2×D47)⋊C8—42no—
62C4×C47⋊C8—21no—
63C4×C47⋊C8D412yes—
64C47⋊#95—21no—
65C47⋊#95—21no—
66C47⋊#95—21no—
67C47⋊#95—21no—
68C22×C8×C47—21no—
69C22×C8×C47—21no—
70C2×C4⋊C4×C47C2×C411yescharacteristic
71C2×C4⋊C4×C47C2×C411yescharacteristic
72C2×C42×C47—21no—
73C2×C42×C47C2311yescharacteristic
74C4⋊C8×C47—21no—
75C4⋊C8×C47—21no—
76C4×C8×C47—21no—
77C4×C8×C47D412yes—
78#95×C47—21no—
79C23×D47C22⋊C411yescharacteristic
80C22×C4×C47—21no—
81C22×C4×C47—21no—
82C22×C4×C47C22×C411yescharacteristic
83C22×C4×C47C2×D411yescharacteristic
84C22×C4×C47C2×D411yescharacteristic
85C22×Dic47—21no—
86C22×Dic47—21no—
87C22×Dic47C22⋊C411yescharacteristic
88C22×Dic47C22⋊C411yescharacteristic
89C22×Dic47C22⋊C411yescharacteristic
90C2×C4×D47—21no—
91C2×C4×D47—21no—
92C2×C4×D47—21no—
93C2×C4×D47—21no—
94C2×C4×D47—21no—
95C2×C4×D47—21no—
96C2×C4×D47—21no—
97C2×C4×D47—21no—
98C2×C4×D47—21no—
99C2×C4×D47—21no—
100C2×C4×D47—21no—
101C2×C4×D47—21no—
102C2×C4×D47—41no—
103C2×C4×D47—41no—
104C2×C4×D47SD1612yes—
105C2×C4×D47Q1612yes—
106C2×Dic94—21no—
107C2×Dic94—21no—
108C2×Dic94—21no—
109C2×Dic94—21no—
110C2×Dic94—21no—
111C2×Dic94M1612yes—
112C2×C8×C47—22no—
113C2×C8×C47—41no—
114C2×C8×C47—41no—
115C2×C8×C47—41no—
116C2×C8×C47—41no—
117C2×C8×C47—41no—
118C4⋊C4×C47—21no—
119C4⋊C4×C47—21no—
120C4⋊C4×C47—21no—
121C4⋊C4×C47M1612yes—
122C42×C47—41no—
123C42×C47—41no—
124C42×C47C2×D411yescharacteristic
125C42×C47C2×D411yescharacteristic
126C42×C47#4111yescharacteristic
127C42×C47#4111yescharacteristic
128(C2×D47)⋊C4—24no—
129(C2×D47)⋊C4—42no—
130C4⋊Dic47—24no—
131C4⋊Dic47—21no—
132C4⋊Dic47—21no—
133C4⋊Dic47—42no—
134Dic47⋊C4—41no—
135Dic47⋊C4—41no—
136C4×Dic47—21no—
137C4×Dic47—21no—
138C4×Dic47—21no—
139C4×Dic47—21no—
140C4×Dic47—21no—
141C4×Dic47—21no—
142C4×Dic47—41no—
143C4×Dic47—41no—
144C2×C47⋊C8—22no—
145C2×C47⋊C8—41no—
146C2×C47⋊C8—41no—
147C2×C47⋊C8—41no—
148C2×C47⋊C8—41no—
149C2×C47⋊C8—41no—
150C23×C47C2×C22⋊C411yescharacteristic
151C22×D47—21no—
152C22×D47—21no—
153C22×D47—21no—
154C22×D47—21no—
155C22×D47—21no—
156C22×D47—21no—
157C22×D47#10312yes—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—22no—
161C2×C4×C47—41no—
162C2×C4×C47—41no—
163C2×C4×C47—41no—
164C2×C4×C47—41no—
165C2×C4×C47—41no—
166C2×C4×C47C4×D411yescharacteristic
167C2×C4×C47C4×D411yescharacteristic
168C2×C4×C47#12011yescharacteristic
169C2×C4×C47#12111yescharacteristic
170C2×C4×C47#12111yescharacteristic
171C2×C4×C47#12311yescharacteristic
172C2×C4×C47C2×M1611yescharacteristic
173C2×C4×C47C2×M1611yescharacteristic
174C2×C4×C47#13111yescharacteristic
175C2×C4×C47#13111yescharacteristic
176C2×C4×C47C2×SD1611yescharacteristic
177C2×C4×C47C2×Q1611yescharacteristic
178C2×C4×C47#13511yescharacteristic
179C2×C4×C47#13511yescharacteristic
180C2×Dic47—21no—
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—22no—
186C2×Dic47—21no—
187C2×Dic47—21no—
188C2×Dic47—21no—
189C2×Dic47—41no—
190C2×Dic47—41no—
191C2×Dic47—41no—
192C2×Dic47—41no—
193C2×Dic47—41no—
194C2×Dic47#10312yes—
195C4×D47—22no—
196C4×D47—22no—
197C4×D47—22no—
198C4×D47—22no—
199C4×D47—42no—
200C4×D47—42no—
201C4×D47—41no—
202C4×D47—41no—
203C4×D47—41no—
204C4×D47—41no—
205Dic94—22no—
206Dic94—22no—
207Dic94—41no—
208Dic94—41no—
209C8×C47—42no—
210C8×C47—81no—
211C47⋊C8—42no—
212C47⋊C8—81no—
213#9075—471nomaximal, Sylow
214C22×C47#38611yescharacteristic
215C22×C47#40711yescharacteristic
216C22×C47#40811yescharacteristic
217C22×C47C2×#10311yescharacteristic
218C22×C47#41611yescharacteristic
219C22×C47#42111yescharacteristic
220C22×C47#42111yescharacteristic
221C2×D47—22no—
222C2×D47—22no—
223C2×D47—22no—
224C2×D47—41no—
225C2×D47—41no—
226C2×D47—41no—
227C2×D47—41no—
228C4×C47—21no—
229C4×C47—21no—
230C4×C47—42no—
231C4×C47—81no—
232C4×C47#43511yescharacteristic
233C4×C47#43511yescharacteristic
234C4×C47#43611yescharacteristic
235C4×C47#43611yescharacteristic
236C4×C47#46511yescharacteristic
237C4×C47#46511yescharacteristic
238C4×C47#46711yescharacteristic
239C4×C47#46711yescharacteristic
240Dic47—22no—
241Dic47—42no—
242Dic47—41no—
243Dic47—41no—
244Dic47—81no—
245C2×#431—471no—
246C4×C22⋊Q8—471no—
247#1797—471no—
248C2×Q8⋊C8—471no—
249C2×Q8⋊C8—471no—
250#1279—471no—
251#1279D4711yescharacteristic, complemented
252C2×C47#148111yescharacteristic
253C2×C47#148211yescharacteristic
254C2×C47#148711yescharacteristic
255C2×C47#148811yescharacteristic
256C2×C47#187011yescharacteristic
257C2×C47#189211yescharacteristic
258C2×C47#189711yescharacteristic
259D47—42no—
260C2×C22⋊Q8—471no—
261C2×C4×Q8—471no—
262C22×C42—471no—
263#431—942no—
264#431—942no—
265C2×C4⋊C8—471no—
266C2×C4⋊C8—941no—
267C2×C4⋊C8C2×D4711yescharacteristic
268C2×C22⋊C8—941no—
269C2×C22⋊C8—941no—
270C2×C4×C8—471no—
271C2×C4×C8C2×D4711yescharacteristic
272#391—471no—
273#389—471no—
274#387—941no—
275#385—941no—
276#380—471no—
277C4×C4⋊C4—941no—
278C4×C4⋊C4C2×D4711yescharacteristic
279C4×C22⋊C4—941no—
280#336—941no—
281Q8⋊C8—942no—
282Q8⋊C8—942no—
283C47#907511yescharacteristic, complemented, Sylow
284C22×Q8—471no—
285C23×C4—471no—
286C23×C4—471no—
287C23×C4—471no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—941no—
291C22×C8—941no—
292C22⋊Q8—942no—
293C22⋊Q8—942no—
294C4×Q8—941no—
295C4×Q8—941no—
296C4×Q8—941no—
297C4×Q8—941no—
298C2×C4⋊C4—471no—
299C2×C4⋊C4—941no—
300C2×C4⋊C4—941no—
301C2×C4⋊C4—941no—
302C2×C4⋊C4C4×D4711yescharacteristic
303C2×C4⋊C4C4×D4711yescharacteristic
304C2×C22⋊C4—941no—
305C2×C22⋊C4—941no—
306C2×C42—21no—
307C2×C42—471no—
308C2×C42—471no—
309C2×C42—471no—
310C2×C42—941no—
311C2×C42—941no—
312C2×C42—941no—
313C2×C42—941no—
314C2×C42—941no—
315C2×C42C22×D4711yescharacteristic
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8—944no—
319C4⋊C8—941no—
320C4⋊C8—941no—
321C22⋊C8—944no—
322C22⋊C8—1882no—
323C4×C8—21no—
324C4×C8—472no—
325C4×C8—941no—
326C4×C8D18812yes—
327#95—21no—
328#95—941no—
329#95—941no—
330#95—941no—
331#95—941no—
332C24—471no—
333C2×Q8—472no—
334C2×Q8—941no—
335C2×Q8—941no—
336C2×Q8—941no—
337C2×Q8—941no—
338C2×Q8—941no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—471no—
342C22×C4—472no—
343C22×C4—472no—
344C22×C4—471no—
345C22×C4—471no—
346C22×C4—941no—
347C22×C4—941no—
348C22×C4—941no—
349C22×C4—941no—
350C22×C4—941no—
351C22×C4—941no—
352C22×C4—941no—
353C22×C4—941no—
354C22×C4—941no—
355C22×C4—941no—
356C22×C4—941no—
357C22×C4—941no—
358C22×C4—941no—
359C22×C4—941no—
360C22×C4—1881no—
361C22×C4—1881no—
362C22×C4C2×C4×D4711yescharacteristic
363C22×C4D4×D4711yescharacteristic
364C22×C4D4×D4711yescharacteristic
365C2×C8—22no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—942no—
372C2×C8—1881no—
373C2×C8—1881no—
374C2×C8—1881no—
375C2×C8—1881no—
376C2×C8—1881no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—944no—
381C4⋊C4—941no—
382C4⋊C4—941no—
383C4⋊C4—1882no—
384C4⋊C4—1881no—
385C4⋊C4—1881no—
386C4⋊C4#1062532412yes—
387C22⋊C4—944no—
388C22⋊C4—1882no—
389C42—41no—
390C42—41no—
391C42—941no—
392C42—941no—
393C42—941no—
394C42—941no—
395C42—941no—
396C42—941no—
397C42—1881no—
398C42—1881no—
399C42C2×D18811yescharacteristic
400C42#1062535011yescharacteristic
401C42D4×D4711yescharacteristic
402C42#1062535411yescharacteristic
403C23—472no—
404C23—941no—
405C23—941no—
406C23—941no—
407C23—941no—
408C23—941no—
409C23—941no—
410C23C22⋊C4×D4711yescharacteristic
411Q8—942no—
412Q8—942no—
413Q8—1881no—
414Q8—1881no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—472no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—942no—
427C2×C4—942no—
428C2×C4—942no—
429C2×C4—942no—
430C2×C4—941no—
431C2×C4—941no—
432C2×C4—942no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—1882no—
438C2×C4—1882no—
439C2×C4—1881no—
440C2×C4—1881no—
441C2×C4—1881no—
442C2×C4—1881no—
443C2×C4—1881no—
444C2×C4—1881no—
445C2×C4—1881no—
446C2×C4—1881no—
447C2×C4—1881no—
448C2×C4#1309398611yescharacteristic
449C2×C4C4×D18811yescharacteristic
450C2×C4#1309399411yescharacteristic
451C2×C4#1309399711yescharacteristic
452C2×C4#1309399911yescharacteristic
453C2×C4#1309400911yescharacteristic
454C2×C4M16×D4711yescharacteristic
455C2×C4C2×#1062532411yescharacteristic
456C2×C4#1309403011yescharacteristic
457C2×C4#1309403211yescharacteristic
458C2×C4SD16×D4711yescharacteristic
459C2×C4Q16×D4711yescharacteristic
460C2×C4#1309404311yescharacteristic
461C2×C4#1309404511yescharacteristic
462C8—42no—
463C8—81no—
464C8—3761no—
465C8—1882no—
466C22—942no—
467C22—942no—
468C22—942no—
469C22—1881no—
470C22—1881no—
471C22—1881no—
472C22—1881no—
473C22#1568900111yescharacteristic
474C22#1568908511yescharacteristic
475C22#1568908811yescharacteristic
476C22#103×D4711yescharacteristic
477C22#1568911611yescharacteristic
478C22#1568913811yescharacteristic
479C22#1568913811yescharacteristic
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—942no—
485C4—3761no—
486C4—1881no—
487C4—1881no—
488C4—1882no—
489C4#1568919311yescharacteristic
490C4#1568919611yescharacteristic
491C4#1568920011yescharacteristic
492C4#1568920211yescharacteristic
493C4#1568935111yescharacteristic
494C4#1568935311yescharacteristic
495C4#1568936311yescharacteristic
496C4#1568936511yescharacteristic
497C2—1882no—
498C2#2024178911yescharacteristic
499C2#2024179311yescharacteristic
500C2#2024181511yescharacteristic
501C2#2024181911yescharacteristic
502C2#2024368411yescharacteristic
503C2#2024381011yescharacteristic
504C2#2024383511yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1279C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1279D47
hypocenterC47#9075
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. C2×#15688855C2semidirect
5. C2×#15688853C2semidirect
6. #20241229C2semidirect
7. C47×#1279C2semidirect
251. #1279D47semidirect
283. C47#9075semidirect

Maximal subgroups

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

subgroupindex
C2×#156891742
C4×#130940042
#202433652
C2×#156888552
C2×#156888532
#202412292
C47×#12792
#907547