Finite Group Databasebeta

← #26316022

Subgroups — #26316022

Order 12032.

742 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
1C4×#13094012C211yesmaximal, characteristic
2#20244956C212yesmaximal, complemented
3#20244629C212yesmaximal
4#20244084C212yesmaximal
5#20244077C212yesmaximal, complemented
6#20243390C211yesmaximal, characteristic, complemented
7#20243390C211yesmaximal, characteristic, complemented
8#20243385C211yesmaximal, characteristic
9#20243385C211yesmaximal, characteristic
10#20243241C211yesmaximal, characteristic, complemented
11C47×#2859C211yesmaximal, characteristic, complemented
12C2×#13094012C2211yescharacteristic
13C2×C4×Dic94C2211yescharacteristic
14C2×C4×D188C2211yescharacteristic
15C2×C4⋊(C47⋊C8)C2211yescharacteristic
16C2×C4⋊(C47⋊C8)C2211yescharacteristic
17C2×#13093947C2212yes—
18C2×#13093947C2212yes—
19C2×#13093944C2212yes—
20C2×#13093944C2212yes—
21C2×#13093935C2212yes—
22#15689029C2211yescharacteristic
23#15689025C2211yescharacteristic
24#15689014—21no—
25#15689014—21no—
26#15688989C2211yescharacteristic
27C4×(C2×D47)⋊C4—21no—
28C4×(C2×D47)⋊C4—21no—
29#15688885C2212yes—
30#15688885C2212yes—
31#15688885C2212yes—
32#15688885C2212yes—
33#15688878C2212yes—
34C2×#125×C47—21no—
35C47×#389—21no—
36C47×#389—21no—
37C47×#389C2212yes—
38C47×#389C2212yes—
39C47×#384C2211yescharacteristic
40C47×#384C2211yescharacteristic
41C47×#382—21no—
42C43×C47C2211yescharacteristic
43C22×Dic94C2311yescharacteristic
44C22×D188C2311yescharacteristic
45C22×C4×D47—21no—
46C22×C47⋊C8C2312yes—
47C22×C47⋊C8C2312yes—
48#13094012—22no—
49#13094012—22no—
50C4×Dic94—22no—
51C4×Dic94—22no—
52C4×D188—22no—
53C4×D188—22no—
54C2×C4⋊Dic47C2311yescharacteristic
55C2×C4⋊Dic47C2311yescharacteristic
56C2×Dic47⋊C4—21no—
57C2×(C2×D47)⋊C4—21no—
58C2×(C2×D47)⋊C4—21no—
59C2×(C2×D47)⋊C4—21no—
60C2×(C2×D47)⋊C4—21no—
61C2×(C2×D47)⋊C4—21no—
62C2×C4×Dic47—21no—
63C4⋊(C47⋊C8)—22no—
64C4⋊(C47⋊C8)—22no—
65#13093947—24no—
66#13093947—42no—
67#13093944—24no—
68#13093944—42no—
69#13093935—42no—
70C47⋊#95—21no—
71C47⋊#95—21no—
72C47⋊#95—21no—
73C47⋊#95—21no—
74#125×C47—44no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—22no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47C2312yes—
82C2×C4⋊C4×C47C2312yes—
83C2×C42×C47D411yescharacteristic
84C2×C42×C47D411yescharacteristic
85C2×C42×C47D411yescharacteristic
86C2×C42×C47D411yescharacteristic
87C2×C42×C47C2311yescharacteristic
88C2×C42×C47C2311yescharacteristic
89C2×C42×C47C2311yescharacteristic
90#95×C47—22no—
91#95×C47—22no—
92C23×D47—21no—
93C22×C4×C47—22no—
94C22×C4×C47—22no—
95C22×C4×C47C2×D411yescharacteristic
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2411yescharacteristic
102C22×Dic47—21no—
103C22×Dic47—21no—
104C22×Dic47—21no—
105C2×D188—21no—
106C2×D188—21no—
107C2×D188—21no—
108C2×D188—21no—
109C2×D188—21no—
110C2×D188#4112yes—
111C2×C4×D47—42no—
112C2×C4×D47—42no—
113C2×C4×D47—42no—
114C2×Dic94—21no—
115C2×Dic94—21no—
116C2×Dic94—21no—
117C2×Dic94—21no—
118C2×Dic94—21no—
119C2×Dic94#4112yes—
120C4⋊C4×C47—22no—
121C4⋊C4×C47—22no—
122C4⋊C4×C47—22no—
123C4⋊C4×C47—22no—
124C4⋊C4×C47—42no—
125C4⋊C4×C47—42no—
126C4⋊C4×C47—44no—
127C4⋊C4×C47—44no—
128C4⋊C4×C47—42no—
129C4⋊C4×C47—42no—
130C42×C47—22no—
131C42×C47—22no—
132C42×C47—21no—
133C42×C47—21no—
134C42×C47—21no—
135C42×C47—21no—
136C42×C47—41no—
137C42×C47—41no—
138C42×C47#4112yes—
139C42×C47#4112yes—
140(C2×D47)⋊C4—24no—
141(C2×D47)⋊C4—24no—
142(C2×D47)⋊C4—42no—
143(C2×D47)⋊C4—42no—
144(C2×D47)⋊C4—42no—
145C4⋊Dic47—21no—
146C4⋊Dic47—21no—
147C4⋊Dic47—21no—
148C4⋊Dic47—21no—
149Dic47⋊C4—42no—
150C4×Dic47—42no—
151C2×C47⋊C8—22no—
152C2×C47⋊C8—22no—
153C2×C47⋊C8—22no—
154C2×C47⋊C8—22no—
155C2×C47⋊C8—22no—
156C2×C47⋊C8—22no—
157C23×C47C22×D411yescharacteristic
158C22×D47—22no—
159C22×D47—41no—
160C22×D47—41no—
161C22×D47—41no—
162C22×D47—41no—
163C22×D47—41no—
164C22×D47—41no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—21no—
172C2×C4×C47—21no—
173C2×C4×C47—21no—
174C2×C4×C47—21no—
175C2×C4×C47—21no—
176C2×C4×C47—21no—
177C2×C4×C47—21no—
178C2×C4×C47—21no—
179C2×C4×C47—42no—
180C2×C4×C47—42no—
181C2×C4×C47—42no—
182C2×C4×C47—42no—
183C2×C4×C47—42no—
184C2×C4×C47—42no—
185C2×C4×C47#12412yes—
186C2×C4×C47#12412yes—
187C2×C4×C47AGL(1,ℤ/8)12yes—
188C2×C4×C47#13712yes—
189C2×C4×C47C2×#4111yescharacteristic
190C2×C4×C47C2×#4111yescharacteristic
191C2×C4×C47C2×#4111yescharacteristic
192C2×C4×C47C2×#4111yescharacteristic
193C2×C4×C47H(5,𝔽2)11yescharacteristic
194C2×C4×C472−1+411yescharacteristic
195C2×Dic47—22no—
196C2×Dic47—41no—
197C2×Dic47—41no—
198C2×Dic47—41no—
199C2×Dic47—41no—
200C2×Dic47—41no—
201C2×Dic47—41no—
202C2×Dic47—41no—
203C2×Dic47—41no—
204D188—22no—
205D188—22no—
206D188—41no—
207D188—41no—
208C4×D47—84no—
209Dic94—22no—
210Dic94—22no—
211Dic94—41no—
212Dic94—41no—
213C47⋊C8—42no—
214C47⋊C8—42no—
215#29131—471nomaximal, Sylow
216C22×C47#52511yescharacteristic
217C22×C47C2×#12411yescharacteristic
218C22×C47#53711yescharacteristic
219C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
220C22×C47C2×#13711yescharacteristic
221C22×C47#57511yescharacteristic
222C22×C47#57511yescharacteristic
223C2×D47—42no—
224C2×D47—42no—
225C2×D47—42no—
226C2×D47—81no—
227C2×D47—81no—
228C2×D47—81no—
229C2×D47—81no—
230C4×C47—22no—
231C4×C47—41no—
232C4×C47—41no—
233C4×C47—41no—
234C4×C47—41no—
235C4×C47—82no—
236C4×C47—82no—
237C4×C47#48914yes—
238C4×C47#55211yescharacteristic
239C4×C47#55211yescharacteristic
240C4×C47#55311yescharacteristic
241C4×C47#55311yescharacteristic
242Dic47—42no—
243Dic47—81no—
244Dic47—81no—
245#2859D4711yescharacteristic, complemented
246C4×#124—471no—
247#2101—472no—
248#2042—472no—
249#1936—472no—
250#1935—472no—
251#1803—471no—
252#1803—471no—
253#1802—471no—
254#1802—471no—
255#1767—471no—
256C2×C47#256211yescharacteristic
257C2×C47#311511yescharacteristic
258C2×C47#311611yescharacteristic
259C2×C47C2×#48911yescharacteristic
260C2×C47#314211yescharacteristic
261C2×C47#325111yescharacteristic
262C2×C47#325211yescharacteristic
263D47—82no—
264C2×#125—21no—
265C2×#124—471no—
266C2×C4×Q8—471no—
267C2×C4×D4—471no—
268C2×C4⋊C8—471no—
269C2×C4⋊C8—471no—
270C2×#103—472no—
271C2×#103—472no—
272C2×#102—472no—
273C2×#102—472no—
274C2×#97—472no—
275#391—471no—
276#390—471no—
277#389—21no—
278#389—21no—
279#389C2×D4712yes—
280#389C2×D4712yes—
281#388—941no—
282#388—941no—
283#384C2×D4711yescharacteristic
284#384C2×D4711yescharacteristic
285#382—21no—
286#382—471no—
287C4×C22⋊C4—941no—
288C4×C22⋊C4—941no—
289C43C2×D4711yescharacteristic
290#340—472no—
291#340—472no—
292#340—472no—
293#340—472no—
294#336—472no—
295C47#2913111yescharacteristic, complemented, Sylow
296C22×Q8—471no—
297C22×D4—471no—
298C23×C4—941no—
299C22×C8—472no—
300C22×C8—472no—
301#125—44no—
302#124—942no—
303#124—942no—
304C4×Q8—942no—
305C4×Q8—942no—
306C4×D4—942no—
307C4×D4—942no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—471no—
315C2×C4⋊C4—471no—
316C2×C4⋊C4—941no—
317C2×C4⋊C4C22×D4712yes—
318C2×C4⋊C4C22×D4712yes—
319C2×C22⋊C4—941no—
320C2×C22⋊C4—941no—
321C2×C22⋊C4—941no—
322C2×C22⋊C4—941no—
323C2×C22⋊C4—941no—
324C2×C42—941no—
325C2×C42C22⋊D4711yescharacteristic
326C2×C42C22⋊D4711yescharacteristic
327C2×C42C22⋊D4711yescharacteristic
328C2×C42C22⋊D4711yescharacteristic
329C2×C42C22×D4711yescharacteristic
330C2×C42C22×D4711yescharacteristic
331C2×C42C22×D4711yescharacteristic
332C4⋊C8—942no—
333C4⋊C8—942no—
334#103—944no—
335#103—1882no—
336#102—944no—
337#102—1882no—
338#97—1882no—
339#95—22no—
340#95—22no—
341#95—941no—
342#95—941no—
343#95—941no—
344#95—941no—
345C24—941no—
346C2×Q8—472no—
347C2×Q8—941no—
348C2×Q8—941no—
349C2×Q8—941no—
350C2×Q8—941no—
351C2×Q8—941no—
352C2×D4—472no—
353C2×D4—941no—
354C2×D4—941no—
355C2×D4—941no—
356C2×D4—941no—
357C2×D4—941no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—941no—
361C22×C4—941no—
362C22×C4—941no—
363C22×C4—1882no—
364C22×C4—1882no—
365C22×C4—1882no—
366C22×C4C2×C22⋊D4711yescharacteristic
367C22×C4C2×C22⋊D4711yescharacteristic
368C22×C4C2×C22⋊D4711yescharacteristic
369C22×C4C2×C22⋊D4711yescharacteristic
370C22×C4C2×C22⋊D4711yescharacteristic
371C22×C4C2×C22⋊D4711yescharacteristic
372C22×C4C23×D4711yescharacteristic
373C2×C8—942no—
374C2×C8—942no—
375C2×C8—942no—
376C2×C8—942no—
377C2×C8—942no—
378C2×C8—942no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—44no—
386C4⋊C4—44no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—941no—
390C4⋊C4—941no—
391C4⋊C4—941no—
392C4⋊C4—941no—
393C4⋊C4—1882no—
394C22⋊C4—944no—
395C22⋊C4—944no—
396C22⋊C4—1882no—
397C22⋊C4—1882no—
398C22⋊C4—1882no—
399C42—22no—
400C42—22no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—21no—
405C42—41no—
406C42—41no—
407C42—1882no—
408C42#1062535412yes—
409C42#1062535412yes—
410C23—942no—
411C23—1881no—
412C23—1881no—
413C23—1881no—
414C23—1881no—
415C23—1881no—
416C23—1881no—
417C23C22×C22⋊D4711yescharacteristic
418Q8—942no—
419Q8—942no—
420Q8—1881no—
421Q8—1881no—
422D4—942no—
423D4—942no—
424D4—1881no—
425D4—1881no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—942no—
447C2×C4—3764no—
448C2×C4—1881no—
449C2×C4—1881no—
450C2×C4—1881no—
451C2×C4—1881no—
452C2×C4—1881no—
453C2×C4—1881no—
454C2×C4—1881no—
455C2×C4—1881no—
456C2×C4#1309401312yes—
457C2×C4#1309401312yes—
458C2×C4#1309405012yes—
459C2×C4#1309405512yes—
460C2×C4#41×D4711yescharacteristic
461C2×C4#41×D4711yescharacteristic
462C2×C4C2×#1062535411yescharacteristic
463C2×C4C2×#1062535411yescharacteristic
464C2×C4#1309407011yescharacteristic
465C2×C4#1309407111yescharacteristic
466C8—1882no—
467C8—1882no—
468C22—3761no—
469C22—3761no—
470C22—3761no—
471C22—3761no—
472C22—1882no—
473C22—1882no—
474C22—1882no—
475C22#1568963011yescharacteristic
476C22C2×#1309401311yescharacteristic
477C22#1568970111yescharacteristic
478C22C2×#1309405011yescharacteristic
479C22C2×#1309405511yescharacteristic
480C22#1568992111yescharacteristic
481C22#1568992111yescharacteristic
482C4—22no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—82no—
488C4—82no—
489C4—3761no—
490C4—3761no—
491C4—1882no—
492C4#1568948514yes—
493C4#1568981111yescharacteristic
494C4#1568981111yescharacteristic
495C4#1568982611yescharacteristic
496C4#1568982611yescharacteristic
497C2—3762no—
498C2#2024855511yescharacteristic
499C2#2025353311yescharacteristic
500C2#2025354411yescharacteristic
501C2C2×#1568948511yescharacteristic
502C2#2025379111yescharacteristic
503C2#2025474411yescharacteristic
504C2#2025475511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2859C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#2859D47
hypocenterC47#29131
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ #2859

Complements

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

NH ≅ G/Ntype
2. #20244956C2semidirect
5. #20244077C2semidirect
6. #20243390C2semidirect
7. #20243390C2semidirect
10. #20243241C2semidirect
11. C47×#2859C2semidirect
245. #2859D47semidirect
295. C47#29131semidirect

Maximal subgroups

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

subgroupindex
C4×#130940122
#202449562
#202446292
#202440842
#202440772
#202433902
#202433852
#202432412
C47×#28592
#2913147