Finite Group Databasebeta

← #26188573

Subgroups — #26188573

Order 12032.

928 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256793C211yesmaximal, characteristic
2#20253427C212yesmaximal, complemented
3#20242429C212yesmaximal, complemented
4#20242412C212yesmaximal
5#20242361C212yesmaximal, complemented
6#20242344C212yesmaximal
7#20241886C212yesmaximal, complemented
8#20241702C211yesmaximal, characteristic
9C47×#2396C211yesmaximal, characteristic
10#15689754—21no—
11#15689754C2212yes—
12#15689751—22no—
13#15689751—22no—
14#15689749—21no—
15#15689749C2212yes—
16#15689680—21no—
17#15689680C2212yes—
18#15689676—24no—
19C2×#13093983—21no—
20#15689458C2214yes—
21#15689418—22no—
22#15689333—22no—
23#15689279C2214yes—
24C4×#10625337—24no—
25#15689176C2212yes—
26#15688859C2214yes—
27#15688859C2214yes—
28#15688849C2212yes—
29#15688847C2212yes—
30C2×C4×Q8×C47C2211yescharacteristic
31C2×#117×C47C2211yescharacteristic
32C47×#400C2211yescharacteristic
33C47×#399C2211yescharacteristic
34C47×#398—21no—
35C47×#396—21no—
36C47×#395C2211yescharacteristic
37C47×#393C2211yescharacteristic
38C4×C4⋊C4×C47—21no—
39C4×C4⋊C4×C47C2211yescharacteristic
40C4×C22⋊C4×C47—21no—
41C2×#10625337—24no—
42#13094024—21no—
43#13094024—21no—
44#13094024D412yes—
45#13094024D412yes—
46#13094023—24no—
47#13094023—24no—
48#13094016—22no—
49#13094016—22no—
50#13094015—24no—
51#13094015—24no—
52#13094003—22no—
53#13094003—22no—
54#13094003—22no—
55#13094003C2314yes—
56#13094001—24no—
57#13094001—24no—
58#13094001—24no—
59#13094001—24no—
60C4×Dic94—22no—
61C4×Dic94—22no—
62C4×Dic94—22no—
63C4×Dic94D414yes—
64#13093983—22no—
65#13093983—22no—
66#13093983—22no—
67#13093983—22no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C22⋊Dic47—22no—
71C2×C4×Dic47—22no—
72#13093957—24no—
73C4⋊(C47⋊C8)—22no—
74#13093948—24no—
75#13093947—24no—
76C22⋊(C47⋊C8)C2314yes—
77C4×C47⋊C8—22no—
78C22×Q8×C47C2311yescharacteristic
79C23×C4×C47D411yescharacteristic
80C4×Q8×C47—22no—
81C4×Q8×C47—22no—
82#117×C47—22no—
83#117×C47—22no—
84C2×C4⋊C4×C47—21no—
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47D411yescharacteristic
89C2×C4⋊C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47C2311yescharacteristic
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47D411yescharacteristic
94C2×C22⋊C4×C47C2311yescharacteristic
95C2×C42×C47—21no—
96C2×C42×C47—21no—
97C2×C42×C47D411yescharacteristic
98C2×C42×C47C2311yescharacteristic
99#95×C47—21no—
100#95×C47—21no—
101#95×C47—21no—
102#95×C47—21no—
103#95×C47C2311yescharacteristic
104#95×C47C2311yescharacteristic
105C24×C47C2×D411yescharacteristic
106C2×Q8×C47—22no—
107C2×Q8×C47—42no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47Q1614yescomplemented
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×D411yescharacteristic
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2411yescharacteristic
122C22×Dic47—22no—
123C22×Dic47—22no—
124C2×Dic94—22no—
125C2×Dic94—22no—
126C2×Dic94—22no—
127C2×Dic94C2×D414yes—
128C4⋊C4×C47—22no—
129C4⋊C4×C47—22no—
130C4⋊C4×C47—22no—
131C4⋊C4×C47—42no—
132C4⋊C4×C47—42no—
133C4⋊C4×C47—42no—
134C4⋊C4×C47—42no—
135C22⋊C4×C47—22no—
136C22⋊C4×C47—22no—
137C22⋊C4×C47—42no—
138C22⋊C4×C47—42no—
139C42×C47—21no—
140C42×C47—21no—
141C42×C47—41no—
142C42×C47—41no—
143C42×C47—42no—
144C42×C47C2×D412yes—
145C42×C47C2×D412yes—
146C22⋊Dic47—24no—
147C22⋊Dic47—24no—
148#10625337—48no—
149C4⋊Dic47—22no—
150C4⋊Dic47—22no—
151C4⋊Dic47—22no—
152C4⋊Dic47—22no—
153C4⋊Dic47—22no—
154C4⋊Dic47—22no—
155C4⋊Dic47—22no—
156C4⋊Dic47C2×D414yes—
157Dic47⋊C4—24no—
158Dic47⋊C4—24no—
159Dic47⋊C4—24no—
160Dic47⋊C4—24no—
161C4×Dic47—24no—
162C4×Dic47—24no—
163C2×C47⋊C8—24no—
164C23×C47—21no—
165C23×C47—21no—
166C23×C47—41no—
167C23×C47—41no—
168C23×C47C2×Q1612yes—
169C23×C47C22×D411yescharacteristic
170Q8×C47—24no—
171Q8×C47—42no—
172C2×C4×C47—21no—
173C2×C4×C47—21no—
174C2×C4×C47—24no—
175C2×C4×C47—24no—
176C2×C4×C47—22no—
177C2×C4×C47—22no—
178C2×C4×C47—21no—
179C2×C4×C47—21no—
180C2×C4×C47—41no—
181C2×C4×C47—41no—
182C2×C4×C47—41no—
183C2×C4×C47—41no—
184C2×C4×C47—41no—
185C2×C4×C47—41no—
186C2×C4×C47—41no—
187C2×C4×C47—41no—
188C2×C4×C47—41no—
189C2×C4×C47—41no—
190C2×C4×C47—41no—
191C2×C4×C47—41no—
192C2×C4×C47—41no—
193C2×C4×C47—41no—
194C2×C4×C47#12012yes—
195C2×C4×C47#12011yescharacteristic
196C2×C4×C47#12011yescharacteristic
197C2×C4×C47C2×Q1612yes—
198C2×C4×C47C2×Q1612yes—
199C2×C4×C47#13712yes—
200C2×C4×C47C22×D412yes—
201C2×Dic47—24no—
202C2×Dic47—24no—
203C2×Dic47—82no—
204C2×Dic47—82no—
205Dic94—44no—
206Dic94—82no—
207Dic94—82no—
208Dic94—82no—
209C47⋊C8—44no—
210#18125—471nomaximal, Sylow
211C22×C47—21no—
212C22×C47—21no—
213C22×C47—22no—
214C22×C47—42no—
215C22×C47—41no—
216C22×C47—41no—
217C22×C47—81no—
218C22×C47C2×#12011yescharacteristic
219C22×C47C22×Q1611yescharacteristic
220C22×C47C2×#13711yescharacteristic
221C4×C47—22no—
222C4×C47—22no—
223C4×C47—22no—
224C4×C47—42no—
225C4×C47—41no—
226C4×C47—41no—
227C4×C47—42no—
228C4×C47—81no—
229C4×C47—81no—
230C4×C47#45112yes—
231C4×C47#45112yes—
232Dic47—44no—
233Dic47—44no—
234#3458—471no—
235#3104—472no—
236#2396D4711yescharacteristic
237#1617—472no—
238#1614—472no—
239#1605—472no—
240#1602—472no—
241#1503—472no—
242#1458—471no—
243C2×C47—21no—
244C2×C47—21no—
245C2×C47—42no—
246C2×C47C2×#45111yescharacteristic
247C2×C47#301811yescharacteristic
248C2×C47#302511yescharacteristic
249#544—472no—
250#544—942no—
251#544—942no—
252#544—941no—
253#543—472no—
254#543—941no—
255#533—472no—
256#533—944no—
257#533—941no—
258C2×C4×Q8C2×D4711yescharacteristic
259C2×#117—941no—
260C2×#117C2×D4711yescharacteristic
261#484—474no—
262#477—942no—
263#462—942no—
264#451—474no—
265C4×Q16—944no—
266#431—472no—
267#400C2×D4711yescharacteristic
268#399C2×D4711yescharacteristic
269#398—21no—
270#396—21no—
271#395C2×D4711yescharacteristic
272#393C2×D4711yescharacteristic
273C4×C4⋊C4—21no—
274C4×C4⋊C4C2×D4711yescharacteristic
275C4×C22⋊C4—21no—
276#328—474no—
277#328—474no—
278#324—472no—
279#323—472no—
280C47#1812511yescharacteristic, complemented, Sylow
281C22×Q8C22×D4711yescharacteristic
282C23×C4C22⋊D4711yescharacteristic
283C2×Q16—944no—
284C4⋊Q8—472no—
285C4⋊Q8—472no—
286C4⋊Q8—941no—
287C4⋊Q8—941no—
288C4⋊Q8—944no—
289C4⋊Q8—944no—
290#125—942no—
291#125—944no—
292#125—944no—
293#125—942no—
294C22⋊Q8—474no—
295C22⋊Q8—944no—
296C22⋊Q8—944no—
297C22⋊Q8—944no—
298C22⋊Q8—944no—
299C22⋊Q8—942no—
300C22⋊Q8—942no—
301C22⋊Q8—942no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—474no—
305C4×Q8—942no—
306C4×Q8—942no—
307C4×Q8—942no—
308#117—22no—
309#117—22no—
310#117—942no—
311#117—942no—
312#117—942no—
313#117—942no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—941no—
319C2×C4⋊C4—941no—
320C2×C4⋊C4C22⋊D4711yescharacteristic
321C2×C4⋊C4C22×D4711yescharacteristic
322C2×C4⋊C4C22×D4711yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—942no—
326C2×C22⋊C4C22⋊D4711yescharacteristic
327C2×C22⋊C4C22×D4711yescharacteristic
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—942no—
331C2×C42C22⋊D4711yescharacteristic
332C2×C42C22×D4711yescharacteristic
333#107—944no—
334C4⋊C8—942no—
335#103—944no—
336#103—944no—
337C22⋊C8—474no—
338C4×C8—942no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95C22×D4711yescharacteristic
344#95C22×D4711yescharacteristic
345C24C2×C22⋊D4711yescharacteristic
346C2×Q8—22no—
347C2×Q8—42no—
348C2×Q8—474no—
349C2×Q8—942no—
350C2×Q8—942no—
351C2×Q8—942no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—942no—
360C22×C4—942no—
361C22×C4#1062533714yescomplemented
362C22×C4C2×C22⋊D4711yescharacteristic
363C22×C4C2×C22⋊D4711yescharacteristic
364C22×C4C2×C22⋊D4711yescharacteristic
365C22×C4C2×C22⋊D4711yescharacteristic
366C22×C4C2×C22⋊D4711yescharacteristic
367C22×C4C23×D4711yescharacteristic
368Q16—1888no—
369C2×C8—944no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—474no—
378C4⋊C4—944no—
379C4⋊C4—944no—
380C4⋊C4—942no—
381C4⋊C4—942no—
382C4⋊C4—942no—
383C4⋊C4—942no—
384C4⋊C4—944no—
385C4⋊C4—942no—
386C4⋊C4—942no—
387C4⋊C4—942no—
388C4⋊C4—944no—
389C22⋊C4—22no—
390C22⋊C4—22no—
391C22⋊C4—42no—
392C22⋊C4—42no—
393C22⋊C4—944no—
394C22⋊C4—944no—
395C42—21no—
396C42—21no—
397C42—41no—
398C42—41no—
399C42—42no—
400C42—944no—
401C42—944no—
402C42D4×D4712yes—
403C42D4×D4712yes—
404C23—21no—
405C23—21no—
406C23—41no—
407C23—41no—
408C23C2×#1062533712yes—
409C23C22×C22⋊D4711yescharacteristic
410Q8—24no—
411Q8—42no—
412Q8—3762no—
413Q8—3762no—
414Q8—3762no—
415Q8—1884no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—944no—
439C2×C4—944no—
440C2×C4—3762no—
441C2×C4—3762no—
442C2×C4#1309399212yes—
443C2×C4#1309399211yescharacteristic
444C2×C4#1309399211yescharacteristic
445C2×C4C2×#1062533712yes—
446C2×C4C2×#1062533712yes—
447C2×C4#1309405412yes—
448C2×C4C2×D4×D4712yes—
449C8—1884no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—81no—
457C22C2×#1309399211yescharacteristic
458C22C22×#1062533711yescharacteristic
459C22C2×#1309405411yescharacteristic
460C4—22no—
461C4—22no—
462C4—22no—
463C4—42no—
464C4—41no—
465C4—42no—
466C4—41no—
467C4—81no—
468C4—81no—
469C4—1884no—
470C4—1884no—
471C4#1568927812yes—
472C4#1568927812yes—
473C2—21no—
474C2—21no—
475C2—42no—
476C2C2×#1568927811yescharacteristic
477C2#2025273611yescharacteristic
478C2#2025277911yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2396C2
socleC22×C47C2×#120
prime radicalC24×C47C2×D4
hypercenter#2396D47
hypocenterC47#18125
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2396

Complements

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

NH ≅ G/Ntype
2. #20253427C2semidirect
3. #20242429C2semidirect
5. #20242361C2semidirect
7. #20241886C2semidirect
115. C22×C4×C47Q16semidirect
280. C47#18125semidirect
361. C22×C4#10625337semidirect

Maximal subgroups

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

subgroupindex
#202567932
#202534272
#202424292
#202424122
#202423612
#202423442
#202418862
#202417022
C47×#23962
#1812547