Finite Group Databasebeta

← #26112069

Subgroups — #26112069

Order 12032.

980 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 980 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688986C211yesmaximal, characteristic, complemented
2#20243298C211yesmaximal, characteristic, complemented
3C2×#15688857C212yesmaximal, complemented
4#20241266C212yesmaximal, complemented
5C47×#2847C211yesmaximal, characteristic
6C22×C22⋊Dic47—21no—
7C2×C22⋊(C47⋊C8)—22no—
8C2×C22⋊(C47⋊C8)C2212yes—
9#15688986—24no—
10C2×C47⋊#95—21no—
11C2×C47⋊#95C2212yes—
12#15688857—24no—
13C24×C4×C47C2211yescharacteristic
14C2×#121×C47C412yescomplemented
15C2×#121×C47C2211yescharacteristic
16C2×#120×C47—21no—
17C47×#386—22no—
18C47×#386—21no—
19C47×#380C412yescomplemented
20C47×#380C2211yescharacteristic
21C23×Dic47—22no—
22C22×C47⋊C8—22no—
23C2×C22⋊Dic47—24no—
24C2×C22⋊Dic47—44no—
25C22⋊(C47⋊C8)—22no—
26C22⋊(C47⋊C8)—22no—
27C22⋊(C47⋊C8)—44no—
28C47⋊#95—24no—
29C47⋊#95—22no—
30C47⋊#95D414yescomplemented
31C25×C47D411yescharacteristic
32C22×D4×C47—22no—
33C22×D4×C47—21no—
34C22×D4×C47C2×C411yescharacteristic
35C23×C4×C47—22no—
36C23×C4×C47—22no—
37C23×C4×C47—44no—
38C23×C4×C47C2×C412yes—
39C23×C4×C47D412yes—
40C23×C4×C47D411yescharacteristic
41C23×C4×C47C2311yescharacteristic
42#121×C47—22no—
43#121×C47—22no—
44#121×C47—44no—
45#120×C47—44no—
46C2×C4⋊C4×C47C2×C411yescharacteristic
47C2×C4⋊C4×C47C2×C412yes—
48C2×C22⋊C4×C47—22no—
49C2×C22⋊C4×C47—21no—
50C2×C22⋊C4×C47—22no—
51C2×C22⋊C4×C47—21no—
52#95×C47—22no—
53#95×C47—21no—
54C24×C47—24no—
55C24×C47—21no—
56C24×C47—21no—
57C24×C47—22no—
58C24×C47—22no—
59C24×C47—21no—
60C24×C47—42no—
61C24×C47C22⋊C412yes—
62C24×C47C2×D411yescharacteristic
63C2×D4×C47—22no—
64C2×D4×C47—42no—
65C2×D4×C47—44no—
66C2×D4×C47—44no—
67C2×D4×C47—44no—
68C2×D4×C47—41no—
69C2×D4×C47—41no—
70C2×D4×C47—42no—
71C2×D4×C47—42no—
72C22×C4×C47—24no—
73C22×C4×C47—24no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—24no—
77C22×C4×C47—24no—
78C22×C4×C47—21no—
79C22×C4×C47—22no—
80C22×C4×C47—42no—
81C22×C4×C47—42no—
82C22×C4×C47—42no—
83C22×C4×C47—42no—
84C22×C4×C47—48no—
85C22×C4×C47—48no—
86C22×C4×C47C22⋊C412yes—
87C22×C4×C47C22×C411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D412yes—
90C22×C4×C47#4112yes—
91C22×Dic47—24no—
92C22×Dic47—44no—
93C22×Dic47—44no—
94C22×Dic47—42no—
95C22×Dic47—42no—
96C4⋊C4×C47—22no—
97C4⋊C4×C47—42no—
98C22⋊C4×C47—44no—
99C22⋊C4×C47—44no—
100C22⋊C4×C47—42no—
101C22⋊C4×C47—42no—
102C22⋊Dic47—48no—
103C2×C47⋊C8—44no—
104C2×C47⋊C8—42no—
105C23×C47—22no—
106C23×C47—22no—
107C23×C47—24no—
108C23×C47—24no—
109C23×C47—22no—
110C23×C47—22no—
111C23×C47—22no—
112C23×C47—22no—
113C23×C47—22no—
114C23×C47—22no—
115C23×C47—48no—
116C23×C47—48no—
117C23×C47—42no—
118C23×C47—42no—
119C23×C47—42no—
120C23×C47—42no—
121C23×C47—41no—
122C23×C47—42no—
123C23×C47—41no—
124C23×C47—41no—
125C23×C47—42no—
126C23×C47#9914yes—
127C23×C47C2×C22⋊C411yescharacteristic
128C23×C47#12011yescharacteristic
129C23×C47#12311yescharacteristic
130C23×C47#13512yes—
131C23×C47AGL(1,ℤ/8)12yes—
132D4×C47—82no—
133D4×C47—88no—
134D4×C47—82no—
135D4×C47—82no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—22no—
139C2×C4×C47—22no—
140C2×C4×C47—22no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47—48no—
144C2×C4×C47—48no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47—41no—
148C2×C4×C47—42no—
149C2×C4×C47—41no—
150C2×C4×C47—41no—
151C2×C4×C47—42no—
152C2×C4×C47—42no—
153C2×C4×C47C4×D412yes—
154C2×C4×C47#12112yes—
155C2×Dic47—44no—
156C2×Dic47—44no—
157C2×Dic47—44no—
158C2×Dic47—84no—
159C2×Dic47—84no—
160C47⋊C8—82no—
161#9158—471nomaximal, Sylow
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—24no—
167C22×C47—24no—
168C22×C47—24no—
169C22×C47—24no—
170C22×C47—24no—
171C22×C47—48no—
172C22×C47—48no—
173C22×C47—42no—
174C22×C47—42no—
175C22×C47—42no—
176C22×C47—42no—
177C22×C47—81no—
178C22×C47—81no—
179C22×C47—81no—
180C22×C47—82no—
181C22×C47—82no—
182C22×C47#38611yescharacteristic
183C22×C47C2×#9912yes—
184C22×C47#41611yescharacteristic
185C22×C47#41811yescharacteristic
186C22×C47#42112yes—
187C22×C47#44912yes—
188C22×C47#48212yes—
189C4×C47—22no—
190C4×C47—22no—
191C4×C47—42no—
192C4×C47—81no—
193C4×C47—82no—
194Dic47—84no—
195#2847D4711yescharacteristic
196C2×#381—471no—
197#1779—471no—
198C2×#327—472no—
199#1294—472no—
200C2×C47—22no—
201C2×C47—22no—
202C2×C47—44no—
203C2×C47—161no—
204C2×C47#151012yes—
205C2×C47#151612yes—
206C2×C47#187511yescharacteristic
207C2×C47#189711yescharacteristic
208C2×C47#189811yescharacteristic
209C24×C4C2×D4711yescharacteristic
210C2×#121Dic4712yescomplemented
211C2×#121C2×D4711yescharacteristic
212C2×#120—21no—
213C22×C22⋊C4—941no—
214C2×C22⋊C8—472no—
215C2×C22⋊C8—942no—
216#386—21no—
217#386—22no—
218#381—944no—
219#380Dic4712yescomplemented
220#380C2×D4711yescharacteristic
221C2×#95—472no—
222C2×#95—941no—
223#327—944no—
224C47#915811yescharacteristic, complemented, Sylow
225C25C22⋊D4711yescharacteristic
226C22×D4—22no—
227C22×D4—21no—
228C22×D4C2×Dic4711yescharacteristic
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—44no—
232C23×C4—942no—
233C23×C4C2×Dic4712yes—
234C23×C4C22⋊D4712yes—
235C23×C4C22⋊D4711yescharacteristic
236C23×C4C22×D4711yescharacteristic
237C22×C8—942no—
238#121—22no—
239#121—22no—
240#121—44no—
241#120—44no—
242C2×C4⋊C4C2×Dic4711yescharacteristic
243C2×C4⋊C4C2×Dic4712yes—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—944no—
249C2×C22⋊C4—1884no—
250C22⋊C8—942no—
251C22⋊C8—942no—
252C22⋊C8—1884no—
253#95—22no—
254#95—21no—
255#95—474no—
256#95—944no—
257#95—942no—
258C24—24no—
259C24—21no—
260C24—21no—
261C24—22no—
262C24—22no—
263C24—21no—
264C24—42no—
265C24C22⋊Dic4712yes—
266C24C2×C22⋊D4711yescharacteristic
267C2×D4—22no—
268C2×D4—42no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—42no—
275C2×D4—42no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—48no—
289C22×C4—48no—
290C22×C4—944no—
291C22×C4—1884no—
292C22×C4—1884no—
293C22×C4—1882no—
294C22×C4—1882no—
295C22×C4C22⋊Dic4712yes—
296C22×C4D4×D4712yes—
297C22×C4#1062535212yes—
298C22×C4C22×Dic4711yescharacteristic
299C22×C4C2×C22⋊D4711yescharacteristic
300C2×C8—1884no—
301C2×C8—1882no—
302C4⋊C4—22no—
303C4⋊C4—42no—
304C22⋊C4—44no—
305C22⋊C4—44no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—1888no—
309C23—22no—
310C23—22no—
311C23—24no—
312C23—24no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—48no—
320C23—48no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—41no—
326C23—42no—
327C23—41no—
328C23—41no—
329C23—42no—
330C23#1309393914yes—
331C23C2×C22⋊Dic4711yescharacteristic
332C23#1309399211yescharacteristic
333C23#1309400511yescharacteristic
334C23#1309404412yes—
335C23#1309405012yes—
336D4—82no—
337D4—88no—
338D4—82no—
339D4—82no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—48no—
348C2×C4—48no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—3764no—
358C2×C4—3764no—
359C2×C4—1884no—
360C2×C4—1884no—
361C2×C4—1884no—
362C2×C4D4×Dic4712yes—
363C2×C4#1309399612yes—
364C8—3762no—
365C22—24no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—24no—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—48no—
375C22—48no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22—82no—
384C22—81no—
385C22#1568900311yescharacteristic
386C22C2×#1309393912yes—
387C22#1568911911yescharacteristic
388C22#1568912811yescharacteristic
389C22#1568914012yes—
390C22#1568926612yes—
391C22#1568944412yes—
392C4—22no—
393C4—22no—
394C4—42no—
395C4—82no—
396C4—81no—
397C4—3764no—
398C2—22no—
399C2—22no—
400C2—44no—
401C2—161no—
402C2#2024191712yes—
403C2#2024194412yes—
404C2#2024371111yescharacteristic
405C2#2024383711yescharacteristic
406C2#2024384211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
Fitting, prime radicalC47×#2847C2
socleC23×C47C2×C22⋊C4
cosocleC23×C4×C47C23
hypercenter#2847D47
hypocenterC47#9158
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#15688986C2semidirect
2. #20243298C2semidirect
3. C2×#15688857C2semidirect
4. #20241266C2semidirect
14. C2×#121×C47C4semidirect
19. C47×#380C4semidirect
30. C47⋊#95D4semidirect
210. C2×#121Dic47semidirect
219. #380Dic47semidirect
224. C47#9158semidirect

Maximal subgroups

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

subgroupindex
C2×#156889862
#202432982
C2×#156888572
#202412662
C47×#28472
#915847