Finite Group Databasebeta

← #26122989

Subgroups — #26122989

Order 12032.

2118 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093945C214yesmaximal, complemented
2C2×#15688878C211yesmaximal, characteristic, complemented
3#20241618C211yesmaximal, characteristic, complemented
4C22×#127×C47C211yesmaximal, characteristic
5C23×C47⋊C8C2212yes—
6C22×C4⋊Dic47C2212yes—
7C2×#13093945—28no—
8C2×#13093945—28no—
9C2×#13093945—28no—
10C2×C47⋊#95—22no—
11#15688878—22no—
12C23×D4×C47—22no—
13C23×D4×C47C2212yes—
14C2×#127×C47—28no—
15C2×#127×C47—22no—
16C2×#127×C47C414yescomplemented
17C22×C42×C47C2211yescharacteristic
18C23×Dic47—22no—
19C22×C47⋊C8—24no—
20C22×C47⋊C8—24no—
21C22×C47⋊C8—22no—
22C22×C47⋊C8—22no—
23C22×C47⋊C8D414yescomplemented
24C2×C4⋊Dic47—24no—
25C2×C4⋊Dic47—24no—
26C2×C4⋊Dic47—22no—
27C2×C4⋊Dic47D414yescomplemented
28#13093945—232no—
29C47⋊#95—44no—
30C25×C47—22no—
31C22×D4×C47—216no—
32C22×D4×C47—28no—
33C22×D4×C47—24no—
34C22×D4×C47—24no—
35C22×D4×C47—24no—
36C22×D4×C47—22no—
37C22×D4×C47—24no—
38C22×D4×C47—24no—
39C22×D4×C47—48no—
40C22×D4×C47—44no—
41C22×D4×C47—44no—
42C22×D4×C47C2×C414yes—
43C22×D4×C47D418yes—
44C23×C4×C47D412yes—
45C23×C4×C47C2311yescharacteristic
46#127×C47—216no—
47#127×C47—216no—
48C2×C42×C47—24no—
49C2×C42×C47C2×C412yes—
50C2×C42×C47D412yes—
51C24×C47—24no—
52C24×C47—28no—
53C24×C47—44no—
54C24×C47—42no—
55C24×C47—42no—
56C24×C47—44no—
57C24×C47—44no—
58C24×C47—48no—
59C24×C47C2×D411yescharacteristic
60C2×D4×C47—232no—
61C2×D4×C47—24no—
62C2×D4×C47—28no—
63C2×D4×C47—28no—
64C2×D4×C47—28no—
65C2×D4×C47—28no—
66C2×D4×C47—28no—
67C2×D4×C47—28no—
68C2×D4×C47—28no—
69C2×D4×C47—416no—
70C2×D4×C47—432no—
71C2×D4×C47—432no—
72C2×D4×C47—416no—
73C2×D4×C47—44no—
74C2×D4×C47—44no—
75C2×D4×C47—44no—
76C2×D4×C47—44no—
77C2×D4×C47—44no—
78C2×D4×C47—42no—
79C2×D4×C47—42no—
80C2×D4×C47C22⋊C418yes—
81C22×C4×C47—24no—
82C22×C4×C47—24no—
83C22×C4×C47C22⋊C414yes—
84C22×C4×C47D814yes—
85C22×C4×C47SD1614yes—
86C22×C4×C47C22×C411yescharacteristic
87C22×C4×C47C2×D414yes—
88C22×C4×C47C2×D412yes—
89C22×C4×C47C2×D412yes—
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47#4112yes—
92C22×C4×C47#4112yes—
93C22×Dic47—24no—
94C22×Dic47—42no—
95C22×Dic47—42no—
96C22×Dic47—44no—
97C22×Dic47—44no—
98C42×C47—24no—
99C42×C47—24no—
100C4⋊Dic47—28no—
101C4⋊Dic47—44no—
102C2×C47⋊C8—28no—
103C2×C47⋊C8—24no—
104C2×C47⋊C8—42no—
105C2×C47⋊C8—44no—
106C2×C47⋊C8—42no—
107C23×C47—28no—
108C23×C47—44no—
109C23×C47—44no—
110C23×C47—48no—
111C23×C47—48no—
112C23×C47—48no—
113C23×C47—48no—
114C23×C47—416no—
115C23×C47—416no—
116C23×C47—88no—
117C23×C47—88no—
118C23×C47—84no—
119C23×C47—84no—
120C23×C47—82no—
121C23×C47—82no—
122C23×C47—84no—
123C23×C47C2×C22⋊C411yescharacteristic
124C23×C47#12012yes—
125C23×C47#12112yes—
126C23×C47#12411yescharacteristic
127C23×C47#12711yescharacteristic
128C23×C47C2×D812yes—
129C23×C47C2×SD1612yes—
130C23×C47AGL(1,ℤ/8)14yes—
131D4×C47—216no—
132D4×C47—464no—
133D4×C47—48no—
134D4×C47—48no—
135D4×C47—48no—
136C2×C4×C47—24no—
137C2×C4×C47—24no—
138C2×C4×C47—28no—
139C2×C4×C47—28no—
140C2×C4×C47#10218yescomplemented
141C2×C4×C47C2×C22⋊C412yes—
142C2×C4×C47C4×D412yes—
143C2×C4×C47C4×D412yes—
144C2×C4×C47#12014yes—
145C2×C4×C47#12012yes—
146C2×C4×C47#12112yes—
147C2×C4×C47#12114yes—
148C2×C4×C47#12114yes—
149C2×C4×C47#12314yes—
150C2×C4×C47#12411yescharacteristic
151C2×C4×C47#12711yescharacteristic
152C2×Dic47—44no—
153C2×Dic47—48no—
154C2×Dic47—84no—
155C2×Dic47—82no—
156C2×Dic47—82no—
157C47⋊C8—44no—
158#11008—471nomaximal, Sylow
159C22×C47—48no—
160C22×C47—416no—
161C22×C47—84no—
162C22×C47—84no—
163C22×C47—88no—
164C22×C47—88no—
165C22×C47—88no—
166C22×C47—816no—
167C22×C47#37911yescharacteristic
168C22×C47#39011yescharacteristic
169C22×C47#39011yescharacteristic
170C22×C47#39212yes—
171C22×C47#39412yes—
172C22×C47C2×#10212yes—
173C22×C47#41812yes—
174C22×C47#44714yes—
175C22×C47#45014yes—
176C22×C47#45914yes—
177C22×C47#46014yes—
178C22×C47#48612yes—
179C22×C47#49012yes—
180C22×C47#49211yescharacteristic
181C22×C47#49311yescharacteristic
182C22×C47#49612yes—
183C4×C47—28no—
184C4×C47#38614yes—
185C4×C47#39212yes—
186C4×C47#39412yes—
187Dic47—84no—
188C22×#127D4711yescharacteristic
189C22×#102—474no—
190C2×#336—471no—
191C4⋊#95—471no—
192C2×C47—88no—
193C2×C47#143811yescharacteristic
194C2×C47#178612yes—
195C2×C47#195711yescharacteristic
196C2×C47#196111yescharacteristic
197C2×C47#198212yes—
198C2×C47#201112yes—
199C2×C47#201412yes—
200C2×C47#204114yes—
201C23×D4—22no—
202C23×D4C2×D4712yes—
203C23×C8—472no—
204C2×#127—28no—
205C2×#127—22no—
206C2×#127Dic4714yescomplemented
207C22×C4⋊C4—472no—
208C22×C42C2×D4711yescharacteristic
209C2×#102—948no—
210C2×#102—948no—
211C2×#102—948no—
212C2×#95—942no—
213#336—942no—
214C47#1100811yescharacteristic, complemented, Sylow
215C25—22no—
216C22×D4—216no—
217C22×D4—28no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—22no—
224C22×D4—48no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4C2×Dic4714yes—
228C22×D4C22⋊D4718yes—
229C23×C4—942no—
230C23×C4C22⋊D4712yes—
231C23×C4C22×D4711yescharacteristic
232C22×C8—474no—
233C22×C8—944no—
234C22×C8—942no—
235C22×C8—942no—
236C22×C8—944no—
237#127—216no—
238#127—216no—
239C2×C4⋊C4—474no—
240C2×C4⋊C4—944no—
241C2×C4⋊C4—944no—
242C2×C4⋊C4—942no—
243C2×C42—24no—
244C2×C42C2×Dic4712yes—
245C2×C42C22⋊D4712yes—
246#102—9432no—
247#95—1884no—
248C24—24no—
249C24—28no—
250C24—44no—
251C24—42no—
252C24—42no—
253C24—44no—
254C24—44no—
255C24—48no—
256C24C2×C22⋊D4711yescharacteristic
257C2×D4—232no—
258C2×D4—24no—
259C2×D4—28no—
260C2×D4—28no—
261C2×D4—28no—
262C2×D4—28no—
263C2×D4—28no—
264C2×D4—28no—
265C2×D4—28no—
266C2×D4—432no—
267C2×D4—432no—
268C2×D4—416no—
269C2×D4—416no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4C22⋊Dic4718yes—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—944no—
281C22×C4—1882no—
282C22×C4—1882no—
283C22×C4—1884no—
284C22×C4—1884no—
285C22×C4#1062533414yes—
286C22×C4#1062533514yes—
287C22×C4C22⋊Dic4714yes—
288C22×C4D4×D4712yes—
289C22×C4D4×D4712yes—
290C22×C4#1062535212yes—
291C22×C4#1062535212yes—
292C22×C4C22×Dic4711yescharacteristic
293C22×C4C2×C22⋊D4714yes—
294C22×C4C2×C22⋊D4711yescharacteristic
295C2×C8—948no—
296C2×C8—944no—
297C2×C8—1882no—
298C2×C8—1884no—
299C2×C8—1882no—
300C4⋊C4—948no—
301C4⋊C4—1884no—
302C42—24no—
303C42—24no—
304C23—28no—
305C23—416no—
306C23—416no—
307C23—44no—
308C23—44no—
309C23—48no—
310C23—48no—
311C23—48no—
312C23—48no—
313C23—84no—
314C23—82no—
315C23—82no—
316C23—84no—
317C23—88no—
318C23—88no—
319C23—84no—
320C23C2×C22⋊Dic4711yescharacteristic
321C23#1309399312yes—
322C23#1309399512yes—
323C23#1309401111yescharacteristic
324C23#1309402011yescharacteristic
325C23C2×#1062533412yes—
326C23C2×#1062533512yes—
327C23#1309405014yes—
328D4—216no—
329D4—464no—
330D4—48no—
331D4—48no—
332D4—48no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—24no—
337C2×C4—3762no—
338C2×C4—3762no—
339C2×C4—3764no—
340C2×C4—1884no—
341C2×C4—1888no—
342C2×C4#1309394518yescomplemented
343C2×C4C2×C22⋊Dic4712yes—
344C2×C4D4×Dic4712yes—
345C2×C4D4×Dic4712yes—
346C2×C4#1309399214yes—
347C2×C4#1309399312yes—
348C2×C4#1309399512yes—
349C2×C4#1309399614yes—
350C2×C4#1309399614yes—
351C2×C4#1309400514yes—
352C2×C4#1309401111yescharacteristic
353C2×C4#1309402011yescharacteristic
354C8—1884no—
355C22—416no—
356C22—48no—
357C22—88no—
358C22—816no—
359C22—84no—
360C22—88no—
361C22—84no—
362C22—88no—
363C22#1568897911yescharacteristic
364C22#1568902611yescharacteristic
365C22#1568902611yescharacteristic
366C22#1568903112yes—
367C22#1568903712yes—
368C22C2×#1309394512yes—
369C22#1568912812yes—
370C22#1568925714yes—
371C22#1568927414yes—
372C22#1568931514yes—
373C22#1568932014yes—
374C22#1568946912yes—
375C22#1568948712yes—
376C22#1568949511yescharacteristic
377C22#1568949911yescharacteristic
378C22#1568951012yes—
379C4—28no—
380C4—3764no—
381C4#1568900314yes—
382C4#1568903112yes—
383C4#1568903712yes—
384C2—88no—
385C2#2024162911yescharacteristic
386C2#2024331912yes—
387C2#2024419511yescharacteristic
388C2#2024421311yescharacteristic
389C2#2024431612yes—
390C2#2024445912yes—
391C2#2024447612yes—
392C2#2024461914yes—
subgroupG/H
centerC24C2×C22⋊D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
Fitting, prime radicalC22×#127×C47C2
socleC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC22×#127D47
hypocenterC47#11008
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C22×#13093945C2semidirect
2. C2×#15688878C2semidirect
3. #20241618C2semidirect
16. C2×#127×C47C4semidirect
23. C22×C47⋊C8D4semidirect
27. C2×C4⋊Dic47D4semidirect
140. C2×C4×C47#102semidirect
206. C2×#127Dic47semidirect
214. C47#11008semidirect
342. C2×C4#13093945semidirect

Maximal subgroups

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

subgroupindex
C22×#130939452
C2×#156888782
#202416182
C22×#127×C472
#1100847