Finite Group Databasebeta

← #26122487

Subgroups — #26122487

Order 12032.

974 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246000C211yesmaximal, characteristic
2C2×#15688890C211yesmaximal, characteristic
3C2×#15688889C212yesmaximal
4C2×#15688889C212yesmaximal
5C47×#2273C211yesmaximal, characteristic
6C22×C22⋊Dic47C2211yescharacteristic
7C22×C22⋊Dic47C2212yes—
8C22×C22⋊Dic47C2211yescharacteristic
9#15688996—22no—
10#15688995C414yescomplemented
11#15688981—22no—
12#15688890—22no—
13#15688889—24no—
14#15688889C418yescomplemented
15C22×C22⋊C4×C47C2211yescharacteristic
16C22×C22⋊C4×C47C2212yes—
17C4×C22⋊C4×C47—22no—
18C4×C22⋊C4×C47—24no—
19C23×Dic47—21no—
20C23×Dic47—22no—
21C23×Dic47C2×C412yes—
22C2×Dic47⋊C4—24no—
23C2×C22⋊Dic47—21no—
24C2×C22⋊Dic47—22no—
25C2×C22⋊Dic47—22no—
26C2×C22⋊Dic47—22no—
27C2×C22⋊Dic47—22no—
28C2×C22⋊Dic47—22no—
29C2×C22⋊Dic47—21no—
30C2×C22⋊Dic47—21no—
31C2×C22⋊Dic47—22no—
32C2×C22⋊Dic47—22no—
33C2×C22⋊Dic47—22no—
34C2×C22⋊Dic47C2×C414yes—
35C2×C22⋊Dic47C2×C412yes—
36C2×C22⋊Dic47C2×C414yes—
37C47⋊#95—24no—
38C25×C47C2311yescharacteristic
39C23×C4×C47—22no—
40C23×C4×C47D412yes—
41C2×C22⋊C4×C47—22no—
42C2×C22⋊C4×C47—22no—
43C2×C22⋊C4×C47—22no—
44C2×C22⋊C4×C47—22no—
45C2×C22⋊C4×C47—22no—
46C2×C22⋊C4×C47C2×C412yes—
47C2×C22⋊C4×C47C2×C414yes—
48C2×C22⋊C4×C47D412yes—
49C2×C22⋊C4×C47D414yes—
50C2×C22⋊C4×C47Q814yes—
51C2×C42×C47—24no—
52#95×C47—24no—
53C24×C47—82no—
54C24×C47C22×C411yescharacteristic
55C24×C47C22×C412yes—
56C24×C47C2×D411yescharacteristic
57C24×C47C2×D411yescharacteristic
58C24×C47C2×D412yes—
59C24×C47C2×Q812yes—
60C24×C47#4112yes—
61C24×C47#4112yes—
62C24×C47#4112yes—
63C22×C4×C47—22no—
64C22×C4×C47—24no—
65C22×C4×C47—24no—
66C22×C4×C47—24no—
67C22×C4×C47—22no—
68C22×C4×C47—82no—
69C22×C4×C47—84no—
70C22×C4×C47C22⋊C414yes—
71C22×Dic47—22no—
72C22×Dic47—24no—
73C22×Dic47—22no—
74C22×Dic47—24no—
75C22×Dic47—24no—
76C22×Dic47—42no—
77C22×Dic47—42no—
78C22×Dic47—82no—
79C22×Dic47—82no—
80C22×Dic47—84no—
81C22⋊C4×C47—24no—
82C22⋊C4×C47—24no—
83C22⋊C4×C47—24no—
84C22⋊C4×C47—24no—
85C22⋊C4×C47—24no—
86C22⋊C4×C47C4⋊C418yescomplemented
87C42×C47—84no—
88C22⋊Dic47—22no—
89C22⋊Dic47—24no—
90C22⋊Dic47—24no—
91C22⋊Dic47—24no—
92C22⋊Dic47—41no—
93C22⋊Dic47—42no—
94C22⋊Dic47—41no—
95C22⋊Dic47—42no—
96C22⋊Dic47—42no—
97C22⋊Dic47C4214yescomplemented
98Dic47⋊C4—84no—
99C23×C47—42no—
100C23×C47—42no—
101C23×C47—44no—
102C23×C47—42no—
103C23×C47—44no—
104C23×C47—82no—
105C23×C47—82no—
106C23×C47—82no—
107C23×C47—82no—
108C23×C47C2×C4211yescharacteristic
109C23×C47C2×C22⋊C411yescharacteristic
110C23×C47C2×C4⋊C412yes—
111C23×C47#11711yescharacteristic
112C23×C47#11712yes—
113C23×C47C4×D412yes—
114C23×C47C4×D412yes—
115C23×C47C4×D412yes—
116C23×C47C4×D412yes—
117C23×C47C4×Q812yes—
118C23×C47C4×Q812yes—
119C23×C47#12011yescharacteristic
120C23×C47#12112yes—
121C23×C47C22⋊Q812yes—
122C23×C47C22⋊Q812yes—
123C23×C47#12311yescharacteristic
124C23×C47#12312yes—
125C23×C47#12411yescharacteristic
126C23×C47#12512yes—
127C23×C47#12612yes—
128C23×C47C4⋊Q811yescharacteristic
129C2×C4×C47—28no—
130C2×C4×C47—24no—
131C2×C4×C47—48no—
132C2×C4×C47—44no—
133C2×C4×C47—44no—
134C2×C4×C47—82no—
135C2×C4×C47—84no—
136C2×C4×C47—84no—
137C2×Dic47—24no—
138C2×Dic47—44no—
139C2×Dic47—44no—
140C2×Dic47—42no—
141C2×Dic47—44no—
142C2×Dic47—84no—
143C2×Dic47—84no—
144C2×Dic47—84no—
145C2×Dic47—84no—
146C2×Dic47—84no—
147#10915—471nomaximal, Sylow
148C22×C47—22no—
149C22×C47—24no—
150C22×C47—24no—
151C22×C47—22no—
152C22×C47—22no—
153C22×C47—42no—
154C22×C47—42no—
155C22×C47—42no—
156C22×C47—42no—
157C22×C47—42no—
158C22×C47—41no—
159C22×C47—42no—
160C22×C47—41no—
161C22×C47—42no—
162C22×C47—42no—
163C22×C47—42no—
164C22×C47—42no—
165C22×C47—42no—
166C22×C47—41no—
167C22×C47—42no—
168C22×C47—41no—
169C22×C47C4×C22⋊C411yescharacteristic
170C22×C47C4×C4⋊C412yes—
171C22×C47#38512yes—
172C22×C47#38611yescharacteristic
173C22×C47#38712yes—
174C22×C47#38712yes—
175C22×C47#38812yes—
176C22×C47#38912yes—
177C22×C47#39111yescharacteristic
178C4×C47—48no—
179C4×C47—44no—
180Dic47—44no—
181Dic47—84no—
182Dic47—82no—
183#2315—471no—
184#2273D4711yescharacteristic
185C2×#342—472no—
186C2×#342—472no—
187C2×#342—471no—
188C2×C47—21no—
189C2×C47—22no—
190C2×C47—22no—
191C2×C47—22no—
192C2×C47—22no—
193C2×C47—22no—
194C2×C47—22no—
195C2×C47—21no—
196C2×C47#143611yescharacteristic
197C2×C47#191312yes—
198C22×C22⋊C4—471no—
199C22×C22⋊C4—472no—
200C22×C22⋊C4—471no—
201C22×C22⋊C4C2×D4711yescharacteristic
202C22×C22⋊C4C2×D4712yes—
203#385—474no—
204#385—942no—
205#380—942no—
206C4×C22⋊C4—22no—
207C4×C22⋊C4—24no—
208#342—478no—
209#342—942no—
210#342—944no—
211C47#1091511yescharacteristic, complemented, Sylow
212C25C22×D4711yescharacteristic
213C23×C4—22no—
214C23×C4—472no—
215C23×C4—941no—
216C23×C4—942no—
217C23×C4C22⋊D4712yes—
218C2×C4⋊C4—944no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—474no—
225C2×C22⋊C4—472no—
226C2×C22⋊C4—474no—
227C2×C22⋊C4—942no—
228C2×C22⋊C4—941no—
229C2×C22⋊C4—942no—
230C2×C22⋊C4—942no—
231C2×C22⋊C4—942no—
232C2×C22⋊C4—942no—
233C2×C22⋊C4—941no—
234C2×C22⋊C4—942no—
235C2×C22⋊C4—942no—
236C2×C22⋊C4—942no—
237C2×C22⋊C4—941no—
238C2×C22⋊C4Dic9414yes—
239C2×C22⋊C4C4×D4712yes—
240C2×C22⋊C4C4×D4714yes—
241C2×C22⋊C4D18812yes—
242C2×C22⋊C4C22⋊D4714yes—
243C2×C42—24no—
244#95—24no—
245#95—944no—
246C24—82no—
247C24C2×Dic9412yes—
248C24C2×C4×D4711yescharacteristic
249C24C2×C4×D4712yes—
250C24C2×D18811yescharacteristic
251C24#1062535012yes—
252C24#1062535012yes—
253C24#1062535012yes—
254C24C2×C22⋊D4711yescharacteristic
255C24C2×C22⋊D4712yes—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—82no—
262C22×C4—84no—
263C22×C4—944no—
264C22×C4—942no—
265C22×C4—944no—
266C22×C4—944no—
267C22×C4—942no—
268C22×C4—3764no—
269C22×C4—3762no—
270C22×C4—3762no—
271C22×C4—1882no—
272C22×C4—1882no—
273C22×C4(C2×D47)⋊C414yes—
274C4⋊C4—3764no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—24no—
278C22⋊C4—24no—
279C22⋊C4—24no—
280C22⋊C4—474no—
281C22⋊C4—942no—
282C22⋊C4—944no—
283C22⋊C4—944no—
284C22⋊C4—944no—
285C22⋊C4—1881no—
286C22⋊C4—1882no—
287C22⋊C4—1881no—
288C22⋊C4—1882no—
289C22⋊C4—1882no—
290C22⋊C4Dic47⋊C418yescomplemented
291C42—84no—
292C23—42no—
293C23—44no—
294C23—42no—
295C23—42no—
296C23—44no—
297C23—82no—
298C23—82no—
299C23—82no—
300C23—82no—
301C23C42×D4711yescharacteristic
302C23C2×(C2×D47)⋊C411yescharacteristic
303C23C2×Dic47⋊C412yes—
304C23#1309398111yescharacteristic
305C23#1309398112yes—
306C23C4×C22⋊D4712yes—
307C23C4×C22⋊D4712yes—
308C23C4×C22⋊D4712yes—
309C23C4×D18812yes—
310C23C4×Dic9412yes—
311C23C4×Dic9412yes—
312C23#1309399311yescharacteristic
313C23#1309399812yes—
314C23#1309400312yes—
315C23#1309400312yes—
316C23#1309400711yescharacteristic
317C23#1309400712yes—
318C23#1309401211yescharacteristic
319C23#1309401612yes—
320C23#1309401812yes—
321C23#1309402411yescharacteristic
322C2×C4—28no—
323C2×C4—24no—
324C2×C4—48no—
325C2×C4—44no—
326C2×C4—44no—
327C2×C4—82no—
328C2×C4—84no—
329C2×C4—84no—
330C2×C4—944no—
331C2×C4—3764no—
332C2×C4—3764no—
333C2×C4—3764no—
334C2×C4—3764no—
335C2×C4—3764no—
336C2×C4—1884no—
337C2×C4—1882no—
338C2×C4—1884no—
339C2×C4—1884no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—24no—
344C22—24no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—41no—
351C22—42no—
352C22—41no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—41no—
359C22—42no—
360C22—41no—
361C22C4×(C2×D47)⋊C411yescharacteristic
362C22C4×Dic47⋊C412yes—
363C22#1568899612yes—
364C22#1568900211yescharacteristic
365C22#1568900712yes—
366C22#1568900712yes—
367C22#1568901412yes—
368C22#1568902112yes—
369C22#1568902911yescharacteristic
370C4—48no—
371C4—44no—
372C4—3764no—
373C4—3762no—
374C4—1884no—
375C2—22no—
376C2—22no—
377C2—21no—
378C2—22no—
379C2—22no—
380C2—22no—
381C2—22no—
382C2—21no—
383C2#2024162111yescharacteristic
384C2#2024393012yes—
subgroupG/H
centerC22#15689002
commutatorC23×C47C2×C42
FrattiniC25C22×D47
FittingC47×#2273C2
socleC22×C47#386
prime radical, cosocleC25×C47C23
hypercenter#2273D47
hypocenterC47#10915
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ #2273

Complements

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

NH ≅ G/Ntype
10. #15688995C4semidirect
14. #15688889C4semidirect
86. C22⋊C4×C47C4⋊C4semidirect
97. C22⋊Dic47C42semidirect
211. C47#10915semidirect
290. C22⋊C4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
#202460002
C2×#156888902
C2×#156888892
C47×#22732
#1091547