Finite Group Databasebeta

← #26115223

Subgroups — #26115223

Order 12032.

466 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
1C2×C4×#10625336C211yesmaximal, characteristic
2#20242134C211yesmaximal, characteristic, complemented
3#20241778C211yesmaximal, characteristic
4#20241712C211yesmaximal, characteristic, complemented
5#20241708C211yesmaximal, characteristic
6#20241681C211yesmaximal, characteristic, complemented
7C47×#1479C211yesmaximal, characteristic, complemented
8C22×#10625336C411yescharacteristic
9C2×C4×D188C2211yescharacteristic
10C4×#10625336—21no—
11C4×#10625336—21no—
12C4×#10625336—21no—
13C4×#10625336—21no—
14#15689176C2211yescharacteristic
15#15689176C2211yescharacteristic
16C2×#13093955C411yescharacteristic
17C2×#13093948C411yescharacteristic
18C2×#13093944C411yescharacteristic
19C2×C4×C47⋊C8C2211yescharacteristic
20#15688875—21no—
21#15688873—21no—
22#15688850—22no—
23#15688849—22no—
24#15688846—22no—
25#15688845—21no—
26#15688844—21no—
27C2×C4×Q8×C47C2211yescharacteristic
28C47×#431C2211yescharacteristic
29C47×#431C2211yescharacteristic
30C47×Q8⋊C8—22no—
31C22×D188C2×C411yescharacteristic
32C22×C4×D47—21no—
33C2×#10625336—22no—
34C2×#10625336—22no—
35C2×#10625336—21no—
36C2×#10625336—21no—
37C22×C47⋊C8C2×C411yescharacteristic
38C22×C47⋊C8C2×C411yescharacteristic
39C4×D188—21no—
40C4×D188—21no—
41C4×D188—21no—
42C4×D188—21no—
43C2×C4⋊Dic47C2×C411yescharacteristic
44C2×(C2×D47)⋊C4—21no—
45#13093955—21no—
46#13093955—21no—
47C4⋊(C47⋊C8)—21no—
48C4⋊(C47⋊C8)—21no—
49#13093948—21no—
50#13093948—21no—
51#13093944—21no—
52#13093944—21no—
53C22⋊(C47⋊C8)—21no—
54C22⋊(C47⋊C8)D412yes—
55C4×C47⋊C8—21no—
56C4×C47⋊C8—21no—
57C4×C47⋊C8D411yescharacteristic
58C4×C47⋊C8D411yescharacteristic
59C4×C47⋊C8D411yescharacteristic
60C4×C47⋊C8D411yescharacteristic
61C22×Q8×C47C2×C411yescharacteristic
62C4×Q8×C47—21no—
63C4×Q8×C47—21no—
64C4×Q8×C47—21no—
65C4×Q8×C47—21no—
66C2×C4⋊C4×C47—21no—
67C2×C4⋊C4×C47C2×C411yescharacteristic
68C2×C42×C47—21no—
69C2×C42×C47C2311yescharacteristic
70C4⋊C8×C47—21no—
71C4⋊C8×C47D412yes—
72C22⋊C8×C47—21no—
73C22⋊C8×C47—21no—
74C4×C8×C47—21no—
75C4×C8×C47—21no—
76C23×D47—21no—
77C2×Q8×C47—21no—
78C2×Q8×C47—21no—
79C2×Q8×C47—21no—
80C2×Q8×C47—21no—
81C2×Q8×C47—21no—
82C2×Q8×C47M1612yes—
83C22×C4×C47—21no—
84C22×C4×C47—21no—
85C22×C4×C47C22×C411yescharacteristic
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47#4111yescharacteristic
88C22×Dic47—21no—
89C2×D188—21no—
90C2×D188—21no—
91C2×D188—21no—
92C2×D188—21no—
93C2×D188—21no—
94C2×D188M1612yes—
95C2×C4×D47—41no—
96C2×C4×D47—41no—
97C2×C4×D47—82no—
98C2×C8×C47—22no—
99C2×C8×C47—41no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—21no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C42×C47—41no—
105C42×C47—41no—
106C42×C47C2×D411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47C2×D411yescharacteristic
109C42×C47#4111yescharacteristic
110#10625336—24no—
111#10625336—24no—
112(C2×D47)⋊C4—41no—
113(C2×D47)⋊C4—41no—
114C4⋊Dic47—21no—
115C4⋊Dic47—21no—
116C2×C47⋊C8—21no—
117C2×C47⋊C8—21no—
118C2×C47⋊C8—21no—
119C2×C47⋊C8—21no—
120C2×C47⋊C8—22no—
121C2×C47⋊C8—41no—
122C2×C47⋊C8C22⋊C411yescharacteristic
123C2×C47⋊C8C22⋊C411yescharacteristic
124C2×C47⋊C8C22⋊C411yescharacteristic
125C2×C47⋊C8C22⋊C411yescharacteristic
126C23×C47C4×D411yescharacteristic
127C22×D47—22no—
128C22×D47—41no—
129C22×D47—41no—
130C22×D47—81no—
131C22×D47—81no—
132Q8×C47—22no—
133Q8×C47—22no—
134Q8×C47—41no—
135Q8×C47—41no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—41no—
142C2×C4×C47—81no—
143C2×C4×C47C2×C22⋊C411yescharacteristic
144C2×C4×C47C4×D411yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47#12111yescharacteristic
147C2×C4×C47#12411yescharacteristic
148C2×C4×C47#12711yescharacteristic
149C2×C4×C47C2×M1611yescharacteristic
150C2×C4×C47C2×M1611yescharacteristic
151C2×C4×C47#13111yescharacteristic
152C2×C4×C47#13111yescharacteristic
153C2×Dic47—41no—
154C2×Dic47—81no—
155D188—22no—
156D188—22no—
157D188—41no—
158D188—41no—
159C4×D47—82no—
160C4×D47—82no—
161C8×C47—42no—
162C8×C47—81no—
163C47⋊C8—21no—
164C47⋊C8—21no—
165C47⋊C8—21no—
166C47⋊C8—21no—
167C47⋊C8—42no—
168C47⋊C8—81no—
169#9672—471nomaximal, Sylow
170C22×C47—21no—
171C22×C47—21no—
172C22×C47#39011yescharacteristic
173C22×C47#43511yescharacteristic
174C22×C47#43511yescharacteristic
175C2×D47—42no—
176C2×D47—82no—
177C2×D47—81no—
178C2×D47—81no—
179C2×D47—82no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—21no—
183C4×C47—42no—
184C4×C47—81no—
185C4×C47#40711yescharacteristic
186C4×C47#40811yescharacteristic
187C4×C47#43511yescharacteristic
188C4×C47#43511yescharacteristic
189C4×C47#47112yes—
190Dic47—81no—
191C2×C4×SD16—471no—
192#1564—471no—
193#1479D4711yescharacteristic, complemented
194#1478—471no—
195#1461—471no—
196#1460—471no—
197#1452—471no—
198C2×C47—21no—
199C2×C47—21no—
200C2×C47#195511yescharacteristic
201C2×C47#197611yescharacteristic
202C2×C47#197711yescharacteristic
203D47—82no—
204C22×SD16—471no—
205C2×C4×Q8C2×D4711yescharacteristic
206C2×C4×D4—471no—
207C4×SD16—941no—
208C4×SD16—941no—
209C4×SD16—941no—
210C4×SD16—941no—
211#431—471no—
212#431—471no—
213#431C2×D4711yescharacteristic
214#431C2×D4711yescharacteristic
215C2×#106—471no—
216C2×#103—471no—
217C2×#102—471no—
218C2×C4×C8—471no—
219#335—941no—
220#334—941no—
221Q8⋊C8—22no—
222D4⋊C8—942no—
223#324—942no—
224#323—942no—
225#322—941no—
226#322—941no—
227C47#967211yescharacteristic, complemented, Sylow
228C22×Q8C4×D4711yescharacteristic
229C22×D4—471no—
230C23×C4—941no—
231C2×SD16—941no—
232C2×SD16—941no—
233C2×SD16—942no—
234C2×SD16—942no—
235C22×C8—471no—
236C22×C8—471no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—941no—
242C4×D4—941no—
243C4×D4—941no—
244C4×D4—941no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4C4×D4711yescharacteristic
248C2×C22⋊C4—941no—
249C2×C42—21no—
250C2×C42C22×D4711yescharacteristic
251#106—941no—
252#106—941no—
253C4⋊C8—21no—
254C4⋊C8—941no—
255C4⋊C8—941no—
256C4⋊C8C22⋊D4712yes—
257#103—941no—
258#103—941no—
259#102—941no—
260#102—941no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—472no—
264C22⋊C8—941no—
265C4×C8—21no—
266C4×C8—21no—
267C4×C8—471no—
268C4×C8—471no—
269C4×C8—471no—
270C4×C8—471no—
271C4×C8—941no—
272C4×C8—941no—
273C24—941no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8#1062532412yes—
280C2×D4—472no—
281C2×D4—941no—
282C2×D4—941no—
283C2×D4—941no—
284C2×D4—941no—
285C2×D4—941no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—941no—
289C22×C4—3762no—
290C22×C4—1881no—
291C22×C4—1881no—
292C22×C4C2×C4×D4711yescharacteristic
293C22×C4D4×D4711yescharacteristic
294C22×C4#1062535211yescharacteristic
295SD16—944no—
296SD16—944no—
297C2×C8—22no—
298C2×C8—41no—
299C2×C8—471no—
300C2×C8—471no—
301C2×C8—471no—
302C2×C8—471no—
303C2×C8—941no—
304C2×C8—941no—
305C2×C8—941no—
306C2×C8—941no—
307C2×C8—942no—
308C2×C8—1881no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—941no—
314C4⋊C4—941no—
315C22⋊C4—1881no—
316C22⋊C4—1881no—
317C42—41no—
318C42—41no—
319C42#1062535011yescharacteristic
320C42D4×D4711yescharacteristic
321C42D4×D4711yescharacteristic
322C42C2×C22⋊D4711yescharacteristic
323C23—942no—
324C23—3761no—
325C23—3761no—
326C23—1881no—
327C23—1881no—
328C23(C22⋊D47)⋊C411yescharacteristic
329Q8—22no—
330Q8—22no—
331Q8—41no—
332Q8—41no—
333D4—942no—
334D4—942no—
335D4—1881no—
336D4—1881no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—3762no—
345C2×C4—3762no—
346C2×C4—3761no—
347C2×C4—1881no—
348C2×C4C22⋊C4×D4711yescharacteristic
349C2×C4C4×C22⋊D4711yescharacteristic
350C2×C4#1309399611yescharacteristic
351C2×C4#1309399711yescharacteristic
352C2×C4#1309401011yescharacteristic
353C2×C4#1309402011yescharacteristic
354C2×C4M16×D4711yescharacteristic
355C2×C4C2×#1062532411yescharacteristic
356C2×C4#1309403011yescharacteristic
357C2×C4#1309403211yescharacteristic
358C8—42no—
359C8—81no—
360C8—941no—
361C8—941no—
362C8—941no—
363C8—941no—
364C8—3761no—
365C8—1882no—
366C22—21no—
367C22—21no—
368C22—3762no—
369C22—3762no—
370C22—3761no—
371C22—3761no—
372C22—1882no—
373C22#1568902311yescharacteristic
374C22#1568919111yescharacteristic
375C22#1568919711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—81no—
381C4—3761no—
382C4#1568908511yescharacteristic
383C4#1568908811yescharacteristic
384C4#1568919211yescharacteristic
385C4#1568919411yescharacteristic
386C4#1568938812yes—
387C2—21no—
388C2—21no—
389C2—3762no—
390C2#2024418411yescharacteristic
391C2#2024428511yescharacteristic
392C2#2024429011yescharacteristic
subgroupG/H
centerC2×C4#13093996
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1479C2
socleC22×C47#390
prime radicalC22×D188C2×C4
cosocleC2×C42×C47C23
hypercenter#1479D47
hypocenterC47#9672
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #20242134C2semidirect
4. #20241712C2semidirect
6. #20241681C2semidirect
7. C47×#1479C2semidirect
193. #1479D47semidirect
227. C47#9672semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253362
#202421342
#202417782
#202417122
#202417082
#202416812
C47×#14792
#967247