Finite Group Databasebeta

← #26110966

Subgroups — #26110966

Order 12032.

626 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252412C211yesmaximal, characteristic
2C4×#13094005C211yesmaximal, characteristic
3#20243454C212yesmaximal, complemented
4#20241234C212yesmaximal, complemented
5C47×#1459C211yesmaximal, characteristic
6C2×#13094005C411yescharacteristic
7C22×C4×Dic47C2211yescharacteristic
8D4×C47⋊C8—24no—
9#15689176—21no—
10C2×C22⋊(C47⋊C8)—21no—
11C2×C22⋊(C47⋊C8)C2212yes—
12#15689011—21no—
13#15689004—21no—
14#15689003C411yescharacteristic
15#15688995C411yescharacteristic
16#15688984C411yescharacteristic
17C4×Dic47⋊C4—21no—
18C4×C22⋊Dic47—21no—
19C4×C22⋊Dic47C2211yescharacteristic
20#15688877—24no—
21C2×C4×D4×C47C2211yescharacteristic
22C2×C22⋊C8×C47C2212yes—
23C47×#324—21no—
24C47×#323—21no—
25C23×Dic47C2×C411yescharacteristic
26C23×Dic47C2×C411yescharacteristic
27C22×C47⋊C8—22no—
28C22×C47⋊C8D414yes—
29#13094005—22no—
30#13094005C814yescomplemented
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×C22⋊Dic47—21no—
34C2×C22⋊Dic47—21no—
35C2×C22⋊Dic47C2×C411yescharacteristic
36C2×C22⋊Dic47C2×C411yescharacteristic
37C2×C4×Dic47—21no—
38C2×C4×Dic47—21no—
39C2×C4×Dic47—21no—
40C2×C4×Dic47—22no—
41C2×C4×Dic47—22no—
42C4⋊(C47⋊C8)—22no—
43C22⋊(C47⋊C8)—22no—
44C22⋊(C47⋊C8)—22no—
45C22⋊(C47⋊C8)—22no—
46C4×C47⋊C8—22no—
47C47⋊#95—21no—
48C47⋊#95—21no—
49C47⋊#95—21no—
50C47⋊#95—21no—
51C47⋊#95—21no—
52C22×D4×C47C2×C411yescharacteristic
53C23×C4×C47D411yescharacteristic
54C23×C4×C47C2311yescharacteristic
55C22×C8×C47—22no—
56C4×D4×C47—22no—
57C4×D4×C47—22no—
58C2×C4⋊C4×C47D411yescharacteristic
59C2×C22⋊C4×C47C2×C411yescharacteristic
60C2×C22⋊C4×C47D411yescharacteristic
61C2×C42×C47D411yescharacteristic
62C22⋊C8×C47—22no—
63C22⋊C8×C47—22no—
64C24×C47C22⋊C411yescharacteristic
65C24×C47C22×C411yescharacteristic
66C2×D4×C47—22no—
67C2×D4×C47—22no—
68C2×D4×C47C2×C812yes—
69C2×D4×C47M1612yes—
70C22×C4×C47—21no—
71C22×C4×C47—21no—
72C22×C4×C47—42no—
73C22×C4×C47—42no—
74C22×C4×C47C22⋊C411yescharacteristic
75C22×C4×C47C22⋊C411yescharacteristic
76C22×C4×C47C22⋊C411yescharacteristic
77C22×C4×C47C2×D412yes—
78C22×C4×C47C2×D411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4112yes—
81C22×Dic47—21no—
82C22×Dic47—21no—
83C22×Dic47—21no—
84C22×Dic47—22no—
85C22×Dic47—22no—
86C22×Dic47—21no—
87C22×Dic47—22no—
88C22×Dic47—21no—
89C22×Dic47—42no—
90C22×Dic47C2×C812yescomplemented
91C2×C8×C47—44no—
92C2×C8×C47—42no—
93C4⋊C4×C47—22no—
94C22⋊C4×C47—22no—
95C22⋊C4×C47—22no—
96C42×C47—21no—
97C42×C47—21no—
98C22⋊Dic47—24no—
99C22⋊Dic47—21no—
100C22⋊Dic47—22no—
101C22⋊Dic47—42no—
102C22⋊Dic47C2×C812yescomplemented
103Dic47⋊C4—24no—
104Dic47⋊C4—42no—
105C4×Dic47—42no—
106C4×Dic47—41no—
107C4×Dic47—42no—
108C4×Dic47—41no—
109C2×C47⋊C8—24no—
110C2×C47⋊C8—44no—
111C2×C47⋊C8—82no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—41no—
115C23×C47—41no—
116C23×C47—41no—
117C23×C47—41no—
118C23×C47C22⋊C812yes—
119C23×C47C2×C22⋊C411yescharacteristic
120C23×C47C4×D412yes—
121C23×C47C22×C811yescharacteristic
122C23×C47C2×M1611yescharacteristic
123C23×C47#13112yes—
124D4×C47—24no—
125D4×C47—24no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—24no—
129C2×C4×C47—22no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—41no—
133C2×C4×C47—42no—
134C2×C4×C47—42no—
135C2×C4×C47—41no—
136C2×C4×C47—41no—
137C2×C4×C47—81no—
138C2×C4×C47C22⋊C812yes—
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47#12112yes—
141C2×C4×C47#12311yescharacteristic
142C2×Dic47—22no—
143C2×Dic47—24no—
144C2×Dic47—22no—
145C2×Dic47—22no—
146C2×Dic47—24no—
147C2×Dic47—41no—
148C2×Dic47—41no—
149C2×Dic47—41no—
150C2×Dic47—42no—
151C2×Dic47—41no—
152C2×Dic47—41no—
153C2×Dic47—41no—
154C2×Dic47—42no—
155C2×Dic47—41no—
156C2×Dic47—41no—
157C2×Dic47—41no—
158C8×C47—82no—
159C47⋊C8—44no—
160#8966—471nomaximal, Sylow
161C22×C47—21no—
162C22×C47—22no—
163C22×C47—21no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—42no—
169C22×C47—42no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—81no—
173C22×C47#38611yescharacteristic
174C22×C47C2×C22⋊C811yescharacteristic
175C22×C47#40811yescharacteristic
176C22×C47C8×D412yes—
177C22×C47#43512yes—
178C4×C47—22no—
179C4×C47—22no—
180C4×C47—21no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47#45812yes—
184Dic47—42no—
185Dic47—42no—
186Dic47—42no—
187Dic47—81no—
188#2972—471no—
189C4×#123—471no—
190#1817—472no—
191#1459D4711yescharacteristic
192#1282—472no—
193C2×C47—21no—
194C2×C47—21no—
195C2×C47—22no—
196C2×C47—22no—
197C2×C47—42no—
198C2×C47#186911yescharacteristic
199C2×C47#189011yescharacteristic
200C2×C47#189111yescharacteristic
201C2×#123—471no—
202C2×C4×D4C2×D4711yescharacteristic
203C22×C42—471no—
204C8×D4—944no—
205#431—941no—
206C2×C22⋊C8—472no—
207C2×C22⋊C8—941no—
208C2×C22⋊C8C2×D4712yes—
209#388—941no—
210#387—941no—
211#386—471no—
212#385—471no—
213#381—471no—
214C4×C4⋊C4—941no—
215C4×C22⋊C4—471no—
216C4×C22⋊C4—941no—
217#336—944no—
218#324—21no—
219#323—21no—
220C47#896611yescharacteristic, complemented, Sylow
221C22×D4C4×D4711yescharacteristic
222C23×C4—471no—
223C23×C4—471no—
224C23×C4D18811yescharacteristic
225C23×C4C22×D4711yescharacteristic
226C22×C8—22no—
227C22×C8—474no—
228C22×C8—942no—
229#123—474no—
230#123—942no—
231C4×D4—22no—
232C4×D4—22no—
233C2×C4⋊C4—941no—
234C2×C4⋊C4—941no—
235C2×C4⋊C4C22⋊D4711yescharacteristic
236C2×C22⋊C4—471no—
237C2×C22⋊C4—471no—
238C2×C22⋊C4—941no—
239C2×C22⋊C4—941no—
240C2×C22⋊C4C4×D4711yescharacteristic
241C2×C22⋊C4C22⋊D4711yescharacteristic
242C2×C42—941no—
243C2×C42—941no—
244C2×C42—942no—
245C2×C42—942no—
246C2×C42—941no—
247C2×C42D18811yescharacteristic
248C4⋊C8—942no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—942no—
252C22⋊C8—942no—
253C22⋊C8—942no—
254C4×C8—942no—
255#95—941no—
256#95—941no—
257#95—941no—
258#95—941no—
259#95—941no—
260C24(C2×D47)⋊C411yescharacteristic
261C24C2×C4×D4711yescharacteristic
262C2×D4—22no—
263C2×D4—22no—
264C2×D4C8×D4712yes—
265C2×D4#1062532412yes—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—472no—
271C22×C4—941no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—942no—
275C22×C4—942no—
276C22×C4—941no—
277C22×C4—942no—
278C22×C4—941no—
279C22×C4—1882no—
280C22×C4(C2×D47)⋊C411yescharacteristic
281C22×C4(C2×D47)⋊C411yescharacteristic
282C22×C4(C2×D47)⋊C411yescharacteristic
283C22×C4C2×D18811yescharacteristic
284C22×C4D4×D4712yes—
285C22×C4#1062535212yes—
286C22×C4C2×C22⋊D4711yescharacteristic
287C2×C8—44no—
288C2×C8—42no—
289C2×C8—944no—
290C2×C8—3762no—
291C2×C8—1884no—
292C4⋊C4—22no—
293C4⋊C4—944no—
294C4⋊C4—1882no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—472no—
298C22⋊C4—944no—
299C22⋊C4—941no—
300C22⋊C4—942no—
301C22⋊C4—1882no—
302C42—21no—
303C42—21no—
304C42—1882no—
305C42—1881no—
306C42—1882no—
307C42—1881no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23(C2×D47)⋊C812yes—
315C23C2×(C2×D47)⋊C411yescharacteristic
316C23(C22⋊D47)⋊C412yes—
317C23C2×C8×D4711yescharacteristic
318C23C2×#1062532411yescharacteristic
319C23#1309403212yes—
320D4—24no—
321D4—24no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—942no—
335C2×C4—944no—
336C2×C4—942no—
337C2×C4—942no—
338C2×C4—944no—
339C2×C4—1881no—
340C2×C4—1881no—
341C2×C4—1881no—
342C2×C4—1881no—
343C2×C4—1881no—
344C2×C4—1881no—
345C2×C4—1882no—
346C2×C4—1881no—
347C2×C4—1881no—
348C2×C4—1881no—
349C2×C4—1882no—
350C2×C4(C2×D47)⋊C812yes—
351C2×C4#1309399411yescharacteristic
352C2×C4#1309399612yes—
353C2×C4#1309400811yescharacteristic
354C8—82no—
355C8—1884no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22#1568900011yescharacteristic
369C22C2×(C2×D47)⋊C811yescharacteristic
370C22#1568909111yescharacteristic
371C22(C22⋊D47)⋊C812yes—
372C22#1568919112yes—
373C4—22no—
374C4—21no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—3761no—
379C4—1882no—
380C4—1882no—
381C4—1882no—
382C4#1568931412yes—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—22no—
387C2—42no—
388C2#2024367811yescharacteristic
389C2#2024379911yescharacteristic
390C2#2024380411yescharacteristic
subgroupG/H
centerC2×C4#13093994
commutatorC23×C47C22×C8
FrattiniC23×C4C22×D47
FittingC47×#1459C2
socleC22×C47#386
prime radicalC22×D4×C47C2×C4
cosocleC23×C4×C47C23
hypercenter#1459D47
hypocenterC47#8966
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #20243454C2semidirect
4. #20241234C2semidirect
30. #13094005C8semidirect
90. C22×Dic47C2×C8semidirect
102. C22⋊Dic47C2×C8semidirect
220. C47#8966semidirect

Maximal subgroups

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

subgroupindex
#202524122
C4×#130940052
#202434542
#202412342
C47×#14592
#896647