Finite Group Databasebeta

← #26104313

Subgroups — #26104313

Order 12032.

522 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13094003C211yesmaximal, characteristic
2#20243456C211yesmaximal, characteristic
3#20241213C212yesmaximal, complemented
4#20241210C212yesmaximal, complemented
5C4×C22⋊C8×C47C211yesmaximal, characteristic
6C2×#13094003C411yescharacteristic
7C2×C4×Dic94C411yescharacteristic
8C2×C22⋊(C47⋊C8)—21no—
9#15689029C2211yescharacteristic
10#15689021C2211yescharacteristic
11#15689007—21no—
12#15688996—21no—
13#15688983C411yescharacteristic
14C4×Dic47⋊C4—21no—
15C4×C4⋊Dic47C411yescharacteristic
16C4×C22⋊Dic47—21no—
17#15688878—21no—
18#15688878C2212yes—
19C22×C42×C47C2211yescharacteristic
20C2×C22⋊C8×C47—21no—
21C2×C4×C8×C47—21no—
22C47×#336C2212yes—
23C22×Dic94C2×C411yescharacteristic
24C22×C47⋊C8—22no—
25#13094003—22no—
26#13094003C814yescomplemented
27C4×Dic94—42no—
28C2×C4⋊Dic47C2×C411yescharacteristic
29C2×C4⋊Dic47C2×C411yescharacteristic
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×Dic47⋊C4—21no—
32C2×Dic47⋊C4—21no—
33C2×Dic47⋊C4—21no—
34C2×C22⋊Dic47—21no—
35C2×C22⋊Dic47—21no—
36C2×C4×Dic47—21no—
37C2×C4×Dic47—21no—
38C22⋊(C47⋊C8)—42no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C23×C4×C47C2×C411yescharacteristic
45C23×C4×C47D411yescharacteristic
46C23×C4×C47D411yescharacteristic
47C22×C8×C47—22no—
48C2×C42×C47—42no—
49C2×C42×C47C2×C411yescharacteristic
50C2×C42×C47D411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47C2311yescharacteristic
53C22⋊C8×C47—24no—
54C4×C8×C47—42no—
55C24×C47C22⋊C411yescharacteristic
56C22×C4×C47—22no—
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47—41no—
63C22×C4×C47—41no—
64C22×C4×C47C22⋊C411yescharacteristic
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C2×C812yes—
68C22×C4×C47M1612yes—
69C22×C4×C47C22×C411yescharacteristic
70C22×C4×C47C2×D411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76C2×Dic94—21no—
77C2×Dic94—41no—
78C2×Dic94—41no—
79C2×Dic94C2×C812yes—
80C2×C8×C47—24no—
81C2×C8×C47—42no—
82C2×C8×C47—42no—
83C42×C47—22no—
84C42×C47—22no—
85C42×C47—41no—
86C42×C47—41no—
87C22⋊Dic47—24no—
88C22⋊Dic47—42no—
89C4⋊Dic47—21no—
90C4⋊Dic47—41no—
91C4⋊Dic47—41no—
92C4⋊Dic47C2×C812yes—
93Dic47⋊C4—24no—
94Dic47⋊C4—42no—
95Dic47⋊C4—42no—
96C4×Dic47—42no—
97C4×Dic47—42no—
98C2×C47⋊C8—42no—
99C2×C47⋊C8—42no—
100C2×C47⋊C8—42no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47C22⋊C812yes—
108C23×C47C2×C22⋊C411yescharacteristic
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—44no—
124C2×C4×C47—44no—
125C2×C4×C47C22⋊C812yes—
126C2×C4×C47#9912yes—
127C2×C4×C47#10412yes—
128C2×C4×C47C22×C811yescharacteristic
129C2×C4×C47C2×M1611yescharacteristic
130C2×C4×C47#13512yes—
131C2×C4×C47#13712yes—
132C2×Dic47—22no—
133C2×Dic47—22no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144Dic94—42no—
145Dic94—42no—
146C8×C47—44no—
147C47⋊C8—82no—
148#7583—471nomaximal, Sylow
149C22×C47—22no—
150C22×C47—22no—
151C22×C47—22no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47C2×C22⋊C811yescharacteristic
157C22×C47C2×#9911yescharacteristic
158C22×C47#41311yescharacteristic
159C22×C47#41611yescharacteristic
160C22×C47#41911yescharacteristic
161C22×C47C2×#10411yescharacteristic
162C22×C47#42111yescharacteristic
163C4×C47—21no—
164C4×C47—21no—
165C4×C47—22no—
166C4×C47—22no—
167C4×C47—22no—
168C4×C47—22no—
169C4×C47—22no—
170Dic47—42no—
171Dic47—42no—
172Dic47—81no—
173Dic47—81no—
174C4×C22⋊Q8—471no—
175#1817—471no—
176C4×C22⋊C8D4711yescharacteristic
177#1272—472no—
178#1271—472no—
179C2×C47—42no—
180C2×C47#145911yescharacteristic
181C2×C47#147611yescharacteristic
182C2×C47#147911yescharacteristic
183C2×C47#150811yescharacteristic
184C2×C47#151611yescharacteristic
185C2×C47#152911yescharacteristic
186C2×C47#155411yescharacteristic
187C2×C22⋊Q8—471no—
188C2×C4×Q8—471no—
189C22×C42C2×D4711yescharacteristic
190C2×C22⋊C8—21no—
191C2×C22⋊C8—941no—
192C2×C4×C8—21no—
193#391—471no—
194#389—471no—
195#387—941no—
196#385—941no—
197#380—471no—
198C4×C4⋊C4—471no—
199C4×C4⋊C4—941no—
200C4×C22⋊C4—941no—
201#336—472no—
202#336—941no—
203#336C2×D4712yes—
204C47#758311yescharacteristic, complemented, Sylow
205C22×Q8—471no—
206C23×C4C4×D4711yescharacteristic
207C23×C4D18811yescharacteristic
208C23×C4C22⋊D4711yescharacteristic
209C22×C8—22no—
210C22×C8—942no—
211C22⋊Q8—474no—
212C22⋊Q8—942no—
213C4×Q8—1882no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4—471no—
217C2×C4⋊C4—941no—
218C2×C4⋊C4—941no—
219C2×C4⋊C4—941no—
220C2×C22⋊C4—941no—
221C2×C22⋊C4—941no—
222C2×C42—42no—
223C2×C42—941no—
224C2×C42—941no—
225C2×C42C4×D4711yescharacteristic
226C2×C42D18811yescharacteristic
227C2×C42C22⋊D4711yescharacteristic
228C2×C42C22×D4711yescharacteristic
229C22⋊C8—24no—
230C22⋊C8—1882no—
231C4×C8—42no—
232#95—941no—
233#95—941no—
234#95—941no—
235#95—941no—
236#95—941no—
237C24(C2×D47)⋊C411yescharacteristic
238C2×Q8—472no—
239C2×Q8—941no—
240C2×Q8—1881no—
241C2×Q8—1881no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4C8×D4712yes—
255C22×C4#1062532412yes—
256C22×C4(C2×D47)⋊C411yescharacteristic
257C22×C4(C2×D47)⋊C411yescharacteristic
258C22×C4(C2×D47)⋊C411yescharacteristic
259C22×C4C2×C4×D4711yescharacteristic
260C22×C4C2×D18811yescharacteristic
261C22×C4C2×C22⋊D4711yescharacteristic
262C2×C8—24no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—1882no—
266C2×C8—1882no—
267C2×C8—1882no—
268C4⋊C4—472no—
269C4⋊C4—944no—
270C4⋊C4—941no—
271C4⋊C4—1881no—
272C4⋊C4—1881no—
273C4⋊C4—1882no—
274C4⋊C4—1882no—
275C22⋊C4—944no—
276C22⋊C4—1882no—
277C42—22no—
278C42—22no—
279C42—41no—
280C42—41no—
281C42—1882no—
282C42—1882no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23(C2×D47)⋊C812yes—
290C23C2×(C2×D47)⋊C411yescharacteristic
291Q8—1882no—
292Q8—1882no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4—1881no—
312C2×C4—1881no—
313C2×C4—1881no—
314C2×C4—1881no—
315C2×C4—1881no—
316C2×C4—1881no—
317C2×C4—1881no—
318C2×C4—1881no—
319C2×C4—1881no—
320C2×C4—1881no—
321C2×C4(C2×D47)⋊C812yes—
322C2×C4#1309393812yes—
323C2×C4#1309395212yes—
324C2×C4C2×C8×D4711yescharacteristic
325C2×C4C2×#1062532411yescharacteristic
326C2×C4#1309404612yes—
327C2×C4#1309405412yes—
328C8—44no—
329C8—3762no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×(C2×D47)⋊C811yescharacteristic
338C22C2×#1309393811yescharacteristic
339C22#1568910511yescharacteristic
340C22#1568912011yescharacteristic
341C22#1568913111yescharacteristic
342C22C2×#1309395211yescharacteristic
343C22#1568913911yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—21no—
348C4—21no—
349C4—22no—
350C4—22no—
351C4—3761no—
352C4—3761no—
353C4—1882no—
354C4—1882no—
355C2—42no—
356C2#2024170411yescharacteristic
357C2#2024177111yescharacteristic
358C2#2024178211yescharacteristic
359C2#2024190711yescharacteristic
360C2#2024194511yescharacteristic
361C2#2024199311yescharacteristic
362C2#2024209611yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC4×C22⋊C8×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×C22⋊C8D47
hypocenterC47#7583
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #20241213C2semidirect
4. #20241210C2semidirect
26. #13094003C8semidirect
204. C47#7583semidirect

Maximal subgroups

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

subgroupindex
C4×#130940032
#202434562
#202412132
#202412102
C4×C22⋊C8×C472
#758347