Finite Group Databasebeta

← #26104232

Subgroups — #26104232

Order 12032.

550 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245871C211yesmaximal, characteristic
2C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic
3#20241212C212yesmaximal, complemented
4#20241210C212yesmaximal, complemented
5C4×C22⋊C8×C47C211yesmaximal, characteristic
6C2×#13093983C411yescharacteristic
7C2×#13093983C411yescharacteristic
8C2×C22⋊(C47⋊C8)—21no—
9C2×C4×C47⋊C8—21no—
10#15689021C411yescharacteristic
11#15689021C411yescharacteristic
12#15689021C2211yescharacteristic
13#15689021C2211yescharacteristic
14#15688996—21no—
15#15688996—21no—
16C4×Dic47⋊C4—21no—
17C4×Dic47⋊C4—21no—
18#15688878C2212yes—
19C22×C42×C47C2211yescharacteristic
20C2×C22⋊C8×C47—21no—
21C2×C4×C8×C47—21no—
22C47×#336C2212yes—
23C22×C47⋊C8—22no—
24#13093983—22no—
25#13093983—42no—
26#13093983C814yescomplemented
27C2×C4⋊Dic47C2×C411yescharacteristic
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×Dic47⋊C4—21no—
35C2×C22⋊Dic47—21no—
36C2×C22⋊Dic47—21no—
37C2×C4×Dic47—21no—
38C2×C4×Dic47—21no—
39C22⋊(C47⋊C8)—24no—
40C4×C47⋊C8—42no—
41C47⋊#95—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C23×C4×C47C2×C411yescharacteristic
46C23×C4×C47D411yescharacteristic
47C23×C4×C47D411yescharacteristic
48C22×C8×C47—22no—
49C2×C42×C47—42no—
50C2×C42×C47C2×C411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47C2311yescharacteristic
54C22⋊C8×C47—24no—
55C4×C8×C47—42no—
56C24×C47C22⋊C411yescharacteristic
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47—22no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C2×C812yes—
69C22×C4×C47M1612yes—
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C2×D411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C2×C8×C47—24no—
78C2×C8×C47—42no—
79C2×C8×C47—42no—
80C42×C47—22no—
81C42×C47—22no—
82C42×C47—41no—
83C42×C47—41no—
84C22⋊Dic47—24no—
85C22⋊Dic47—42no—
86C4⋊Dic47—21no—
87C4⋊Dic47—21no—
88C4⋊Dic47—41no—
89C4⋊Dic47—41no—
90C4⋊Dic47C2×C812yes—
91C4⋊Dic47C2×C812yes—
92Dic47⋊C4—42no—
93Dic47⋊C4—42no—
94Dic47⋊C4—42no—
95Dic47⋊C4—42no—
96C4×Dic47—24no—
97C4×Dic47—42no—
98C2×C47⋊C8—24no—
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—24no—
120C2×C4×C47—24no—
121C2×C4×C47—44no—
122C2×C4×C47—44no—
123C2×C4×C47C22⋊C812yes—
124C2×C4×C47#9912yes—
125C2×C4×C47#10112yes—
126C2×C4×C47#10412yes—
127C2×C4×C47#10412yes—
128C2×C4×C47C22×C811yescharacteristic
129C2×C4×C47C2×M1611yescharacteristic
130C2×C4×C47#13512yes—
131C2×C4×C47#13512yes—
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—
144C8×C47—44no—
145C47⋊C8—44no—
146#7564—471nomaximal, Sylow
147C22×C47—22no—
148C22×C47—22no—
149C22×C47—22no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C2×C22⋊C811yescharacteristic
155C22×C47C2×#9911yescharacteristic
156C22×C47C2×#10111yescharacteristic
157C22×C47#41611yescharacteristic
158C22×C47#41611yescharacteristic
159C22×C47C2×#10411yescharacteristic
160C22×C47C2×#10411yescharacteristic
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—22no—
164C4×C47—22no—
165C4×C47—22no—
166C4×C47—22no—
167C4×C47#32414yes—
168Dic47—42no—
169Dic47—42no—
170Dic47—81no—
171Dic47—81no—
172#2296—471no—
173C4×C22⋊C8—471no—
174C4×C22⋊C8D4711yescharacteristic
175#1271—472no—
176#1271—472no—
177C2×C47—42no—
178C2×C47C2×#32411yescharacteristic
179C2×C47#147611yescharacteristic
180C2×C47#147611yescharacteristic
181C2×C47#150111yescharacteristic
182C2×C47#150111yescharacteristic
183C2×C47#152611yescharacteristic
184C2×C47#154411yescharacteristic
185C2×#117—471no—
186C2×#117—471no—
187C22×C42C2×D4711yescharacteristic
188C2×C22⋊C8—21no—
189C2×C22⋊C8—941no—
190C2×C4×C8—21no—
191C2×C4×C8—941no—
192#389—471no—
193#389—471no—
194#389—471no—
195#389—471no—
196#385—941no—
197#385—941no—
198C4×C4⋊C4—941no—
199C4×C4⋊C4—941no—
200#336—472no—
201#336C2×D4712yes—
202C47#756411yescharacteristic, complemented, Sylow
203C23×C4C4×D4711yescharacteristic
204C23×C4D18811yescharacteristic
205C23×C4C22⋊D4711yescharacteristic
206C22×C8—22no—
207C22×C8—942no—
208#117—474no—
209#117—942no—
210#117—1882no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—941no—
216C2×C4⋊C4—941no—
217C2×C4⋊C4—941no—
218C2×C4⋊C4—941no—
219C2×C22⋊C4—941no—
220C2×C22⋊C4—941no—
221C2×C42—42no—
222C2×C42—941no—
223C2×C42—941no—
224C2×C42C4×D4711yescharacteristic
225C2×C42D18811yescharacteristic
226C2×C42C22⋊D4711yescharacteristic
227C2×C42C22×D4711yescharacteristic
228C22⋊C8—24no—
229C22⋊C8—944no—
230C4×C8—42no—
231C4×C8—1882no—
232#95—941no—
233#95—941no—
234#95—941no—
235#95—941no—
236C24(C2×D47)⋊C411yescharacteristic
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—941no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4C8×D4712yes—
250C22×C4#1062532412yes—
251C22×C4(C2×D47)⋊C411yescharacteristic
252C22×C4(C2×D47)⋊C411yescharacteristic
253C22×C4(C2×D47)⋊C411yescharacteristic
254C22×C4C2×C4×D4711yescharacteristic
255C22×C4C2×D18811yescharacteristic
256C22×C4C2×C22⋊D4711yescharacteristic
257C2×C8—24no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—944no—
261C2×C8—1882no—
262C2×C8—1882no—
263C4⋊C4—472no—
264C4⋊C4—472no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—1881no—
268C4⋊C4—1881no—
269C4⋊C4—1882no—
270C4⋊C4—1882no—
271C4⋊C4—1882no—
272C4⋊C4—1882no—
273C22⋊C4—944no—
274C22⋊C4—1882no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C42—944no—
280C42—1882no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23(C2×D47)⋊C812yes—
288C23C2×(C2×D47)⋊C411yescharacteristic
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—942no—
304C2×C4—942no—
305C2×C4—1881no—
306C2×C4—1881no—
307C2×C4—1881no—
308C2×C4—1881no—
309C2×C4—1881no—
310C2×C4—1881no—
311C2×C4—1881no—
312C2×C4—1881no—
313C2×C4—1881no—
314C2×C4—1881no—
315C2×C4(C2×D47)⋊C812yes—
316C2×C4#1309393812yes—
317C2×C4#1309394212yes—
318C2×C4#1309395012yes—
319C2×C4#1309395212yes—
320C2×C4C2×C8×D4711yescharacteristic
321C2×C4C2×#1062532411yescharacteristic
322C2×C4#1309404412yes—
323C2×C4#1309404612yes—
324C8—44no—
325C8—1884no—
326C22—22no—
327C22—22no—
328C22—22no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22C2×(C2×D47)⋊C811yescharacteristic
334C22C2×#1309393811yescharacteristic
335C22C2×#1309394211yescharacteristic
336C22#1568911711yescharacteristic
337C22#1568912011yescharacteristic
338C22C2×#1309395011yescharacteristic
339C22C2×#1309395211yescharacteristic
340C4—21no—
341C4—21no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—22no—
346C4—3761no—
347C4—3761no—
348C4—1882no—
349C4—1882no—
350C4#1568884814yes—
351C2—42no—
352C2C2×#1568884811yescharacteristic
353C2#2024176811yescharacteristic
354C2#2024177111yescharacteristic
355C2#2024187711yescharacteristic
356C2#2024188011yescharacteristic
357C2#2024198211yescharacteristic
358C2#2024205211yescharacteristic
subgroupG/H
centerC22×C4(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#7564
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #20241212C2semidirect
4. #20241210C2semidirect
26. #13093983C8semidirect
202. C47#7564semidirect

Maximal subgroups

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

subgroupindex
#202458712
C4×C22⋊(C47⋊C8)2
#202412122
#202412102
C4×C22⋊C8×C472
#756447