Finite Group Databasebeta

← #24986954

Subgroups — #24986954

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143228C211yesmaximal, characteristic
2#19136993C211yesmaximal, characteristic
3#19132500C214yesmaximal
4C43×#2920C211yesmaximal, characteristic
5#14582956—21no—
6#14582956C412yescomplemented
7#14582952—21no—
8#14582952C412yescomplemented
9#14582923—21no—
10#14582863C2212yes—
11C4×#10621877—21no—
12#14582767—21no—
13#14582765—21no—
14#14582762C412yes—
15#14582759C2212yes—
16C4×C4⋊Dic43—21no—
17C4×C22⋊Dic43C412yes—
18#14582745—21no—
19C22×C42×C43C2211yescharacteristic
20C43×#432—21no—
21C43×#432—21no—
22C43×#431—21no—
23C43×#431—21no—
24C43×#423C412yescomplemented
25C43×#407C2212yes—
26C4×M16×C43C412yescomplemented
27C2×#10621877—22no—
28C2×C4⋊Dic43—22no—
29C2×C22⋊Dic43C2×C414yes—
30C2×C4×Dic43—22no—
31C4⋊(C43⋊C8)—22no—
32C4⋊(C43⋊C8)—22no—
33C22⋊(C43⋊C8)—22no—
34C22⋊(C43⋊C8)C2×C414yes—
35#13063236—22no—
36C4×C43⋊C8—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C23×C4×C43C2×C411yescharacteristic
42C23×C4×C43C2×C411yescharacteristic
43C23×C4×C43C2311yescharacteristic
44C2×M16×C43C2×C414yes—
45C2×C42×C43C2×C411yescharacteristic
46C2×C42×C43C2×C411yescharacteristic
47C2×C42×C43C2×C411yescharacteristic
48C2×C42×C43C2×C411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C2×C42×C43D411yescharacteristic
51C2×C42×C43D411yescharacteristic
52C2×C42×C43D411yescharacteristic
53C2×C42×C43D411yescharacteristic
54C2×C42×C43D411yescharacteristic
55C2×C42×C43Q811yescharacteristic
56C2×C42×C43Q811yescharacteristic
57C4⋊C8×C43—22no—
58C4⋊C8×C43—22no—
59C22⋊C8×C43—22no—
60C22⋊C8×C43—22no—
61#97×C43—22no—
62C4×C8×C43—22no—
63C24×C43C22×C411yescharacteristic
64C22×C4×C43—42no—
65C22×C4×C43—42no—
66C22×C4×C43—42no—
67C22×C4×C43C4211yescharacteristic
68C22×C4×C43C4211yescharacteristic
69C22×C4×C43C4211yescharacteristic
70C22×C4×C43C4211yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22⋊C411yescharacteristic
74C22×C4×C43C22⋊C411yescharacteristic
75C22×C4×C43C4⋊C411yescharacteristic
76C22×C4×C43C4⋊C411yescharacteristic
77C22×C4×C43C4⋊C411yescharacteristic
78C22×C4×C43C4⋊C411yescharacteristic
79C22×C4×C43C22×C411yescharacteristic
80C22×C4×C43C22×C411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×Q811yescharacteristic
85C22×Dic43—24no—
86M16×C43—44no—
87C2×C8×C43—24no—
88C42×C43C22⋊C411yescharacteristic
89C42×C43C22⋊C411yescharacteristic
90C42×C43C22⋊C411yescharacteristic
91C42×C43C22⋊C411yescharacteristic
92C42×C43C22⋊C411yescharacteristic
93C42×C43C22⋊C411yescharacteristic
94C42×C43C22⋊C411yescharacteristic
95C42×C43C22⋊C411yescharacteristic
96C42×C43C4⋊C411yescharacteristic
97C42×C43C4⋊C411yescharacteristic
98C42×C43C4⋊C411yescharacteristic
99C42×C43C4⋊C411yescharacteristic
100C42×C43C4⋊C411yescharacteristic
101C42×C43C4⋊C411yescharacteristic
102C42×C43C4⋊C411yescharacteristic
103C42×C43C4⋊C411yescharacteristic
104C22⋊Dic43—44no—
105C4⋊Dic43—44no—
106C4×Dic43—44no—
107#10621877—44no—
108C2×C43⋊C8—24no—
109C23×C43—22no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43C2×C4211yescharacteristic
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43C2×C4⋊C411yescharacteristic
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43#9511yescharacteristic
134C2×C4×C43#9511yescharacteristic
135C2×C4×C43#9511yescharacteristic
136C2×C4×C43#9511yescharacteristic
137C2×C4×C43#9511yescharacteristic
138C2×C4×C43#9511yescharacteristic
139C2×C4×C43#9511yescharacteristic
140C2×C4×C43#9511yescharacteristic
141C2×C4×C43C2×C22⋊C411yescharacteristic
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43C2×C4⋊C411yescharacteristic
144C2×C4×C43C2×C4⋊C411yescharacteristic
145C2×Dic43—44no—
146C2×Dic43—44no—
147C2×Dic43—44no—
148C8×C43—44no—
149C43⋊C8—44no—
150#8110—431nomaximal, Sylow
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—44no—
160C22×C43C2×#9511yescharacteristic
161C22×C43#41312yes—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43#34412yes—
173C4×C43#41012yes—
174Dic43—84no—
175#2920—431no—
176#2920D4311yescharacteristic
177#2283—431no—
178#1305—434no—
179C2×C43—22no—
180C2×C43—41no—
181C2×C43—41no—
182C2×C43#174011yescharacteristic
183C2×C43#174211yescharacteristic
184C2×C43C2×#34411yescharacteristic
185C22×C42C2×D4311yescharacteristic
186#432—21no—
187#432—21no—
188#432—432no—
189#432—861no—
190#431—21no—
191#431—21no—
192#431—432no—
193#431—861no—
194#423—861no—
195#423Dic4312yescomplemented
196#407—432no—
197#407C2×D4312yes—
198C4×M16—861no—
199C4×M16Dic4312yescomplemented
200#383—861no—
201#382—861no—
202#381—432no—
203#380—432no—
204C4×C4⋊C4—861no—
205C4×C22⋊C4—432no—
206#376—861no—
207C43#811011yescharacteristic, complemented, Sylow
208C23×C4C4×D4311yescharacteristic
209C23×C4C4×D4311yescharacteristic
210C23×C4C22×D4311yescharacteristic
211C2×M16—862no—
212C2×M16C2×Dic4314yes—
213C2×C4⋊C4—862no—
214C2×C22⋊C4—434no—
215C2×C42—862no—
216C2×C42Dic8611yescharacteristic
217C2×C42Dic8611yescharacteristic
218C2×C42C4×D4311yescharacteristic
219C2×C42C4×D4311yescharacteristic
220C2×C42D17211yescharacteristic
221C2×C42D17211yescharacteristic
222C2×C42C2×Dic4311yescharacteristic
223C2×C42C2×Dic4311yescharacteristic
224C2×C42C22⋊D4311yescharacteristic
225C2×C42C22⋊D4311yescharacteristic
226C2×C42C22⋊D4311yescharacteristic
227C2×C42C22⋊D4311yescharacteristic
228C4⋊C8—22no—
229C4⋊C8—22no—
230C4⋊C8—862no—
231C4⋊C8—862no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234C22⋊C8—434no—
235C22⋊C8—862no—
236#97—22no—
237#97—862no—
238C4×C8—22no—
239C4×C8—862no—
240#95—862no—
241#95—862no—
242#95—862no—
243#95—862no—
244C24C2×C4×D4311yescharacteristic
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—864no—
249C22×C4C4×Dic4311yescharacteristic
250C22×C4C4×Dic4311yescharacteristic
251C22×C4C4×Dic4311yescharacteristic
252C22×C4C4×Dic4311yescharacteristic
253C22×C4Dic43⋊C411yescharacteristic
254C22×C4Dic43⋊C411yescharacteristic
255C22×C4Dic43⋊C411yescharacteristic
256C22×C4Dic43⋊C411yescharacteristic
257C22×C4(C2×D43)⋊C411yescharacteristic
258C22×C4(C2×D43)⋊C411yescharacteristic
259C22×C4(C2×D43)⋊C411yescharacteristic
260C22×C4(C2×D43)⋊C411yescharacteristic
261C22×C4C2×Dic8611yescharacteristic
262C22×C4C2×C4×D4311yescharacteristic
263C22×C4C2×D17211yescharacteristic
264C22×C4C22×Dic4311yescharacteristic
265C22×C4C2×C22⋊D4311yescharacteristic
266C22×C4C2×C22⋊D4311yescharacteristic
267M16—44no—
268M16—1724no—
269C2×C8—24no—
270C2×C8—864no—
271C4⋊C4—1724no—
272C22⋊C4—1724no—
273C42—1724no—
274C42Dic43⋊C411yescharacteristic
275C42Dic43⋊C411yescharacteristic
276C42Dic43⋊C411yescharacteristic
277C42Dic43⋊C411yescharacteristic
278C42C4⋊Dic4311yescharacteristic
279C42C4⋊Dic4311yescharacteristic
280C42C4⋊Dic4311yescharacteristic
281C42C4⋊Dic4311yescharacteristic
282C42(C2×D43)⋊C411yescharacteristic
283C42(C2×D43)⋊C411yescharacteristic
284C42(C2×D43)⋊C411yescharacteristic
285C42(C2×D43)⋊C411yescharacteristic
286C42C22⋊Dic4311yescharacteristic
287C42C22⋊Dic4311yescharacteristic
288C42C22⋊Dic4311yescharacteristic
289C42C22⋊Dic4311yescharacteristic
290C23—22no—
291C23—41no—
292C23—41no—
293C23C2×C4×Dic4311yescharacteristic
294C23C2×(C2×D43)⋊C411yescharacteristic
295C23C2×Dic43⋊C411yescharacteristic
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—1724no—
315C2×C4—1724no—
316C2×C4—1724no—
317C2×C4C43⋊#9511yescharacteristic
318C2×C4C43⋊#9511yescharacteristic
319C2×C4C43⋊#9511yescharacteristic
320C2×C4C43⋊#9511yescharacteristic
321C2×C4C43⋊#9511yescharacteristic
322C2×C4C43⋊#9511yescharacteristic
323C2×C4C43⋊#9511yescharacteristic
324C2×C4C43⋊#9511yescharacteristic
325C2×C4C2×(C2×D43)⋊C411yescharacteristic
326C2×C4C2×C22⋊Dic4311yescharacteristic
327C2×C4C2×Dic43⋊C411yescharacteristic
328C2×C4C2×C4⋊Dic4311yescharacteristic
329C8—44no—
330C8—1724no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—44no—
340C22C2×C43⋊#9511yescharacteristic
341C22#1458288112yes—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—3444no—
353C4#1458267112yes—
354C4#1458287312yes—
355C2—22no—
356C2—41no—
357C2—41no—
358C2#1913432811yescharacteristic
359C2#1913433311yescharacteristic
360C2C2×#1458267111yescharacteristic
subgroupG/H
centerC22C2×C43⋊#95
commutatorC23×C43C2×C42
FrattiniC23×C4C22×D43
FittingC43×#2920C2
socleC22×C43C2×#95
prime radicalC24×C43C22×C4
cosocleC23×C4×C43C23
hypercenter#2920D43
hypocenterC43#8110
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
6. #14582956C4semidirect
8. #14582952C4semidirect
24. C43×#423C4semidirect
26. C4×M16×C43C4semidirect
195. #423Dic43semidirect
199. C4×M16Dic43semidirect
207. C43#8110semidirect

Maximal subgroups

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

subgroupindex
#191432282
#191369932
#191325002
C43×#29202
#811043