Finite Group Databasebeta

← #25105949

Subgroups — #25105949

Order 11008.

1990 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582956C211yesmaximal, characteristic, complemented
2#19136993C211yesmaximal, characteristic, complemented
3#19135523C214yesmaximal, complemented
4#19135420C214yesmaximal, complemented
5#19134526C214yesmaximal, complemented
6C22×#127×C43C211yesmaximal, characteristic
7#14582956—24no—
8C2×C4⋊(C43⋊C8)C2212yescomplemented
9C2×#13063246C22116yescomplemented
10C2×C22⋊(C43⋊C8)C2212yes—
11C2×#13063236C2212yescomplemented
12#14582767—21no—
13#14582765C2212yescomplemented
14#14582762—21no—
15#14582759C2212yes—
16C4×C4⋊Dic43C2212yescomplemented
17C4×C22⋊Dic43—21no—
18#14582745—21no—
19C23×D4×C43—21no—
20C23×D4×C43—21no—
21C23×D4×C43C2212yes—
22C2×#127×C43—21no—
23C2×#127×C43—21no—
24C2×#127×C43—24no—
25C2×#127×C43C418yescomplemented
26C2×#127×C43C2212yes—
27C2×#127×C43C2212yes—
28C22×C42×C43C2211yescharacteristic
29C22×C43⋊C8C2314yes—
30C2×C4⋊Dic43C2314yes—
31C2×C22⋊Dic43—22no—
32C2×C4×Dic43—22no—
33C4⋊(C43⋊C8)—24no—
34#13063246—416no—
35C22⋊(C43⋊C8)—24no—
36#13063236—24no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C43⋊#95—22no—
40C43⋊#95—22no—
41C25×C43—22no—
42C22×D4×C43—28no—
43C22×D4×C43—28no—
44C22×D4×C43—24no—
45C22×D4×C43—22no—
46C22×D4×C43—22no—
47C22×D4×C43—22no—
48C22×D4×C43—22no—
49C22×D4×C43—22no—
50C22×D4×C43—48no—
51C22×D4×C43—48no—
52C22×D4×C43—48no—
53C22×D4×C43C2×C418yes—
54C22×D4×C43C2314yes—
55C23×C4×C43D411yescharacteristic
56C23×C4×C43D411yescharacteristic
57C23×C4×C43C2311yescharacteristic
58#127×C43—28no—
59#127×C43—28no—
60#127×C43—24no—
61#127×C43—24no—
62#127×C43C2×C418yes—
63#127×C43C2×C418yes—
64C2×C42×C43C2×C414yes—
65C2×C42×C43D411yescharacteristic
66C2×C42×C43D411yescharacteristic
67C2×C42×C43D414yes—
68C2×C42×C43C2311yescharacteristic
69C2×C42×C43C2311yescharacteristic
70C24×C43—28no—
71C24×C43—24no—
72C24×C43—48no—
73C24×C43—48no—
74C24×C43—48no—
75C24×C43C2×D411yescharacteristic
76C2×D4×C43—28no—
77C2×D4×C43—28no—
78C2×D4×C43—28no—
79C2×D4×C43—28no—
80C2×D4×C43—28no—
81C2×D4×C43—24no—
82C2×D4×C43—216no—
83C2×D4×C43—416no—
84C2×D4×C43—416no—
85C2×D4×C43—432no—
86C2×D4×C43—48no—
87C2×D4×C43—48no—
88C2×D4×C43—48no—
89C2×D4×C43—48no—
90C2×D4×C43—432no—
91C2×D4×C43—48no—
92C2×D4×C43C22×C418yes—
93C22×C4×C43—24no—
94C22×C4×C43—24no—
95C22×C4×C43—24no—
96C22×C4×C43C22⋊C414yes—
97C22×C4×C43C22⋊C414yes—
98C22×C4×C43C22×C412yes—
99C22×C4×C43C2×D412yes—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2411yescharacteristic
106C22×Dic43—24no—
107C42×C43C22⋊C414yes—
108C42×C43C22⋊C414yes—
109C42×C43C22×C412yes—
110C42×C43C22×C412yes—
111C42×C43C2×D412yes—
112C42×C43C2×D412yes—
113C22⋊Dic43—44no—
114C4⋊Dic43—28no—
115C4×Dic43—44no—
116C2×C43⋊C8—24no—
117C2×C43⋊C8—28no—
118C23×C43—22no—
119C23×C43—22no—
120C23×C43—28no—
121C23×C43—416no—
122C23×C43—416no—
123C23×C43—48no—
124C23×C43—48no—
125C23×C43—48no—
126C23×C43—416no—
127C23×C43—832no—
128C23×C43C2×C22⋊C412yes—
129C23×C43AGL(1,ℤ/8)14yes—
130C23×C43C22×D411yescharacteristic
131D4×C43—216no—
132D4×C43—416no—
133D4×C43—416no—
134D4×C43—416no—
135D4×C43—416no—
136D4×C43—48no—
137D4×C43—416no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—28no—
143C2×C4×C43—24no—
144C2×C4×C43—24no—
145C2×C4×C43—28no—
146C2×C4×C43C2×C22⋊C412yes—
147C2×C4×C43C2×C22⋊C412yes—
148C2×C4×C43C2×C22⋊C412yes—
149C2×C4×C43C2×C22⋊C412yes—
150C2×C4×C43C2×C22⋊C412yes—
151C2×C4×C43AGL(1,ℤ/8)14yes—
152C2×C4×C43C23×C411yescharacteristic
153C2×C4×C43C22×D411yescharacteristic
154C2×C4×C43H(5,𝔽2)14yes—
155C2×Dic43—44no—
156C2×Dic43—44no—
157C2×Dic43—44no—
158C43⋊C8—44no—
159#21810—431nomaximal, Sylow
160C22×C43—22no—
161C22×C43—22no—
162C22×C43—28no—
163C22×C43—48no—
164C22×C43—48no—
165C22×C43—48no—
166C22×C43—832no—
167C22×C43—816no—
168C22×C43#41814yes—
169C22×C43C22×C22⋊C411yescharacteristic
170C22×C43#53512yes—
171C22×C43C2×AGL(1,ℤ/8)12yes—
172C22×C43C2×AGL(1,ℤ/8)12yes—
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—22no—
176C4×C43—22no—
177C4×C43#41814yes—
178C4×C43#51812yes—
179C4×C43#53512yes—
180Dic43—84no—
181C22×#127D4311yescharacteristic
182C2×#432—431no—
183#2283—431no—
184#1982—434no—
185#1961—434no—
186#1786—434no—
187C2×C43—24no—
188C2×C43—88no—
189C2×C43#230911yescharacteristic
190C2×C43C2×#41811yescharacteristic
191C2×C43C2×#41811yescharacteristic
192C2×C43#321714yes—
193C23×D4—21no—
194C23×D4—21no—
195C23×D4C2×D4312yes—
196C2×#127—21no—
197C2×#127—21no—
198C2×#127—24no—
199C2×#127Dic4318yescomplemented
200C2×#127C2×D4312yes—
201C2×#127C2×D4312yes—
202C22×C42C2×D4311yescharacteristic
203#432—864no—
204C2×C4⋊C8—432no—
205C2×#102—4316no—
206C2×C22⋊C8—432no—
207C2×#97—432no—
208#383—861no—
209#382—432no—
210#381—861no—
211#380—432no—
212C4×C4⋊C4—432no—
213C4×C22⋊C4—861no—
214#376—861no—
215C43#2181011yescharacteristic, complemented, Sylow
216C25—22no—
217C22×D4—28no—
218C22×D4—28no—
219C22×D4—22no—
220C22×D4—24no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—48no—
226C22×D4—48no—
227C22×D4—48no—
228C22×D4C2×Dic4318yes—
229C22×D4C22×D4314yes—
230C23×C4C22⋊D4311yescharacteristic
231C23×C4C22⋊D4311yescharacteristic
232C23×C4C22×D4311yescharacteristic
233C22×C8—434no—
234#127—28no—
235#127—28no—
236#127—24no—
237#127—24no—
238#127C2×Dic4318yes—
239#127C2×Dic4318yes—
240C2×C4⋊C4—434no—
241C2×C22⋊C4—862no—
242C2×C42—862no—
243C2×C42C2×Dic4314yes—
244C2×C42C22⋊D4311yescharacteristic
245C2×C42C22⋊D4311yescharacteristic
246C2×C42C22⋊D4314yes—
247C2×C42C22×D4311yescharacteristic
248C2×C42C22×D4311yescharacteristic
249C4⋊C8—864no—
250#102—17216no—
251C22⋊C8—864no—
252#97—864no—
253#95—862no—
254#95—862no—
255#95—862no—
256#95—862no—
257C24—28no—
258C24—24no—
259C24—48no—
260C24—48no—
261C24—48no—
262C24C2×C22⋊D4311yescharacteristic
263C2×D4—28no—
264C2×D4—28no—
265C2×D4—28no—
266C2×D4—28no—
267C2×D4—28no—
268C2×D4—24no—
269C2×D4—216no—
270C2×D4—416no—
271C2×D4—432no—
272C2×D4—48no—
273C2×D4—48no—
274C2×D4—48no—
275C2×D4—48no—
276C2×D4—432no—
277C2×D4—416no—
278C2×D4—48no—
279C2×D4C22×Dic4318yes—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—864no—
284C22×C4C22⋊Dic4314yes—
285C22×C4C22⋊Dic4314yes—
286C22×C4C22×Dic4312yes—
287C22×C4C2×C22⋊D4311yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289C22×C4C2×C22⋊D4311yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291C22×C4C2×C22⋊D4312yes—
292C22×C4C2×C22⋊D4311yescharacteristic
293C22×C4C23×D4311yescharacteristic
294C2×C8—864no—
295C2×C8—868no—
296C4⋊C4—868no—
297C22⋊C4—1724no—
298C42—1724no—
299C42C22⋊Dic4314yes—
300C42C22⋊Dic4314yes—
301C42C22×Dic4312yes—
302C42C22×Dic4312yes—
303C42C2×C22⋊D4312yes—
304C42C2×C22⋊D4312yes—
305C23—22no—
306C23—22no—
307C23—28no—
308C23—416no—
309C23—416no—
310C23—416no—
311C23—48no—
312C23—48no—
313C23—48no—
314C23—832no—
315C23C2×C22⋊Dic4312yes—
316C23#1306335114yes—
317C23C22×C22⋊D4311yescharacteristic
318D4—216no—
319D4—416no—
320D4—416no—
321D4—416no—
322D4—416no—
323D4—416no—
324D4—48no—
325C2×C4—28no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—24no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—1724no—
334C2×C4—1724no—
335C2×C4—1724no—
336C2×C4C2×C22⋊Dic4312yes—
337C2×C4C2×C22⋊Dic4312yes—
338C2×C4C2×C22⋊Dic4312yes—
339C2×C4C2×C22⋊Dic4312yes—
340C2×C4C2×C22⋊Dic4312yes—
341C2×C4#1306335114yes—
342C2×C4C23×Dic4311yescharacteristic
343C2×C4C22×C22⋊D4311yescharacteristic
344C2×C4#1306337014yes—
345C8—1724no—
346C22—28no—
347C22—22no—
348C22—22no—
349C22—48no—
350C22—48no—
351C22—48no—
352C22—832no—
353C22—816no—
354C22#1458290414yes—
355C22C22×C22⋊Dic4311yescharacteristic
356C22#1458346612yes—
357C22C2×#1306335112yes—
358C22C2×#1306335112yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—3444no—
364C4#1458290414yes—
365C4#1458337412yes—
366C4#1458346612yes—
367C2—24no—
368C2—88no—
369C2#1913717711yescharacteristic
370C2C2×#1458290411yescharacteristic
371C2C2×#1458290411yescharacteristic
372C2#1914561314yes—
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC22×#127×C43C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC22×#127D43
hypocenterC43#21810
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C2×#14582956C2semidirect
2. #19136993C2semidirect
3. #19135523C2semidirect
4. #19135420C2semidirect
5. #19134526C2semidirect
8. C2×C4⋊(C43⋊C8)C22semidirect
9. C2×#13063246C22semidirect
11. C2×#13063236C22semidirect
13. #14582765C22semidirect
16. C4×C4⋊Dic43C22semidirect
25. C2×#127×C43C4semidirect
199. C2×#127Dic43semidirect
215. C43#21810semidirect

Maximal subgroups

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

subgroupindex
C2×#145829562
#191369932
#191355232
#191354202
#191345262
C22×#127×C432
#2181043