Finite Group Databasebeta

← #24995918

Subgroups — #24995918

Order 11008.

526 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583245C211yesmaximal, characteristic
2#19135523C211yesmaximal, characteristic
3#19135517C211yesmaximal, characteristic, complemented
4#19134465C211yesmaximal, characteristic, complemented
5C2×#14582649C211yesmaximal, characteristic, complemented
6C2×#14582644C211yesmaximal, characteristic, complemented
7C2×C43×#331C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583245—22no—
10#14583245C414yescomplemented
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063250—22no—
13C2×#13063246—21no—
14C2×#13063246—21no—
15C2×#13063246—22no—
16C2×#13063235—21no—
17C2×C4×C43⋊C8C2211yescharacteristic
18C4×C4⋊Dic43C2211yescharacteristic
19#14582653—21no—
20#14582649—22no—
21#14582644—22no—
22C2×#127×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C43×#331—22no—
26C22×Dic86—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8D411yescharacteristic
29C22×C43⋊C8D411yescharacteristic
30#13063325—21no—
31#13063325—21no—
32#13063325—21no—
33#13063325C2×C412yes—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D412yes—
37C2×C4×Dic43—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40#13063250—44no—
41#13063246—24no—
42#13063246—24no—
43#13063246—44no—
44#13063235—42no—
45C4×C43⋊C8C2×C412yes—
46C4×C43⋊C8D412yes—
47C43⋊#95—21no—
48C22×D4×C43—21no—
49C22×D4×C43—21no—
50C22×D4×C43—21no—
51C22×C8×C43—21no—
52C22×C8×C43—21no—
53#127×C43—21no—
54#127×C43—21no—
55#127×C43—21no—
56#127×C43C2×C412yes—
57C2×C42×C43C2311yescharacteristic
58C4⋊C8×C43—21no—
59C4⋊C8×C43—21no—
60C4⋊C8×C43—21no—
61C4⋊C8×C43D412yes—
62C24×C43—41no—
63C2×D4×C43—22no—
64C2×D4×C43—22no—
65C2×D4×C43—22no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—42no—
73C2×D4×C43—42no—
74C2×D4×C43—41no—
75C2×D4×C43—82no—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×Dic43—22no—
80C22×Dic43—41no—
81C2×Dic86—22no—
82C2×Dic86—42no—
83C2×Dic86—42no—
84C2×Dic86—41no—
85C2×C8×C43—22no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—42no—
90C42×C43C22×C411yescharacteristic
91C42×C43C2×D411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43#4111yescharacteristic
94C4⋊Dic43—22no—
95C4⋊Dic43—22no—
96C4⋊Dic43—22no—
97C4⋊Dic43—22no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100C4×Dic43—41no—
101C4×Dic43—41no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—42no—
108C2×C43⋊C8C22⋊C412yes—
109C2×C43⋊C8C22⋊C412yes—
110C23×C43—42no—
111C23×C43—81no—
112C23×C43—81no—
113C23×C43—82no—
114C23×C43—82no—
115C23×C43#12111yescharacteristic
116D4×C43—42no—
117D4×C43—42no—
118D4×C43—44no—
119D4×C43—82no—
120D4×C43—82no—
121D4×C43—81no—
122D4×C43—81no—
123D4×C43—81no—
124D4×C43—81no—
125C2×C4×C43—22no—
126C2×C4×C43C2×C22⋊C411yescharacteristic
127C2×C4×C43C4×D411yescharacteristic
128C2×C4×C43C4×D411yescharacteristic
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12411yescharacteristic
131C2×C4×C43#12711yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)12yes—
136C2×C4×C43AGL(1,ℤ/8)12yes—
137C2×C4×C43#13711yescharacteristic
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43—42no—
142C2×Dic43—82no—
143Dic86—44no—
144Dic86—81no—
145Dic86—81no—
146C8×C43—42no—
147C8×C43—81no—
148C43⋊C8—22no—
149C43⋊C8—22no—
150C43⋊C8—81no—
151#9746—431nomaximal, Sylow
152C22×C43—82no—
153C22×C43—82no—
154C22×C43—82no—
155C22×C43—162no—
156C22×C43—162no—
157C22×C43#39011yescharacteristic
158C22×C43#46311yescharacteristic
159C22×C43#46411yescharacteristic
160C22×C43#46912yes—
161C22×C43#47112yes—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43#41611yescharacteristic
165C4×C43#41711yescharacteristic
166C4×C43#44212yes—
167C4×C43#46311yescharacteristic
168C4×C43#46411yescharacteristic
169C4×C43#49611yescharacteristic
170C4×C43#49611yescharacteristic
171Dic43—82no—
172Dic43—82no—
173C2×#486—431no—
174#1982—431no—
175#1981—431no—
176#1770—431no—
177C2×#334—431no—
178C2×#332—431no—
179C2×#331D4311yescharacteristic
180C2×C43—162no—
181C2×C43#170112yes—
182C2×C43#170212yes—
183C2×C43#197211yescharacteristic
184C2×C43#197711yescharacteristic
185C2×C43#198311yescharacteristic
186C2×C4⋊Q8—431no—
187C2×#127C2×D4311yescharacteristic
188#486—434no—
189#486—862no—
190C2×C4⋊C8—431no—
191C2×C4⋊C8C2×D4311yescharacteristic
192C2×C4⋊C8C2×D4311yescharacteristic
193C2×#103—862no—
194C2×#102—861no—
195C2×#102—861no—
196C2×#102—862no—
197C2×#97—861no—
198C2×C4×C8—431no—
199C4×C4⋊C4—431no—
200#336—861no—
201#334—862no—
202#332—862no—
203#331—22no—
204C43#974611yescharacteristic, complemented, Sylow
205C22×Q8—861no—
206C22×D4—21no—
207C22×D4—21no—
208C22×D4—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—431no—
212C22×C8—431no—
213C22×C8—861no—
214C4⋊Q8—432no—
215C4⋊Q8—861no—
216C4⋊Q8—861no—
217C4⋊Q8—861no—
218#127—21no—
219#127—21no—
220#127—21no—
221#127C4×D4312yes—
222C2×C4⋊C4—432no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C42—861no—
226C2×C42C22×D4311yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—861no—
231C4⋊C8—861no—
232C4⋊C8C22⋊D4312yes—
233#103—1724no—
234#102—864no—
235#102—864no—
236#102—1724no—
237#97—1722no—
238C4×C8—432no—
239C4×C8—432no—
240#95—861no—
241C24—41no—
242C2×Q8—862no—
243C2×Q8—1722no—
244C2×Q8—1722no—
245C2×Q8—1721no—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—22no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—41no—
258C2×D4—82no—
259C22×C4—862no—
260C22×C4—1721no—
261C22×C4#1062189811yescharacteristic
262C22×C4D4×D4311yescharacteristic
263C22×C4D4×D4311yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—42no—
269C2×C8—432no—
270C2×C8—432no—
271C2×C8—861no—
272C2×C8—861no—
273C2×C8—861no—
274C2×C8—861no—
275C2×C8—1721no—
276C2×C8—1722no—
277C4⋊C4—862no—
278C4⋊C4—862no—
279C4⋊C4—862no—
280C4⋊C4—862no—
281C4⋊C4—1721no—
282C4⋊C4—1721no—
283C42—1721no—
284C42—1721no—
285C42C2×C4×D4311yescharacteristic
286C42D4×D4311yescharacteristic
287C42#1062190011yescharacteristic
288C42C2×C22⋊D4311yescharacteristic
289C23—42no—
290C23—81no—
291C23—81no—
292C23—82no—
293C23—82no—
294C23#1306329811yescharacteristic
295Q8—3441no—
296Q8—3441no—
297Q8—1724no—
298D4—42no—
299D4—42no—
300D4—44no—
301D4—82no—
302D4—82no—
303D4—81no—
304D4—81no—
305D4—81no—
306D4—81no—
307C2×C4—22no—
308C2×C4—3442no—
309C2×C4—1722no—
310C2×C4—1722no—
311C2×C4—1722no—
312C2×C4—1722no—
313C2×C4C22⋊C4×D4311yescharacteristic
314C2×C4(C22⋊D43)⋊C411yescharacteristic
315C2×C4C4×C22⋊D4311yescharacteristic
316C2×C4#1306329711yescharacteristic
317C2×C4#1306331111yescharacteristic
318C2×C4#1306332111yescharacteristic
319C2×C4#1306334411yescharacteristic
320C2×C4#1306334611yescharacteristic
321C2×C4#1306334911yescharacteristic
322C2×C4#1306334912yes—
323C2×C4#1306335212yes—
324C2×C4#1306335411yescharacteristic
325C8—42no—
326C8—81no—
327C8—862no—
328C8—862no—
329C8—3441no—
330C22—82no—
331C22—82no—
332C22—82no—
333C22—162no—
334C22—162no—
335C22#1458279911yescharacteristic
336C22#1458311311yescharacteristic
337C22#1458312011yescharacteristic
338C22#1458315112yes—
339C22#1458316112yes—
340C4—21no—
341C4—21no—
342C4—3442no—
343C4—3442no—
344C4#1458289211yescharacteristic
345C4#1458289711yescharacteristic
346C4#1458300812yes—
347C4#1458311211yescharacteristic
348C4#1458311911yescharacteristic
349C4#1458328511yescharacteristic
350C4#1458328711yescharacteristic
351C2—162no—
352C2#1913415512yes—
353C2#1913416212yes—
354C2#1913546811yescharacteristic
355C2#1913549511yescharacteristic
356C2#1913552611yescharacteristic
subgroupG/H
centerC23#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#331C2
socleC23×C43#121
prime radicalC2×#127×C43C22
cosocleC2×C42×C43C23
hypercenterC2×#331D43
hypocenterC43#9746
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
3. #19135517C2semidirect
4. #19134465C2semidirect
5. C2×#14582649C2semidirect
6. C2×#14582644C2semidirect
10. #14583245C4semidirect
204. C43#9746semidirect

Maximal subgroups

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

subgroupindex
C2×#145832452
#191355232
#191355172
#191344652
C2×#145826492
C2×#145826442
C2×C43×#3312
#974643