Finite Group Databasebeta

← #25081826

Subgroups — #25081826

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145720C211yesmaximal, characteristic, complemented
2C2×#14583189C211yesmaximal, characteristic, complemented
3#19143619C211yesmaximal, characteristic, complemented
4#19134002C214yesmaximal, complemented
5#19133968C214yesmaximal, complemented
6#19133367C211yesmaximal, characteristic, complemented
7#19133277C211yesmaximal, characteristic, complemented
8#19133244C211yesmaximal, characteristic, complemented
9C43×#3036C211yesmaximal, characteristic
10C2×#13063325C2211yescharacteristic
11#14583295C2212yescomplemented
12#14583245C2212yescomplemented
13#14583215—22no—
14#14583189—22no—
15#14583189—22no—
16#14583189C2214yes—
17D4×C43⋊C8—22no—
18D4×C43⋊C8C2214yes—
19#14582952C2211yescharacteristic
20#14582952C2211yescharacteristic
21C2×#13063256—21no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063246—21no—
24C2×C22⋊(C43⋊C8)—22no—
25#14582649C2214yescomplemented
26#14582647C2214yescomplemented
27#14582645C2212yescomplemented
28#14582643C2212yescomplemented
29C2×AGL(1,ℤ/8)×C43—21no—
30C43×#532C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C43×#463—22no—
33C43×#461C2212yes—
34C43×#459C2212yes—
35C43×#423C2211yescharacteristic
36C43×#417—21no—
37C22×Dic86—21no—
38C22×C43⋊C8—21no—
39C22×C43⋊C8—24no—
40#13063325—21no—
41#13063325—21no—
42#13063325—21no—
43#13063325C2312yes—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46#13063256—24no—
47#13063256—24no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)D412yes—
50C4⋊(C43⋊C8)C2312yes—
51C4⋊(C43⋊C8)C2312yes—
52#13063246—24no—
53#13063246—24no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—24no—
56C22⋊(C43⋊C8)D412yes—
57C4×C43⋊C8—21no—
58C4×C43⋊C8C2312yes—
59C2×#41×C43—21no—
60C22×D4×C43D411yescharacteristic
61C23×C4×C43—21no—
62AGL(1,ℤ/8)×C43—44no—
63C2×SD16×C43—22no—
64C2×D8×C43—22no—
65C2×M16×C43—21no—
66C4⋊Q8×C43C2311yescharacteristic
67#127×C43C2311yescharacteristic
68#124×C43—21no—
69#121×C43—21no—
70#121×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—21no—
75C4×D4×C43D412yes—
76C4×D4×C43C2312yes—
77C2×C4⋊C4×C43D411yescharacteristic
78C2×C22⋊C4×C43—21no—
79C2×C42×C43C2311yescharacteristic
80C4⋊C8×C43—21no—
81C4⋊C8×C43C2312yes—
82#103×C43—22no—
83#102×C43—22no—
84C24×C43—21no—
85#41×C43—42no—
86#41×C43—42no—
87C2×Q8×C43—21no—
88C2×D4×C43—21no—
89C2×D4×C43—22no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—41no—
94C2×D4×C43SD1614yes—
95C2×D4×C43C2×D412yes—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—41no—
100C22×C4×C43—82no—
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×Dic43—41no—
105C2×Dic86—22no—
106C2×Dic86—41no—
107C2×Dic86—82no—
108SD16×C43—44no—
109D8×C43—44no—
110M16×C43—42no—
111C2×C8×C43—22no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43C2×D412yes—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—22no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43#4111yescharacteristic
123C42×C43C2411yescharacteristic
124C4⋊Dic43—22no—
125C4⋊Dic43—22no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—42no—
131C2×C43⋊C8—84no—
132C2×C43⋊C8C2×D414yes—
133C23×C43—22no—
134C23×C43—24no—
135C23×C43—41no—
136C23×C43—81no—
137C23×C43—81no—
138C23×C43#12111yescharacteristic
139Q8×C43—41no—
140Q8×C43—41no—
141D4×C43—22no—
142D4×C43—24no—
143D4×C43—41no—
144D4×C43—41no—
145D4×C43—42no—
146D4×C43—81no—
147D4×C43—82no—
148D4×C43C2×SD1614yes—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—41no—
152C2×C4×C43—44no—
153C2×C4×C43—41no—
154C2×C4×C43—82no—
155C2×C4×C43—81no—
156C2×C4×C43—82no—
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43C2×SD1612yes—
161C2×C4×C43#13512yes—
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C2×#4111yescharacteristic
165C2×Dic43—42no—
166C2×Dic43—82no—
167Dic86—82no—
168Dic86—82no—
169C8×C43—42no—
170C43⋊C8—24no—
171C43⋊C8—42no—
172C43⋊C8—42no—
173#19391—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—24no—
177C22×C43—42no—
178C22×C43—42no—
179C22×C43—84no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43#46512yes—
184C22×C43C2×#12111yescharacteristic
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—42no—
189C4×C43—81no—
190C4×C43#46512yes—
191C4×C43C22×SD1611yescharacteristic
192C4×C43C2×#13511yescharacteristic
193C4×C43#57712yes—
194Dic43—82no—
195#3227—431no—
196C2×#476—431no—
197#3036D4311yescharacteristic
198#2972—431no—
199#1677—434no—
200#1671—434no—
201#1570—431no—
202#1548—431no—
203#1540—431no—
204C2×C43—22no—
205C2×C43—44no—
206C2×C43—161no—
207C2×C43#304211yescharacteristic
208C2×C43C2×#46511yescharacteristic
209C2×C43#306811yescharacteristic
210C2×AGL(1,ℤ/8)—21no—
211#532C2×D4311yescharacteristic
212C2×C4⋊Q8—431no—
213C2×C4×D4C2×D4311yescharacteristic
214#498—432no—
215#486—432no—
216#481—862no—
217#476—434no—
218#476—862no—
219#476—862no—
220#463—22no—
221#461C2×D4312yes—
222#459C2×D4312yes—
223C8×D4—434no—
224C8×D4—862no—
225#431—431no—
226#431—431no—
227C2×#106—861no—
228#423C2×D4311yescharacteristic
229C2×C4⋊C8—431no—
230#417—21no—
231C2×#102—861no—
232C2×C22⋊C8—862no—
233#334—434no—
234#333—434no—
235#332—432no—
236#331—432no—
237C43#1939111yescharacteristic, complemented, Sylow
238C2×#41—21no—
239C22×Q8—861no—
240C22×D4C22⋊D4311yescharacteristic
241C23×C4—21no—
242AGL(1,ℤ/8)—44no—
243C2×SD16—22no—
244C2×D8—22no—
245C2×M16—21no—
246C22×C8—864no—
247C22×C8—861no—
248C4⋊Q8—432no—
249C4⋊Q8—861no—
250C4⋊Q8—861no—
251C4⋊Q8—861no—
252C4⋊Q8C22×D4311yescharacteristic
253#127C22×D4311yescharacteristic
254#124—21no—
255#121—21no—
256#121—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4C22⋊D4312yes—
262C4×D4C22×D4312yes—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4C22⋊D4311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C22×D4311yescharacteristic
268#106—864no—
269#106—864no—
270C4⋊C8—21no—
271C4⋊C8—432no—
272C4⋊C8—432no—
273C4⋊C8—432no—
274C4⋊C8—861no—
275C4⋊C8C22×D4312yes—
276#103—22no—
277#102—22no—
278#102—864no—
279#102—864no—
280C22⋊C8—432no—
281C22⋊C8—864no—
282C22⋊C8—861no—
283C4×C8—432no—
284C4×C8—861no—
285C24—21no—
286#41—42no—
287#41—42no—
288C2×Q8—21no—
289C2×Q8—862no—
290C2×Q8—3442no—
291C2×Q8—1721no—
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4#1062188314yes—
299C2×D4C2×C22⋊D4312yes—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—82no—
305C22×C4—1721no—
306C22×C4D4×D4311yescharacteristic
307C22×C4#1062190011yescharacteristic
308C22×C4C2×C22⋊D4311yescharacteristic
309SD16—44no—
310D8—44no—
311M16—42no—
312C2×C8—22no—
313C2×C8—434no—
314C2×C8—862no—
315C2×C8—862no—
316C2×C8—3444no—
317C2×C8—1722no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—862no—
322C4⋊C4—862no—
323C4⋊C4—1721no—
324C4⋊C4—1721no—
325C4⋊C4C2×C22⋊D4312yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C42D4×D4311yescharacteristic
331C42#1062190011yescharacteristic
332C42C2×C22⋊D4311yescharacteristic
333C42C23×D4311yescharacteristic
334C23—22no—
335C23—24no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23#1306329711yescharacteristic
340Q8—41no—
341Q8—41no—
342Q8—3442no—
343Q8—3442no—
344D4—24no—
345D4—22no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—82no—
351D4C2×#1062188314yes—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—41no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—3442no—
361C2×C4—1722no—
362C2×C4#1306329711yescharacteristic
363C2×C4#1306329711yescharacteristic
364C2×C4#1306329711yescharacteristic
365C2×C4C2×#1062188312yes—
366C2×C4#1306334512yes—
367C2×C4C2×D4×D4311yescharacteristic
368C2×C4C22×C22⋊D4311yescharacteristic
369C2×C4C2×#1062190011yescharacteristic
370C8—42no—
371C8—864no—
372C8—1722no—
373C8—1722no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22#1458312612yes—
384C22C2×#1306329711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—81no—
390C4—3442no—
391C4#1458312612yes—
392C4C22×#1062188311yescharacteristic
393C4C2×#1306334511yescharacteristic
394C4#1458370912yes—
395C2—22no—
396C2—44no—
397C2—161no—
398C2#1914410911yescharacteristic
399C2C2×#1458312611yescharacteristic
400C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3036C2
socleC22×C43C2×#121
hypercenter#3036D43
hypocenterC43#19391
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #19145720C2semidirect
2. C2×#14583189C2semidirect
3. #19143619C2semidirect
4. #19134002C2semidirect
5. #19133968C2semidirect
6. #19133367C2semidirect
7. #19133277C2semidirect
8. #19133244C2semidirect
11. #14583295C22semidirect
12. #14583245C22semidirect
25. #14582649C22semidirect
26. #14582647C22semidirect
27. #14582645C22semidirect
28. #14582643C22semidirect
237. C43#19391semidirect

Maximal subgroups

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

subgroupindex
#191457202
C2×#145831892
#191436192
#191340022
#191339682
#191333672
#191332772
#191332442
C43×#30362
#1939143