Finite Group Databasebeta

← #25081821

Subgroups — #25081821

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#19145723C211yesmaximal, characteristic, complemented
2#19144059C211yesmaximal, characteristic
3#19143619C211yesmaximal, characteristic, complemented
4#19134006C214yesmaximal, complemented
5#19133972C214yesmaximal, complemented
6#19133365C211yesmaximal, characteristic, complemented
7#19133276C211yesmaximal, characteristic, complemented
8#19133245C211yesmaximal, characteristic, complemented
9C2×C43×#476C211yesmaximal, characteristic, complemented
10C2×#13063351—21no—
11#14583449C2211yescharacteristic
12#14583295C2212yescomplemented
13#14583247C2212yescomplemented
14#14583217—22no—
15#14583186—22no—
16#14583114—22no—
17#14583104C2212yes—
18#14583094C2212yes—
19D4×C43⋊C8—22no—
20D4×C43⋊C8C2214yes—
21#14582952C2211yescharacteristic
22#14582952C2211yescharacteristic
23#14582923C2211yescharacteristic
24#14582898—21no—
25C2×C22⋊(C43⋊C8)—22no—
26#14582649C2214yescomplemented
27#14582648C2214yescomplemented
28#14582646C2212yescomplemented
29#14582642C2212yescomplemented
30C2×C4⋊Q8×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C43×#476—22no—
33C43×#476C2214yes—
34C2×#106×C43—21no—
35C2×C4⋊C8×C43C2211yescharacteristic
36C2×#102×C43—21no—
37C2×#10621898—21no—
38#13063351—44no—
39C2×#10621883—22no—
40C2×#10621882—22no—
41C2×#10621877—21no—
42C22×C43⋊C8—24no—
43#13063325C2311yescharacteristic
44#13063322C2311yescharacteristic
45#13063313—21no—
46#13063299—21no—
47#13063299—21no—
48C4×D172—21no—
49C4×D172—21no—
50#13063256—24no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)D412yes—
53C4⋊(C43⋊C8)C2312yes—
54C4⋊(C43⋊C8)C2312yes—
55#13063248—22no—
56#13063245—22no—
57#13063245—24no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—24no—
60C22⋊(C43⋊C8)D412yes—
61C4×C43⋊C8—21no—
62C4×C43⋊C8C2312yes—
63C22×Q8×C43—21no—
64C22×D4×C43D411yescharacteristic
65C23×C4×C43—21no—
66C22×C8×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43—21no—
70C4⋊Q8×C43C2312yes—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43D412yes—
74C4×D4×C43C2312yes—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43D411yescharacteristic
78C2×C22⋊C4×C43—21no—
79C2×C42×C43C2311yescharacteristic
80#106×C43—24no—
81C4⋊C8×C43—21no—
82C4⋊C8×C43C2312yes—
83#102×C43—24no—
84C24×C43—21no—
85C2×Q8×C43—22no—
86C2×Q8×C43—41no—
87C2×Q8×C43—82no—
88C2×D4×C43—21no—
89C2×D4×C43—22no—
90C2×D4×C43SD1614yes—
91C2×D4×C43C2×D412yes—
92C22×C4×C43—22no—
93C22×C4×C43—22no—
94C22×C4×C43—21no—
95C22×C4×C43—41no—
96C22×C4×C43—82no—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—41no—
101#10621898—42no—
102#10621898—42no—
103C2×D172—21no—
104C2×D172—21no—
105C2×D172—21no—
106C2×C4×D43—41no—
107C2×Dic86—21no—
108C2×C8×C43—22no—
109C2×C8×C43—42no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43C2×D412yes—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—22no—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C42×C43C2411yescharacteristic
122#10621883—44no—
123#10621882—44no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128#10621877—42no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—84no—
132C2×C43⋊C8C2×D414yes—
133C23×C43—22no—
134C23×C43—24no—
135C23×C43—81no—
136C23×C43—81no—
137C23×C43#12111yescharacteristic
138C22×D43—41no—
139Q8×C43—82no—
140Q8×C43—82no—
141D4×C43—22no—
142D4×C43—24no—
143D4×C43C2×SD1614yes—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—44no—
148C2×C4×C43—42no—
149C2×C4×C43—82no—
150C2×C4×C43—81no—
151C2×C4×C43—82no—
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43C2×SD1612yes—
156C2×C4×C43#13512yes—
157C2×C4×C43C22×D411yescharacteristic
158C2×C4×C43C22×D411yescharacteristic
159C2×C4×C43C2×#4111yescharacteristic
160C22⋊D43—82no—
161C2×Dic43—41no—
162D172—41no—
163D172—41no—
164D172—42no—
165D172—81no—
166C4×D43—82no—
167Dic86—41no—
168Dic86—41no—
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#46512yes—
181C22×C43C2×#12111yescharacteristic
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—42no—
189C4×C43—82no—
190C4×C43#46512yes—
191C4×C43C22×SD1611yescharacteristic
192C4×C43C2×#13511yescharacteristic
193C4×C43#57712yes—
194Dic43—81no—
195#3227—431no—
196C2×#476D4311yescharacteristic, complemented
197#3036—431no—
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#304211yescharacteristic
207C2×C43C2×#46511yescharacteristic
208C2×C43#306811yescharacteristic
209D43—161no—
210C2×AGL(1,ℤ/8)—861no—
211#532—431no—
212C2×C4⋊Q8C2×D4311yescharacteristic
213C2×C4×D4C2×D4311yescharacteristic
214#498—432no—
215#486—432no—
216#481—862no—
217#476—22no—
218#476—862no—
219#476C2×D4314yes—
220#463—862no—
221#461—432no—
222#459—432no—
223C8×D4—434no—
224C8×D4—862no—
225#431—431no—
226#431—431no—
227C2×#106—21no—
228#423—431no—
229C2×C4⋊C8C2×D4311yescharacteristic
230#417—861no—
231C2×#102—21no—
232C2×C22⋊C8—862no—
233#334—434no—
234#333—434no—
235#332—432no—
236#331—432no—
237C43#1939111yescharacteristic, complemented, Sylow
238C2×#41—861no—
239C22×Q8—21no—
240C22×D4C22⋊D4311yescharacteristic
241C23×C4—21no—
242AGL(1,ℤ/8)—1724no—
243C2×SD16—862no—
244C2×D8—862no—
245C2×M16—861no—
246C22×C8—21no—
247C22×C8—864no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—431no—
252C4⋊Q8C22×D4312yes—
253#127—431no—
254#124—861no—
255#121—861no—
256#121—861no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—861no—
260C4×D4—861no—
261C4×D4C22⋊D4312yes—
262C4×D4C22×D4312yes—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C22⋊D4311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C22×D4311yescharacteristic
268#106—24no—
269#106—864no—
270C4⋊C8—21no—
271C4⋊C8—432no—
272C4⋊C8—432no—
273C4⋊C8—432no—
274C4⋊C8—861no—
275C4⋊C8C22×D4312yes—
276#103—862no—
277#102—24no—
278#102—864no—
279#102—862no—
280C22⋊C8—432no—
281C22⋊C8—864no—
282C22⋊C8—861no—
283C4×C8—432no—
284C4×C8—861no—
285C24—21no—
286#41—1722no—
287#41—1722no—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—82no—
291C2×Q8—861no—
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—1721no—
298C2×D4#1062188414yes—
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—1724no—
310D8—1724no—
311M16—1722no—
312C2×C8—22no—
313C2×C8—42no—
314C2×C8—434no—
315C2×C8—862no—
316C2×C8—862no—
317C2×C8—3444no—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4C2×C22⋊D4312yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—1721no—
329C22⋊C4—1721no—
330C42D4×D4311yescharacteristic
331C42#1062190011yescharacteristic
332C42C2×C22⋊D4311yescharacteristic
333C42C23×D4311yescharacteristic
334C23—22no—
335C23—24no—
336C23—81no—
337C23—81no—
338C23—1721no—
339C23#1306329711yescharacteristic
340Q8—82no—
341Q8—82no—
342Q8—1721no—
343Q8—1721no—
344D4—24no—
345D4—22no—
346D4—3441no—
347D4—3442no—
348D4—1721no—
349D4—1721no—
350D4—1722no—
351D4C2×#1062188414yes—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—3442no—
361C2×C4—1721no—
362C2×C4#1306329711yescharacteristic
363C2×C4#1306329711yescharacteristic
364C2×C4#1306329711yescharacteristic
365C2×C4C2×#1062188412yes—
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—3441no—
381C22—3441no—
382C22—3441no—
383C22#1458313012yes—
384C22C2×#1306329711yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—82no—
390C4—3441no—
391C4#1458313012yes—
392C4C22×#1062188411yescharacteristic
393C4C2×#1306334511yescharacteristic
394C4#1458370512yes—
395C2—22no—
396C2—44no—
397C2—6881no—
398C2#1914410411yescharacteristic
399C2C2×#1458313011yescharacteristic
400C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#476C2
socleC22×C43C2×#121
prime radical#19144059C2
hypercenterC2×#476D43
hypocenterC43#19391
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #19145723C2semidirect
3. #19143619C2semidirect
4. #19134006C2semidirect
5. #19133972C2semidirect
6. #19133365C2semidirect
7. #19133276C2semidirect
8. #19133245C2semidirect
9. C2×C43×#476C2semidirect
12. #14583295C22semidirect
13. #14583247C22semidirect
26. #14582649C22semidirect
27. #14582648C22semidirect
28. #14582646C22semidirect
29. #14582642C22semidirect
196. C2×#476D43semidirect
237. C43#19391semidirect

Maximal subgroups

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

subgroupindex
#191457232
#191440592
#191436192
#191340062
#191339722
#191333652
#191332762
#191332452
C2×C43×#4762
#1939143