Finite Group Databasebeta

← #25081867

Subgroups — #25081867

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145750C211yesmaximal, characteristic, complemented
2#19144690C211yesmaximal, characteristic
3#19144604C211yesmaximal, characteristic
4#19143618C211yesmaximal, characteristic
5#19134045C212yesmaximal, complemented
6#19134017C212yesmaximal, complemented
7#19133983C212yesmaximal, complemented
8#19133969C212yesmaximal, complemented
9#19133373C211yesmaximal, characteristic, complemented
10#19133303C211yesmaximal, characteristic, complemented
11C43×#1544C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13C2×C4×D172C2211yescharacteristic
14#14583302C2211yescharacteristic, complemented
15#14583295C2211yescharacteristic, complemented
16#14583249C2211yescharacteristic, complemented
17#14583249C2211yescharacteristic, complemented
18#14583237—22no—
19#14583232—21no—
20#14583230—21no—
21#14583206—22no—
22#14583190C2212yes—
23#14583176C2212yes—
24#14583105C2212yes—
25#14583101C2212yes—
26#14583052—21no—
27#14583049—21no—
28#14582997—22no—
29C4×#10621873—22no—
30C8×D172—22no—
31#14582964C2212yes—
32#14582964C2212yes—
33#14582956C2211yescharacteristic
34#14582952C2211yescharacteristic
35C22⋊C8×D43—22no—
36#14582651C2212yescomplemented
37#14582649C2212yescomplemented
38#14582647C2212yescomplemented
39#14582644C2212yescomplemented
40C43×#533C2211yescharacteristic
41C43×#431C2211yescharacteristic
42C43×#431C2211yescharacteristic
43C43×#332C2212yescomplemented
44C43×#332C2212yescomplemented
45C22×D172D411yescharacteristic
46C22×C4×D43—21no—
47C2×#10621873—22no—
48C2×#10621884—22no—
49C2×C8×D43—22no—
50C2×C8×D43—22no—
51#13063325C2311yescharacteristic
52#13063325C2311yescharacteristic
53#13063317—21no—
54#13063304—21no—
55#13063304—21no—
56C4×Dic86—21no—
57C4×Dic86—21no—
58C4×D172—21no—
59C4×D172—21no—
60C4×D172D412yes—
61C4×D172C2312yes—
62#13063284—21no—
63C2×C4⋊Dic43D411yescharacteristic
64C2×(C2×D43)⋊C4—21no—
65#13063258—22no—
66#13063258—22no—
67#13063257—22no—
68#13063256—22no—
69C4⋊(C43⋊C8)D412yes—
70C4⋊(C43⋊C8)C2312yes—
71#13063250—22no—
72#13063249—22no—
73#13063249—22no—
74#13063249—22no—
75#13063247—22no—
76#13063245—22no—
77C22⋊(C43⋊C8)—21no—
78C22⋊(C43⋊C8)D412yes—
79(C2×D43)⋊C8—22no—
80(C2×D43)⋊C8—22no—
81#13063236—21no—
82C4×C43⋊C8C2311yescharacteristic
83C4×C43⋊C8C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#125×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91#117×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C4⋊C8×C43C2312yes—
94C4⋊C8×C43C2312yes—
95C22⋊C8×C43—21no—
96C22⋊C8×C43—21no—
97C4×C8×C43—21no—
98C4×C8×C43—21no—
99C23×D43—21no—
100C2×Q8×C43—21no—
101C2×Q8×C43—21no—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C22×Dic43—21no—
106C2×D172—21no—
107C2×D172—24no—
108C2×D172C2×D412yes—
109C2×C4×D43—22no—
110C2×C4×D43—22no—
111C2×C4×D43—82no—
112C2×Dic86—21no—
113C2×Dic86—21no—
114C2×C8×C43—22no—
115C2×C8×C43—22no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C42×C43—41no—
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D411yescharacteristic
126C42×C43#4111yescharacteristic
127C42×C43C2411yescharacteristic
128C22⋊Dic43—41no—
129#10621884—44no—
130(C2×D43)⋊C4—22no—
131(C2×D43)⋊C4—22no—
132C4⋊Dic43—21no—
133C4⋊Dic43—21no—
134C4⋊Dic43—21no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43C2×D412yes—
138Dic43⋊C4—41no—
139Dic43⋊C4—41no—
140C4×Dic43—41no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8C2×D412yes—
143C2×C43⋊C8C2×D412yes—
144#10621873—44no—
145C8×D43—82no—
146C8×D43—82no—
147C23×C43#12111yescharacteristic
148C22×D43—22no—
149C22×D43—24no—
150C22×D43—81no—
151C22×D43—81no—
152Q8×C43—42no—
153Q8×C43—42no—
154C2×C4×C43—22no—
155C2×C4×C43—22no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C2×#4111yescharacteristic
165C2×Dic43—22no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—81no—
169D172—24no—
170D172—22no—
171D172#13514yes—
172C4×D43—42no—
173C4×D43—42no—
174C4×D43—82no—
175Dic86—42no—
176Dic86—81no—
177C8×C43—42no—
178C8×C43—42no—
179C43⋊C8—22no—
180C43⋊C8—22no—
181C43⋊C8—42no—
182#19395—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43C2×#12111yescharacteristic
187C2×D43—24no—
188C2×D43—42no—
189C2×D43—42no—
190C2×D43—84no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—81no—
196C4×C43—81no—
197C4×C43C2×#13512yes—
198C4×C43#57712yes—
199Dic43—42no—
200Dic43—81no—
201Dic43—81no—
202#3231—431no—
203#3110—431no—
204#3101—431no—
205#2972—431no—
206#1683—432no—
207#1679—432no—
208#1673—432no—
209#1671—432no—
210#1572—431no—
211#1554—431no—
212#1544D4311yescharacteristic, complemented
213C2×C43—41no—
214C2×C43#304211yescharacteristic
215C2×C43#305011yescharacteristic
216C2×C43#306911yescharacteristic
217D43—44no—
218#533—431no—
219#533C2×D4311yescharacteristic
220C2×C4×D4—431no—
221#500—431no—
222#498—431no—
223#487—431no—
224#487—431no—
225#485—862no—
226#484—861no—
227#483—861no—
228#479—862no—
229#476—432no—
230#474—432no—
231#461—432no—
232#461—432no—
233#450—861no—
234#450—861no—
235#440—862no—
236C4×SD16—862no—
237C8×D4—432no—
238C8×D4—432no—
239C8×D4—862no—
240#432—431no—
241#431—431no—
242#431C2×D4311yescharacteristic
243#431C2×D4311yescharacteristic
244C2×C22⋊C8—862no—
245#335—432no—
246#334—432no—
247#333—432no—
248#332—432no—
249#332C2×D4312yescomplemented
250#332C2×D4312yescomplemented
251C43#1939511yescharacteristic, complemented, Sylow
252C22×D4—431no—
253C23×C4—861no—
254C2×SD16—862no—
255C2×SD16—862no—
256C22×C8—862no—
257C22×C8—862no—
258C4⋊Q8—431no—
259C4⋊Q8—431no—
260C4⋊Q8C22×D4311yescharacteristic
261C4⋊Q8C22×D4311yescharacteristic
262#125—21no—
263#125—861no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—861no—
267C22⋊Q8—861no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—861no—
271C4×Q8—861no—
272C4×D4—432no—
273C4×D4—432no—
274C4×D4—861no—
275C4×D4—861no—
276#117—21no—
277#117—861no—
278C2×C4⋊C4—431no—
279C2×C22⋊C4—861no—
280C2×C42C22×D4311yescharacteristic
281#107—862no—
282#107—862no—
283#106—862no—
284#106—862no—
285C4⋊C8—432no—
286C4⋊C8—432no—
287C4⋊C8C22×D4312yes—
288C4⋊C8C22×D4312yes—
289#103—862no—
290#103—862no—
291#103—862no—
292#103—862no—
293#102—862no—
294#102—862no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—432no—
298C22⋊C8—862no—
299C22⋊C8—862no—
300C22⋊C8—861no—
301#97—861no—
302C4×C8—21no—
303C4×C8—21no—
304C4×C8—431no—
305C4×C8—431no—
306C24—861no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—861no—
310C2×Q8—861no—
311C2×D4—432no—
312C2×D4—864no—
313C2×D4—861no—
314C22×C4—861no—
315C22×C4—862no—
316C22×C4—862no—
317C22×C4—3442no—
318C22×C4#1062189811yescharacteristic
319C22×C4D4×D4311yescharacteristic
320C22×C4D4×D4311yescharacteristic
321SD16—1724no—
322SD16—1724no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—432no—
326C2×C8—432no—
327C2×C8—862no—
328C2×C8—3442no—
329C2×C8—3442no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—432no—
337C4⋊C4—861no—
338C4⋊C4—861no—
339C4⋊C4—861no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C4⋊C4—1721no—
343C4⋊C4—1721no—
344C22⋊C4—41no—
345C22⋊C4—862no—
346C22⋊C4—862no—
347C22⋊C4—1721no—
348C42—41no—
349C42—1721no—
350C42#1062189811yescharacteristic
351C42D4×D4311yescharacteristic
352C42D4×D4311yescharacteristic
353C42C23×D4311yescharacteristic
354C23—864no—
355C23—862no—
356C23—3441no—
357C23—3441no—
358C23#1306329811yescharacteristic
359Q8—42no—
360Q8—42no—
361Q8—3441no—
362Q8—1722no—
363D4—434no—
364D4—864no—
365D4—862no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—862no—
372C2×C4—3442no—
373C2×C4—3441no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1722no—
377C2×C4—1722no—
378C2×C4#1306329811yescharacteristic
379C2×C4#1306329811yescharacteristic
380C2×C4#1306329811yescharacteristic
381C2×C4C2×D4×D4311yescharacteristic
382C2×C4C2×D4×D4311yescharacteristic
383C2×C4C2×#1062189811yescharacteristic
384C8—42no—
385C8—42no—
386C8—862no—
387C8—862no—
388C8—1722no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—864no—
393C22—3444no—
394C22—1722no—
395C22—1722no—
396C22C2×#1306329811yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—81no—
402C4—81no—
403C4—3441no—
404C4—3441no—
405C4—1722no—
406C4#135×D4312yes—
407C4#1458370612yes—
408C2—41no—
409C2—1724no—
410C2#1914411011yescharacteristic
411C2#1914417511yescharacteristic
412C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1544C2
socleC22×C43C2×#121
prime radicalC22×D172D4
hypercenter#1544D43
hypocenterC43#19395
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
1. #19145750C2semidirect
5. #19134045C2semidirect
6. #19134017C2semidirect
7. #19133983C2semidirect
8. #19133969C2semidirect
9. #19133373C2semidirect
10. #19133303C2semidirect
11. C43×#1544C2semidirect
14. #14583302C22semidirect
15. #14583295C22semidirect
16. #14583249C22semidirect
17. #14583249C22semidirect
36. #14582651C22semidirect
37. #14582649C22semidirect
38. #14582647C22semidirect
39. #14582644C22semidirect
43. C43×#332C22semidirect
44. C43×#332C22semidirect
212. #1544D43semidirect
249. #332C2×D43semidirect
250. #332C2×D43semidirect
251. C43#19395semidirect

Maximal subgroups

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

subgroupindex
#191457502
#191446902
#191446042
#191436182
#191340452
#191340172
#191339832
#191339692
#191333732
#191333032
C43×#15442
#1939543