Finite Group Databasebeta

← #25081836

Subgroups — #25081836

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145713C211yesmaximal, characteristic, complemented
2#19144055C211yesmaximal, characteristic
3C2×#14583105C211yesmaximal, characteristic, complemented
4#19143618C211yesmaximal, characteristic, complemented
5#19134031C214yesmaximal, complemented
6#19133983C214yesmaximal, complemented
7#19133369C211yesmaximal, characteristic, complemented
8#19133266C211yesmaximal, characteristic, complemented
9C43×#1540C211yesmaximal, characteristic, complemented
10C2×#13063350—21no—
11C22×#10621873—21no—
12C2×#13063325C2211yescharacteristic
13C2×C4×D172C2211yescharacteristic
14#14583302C2212yescomplemented
15#14583245C2212yescomplemented
16#14583210—22no—
17#14583179—22no—
18#14583111—22no—
19#14583105—22no—
20#14583105C2214yes—
21#14583101C2212yes—
22#14583091C2212yes—
23C8×D172—22no—
24#14582964C2214yes—
25#14582952C2211yescharacteristic
26#14582923C2211yescharacteristic
27#14582900—21no—
28C2×#13063250—21no—
29C22⋊C8×D43—22no—
30#14582651C2214yescomplemented
31#14582644C2214yescomplemented
32C43×#532C2211yescharacteristic
33C43×#431C2211yescharacteristic
34C2×C4⋊C8×C43C2211yescharacteristic
35C43×#332C2212yescomplemented
36C43×#331C2212yescomplemented
37C22×Dic86—21no—
38C22×D172D411yescharacteristic
39C22×C4×D43—21no—
40#13063350—44no—
41C2×#10621873—24no—
42C2×#10621873—44no—
43C2×#10621884—22no—
44C2×#10621882—22no—
45C2×#10621877—21no—
46C2×C8×D43—24no—
47#13063325—21no—
48#13063325—21no—
49#13063325—21no—
50#13063325C2312yes—
51C4×D172—21no—
52C4×D172—21no—
53C4×D172D412yes—
54C4×D172C2312yes—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43D411yescharacteristic
58C2×(C2×D43)⋊C4—21no—
59#13063258—24no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)D412yes—
62C4⋊(C43⋊C8)C2312yes—
63#13063250—24no—
64#13063249—22no—
65#13063246—22no—
66#13063246—24no—
67C22⋊(C43⋊C8)D412yes—
68(C2×D43)⋊C8—24no—
69C4×C43⋊C8C2312yes—
70C2×#41×C43—21no—
71C22×C8×C43—21no—
72C4⋊Q8×C43C2311yescharacteristic
73#127×C43C2311yescharacteristic
74#124×C43—21no—
75#121×C43—21no—
76#121×C43—21no—
77C4×D4×C43—21no—
78C4×D4×C43—21no—
79C2×C42×C43C2311yescharacteristic
80C4⋊C8×C43—21no—
81C4⋊C8×C43C2312yes—
82C4⋊C8×C43C2312yes—
83C22⋊C8×C43—21no—
84C4×C8×C43—21no—
85C23×D43—21no—
86#41×C43—42no—
87#41×C43—42no—
88C2×Q8×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×Dic43—21no—
98C22×Dic43—41no—
99C2×D172—21no—
100C2×D172—22no—
101C2×D172D814yes—
102C2×D172C2×D412yes—
103C2×C4×D43—22no—
104C2×C4×D43—22no—
105C2×C4×D43—82no—
106C2×Dic86—22no—
107C2×Dic86—42no—
108C2×Dic86—42no—
109C2×Dic86—41no—
110C2×C8×C43—22no—
111C2×C8×C43—22no—
112C2×C8×C43—42no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C42×C43C2411yescharacteristic
121#10621884—44no—
122#10621882—44no—
123(C2×D43)⋊C4—22no—
124(C2×D43)⋊C4—22no—
125C4⋊Dic43—21no—
126C4⋊Dic43—22no—
127C4⋊Dic43—22no—
128C4⋊Dic43—41no—
129C4⋊Dic43—41no—
130C4⋊Dic43C2×D412yes—
131#10621877—42no—
132C2×C43⋊C8—22no—
133C2×C43⋊C8C2×D414yes—
134#10621873—48no—
135C8×D43—84no—
136C23×C43—41no—
137C23×C43#12111yescharacteristic
138C22×D43—22no—
139C22×D43—24no—
140C22×D43—81no—
141C22×D43—81no—
142Q8×C43—41no—
143Q8×C43—41no—
144D4×C43—41no—
145D4×C43—41no—
146D4×C43—42no—
147D4×C43—81no—
148D4×C43—82no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—82no—
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43C2×D812yes—
157C2×C4×C43#13512yes—
158C2×C4×C43C22×D411yescharacteristic
159C2×C4×C43C22×D411yescharacteristic
160C2×C4×C43C2×#4111yescharacteristic
161C2×Dic43—22no—
162C2×Dic43—42no—
163C2×Dic43—81no—
164C2×Dic43—82no—
165D172—22no—
166D172—24no—
167D172C2×D814yes—
168C4×D43—44no—
169C4×D43—82no—
170Dic86—42no—
171Dic86—42no—
172Dic86—82no—
173C8×C43—42no—
174C8×C43—42no—
175C43⋊C8—24no—
176C43⋊C8—42no—
177#19392—431nomaximal, Sylow
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43#46612yes—
184C22×C43C2×#12111yescharacteristic
185C2×D43—24no—
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—84no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—81no—
193C4×C43#46612yes—
194C4×C43C22×D811yescharacteristic
195C4×C43C2×#13511yescharacteristic
196C4×C43#57712yes—
197Dic43—42no—
198Dic43—82no—
199#3226—431no—
200#3036—431no—
201C2×#461—431no—
202#2972—431no—
203#1681—434no—
204#1673—434no—
205#1571—431no—
206#1546—431no—
207#1540D4311yescharacteristic, complemented
208C2×C43—22no—
209C2×C43—161no—
210C2×C43#304211yescharacteristic
211C2×C43C2×#46611yescharacteristic
212C2×C43#306911yescharacteristic
213D43—44no—
214C2×AGL(1,ℤ/8)—861no—
215C22×SD16—861no—
216#532C2×D4311yescharacteristic
217C2×C4⋊Q8—431no—
218C2×C4×D4—431no—
219#500—432no—
220#486—432no—
221#480—862no—
222#474—862no—
223#463—862no—
224#461—432no—
225#461—434no—
226#461—862no—
227#459—432no—
228C8×D4—434no—
229C8×D4—862no—
230#431—431no—
231#431C2×D4311yescharacteristic
232#423—431no—
233C2×C4⋊C8C2×D4311yescharacteristic
234#417—861no—
235C2×#103—861no—
236C2×C22⋊C8—862no—
237#335—434no—
238#332—434no—
239#332C2×D4312yescomplemented
240#331C2×D4312yescomplemented
241C43#1939211yescharacteristic, complemented, Sylow
242C2×#41—21no—
243C22×Q8—861no—
244C22×D4—431no—
245C23×C4—861no—
246AGL(1,ℤ/8)—1724no—
247C2×SD16—864no—
248C2×SD16—862no—
249C2×SD16—1724no—
250C2×D8—862no—
251C2×M16—861no—
252C22×C8—21no—
253C22×C8—864no—
254C4⋊Q8—432no—
255C4⋊Q8—861no—
256C4⋊Q8—861no—
257C4⋊Q8—861no—
258C4⋊Q8C22×D4311yescharacteristic
259#127C22×D4311yescharacteristic
260#124—21no—
261#121—21no—
262#121—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—432no—
266C4×D4—432no—
267C4×D4—861no—
268C4×D4—861no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C42C22×D4311yescharacteristic
274#107—864no—
275C4⋊C8—21no—
276C4⋊C8—432no—
277C4⋊C8—432no—
278C4⋊C8—861no—
279C4⋊C8C22×D4312yes—
280C4⋊C8C22×D4312yes—
281#103—864no—
282#103—862no—
283#102—862no—
284#102—864no—
285C22⋊C8—21no—
286C22⋊C8—432no—
287C22⋊C8—864no—
288C4×C8—21no—
289C4×C8—432no—
290C24—861no—
291#41—42no—
292#41—42no—
293C2×Q8—21no—
294C2×Q8—862no—
295C2×Q8—1722no—
296C2×Q8—1722no—
297C2×Q8—1721no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—434no—
303C2×D4—432no—
304C2×D4—861no—
305C2×D4—862no—
306C22×C4—41no—
307C22×C4—861no—
308C22×C4—862no—
309C22×C4—862no—
310C22×C4—3442no—
311C22×C4—1721no—
312C22×C4#1062189811yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C22×C4D4×D4311yescharacteristic
315SD16—1728no—
316SD16—1724no—
317D8—1724no—
318M16—1722no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—42no—
322C2×C8—434no—
323C2×C8—862no—
324C2×C8—3444no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—432no—
328C4⋊C4—861no—
329C4⋊C4—862no—
330C4⋊C4—862no—
331C4⋊C4—1721no—
332C4⋊C4—1721no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—862no—
336C22⋊C4—862no—
337C42#1062189811yescharacteristic
338C42D4×D4311yescharacteristic
339C42D4×D4311yescharacteristic
340C42C23×D4311yescharacteristic
341C23—41no—
342C23—864no—
343C23—862no—
344C23—3441no—
345C23—3441no—
346C23#1306329811yescharacteristic
347Q8—41no—
348Q8—41no—
349Q8—3442no—
350Q8—1722no—
351Q8—1722no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—81no—
356D4—82no—
357D4—434no—
358D4—864no—
359D4—862no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—82no—
364C2×C4—862no—
365C2×C4—3442no—
366C2×C4—3442no—
367C2×C4—3441no—
368C2×C4—1722no—
369C2×C4—1724no—
370C2×C4#1306329811yescharacteristic
371C2×C4#1306329811yescharacteristic
372C2×C4#1306329811yescharacteristic
373C2×C4D8×D4312yes—
374C2×C4#1306334612yes—
375C2×C4C2×D4×D4311yescharacteristic
376C2×C4C2×D4×D4311yescharacteristic
377C2×C4C2×#1062189811yescharacteristic
378C8—42no—
379C8—42no—
380C8—864no—
381C8—1722no—
382C22—21no—
383C22—21no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—864no—
388C22—3444no—
389C22—1722no—
390C22—1722no—
391C22#1458313412yes—
392C22C2×#1306329811yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—3442no—
398C4—1722no—
399C4#1458313412yes—
400C4C2×D8×D4311yescharacteristic
401C4C2×#1306334611yescharacteristic
402C4#1458370612yes—
403C2—22no—
404C2—161no—
405C2—1724no—
406C2#1914411011yescharacteristic
407C2C2×#1458313411yescharacteristic
408C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1540C2
socleC22×C43C2×#121
prime radical#19144055C2
hypercenter#1540D43
hypocenterC43#19392
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
1. #19145713C2semidirect
3. C2×#14583105C2semidirect
4. #19143618C2semidirect
5. #19134031C2semidirect
6. #19133983C2semidirect
7. #19133369C2semidirect
8. #19133266C2semidirect
9. C43×#1540C2semidirect
14. #14583302C22semidirect
15. #14583245C22semidirect
30. #14582651C22semidirect
31. #14582644C22semidirect
35. C43×#332C22semidirect
36. C43×#331C22semidirect
207. #1540D43semidirect
239. #332C2×D43semidirect
240. #331C2×D43semidirect
241. C43#19392semidirect

Maximal subgroups

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

subgroupindex
#191457132
#191440552
C2×#145831052
#191436182
#191340312
#191339832
#191333692
#191332662
C43×#15402
#1939243