Finite Group Databasebeta

← #24991826

Subgroups — #24991826

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic
2#19143542C211yesmaximal, characteristic, complemented
3#19135514C211yesmaximal, characteristic
4#19133095C211yesmaximal, characteristic, complemented
5#19132995C211yesmaximal, characteristic
6#19132435C211yesmaximal, characteristic, complemented
7C43×#1278C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9#14583449C2211yescharacteristic
10#14583297C411yescharacteristic, complemented
11#14583272C411yescharacteristic, complemented
12#14583250C411yescharacteristic, complemented
13#14583246C411yescharacteristic, complemented
14#14583128—22no—
15#14583029—21no—
16#14583027—22no—
17C8×Dic86—21no—
18C4×#10621873—22no—
19#14582927—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063251—21no—
22C2×#13063251—21no—
23#14582857—21no—
24C4×C4⋊Dic43C2211yescharacteristic
25#14582637—22no—
26#14582628—21no—
27#14582628—21no—
28C43×#431C2211yescharacteristic
29C4×M16×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C2×#10621898—21no—
32C2×#10621873—22no—
33C22×C43⋊C8—21no—
34#13063325C2×C411yescharacteristic
35#13063325C2×C411yescharacteristic
36#13063325C2×C411yescharacteristic
37#13063322C2×C411yescharacteristic
38#13063317—21no—
39#13063313—21no—
40#13063304—21no—
41#13063304D412yes—
42#13063299—21no—
43#13063299—21no—
44C4×Dic86—21no—
45C4×Dic86D412yes—
46C4×D172—21no—
47C4×D172—21no—
48#13063284—21no—
49C2×C4⋊Dic43—21no—
50C2×C4×Dic43—21no—
51#13063257—22no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)D411yescharacteristic
54C4⋊(C43⋊C8)D411yescharacteristic
55Dic43⋊C8—22no—
56Dic43⋊C8—22no—
57#13063251—42no—
58#13063251—42no—
59#13063250—22no—
60#13063247—22no—
61#13063235—22no—
62C8×Dic43—22no—
63C43⋊#95—21no—
64C2×M16×C43D411yescharacteristic
65C2×M16×C43D411yescharacteristic
66C22×C8×C43—21no—
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70#97×C43—21no—
71C4×C8×C43—21no—
72C4×C8×C43—21no—
73C4×C8×C43—21no—
74C4×C8×C43C2×C411yescharacteristic
75C4×C8×C43C2×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—41no—
80C22×Dic43—41no—
81#10621898—41no—
82#10621898—41no—
83#10621898—41no—
84#10621898—41no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172—21no—
88C2×C4×D43—41no—
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×Dic86C22⋊C412yes—
92M16×C43—21no—
93M16×C43—21no—
94M16×C43—21no—
95M16×C43SD1612yescomplemented
96C2×C8×C43—21no—
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43—21no—
100C2×C8×C43—42no—
101C2×C8×C43—41no—
102C42×C43C22×C411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C22⋊Dic43—22no—
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—41no—
109C4⋊Dic43—21no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—22no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—41no—
116C4⋊Dic43C22⋊C412yes—
117Dic43⋊C4—22no—
118Dic43⋊C4—22no—
119C4×Dic43—22no—
120C4×Dic43—41no—
121C4×Dic43—41no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126#10621873—44no—
127C23×C43#12111yescharacteristic
128C22×D43—41no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43C2×C22⋊C411yescharacteristic
133C2×C4×C43C4×D411yescharacteristic
134C2×C4×C43C4×D411yescharacteristic
135C2×C4×C43#12011yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12311yescharacteristic
138C2×C4×C43C2×SD1611yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43—42no—
147C2×Dic43—41no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150D172—42no—
151D172—41no—
152D172—41no—
153D172—41no—
154D172—41no—
155C4×D43—81no—
156C4×D43—81no—
157Dic86—41no—
158Dic86—41no—
159Dic86—42no—
160Dic86—41no—
161Dic86—41no—
162C8×C43—22no—
163C8×C43—22no—
164C8×C43—41no—
165C8×C43—41no—
166C8×C43—81no—
167C43⋊C8—41no—
168C43⋊C8—41no—
169#9054—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38611yescharacteristic
173C22×C43#46011yescharacteristic
174C22×C43#46411yescharacteristic
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43C4×SD1611yescharacteristic
182C4×C43#44011yescharacteristic
183C4×C43#44311yescharacteristic
184C4×C43#44411yescharacteristic
185C4×C43#44811yescharacteristic
186C4×C43#44911yescharacteristic
187Dic43—42no—
188Dic43—42no—
189Dic43—82no—
190Dic43—81no—
191#3167—431no—
192#2962—431no—
193#1980—431no—
194#1503—431no—
195#1480—431no—
196#1279—431no—
197#1278D4311yescharacteristic, complemented
198C2×C43—21no—
199C2×C43—21no—
200C2×C43#187611yescharacteristic
201C2×C43#188011yescharacteristic
202C2×C43#188411yescharacteristic
203D43—161no—
204#533—431no—
205#532—431no—
206#498—431no—
207#492—431no—
208#487—431no—
209#486—431no—
210#465—862no—
211#446—861no—
212#446—862no—
213C8×Q8—861no—
214C4×SD16—862no—
215#431C2×D4311yescharacteristic
216#424—861no—
217C2×C4⋊C8—431no—
218C2×#104—861no—
219C2×#104—861no—
220#405—861no—
221C4×M16C2×D4311yescharacteristic
222C2×C4×C8C2×D4311yescharacteristic
223C4×C4⋊C4—431no—
224#328—862no—
225D4⋊C8—861no—
226D4⋊C8—861no—
227C43#905411yescharacteristic, complemented, Sylow
228C2×#41—861no—
229C2×SD16—862no—
230C2×M16D17211yescharacteristic
231C2×M16D17211yescharacteristic
232C22×C8—21no—
233C22×C8—861no—
234C4⋊Q8—431no—
235C4⋊Q8—431no—
236C4⋊Q8—431no—
237#127—431no—
238#125—861no—
239#124—861no—
240C22⋊Q8—432no—
241C22⋊Q8—861no—
242#121—861no—
243#121—861no—
244C4×Q8—432no—
245C4×Q8—861no—
246C4×D4—861no—
247C4×D4—861no—
248#117—861no—
249C2×C4⋊C4—861no—
250C2×C42—861no—
251C2×C42C22×D4311yescharacteristic
252#106—862no—
253C4⋊C8—21no—
254C4⋊C8—431no—
255C4⋊C8—431no—
256C4⋊C8—862no—
257C4⋊C8—862no—
258C4⋊C8—861no—
259#104—1722no—
260#104—1722no—
261#103—862no—
262#102—862no—
263C22⋊C8—21no—
264#97—21no—
265#97—862no—
266C4×C8—21no—
267C4×C8—21no—
268C4×C8—21no—
269C4×C8—862no—
270C4×C8C4×D4311yescharacteristic
271C4×C8C4×D4311yescharacteristic
272#95—861no—
273#41—1721no—
274#41—1721no—
275#41—1721no—
276#41—1721no—
277C2×Q8—432no—
278C2×Q8—861no—
279C2×Q8—861no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4—1721no—
284C22×C4—1721no—
285C22×C4—1721no—
286C22×C4C2×D17211yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4#1062190211yescharacteristic
289SD16—1724no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16#1062187312yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—861no—
301C2×C8—861no—
302C2×C8—1721no—
303C2×C8—1721no—
304C4⋊C4—432no—
305C4⋊C4—862no—
306C4⋊C4—861no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—862no—
310C4⋊C4—862no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—1721no—
314C22⋊C4—862no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C42—862no—
318C42—1721no—
319C42—1721no—
320C42C2×C4×D4311yescharacteristic
321C42#1062189811yescharacteristic
322C42D4×D4311yescharacteristic
323C42D4×D4311yescharacteristic
324C23—1721no—
325C23#1306330011yescharacteristic
326Q8—1722no—
327Q8—1721no—
328Q8—1721no—
329Q8—1721no—
330Q8—1721no—
331D4—3441no—
332D4—3441no—
333D4—1722no—
334D4—1721no—
335D4—1721no—
336D4—1721no—
337D4—1721no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—862no—
342C2×C4—862no—
343C2×C4—3441no—
344C2×C4—3441no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—1722no—
348C2×C4—1721no—
349C2×C4C22⋊C4×D4311yescharacteristic
350C2×C4#1306328711yescharacteristic
351C2×C4C4×D17211yescharacteristic
352C2×C4#1306329511yescharacteristic
353C2×C4#1306329811yescharacteristic
354C2×C4#1306331011yescharacteristic
355C2×C4C2×#1062187311yescharacteristic
356C2×C4#1306334711yescharacteristic
357C2×C4#1306335311yescharacteristic
358C2×C4#1306335811yescharacteristic
359C8—22no—
360C8—22no—
361C8—41no—
362C8—41no—
363C8—81no—
364C8—1721no—
365C8—1721no—
366C22—21no—
367C22—21no—
368C22—3441no—
369C22—3441no—
370C22—3441no—
371C22#1458277711yescharacteristic
372C22#1458310011yescharacteristic
373C22#1458312211yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—3442no—
378C4—3441no—
379C4—1722no—
380C4—1722no—
381C4C4×#1062187311yescharacteristic
382C4#1458300111yescharacteristic
383C4#1458301511yescharacteristic
384C4#1458302011yescharacteristic
385C4#1458304011yescharacteristic
386C4#1458304611yescharacteristic
387C2—21no—
388C2—21no—
389C2—6881no—
390C2#1913492311yescharacteristic
391C2#1913494911yescharacteristic
392C2#1913497711yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1278C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1278D43
hypocenterC43#9054
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
2. #19143542C2semidirect
4. #19133095C2semidirect
6. #19132435C2semidirect
7. C43×#1278C2semidirect
10. #14583297C4semidirect
11. #14583272C4semidirect
12. #14583250C4semidirect
13. #14583246C4semidirect
95. M16×C43SD16semidirect
197. #1278D43semidirect
227. C43#9054semidirect
293. M16#10621873semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191435422
#191355142
#191330952
#191329952
#191324352
C43×#12782
#905443