Finite Group Databasebeta

← #24991824

Subgroups — #24991824

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#19143538C211yesmaximal, characteristic, complemented
3#19135513C211yesmaximal, characteristic
4#19133093C211yesmaximal, characteristic, complemented
5#19132993C211yesmaximal, characteristic
6#19132432C211yesmaximal, characteristic, complemented
7C43×#1279C211yesmaximal, characteristic, complemented
8#14583456C2211yescharacteristic
9#14583449C2211yescharacteristic
10#14583297C411yescharacteristic, complemented
11#14583272C411yescharacteristic, complemented
12#14583250C411yescharacteristic, complemented
13#14583246C411yescharacteristic, complemented
14#14583128—22no—
15#14583028—22no—
16#14583026—21no—
17#14583023—21no—
18C4×#10621873—22no—
19#14582952C2211yescharacteristic
20#14582925—21no—
21C2×#13063253—21no—
22C2×#13063253—21no—
23#14582854—21no—
24C4×#10621877C2211yescharacteristic
25#14582635—22no—
26#14582626—21no—
27#14582626—21no—
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4×C8×C43C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621898—21no—
32C2×#10621873—22no—
33C2×#10621877D411yescharacteristic
34C2×#10621877D411yescharacteristic
35#13063325C2×C411yescharacteristic
36#13063325C2×C411yescharacteristic
37#13063325C2×C411yescharacteristic
38#13063322C2×C411yescharacteristic
39#13063317—21no—
40#13063313—21no—
41#13063304—21no—
42#13063304D412yes—
43#13063299—21no—
44#13063299—21no—
45C4×Dic86—21no—
46C4×Dic86D412yes—
47C4×D172—21no—
48C4×D172—21no—
49#13063284—21no—
50#13063257—22no—
51C4⋊(C43⋊C8)—21no—
52Dic43⋊C8—22no—
53Dic43⋊C8—22no—
54#13063253—42no—
55#13063253—42no—
56#13063250—22no—
57#13063247—22no—
58C22⋊(C43⋊C8)—21no—
59#13063236—21no—
60#13063235—22no—
61C4×C43⋊C8—21no—
62C4×C43⋊C8—21no—
63C8×Dic43—22no—
64C22×C8×C43—21no—
65C22×C8×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C42×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43D411yescharacteristic
71C4⋊C8×C43D411yescharacteristic
72C4×C8×C43—21no—
73C4×C8×C43C2×C411yescharacteristic
74C4×C8×C43C2×C411yescharacteristic
75#95×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C2×C22⋊D43—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—
92C2×C8×C43—21no—
93C2×C8×C43—21no—
94C2×C8×C43—21no—
95C2×C8×C43—21no—
96C2×C8×C43—42no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—41no—
101C42×C43—41no—
102C42×C43—41no—
103C42×C43C22×C411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C42×C43C2×D411yescharacteristic
106C42×C43#4111yescharacteristic
107C22⋊Dic43—22no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43C22⋊C412yes—
116Dic43⋊C4—22no—
117Dic43⋊C4—22no—
118C4×Dic43—22no—
119#10621877—21no—
120#10621877—21no—
121#10621877—21no—
122#10621877SD1612yescomplemented
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
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×C43—42no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43#12011yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C2×C4×C43C2×SD1611yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C22⋊D43—81no—
146C22⋊D43—81no—
147C2×Dic43—22no—
148C2×Dic43—22no—
149C2×Dic43—41no—
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—41no—
164C8×C43—41no—
165C8×C43—41no—
166C43⋊C8—22no—
167C43⋊C8—41no—
168C43⋊C8—81no—
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×C43—82no—
182C4×C43C4×SD1611yescharacteristic
183C4×C43#44011yescharacteristic
184C4×C43#44311yescharacteristic
185C4×C43#44411yescharacteristic
186C4×C43#44811yescharacteristic
187C4×C43#44911yescharacteristic
188Dic43—42no—
189Dic43—42no—
190Dic43—81no—
191#3167—431no—
192#2962—431no—
193#1980—431no—
194#1503—431no—
195#1480—431no—
196#1279D4311yescharacteristic, complemented
197#1278—431no—
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—862no—
212#446—861no—
213C8×Q8—861no—
214C4×SD16—862no—
215#431—431no—
216#424—861no—
217C2×C4⋊C8C2×D4311yescharacteristic
218C2×#104—861no—
219C2×#104—861no—
220#405—861no—
221C4×M16—431no—
222C2×C4×C8C2×D4311yescharacteristic
223C4×C4⋊C4C2×D4311yescharacteristic
224#328—862no—
225D4⋊C8—861no—
226D4⋊C8—861no—
227C43#905411yescharacteristic, complemented, Sylow
228C2×#41—861no—
229C2×SD16—862no—
230C2×M16—431no—
231C2×M16—431no—
232C22×C8—21no—
233C22×C8—21no—
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—21no—
250C2×C42—21no—
251C2×C42C22×D4311yescharacteristic
252#106—862no—
253C4⋊C8—21no—
254C4⋊C8—862no—
255C4⋊C8—862no—
256C4⋊C8—861no—
257C4⋊C8D17211yescharacteristic
258C4⋊C8D17211yescharacteristic
259#104—1722no—
260#104—1722no—
261#103—862no—
262#102—862no—
263C22⋊C8—861no—
264#97—862no—
265#97—861no—
266C4×C8—21no—
267C4×C8—862no—
268C4×C8—861no—
269C4×C8—861no—
270C4×C8C4×D4311yescharacteristic
271C4×C8C4×D4311yescharacteristic
272#95—21no—
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—41no—
285C22×C4—1721no—
286C22×C4#1062189811yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289SD16—1724no—
290M16—432no—
291M16—861no—
292M16—861no—
293M16—861no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—1721no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—432no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—862no—
311C4⋊C4—862no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C22⋊C4—862no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C42—41no—
318C42—41no—
319C42—862no—
320C42C2×C4×D4311yescharacteristic
321C42C2×D17211yescharacteristic
322C42D4×D4311yescharacteristic
323C42#1062190211yescharacteristic
324C23—1721no—
325C23#1306329811yescharacteristic
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—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—3441no—
347C2×C4—3441no—
348C2×C4—1721no—
349C2×C4C22⋊C4×D4311yescharacteristic
350C2×C4#1306328711yescharacteristic
351C2×C4C4×D17211yescharacteristic
352C2×C4#1306329511yescharacteristic
353C2×C4#1306330011yescharacteristic
354C2×C4#1306331011yescharacteristic
355C2×C4SD16×D4311yescharacteristic
356C2×C4#1306334611yescharacteristic
357C2×C4#1306334911yescharacteristic
358C2×C4#1306335711yescharacteristic
359C8—22no—
360C8—41no—
361C8—41no—
362C8—41no—
363C8—862no—
364C8—3441no—
365C8—1721no—
366C22—21no—
367C22—21no—
368C22—3441no—
369C22—3441no—
370C22—3441no—
371C22#1458277711yescharacteristic
372C22#1458309811yescharacteristic
373C22#1458312411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—3441no—
379C4—1722no—
380C4—1722no—
381C4#1458298611yescharacteristic
382C4#1458299811yescharacteristic
383C4#1458301711yescharacteristic
384C4#1458302211yescharacteristic
385C4#1458303911yescharacteristic
386C4#1458304511yescharacteristic
387C2—21no—
388C2—21no—
389C2—6881no—
390C2#1913492111yescharacteristic
391C2#1913495111yescharacteristic
392C2#1913497711yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#9054
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #19143538C2semidirect
4. #19133093C2semidirect
6. #19132432C2semidirect
7. C43×#1279C2semidirect
10. #14583297C4semidirect
11. #14583272C4semidirect
12. #14583250C4semidirect
13. #14583246C4semidirect
122. #10621877SD16semidirect
196. #1279D43semidirect
227. C43#9054semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191435382
#191355132
#191330932
#191329932
#191324322
C43×#12792
#905443