Finite Group Databasebeta

← #24991822

Subgroups — #24991822

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#19145150C211yesmaximal, characteristic
2#19143542C211yesmaximal, characteristic, complemented
3#19133093C211yesmaximal, characteristic, complemented
4#19132994C211yesmaximal, characteristic
5#19132436C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C43×#1980C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583295C411yescharacteristic, complemented
10#14583271C411yescharacteristic, complemented
11#14583251C411yescharacteristic, complemented
12#14583245C411yescharacteristic, complemented
13#14583126—22no—
14#14583029—21no—
15#14583027—22no—
16C8×Dic86—21no—
17C4×#10621883—22no—
18#14582952C2211yescharacteristic
19#14582927—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21#14582857—21no—
22C2×C4×C43⋊C8C2211yescharacteristic
23#14582635—22no—
24D4⋊(C43⋊C8)—21no—
25D4⋊(C43⋊C8)—21no—
26C43×#532C2211yescharacteristic
27C2×#104×C43—21no—
28C2×#104×C43—21no—
29C4×M16×C43C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621883—22no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34#13063325C2×C411yescharacteristic
35#13063325C2×C411yescharacteristic
36#13063317—21no—
37#13063304—21no—
38#13063304D412yes—
39C4×Dic86—21no—
40C4×Dic86D412yes—
41#13063284—21no—
42#13063256—22no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)D411yescharacteristic
46C4⋊(C43⋊C8)D411yescharacteristic
47Dic43⋊C8—22no—
48Dic43⋊C8—22no—
49#13063248—22no—
50#13063246—22no—
51C22⋊(C43⋊C8)—21no—
52#13063235—22no—
53C4×C43⋊C8—21no—
54C4×C43⋊C8—21no—
55C4×C43⋊C8C2×C411yescharacteristic
56C4×C43⋊C8C2×C411yescharacteristic
57C8×Dic43—22no—
58C2×#41×C43—21no—
59C2×M16×C43D411yescharacteristic
60C2×M16×C43D411yescharacteristic
61C4⋊Q8×C43C2×C411yescharacteristic
62#127×C43C2×C411yescharacteristic
63#124×C43—21no—
64#121×C43—21no—
65#121×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C42×C43—21no—
70C2×C42×C43C2311yescharacteristic
71#104×C43—42no—
72#104×C43—42no—
73#97×C43—21no—
74C4×C8×C43—21no—
75#95×C43—21no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79#41×C43—41no—
80C2×Q8×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
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—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C42×C43—41no—
105C42×C43—41no—
106C42×C43C22×C411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110C22⋊Dic43—22no—
111#10621883—44no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43C22⋊C412yes—
116Dic43⋊C4—22no—
117Dic43⋊C4—22no—
118C4×Dic43—22no—
119C2×C43⋊C8—21no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—42no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C23×C43—41no—
128C23×C43#12111yescharacteristic
129Q8×C43—41no—
130Q8×C43—41no—
131D4×C43—42no—
132D4×C43—41no—
133D4×C43—41no—
134D4×C43—41no—
135D4×C43—41no—
136D4×C43—81no—
137D4×C43—81no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—81no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43C2×C22⋊C411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12311yescharacteristic
153C2×C4×C43C2×SD1611yescharacteristic
154C2×C4×C43#13511yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C43#13711yescharacteristic
157C2×Dic43—22no—
158C2×Dic43—22no—
159Dic86—41no—
160Dic86—41no—
161Dic86—42no—
162C8×C43—22no—
163C8×C43—41no—
164C43⋊C8—22no—
165C43⋊C8—41no—
166C43⋊C8—41no—
167C43⋊C8—41no—
168C43⋊C8—81no—
169#9054—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—81no—
173C22×C43—81no—
174C22×C43—81no—
175C22×C43#38611yescharacteristic
176C22×C43#46011yescharacteristic
177C22×C43#46411yescharacteristic
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—82no—
182C4×C43—81no—
183C4×C43C4×SD1611yescharacteristic
184C4×C43#44011yescharacteristic
185C4×C43#44311yescharacteristic
186C4×C43#44411yescharacteristic
187C4×C43#44811yescharacteristic
188C4×C43#44911yescharacteristic
189Dic43—42no—
190Dic43—42no—
191#3167—431no—
192#2962—431no—
193#1980D4311yescharacteristic
194#1503—431no—
195#1480—431no—
196#1279—431no—
197#1278—431no—
198C2×C43—21no—
199C2×C43—21no—
200C2×C43—161no—
201C2×C43#187611yescharacteristic
202C2×C43#188011yescharacteristic
203C2×C43#188411yescharacteristic
204#533—431no—
205#532C2×D4311yescharacteristic
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#431—431no—
216#424—861no—
217C2×C4⋊C8—431no—
218C2×#104—21no—
219C2×#104—21no—
220#405—861no—
221C4×M16C2×D4311yescharacteristic
222C2×C4×C8—431no—
223C4×C4⋊C4C2×D4311yescharacteristic
224#328—862no—
225D4⋊C8—861no—
226D4⋊C8—861no—
227C43#905411yescharacteristic, complemented, Sylow
228C2×#41—21no—
229C2×SD16—862no—
230C2×M16C22⋊D4311yescharacteristic
231C2×M16C22⋊D4311yescharacteristic
232C22×C8—861no—
233C22×C8—861no—
234C4⋊Q8—431no—
235C4⋊Q8—431no—
236C4⋊Q8C4×D4311yescharacteristic
237#127C4×D4311yescharacteristic
238#125—861no—
239#124—21no—
240C22⋊Q8—432no—
241C22⋊Q8—861no—
242#121—21no—
243#121—21no—
244C4×Q8—432no—
245C4×Q8—861no—
246C4×D4—21no—
247C4×D4—21no—
248#117—861no—
249C2×C4⋊C4—21no—
250C2×C42—21no—
251C2×C42C22×D4311yescharacteristic
252#106—862no—
253C4⋊C8—431no—
254C4⋊C8—431no—
255C4⋊C8—862no—
256C4⋊C8—862no—
257C4⋊C8—861no—
258C4⋊C8—861no—
259#104—42no—
260#104—42no—
261#103—862no—
262#102—862no—
263C22⋊C8—861no—
264#97—21no—
265#97—862no—
266C4×C8—21no—
267C4×C8—431no—
268C4×C8—431no—
269C4×C8—862no—
270C4×C8—861no—
271C4×C8—861no—
272#95—21no—
273#41—41no—
274#41—41no—
275#41—41no—
276#41—41no—
277C2×Q8—21no—
278C2×Q8—432no—
279C2×Q8—861no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4D4×D4311yescharacteristic
287C22×C4#1062190011yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289SD16—1724no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16#1062188312yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—861no—
297C2×C8—861no—
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—1722no—
301C2×C8—1721no—
302C2×C8—1721no—
303C2×C8—1721no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—432no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—862no—
313C4⋊C4—862no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—862no—
317C42—41no—
318C42—41no—
319C42—862no—
320C42C2×C4×D4311yescharacteristic
321C42#1062189811yescharacteristic
322C42D4×D4311yescharacteristic
323C42D4×D4311yescharacteristic
324C23—41no—
325C23#1306329611yescharacteristic
326Q8—41no—
327Q8—41no—
328Q8—1722no—
329Q8—1721no—
330Q8—1721no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—862no—
348C2×C4—862no—
349C2×C4C22⋊C4×D4311yescharacteristic
350C2×C4(C22⋊D43)⋊C411yescharacteristic
351C2×C4C4×C22⋊D4311yescharacteristic
352C2×C4#1306329311yescharacteristic
353C2×C4#1306329811yescharacteristic
354C2×C4#1306330711yescharacteristic
355C2×C4C2×#1062188311yescharacteristic
356C2×C4#1306334511yescharacteristic
357C2×C4#1306335111yescharacteristic
358C2×C4#1306335511yescharacteristic
359C8—22no—
360C8—41no—
361C8—862no—
362C8—3441no—
363C8—1721no—
364C8—1721no—
365C8—1721no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22#1458277511yescharacteristic
372C22#1458309611yescharacteristic
373C22#1458311811yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—81no—
379C4—1722no—
380C4—1722no—
381C4C4×#1062188311yescharacteristic
382C4#1458299911yescharacteristic
383C4#1458301311yescharacteristic
384C4#1458301811yescharacteristic
385C4#1458303711yescharacteristic
386C4#1458304211yescharacteristic
387C2—21no—
388C2—21no—
389C2—161no—
390C2#1913491911yescharacteristic
391C2#1913495311yescharacteristic
392C2#1913497511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1980C2
socleC22×C43#386
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#1980D43
hypocenterC43#9054
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #19143542C2semidirect
3. #19133093C2semidirect
5. #19132436C2semidirect
6. #19132433C2semidirect
9. #14583295C4semidirect
10. #14583271C4semidirect
11. #14583251C4semidirect
12. #14583245C4semidirect
95. M16×C43SD16semidirect
227. C43#9054semidirect
293. M16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191451502
#191435422
#191330932
#191329942
#191324362
#191324332
C43×#19802
#905443