Finite Group Databasebeta

← #24991829

Subgroups — #24991829

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145155C211yesmaximal, characteristic
2#19143341C211yesmaximal, characteristic
3#19133089C211yesmaximal, characteristic
4#19132998C211yesmaximal, characteristic, complemented
5#19132436C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C43×#1986C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9#14583449C2211yescharacteristic
10#14583295C411yescharacteristic, complemented
11#14583273C411yescharacteristic, complemented
12#14583249C411yescharacteristic, complemented
13#14583247C411yescharacteristic, complemented
14#14583130—22no—
15C4×#10621884—22no—
16#14582978—21no—
17#14582972—22no—
18C8×D172—21no—
19#14582952C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21#14582867—21no—
22C2×C4×C43⋊C8C2211yescharacteristic
23#14582632—22no—
24Q8⋊(C43⋊C8)—21no—
25Q8⋊(C43⋊C8)—21no—
26C43×#533C2211yescharacteristic
27C4×M16×C43C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C43×#339—21no—
30C43×#339—21no—
31C2×#10621898—21no—
32C2×#10621884—22no—
33#13063333—42no—
34#13063333—42no—
35C2×#10621872—22no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C2×C8×D43—22no—
39#13063325C2×C411yescharacteristic
40#13063322C2×C411yescharacteristic
41#13063313—21no—
42#13063299—21no—
43#13063299D412yes—
44C4×D172—21no—
45C4×D172D412yes—
46#13063256—22no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)D411yescharacteristic
50C4⋊(C43⋊C8)D411yescharacteristic
51#13063249—22no—
52#13063245—22no—
53C22⋊(C43⋊C8)—21no—
54(C2×D43)⋊C8—22no—
55(C2×D43)⋊C8—22no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8—21no—
58C4×C43⋊C8C2×C411yescharacteristic
59C4×C43⋊C8C2×C411yescharacteristic
60C2×M16×C43D411yescharacteristic
61C2×M16×C43D411yescharacteristic
62C4⋊Q8×C43C2×C411yescharacteristic
63C4⋊Q8×C43C2×C411yescharacteristic
64#125×C43—21no—
65C22⋊Q8×C43—21no—
66C22⋊Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69#117×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73#97×C43—21no—
74C4×C8×C43—21no—
75#95×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C2×C22⋊D43—22no—
83#10621898—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87C2×D172—21no—
88C2×D172—21no—
89C2×D172C22⋊C412yes—
90C2×C4×D43—22no—
91C2×Dic86—21no—
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—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C22⋊C4×C43—41no—
107C42×C43—41no—
108C42×C43—41no—
109C42×C43—41no—
110C42×C43C22×C411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114#10621884—44no—
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117C4⋊Dic43—21no—
118C4⋊Dic43C22⋊C412yes—
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—
127#10621872—44no—
128C8×D43—44no—
129C23×C43#12111yescharacteristic
130C22×D43—22no—
131Q8×C43—42no—
132Q8×C43—41no—
133Q8×C43—41no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×C4×C43C2×C22⋊C411yescharacteristic
143C2×C4×C43C4×D411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43#12011yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12311yescharacteristic
148C2×C4×C43C2×SD1611yescharacteristic
149C2×C4×C43#13511yescharacteristic
150C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C43#13711yescharacteristic
152C22⋊D43—42no—
153C22⋊D43—42no—
154C2×Dic43—22no—
155D172—42no—
156D172—41no—
157D172—41no—
158D172—41no—
159D172—41no—
160C4×D43—42no—
161C4×D43—42no—
162Dic86—41no—
163Dic86—41no—
164C8×C43—22no—
165C8×C43—41no—
166C43⋊C8—22no—
167C43⋊C8—41no—
168C43⋊C8—41no—
169C43⋊C8—41no—
170C43⋊C8—81no—
171#9055—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43#38611yescharacteristic
175C22×C43#46111yescharacteristic
176C22×C43#46311yescharacteristic
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—42no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—82no—
184C4×C43—81no—
185C4×C43—81no—
186C4×C43C4×SD1611yescharacteristic
187C4×C43#44011yescharacteristic
188C4×C43#44311yescharacteristic
189C4×C43#44411yescharacteristic
190C4×C43#45011yescharacteristic
191C4×C43#45211yescharacteristic
192Dic43—42no—
193#3167—431no—
194#2935—431no—
195#1986D4311yescharacteristic, complemented
196#1502—431no—
197#1481—431no—
198#1279—431no—
199#1278—431no—
200C2×C43—21no—
201C2×C43—21no—
202C2×C43#187611yescharacteristic
203C2×C43#187711yescharacteristic
204C2×C43#188411yescharacteristic
205D43—82no—
206C2×#131—861no—
207#533C2×D4311yescharacteristic
208#532—431no—
209#498—431no—
210#492—431no—
211#487—431no—
212#486—431no—
213#465—862no—
214C4×SD16—862no—
215#436—861no—
216#435—862no—
217C8×D4—861no—
218#431—431no—
219C2×C4⋊C8—431no—
220#408—861no—
221C4×M16C2×D4311yescharacteristic
222C2×C4×C8—431no—
223C4×C4⋊C4C2×D4311yescharacteristic
224#339—21no—
225#339—21no—
226#327—862no—
227Q8⋊C8—861no—
228Q8⋊C8—861no—
229C43#905511yescharacteristic, complemented, Sylow
230C2×#41—861no—
231C2×SD16—862no—
232#131—1722no—
233#131—1722no—
234C2×M16—862no—
235C2×M16C22⋊D4311yescharacteristic
236C2×M16C22⋊D4311yescharacteristic
237C22×C8—862no—
238C22×C8—861no—
239C22×C8—861no—
240C4⋊Q8—431no—
241C4⋊Q8C4×D4311yescharacteristic
242C4⋊Q8C4×D4311yescharacteristic
243#127—431no—
244#125—21no—
245#124—861no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248#121—432no—
249#121—861no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—432no—
253C4×D4—861no—
254#117—21no—
255C2×C4⋊C4—21no—
256C2×C42—21no—
257C2×C42C22×D4311yescharacteristic
258#106—862no—
259C4⋊C8—431no—
260C4⋊C8—431no—
261C4⋊C8—861no—
262C4⋊C8—861no—
263#103—862no—
264#102—862no—
265C22⋊C8—862no—
266C22⋊C8—862no—
267C22⋊C8—861no—
268#97—21no—
269C4×C8—21no—
270C4×C8—431no—
271C4×C8—431no—
272C4×C8—861no—
273C4×C8—861no—
274#95—21no—
275#41—1721no—
276#41—1721no—
277#41—1721no—
278#41—1721no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—861no—
282C2×D4—432no—
283C2×D4—862no—
284C2×D4—861no—
285C2×D4—861no—
286C22×C4—41no—
287C22×C4—862no—
288C22×C4D4×D4311yescharacteristic
289C22×C4#1062190011yescharacteristic
290C22×C4C2×C22⋊D4311yescharacteristic
291SD16—1724no—
292M16—21no—
293M16—21no—
294M16—21no—
295M16—1724no—
296M16#1062188412yescomplemented
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—861no—
300C2×C8—861no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—1724no—
304C2×C8—1722no—
305C2×C8—1721no—
306C2×C8—1721no—
307C2×C8—1721no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—432no—
317C4⋊C4—861no—
318C22⋊C4—41no—
319C22⋊C4—862no—
320C22⋊C4—862no—
321C42—41no—
322C42—41no—
323C42—41no—
324C42C2×C4×D4311yescharacteristic
325C42#1062189811yescharacteristic
326C42D4×D4311yescharacteristic
327C42D4×D4311yescharacteristic
328C23—862no—
329C23#1306329611yescharacteristic
330Q8—42no—
331Q8—41no—
332Q8—41no—
333Q8—1721no—
334Q8—1721no—
335D4—1722no—
336D4—1722no—
337D4—1722no—
338D4—1721no—
339D4—1721no—
340D4—1721no—
341D4—1721no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—862no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4C22⋊C4×D4311yescharacteristic
354C2×C4(C22⋊D43)⋊C411yescharacteristic
355C2×C4C4×C22⋊D4311yescharacteristic
356C2×C4#1306329311yescharacteristic
357C2×C4#1306329811yescharacteristic
358C2×C4#1306330711yescharacteristic
359C2×C4C2×#1062188411yescharacteristic
360C2×C4#1306334511yescharacteristic
361C2×C4#1306335011yescharacteristic
362C2×C4#1306335611yescharacteristic
363C8—22no—
364C8—41no—
365C8—862no—
366C8—3441no—
367C8—1721no—
368C8—1721no—
369C8—1721no—
370C22—21no—
371C22—21no—
372C22—1722no—
373C22—1722no—
374C22—1722no—
375C22#1458277511yescharacteristic
376C22#1458310111yescharacteristic
377C22#1458311111yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—82no—
382C4—81no—
383C4—81no—
384C4—1722no—
385C4C4×#1062188411yescharacteristic
386C4#1458299711yescharacteristic
387C4#1458301311yescharacteristic
388C4#1458301811yescharacteristic
389C4#1458304911yescharacteristic
390C4#1458305911yescharacteristic
391C2—21no—
392C2—21no—
393C2—3442no—
394C2#1913491911yescharacteristic
395C2#1913493211yescharacteristic
396C2#1913497511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1986C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1986D43
hypocenterC43#9055
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
4. #19132998C2semidirect
5. #19132436C2semidirect
6. #19132433C2semidirect
7. C43×#1986C2semidirect
10. #14583295C4semidirect
11. #14583273C4semidirect
12. #14583249C4semidirect
13. #14583247C4semidirect
95. M16×C43SD16semidirect
195. #1986D43semidirect
229. C43#9055semidirect
296. M16#10621884semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191433412
#191330892
#191329982
#191324362
#191324332
C43×#19862
#905543