Finite Group Databasebeta

← #25081762

Subgroups — #25081762

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583176C211yesmaximal, characteristic, complemented
2#19144055C211yesmaximal, characteristic
3#19143618C211yesmaximal, characteristic, complemented
4#19134015C214yesmaximal, complemented
5#19133933C214yesmaximal, complemented
6#19133366C211yesmaximal, characteristic, complemented
7#19133280C211yesmaximal, characteristic, complemented
8#19133244C211yesmaximal, characteristic, complemented
9C43×#3206C211yesmaximal, characteristic, complemented
10C2×#13063350—21no—
11C2×C4×D172C2211yescharacteristic
12#14583176—22no—
13#14583176C2214yes—
14#14583111—22no—
15#14583101C2212yes—
16#14583091C2212yes—
17C8×D172C2214yes—
18#14582964—22no—
19#14582952C2211yescharacteristic
20C2×#13063258—21no—
21#14582923C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23#14582900—21no—
24C2×#13063245—21no—
25C22⋊C8×D43—22no—
26#14582650C2214yescomplemented
27#14582645C2212yescomplemented
28#14582645C2214yescomplemented
29#14582643C2212yescomplemented
30C43×#532C2211yescharacteristic
31C2×C4⋊Q8×C43C2211yescharacteristic
32C43×#492C2212yescomplemented
33C43×#487C2212yescomplemented
34C43×#461—22no—
35C43×#448—22no—
36C43×#431C2211yescharacteristic
37C22×D172D411yescharacteristic
38C22×C4×D43—21no—
39#13063350—44no—
40C2×#10621884—22no—
41C2×#10621882—22no—
42C2×#10621877—21no—
43C22×C43⋊C8—21no—
44C2×C8×D43—24no—
45C4×D172—21no—
46C4×D172—21no—
47C4×D172D412yes—
48C4×D172C2312yes—
49C2×C4⋊Dic43D411yescharacteristic
50C2×(C2×D43)⋊C4—21no—
51#13063258—24no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)C2312yes—
55C4⋊(C43⋊C8)C2312yes—
56C4⋊(C43⋊C8)C2312yes—
57#13063249—22no—
58#13063246—22no—
59#13063245—24no—
60C22⋊(C43⋊C8)—21no—
61(C2×D43)⋊C8—24no—
62C4×C43⋊C8—21no—
63C2×#41×C43—21no—
64C22×Q8×C43—21no—
65C2×SD16×C43—24no—
66C4⋊Q8×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43C2312yes—
70C4⋊Q8×C43C2311yescharacteristic
71#127×C43C2311yescharacteristic
72#124×C43—21no—
73#121×C43—21no—
74#121×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43—21no—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C42×C43C2311yescharacteristic
80C4⋊C8×C43D412yes—
81#103×C43—24no—
82C22⋊C8×C43D412yes—
83C4×C8×C43C2312yes—
84C23×D43—21no—
85#41×C43—42no—
86#41×C43—42no—
87C2×Q8×C43—22no—
88C2×Q8×C43—21no—
89C2×Q8×C43—41no—
90C2×Q8×C43—82no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C22×Dic43—21no—
101C2×D172—21no—
102C2×D172—22no—
103C2×D172SD1614yescomplemented
104C2×D172C2×D412yes—
105C2×C4×D43—22no—
106C2×C4×D43—22no—
107C2×C4×D43—82no—
108SD16×C43—84no—
109C2×C8×C43C2×D414yes—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C42×C43C2411yescharacteristic
122#10621884—44no—
123#10621882—44no—
124(C2×D43)⋊C4—22no—
125(C2×D43)⋊C4—22no—
126C4⋊Dic43—21no—
127C4⋊Dic43C2×D412yes—
128#10621877—42no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—42no—
133C8×D43—84no—
134C23×C43—41no—
135C23×C43#12111yescharacteristic
136C22×D43—22no—
137C22×D43—24no—
138C22×D43—81no—
139C22×D43—81no—
140Q8×C43—41no—
141Q8×C43—41no—
142Q8×C43—44no—
143Q8×C43—82no—
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—42no—
153C2×C4×C43—82no—
154C2×C4×C43—82no—
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43C2×SD1612yes—
159C2×C4×C43#13512yes—
160C2×C4×C43C22×D411yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C2×C4×C43C2×#4111yescharacteristic
163C2×Dic43—22no—
164C2×Dic43—81no—
165D172—22no—
166D172—24no—
167D172C2×SD1614yes—
168C4×D43—44no—
169C4×D43—82no—
170C8×C43—24no—
171C43⋊C8—42no—
172C43⋊C8—42no—
173C43⋊C8—42no—
174#19385—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43#46512yes—
181C22×C43C2×#12111yescharacteristic
182C2×D43—24no—
183C2×D43—42no—
184C2×D43—42no—
185C2×D43—84no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—82no—
190C4×C43—81no—
191C4×C43#46512yes—
192C4×C43C22×SD1611yescharacteristic
193C4×C43C2×#13511yescharacteristic
194C4×C43#57612yes—
195Dic43—42no—
196#3206D4311yescharacteristic, complemented
197C2×#474—431no—
198#3036—431no—
199#2972—431no—
200#1679—434no—
201#1665—434no—
202#1570—431no—
203#1549—431no—
204#1540—431no—
205C2×C43—22no—
206C2×C43—161no—
207C2×C43#304111yescharacteristic
208C2×C43C2×#46511yescharacteristic
209C2×C43#306911yescharacteristic
210D43—44no—
211C2×AGL(1,ℤ/8)—861no—
212#532C2×D4311yescharacteristic
213C2×C4⋊Q8C2×D4311yescharacteristic
214C2×C4×D4—431no—
215#492C2×D4312yescomplemented
216#487C2×D4312yescomplemented
217#474—434no—
218#474—862no—
219#463—862no—
220#461—22no—
221#461—432no—
222#459—432no—
223#448—22no—
224C8×D4—434no—
225C8×D4—862no—
226#431—431no—
227#431C2×D4311yescharacteristic
228C2×#107—861no—
229#423—431no—
230C2×C4⋊C8—431no—
231#417—861no—
232C2×#102—861no—
233C2×C22⋊C8—862no—
234#334—434no—
235#332—432no—
236#332—434no—
237#331—432no—
238C43#1938511yescharacteristic, complemented, Sylow
239C2×#41—21no—
240C22×Q8—21no—
241C22×D4—431no—
242C23×C4—861no—
243AGL(1,ℤ/8)—1724no—
244C2×SD16—24no—
245C2×SD16—862no—
246C2×D8—862no—
247C2×M16—861no—
248C22×C8—861no—
249C22×C8—864no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8C22×D4312yes—
254C4⋊Q8C22×D4311yescharacteristic
255#127C22×D4311yescharacteristic
256#124—21no—
257#121—21no—
258#121—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—432no—
262C4×D4—432no—
263C4×D4—861no—
264C4×D4—861no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—431no—
268C2×C22⋊C4—861no—
269C2×C42C22×D4311yescharacteristic
270#107—864no—
271C4⋊C8—432no—
272C4⋊C8—432no—
273C4⋊C8—432no—
274C4⋊C8—861no—
275C4⋊C8—861no—
276C4⋊C8C22⋊D4312yes—
277#103—24no—
278#103—862no—
279#102—864no—
280#102—862no—
281C22⋊C8—861no—
282C22⋊C8—864no—
283C22⋊C8C22⋊D4312yes—
284C4×C8—861no—
285C4×C8C22×D4312yes—
286C24—861no—
287#41—42no—
288#41—42no—
289C2×Q8—21no—
290C2×Q8—22no—
291C2×Q8—41no—
292C2×Q8—82no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—434no—
298C2×D4—432no—
299C2×D4—861no—
300C2×D4—862no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—861no—
304C22×C4—862no—
305C22×C4—862no—
306C22×C4—3442no—
307C22×C4D4×D4311yescharacteristic
308C22×C4#1062190011yescharacteristic
309C22×C4C2×C22⋊D4311yescharacteristic
310SD16—84no—
311SD16—1724no—
312D8—1724no—
313M16—1722no—
314C2×C8—862no—
315C2×C8—862no—
316C2×C8—862no—
317C2×C8—3444no—
318C2×C8—1722no—
319C2×C8C2×C22⋊D4314yes—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—432no—
327C4⋊C4—861no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C42D4×D4311yescharacteristic
333C42#1062190011yescharacteristic
334C42C2×C22⋊D4311yescharacteristic
335C42C23×D4311yescharacteristic
336C23—41no—
337C23—864no—
338C23—862no—
339C23—3441no—
340C23—3441no—
341C23#1306329611yescharacteristic
342Q8—41no—
343Q8—41no—
344Q8—44no—
345Q8—82no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—82no—
351D4—434no—
352D4—864no—
353D4—862no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—862no—
361C2×C4—3442no—
362C2×C4—3441no—
363C2×C4—1724no—
364C2×C4#1306329611yescharacteristic
365C2×C4#1306329611yescharacteristic
366C2×C4#1306329611yescharacteristic
367C2×C4SD16×D4312yes—
368C2×C4#1306334612yes—
369C2×C4C2×D4×D4311yescharacteristic
370C2×C4C22×C22⋊D4311yescharacteristic
371C2×C4C2×#1062190011yescharacteristic
372C8—24no—
373C8—1722no—
374C8—1722no—
375C8—1722no—
376C22—21no—
377C22—21no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—864no—
382C22—3444no—
383C22—1722no—
384C22—1722no—
385C22#1458312512yes—
386C22C2×#1306329611yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—82no—
391C4—81no—
392C4—1722no—
393C4#1458312512yes—
394C4C2×SD16×D4311yescharacteristic
395C4C2×#1306334611yescharacteristic
396C4#1458370212yes—
397C2—22no—
398C2—161no—
399C2—1724no—
400C2#1914409411yescharacteristic
401C2C2×#1458312511yescharacteristic
402C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3206C2
socleC22×C43C2×#121
prime radical#19144055C2
hypercenter#3206D43
hypocenterC43#19385
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
1. C2×#14583176C2semidirect
3. #19143618C2semidirect
4. #19134015C2semidirect
5. #19133933C2semidirect
6. #19133366C2semidirect
7. #19133280C2semidirect
8. #19133244C2semidirect
9. C43×#3206C2semidirect
26. #14582650C22semidirect
27. #14582645C22semidirect
28. #14582645C22semidirect
29. #14582643C22semidirect
32. C43×#492C22semidirect
33. C43×#487C22semidirect
103. C2×D172SD16semidirect
196. #3206D43semidirect
215. #492C2×D43semidirect
216. #487C2×D43semidirect
238. C43#19385semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
#191440552
#191436182
#191340152
#191339332
#191333662
#191332802
#191332442
C43×#32062
#1938543