Finite Group Databasebeta

← #25081763

Subgroups — #25081763

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
1#19145520C211yesmaximal, characteristic, complemented
2#19144059C211yesmaximal, characteristic
3#19143619C211yesmaximal, characteristic, complemented
4#19134016C214yesmaximal, complemented
5#19133938C214yesmaximal, complemented
6#19133365C211yesmaximal, characteristic, complemented
7#19133280C211yesmaximal, characteristic, complemented
8#19133245C211yesmaximal, characteristic, complemented
9C2×C43×#474C211yesmaximal, characteristic, complemented
10C2×#13063351—21no—
11#14583449C2211yescharacteristic
12#14583273C2212yescomplemented
13#14583249C2212yescomplemented
14#14583114—22no—
15#14583104C2212yes—
16#14583101—22no—
17#14583094C2212yes—
18#14583038—22no—
19D4×C43⋊C8—22no—
20D4×C43⋊C8C2214yes—
21#14582952C2211yescharacteristic
22#14582952C2211yescharacteristic
23#14582923C2211yescharacteristic
24#14582898—21no—
25C2×C22⋊(C43⋊C8)—22no—
26#14582649C2214yescomplemented
27#14582646C2212yescomplemented
28#14582645C2214yescomplemented
29#14582642C2212yescomplemented
30C2×C4⋊Q8×C43C2211yescharacteristic
31C2×C4×D4×C43C2211yescharacteristic
32C43×#474—22no—
33C43×#474C2214yes—
34C2×#107×C43—21no—
35C2×C4⋊C8×C43C2211yescharacteristic
36C2×#102×C43—21no—
37C2×#10621898—21no—
38#13063351—44no—
39C2×#10621883—22no—
40C2×#10621884—24no—
41C2×#10621882—22no—
42C2×#10621877—21no—
43C22×C43⋊C8—24no—
44#13063325C2311yescharacteristic
45#13063322C2311yescharacteristic
46#13063313—21no—
47#13063299—21no—
48#13063299—21no—
49C4×D172—21no—
50C4×D172—21no—
51C4⋊(C43⋊C8)—21no—
52C4⋊(C43⋊C8)D412yes—
53C4⋊(C43⋊C8)C2312yes—
54C4⋊(C43⋊C8)C2312yes—
55#13063249—24no—
56#13063248—22no—
57#13063245—22no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—24no—
60C22⋊(C43⋊C8)D412yes—
61C4×C43⋊C8—21no—
62C4×C43⋊C8C2312yes—
63C22×Q8×C43—21no—
64C22×D4×C43D411yescharacteristic
65C23×C4×C43—21no—
66C22×C8×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43—21no—
70C4⋊Q8×C43C2312yes—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43D412yes—
74C4×D4×C43C2312yes—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43D411yescharacteristic
78C2×C22⋊C4×C43—21no—
79C2×C42×C43C2311yescharacteristic
80#107×C43—24no—
81C4⋊C8×C43—21no—
82C4⋊C8×C43C2312yes—
83#102×C43—24no—
84C24×C43—21no—
85C2×Q8×C43—22no—
86C2×Q8×C43—41no—
87C2×Q8×C43—82no—
88C2×D4×C43—21no—
89C2×D4×C43—22no—
90C2×D4×C43SD1614yescomplemented
91C2×D4×C43C2×D412yes—
92C22×C4×C43—22no—
93C22×C4×C43—22no—
94C22×C4×C43—21no—
95C22×C4×C43—41no—
96C22×C4×C43—82no—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—41no—
101#10621898—42no—
102#10621898—42no—
103C2×D172—21no—
104C2×D172—21no—
105C2×D172—21no—
106C2×C4×D43—41no—
107C2×Dic86—21no—
108C2×C8×C43—22no—
109C2×C8×C43—42no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—22no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43C2×D412yes—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—22no—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C42×C43C2411yescharacteristic
122#10621884—84no—
123#10621883—44no—
124#10621882—44no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129#10621877—42no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—84no—
133C2×C43⋊C8C2×D414yes—
134C23×C43—22no—
135C23×C43—24no—
136C23×C43—81no—
137C23×C43—81no—
138C23×C43#12111yescharacteristic
139C22×D43—41no—
140Q8×C43—44no—
141Q8×C43—82no—
142D4×C43—22no—
143D4×C43—24no—
144D4×C43C2×SD1614yes—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—41no—
148C2×C4×C43—44no—
149C2×C4×C43—42no—
150C2×C4×C43—82no—
151C2×C4×C43—81no—
152C2×C4×C43—82no—
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43C2×SD1612yes—
157C2×C4×C43#13512yes—
158C2×C4×C43C22×D411yescharacteristic
159C2×C4×C43C22×D411yescharacteristic
160C2×C4×C43C2×#4111yescharacteristic
161C22⋊D43—82no—
162C2×Dic43—41no—
163D172—41no—
164D172—41no—
165D172—42no—
166D172—81no—
167C4×D43—82no—
168Dic86—41no—
169Dic86—41no—
170C8×C43—42no—
171C43⋊C8—24no—
172C43⋊C8—42no—
173C43⋊C8—42no—
174#19385—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—24no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—84no—
181C22×C43#46512yes—
182C22×C43C2×#12111yescharacteristic
183C2×D43—81no—
184C2×D43—81no—
185C2×D43—81no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—42no—
190C4×C43—82no—
191C4×C43#46512yes—
192C4×C43C22×SD1611yescharacteristic
193C4×C43C2×#13511yescharacteristic
194C4×C43#57612yes—
195Dic43—81no—
196#3206—431no—
197C2×#474D4311yescharacteristic, complemented
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—44no—
207C2×C43#304111yescharacteristic
208C2×C43C2×#46511yescharacteristic
209C2×C43#306911yescharacteristic
210D43—161no—
211C2×AGL(1,ℤ/8)—861no—
212#532—431no—
213C2×C4⋊Q8C2×D4311yescharacteristic
214C2×C4×D4C2×D4311yescharacteristic
215#492—432no—
216#487—432no—
217#474—22no—
218#474C2×D4314yes—
219#463—862no—
220#461—432no—
221#461—862no—
222#459—432no—
223#448—862no—
224C8×D4—434no—
225C8×D4—862no—
226#431—431no—
227#431—431no—
228C2×#107—21no—
229#423—431no—
230C2×C4⋊C8C2×D4311yescharacteristic
231#417—861no—
232C2×#102—21no—
233C2×C22⋊C8—862no—
234#334—434no—
235#332—434no—
236#332—432no—
237#331—432no—
238C43#1938511yescharacteristic, complemented, Sylow
239C2×#41—861no—
240C22×Q8—21no—
241C22×D4C22⋊D4311yescharacteristic
242C23×C4—21no—
243AGL(1,ℤ/8)—1724no—
244C2×SD16—864no—
245C2×SD16—862no—
246C2×D8—862no—
247C2×M16—861no—
248C22×C8—21no—
249C22×C8—864no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—431no—
254C4⋊Q8C22×D4312yes—
255#127—431no—
256#124—861no—
257#121—861no—
258#121—861no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—861no—
262C4×D4—861no—
263C4×D4C22⋊D4312yes—
264C4×D4C22×D4312yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4C22⋊D4311yescharacteristic
268C2×C22⋊C4—21no—
269C2×C42C22×D4311yescharacteristic
270#107—24no—
271C4⋊C8—21no—
272C4⋊C8—432no—
273C4⋊C8—432no—
274C4⋊C8—432no—
275C4⋊C8—861no—
276C4⋊C8C22×D4312yes—
277#103—864no—
278#103—862no—
279#102—24no—
280#102—862no—
281C22⋊C8—432no—
282C22⋊C8—864no—
283C22⋊C8—861no—
284C4×C8—432no—
285C4×C8—861no—
286C24—21no—
287#41—1722no—
288#41—1722no—
289C2×Q8—22no—
290C2×Q8—41no—
291C2×Q8—82no—
292C2×Q8—861no—
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4—1721no—
299C2×D4#1062188414yescomplemented
300C2×D4C2×C22⋊D4312yes—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—82no—
306C22×C4—1721no—
307C22×C4D4×D4311yescharacteristic
308C22×C4#1062190011yescharacteristic
309C22×C4C2×C22⋊D4311yescharacteristic
310SD16—3444no—
311SD16—1724no—
312D8—1724no—
313M16—1722no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—434no—
317C2×C8—862no—
318C2×C8—862no—
319C2×C8—3444no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4C2×C22⋊D4312yes—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—1721no—
331C22⋊C4—1721no—
332C42D4×D4311yescharacteristic
333C42#1062190011yescharacteristic
334C42C2×C22⋊D4311yescharacteristic
335C42C23×D4311yescharacteristic
336C23—22no—
337C23—24no—
338C23—81no—
339C23—81no—
340C23—1721no—
341C23#1306329711yescharacteristic
342Q8—44no—
343Q8—82no—
344Q8—1721no—
345Q8—1721no—
346D4—24no—
347D4—22no—
348D4—3441no—
349D4—3442no—
350D4—1721no—
351D4—1721no—
352D4—1722no—
353D4C2×#1062188414yes—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4—3442no—
363C2×C4—1721no—
364C2×C4#1306329711yescharacteristic
365C2×C4#1306329711yescharacteristic
366C2×C4#1306329711yescharacteristic
367C2×C4C2×#1062188412yes—
368C2×C4#1306334512yes—
369C2×C4C2×D4×D4311yescharacteristic
370C2×C4C22×C22⋊D4311yescharacteristic
371C2×C4C2×#1062190011yescharacteristic
372C8—42no—
373C8—864no—
374C8—1722no—
375C8—1722no—
376C22—21no—
377C22—21no—
378C22—24no—
379C22—42no—
380C22—42no—
381C22—84no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22#1458313012yes—
386C22C2×#1306329711yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—82no—
392C4—3441no—
393C4#1458313012yes—
394C4C22×#1062188411yescharacteristic
395C4C2×#1306334511yescharacteristic
396C4#1458370012yes—
397C2—22no—
398C2—44no—
399C2—6881no—
400C2#1914409511yescharacteristic
401C2C2×#1458313011yescharacteristic
402C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#474C2
socleC22×C43C2×#121
prime radical#19144059C2
hypercenterC2×#474D43
hypocenterC43#19385
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #19145520C2semidirect
3. #19143619C2semidirect
4. #19134016C2semidirect
5. #19133938C2semidirect
6. #19133365C2semidirect
7. #19133280C2semidirect
8. #19133245C2semidirect
9. C2×C43×#474C2semidirect
12. #14583273C22semidirect
13. #14583249C22semidirect
26. #14582649C22semidirect
27. #14582646C22semidirect
28. #14582645C22semidirect
29. #14582642C22semidirect
90. C2×D4×C43SD16semidirect
197. C2×#474D43semidirect
238. C43#19385semidirect
299. C2×D4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191455202
#191440592
#191436192
#191340162
#191339382
#191333652
#191332802
#191332452
C2×C43×#4742
#1938543