Finite Group Databasebeta

← #25251841

Subgroups — #25251841

Order 11008.

526 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#19143506C211yesmaximal, characteristic, complemented
2#19136812C211yesmaximal, characteristic, complemented
3#19136807C211yesmaximal, characteristic, complemented
4#19136768C212yesmaximal, complemented
5#19136661C212yesmaximal, complemented
6#19136545C211yesmaximal, characteristic, complemented
7#19136540C211yesmaximal, characteristic
8#19136491C212yesmaximal, complemented
9#19136484C212yesmaximal, complemented
10#19136407C211yesmaximal, characteristic, complemented
11C43×#3183C211yesmaximal, characteristic, complemented
12#14583699C2211yescharacteristic
13#14583665—21no—
14#14583340C2212yes—
15#14583335C2212yes—
16#14583022—21no—
17#14583022C2212yes—
18#14583017—21no—
19#14583017C2212yes—
20#14582948C2211yescharacteristic
21C2×#13063253—21no—
22#14582721C2212yescomplemented
23#14582721C2212yescomplemented
24#14582720C2212yescomplemented
25#14582715C2212yescomplemented
26#14582712C2212yescomplemented
27#14582708C2212yes—
28#14582708C2212yes—
29#14582681C2211yescharacteristic
30#14582681C2211yescharacteristic
31#14582677C2212yescomplemented
32C43×#529—21no—
33C43×#499C2211yescharacteristic, complemented
34C43×#495C2211yescharacteristic, complemented
35C43×#488—21no—
36C43×#470C2211yescharacteristic
37C43×#469C2211yescharacteristic
38C43×#468—21no—
39C43×#442C2211yescharacteristic, complemented
40C43×#441C2211yescharacteristic, complemented
41C43×#440—21no—
42C4×M16×C43C2211yescharacteristic
43C2×#10621898—21no—
44#13063358—22no—
45#13063353—22no—
46#13063347—21no—
47#13063347C2312yes—
48#13063333—42no—
49#13063331—22no—
50#13063331—22no—
51C2×#10621877—21no—
52M16×D43—42no—
53#13063271—22no—
54#13063269—22no—
55#13063268—22no—
56#13063266—22no—
57#13063265C2312yes—
58#13063265C2312yes—
59#13063261—21no—
60#13063261C2312yes—
61#13063253—22no—
62#13063253—22no—
63C2×Q16×C43C2311yescharacteristic
64C2×SD16×C43—21no—
65C2×D8×C43C2311yescharacteristic
66C2×M16×C43D411yescharacteristic
67C2×M16×C43C2311yescharacteristic
68#126×C43—41no—
69#125×C43—21no—
70#124×C43—21no—
71#123×C43—41no—
72C22⋊Q8×C43—21no—
73#121×C43—21no—
74C4×Q8×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43—41no—
77#117×C43—41no—
78C2×C42×C43D411yescharacteristic
79#107×C43—21no—
80#106×C43C2311yescharacteristic
81#106×C43C2311yescharacteristic
82#103×C43—21no—
83#103×C43—21no—
84#102×C43—21no—
85#102×C43—21no—
86#97×C43D411yescharacteristic
87#97×C43C2311yescharacteristic
88C4×C8×C43D411yescharacteristic
89C4×C8×C43C2311yescharacteristic
90C2×Q8×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—41no—
93C22×C4×C43—21no—
94C22×C4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C2×C22⋊D43—41no—
97#10621898—22no—
98#10621898—22no—
99#10621898—41no—
100#10621898—41no—
101C2×D172—21no—
102C2×C4×D43—41no—
103C2×Dic86—21no—
104Q16×C43—22no—
105SD16×C43—42no—
106D8×C43—22no—
107M16×C43—22no—
108M16×C43—22no—
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2411yescharacteristic
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—41no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C22⋊C4×C43—41no—
124C42×C43—21no—
125C42×C43—41no—
126C42×C43C2×D411yescharacteristic
127C42×C43C2×D411yescharacteristic
128#10621877—22no—
129#10621877—41no—
130C2×C43⋊C8—41no—
131Dic172—21no—
132Dic172#4112yes—
133D344—21no—
134D344#4112yes—
135#10621873—22no—
136#10621873—22no—
137#10621872—42no—
138#10621872—42no—
139C8×D43—42no—
140C8×D43—42no—
141C43⋊C16—22no—
142C43⋊C16—22no—
143C23×C43—41no—
144C23×C43AGL(1,ℤ/8)11yescharacteristic
145C22×D43—41no—
146Q8×C43—41no—
147Q8×C43—41no—
148D4×C43—41no—
149D4×C43—41no—
150D4×C43—82no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—81no—
159C2×C4×C43—82no—
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C22⋊D43—42no—
163C22⋊D43—42no—
164C2×Dic43—41no—
165D172—22no—
166D172—41no—
167C4×D43—42no—
168C4×D43—42no—
169Dic86—22no—
170Dic86—41no—
171C8×C43—21no—
172C8×C43—21no—
173C8×C43AGL(1,ℤ/8)12yes—
174C8×C43C2×#4112yes—
175C43⋊C8—42no—
176#33690—431nomaximal, Sylow
177C22×C43—21no—
178C22×C43—41no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
183C2×D43—42no—
184C2×D43—161no—
185C4×C43—21no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43—81no—
189C4×C43—81no—
190C4×C43—81no—
191C4×C43#52511yescharacteristic
192C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
193Dic43—42no—
194#3183D4311yescharacteristic, complemented
195#2956—431no—
196#2239—431no—
197#2238—431no—
198#2231—432no—
199#2212—432no—
200#2191—431no—
201#2190—431no—
202AGL(1,ℤ/16)—432no—
203#2180—432no—
204#2165—431no—
205C2×C43—21no—
206C2×C43—41no—
207C2×C43—161no—
208C2×C43#310911yescharacteristic
209D43—82no—
210#575—431no—
211#568—861no—
212#529—21no—
213#510—432no—
214#509—432no—
215#499C2×D4311yescharacteristic, complemented
216#495C2×D4311yescharacteristic, complemented
217#488—21no—
218#470C2×D4311yescharacteristic
219#469C2×D4311yescharacteristic
220#468—21no—
221#444—432no—
222#444—861no—
223#443—432no—
224#443—861no—
225#442C2×D4311yescharacteristic, complemented
226#441C2×D4311yescharacteristic, complemented
227#440—21no—
228#430—431no—
229C2×#104—861no—
230C4×M16C2×D4311yescharacteristic
231#365—432no—
232#365—432no—
233#364—432no—
234#362—432no—
235#361—432no—
236#360—432no—
237#360—432no—
238#349—431no—
239#349—431no—
240#347—432no—
241C43#3369011yescharacteristic, complemented, Sylow
242C2×#41—861no—
243#137—862no—
244AGL(1,ℤ/8)—862no—
245#135—432no—
246#135—861no—
247C2×Q16C22×D4311yescharacteristic
248C2×SD16—21no—
249C2×D8C22×D4311yescharacteristic
250#131—862no—
251#131—862no—
252#131—1722no—
253C2×M16—861no—
254C2×M16—1722no—
255C2×M16C22⋊D4311yescharacteristic
256C2×M16C22×D4311yescharacteristic
257#126—41no—
258#125—21no—
259#124—21no—
260#123—41no—
261C22⋊Q8—21no—
262#121—21no—
263C4×Q8—21no—
264C4×D4—21no—
265C4×D4—41no—
266#117—41no—
267C2×C42C22⋊D4311yescharacteristic
268Q32—862no—
269SD32—862no—
270SD32—862no—
271D16—862no—
272M32—432no—
273M32—432no—
274#108—432no—
275#108—861no—
276#107—21no—
277#106C22×D4311yescharacteristic
278#106C22×D4311yescharacteristic
279#104—862no—
280#104—862no—
281#103—21no—
282#103—21no—
283#102—21no—
284#102—21no—
285#97C22⋊D4311yescharacteristic
286#97C22×D4311yescharacteristic
287C4×C8C22⋊D4311yescharacteristic
288C4×C8C22×D4311yescharacteristic
289#41—862no—
290#41—862no—
291#41—1721no—
292#41—1721no—
293C2×Q8—21no—
294C2×Q8—861no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—861no—
298C2×D4—1721no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—1721no—
302C22×C4C2×C22⋊D4311yescharacteristic
303Q16—22no—
304Q16—432no—
305Q16—861no—
306SD16—42no—
307SD16—862no—
308SD16—862no—
309D8—22no—
310D8—432no—
311D8—861no—
312M16—22no—
313M16—22no—
314M16—862no—
315M16—1722no—
316M16—1721no—
317M16—1722no—
318C2×C8—1722no—
319C2×C8—1721no—
320C2×C8—1722no—
321C2×C8C2×C22⋊D4311yescharacteristic
322C2×C8C2×C22⋊D4311yescharacteristic
323C2×C8C2×C22⋊D4311yescharacteristic
324C2×C8C23×D4311yescharacteristic
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42—21no—
337C42—41no—
338C42C2×C22⋊D4311yescharacteristic
339C42C2×C22⋊D4311yescharacteristic
340C16—862no—
341C16—862no—
342C23—41no—
343C23—1721no—
344C23#1306335111yescharacteristic
345Q8—41no—
346Q8—41no—
347Q8—862no—
348Q8—1721no—
349D4—41no—
350D4—41no—
351D4—82no—
352D4—862no—
353D4—1721no—
354D4—1722no—
355D4—1722no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—82no—
365C2×C4—1722no—
366C2×C4—1721no—
367C2×C4—1722no—
368C2×C4#1306335111yescharacteristic
369C2×C4C22×C22⋊D4311yescharacteristic
370C8—21no—
371C8—21no—
372C8—1722no—
373C8#1306335012yes—
374C8#41×D4312yes—
375C22—21no—
376C22—41no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—1722no—
381C22—6881no—
382C22C2×#1306335111yescharacteristic
383C4—21no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—1722no—
390C4#1458340611yescharacteristic
391C4C2×#1306335011yescharacteristic
392C2—21no—
393C2—41no—
394C2—161no—
395C2—3442no—
396C2#1914468211yescharacteristic
subgroupG/H
centerC2#19144682
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3183C2
socleC2×C43#3109
prime radical#19136540C2
hypercenter#3183D43
hypocenterC43#33690
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3183

Complements

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

NH ≅ G/Ntype
1. #19143506C2semidirect
2. #19136812C2semidirect
3. #19136807C2semidirect
4. #19136768C2semidirect
5. #19136661C2semidirect
6. #19136545C2semidirect
8. #19136491C2semidirect
9. #19136484C2semidirect
10. #19136407C2semidirect
11. C43×#3183C2semidirect
22. #14582721C22semidirect
23. #14582721C22semidirect
24. #14582720C22semidirect
25. #14582715C22semidirect
26. #14582712C22semidirect
31. #14582677C22semidirect
33. C43×#499C22semidirect
34. C43×#495C22semidirect
39. C43×#442C22semidirect
40. C43×#441C22semidirect
194. #3183D43semidirect
215. #499C2×D43semidirect
216. #495C2×D43semidirect
225. #442C2×D43semidirect
226. #441C2×D43semidirect
241. C43#33690semidirect

Maximal subgroups

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

subgroupindex
#191435062
#191368122
#191368072
#191367682
#191366612
#191365452
#191365402
#191364912
#191364842
#191364072
C43×#31832
#3369043