Finite Group Databasebeta

← #25251845

Subgroups — #25251845

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#19145324C211yesmaximal, characteristic, complemented
2#19136814C211yesmaximal, characteristic, complemented
3#19136809C211yesmaximal, characteristic, complemented
4#19136771C212yesmaximal, complemented
5#19136664C212yesmaximal, complemented
6#19136546C211yesmaximal, characteristic, complemented
7#19136541C211yesmaximal, characteristic
8#19136493C212yesmaximal, complemented
9#19136486C212yesmaximal, complemented
10#19136407C211yesmaximal, characteristic, complemented
11C43×#2956C211yesmaximal, characteristic, complemented
12#14583433—21no—
13#14583339C2212yes—
14#14583334C2212yes—
15#14583301C2211yescharacteristic, complemented
16#14583283C2211yescharacteristic, complemented
17#14583254—21no—
18#14583157C2211yescharacteristic
19#14583152C2211yescharacteristic
20#14583145—21no—
21#14583012C2211yescharacteristic, complemented
22#14583007C2211yescharacteristic, complemented
23#14583001—21no—
24#14582723C2212yescomplemented
25#14582723C2212yescomplemented
26#14582720C2212yescomplemented
27#14582714C2212yescomplemented
28#14582711C2212yescomplemented
29#14582709C2212yes—
30#14582709C2212yes—
31#14582681C2211yescharacteristic
32#14582681C2211yescharacteristic
33#14582677C2212yescomplemented
34C43×#575C2211yescharacteristic
35C43×#568—21no—
36C43×#444—21no—
37C43×#444C2212yes—
38C43×#443—21no—
39C43×#443C2212yes—
40C43×#430C2211yescharacteristic
41C2×#104×C43—21no—
42C4×M16×C43C2211yescharacteristic
43C2×Dic172C2311yescharacteristic
44C2×#10621873—21no—
45C2×D344C2311yescharacteristic
46#13063319—41no—
47#13063317—21no—
48#13063313—21no—
49#13063308—41no—
50#13063304—21no—
51#13063299—21no—
52C4×Dic86—21no—
53C4×D172—21no—
54C4×C22⋊D43—41no—
55#13063282—41no—
56#13063271—22no—
57#13063269—22no—
58#13063268—22no—
59#13063266—22no—
60#13063265C2312yes—
61#13063265C2312yes—
62#13063259—21no—
63#13063257C2311yescharacteristic
64#13063257C2311yescharacteristic
65#13063250—21no—
66#13063250—21no—
67#13063247—21no—
68#13063247—21no—
69C2×#41×C43—21no—
70#137×C43—22no—
71AGL(1,ℤ/8)×C43—22no—
72#135×C43—21no—
73#135×C43C2312yes—
74#131×C43—22no—
75#131×C43—22no—
76#131×C43—42no—
77C2×M16×C43—21no—
78C2×M16×C43—42no—
79C2×M16×C43D411yescharacteristic
80C2×M16×C43C2311yescharacteristic
81C2×C42×C43D411yescharacteristic
82#108×C43—21no—
83#108×C43C2312yes—
84#104×C43—22no—
85#104×C43—22no—
86#97×C43D411yescharacteristic
87#97×C43C2311yescharacteristic
88C4×C8×C43D411yescharacteristic
89C4×C8×C43C2311yescharacteristic
90#41×C43—22no—
91#41×C43—22no—
92#41×C43—41no—
93#41×C43—41no—
94C2×Q8×C43—21no—
95C2×D4×C43—21no—
96C2×D4×C43—41no—
97C22×C4×C43—21no—
98C22×C4×C43—41no—
99C22×C4×C43C2×D411yescharacteristic
100C2×C22⋊D43—41no—
101C2×D172—21no—
102C2×C4×D43—41no—
103C2×Dic86—21no—
104Q16×C43—21no—
105Q16×C43#4112yes—
106SD16×C43—22no—
107SD16×C43—22no—
108D8×C43—21no—
109D8×C43#4112yes—
110M16×C43—22no—
111M16×C43—22no—
112M16×C43—22no—
113M16×C43—42no—
114M16×C43—41no—
115M16×C43—42no—
116C2×C8×C43—42no—
117C2×C8×C43—41no—
118C2×C8×C43—42no—
119C2×C8×C43C2×D411yescharacteristic
120C2×C8×C43C2×D411yescharacteristic
121C2×C8×C43C2×D411yescharacteristic
122C2×C8×C43C2411yescharacteristic
123C42×C43—21no—
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D411yescharacteristic
126C22⋊Dic43—41no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—41no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133Dic43⋊C4—41no—
134Dic43⋊C4—41no—
135Dic43⋊C4—41no—
136Dic43⋊C4—41no—
137C4×Dic43—41no—
138Dic172—22no—
139D344—22no—
140#10621873—42no—
141C43⋊C16—22no—
142C43⋊C16—22no—
143C23×C43—41no—
144C23×C43AGL(1,ℤ/8)11yescharacteristic
145C22×D43—41no—
146Q8×C43—22no—
147Q8×C43—41no—
148D4×C43—22no—
149D4×C43—41no—
150D4×C43—42no—
151D4×C43—42no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—42no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—81no—
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C22⋊D43—82no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166D172—41no—
167D172—41no—
168C4×D43—82no—
169Dic86—41no—
170Dic86—41no—
171C8×C43—21no—
172C8×C43—21no—
173C8×C43—42no—
174C8×C43AGL(1,ℤ/8)12yes—
175C8×C43C2×#4112yes—
176#33690—431nomaximal, Sylow
177C22×C43—21no—
178C22×C43—41no—
179C22×C43—42no—
180C22×C43—161no—
181C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C4×C43—21no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43—42no—
189C4×C43#52511yescharacteristic
190C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
191Dic43—81no—
192Dic43—81no—
193Dic43—81no—
194#3183—431no—
195#2956D4311yescharacteristic, complemented
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—82no—
208C2×C43#310911yescharacteristic
209D43—161no—
210#575C2×D4311yescharacteristic
211#568—21no—
212#529—861no—
213#510—432no—
214#509—432no—
215#499—431no—
216#495—431no—
217#488—861no—
218#470—431no—
219#469—431no—
220#468—861no—
221#444—21no—
222#444C2×D4312yes—
223#443—21no—
224#443C2×D4312yes—
225#442—431no—
226#441—431no—
227#440—861no—
228#430C2×D4311yescharacteristic
229C2×#104—21no—
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—21no—
243#137—22no—
244AGL(1,ℤ/8)—22no—
245#135—21no—
246#135C22×D4312yes—
247C2×Q16—431no—
248C2×SD16—861no—
249C2×D8—431no—
250#131—22no—
251#131—22no—
252#131—42no—
253C2×M16—21no—
254C2×M16—42no—
255C2×M16C22⋊D4311yescharacteristic
256C2×M16C22×D4311yescharacteristic
257#126—1721no—
258#125—861no—
259#124—861no—
260#123—1721no—
261C22⋊Q8—861no—
262#121—861no—
263C4×Q8—861no—
264C4×D4—861no—
265C4×D4—1721no—
266#117—1721no—
267C2×C42C22⋊D4311yescharacteristic
268Q32—862no—
269SD32—862no—
270SD32—862no—
271D16—862no—
272M32—432no—
273M32—432no—
274#108—21no—
275#108C22×D4312yes—
276#107—861no—
277#106—431no—
278#106—431no—
279#104—22no—
280#104—22no—
281#103—861no—
282#103—861no—
283#102—861no—
284#102—861no—
285#97C22⋊D4311yescharacteristic
286#97C22×D4311yescharacteristic
287C4×C8C22⋊D4311yescharacteristic
288C4×C8C22×D4311yescharacteristic
289#41—22no—
290#41—22no—
291#41—41no—
292#41—41no—
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—21no—
304Q16—862no—
305Q16#1062189812yes—
306SD16—22no—
307SD16—22no—
308SD16—1722no—
309D8—21no—
310D8—862no—
311D8#1062189812yes—
312M16—22no—
313M16—22no—
314M16—22no—
315M16—42no—
316M16—41no—
317M16—42no—
318C2×C8—42no—
319C2×C8—41no—
320C2×C8—42no—
321C2×C8C2×C22⋊D4311yescharacteristic
322C2×C8C2×C22⋊D4311yescharacteristic
323C2×C8C2×C22⋊D4311yescharacteristic
324C2×C8C23×D4311yescharacteristic
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—1721no—
328C4⋊C4—1721no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C22⋊C4—1721no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C22⋊C4—1721no—
336C42—21no—
337C42—1721no—
338C42C2×C22⋊D4311yescharacteristic
339C42C2×C22⋊D4311yescharacteristic
340C16—862no—
341C16—862no—
342C23—41no—
343C23—1721no—
344C23#1306335011yescharacteristic
345Q8—22no—
346Q8—41no—
347Q8—1721no—
348Q8—1721no—
349D4—22no—
350D4—41no—
351D4—42no—
352D4—42no—
353D4—3442no—
354D4—1721no—
355D4—1721no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—81no—
364C2×C4—3442no—
365C2×C4—1721no—
366C2×C4—1721no—
367C2×C4—1721no—
368C2×C4#1306335011yescharacteristic
369C2×C4C22×C22⋊D4311yescharacteristic
370C8—21no—
371C8—21no—
372C8—42no—
373C8#1306335112yes—
374C8C2×#1062189812yes—
375C22—21no—
376C22—41no—
377C22—42no—
378C22—161no—
379C22—3441no—
380C22—3441no—
381C22—3441no—
382C22C2×#1306335011yescharacteristic
383C4—21no—
384C4—41no—
385C4—41no—
386C4—42no—
387C4—3441no—
388C4—3441no—
389C4—3441no—
390C4#1458341011yescharacteristic
391C4C2×#1306335111yescharacteristic
392C2—21no—
393C2—41no—
394C2—82no—
395C2—6881no—
396C2#1914468611yescharacteristic
subgroupG/H
centerC2#19144686
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2956C2
socleC2×C43#3109
prime radical#19136541C2
hypercenter#2956D43
hypocenterC43#33690
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2956

Complements

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

NH ≅ G/Ntype
1. #19145324C2semidirect
2. #19136814C2semidirect
3. #19136809C2semidirect
4. #19136771C2semidirect
5. #19136664C2semidirect
6. #19136546C2semidirect
8. #19136493C2semidirect
9. #19136486C2semidirect
10. #19136407C2semidirect
11. C43×#2956C2semidirect
15. #14583301C22semidirect
16. #14583283C22semidirect
21. #14583012C22semidirect
22. #14583007C22semidirect
24. #14582723C22semidirect
25. #14582723C22semidirect
26. #14582720C22semidirect
27. #14582714C22semidirect
28. #14582711C22semidirect
33. #14582677C22semidirect
195. #2956D43semidirect
241. C43#33690semidirect

Maximal subgroups

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

subgroupindex
#191453242
#191368142
#191368092
#191367712
#191366642
#191365462
#191365412
#191364932
#191364862
#191364072
C43×#29562
#3369043