Finite Group Databasebeta

← #25251856

Subgroups — #25251856

Order 11008.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145212C211yesmaximal, characteristic, complemented
2#19136814C211yesmaximal, characteristic, complemented
3#19136809C211yesmaximal, characteristic, complemented
4#19136766C212yesmaximal, complemented
5#19136664C212yesmaximal, complemented
6#19136546C211yesmaximal, characteristic, complemented
7#19136541C211yesmaximal, characteristic
8#19136493C212yesmaximal, complemented
9#19136486C212yesmaximal, complemented
10#19136411C211yesmaximal, characteristic, complemented
11C43×#2955C211yesmaximal, characteristic, complemented
12#14583520—21no—
13#14583339C2212yes—
14#14583334C2212yes—
15#14583297C2211yescharacteristic, complemented
16#14583283C2211yescharacteristic, complemented
17#14583259—21no—
18#14583157C2211yescharacteristic
19#14583152C2211yescharacteristic
20#14583128—21no—
21#14583012C2211yescharacteristic, complemented
22#14583007C2211yescharacteristic, complemented
23C4×#10621873—21no—
24#14582723C2212yescomplemented
25#14582723C2212yescomplemented
26#14582720C2212yescomplemented
27#14582714C2212yescomplemented
28#14582711C2212yescomplemented
29#14582709C2212yes—
30#14582709C2212yes—
31#14582681C2211yescharacteristic
32#14582681C2211yescharacteristic
33#14582677C2212yescomplemented
34C43×#575C2211yescharacteristic
35C2×#131×C43—21no—
36C43×#444—21no—
37C43×#444C2212yes—
38C43×#443—21no—
39C43×#443C2212yes—
40C43×#430C2211yescharacteristic
41C43×#421—21no—
42C43×#405C2211yescharacteristic
43C2×Dic172C2311yescharacteristic
44C2×#10621873—21no—
45C2×D344C2311yescharacteristic
46#13063325—21no—
47#13063320—41no—
48#13063313—21no—
49#13063311—41no—
50#13063307—41no—
51#13063304—21no—
52#13063303—41no—
53#13063299—21no—
54C4×Dic86—21no—
55C4×D172—21no—
56#13063271—22no—
57#13063269—22no—
58#13063268—22no—
59#13063266—22no—
60#13063265C2312yes—
61#13063265C2312yes—
62#13063257—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—41no—
77#131×C43—41no—
78C2×M16×C43—21no—
79C2×M16×C43—41no—
80C2×M16×C43C2311yescharacteristic
81C22×C8×C43—41no—
82C22×C8×C43D411yescharacteristic
83#117×C43D411yescharacteristic
84#108×C43—21no—
85#108×C43C2312yes—
86#104×C43—22no—
87#104×C43—22no—
88#97×C43D411yescharacteristic
89#97×C43C2311yescharacteristic
90C4×C8×C43D411yescharacteristic
91C4×C8×C43C2311yescharacteristic
92#41×C43—22no—
93#41×C43—22no—
94#41×C43—41no—
95#41×C43—41no—
96C2×Q8×C43—21no—
97C2×D4×C43—21no—
98C2×D4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43C2×D411yescharacteristic
101C2×C22⋊D43—41no—
102C2×D172—21no—
103C2×C4×D43—41no—
104C2×Dic86—21no—
105C2×Dic86—41no—
106Q16×C43—21no—
107Q16×C43#4112yes—
108SD16×C43—22no—
109SD16×C43—22no—
110D8×C43—21no—
111D8×C43#4112yes—
112M16×C43—22no—
113M16×C43—22no—
114M16×C43—42no—
115M16×C43—41no—
116M16×C43—42no—
117C2×C8×C43—21no—
118C2×C8×C43—21no—
119C2×C8×C43—42no—
120C2×C8×C43—41no—
121C2×C8×C43—42no—
122C2×C8×C43C2×D411yescharacteristic
123C2×C8×C43C2×D411yescharacteristic
124C2×C8×C43C2×D411yescharacteristic
125C2×C8×C43C2411yescharacteristic
126C4⋊C4×C43—21no—
127C22⋊C4×C43—21no—
128C42×C43C2×D411yescharacteristic
129C42×C43C2×D411yescharacteristic
130C22⋊Dic43—41no—
131(C2×D43)⋊C4—41no—
132(C2×D43)⋊C4—41no—
133(C2×D43)⋊C4—41no—
134(C2×D43)⋊C4—41no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43—41no—
138Dic43⋊C4—41no—
139Dic43⋊C4—41no—
140C4×Dic43—41no—
141Dic172—22no—
142D344—22no—
143#10621873—41no—
144#10621873—41no—
145C43⋊C16—22no—
146C43⋊C16—22no—
147C23×C43—41no—
148C23×C43AGL(1,ℤ/8)11yescharacteristic
149C22×D43—41no—
150Q8×C43—22no—
151Q8×C43—41no—
152D4×C43—22no—
153D4×C43—41no—
154D4×C43—42no—
155D4×C43—42no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—42no—
163C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C43C22×D411yescharacteristic
165C22⋊D43—161no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169D172—41no—
170D172—41no—
171C4×D43—161no—
172Dic86—41no—
173Dic86—41no—
174Dic86—161no—
175C8×C43—21no—
176C8×C43—21no—
177C8×C43—42no—
178C8×C43AGL(1,ℤ/8)11yescharacteristic
179C8×C43AGL(1,ℤ/8)11yescharacteristic
180C8×C43C2×#4112yes—
181#33691—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—41no—
184C22×C43—42no—
185C22×C43—82no—
186C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
187C2×D43—81no—
188C2×D43—81no—
189C2×D43—81no—
190C4×C43—21no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43—42no—
194C4×C43#52511yescharacteristic
195C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
196Dic43—81no—
197Dic43—81no—
198Dic43—81no—
199#3173—431no—
200#2955D4311yescharacteristic, complemented
201#2239—431no—
202#2238—431no—
203#2230—432no—
204#2212—432no—
205#2191—431no—
206#2190—431no—
207AGL(1,ℤ/16)—432no—
208#2180—432no—
209#2166—431no—
210C2×C43—21no—
211C2×C43—41no—
212C2×C43—82no—
213C2×C43#310911yescharacteristic
214D43—161no—
215#575C2×D4311yescharacteristic
216C2×#131—21no—
217#542—861no—
218#510—432no—
219#509—432no—
220#498—431no—
221#495—431no—
222#489—861no—
223#470—431no—
224#469—431no—
225#465—861no—
226#444—21no—
227#444C2×D4312yes—
228#443—21no—
229#443C2×D4312yes—
230#442—431no—
231#441—431no—
232C4×SD16—861no—
233#430C2×D4311yescharacteristic
234#421—21no—
235#405C2×D4311yescharacteristic
236#365—432no—
237#365—432no—
238#364—432no—
239#362—432no—
240#361—432no—
241#360—432no—
242#360—432no—
243#349—431no—
244#349—431no—
245#347—432no—
246C43#3369111yescharacteristic, complemented, Sylow
247C2×#41—21no—
248#137—22no—
249AGL(1,ℤ/8)—22no—
250#135—21no—
251#135C22×D4312yes—
252C2×Q16—431no—
253C2×SD16—861no—
254C2×D8—431no—
255#131—22no—
256#131—22no—
257#131—41no—
258#131—41no—
259C2×M16—21no—
260C2×M16—41no—
261C2×M16C22×D4311yescharacteristic
262C22×C8—41no—
263C22×C8C22⋊D4311yescharacteristic
264C4⋊Q8—861no—
265#126—1721no—
266#124—861no—
267#124—1721no—
268#123—1721no—
269C22⋊Q8—861no—
270C22⋊Q8—1721no—
271#121—861no—
272C4×Q8—861no—
273C4×D4—861no—
274#117C22⋊D4311yescharacteristic
275Q32—862no—
276SD32—862no—
277SD32—862no—
278D16—862no—
279M32—432no—
280M32—432no—
281#108—21no—
282#108C22×D4312yes—
283#106—431no—
284#106—431no—
285#106—861no—
286#104—22no—
287#104—22no—
288#103—861no—
289#103—861no—
290#102—861no—
291#102—861no—
292#97C22⋊D4311yescharacteristic
293#97C22×D4311yescharacteristic
294C4×C8C22⋊D4311yescharacteristic
295C4×C8C22×D4311yescharacteristic
296#41—22no—
297#41—22no—
298#41—41no—
299#41—41no—
300C2×Q8—21no—
301C2×Q8—861no—
302C2×Q8—1721no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—861no—
306C2×D4—1721no—
307C22×C4—41no—
308C22×C4—1721no—
309C22×C4C2×C22⋊D4311yescharacteristic
310Q16—21no—
311Q16—862no—
312Q16#1062189812yes—
313SD16—22no—
314SD16—22no—
315SD16—1721no—
316SD16—1721no—
317D8—21no—
318D8—862no—
319D8#1062189812yes—
320M16—22no—
321M16—22no—
322M16—42no—
323M16—41no—
324M16—42no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—42no—
328C2×C8—41no—
329C2×C8—42no—
330C2×C8C2×C22⋊D4311yescharacteristic
331C2×C8C2×C22⋊D4311yescharacteristic
332C2×C8C2×C22⋊D4311yescharacteristic
333C2×C8C23×D4311yescharacteristic
334C4⋊C4—21no—
335C4⋊C4—861no—
336C4⋊C4—861no—
337C4⋊C4—1721no—
338C4⋊C4—1721no—
339C4⋊C4—1721no—
340C22⋊C4—21no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C42—1721no—
347C42C2×C22⋊D4311yescharacteristic
348C42C2×C22⋊D4311yescharacteristic
349C16—862no—
350C16—862no—
351C23—41no—
352C23—1721no—
353C23#1306335011yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—1721no—
357Q8—1721no—
358Q8—6881no—
359D4—22no—
360D4—41no—
361D4—42no—
362D4—42no—
363D4—1721no—
364D4—1721no—
365D4—6881no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—6881no—
377C2×C4#1306335011yescharacteristic
378C2×C4C22×C22⋊D4311yescharacteristic
379C8—21no—
380C8—21no—
381C8—42no—
382C8#1306335111yescharacteristic
383C8#1306335111yescharacteristic
384C8C2×#1062189812yes—
385C22—21no—
386C22—41no—
387C22—42no—
388C22—82no—
389C22—3441no—
390C22—3441no—
391C22—3441no—
392C22C2×#1306335011yescharacteristic
393C4—21no—
394C4—41no—
395C4—41no—
396C4—42no—
397C4—3441no—
398C4—3441no—
399C4—3441no—
400C4#1458341011yescharacteristic
401C4C2×#1306335111yescharacteristic
402C2—21no—
403C2—41no—
404C2—82no—
405C2—6881no—
406C2#1914468611yescharacteristic
subgroupG/H
centerC2#19144686
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2955C2
socleC2×C43#3109
prime radical#19136541C2
hypercenter#2955D43
hypocenterC43#33691
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2955

Complements

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

NH ≅ G/Ntype
1. #19145212C2semidirect
2. #19136814C2semidirect
3. #19136809C2semidirect
4. #19136766C2semidirect
5. #19136664C2semidirect
6. #19136546C2semidirect
8. #19136493C2semidirect
9. #19136486C2semidirect
10. #19136411C2semidirect
11. C43×#2955C2semidirect
15. #14583297C22semidirect
16. #14583283C22semidirect
21. #14583012C22semidirect
22. #14583007C22semidirect
24. #14582723C22semidirect
25. #14582723C22semidirect
26. #14582720C22semidirect
27. #14582714C22semidirect
28. #14582711C22semidirect
33. #14582677C22semidirect
200. #2955D43semidirect
246. C43#33691semidirect

Maximal subgroups

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

subgroupindex
#191452122
#191368142
#191368092
#191367662
#191366642
#191365462
#191365412
#191364932
#191364862
#191364112
C43×#29552
#3369143