Finite Group Databasebeta

← #25251852

Subgroups — #25251852

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#19143499C211yesmaximal, characteristic, complemented
2#19136812C211yesmaximal, characteristic, complemented
3#19136807C211yesmaximal, characteristic, complemented
4#19136763C212yesmaximal, complemented
5#19136661C212yesmaximal, complemented
6#19136545C211yesmaximal, characteristic, complemented
7#19136540C211yesmaximal, characteristic
8#19136491C212yesmaximal, complemented
9#19136484C212yesmaximal, complemented
10#19136411C211yesmaximal, characteristic, complemented
11C43×#3173C211yesmaximal, characteristic, complemented
12#14583699C2211yescharacteristic
13C2×#13063331—21no—
14#14583340C2212yes—
15#14583335C2212yes—
16#14583022—21no—
17#14583022C2212yes—
18#14583017—21no—
19#14583017C2212yes—
20#14582948C2211yescharacteristic
21#14582917—21no—
22#14582721C2212yescomplemented
23#14582721C2212yescomplemented
24#14582720C2212yescomplemented
25#14582715C2212yescomplemented
26#14582712C2212yescomplemented
27#14582708C2212yes—
28#14582708C2212yes—
29#14582681C2211yescharacteristic
30#14582681C2211yescharacteristic
31#14582677C2212yescomplemented
32C43×#542—21no—
33C43×#498C2211yescharacteristic, complemented
34C43×#495C2211yescharacteristic, complemented
35C43×#489—21no—
36C43×#470C2211yescharacteristic
37C43×#469C2211yescharacteristic
38C43×#465—21no—
39C43×#442C2211yescharacteristic, complemented
40C43×#441C2211yescharacteristic, complemented
41C4×SD16×C43—21no—
42C43×#405C2211yescharacteristic
43C2×#10621898—21no—
44#13063358—22no—
45#13063353—22no—
46#13063347—21no—
47#13063347C2312yes—
48#13063331—22no—
49#13063331—22no—
50#13063331—41no—
51#13063331—41no—
52C2×#10621877—21no—
53C2×#10621872—41no—
54C2×C8×D43—41no—
55#13063271—22no—
56#13063269—22no—
57#13063268—22no—
58#13063266—22no—
59#13063265C2312yes—
60#13063265C2312yes—
61#13063261—21no—
62#13063261C2312yes—
63#13063253—22no—
64#13063253—22no—
65C2×Q16×C43C2311yescharacteristic
66C2×SD16×C43—21no—
67C2×D8×C43C2311yescharacteristic
68C2×M16×C43C2311yescharacteristic
69C22×C8×C43D411yescharacteristic
70C4⋊Q8×C43—21no—
71#126×C43—41no—
72#124×C43—21no—
73#124×C43—41no—
74#123×C43—41no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43—41no—
77#121×C43—21no—
78C4×Q8×C43—21no—
79C4×D4×C43—21no—
80#117×C43D411yescharacteristic
81#106×C43—21no—
82#106×C43C2311yescharacteristic
83#106×C43C2311yescharacteristic
84#103×C43—21no—
85#103×C43—21no—
86#102×C43—21no—
87#102×C43—21no—
88#97×C43D411yescharacteristic
89#97×C43C2311yescharacteristic
90C4×C8×C43D411yescharacteristic
91C4×C8×C43C2311yescharacteristic
92C2×Q8×C43—21no—
93C2×Q8×C43—41no—
94C2×D4×C43—21no—
95C2×D4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43C2×D411yescharacteristic
98C2×C22⋊D43—41no—
99#10621898—22no—
100#10621898—22no—
101#10621898—41no—
102#10621898—41no—
103C2×D172—21no—
104C2×C4×D43—41no—
105C2×Dic86—21no—
106Q16×C43—22no—
107SD16×C43—41no—
108SD16×C43—41no—
109D8×C43—22no—
110M16×C43—22no—
111C2×C8×C43—21no—
112C2×C8×C43—21no—
113C2×C8×C43C2×D411yescharacteristic
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43C2411yescharacteristic
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C22⋊C4×C43—21no—
124C22⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—41no—
127C22⋊C4×C43—41no—
128C22⋊C4×C43—41no—
129C42×C43—41no—
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132#10621877—22no—
133#10621877—41no—
134C2×C43⋊C8—41no—
135Dic172—21no—
136Dic172#4112yes—
137D344—21no—
138D344#4112yes—
139#10621873—22no—
140#10621873—22no—
141#10621872—42no—
142#10621872—42no—
143C8×D43—42no—
144C8×D43—42no—
145C43⋊C16—22no—
146C43⋊C16—22no—
147C23×C43—41no—
148C23×C43AGL(1,ℤ/8)11yescharacteristic
149C22×D43—41no—
150Q8×C43—41no—
151Q8×C43—41no—
152Q8×C43—161no—
153D4×C43—41no—
154D4×C43—41no—
155D4×C43—161no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—161no—
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43C22×D411yescharacteristic
166C22⋊D43—42no—
167C22⋊D43—42no—
168C2×Dic43—41no—
169D172—22no—
170D172—41no—
171C4×D43—42no—
172C4×D43—42no—
173Dic86—22no—
174Dic86—41no—
175C8×C43—21no—
176C8×C43—21no—
177C8×C43AGL(1,ℤ/8)11yescharacteristic
178C8×C43AGL(1,ℤ/8)11yescharacteristic
179C8×C43C2×#4112yes—
180C43⋊C8—42no—
181#33691—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—41no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
188C2×D43—42no—
189C2×D43—82no—
190C4×C43—21no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43—81no—
194C4×C43—81no—
195C4×C43—81no—
196C4×C43#52511yescharacteristic
197C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
198Dic43—42no—
199#3173D4311yescharacteristic, complemented
200#2955—431no—
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—161no—
213C2×C43#310911yescharacteristic
214D43—82no—
215#575—431no—
216C2×#131—861no—
217#542—21no—
218#510—432no—
219#509—432no—
220#498C2×D4311yescharacteristic, complemented
221#495C2×D4311yescharacteristic, complemented
222#489—21no—
223#470C2×D4311yescharacteristic
224#469C2×D4311yescharacteristic
225#465—21no—
226#444—432no—
227#444—861no—
228#443—432no—
229#443—861no—
230#442C2×D4311yescharacteristic, complemented
231#441C2×D4311yescharacteristic, complemented
232C4×SD16—21no—
233#430—431no—
234#421—861no—
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—861no—
248#137—862no—
249AGL(1,ℤ/8)—862no—
250#135—432no—
251#135—861no—
252C2×Q16C22×D4311yescharacteristic
253C2×SD16—21no—
254C2×D8C22×D4311yescharacteristic
255#131—862no—
256#131—862no—
257#131—1721no—
258#131—1721no—
259C2×M16—861no—
260C2×M16—1721no—
261C2×M16C22×D4311yescharacteristic
262C22×C8—1721no—
263C22×C8C22⋊D4311yescharacteristic
264C4⋊Q8—21no—
265#126—41no—
266#124—21no—
267#124—41no—
268#123—41no—
269C22⋊Q8—21no—
270C22⋊Q8—41no—
271#121—21no—
272C4×Q8—21no—
273C4×D4—21no—
274#117C22⋊D4311yescharacteristic
275Q32—862no—
276SD32—862no—
277SD32—862no—
278D16—862no—
279M32—432no—
280M32—432no—
281#108—432no—
282#108—861no—
283#106—21no—
284#106C22×D4311yescharacteristic
285#106C22×D4311yescharacteristic
286#104—862no—
287#104—862no—
288#103—21no—
289#103—21no—
290#102—21no—
291#102—21no—
292#97C22⋊D4311yescharacteristic
293#97C22×D4311yescharacteristic
294C4×C8C22⋊D4311yescharacteristic
295C4×C8C22×D4311yescharacteristic
296#41—862no—
297#41—862no—
298#41—1721no—
299#41—1721no—
300C2×Q8—21no—
301C2×Q8—41no—
302C2×Q8—861no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—861no—
306C2×D4—1721no—
307C22×C4—41no—
308C22×C4—1721no—
309C22×C4C2×C22⋊D4311yescharacteristic
310Q16—22no—
311Q16—432no—
312Q16—861no—
313SD16—41no—
314SD16—41no—
315SD16—862no—
316SD16—862no—
317D8—22no—
318D8—432no—
319D8—861no—
320M16—22no—
321M16—862no—
322M16—1722no—
323M16—1721no—
324M16—1722no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—1722no—
328C2×C8—1721no—
329C2×C8—1722no—
330C2×C8C2×C22⋊D4311yescharacteristic
331C2×C8C2×C22⋊D4311yescharacteristic
332C2×C8C2×C22⋊D4311yescharacteristic
333C2×C8C23×D4311yescharacteristic
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—41no—
347C42C2×C22⋊D4311yescharacteristic
348C42C2×C22⋊D4311yescharacteristic
349C16—862no—
350C16—862no—
351C23—41no—
352C23—1721no—
353C23#1306335111yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—161no—
357Q8—862no—
358Q8—1721no—
359D4—41no—
360D4—41no—
361D4—161no—
362D4—862no—
363D4—1721no—
364D4—1722no—
365D4—1722no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—161no—
374C2×C4—1722no—
375C2×C4—1721no—
376C2×C4—1722no—
377C2×C4#1306335111yescharacteristic
378C2×C4C22×C22⋊D4311yescharacteristic
379C8—21no—
380C8—21no—
381C8—1722no—
382C8#1306335011yescharacteristic
383C8#1306335011yescharacteristic
384C8#41×D4312yes—
385C22—21no—
386C22—41no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—3442no—
391C22—1722no—
392C22C2×#1306335111yescharacteristic
393C4—21no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—81no—
398C4—81no—
399C4—1722no—
400C4#1458340611yescharacteristic
401C4C2×#1306335011yescharacteristic
402C2—21no—
403C2—41no—
404C2—161no—
405C2—3442no—
406C2#1914468211yescharacteristic
subgroupG/H
centerC2#19144682
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3173C2
socleC2×C43#3109
prime radical#19136540C2
hypercenter#3173D43
hypocenterC43#33691
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #3173

Complements

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

NH ≅ G/Ntype
1. #19143499C2semidirect
2. #19136812C2semidirect
3. #19136807C2semidirect
4. #19136763C2semidirect
5. #19136661C2semidirect
6. #19136545C2semidirect
8. #19136491C2semidirect
9. #19136484C2semidirect
10. #19136411C2semidirect
11. C43×#3173C2semidirect
22. #14582721C22semidirect
23. #14582721C22semidirect
24. #14582720C22semidirect
25. #14582715C22semidirect
26. #14582712C22semidirect
31. #14582677C22semidirect
33. C43×#498C22semidirect
34. C43×#495C22semidirect
39. C43×#442C22semidirect
40. C43×#441C22semidirect
199. #3173D43semidirect
220. #498C2×D43semidirect
221. #495C2×D43semidirect
230. #442C2×D43semidirect
231. #441C2×D43semidirect
246. C43#33691semidirect

Maximal subgroups

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

subgroupindex
#191434992
#191368122
#191368072
#191367632
#191366612
#191365452
#191365402
#191364912
#191364842
#191364112
C43×#31732
#3369143