Finite Group Databasebeta

← #25250059

Subgroups — #25250059

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147729C211yesmaximal, characteristic
2#19143511C211yesmaximal, characteristic, complemented
3#19143479C211yesmaximal, characteristic, complemented
4#19136496C214yesmaximal, complemented
5#19136489C214yesmaximal, complemented
6C2×#14582723C211yesmaximal, characteristic, complemented
7C2×#14582710C211yesmaximal, characteristic, complemented
8#19136199C211yesmaximal, characteristic, complemented
9C43×#2148C211yesmaximal, characteristic, complemented
10C2×#13063347C2211yescharacteristic
11#14583665—21no—
12#14583382—21no—
13#14583340C2212yes—
14#14583339C412yescomplemented
15#14583335C2212yes—
16#14583334C412yescomplemented
17#14583329C414yescomplemented
18C2×#13063265C2211yescharacteristic
19#14583020C2214yes—
20#14583015—22no—
21#14583011C2212yescomplemented
22#14583006C2212yescomplemented
23SD16×Dic43—22no—
24C2×#13063257C2211yescharacteristic
25#14582915—21no—
26#14582900—21no—
27#14582854C2211yescharacteristic
28#14582723C2214yescomplemented
29#14582710C2214yes—
30#14582676C2214yescomplemented
31C2×#135×C43C2211yescharacteristic
32C2×M32×C43C2211yescharacteristic
33C2×#108×C43C2211yescharacteristic
34C43×#362C2212yescomplemented
35C43×#361C2212yescomplemented
36C2×#10621898—21no—
37#13063347—21no—
38#13063347—21no—
39#13063347C2×C412yescomplemented
40#13063347C2312yes—
41C2×Dic172C2×C411yescharacteristic, complemented
42C2×#10621873—21no—
43C2×D344C2×C411yescharacteristic, complemented
44#13063333—24no—
45#13063331—42no—
46C2×#10621877D411yescharacteristic
47M16×D43—42no—
48Q8×Dic43—22no—
49D4×Dic43—22no—
50D4×Dic43—42no—
51#13063284—41no—
52#13063284D411yescharacteristic
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—41no—
55#13063271C2×C414yescomplemented
56#13063269C2×C414yescomplemented
57#13063268C2×C414yescomplemented
58#13063266C2×C414yescomplemented
59#13063265C2×C412yescomplemented
60#13063265C2312yes—
61C2×C43⋊C16C2×C412yescomplemented
62#13063257—21no—
63#13063257C2312yes—
64#13063251—24no—
65#13063249—22no—
66#13063246—22no—
67#13063235C2312yes—
68C8×Dic43D412yes—
69C2×#41×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72#135×C43C2×C412yes—
73#135×C43C2×C412yes—
74C2×Q16×C43C2311yescharacteristic
75C2×SD16×C43—21no—
76C2×D8×C43C2311yescharacteristic
77C2×M16×C43—21no—
78C22×C8×C43C2311yescharacteristic
79M32×C43—21no—
80M32×C43C2312yes—
81C2×C16×C43—21no—
82#108×C43—21no—
83#108×C43C2312yes—
84#41×C43—22no—
85#41×C43—22no—
86#41×C43—41no—
87#41×C43—41no—
88C2×Q8×C43—21no—
89C2×D4×C43—21no—
90C2×D4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C2×C22⋊D43—41no—
94C22×Dic43—42no—
95C22×Dic43—41no—
96#10621898—22no—
97#10621898—22no—
98#10621898—41no—
99#10621898—41no—
100C2×D172—21no—
101C2×C4×D43—41no—
102C2×Dic86—21no—
103Q16×C43—21no—
104Q16×C43C22×C412yes—
105SD16×C43—22no—
106SD16×C43—22no—
107D8×C43—21no—
108D8×C43C22×C412yes—
109M16×C43—22no—
110M16×C43—41no—
111C2×C8×C43—41no—
112C2×C8×C43C22×C411yescharacteristic
113C2×C8×C43C22×C411yescharacteristic
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43#4111yescharacteristic
116C2×C8×C43#4111yescharacteristic
117C2×C8×C43C2411yescharacteristic
118C22⋊Dic43—21no—
119C22⋊Dic43—42no—
120C4⋊Dic43—21no—
121C4⋊Dic43—22no—
122C4⋊Dic43—42no—
123C4⋊Dic43—41no—
124C4×Dic43—42no—
125C4×Dic43C2×D412yes—
126#10621877—21no—
127#10621877—21no—
128C2×C43⋊C8C2×D412yes—
129Dic172—21no—
130Dic172C22×C412yes—
131D344—21no—
132D344C22×C412yes—
133#10621873—22no—
134#10621873—22no—
135#10621872—44no—
136C8×D43—44no—
137C16×C43—22no—
138C43⋊C16C22×C414yes—
139C23×C43—41no—
140C23×C43AGL(1,ℤ/8)11yescharacteristic
141C22×D43—41no—
142Q8×C43—22no—
143Q8×C43—41no—
144D4×C43—22no—
145D4×C43—42no—
146D4×C43—42no—
147D4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—42no—
150C2×C4×C43—42no—
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C43C22×D411yescharacteristic
157C22⋊D43—42no—
158C22⋊D43—42no—
159C2×Dic43—22no—
160C2×Dic43—41no—
161C2×Dic43—42no—
162C2×Dic43—162no—
163C2×Dic43—161no—
164D172—22no—
165D172—41no—
166C4×D43—42no—
167C4×D43—42no—
168Dic86—22no—
169Dic86—41no—
170C8×C43—42no—
171C8×C43C4×D411yescharacteristic
172C8×C43C4×D411yescharacteristic
173C8×C43C23×C411yescharacteristic
174C8×C43C2×#4111yescharacteristic
175C43⋊C8—22no—
176#33469—431nomaximal, Sylow
177C22×C43—41no—
178C22×C43—42no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43#44211yescharacteristic
182C22×C43#44211yescharacteristic
183C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
184C2×D43—42no—
185C2×D43—161no—
186C4×C43—42no—
187C4×C43#44211yescharacteristic
188C4×C43#44211yescharacteristic
189C4×C43C2×C4×D411yescharacteristic
190C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
191Dic43—42no—
192Dic43—42no—
193Dic43—82no—
194#3414—431no—
195#2957—431no—
196#2952—431no—
197AGL(1,ℤ/16)—434no—
198#2180—434no—
199C2×#365—431no—
200#2148D4311yescharacteristic, complemented
201C2×#360—431no—
202#2110—431no—
203C2×C43—21no—
204C2×C43—21no—
205C2×C43—21no—
206C2×C43—82no—
207C2×C43C2×#44211yescharacteristic
208D43—82no—
209C2×#135—431no—
210C2×#135C2×D4311yescharacteristic
211#568—861no—
212#520—861no—
213#510—432no—
214#510—432no—
215#509—432no—
216#509—432no—
217#508—434no—
218C2×M32—431no—
219C2×M32C2×D4311yescharacteristic
220#444—434no—
221#443—862no—
222#442—432no—
223#441—432no—
224C4×SD16—862no—
225C2×#108C2×D4311yescharacteristic
226C2×#106—431no—
227#421—861no—
228#417—861no—
229#405—431no—
230#365—434no—
231#362C2×D4312yescomplemented
232#361C2×D4312yescomplemented
233#360—434no—
234#347—434no—
235C43#3346911yescharacteristic, complemented, Sylow
236C2×#41—21no—
237C2×#41—861no—
238#135—21no—
239#135—21no—
240#135—432no—
241#135—432no—
242#135—861no—
243#135—861no—
244#135C4×D4312yes—
245#135C4×D4312yes—
246C2×Q16—431no—
247C2×Q16C22×D4311yescharacteristic
248C2×SD16—21no—
249C2×SD16—861no—
250C2×D8—431no—
251C2×D8C22×D4311yescharacteristic
252#131—864no—
253#131—1722no—
254C2×M16—21no—
255C2×M16—431no—
256C2×M16—1722no—
257C22×C8C22×D4311yescharacteristic
258C4×Q8—862no—
259C4×D4—862no—
260C4×D4—1722no—
261#117—431no—
262#117—1721no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—1721no—
265Q32—434no—
266SD32—434no—
267SD32—434no—
268D16—434no—
269M32—21no—
270M32—432no—
271M32—432no—
272M32C22×D4312yes—
273C2×C16—21no—
274C2×C16—432no—
275#108—21no—
276#108C22×D4312yes—
277#106—432no—
278#106—861no—
279#104—864no—
280#103—862no—
281#102—862no—
282#97—432no—
283C4×C8—432no—
284#41—22no—
285#41—22no—
286#41—41no—
287#41—41no—
288#41—862no—
289#41—862no—
290#41—1721no—
291#41—1721no—
292C2×Q8—21no—
293C2×Q8—861no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—861no—
297C2×D4—1721no—
298C22×C4—41no—
299C22×C4—1722no—
300C22×C4—1721no—
301C22×C4—1721no—
302C22×C4D4×D4311yescharacteristic
303Q16—21no—
304Q16—432no—
305Q16—861no—
306Q16C2×C4×D4312yes—
307SD16—22no—
308SD16—22no—
309SD16—862no—
310SD16—862no—
311D8—21no—
312D8—432no—
313D8—861no—
314D8C2×C4×D4312yes—
315M16—22no—
316M16—41no—
317M16—861no—
318M16—861no—
319M16—1724no—
320C2×C8—41no—
321C2×C8—432no—
322C2×C8—1724no—
323C2×C8C2×C4×D4311yescharacteristic
324C2×C8C2×C4×D4311yescharacteristic
325C2×C8D4×D4311yescharacteristic
326C2×C8#1062190011yescharacteristic
327C2×C8#1062190011yescharacteristic
328C2×C8C23×D4311yescharacteristic
329C4⋊C4—861no—
330C4⋊C4—862no—
331C4⋊C4—1722no—
332C4⋊C4—1721no—
333C22⋊C4—861no—
334C22⋊C4—1722no—
335C42—432no—
336C42—1722no—
337C16—22no—
338C16—434no—
339C23—41no—
340C23—1721no—
341C23#1306335211yescharacteristic
342Q8—22no—
343Q8—41no—
344Q8—862no—
345Q8—1721no—
346D4—22no—
347D4—42no—
348D4—42no—
349D4—41no—
350D4—862no—
351D4—1722no—
352D4—1722no—
353D4—1721no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—862no—
358C2×C4—1722no—
359C2×C4—1721no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4—6881no—
363C2×C4—6882no—
364C2×C4(C22⋊D43)⋊C411yescharacteristic
365C2×C4(C22⋊D43)⋊C411yescharacteristic
366C2×C4#1306334911yescharacteristic
367C2×C4#1306334911yescharacteristic
368C2×C4#1306335211yescharacteristic
369C2×C4C2×D4×D4311yescharacteristic
370C8—42no—
371C8—862no—
372C8(C22⋊D43)⋊C411yescharacteristic
373C8(C22⋊D43)⋊C411yescharacteristic
374C8C22×C4×D4311yescharacteristic
375C8C2×#1062190011yescharacteristic
376C22—41no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—1722no—
381C22—6881no—
382C22#1458300811yescharacteristic
383C22#1458300811yescharacteristic
384C22C2×#1306335211yescharacteristic
385C4—42no—
386C4—3442no—
387C4—1722no—
388C4—1722no—
389C4#1458300811yescharacteristic
390C4#1458300811yescharacteristic
391C4C2×(C22⋊D43)⋊C411yescharacteristic
392C4C2×#1306334911yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—3442no—
398C2C2×#1458300811yescharacteristic
subgroupG/H
centerC2C2×#14583008
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC43×#2148C2
socleC2×C43C2×#442
prime radical#19147729C2
cosocleC2×C8×C43C24
hypercenter#2148D43
hypocenterC43#33469
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2148

Complements

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

NH ≅ G/Ntype
2. #19143511C2semidirect
3. #19143479C2semidirect
4. #19136496C2semidirect
5. #19136489C2semidirect
6. C2×#14582723C2semidirect
7. C2×#14582710C2semidirect
8. #19136199C2semidirect
9. C43×#2148C2semidirect
14. #14583339C4semidirect
16. #14583334C4semidirect
17. #14583329C4semidirect
21. #14583011C22semidirect
22. #14583006C22semidirect
28. #14582723C22semidirect
30. #14582676C22semidirect
34. C43×#362C22semidirect
35. C43×#361C22semidirect
39. #13063347C2×C4semidirect
41. C2×Dic172C2×C4semidirect
43. C2×D344C2×C4semidirect
55. #13063271C2×C4semidirect
56. #13063269C2×C4semidirect
57. #13063268C2×C4semidirect
58. #13063266C2×C4semidirect
59. #13063265C2×C4semidirect
61. C2×C43⋊C16C2×C4semidirect
200. #2148D43semidirect
231. #362C2×D43semidirect
232. #361C2×D43semidirect
235. C43#33469semidirect

Maximal subgroups

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

subgroupindex
#191477292
#191435112
#191434792
#191364962
#191364892
C2×#145827232
C2×#145827102
#191361992
C43×#21482
#3346943