Finite Group Databasebeta

← #25960945

Subgroups — #25960945

Order 11008.

2604 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149369C211yesmaximal, characteristic
2#19149306C212yesmaximal, complemented
3#19143513C216yesmaximal, complemented
4#19143506C216yesmaximal, complemented
5#19143499C216yesmaximal, complemented
6C2×#14583022C216yesmaximal, complemented
7#19143206C211yesmaximal, characteristic, complemented
8#19143143C212yesmaximal, complemented
9C43×#2875C211yesmaximal, characteristic, complemented
10#14583735C2212yes—
11#14583716C414yescomplemented
12#14583711C418yescomplemented
13#14583704C414yescomplemented
14#14583699C2216yes—
15C2×#13063347C2216yes—
16#14583666C2212yes—
17#14583665C22112yescomplemented
18#14583664—28no—
19C2×#13063331C22112yescomplemented
20#131×D43—28no—
21#14583022C2214yescomplemented
22#14583022C22112yescomplemented
23#14583022C22112yescomplemented
24#14583022C22112yescomplemented
25#14583017C22124yescomplemented
26#14582948C2216yescomplemented
27C2×#13063261C2216yescomplemented
28#14582917C22112yescomplemented
29C2×#13063253C22112yescomplemented
30C2×#131×C43C2211yescharacteristic
31C2×#131×C43C2211yescharacteristic
32C4×#41×C43C2211yescharacteristic
33C43×#405C2213yescomplemented
34C43×#405C2213yescomplemented
35C4×M16×C43C2213yescomplemented
36C2×#97×C43C2213yescomplemented
37#13063373—22no—
38#13063372C2×C418yes—
39#13063371C2×C418yes—
40#13063370—26no—
41C2×#10621898C23112yes—
42#41×D43—28no—
43#13063358C2×C4124yescomplemented
44#13063353C2×C4124yescomplemented
45#13063347C2×C4112yescomplemented
46#13063347C2×C4112yescomplemented
47#13063347C2314yes—
48#13063347C23112yes—
49C2×Dic172C2×C416yescomplemented
50C2×#10621873C2×C4112yescomplemented
51C2×D344C2×C416yescomplemented
52#13063333—224no—
53#13063332—28no—
54#13063331—212no—
55#13063331—212no—
56#13063331C2318yes—
57#13063331C23124yes—
58C2×#10621877C23112yes—
59C2×#10621872—212no—
60M16×D43—224no—
61C2×C8×D43—212no—
62#13063261C2314yes—
63#13063261C23112yes—
64#13063253C2318yes—
65#13063253C23124yes—
66C2×#41×C43C2311yescharacteristic
67#131×C43C2×C414yes—
68#131×C43C2×C414yes—
69#131×C43D418yes—
70C2×M16×C43C2313yes—
71C2×M16×C43C2313yes—
72C22×C8×C43C2313yes—
73C22×C8×C43C2313yes—
74C4×Q8×C43—21no—
75C4×D4×C43—23no—
76#117×C43C2313yes—
77C2×C42×C43C2313yes—
78#97×C43C2311yescharacteristic
79#97×C43C2313yes—
80#97×C43C2313yes—
81#97×C43C2313yes—
82C4×C8×C43C2316yes—
83#41×C43C22×C414yes—
84#41×C43C2×D414yes—
85C2×Q8×C43#4111yescharacteristic
86C2×D4×C43#4113yes—
87C22×C4×C43—23no—
88C22×C4×C43C2413yes—
89C2×C22⋊D43—212no—
90#10621902—28no—
91Q8×D43—28no—
92#10621900—224no—
93D4×D43—224no—
94#10621898—212no—
95#10621898—212no—
96#10621898C22×C4124yes—
97#10621898C2418yes—
98C2×D172C22×C4112yes—
99C2×C4×D43—212no—
100C2×Dic86C22×C4112yes—
101M16×C43C22×C4112yes—
102M16×C43C2×D4112yes—
103C2×C8×C43C22×C416yes—
104C2×C8×C43C22×C416yes—
105C2×C8×C43C2×D4112yes—
106C2×C8×C43C2413yes—
107C2×C8×C43C2411yescharacteristic
108C2×C8×C43C2413yes—
109C2×C8×C43C2411yescharacteristic
110C4⋊C4×C43—23no—
111C22⋊C4×C43—23no—
112C42×C43—23no—
113C42×C43C2413yes—
114C42×C43C2411yescharacteristic
115#10621877—212no—
116#10621877C2418yes—
117C2×C43⋊C8—212no—
118Dic172C22×C414yes—
119Dic172C22×C4112yes—
120D344C22×C414yes—
121D344C22×C4112yes—
122#10621873C22×C418yes—
123#10621873C22×C4124yes—
124#10621872—224no—
125#10621872—28no—
126C8×D43—28no—
127C8×D43—224no—
128C23×C43C2×#4113yes—
129C22×D43—212no—
130Q8×C43C4×D414yes—
131D4×C43C4×D4112yes—
132C2×C4×C43—21no—
133C2×C4×C43—23no—
134C2×C4×C43—83no—
135C2×C4×C43C23×C416yes—
136C2×C4×C43C22×D416yes—
137C2×C4×C43C2×#4113yes—
138C2×C4×C43C2511yescharacteristic
139C22⋊D43—224no—
140C22⋊D43—28no—
141C2×Dic43—212no—
142D172—212no—
143D172C23×C418yes—
144C4×D43—224no—
145C4×D43—28no—
146Dic86—212no—
147Dic86C23×C418yes—
148C8×C43C23×C411yescharacteristic
149C8×C43C23×C416yes—
150C8×C43C23×C411yescharacteristic
151C8×C43C22×D412yes—
152C8×C43C22×D416yes—
153C43⋊C8—28no—
154#60184—431nomaximal, Sylow
155C22×C43—43no—
156C22×C43C2×C4×D416yes—
157C22×C43C22×#4111yescharacteristic
158C2×D43—28no—
159C2×D43—812no—
160C4×C43—43no—
161C4×C43—41no—
162C4×C43C2×C4×D416yes—
163C4×C43C24×C411yescharacteristic
164C4×C43C23×D411yescharacteristic
165Dic43—28no—
166#3584—431no—
167#3573—432no—
168#2957—436no—
169#2956—436no—
170#2955—436no—
171C2×#444—436no—
172#2916—431no—
173#2901—432no—
174#2875D4311yescharacteristic, complemented
175C2×C43—21no—
176C2×C43—26no—
177C2×C43C22×C4×D411yescharacteristic
178D43—48no—
179#585—432no—
180#578—434no—
181#577—438no—
182#576—434no—
183#575—436no—
184C2×#135—436no—
185#568—432no—
186#568—4312no—
187#568—868no—
188C2×#131—4312no—
189C2×#131—868no—
190C2×#131C2×D4311yescharacteristic
191C2×#131C2×D4311yescharacteristic
192C4×#41C2×D4311yescharacteristic
193#444—434no—
194#444—4312no—
195#444—4312no—
196#444—4312no—
197#443—4324no—
198#430—436no—
199C2×#108—436no—
200#421—4312no—
201C2×#104—4312no—
202#405C2×D4313yescomplemented
203#405C2×D4313yescomplemented
204C4×M16C2×D4313yescomplemented
205C2×#97C2×D4313yescomplemented
206C43#6018411yescharacteristic, complemented, Sylow
2072−1+4—438no—
2082−1+4—862no—
209H(5,𝔽2)—438no—
210H(5,𝔽2)—866no—
211C2×#41—4312no—
212C2×#41—868no—
213C2×#41C22×D4311yescharacteristic
214#137—4324no—
215AGL(1,ℤ/8)—4324no—
216#135—4312no—
217#135—4312no—
218#135—434no—
219#135—4312no—
220C2×Q16—436no—
221C2×SD16—4312no—
222C2×D8—436no—
223#131—438no—
224#131—4324no—
225#131—868no—
226#131—8624no—
227#131—8612no—
228#131—8612no—
229#131C4×D4314yes—
230#131C4×D4314yes—
231#131D17218yes—
232C2×M16—4312no—
233C2×M16—8624no—
234C2×M16—8612no—
235C2×M16C22×D4313yes—
236C2×M16C22×D4313yes—
237C22×C8—8612no—
238C22×C8C22×D4313yes—
239C22×C8C22×D4313yes—
240C4×Q8—21no—
241C4×D4—23no—
242#117C22×D4313yes—
243C2×C42C22×D4313yes—
244#108—434no—
245#108—4312no—
246#104—438no—
247#104—4324no—
248#97C22×D4311yescharacteristic
249#97C22×D4313yes—
250#97C22×D4313yes—
251#97C22×D4313yes—
252C4×C8C22×D4316yes—
253#41—4324no—
254#41—438no—
255#41—868no—
256#41—8624no—
257#41—8612no—
258#41—8612no—
259#41C2×C4×D4314yes—
260#41C2×D17214yes—
261C2×Q8—4312no—
262C2×Q8—868no—
263C2×Q8#1062189811yescharacteristic
264C2×D4—4312no—
265C2×D4—8612no—
266C2×D4—8624no—
267C2×D4#1062189813yes—
268C22×C4—23no—
269C22×C4—8612no—
270C22×C4C23×D4313yes—
271Q16—434no—
272Q16—4312no—
273SD16—438no—
274SD16—4324no—
275D8—434no—
276D8—4312no—
277M16—438no—
278M16—8612no—
279M16—868no—
280M16—8624no—
281M16C2×C4×D43112yes—
282M16C2×D172112yes—
283C2×C8—8612no—
284C2×C8—868no—
285C2×C8—8624no—
286C2×C8C2×C4×D4316yes—
287C2×C8C2×C4×D4316yes—
288C2×C8C2×D172112yes—
289C2×C8C23×D4313yes—
290C2×C8C23×D4311yescharacteristic
291C2×C8C23×D4313yes—
292C2×C8C23×D4311yescharacteristic
293C4⋊C4—23no—
294C22⋊C4—23no—
295C42—23no—
296C42C23×D4313yes—
297C42C23×D4311yescharacteristic
298C23—8612no—
299C23C2×#1062189813yes—
300Q8—438no—
301Q8—8612no—
302Q8C4×D17214yes—
303D4—438no—
304D4—8624no—
305D4—868no—
306D4—8612no—
307D4C4×D172112yes—
308C2×C4—21no—
309C2×C4—23no—
310C2×C4—83no—
311C2×C4—8612no—
312C2×C4—8624no—
313C2×C4—868no—
314C2×C4C22×C4×D4316yes—
315C2×C4C22×D17216yes—
316C2×C4C2×#1062189813yes—
317C2×C4C24×D4311yescharacteristic
318C8—868no—
319C8C22×C4×D4311yescharacteristic
320C8C22×C4×D4311yescharacteristic
321C8C22×C4×D4316yes—
322C8C22×D17212yes—
323C8C22×D17216yes—
324C22—43no—
325C22—868no—
326C22—34412no—
327C22C2×C4×D17216yes—
328C22C22×#1062189811yescharacteristic
329C4—41no—
330C4—43no—
331C4—868no—
332C4C2×C4×D17216yes—
333C4C23×C4×D4311yescharacteristic
334C4C23×D17211yescharacteristic
335C2—21no—
336C2—26no—
337C2—1728no—
338C2C22×C4×D17211yescharacteristic
subgroupG/H
centerC4C23×D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC43×#2875C2
socleC2×C43C22×C4×D4
prime radical#19149369C2
cosocleC2×C4×C43C25
hypercenter#2875D43
hypocenterC43#60184
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×#131 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. #19149306C2semidirect
3. #19143513C2semidirect
4. #19143506C2semidirect
5. #19143499C2semidirect
6. C2×#14583022C2semidirect
7. #19143206C2semidirect
8. #19143143C2semidirect
9. C43×#2875C2semidirect
11. #14583716C4semidirect
12. #14583711C4semidirect
13. #14583704C4semidirect
17. #14583665C22semidirect
19. C2×#13063331C22semidirect
21. #14583022C22semidirect
22. #14583022C22semidirect
23. #14583022C22semidirect
24. #14583022C22semidirect
25. #14583017C22semidirect
26. #14582948C22semidirect
27. C2×#13063261C22semidirect
28. #14582917C22semidirect
29. C2×#13063253C22semidirect
33. C43×#405C22semidirect
34. C43×#405C22semidirect
35. C4×M16×C43C22semidirect
36. C2×#97×C43C22semidirect
43. #13063358C2×C4semidirect
44. #13063353C2×C4semidirect
45. #13063347C2×C4semidirect
46. #13063347C2×C4semidirect
49. C2×Dic172C2×C4semidirect
50. C2×#10621873C2×C4semidirect
51. C2×D344C2×C4semidirect
174. #2875D43semidirect
202. #405C2×D43semidirect
203. #405C2×D43semidirect
204. C4×M16C2×D43semidirect
205. C2×#97C2×D43semidirect
206. C43#60184semidirect

Maximal subgroups

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

subgroupindex
#191493692
#191493062
#191435132
#191435062
#191434992
C2×#145830222
#191432062
#191431432
C43×#28752
#6018443