Finite Group Databasebeta

← #25077924

Subgroups — #25077924

Order 11008.

938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583647C211yesmaximal, characteristic
2#19145600C212yesmaximal, complemented
3#19145144C211yesmaximal, characteristic, complemented
4#19133914C218yesmaximal, complemented
5#19133194C212yesmaximal, complemented
6C43×#1534C211yesmaximal, characteristic, complemented
7#14583647—24no—
8#14583647—22no—
9#14583647C2214yes—
10#14583456C2211yescharacteristic
11C2×#13063313C2212yes—
12C2×#13063310—22no—
13C2×#13063303—22no—
14C2×#13063300—22no—
15#14583309C2214yescomplemented
16#14583298—22no—
17#14583293C2214yescomplemented
18#14583259C2214yescomplemented
19#14583122—24no—
20#14583057—22no—
21#14583052—22no—
22#14582939—22no—
23C4×#10621877C2211yescharacteristic
24#14582638C2218yescomplemented
25C2×#125×C43C2211yescharacteristic
26C43×#432C2212yes—
27C43×#330C2214yescomplemented
28C22×Dic86D412yes—
29C22×D172—22no—
30C22×D172D412yes—
31C22×C4×D43—22no—
32C2×Dic172—24no—
33C2×#10621873—24no—
34C2×#10621877—21no—
35#13063325C2312yes—
36#13063317—21no—
37#13063313—22no—
38#13063313—22no—
39#13063313D414yes—
40#13063313C2314yes—
41#13063310—28no—
42#13063310—28no—
43#13063304—22no—
44#13063303—28no—
45#13063303—28no—
46#13063300—28no—
47#13063300—28no—
48C4×Dic86—22no—
49#13063284—21no—
50C2×Dic43⋊C4—22no—
51C2×(C2×D43)⋊C4—22no—
52C2×(C2×D43)⋊C4—22no—
53C2×(C2×D43)⋊C4—22no—
54#13063258—24no—
55#13063256—24no—
56#13063250—24no—
57#13063247—24no—
58#13063236C2312yes—
59C4×C43⋊C8—21no—
60#125×C43—22no—
61#125×C43D412yes—
62#125×C43C2312yes—
63C2×C4⋊C4×C43—22no—
64C2×C4⋊C4×C43D412yes—
65C2×C42×C43C2311yescharacteristic
66C4⋊C8×C43—22no—
67C22⋊C8×C43—22no—
68#97×C43C2314yes—
69C23×D43—22no—
70C22×C4×C43—22no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D412yes—
73C22×Dic43—22no—
74C2×D172—28no—
75C2×D172—22no—
76C2×D172—82no—
77C2×D172—84no—
78C2×D172C2×D414yes—
79C2×C4×D43—28no—
80C2×C4×D43—84no—
81C2×Dic86—22no—
82C2×Dic86—22no—
83C2×Dic86—82no—
84C2×Dic86C2×D414yes—
85C2×C8×C43—24no—
86C4⋊C4×C43—24no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—24no—
89C4⋊C4×C43C2×D414yes—
90C42×C43C2×D411yescharacteristic
91C42×C43C2×D412yes—
92C42×C43C2411yescharacteristic
93C22⋊Dic43—41no—
94(C2×D43)⋊C4—28no—
95(C2×D43)⋊C4—24no—
96(C2×D43)⋊C4—24no—
97(C2×D43)⋊C4—24no—
98(C2×D43)⋊C4—24no—
99C4⋊Dic43—22no—
100C4⋊Dic43—22no—
101Dic43⋊C4—28no—
102Dic43⋊C4—42no—
103C4×Dic43—41no—
104#10621877—24no—
105C2×C43⋊C8—22no—
106Dic172—84no—
107#10621873—84no—
108C23×C43#12011yescharacteristic
109C22×D43—24no—
110C22×D43—44no—
111C22×D43—44no—
112C22×D43—44no—
113C2×C4×C43—22no—
114C2×C4×C43—24no—
115C2×C4×C43—42no—
116C2×C4×C43—44no—
117C2×C4×C43#12011yescharacteristic
118C2×C4×C43#12012yes—
119C2×C4×C43C22×D412yes—
120C2×C4×C43C22×D411yescharacteristic
121C2×Dic43—24no—
122C2×Dic43—44no—
123C2×Dic43—42no—
124D172—44no—
125D172—82no—
126D172—88no—
127C4×D43—88no—
128Dic86—44no—
129Dic86—44no—
130Dic86—82no—
131C8×C43—44no—
132C43⋊C8—24no—
133#19006—431nomaximal, Sylow
134C22×C43—22no—
135C22×C43#45612yes—
136C22×C43C2×#12011yescharacteristic
137C2×D43—44no—
138C2×D43—44no—
139C2×D43—44no—
140C2×D43—88no—
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—22no—
144C4×C43—22no—
145C4×C43—44no—
146Dic43—44no—
147Dic43—82no—
148C2×#562—431no—
149#3215—432no—
150#3166—431no—
151#1661—438no—
152#1534D4311yescharacteristic, complemented
153#1527—432no—
154C2×C43—22no—
155C2×C43C2×#45611yescharacteristic
156C2×C43#301912yes—
157D43—84no—
158#562—434no—
159#562—864no—
160#562—862no—
161#533—431no—
162C2×#125C2×D4311yescharacteristic
163C2×#124—432no—
164C2×#123—862no—
165C2×C22⋊Q8—862no—
166C2×#121—862no—
167#501—434no—
168#499—862no—
169#497—434no—
170#489—434no—
171#464—864no—
172#451—862no—
173#450—862no—
174#432C2×D4312yes—
175#428—862no—
176C4×M16—431no—
177#330C2×D4314yescomplemented
178#329—438no—
179C43#1900611yescharacteristic, complemented, Sylow
180C22×Q8—432no—
181C22×D4—432no—
182C22×D4—862no—
183C23×C4—862no—
184C2×Q16—864no—
185C2×SD16—864no—
186C2×M16—861no—
187C4⋊Q8—432no—
188#125—22no—
189#125—861no—
190#125D17212yes—
191#125C22×D4312yes—
192#124—434no—
193#124—434no—
194#124—862no—
195#124—862no—
196#123—868no—
197#123—868no—
198C22⋊Q8—868no—
199C22⋊Q8—868no—
200C22⋊Q8—862no—
201#121—868no—
202#121—868no—
203C4×Q8—862no—
204#117—861no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—862no—
207C2×C4⋊C4D17212yes—
208C2×C22⋊C4—862no—
209C2×C22⋊C4—862no—
210C2×C22⋊C4—862no—
211C2×C42C22×D4311yescharacteristic
212#107—864no—
213#106—864no—
214C4⋊C8—22no—
215#103—864no—
216#102—864no—
217C22⋊C8—22no—
218#97—432no—
219#97C22×D4314yes—
220C4×C8—861no—
221C24—862no—
222C2×Q8—434no—
223C2×Q8—862no—
224C2×Q8—862no—
225C2×Q8—3442no—
226C2×D4—434no—
227C2×D4—868no—
228C2×D4—862no—
229C2×D4—3444no—
230C2×D4—3442no—
231C22×C4—22no—
232C22×C4—868no—
233C22×C4—862no—
234C22×C4—3444no—
235C22×C4C2×D17211yescharacteristic
236C22×C4D4×D4312yes—
237Q16—3444no—
238SD16—3444no—
239M16—864no—
240C2×C8—24no—
241C2×C8—862no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—24no—
245C4⋊C4—868no—
246C4⋊C4—862no—
247C4⋊C4—862no—
248C4⋊C4—1722no—
249C4⋊C4C2×D17214yes—
250C22⋊C4—868no—
251C22⋊C4—864no—
252C22⋊C4—864no—
253C22⋊C4—864no—
254C22⋊C4—864no—
255C22⋊C4—1721no—
256C42—1721no—
257C42C2×D17211yescharacteristic
258C42D4×D4312yes—
259C42C23×D4311yescharacteristic
260C23—864no—
261C23—1724no—
262C23—1724no—
263C23—1724no—
264C23#1306329511yescharacteristic
265Q8—3442no—
266Q8—1724no—
267Q8—1724no—
268D4—3442no—
269D4—3448no—
270D4—1724no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—42no—
274C2×C4—44no—
275C2×C4—864no—
276C2×C4—3448no—
277C2×C4—1722no—
278C2×C4—1724no—
279C2×C4#1306329511yescharacteristic
280C2×C4#1306329512yes—
281C2×C4C2×D4×D4312yes—
282C2×C4C22×D17211yescharacteristic
283C8—44no—
284C8—864no—
285C22—22no—
286C22—3448no—
287C22—1724no—
288C22—1724no—
289C22—1724no—
290C22#1458308412yes—
291C22C2×#1306329511yescharacteristic
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—44no—
297C4—3442no—
298C4—1724no—
299C2—22no—
300C2—3444no—
301C2C2×#1458308411yescharacteristic
302C2#1914395412yes—
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1534C2
socleC22×C43C2×#120
prime radicalC2×#14583647C2
hypercenter#1534D43
hypocenterC43#19006
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1534

Complements

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

NH ≅ G/Ntype
2. #19145600C2semidirect
3. #19145144C2semidirect
4. #19133914C2semidirect
5. #19133194C2semidirect
6. C43×#1534C2semidirect
15. #14583309C22semidirect
17. #14583293C22semidirect
18. #14583259C22semidirect
24. #14582638C22semidirect
27. C43×#330C22semidirect
152. #1534D43semidirect
177. #330C2×D43semidirect
179. C43#19006semidirect

Maximal subgroups

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

subgroupindex
C2×#145836472
#191456002
#191451442
#191339142
#191331942
C43×#15342
#1900643