Finite Group Databasebeta

← #25077882

Subgroups — #25077882

Order 11008.

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

normal subgroups only

This group has 960 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, complemented
2#19145578C212yesmaximal, complemented
3#19133916C214yesmaximal, complemented
4#19133887C214yesmaximal, complemented
5#19133222C211yesmaximal, characteristic, complemented
6#19133192C212yesmaximal, complemented
7C43×#3142C211yesmaximal, characteristic, complemented
8#14583647—24no—
9#14583647—22no—
10#14583647C2214yes—
11C2×#13063313C2212yes—
12C2×#13063310—22no—
13C2×#13063303—22no—
14C2×#13063300—22no—
15#14583286C2214yescomplemented
16#14583261C2214yescomplemented
17#14583114—24no—
18#14583037—22no—
19#14583032—22no—
20#14582956C2212yes—
21#14582641C2214yescomplemented
22#14582638C2218yescomplemented
23C43×#532C2211yescharacteristic
24C2×#125×C43C2211yescharacteristic
25C43×#491C2212yescomplemented
26C43×#490C2212yescomplemented
27C43×#488—22no—
28C43×#417—22no—
29C4×M16×C43C2211yescharacteristic
30C22×Dic86D412yes—
31C22×D172—22no—
32C22×D172D412yes—
33C22×C4×D43—22no—
34C2×#10621883—24no—
35C2×#10621882—24no—
36#13063313—22no—
37#13063313—22no—
38#13063313D414yes—
39#13063313C2314yes—
40#13063310—28no—
41#13063310—28no—
42#13063303—28no—
43#13063303—28no—
44#13063300—28no—
45#13063300—28no—
46C2×Dic43⋊C4—22no—
47C2×(C2×D43)⋊C4—22no—
48C2×(C2×D43)⋊C4—22no—
49C2×(C2×D43)⋊C4—22no—
50C4⋊(C43⋊C8)—22no—
51#13063248—24no—
52#13063245—24no—
53C22⋊(C43⋊C8)—22no—
54#13063236C2314yes—
55C2×#41×C43—21no—
56C2×M16×C43—21no—
57C4⋊Q8×C43C2311yescharacteristic
58#127×C43C2311yescharacteristic
59#125×C43—22no—
60#125×C43D412yes—
61#125×C43C2312yes—
62#124×C43—21no—
63#121×C43—22no—
64C4×D4×C43—22no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43D412yes—
67C2×C42×C43C2311yescharacteristic
68#103×C43—24no—
69#102×C43—24no—
70#97×C43C2312yes—
71C4×C8×C43—21no—
72C23×D43—22no—
73#41×C43—44no—
74C2×Q8×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—22no—
77C2×D4×C43—41no—
78C22×C4×C43—22no—
79C22×C4×C43—41no—
80C22×C4×C43C2×D412yes—
81C22×C4×C43C2×D411yescharacteristic
82C22×Dic43—22no—
83C2×D172—28no—
84C2×D172—22no—
85C2×D172—82no—
86C2×D172—84no—
87C2×D172C2×D414yes—
88C2×C4×D43—28no—
89C2×C4×D43—84no—
90C2×Dic86—22no—
91C2×Dic86—82no—
92C2×Dic86C2×D414yes—
93M16×C43—42no—
94C2×C8×C43—22no—
95C4⋊C4×C43—24no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—24no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43C2×D414yes—
100C22⋊C4×C43—42no—
101C42×C43C2×D412yes—
102C42×C43C2×D411yescharacteristic
103C42×C43C2411yescharacteristic
104#10621883—84no—
105#10621882—84no—
106(C2×D43)⋊C4—28no—
107(C2×D43)⋊C4—24no—
108(C2×D43)⋊C4—24no—
109(C2×D43)⋊C4—24no—
110(C2×D43)⋊C4—24no—
111Dic43⋊C4—28no—
112C2×C43⋊C8—24no—
113C23×C43—41no—
114C23×C43#12011yescharacteristic
115C22×D43—24no—
116C22×D43—44no—
117C22×D43—44no—
118C22×D43—44no—
119Q8×C43—42no—
120D4×C43—44no—
121D4×C43—42no—
122D4×C43—82no—
123C2×C4×C43—22no—
124C2×C4×C43—24no—
125C2×C4×C43—42no—
126C2×C4×C43—44no—
127C2×C4×C43—41no—
128C2×C4×C43—82no—
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43#12012yes—
131C2×C4×C43C22×D412yes—
132C2×C4×C43C22×D411yescharacteristic
133C2×Dic43—24no—
134C2×Dic43—44no—
135D172—44no—
136D172—82no—
137D172—88no—
138C4×D43—88no—
139Dic86—44no—
140Dic86—82no—
141C8×C43—42no—
142C43⋊C8—44no—
143#19001—431nomaximal, Sylow
144C22×C43—22no—
145C22×C43—81no—
146C22×C43—82no—
147C22×C43#45412yes—
148C22×C43C2×#12011yescharacteristic
149C2×D43—44no—
150C2×D43—44no—
151C2×D43—44no—
152C2×D43—88no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—22no—
156C4×C43—22no—
157C4×C43—44no—
158C4×C43—81no—
159Dic43—44no—
160C2×#562—431no—
161#3213—432no—
162#3142D4311yescharacteristic, complemented
163#1662—434no—
164#1656—434no—
165#1534—431no—
166#1527—432no—
167C2×C43—22no—
168C2×C43—161no—
169C2×C43C2×#45411yescharacteristic
170C2×C43#301912yes—
171D43—84no—
172#562—434no—
173#562—864no—
174#562—862no—
175#532C2×D4311yescharacteristic
176C2×#125C2×D4311yescharacteristic
177C2×#124—432no—
178C2×#123—862no—
179C2×C22⋊Q8—862no—
180C2×#121—862no—
181#496—434no—
182#491C2×D4312yescomplemented
183#490C2×D4312yescomplemented
184#489—434no—
185#488—22no—
186#463—864no—
187#448—862no—
188#447—862no—
189#432—432no—
190#417—22no—
191C4×M16C2×D4311yescharacteristic
192#330—434no—
193#329—438no—
194C43#1900111yescharacteristic, complemented, Sylow
195C2×#41—21no—
196C22×Q8—432no—
197C22×D4—432no—
198C22×D4—862no—
199C23×C4—862no—
200C2×SD16—864no—
201C2×D8—864no—
202C2×M16—21no—
203C4⋊Q8C22×D4311yescharacteristic
204#127C22×D4311yescharacteristic
205#125—22no—
206#125C22⋊D4312yes—
207#125C22×D4312yes—
208#124—21no—
209#124—434no—
210#124—434no—
211#124—862no—
212#124—862no—
213#123—868no—
214#123—868no—
215C22⋊Q8—868no—
216C22⋊Q8—868no—
217#121—22no—
218#121—868no—
219#121—868no—
220C4×D4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—862no—
223C2×C4⋊C4C22⋊D4312yes—
224C2×C22⋊C4—862no—
225C2×C22⋊C4—862no—
226C2×C22⋊C4—862no—
227C2×C42C22×D4311yescharacteristic
228C4⋊C8—862no—
229#103—24no—
230#103—864no—
231#102—24no—
232#102—864no—
233C22⋊C8—862no—
234#97—434no—
235#97C22×D4312yes—
236C4×C8—21no—
237C24—862no—
238#41—44no—
239C2×Q8—21no—
240C2×Q8—434no—
241C2×Q8—862no—
242C2×Q8—3442no—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—41no—
246C2×D4—434no—
247C2×D4—868no—
248C2×D4—862no—
249C2×D4—3444no—
250C2×D4—3442no—
251C22×C4—22no—
252C22×C4—41no—
253C22×C4—868no—
254C22×C4—862no—
255C22×C4—3444no—
256C22×C4D4×D4312yes—
257C22×C4C2×C22⋊D4311yescharacteristic
258SD16—3444no—
259D8—3444no—
260M16—42no—
261C2×C8—22no—
262C2×C8—864no—
263C4⋊C4—24no—
264C4⋊C4—22no—
265C4⋊C4—24no—
266C4⋊C4—22no—
267C4⋊C4—868no—
268C4⋊C4C2×C22⋊D4314yes—
269C22⋊C4—42no—
270C22⋊C4—868no—
271C22⋊C4—864no—
272C22⋊C4—864no—
273C22⋊C4—864no—
274C22⋊C4—864no—
275C42D4×D4312yes—
276C42C2×C22⋊D4311yescharacteristic
277C42C23×D4311yescharacteristic
278C23—41no—
279C23—864no—
280C23—1724no—
281C23—1724no—
282C23—1724no—
283C23#1306329311yescharacteristic
284Q8—42no—
285Q8—3442no—
286Q8—1724no—
287D4—44no—
288D4—42no—
289D4—82no—
290D4—3442no—
291D4—3448no—
292D4—1724no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—41no—
298C2×C4—82no—
299C2×C4—864no—
300C2×C4—3448no—
301C2×C4—1724no—
302C2×C4#1306329311yescharacteristic
303C2×C4#1306329312yes—
304C2×C4C2×D4×D4312yes—
305C2×C4C22×C22⋊D4311yescharacteristic
306C8—42no—
307C8—1724no—
308C22—22no—
309C22—82no—
310C22—81no—
311C22—3448no—
312C22—1724no—
313C22—1724no—
314C22—1724no—
315C22#1458307112yes—
316C22C2×#1306329311yescharacteristic
317C4—22no—
318C4—22no—
319C4—21no—
320C4—21no—
321C4—44no—
322C4—81no—
323C4—1724no—
324C2—22no—
325C2—161no—
326C2—3444no—
327C2C2×#1458307111yescharacteristic
328C2#1914395012yes—
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3142C2
socleC22×C43C2×#120
hypercenter#3142D43
hypocenterC43#19001
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. C2×#14583647C2semidirect
2. #19145578C2semidirect
3. #19133916C2semidirect
4. #19133887C2semidirect
5. #19133222C2semidirect
6. #19133192C2semidirect
7. C43×#3142C2semidirect
15. #14583286C22semidirect
16. #14583261C22semidirect
21. #14582641C22semidirect
22. #14582638C22semidirect
25. C43×#491C22semidirect
26. C43×#490C22semidirect
162. #3142D43semidirect
182. #491C2×D43semidirect
183. #490C2×D43semidirect
194. C43#19001semidirect

Maximal subgroups

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

subgroupindex
C2×#145836472
#191455782
#191339162
#191338872
#191332222
#191331922
C43×#31422
#1900143