Finite Group Databasebeta

← #25077884

Subgroups — #25077884

Order 11008.

960 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 960 conjugacy classes of subgroups — too many to draw. Only its 171 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
1#19145582C212yesmaximal, complemented
2#19144998C211yesmaximal, characteristic, complemented
3#19133918C214yesmaximal, complemented
4#19133888C214yesmaximal, complemented
5#19133222C211yesmaximal, characteristic, complemented
6#19133193C212yesmaximal, complemented
7C2×C43×#562C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583289C2214yescomplemented
10#14583269C2212yescomplemented
11#14583265C2212yescomplemented
12#14583258C2214yescomplemented
13#14583256—22no—
14#14583111—24no—
15#14583038—22no—
16#14583033—22no—
17#14582956C2212yes—
18#14582898—22no—
19C4×#10621877C2211yescharacteristic
20#14582641C2214yescomplemented
21#14582639C2218yescomplemented
22C43×#562—22no—
23C43×#562—24no—
24C43×#562C2214yes—
25C2×#125×C43C2211yescharacteristic
26C2×#124×C43C2212yes—
27C2×#123×C43—22no—
28C2×C22⋊Q8×C43—22no—
29C2×#121×C43—22no—
30C2×#10621898—21no—
31C2×#10621884—24no—
32C2×#10621882—24no—
33C2×#10621877—21no—
34#13063325C2311yescharacteristic
35#13063322C2311yescharacteristic
36#13063313—21no—
37#13063299—22no—
38C4×D172—22no—
39C4⋊(C43⋊C8)—22no—
40#13063249—24no—
41#13063248—24no—
42#13063246—24no—
43#13063245—24no—
44C22⋊(C43⋊C8)—22no—
45#13063236C2312yes—
46#13063236C2314yes—
47C4×C43⋊C8—21no—
48C22×Q8×C43D412yes—
49C22×D4×C43—22no—
50C22×D4×C43D412yes—
51C23×C4×C43—22no—
52#125×C43—22no—
53#125×C43D412yes—
54#125×C43C2312yes—
55#124×C43—22no—
56#124×C43—22no—
57#124×C43D414yes—
58#124×C43C2314yes—
59#123×C43—28no—
60#123×C43—28no—
61C22⋊Q8×C43—28no—
62C22⋊Q8×C43—28no—
63#121×C43—28no—
64#121×C43—28no—
65C2×C4⋊C4×C43—22no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43D412yes—
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—22no—
71C2×C42×C43C2311yescharacteristic
72C24×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43—82no—
75C2×Q8×C43C2×D414yes—
76C2×D4×C43—28no—
77C2×D4×C43—22no—
78C2×D4×C43—82no—
79C2×D4×C43—84no—
80C2×D4×C43C2×D414yes—
81C22×C4×C43—28no—
82C22×C4×C43—22no—
83C22×C4×C43—22no—
84C22×C4×C43—84no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D412yes—
87C2×C22⋊D43—41no—
88#10621898—44no—
89C2×D172—21no—
90C2×D172—22no—
91C2×C4×D43—41no—
92C2×Dic86—21no—
93C4⋊C4×C43—28no—
94C4⋊C4×C43—24no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—24no—
97C4⋊C4×C43C2×D414yes—
98C22⋊C4×C43—28no—
99C22⋊C4×C43—24no—
100C22⋊C4×C43—24no—
101C22⋊C4×C43—24no—
102C22⋊C4×C43—24no—
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D412yes—
105C42×C43C2411yescharacteristic
106#10621884—84no—
107#10621882—84no—
108(C2×D43)⋊C4—42no—
109C4⋊Dic43—22no—
110#10621877—42no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—24no—
113C23×C43—24no—
114C23×C43—44no—
115C23×C43—44no—
116C23×C43—44no—
117C23×C43#12011yescharacteristic
118C22×D43—41no—
119Q8×C43—44no—
120Q8×C43—82no—
121D4×C43—44no—
122D4×C43—82no—
123D4×C43—88no—
124C2×C4×C43—22no—
125C2×C4×C43—24no—
126C2×C4×C43—24no—
127C2×C4×C43—42no—
128C2×C4×C43—44no—
129C2×C4×C43—44no—
130C2×C4×C43—88no—
131C2×C4×C43#12012yes—
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43C22×D412yes—
134C2×C4×C43C22×D411yescharacteristic
135C22⋊D43—82no—
136C2×Dic43—41no—
137D172—44no—
138D172—42no—
139C4×D43—82no—
140Dic86—42no—
141C43⋊C8—42no—
142C43⋊C8—44no—
143#19001—431nomaximal, Sylow
144C22×C43—22no—
145C22×C43—44no—
146C22×C43—44no—
147C22×C43—44no—
148C22×C43—88no—
149C22×C43#45412yes—
150C22×C43C2×#12011yescharacteristic
151C2×D43—81no—
152C2×D43—82no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—22no—
156C4×C43—22no—
157C4×C43—44no—
158C4×C43—44no—
159Dic43—81no—
160C2×#562D4311yescharacteristic, complemented
161#3213—432no—
162#3142—431no—
163#1662—434no—
164#1656—434no—
165#1534—431no—
166#1527—432no—
167C2×C43—22no—
168C2×C43—84no—
169C2×C43C2×#45411yescharacteristic
170C2×C43#301912yes—
171D43—161no—
172#562—22no—
173#562—24no—
174#562C2×D4314yes—
175#532—431no—
176C2×#125C2×D4311yescharacteristic
177C2×#124C2×D4312yes—
178C2×#123—22no—
179C2×C22⋊Q8—22no—
180C2×#121—22no—
181#496—434no—
182#491—432no—
183#490—432no—
184#489—434no—
185#488—862no—
186#463—864no—
187#448—862no—
188#447—862no—
189#432—432no—
190#417—862no—
191C4×M16—431no—
192#330—434no—
193#329—438no—
194C43#1900111yescharacteristic, complemented, Sylow
195C2×#41—861no—
196C22×Q8C22⋊D4312yes—
197C22×D4—22no—
198C22×D4C22⋊D4312yes—
199C23×C4—22no—
200C2×SD16—864no—
201C2×D8—864no—
202C2×M16—861no—
203C4⋊Q8—431no—
204#127—431no—
205#125—22no—
206#125C22⋊D4312yes—
207#125C22×D4312yes—
208#124—22no—
209#124—22no—
210#124—861no—
211#124C22⋊D4314yes—
212#124C22×D4314yes—
213#123—28no—
214#123—28no—
215C22⋊Q8—28no—
216C22⋊Q8—28no—
217#121—28no—
218#121—28no—
219#121—862no—
220C4×D4—862no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4C22⋊D4312yes—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C42C22×D4311yescharacteristic
228C4⋊C8—862no—
229#103—864no—
230#103—864no—
231#102—864no—
232#102—864no—
233C22⋊C8—862no—
234#97—432no—
235#97—434no—
236C4×C8—861no—
237C24—22no—
238#41—1724no—
239C2×Q8—22no—
240C2×Q8—82no—
241C2×Q8—861no—
242C2×Q8C2×C22⋊D4314yes—
243C2×D4—28no—
244C2×D4—22no—
245C2×D4—82no—
246C2×D4—84no—
247C2×D4—861no—
248C2×D4—862no—
249C2×D4—1721no—
250C2×D4C2×C22⋊D4314yes—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—28no—
254C22×C4—84no—
255C22×C4—1721no—
256C22×C4C2×C22⋊D4311yescharacteristic
257C22×C4C2×C22⋊D4312yes—
258SD16—3444no—
259D8—3444no—
260M16—1722no—
261C2×C8—862no—
262C2×C8—864no—
263C4⋊C4—28no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—24no—
267C4⋊C4—862no—
268C4⋊C4C2×C22⋊D4314yes—
269C22⋊C4—28no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—24no—
274C22⋊C4—1722no—
275C42C2×C22⋊D4311yescharacteristic
276C42C2×C22⋊D4312yes—
277C42C23×D4311yescharacteristic
278C23—24no—
279C23—44no—
280C23—44no—
281C23—44no—
282C23—1721no—
283C23#1306329411yescharacteristic
284Q8—44no—
285Q8—82no—
286Q8—1722no—
287D4—44no—
288D4—82no—
289D4—88no—
290D4—3442no—
291D4—1724no—
292D4—1722no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—88no—
300C2×C4—3442no—
301C2×C4—1721no—
302C2×C4#1306329411yescharacteristic
303C2×C4#1306329412yes—
304C2×C4C22×C22⋊D4311yescharacteristic
305C2×C4C22×C22⋊D4312yes—
306C8—1722no—
307C8—1724no—
308C22—22no—
309C22—44no—
310C22—44no—
311C22—44no—
312C22—88no—
313C22—3442no—
314C22—3441no—
315C22#1458307212yes—
316C22C2×#1306329411yescharacteristic
317C4—22no—
318C4—22no—
319C4—21no—
320C4—21no—
321C4—44no—
322C4—44no—
323C4—3441no—
324C2—22no—
325C2—84no—
326C2—6881no—
327C2C2×#1458307211yescharacteristic
328C2#1914395212yes—
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#562C2
socleC22×C43C2×#120
hypercenterC2×#562D43
hypocenterC43#19001
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #19145582C2semidirect
2. #19144998C2semidirect
3. #19133918C2semidirect
4. #19133888C2semidirect
5. #19133222C2semidirect
6. #19133193C2semidirect
7. C2×C43×#562C2semidirect
9. #14583289C22semidirect
10. #14583269C22semidirect
11. #14583265C22semidirect
12. #14583258C22semidirect
20. #14582641C22semidirect
21. #14582639C22semidirect
160. C2×#562D43semidirect
194. C43#19001semidirect

Maximal subgroups

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

subgroupindex
#191455822
#191449982
#191339182
#191338882
#191332222
#191331932
C2×C43×#5622
#1900143