Finite Group Databasebeta

← #25072904

Subgroups — #25072904

Order 11008.

982 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 179 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#19144975C211yesmaximal, characteristic, complemented
2#19144694C212yesmaximal, complemented
3#19133823C218yesmaximal, complemented
4#19133321C211yesmaximal, characteristic, complemented
5#19133038C212yesmaximal, complemented
6C2×C43×#555C211yesmaximal, characteristic
7#14583456C2211yescharacteristic
8#14583267—22no—
9#14583249C2214yescomplemented
10#14583234—22no—
11#14583179C2214yescomplemented
12#14583104C2214yescomplemented
13#14583050—22no—
14#14582999—24no—
15#14582956C2212yes—
16#14582908—22no—
17C4×#10621877C2211yescharacteristic
18#14582648C2214yescomplemented
19D4⋊(C43⋊C8)C2218yescomplemented
20C43×#555—22no—
21C43×#555—24no—
22C43×#555C2214yes—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C2×#124×C43—22no—
25C2×#121×C43—22no—
26C2×C4×D4×C43C2212yes—
27C2×#117×C43—22no—
28C2×#10621883—24no—
29C2×#10621877—21no—
30#13063325C2312yes—
31#13063317—21no—
32#13063304—22no—
33C4×Dic86—22no—
34#13063284—21no—
35#13063258—24no—
36C4⋊(C43⋊C8)C2314yes—
37#13063249—28no—
38#13063248—24no—
39#13063246—24no—
40C22⋊(C43⋊C8)—22no—
41#13063236—21no—
42#13063236—22no—
43C4×C43⋊C8C2312yes—
44C22×Q8×C43D412yes—
45C22×D4×C43—22no—
46C22×D4×C43D412yes—
47C23×C4×C43—22no—
48C4⋊Q8×C43—22no—
49C4⋊Q8×C43D412yes—
50C4⋊Q8×C43C2312yes—
51#124×C43—28no—
52#124×C43—28no—
53#121×C43—28no—
54#121×C43—28no—
55C4×D4×C43—22no—
56C4×D4×C43—22no—
57C4×D4×C43D414yes—
58C4×D4×C43C2314yes—
59#117×C43—28no—
60#117×C43—28no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43D412yes—
63C2×C22⋊C4×C43—24no—
64C2×C22⋊C4×C43—22no—
65C2×C42×C43—22no—
66C2×C42×C43C2311yescharacteristic
67C24×C43—22no—
68C2×Q8×C43—22no—
69C2×Q8×C43—44no—
70C2×Q8×C43C2×D414yes—
71C2×D4×C43—28no—
72C2×D4×C43—22no—
73C2×D4×C43—44no—
74C2×D4×C43—84no—
75C2×D4×C43C2×D414yes—
76C22×C4×C43—24no—
77C22×C4×C43—24no—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—48no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D412yes—
83C2×Dic86—22no—
84C4⋊C4×C43—24no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—24no—
87C4⋊C4×C43C2×D414yes—
88C22⋊C4×C43—216no—
89C22⋊C4×C43—24no—
90C22⋊C4×C43—24no—
91C42×C43—28no—
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D412yes—
94C42×C43C2411yescharacteristic
95C22⋊Dic43—41no—
96#10621883—48no—
97C4⋊Dic43—22no—
98C4⋊Dic43—22no—
99Dic43⋊C4—42no—
100C4×Dic43—41no—
101#10621877—42no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—24no—
104C23×C43—24no—
105C23×C43—44no—
106C23×C43—44no—
107C23×C43—44no—
108C23×C43#12011yescharacteristic
109Q8×C43—44no—
110Q8×C43—82no—
111D4×C43—24no—
112D4×C43—24no—
113D4×C43—44no—
114D4×C43—88no—
115C2×C4×C43—22no—
116C2×C4×C43—24no—
117C2×C4×C43—24no—
118C2×C4×C43—24no—
119C2×C4×C43—48no—
120C2×C4×C43—44no—
121C2×C4×C43—44no—
122C2×C4×C43—48no—
123C2×C4×C43#12011yescharacteristic
124C2×C4×C43#12012yes—
125C2×C4×C43C22×D411yescharacteristic
126C2×C4×C43C22×D412yes—
127C2×Dic43—42no—
128Dic86—44no—
129C43⋊C8—42no—
130C43⋊C8—44no—
131#18552—431nomaximal, Sylow
132C22×C43—22no—
133C22×C43—44no—
134C22×C43—44no—
135C22×C43—44no—
136C22×C43—88no—
137C22×C43#45512yes—
138C22×C43C2×#12011yescharacteristic
139C4×C43—22no—
140C4×C43—21no—
141C4×C43—21no—
142C4×C43—44no—
143C4×C43—44no—
144C4×C43#57514yes—
145Dic43—82no—
146C2×#555D4311yescharacteristic
147#3139—431no—
148#3110—432no—
149#1646—438no—
150#1558—431no—
151#1490—432no—
152C2×C43—22no—
153C2×C43—84no—
154C2×C43#300512yes—
155C2×C43C2×#45511yescharacteristic
156#555—22no—
157#555—24no—
158#555C2×D4314yes—
159#533—431no—
160C2×C4⋊Q8C2×D4311yescharacteristic
161C2×#124—22no—
162C2×#121—22no—
163C2×C4×D4C2×D4312yes—
164C2×#117—22no—
165#491—862no—
166#487—434no—
167#484—862no—
168#474—434no—
169#461—434no—
170#450—862no—
171#440—864no—
172#432—432no—
173#419—862no—
174C4×M16—431no—
175#333—434no—
176D4⋊C8—438no—
177C43#1855211yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D4312yes—
179C22×D4—22no—
180C22×D4C22⋊D4312yes—
181C23×C4—22no—
182C2×SD16—864no—
183C2×M16—861no—
184C4⋊Q8—22no—
185C4⋊Q8—432no—
186C4⋊Q8C22⋊D4312yes—
187C4⋊Q8C22×D4312yes—
188#125—861no—
189#124—28no—
190#124—28no—
191C22⋊Q8—862no—
192#121—28no—
193#121—28no—
194C4×Q8—862no—
195C4×D4—22no—
196C4×D4—22no—
197C4×D4C22⋊D4314yes—
198C4×D4C22×D4314yes—
199#117—28no—
200#117—28no—
201#117—861no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4C22⋊D4312yes—
204C2×C22⋊C4—24no—
205C2×C22⋊C4—22no—
206C2×C42—22no—
207C2×C42C22×D4311yescharacteristic
208#107—864no—
209C4⋊C8—434no—
210#103—868no—
211#103—864no—
212#102—864no—
213C22⋊C8—862no—
214#97—861no—
215#97—862no—
216C4×C8—432no—
217C24—22no—
218C2×Q8—22no—
219C2×Q8—44no—
220C2×Q8—862no—
221C2×Q8C2×C22⋊D4314yes—
222C2×D4—28no—
223C2×D4—22no—
224C2×D4—44no—
225C2×D4—84no—
226C2×D4C2×C22⋊D4314yes—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—48no—
232C22×C4C2×C22⋊D4312yes—
233C22×C4C2×C22⋊D4311yescharacteristic
234SD16—1728no—
235M16—1722no—
236C2×C8—862no—
237C2×C8—864no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—24no—
241C4⋊C4—862no—
242C4⋊C4—862no—
243C4⋊C4—1722no—
244C4⋊C4C2×C22⋊D4314yes—
245C22⋊C4—216no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C22⋊C4—1721no—
249C42—28no—
250C42—1721no—
251C42C2×C22⋊D4311yescharacteristic
252C42C2×C22⋊D4312yes—
253C42C23×D4311yescharacteristic
254C23—24no—
255C23—44no—
256C23—44no—
257C23—44no—
258C23#1306329411yescharacteristic
259Q8—44no—
260Q8—82no—
261Q8—1724no—
262D4—24no—
263D4—24no—
264D4—44no—
265D4—88no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—48no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—48no—
274C2×C4—1722no—
275C2×C4#1306329411yescharacteristic
276C2×C4#1306329412yes—
277C2×C4C22×C22⋊D4311yescharacteristic
278C2×C4C22×C22⋊D4312yes—
279C8—1722no—
280C8—1724no—
281C22—22no—
282C22—44no—
283C22—44no—
284C22—44no—
285C22—88no—
286C22#1458307712yes—
287C22C2×#1306329411yescharacteristic
288C4—22no—
289C4—21no—
290C4—21no—
291C4—44no—
292C4—44no—
293C4—3442no—
294C4#1458369714yes—
295C2—22no—
296C2—84no—
297C2#1914383712yes—
298C2C2×#1458307711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC2×C43×#555C2
socleC22×C43C2×#120
hypercenterC2×#555D43
hypocenterC43#18552
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #19144975C2semidirect
2. #19144694C2semidirect
3. #19133823C2semidirect
4. #19133321C2semidirect
5. #19133038C2semidirect
9. #14583249C22semidirect
11. #14583179C22semidirect
12. #14583104C22semidirect
18. #14582648C22semidirect
19. D4⋊(C43⋊C8)C22semidirect
177. C43#18552semidirect

Maximal subgroups

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

subgroupindex
#191449752
#191446942
#191338232
#191333212
#191330382
C2×C43×#5552
#1855243