Finite Group Databasebeta

← #25074586

Subgroups — #25074586

Order 11008.

812 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 163 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#19149090C211yesmaximal, characteristic
2#19145986C212yesmaximal
3#19133869C214yesmaximal, complemented
4#19133834C214yesmaximal, complemented
5#19133333C211yesmaximal, characteristic
6#19133051C212yesmaximal
7C43×#3160C211yesmaximal, characteristic
8C43⋊#564—22no—
9#14583628—22no—
10#14583627—22no—
11#14583624C2214yes—
12#14583511—22no—
13#14583509—24no—
14#14583456C2212yes—
15#14583184—22no—
16#14583181C2214yes—
17#14583155—24no—
18#14583109—22no—
19#14583106C2214yes—
20#14582923C2212yes—
21#14582645C2214yes—
22#14582631C2214yes—
23#14582631C2214yes—
24C43×#533C2211yescharacteristic
25C43×#533C2211yescharacteristic
26C43×#500C2212yes—
27C43×#499—22no—
28C43×#498C2212yes—
29C43×#427—22no—
30C2×C4×C8×C43C2211yescharacteristic
31C2×#10621885—24no—
32C2×#10621877—22no—
33#13063325—22no—
34#13063325D412yes—
35#13063325D412yes—
36#13063323—24no—
37#13063318—28no—
38#13063317—22no—
39#13063317—22no—
40#13063316—28no—
41#13063316—24no—
42#13063315—28no—
43#13063315—28no—
44#13063304—22no—
45#13063304D414yes—
46Q8×Dic43—24no—
47C4×Dic86—24no—
48C4×Dic86—22no—
49C4×Dic86C2314yes—
50#13063290—24no—
51#13063284—22no—
52#13063256—24no—
53C4⋊(C43⋊C8)—22no—
54C4⋊(C43⋊C8)C2314yes—
55#13063249—24no—
56#13063248—24no—
57C22×C8×C43—21no—
58C4⋊Q8×C43C2312yes—
59C4⋊Q8×C43C2312yes—
60#125×C43—21no—
61#125×C43D412yes—
62C22⋊Q8×C43—22no—
63C22⋊Q8×C43—22no—
64C4×Q8×C43—22no—
65C4×Q8×C43—22no—
66#117×C43—21no—
67#117×C43D412yes—
68C2×C42×C43C2311yescharacteristic
69#107×C43—24no—
70#106×C43—24no—
71C4×C8×C43—21no—
72C4×C8×C43C2311yescharacteristic
73C4×C8×C43C2311yescharacteristic
74C2×Q8×C43—22no—
75C2×Q8×C43—22no—
76C22×C4×C43C2×D412yes—
77C22×C4×C43C2×D411yescharacteristic
78C2×Dic86—22no—
79C2×Dic86C2×D414yes—
80C2×C8×C43—24no—
81C2×C8×C43—21no—
82C2×C8×C43—21no—
83C4⋊C4×C43—24no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—42no—
88C4⋊C4×C43C2×D414yes—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—41no—
91C42×C43—22no—
92C42×C43—41no—
93C42×C43C2×D412yes—
94C42×C43C2×D411yescharacteristic
95C42×C43C2411yescharacteristic
96C22⋊Dic43—24no—
97#10621885—84no—
98C4⋊Dic43—28no—
99C4⋊Dic43—22no—
100C4⋊Dic43—22no—
101C4⋊Dic43—22no—
102C4⋊Dic43C2×D414yes—
103Dic43⋊C4—28no—
104Dic43⋊C4—28no—
105Dic43⋊C4—24no—
106Dic43⋊C4—24no—
107C4×Dic43—28no—
108C4×Dic43—24no—
109#10621877—82no—
110C2×C43⋊C8—24no—
111C23×C43#12011yescharacteristic
112Q8×C43—42no—
113Q8×C43—42no—
114Q8×C43—42no—
115Q8×C43—42no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—24no—
120C2×C4×C43—42no—
121C2×C4×C43#12012yes—
122C2×C4×C43#12011yescharacteristic
123C2×C4×C43C22×D412yes—
124C2×C4×C43C22×D411yescharacteristic
125C2×Dic43—24no—
126C2×Dic43—24no—
127Dic86—24no—
128Dic86—24no—
129Dic86—44no—
130C8×C43—22no—
131C8×C43—22no—
132C43⋊C8—44no—
133#18703—431nomaximal, Sylow
134C22×C43—22no—
135C22×C43—21no—
136C22×C43C2×#12011yescharacteristic
137C4×C43—22no—
138C4×C43—21no—
139C4×C43—44no—
140C4×C43—82no—
141C4×C43#45612yes—
142C4×C43#57712yes—
143C4×C43#57812yes—
144Dic43—44no—
145Dic43—44no—
146#3556—431no—
147#3255—432no—
148#3160D4311yescharacteristic
149#1653—434no—
150#1648—434no—
151#1561—431no—
152#1493—432no—
153C2×C43—41no—
154C2×C43#301312yes—
155C2×C43C2×#45611yescharacteristic
156#564—862no—
157#557—434no—
158#557—862no—
159#557—862no—
160#541—864no—
161#541—862no—
162#533—432no—
163#533C2×D4311yescharacteristic
164#533C2×D4311yescharacteristic
165#500C2×D4312yes—
166#499—22no—
167#498C2×D4312yes—
168#475—434no—
169#475—862no—
170#470—864no—
171#462—434no—
172#462—862no—
173#427—22no—
174#423—432no—
175C2×C4×C8C2×D4311yescharacteristic
176#332—434no—
177Q8⋊C8—434no—
178Q8⋊C8—434no—
179C43#1870311yescharacteristic, complemented, Sylow
180C2×Q16—864no—
181C2×M16—862no—
182C22×C8—21no—
183C4⋊Q8—432no—
184C4⋊Q8—432no—
185C4⋊Q8—862no—
186C4⋊Q8—864no—
187C4⋊Q8C22×D4312yes—
188C4⋊Q8C22×D4312yes—
189#126—868no—
190#125—21no—
191#125—862no—
192#125—864no—
193#125—868no—
194#125—868no—
195#125—868no—
196#125—862no—
197#125C22⋊D4312yes—
198C22⋊Q8—22no—
199C22⋊Q8—22no—
200C22⋊Q8—434no—
201C22⋊Q8—862no—
202C4×Q8—22no—
203C4×Q8—22no—
204C4×Q8—434no—
205C4×Q8—864no—
206C4×Q8—864no—
207C4×Q8—864no—
208C4×Q8—862no—
209#117—21no—
210#117—862no—
211#117C22⋊D4312yes—
212C2×C42C22×D4311yescharacteristic
213#107—24no—
214#106—24no—
215#106—864no—
216C4⋊C8—434no—
217C4⋊C8—862no—
218#103—864no—
219#103—864no—
220C4×C8—21no—
221C4×C8C22×D4311yescharacteristic
222C4×C8C22×D4311yescharacteristic
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—434no—
226C2×Q8—862no—
227C22×C4D4×D4312yes—
228C22×C4C2×C22⋊D4311yescharacteristic
229Q16—3444no—
230M16—3442no—
231C2×C8—24no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—864no—
235C4⋊C4—24no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—434no—
241C4⋊C4—868no—
242C4⋊C4—868no—
243C4⋊C4—868no—
244C4⋊C4—862no—
245C4⋊C4—862no—
246C4⋊C4—862no—
247C4⋊C4—864no—
248C4⋊C4—864no—
249C4⋊C4C2×C22⋊D4314yes—
250C22⋊C4—22no—
251C22⋊C4—41no—
252C22⋊C4—864no—
253C42—22no—
254C42—41no—
255C42—868no—
256C42—864no—
257C42D4×D4312yes—
258C42C2×C22⋊D4311yescharacteristic
259C42C23×D4311yescharacteristic
260C23#1306329311yescharacteristic
261Q8—42no—
262Q8—42no—
263Q8—42no—
264Q8—42no—
265Q8—864no—
266Q8—864no—
267Q8—1724no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—42no—
273C2×C4—864no—
274C2×C4—864no—
275C2×C4#1306329312yes—
276C2×C4#1306329311yescharacteristic
277C2×C4C2×D4×D4312yes—
278C2×C4C22×C22⋊D4311yescharacteristic
279C8—22no—
280C8—22no—
281C8—1724no—
282C22—21no—
283C22—22no—
284C22C2×#1306329311yescharacteristic
285C4—21no—
286C4—22no—
287C4—44no—
288C4—82no—
289C4—1724no—
290C4—1724no—
291C4#1458308112yes—
292C4#1458370612yes—
293C4#1458371312yes—
294C2—41no—
295C2#1914390612yes—
296C2C2×#1458308111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3160C2
socleC22×C43C2×#120
prime radicalC23×C43#120
hypercenter#3160D43
hypocenterC43#18703
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3160

Complements

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

NH ≅ G/Ntype
3. #19133869C2semidirect
4. #19133834C2semidirect
179. C43#18703semidirect

Maximal subgroups

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

subgroupindex
#191490902
#191459862
#191338692
#191338342
#191333332
#191330512
C43×#31602
#1870343