Finite Group Databasebeta

← #25078458

Subgroups — #25078458

Order 11008.

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

normal subgroups only

This group has 840 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
1#19149009C211yesmaximal, characteristic
2#19145805C212yesmaximal, complemented
3#19133928C218yesmaximal, complemented
4#19133230C211yesmaximal, characteristic
5#19133209C212yesmaximal, complemented
6C43×#3135C211yesmaximal, characteristic
7#14583649C2214yes—
8#14583635—21no—
9#14583629—21no—
10#14583619—22no—
11D4×Dic86—22no—
12#14583516—24no—
13#14583470—22no—
14#14583456C2212yes—
15#14583305C2214yes—
16#14583267C2214yes—
17#14583237—24no—
18#14583194—22no—
19#14583184—22no—
20#14582956C2212yes—
21#14582640C2218yes—
22#14582639C2214yes—
23C43×#533C2211yescharacteristic
24C43×#532C2211yescharacteristic
25C43×#491—21no—
26C43×#490—21no—
27C43×#489C2214yes—
28C43×#416—22no—
29C2×#97×C43C2211yescharacteristic
30C22×Dic86—22no—
31#13063325D412yes—
32#13063325D412yes—
33#13063324—24no—
34#13063323—24no—
35#13063318—28no—
36#13063317C2314yes—
37#13063312—24no—
38#13063312—24no—
39#13063306—24no—
40#13063306—24no—
41#13063304—24no—
42#13063304—22no—
43#13063304—22no—
44#13063302—28no—
45C4×Dic86—22no—
46C4×Dic86—22no—
47#13063290—24no—
48D4×Dic43—24no—
49#13063284—22no—
50#13063284D414yes—
51#13063258—24no—
52#13063256—24no—
53C4⋊(C43⋊C8)—22no—
54#13063249—24no—
55#13063249—24no—
56C22⋊(C43⋊C8)—22no—
57#13063236C2314yes—
58C2×#41×C43D412yes—
59C22×C8×C43—21no—
60C4⋊Q8×C43D411yescharacteristic
61C4⋊Q8×C43C2312yes—
62#127×C43D411yescharacteristic
63#125×C43—21no—
64#124×C43C2312yes—
65C22⋊Q8×C43—22no—
66#121×C43—22no—
67C4×Q8×C43—22no—
68C4×D4×C43—22no—
69#117×C43—21no—
70C2×C42×C43C2311yescharacteristic
71#103×C43—24no—
72#102×C43—24no—
73#97×C43—21no—
74#97×C43C2312yes—
75#41×C43—44no—
76C2×Q8×C43—22no—
77C2×Q8×C43C2×D412yes—
78C2×D4×C43—22no—
79C2×D4×C43—22no—
80C2×D4×C43C2×D412yes—
81C22×C4×C43—22no—
82C22×C4×C43C2×D412yes—
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—24no—
85C2×Dic86—22no—
86C2×Dic86—22no—
87C2×Dic86—24no—
88C2×Dic86—84no—
89C2×C8×C43—22no—
90C2×C8×C43—42no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—42no—
95C22⋊C4×C43—24no—
96C22⋊C4×C43—41no—
97C42×C43—41no—
98C42×C43C2×D412yes—
99C42×C43C2×D411yescharacteristic
100C42×C43C2411yescharacteristic
101C22⋊Dic43—24no—
102C22⋊Dic43—28no—
103C22⋊Dic43—24no—
104C4⋊Dic43—22no—
105C4⋊Dic43—22no—
106C4⋊Dic43C2×D414yes—
107C4⋊Dic43C2×D414yes—
108Dic43⋊C4—28no—
109Dic43⋊C4—24no—
110Dic43⋊C4—24no—
111C4×Dic43—24no—
112C4×Dic43—24no—
113C2×C43⋊C8—24no—
114C23×C43—22no—
115C23×C43#12011yescharacteristic
116Q8×C43—42no—
117Q8×C43—44no—
118D4×C43—42no—
119D4×C43—44no—
120D4×C43—82no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—42no—
124C2×C4×C43—44no—
125C2×C4×C43—42no—
126C2×C4×C43#12012yes—
127C2×C4×C43#12011yescharacteristic
128C2×C4×C43C22×D412yes—
129C2×C4×C43C22×D411yescharacteristic
130C2×Dic43—24no—
131C2×Dic43—24no—
132C2×Dic43—84no—
133Dic86—44no—
134Dic86—44no—
135Dic86—84no—
136C8×C43—42no—
137C43⋊C8—44no—
138#19058—431nomaximal, Sylow
139C22×C43—21no—
140C22×C43—22no—
141C22×C43—42no—
142C22×C43—44no—
143C22×C43C2×#12011yescharacteristic
144C4×C43—21no—
145C4×C43—22no—
146C4×C43—22no—
147C4×C43—42no—
148C4×C43—82no—
149C4×C43#45512yes—
150Dic43—44no—
151Dic43—44no—
152#3550—431no—
153#3237—432no—
154#3135D4311yescharacteristic
155#1664—438no—
156#1536—431no—
157#1531—432no—
158C2×C43—41no—
159C2×C43—82no—
160C2×C43C2×#45511yescharacteristic
161C2×C43#302012yes—
162#563—434no—
163#559—861no—
164Q82—861no—
165#556—862no—
166D4×Q8—862no—
167#542—864no—
168#536—862no—
169#533—432no—
170#533C2×D4311yescharacteristic
171#532C2×D4311yescharacteristic
172#501—434no—
173#491—21no—
174#491—434no—
175#490—21no—
176#489C2×D4314yes—
177#485—864no—
178#477—862no—
179#475—862no—
180#432—432no—
181#416—22no—
182C2×#97C2×D4311yescharacteristic
183#330—438no—
184#329—434no—
185C43#1905811yescharacteristic, complemented, Sylow
186C2×#41C22⋊D4312yes—
187C22×Q8—862no—
188C22×C8—21no—
189C4⋊Q8—432no—
190C4⋊Q8—432no—
191C4⋊Q8—864no—
192C4⋊Q8—864no—
193C4⋊Q8C22⋊D4311yescharacteristic
194C4⋊Q8C22×D4312yes—
195#127C22⋊D4311yescharacteristic
196#126—868no—
197#125—21no—
198#125—434no—
199#124—864no—
200#124—864no—
201#124C22×D4312yes—
202#123—864no—
203#123—864no—
204C22⋊Q8—22no—
205C22⋊Q8—868no—
206C22⋊Q8—864no—
207C22⋊Q8—862no—
208C22⋊Q8—862no—
209#121—22no—
210C4×Q8—22no—
211C4×Q8—864no—
212C4×Q8—862no—
213C4×Q8—862no—
214C4×D4—22no—
215C4×D4—864no—
216#117—21no—
217#117—434no—
218#117—862no—
219C2×C42C22×D4311yescharacteristic
220#107—864no—
221#106—864no—
222C4⋊C8—862no—
223#103—24no—
224#103—864no—
225#103—864no—
226#102—24no—
227C22⋊C8—862no—
228#97—21no—
229#97—434no—
230#97C22×D4312yes—
231#41—44no—
232C2×Q8—22no—
233C2×Q8—864no—
234C2×Q8—862no—
235C2×Q8—862no—
236C2×Q8—3444no—
237C2×Q8C2×C22⋊D4312yes—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4C2×C22⋊D4312yes—
241C22×C4—22no—
242C22×C4—864no—
243C22×C4D4×D4312yes—
244C22×C4C2×C22⋊D4311yescharacteristic
245C2×C8—22no—
246C2×C8—42no—
247C2×C8—864no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—42no—
252C4⋊C4—434no—
253C4⋊C4—434no—
254C4⋊C4—868no—
255C4⋊C4—862no—
256C4⋊C4—862no—
257C4⋊C4—864no—
258C4⋊C4—864no—
259C22⋊C4—24no—
260C22⋊C4—41no—
261C22⋊C4—864no—
262C22⋊C4—868no—
263C22⋊C4—864no—
264C42—41no—
265C42—864no—
266C42—864no—
267C42D4×D4312yes—
268C42C2×C22⋊D4311yescharacteristic
269C42C23×D4311yescharacteristic
270C23—22no—
271C23#1306329311yescharacteristic
272Q8—42no—
273Q8—44no—
274Q8—3444no—
275Q8—1724no—
276Q8—1724no—
277D4—42no—
278D4—44no—
279D4—82no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—864no—
286C2×C4—864no—
287C2×C4—3444no—
288C2×C4#1306329312yes—
289C2×C4#1306329311yescharacteristic
290C2×C4C2×D4×D4312yes—
291C2×C4C22×C22⋊D4311yescharacteristic
292C8—42no—
293C8—1724no—
294C22—22no—
295C22—21no—
296C22—44no—
297C22—42no—
298C22C2×#1306329311yescharacteristic
299C4—22no—
300C4—22no—
301C4—21no—
302C4—42no—
303C4—82no—
304C4—1724no—
305C4—1724no—
306C4#1458307612yes—
307C2—41no—
308C2—82no—
309C2C2×#1458307611yescharacteristic
310C2#1914395712yes—
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3135C2
socleC22×C43C2×#120
prime radicalC43×#532C22
hypercenter#3135D43
hypocenterC43#19058
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3135

Complements

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

NH ≅ G/Ntype
2. #19145805C2semidirect
3. #19133928C2semidirect
5. #19133209C2semidirect
185. C43#19058semidirect

Maximal subgroups

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

subgroupindex
#191490092
#191458052
#191339282
#191332302
#191332092
C43×#31352
#1905843