Finite Group Databasebeta

← #25078529

Subgroups — #25078529

Order 11008.

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

normal subgroups only

This group has 784 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#19149090C211yesmaximal, characteristic
2#19145805C212yesmaximal
3#19133922C218yesmaximal, complemented
4#19133233C211yesmaximal, characteristic
5#19133209C212yesmaximal
6C43×#3162C211yesmaximal, characteristic
7C43⋊#564C2214yes—
8#14583628—22no—
9#14583627—22no—
10#14583624—22no—
11#14583511—22no—
12#14583509—24no—
13#14583456C2212yes—
14#14583305C2214yes—
15#14583267C2214yes—
16#14583237—24no—
17#14583194—22no—
18#14583184—22no—
19#14582956C2212yes—
20#14582641C2214yes—
21#14582640C2218yes—
22C43×#533C2211yescharacteristic
23C43×#533C2211yescharacteristic
24C43×#501—22no—
25C43×#501C2214yes—
26C43×#427—22no—
27C2×#97×C43C2211yescharacteristic
28#13063325—22no—
29#13063325D412yes—
30#13063325D412yes—
31#13063323—24no—
32#13063318—28no—
33#13063317—22no—
34#13063317C2314yes—
35#13063316—24no—
36#13063316—28no—
37#13063315—28no—
38#13063315—28no—
39#13063304—22no—
40#13063304—22no—
41Q8×Dic43—24no—
42C4×Dic86—24no—
43C4×Dic86—22no—
44C4×Dic86—22no—
45#13063290—24no—
46#13063284D414yes—
47#13063258—24no—
48#13063256—24no—
49C4⋊(C43⋊C8)—22no—
50#13063249—24no—
51#13063249—24no—
52C22⋊(C43⋊C8)—22no—
53#13063236C2314yes—
54C22×C8×C43—21no—
55C4⋊Q8×C43D412yes—
56C4⋊Q8×C43C2312yes—
57#125×C43—21no—
58#125×C43C2312yes—
59C22⋊Q8×C43—22no—
60C22⋊Q8×C43—22no—
61C4×Q8×C43—22no—
62C4×Q8×C43—22no—
63#117×C43—21no—
64#117×C43D412yes—
65C2×C42×C43C2311yescharacteristic
66#107×C43—24no—
67#106×C43—24no—
68#97×C43—21no—
69#97×C43C2312yes—
70C2×Q8×C43—22no—
71C2×Q8×C43—22no—
72C22×C4×C43C2×D412yes—
73C22×C4×C43C2×D411yescharacteristic
74C2×Dic86—22no—
75C2×Dic86—22no—
76C2×C8×C43—24no—
77C2×C8×C43—22no—
78C4⋊C4×C43—22no—
79C4⋊C4×C43—24no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—42no—
83C4⋊C4×C43C2×D414yes—
84C22⋊C4×C43—22no—
85C22⋊C4×C43—41no—
86C42×C43—22no—
87C42×C43—41no—
88C42×C43C2×D412yes—
89C42×C43C2×D411yescharacteristic
90C42×C43C2411yescharacteristic
91C22⋊Dic43—24no—
92C4⋊Dic43—28no—
93C4⋊Dic43—22no—
94C4⋊Dic43—22no—
95C4⋊Dic43C2×D414yes—
96C4⋊Dic43C2×D414yes—
97Dic43⋊C4—28no—
98Dic43⋊C4—28no—
99Dic43⋊C4—24no—
100Dic43⋊C4—24no—
101C4×Dic43—28no—
102C4×Dic43—24no—
103C2×C43⋊C8—24no—
104C23×C43#12011yescharacteristic
105Q8×C43—44no—
106Q8×C43—44no—
107C2×C4×C43—22no—
108C2×C4×C43—24no—
109C2×C4×C43—42no—
110C2×C4×C43—42no—
111C2×C4×C43#12012yes—
112C2×C4×C43#12011yescharacteristic
113C2×C4×C43C22×D412yes—
114C2×C4×C43C22×D411yescharacteristic
115C2×Dic43—24no—
116C2×Dic43—24no—
117Dic86—44no—
118Dic86—44no—
119C8×C43—24no—
120C43⋊C8—44no—
121#19067—431nomaximal, Sylow
122C22×C43—21no—
123C22×C43—22no—
124C22×C43C2×#12011yescharacteristic
125C4×C43—21no—
126C4×C43—22no—
127C4×C43—22no—
128C4×C43—44no—
129C4×C43—82no—
130C4×C43#45612yes—
131Dic43—44no—
132Dic43—44no—
133#3556—431no—
134#3237—432no—
135#3162D4311yescharacteristic
136#1663—438no—
137#1537—431no—
138#1531—432no—
139C2×C43—41no—
140C2×C43C2×#45611yescharacteristic
141C2×C43#302012yes—
142#564—434no—
143#557—862no—
144#557—862no—
145#557—862no—
146#541—864no—
147#541—862no—
148#533—432no—
149#533C2×D4311yescharacteristic
150#533C2×D4311yescharacteristic
151#501—22no—
152#501—434no—
153#501C2×D4314yes—
154#491—434no—
155#485—864no—
156#477—862no—
157#475—862no—
158#432—432no—
159#427—22no—
160C2×#97C2×D4311yescharacteristic
161#330—434no—
162#330—438no—
163C43#1906711yescharacteristic, complemented, Sylow
164C22×C8—21no—
165C4⋊Q8—432no—
166C4⋊Q8—432no—
167C4⋊Q8—862no—
168C4⋊Q8—864no—
169C4⋊Q8C22⋊D4312yes—
170C4⋊Q8C22×D4312yes—
171#126—868no—
172#125—21no—
173#125—434no—
174#125—862no—
175#125—868no—
176#125—868no—
177#125—864no—
178#125—868no—
179#125C22×D4312yes—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—862no—
183C22⋊Q8—862no—
184C4×Q8—22no—
185C4×Q8—22no—
186C4×Q8—864no—
187C4×Q8—864no—
188C4×Q8—864no—
189C4×Q8—862no—
190C4×Q8—862no—
191#117—21no—
192#117—434no—
193#117C22⋊D4312yes—
194C2×C42C22×D4311yescharacteristic
195#107—24no—
196#107—864no—
197#106—24no—
198#106—864no—
199C4⋊C8—862no—
200#103—864no—
201#103—864no—
202C22⋊C8—862no—
203#97—21no—
204#97—434no—
205#97C22×D4312yes—
206C2×Q8—22no—
207C2×Q8—22no—
208C2×Q8—862no—
209C2×Q8—862no—
210C22×C4D4×D4312yes—
211C22×C4C2×C22⋊D4311yescharacteristic
212C2×C8—24no—
213C2×C8—22no—
214C2×C8—864no—
215C4⋊C4—22no—
216C4⋊C4—24no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—42no—
220C4⋊C4—434no—
221C4⋊C4—434no—
222C4⋊C4—868no—
223C4⋊C4—868no—
224C4⋊C4—868no—
225C4⋊C4—862no—
226C4⋊C4—862no—
227C4⋊C4—864no—
228C4⋊C4—864no—
229C4⋊C4C2×C22⋊D4314yes—
230C22⋊C4—22no—
231C22⋊C4—41no—
232C22⋊C4—864no—
233C42—22no—
234C42—41no—
235C42—868no—
236C42—864no—
237C42D4×D4312yes—
238C42C2×C22⋊D4311yescharacteristic
239C42C23×D4311yescharacteristic
240C23#1306329311yescharacteristic
241Q8—44no—
242Q8—44no—
243Q8—1724no—
244Q8—1724no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—864no—
250C2×C4—864no—
251C2×C4#1306329312yes—
252C2×C4#1306329311yescharacteristic
253C2×C4C2×D4×D4312yes—
254C2×C4C22×C22⋊D4311yescharacteristic
255C8—24no—
256C8—1724no—
257C22—21no—
258C22—22no—
259C22C2×#1306329311yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—44no—
264C4—82no—
265C4—1724no—
266C4—1724no—
267C4#1458308112yes—
268C2—41no—
269C2C2×#1458308111yescharacteristic
270C2#1914395712yes—
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3162C2
socleC22×C43C2×#120
prime radicalC23×C43#120
hypercenter#3162D43
hypocenterC43#19067
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
3. #19133922C2semidirect
163. C43#19067semidirect

Maximal subgroups

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

subgroupindex
#191490902
#191458052
#191339222
#191332332
#191332092
C43×#31622
#1906743