Finite Group Databasebeta

← #24989164

Subgroups — #24989164

Order 11008.

656 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 115 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#19135572C212yesmaximal
3#19133333C211yesmaximal, characteristic
4#19133332C212yesmaximal
5C43×#1994C211yesmaximal, characteristic
6C43⋊#564C414yescomplemented
7#14583628—22no—
8#14583627—22no—
9#14583624—22no—
10#14583511—22no—
11#14583509—24no—
12#14583456C2212yes—
13#14582923C2212yes—
14#14582659—24no—
15#14582646—22no—
16#14582645—22no—
17#14582644—22no—
18C43×#533C2211yescharacteristic
19C43×#423C2211yescharacteristic
20C43×C43C2211yescharacteristic
21C43×#339—22no—
22C2×#10621877—22no—
23#13063325—22no—
24#13063325D412yes—
25#13063325D412yes—
26#13063323—24no—
27#13063318—28no—
28#13063317—22no—
29#13063317C2×C414yes—
30#13063316—24no—
31#13063316—28no—
32#13063315—28no—
33#13063315—28no—
34#13063304—22no—
35#13063304—22no—
36Q8×Dic43—24no—
37C4×Dic86—24no—
38C4×Dic86—22no—
39C4×Dic86—22no—
40#13063290—24no—
41#13063284D414yes—
42C4⋊(C43⋊C8)—22no—
43C4⋊(C43⋊C8)—22no—
44C2×M16×C43—21no—
45C4⋊Q8×C43D412yes—
46#125×C43C2×C412yes—
47C22⋊Q8×C43—22no—
48C4×Q8×C43—22no—
49#117×C43D412yes—
50C2×C42×C43—21no—
51C2×C42×C43—22no—
52C2×C42×C43C2311yescharacteristic
53C4⋊C8×C43—22no—
54C2×Q8×C43—22no—
55C22×C4×C43—41no—
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D411yescharacteristic
58C2×Dic86—22no—
59C2×Dic86—22no—
60M16×C43—42no—
61C2×C8×C43—41no—
62C4⋊C4×C43—24no—
63C4⋊C4×C43—22no—
64C4⋊C4×C43C22⋊C414yes—
65C22⋊C4×C43—22no—
66C42×C43—22no—
67C42×C43—22no—
68C42×C43—24no—
69C42×C43—42no—
70C42×C43—41no—
71C42×C43C22×C411yescharacteristic
72C42×C43C2×D411yescharacteristic
73C42×C43C2×D412yes—
74C22⋊Dic43—24no—
75C4⋊Dic43—28no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78C4⋊Dic43C22⋊C414yes—
79C4⋊Dic43C22⋊C414yes—
80Dic43⋊C4—28no—
81Dic43⋊C4—28no—
82Dic43⋊C4—24no—
83Dic43⋊C4—24no—
84C4×Dic43—28no—
85C4×Dic43—24no—
86#10621877—44no—
87C2×C43⋊C8—42no—
88C23×C43#12011yescharacteristic
89Q8×C43—42no—
90Q8×C43—42no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—22no—
95C2×C4×C43—24no—
96C2×C4×C43—42no—
97C2×C4×C43—44no—
98C2×C4×C43C2×C22⋊C412yes—
99C2×C4×C43C2×C22⋊C411yescharacteristic
100C2×C4×C43#12011yescharacteristic
101C2×C4×C43#12012yes—
102C2×Dic43—24no—
103C2×Dic43—24no—
104Dic86—42no—
105Dic86—42no—
106Dic86—42no—
107Dic86—42no—
108C8×C43—81no—
109C43⋊C8—82no—
110#8533—431nomaximal, Sylow
111C22×C43—21no—
112C22×C43—22no—
113C22×C43#37911yescharacteristic
114C4×C43—21no—
115C4×C43—22no—
116C4×C43—44no—
117C4×C43—44no—
118C4×C43#45411yescharacteristic
119C4×C43#45412yes—
120C4×C43#45611yescharacteristic
121C4×C43#45612yes—
122Dic43—44no—
123Dic43—44no—
124#3556—431no—
125#1994—432no—
126#1994D4311yescharacteristic
127#1561—432no—
128#1561—431no—
129C2×C43—41no—
130C2×C43#179311yescharacteristic
131C2×C43#179312yes—
132#564—434no—
133#557—862no—
134#557—862no—
135#557—862no—
136#541—864no—
137#541—862no—
138#533—432no—
139#533C2×D4311yescharacteristic
140#423—432no—
141#423C2×D4311yescharacteristic
142C43C2×D4311yescharacteristic
143#339—22no—
144#339—864no—
145#332—862no—
146#332—862no—
147#332—862no—
148C43#853311yescharacteristic, complemented, Sylow
149C2×M16—21no—
150C2×M16—862no—
151C4⋊Q8—432no—
152C4⋊Q8—432no—
153C4⋊Q8—862no—
154C4⋊Q8—864no—
155C4⋊Q8D17212yes—
156#126—868no—
157#125—434no—
158#125—862no—
159#125—868no—
160#125—868no—
161#125—864no—
162#125—868no—
163#125C4×D4312yes—
164C22⋊Q8—22no—
165C22⋊Q8—862no—
166C22⋊Q8—862no—
167C4×Q8—22no—
168C4×Q8—864no—
169C4×Q8—864no—
170C4×Q8—864no—
171C4×Q8—862no—
172C4×Q8—862no—
173#117—434no—
174#117C22⋊D4312yes—
175C2×C42—22no—
176C2×C42—21no—
177C2×C42C22×D4311yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—862no—
180C4⋊C8—862no—
181C2×Q8—22no—
182C2×Q8—862no—
183C2×Q8—862no—
184C22×C4—41no—
185C22×C4D4×D4312yes—
186C22×C4C2×C22⋊D4311yescharacteristic
187M16—42no—
188M16—1724no—
189C2×C8—41no—
190C2×C8—1722no—
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—434no—
194C4⋊C4—434no—
195C4⋊C4—868no—
196C4⋊C4—868no—
197C4⋊C4—868no—
198C4⋊C4—864no—
199C4⋊C4—864no—
200C4⋊C4—862no—
201C4⋊C4—862no—
202C4⋊C4(C2×D43)⋊C414yes—
203C22⋊C4—22no—
204C22⋊C4—864no—
205C42—22no—
206C42—22no—
207C42—24no—
208C42—41no—
209C42—42no—
210C42—868no—
211C42—864no—
212C42C2×C4×D4311yescharacteristic
213C42C2×D17211yescharacteristic
214C42D4×D4312yes—
215C23#1306329311yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—1722no—
219Q8—1722no—
220Q8—1722no—
221Q8—1722no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—864no—
230C2×C4—864no—
231C2×C4C22⋊C4×D4312yes—
232C2×C4C2×(C2×D43)⋊C411yescharacteristic
233C2×C4#1306329311yescharacteristic
234C2×C4#1306329512yes—
235C8—81no—
236C8—3442no—
237C22—21no—
238C22—22no—
239C22#1458275411yescharacteristic
240C4—21no—
241C4—22no—
242C4—44no—
243C4—44no—
244C4—1724no—
245C4—1724no—
246C4#1458307111yescharacteristic
247C4#1458307312yes—
248C4#1458308111yescharacteristic
249C4#1458308312yes—
250C2—41no—
251C2#1913455311yescharacteristic
252C2#1913455512yes—
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1994C2
socleC22×C43#379
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1994D43
hypocenterC43#8533
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
6. C43⋊#564C4semidirect
148. C43#8533semidirect

Maximal subgroups

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

subgroupindex
#191490902
#191355722
#191333332
#191333322
C43×#19942
#853343