Finite Group Databasebeta

← #24989163

Subgroups — #24989163

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#19135573C211yesmaximal, characteristic
3#19135571C212yesmaximal
4#19133332C212yesmaximal
5C43×#1561C211yesmaximal, characteristic
6C43⋊#564C414yescomplemented
7#14583628—22no—
8#14583627—22no—
9#14583624—22no—
10#14583511—22no—
11#14583509—24no—
12#14583456C2212yes—
13#14582923C2211yescharacteristic
14C42×Dic43C2211yescharacteristic
15#14582660—24no—
16#14582658—22no—
17#14582646—22no—
18#14582644—22no—
19C43×#533C2211yescharacteristic
20C43×#423C2212yes—
21C43×#332—22no—
22C2×#10621877—21no—
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—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—22no—
44C4⋊(C43⋊C8)—22no—
45C2×M16×C43—22no—
46C4⋊Q8×C43D412yes—
47#125×C43C2×C412yes—
48C22⋊Q8×C43—22no—
49C4×Q8×C43—22no—
50#117×C43D412yes—
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—22no—
53C4⋊C8×C43—22no—
54C2×Q8×C43—22no—
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43C2×D412yes—
57C22×Dic43—41no—
58C2×Dic86—22no—
59C2×Dic86—22no—
60M16×C43—44no—
61C2×C8×C43—42no—
62C4⋊C4×C43—24no—
63C4⋊C4×C43—22no—
64C4⋊C4×C43C22⋊C414yes—
65C22⋊C4×C43—22no—
66C42×C43—22no—
67C42×C43C22×C411yescharacteristic
68C42×C43C2×D412yes—
69C42×C43C2×D411yescharacteristic
70C22⋊Dic43—24no—
71C4⋊Dic43—28no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74C4⋊Dic43C22⋊C414yes—
75C4⋊Dic43C22⋊C414yes—
76Dic43⋊C4—28no—
77Dic43⋊C4—28no—
78Dic43⋊C4—24no—
79Dic43⋊C4—24no—
80C4×Dic43—28no—
81C4×Dic43—24no—
82C4×Dic43—22no—
83C4×Dic43—24no—
84C4×Dic43—41no—
85C4×Dic43—42no—
86#10621877—42no—
87C2×C43⋊C8—41no—
88C23×C43#12011yescharacteristic
89Q8×C43—42no—
90Q8×C43—42no—
91C2×C4×C43—21no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—21no—
95C2×C4×C43—24no—
96C2×C4×C43C2×C22⋊C412yes—
97C2×C4×C43C2×C22⋊C411yescharacteristic
98C2×C4×C43#12012yes—
99C2×C4×C43#12011yescharacteristic
100C2×Dic43—24no—
101C2×Dic43—24no—
102C2×Dic43—44no—
103C2×Dic43—42no—
104Dic86—42no—
105Dic86—42no—
106Dic86—42no—
107Dic86—42no—
108C8×C43—82no—
109C43⋊C8—81no—
110#8533—431nomaximal, Sylow
111C22×C43—22no—
112C22×C43—21no—
113C22×C43#37911yescharacteristic
114C4×C43—22no—
115C4×C43—21no—
116C4×C43—44no—
117C4×C43#45412yes—
118C4×C43#45411yescharacteristic
119C4×C43#45612yes—
120C4×C43#45611yescharacteristic
121Dic43—44no—
122Dic43—44no—
123Dic43—44no—
124#3556—431no—
125#1994—432no—
126#1994—431no—
127#1561—432no—
128#1561D4311yescharacteristic
129C2×C43—41no—
130C2×C43#179312yes—
131C2×C43#179311yescharacteristic
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—431no—
141#423C2×D4312yes—
142C43—431no—
143#339—864no—
144#339—862no—
145#332—22no—
146#332—862no—
147#332—862no—
148C43#853311yescharacteristic, complemented, Sylow
149C2×M16—22no—
150C2×M16—861no—
151C4⋊Q8—432no—
152C4⋊Q8—432no—
153C4⋊Q8—862no—
154C4⋊Q8—864no—
155C4⋊Q8C22⋊D4312yes—
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#117D17212yes—
175C2×C42—861no—
176C2×C42—862no—
177C2×C42C22×D4311yescharacteristic
178C4⋊C8—22no—
179C4⋊C8—22no—
180C4⋊C8—862no—
181C2×Q8—22no—
182C2×Q8—862no—
183C2×Q8—862no—
184C22×C4—1721no—
185C22×C4C2×D17211yescharacteristic
186C22×C4D4×D4312yes—
187M16—44no—
188M16—1722no—
189C2×C8—42no—
190C2×C8—1721no—
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—868no—
207C42—864no—
208C42—862no—
209C42—864no—
210C42—1722no—
211C42—1721no—
212C42C2×C4×D4311yescharacteristic
213C42D4×D4312yes—
214C42C2×C22⋊D4311yescharacteristic
215C23#1306329511yescharacteristic
216Q8—42no—
217Q8—42no—
218Q8—1722no—
219Q8—1722no—
220Q8—1722no—
221Q8—1722no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—864no—
228C2×C4—864no—
229C2×C4—1724no—
230C2×C4—1722no—
231C2×C4C22⋊C4×D4312yes—
232C2×C4C2×(C2×D43)⋊C411yescharacteristic
233C2×C4#1306329312yes—
234C2×C4#1306329511yescharacteristic
235C8—82no—
236C8—3441no—
237C22—22no—
238C22—21no—
239C22#1458275411yescharacteristic
240C4—22no—
241C4—21no—
242C4—44no—
243C4—1724no—
244C4—1724no—
245C4—1724no—
246C4#1458307012yes—
247C4#1458307411yescharacteristic
248C4#1458308012yes—
249C4#1458308411yescharacteristic
250C2—41no—
251C2#1913455212yes—
252C2#1913455611yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1561C2
socleC22×C43#379
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1561D43
hypocenterC43#8533
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1561

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
#191355732
#191355712
#191333322
C43×#15612
#853343