Finite Group Databasebeta

← #24997261

Subgroups — #24997261

Order 11008.

502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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#19144544C212yesmaximal
2#19142632C211yesmaximal, characteristic
3#19134670C211yesmaximal, characteristic
4#19133129C212yesmaximal
5C43×#1306C211yesmaximal, characteristic
6C2×#13063304C2212yes—
7C2×#13063284C2211yescharacteristic
8#14583241—24no—
9#14583235—22no—
10#14583230—22no—
11#14582941—22no—
12#14582909—22no—
13#14582839—22no—
14#14582824—22no—
15#14582820—22no—
16#14582762C2211yescharacteristic
17#14582665—22no—
18#14582637—24no—
19C43×#407C2212yes—
20C43×#381C2211yescharacteristic
21C22×Dic86D412yes—
22#13063304—22no—
23#13063304—22no—
24#13063304—22no—
25#13063304—22no—
26#13063284—22no—
27#13063284—22no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43D412yes—
30C2×C4⋊Dic43D412yes—
31C2×Dic43⋊C4—22no—
32C2×C22⋊Dic43—22no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C4×Dic43—21no—
36#13063259—24no—
37#13063257—24no—
38#13063250—24no—
39#13063250—24no—
40C43⋊#95—24no—
41C43⋊#95—22no—
42C43⋊#95—22no—
43C23×C4×C43C2311yescharacteristic
44C2×M16×C43—22no—
45C2×C22⋊C4×C43D412yes—
46C22⋊C8×C43—22no—
47C22⋊C8×C43D414yes—
48#95×C43—22no—
49C24×C43C2×D411yescharacteristic
50C22×C4×C43—22no—
51C22×C4×C43—42no—
52C22×C4×C43C2×D412yes—
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43C2×D412yes—
55C22×C4×C43#4111yescharacteristic
56C22×Dic43—22no—
57C22×Dic43—22no—
58C22×Dic43—22no—
59C22×Dic43—41no—
60C2×Dic86—22no—
61C2×Dic86—22no—
62C2×Dic86—44no—
63M16×C43—44no—
64C2×C8×C43—24no—
65C22⋊C4×C43—42no—
66C22⋊Dic43—42no—
67C22⋊Dic43—41no—
68C22⋊Dic43—42no—
69C22⋊Dic43—41no—
70C22⋊Dic43—42no—
71C4⋊Dic43—22no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43—82no—
76Dic43⋊C4—42no—
77Dic43⋊C4—42no—
78C4×Dic43—42no—
79C23×C43—22no—
80C23×C43—42no—
81C23×C43#12011yescharacteristic
82C23×C43#12111yescharacteristic
83C23×C43#12711yescharacteristic
84C2×C4×C43—24no—
85C2×C4×C43—42no—
86C2×C4×C43—41no—
87C2×C4×C43—41no—
88C2×C4×C43—44no—
89C2×C4×C43—42no—
90C2×C4×C43#12012yes—
91C2×C4×C43#12112yes—
92C2×Dic43—44no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—44no—
97C2×Dic43—82no—
98C2×Dic43—81no—
99C2×Dic43—82no—
100Dic86—44no—
101Dic86—82no—
102C8×C43—44no—
103#9985—431nomaximal, Sylow
104C22×C43—22no—
105C22×C43—22no—
106C22×C43—22no—
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—82no—
110C22×C43#39211yescharacteristic
111C22×C43#45812yes—
112C4×C43—22no—
113C4×C43—22no—
114C4×C43—82no—
115Dic43—82no—
116Dic43—82no—
117Dic43—82no—
118Dic43—161no—
119#3095—432no—
120#2817—431no—
121#1820—431no—
122#1511—432no—
123#1306D4311yescharacteristic
124C2×C43—22no—
125C2×C43—41no—
126C2×C43—41no—
127C2×C43#200912yes—
128C2×C43#202211yescharacteristic
129C2×C22⋊Q8—432no—
130C2×#117—431no—
131#485—864no—
132#484—862no—
133#483—862no—
134#428—862no—
135#419—862no—
136#407C2×D4312yes—
137#400—862no—
138#397—862no—
139#395—862no—
140#381—431no—
141#381C2×D4311yescharacteristic
142#342—862no—
143#328—864no—
144C43#998511yescharacteristic, complemented, Sylow
145C22×Q8—432no—
146C23×C4C22×D4311yescharacteristic
147C2×M16—22no—
148C22⋊Q8—862no—
149C22⋊Q8—862no—
150C22⋊Q8—862no—
151C22⋊Q8—862no—
152#117—862no—
153#117—862no—
154C2×C4⋊C4—432no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—862no—
157C2×C4⋊C4—862no—
158C2×C22⋊C4—861no—
159C2×C22⋊C4—862no—
160C2×C22⋊C4—861no—
161C2×C22⋊C4D17212yes—
162C2×C42—861no—
163#107—864no—
164#106—864no—
165#103—864no—
166#103—864no—
167C22⋊C8—22no—
168C22⋊C8D17214yes—
169#95—22no—
170#95—864no—
171#95—862no—
172#95—862no—
173C24C2×D17211yescharacteristic
174C2×Q8—862no—
175C2×Q8—862no—
176C2×Q8—1724no—
177C22×C4—22no—
178C22×C4—42no—
179C22×C4—862no—
180C22×C4—862no—
181C22×C4—862no—
182C22×C4—1721no—
183C22×C4C2×D17212yes—
184C22×C4D4×D4312yes—
185C22×C4D4×D4311yescharacteristic
186C22×C4#1062190211yescharacteristic
187M16—44no—
188C2×C8—24no—
189C4⋊C4—862no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—3442no—
194C4⋊C4—1722no—
195C4⋊C4—1722no—
196C22⋊C4—42no—
197C22⋊C4—1722no—
198C22⋊C4—1721no—
199C22⋊C4—1722no—
200C22⋊C4—1721no—
201C22⋊C4—1722no—
202C42—1722no—
203C23—22no—
204C23—42no—
205C23#1306329511yescharacteristic
206C23#1306330011yescharacteristic
207C23#1306332211yescharacteristic
208Q8—3442no—
209Q8—1724no—
210C2×C4—24no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—3442no—
217C2×C4—3441no—
218C2×C4—3442no—
219C2×C4—1724no—
220C2×C4—1722no—
221C2×C4—1722no—
222C2×C4—1722no—
223C2×C4—1724no—
224C2×C4#1306329512yes—
225C2×C4#1306330012yes—
226C8—44no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#1458280911yescharacteristic
234C22#1458309012yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—3442no—
239C4—3442no—
240C4—3442no—
241C4—6881no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2#1913565812yes—
246C2#1913572711yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1306C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#1306D43
hypocenterC43#9985
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
144. C43#9985semidirect

Maximal subgroups

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

subgroupindex
#191445442
#191426322
#191346702
#191331292
C43×#13062
#998543