Finite Group Databasebeta

← #24997227

Subgroups — #24997227

Order 11008.

492 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 85 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#19145370C211yesmaximal, characteristic
2#19144544C212yesmaximal
3#19134664C211yesmaximal, characteristic
4#19132960C212yesmaximal
5C43×#1293C211yesmaximal, characteristic
6C2×#13063304C2212yes—
7C2×#13063284C2211yescharacteristic
8#14583241—24no—
9#14583235—22no—
10#14583235—22no—
11#14583230—22no—
12#14583140—22no—
13#14583057—22no—
14#14582941—22no—
15#14582909—22no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582653—22no—
18#14582624—24no—
19C43×#407C2212yes—
20C2×C22⋊C8×C43C2211yescharacteristic
21C22×Dic86D412yes—
22C2×Dic172—22no—
23C22×C43⋊C8—21no—
24#13063304—22no—
25#13063304—22no—
26#13063304—22no—
27#13063304—22no—
28#13063284—22no—
29#13063284—22no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D412yes—
33C2×Dic43⋊C4—22no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—22no—
36C2×C4×Dic43—21no—
37#13063259—22no—
38#13063259—24no—
39#13063257—24no—
40#13063250—24no—
41#13063250—24no—
42#13063250—24no—
43C22⋊(C43⋊C8)—22no—
44C23×C4×C43C2311yescharacteristic
45C2×M16×C43—22no—
46C22×C8×C43D412yes—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43D414yes—
50C24×C43#4111yescharacteristic
51C22×C4×C43—42no—
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43C2×D412yes—
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—21no—
57C22×Dic43—21no—
58C22×Dic43—22no—
59C22×Dic43—22no—
60C2×Dic86—22no—
61C2×Dic86—22no—
62C2×Dic86—44no—
63M16×C43—44no—
64C2×C8×C43—22no—
65C2×C8×C43—24no—
66C2×C8×C43—42no—
67C22⋊Dic43—42no—
68C22⋊Dic43—42no—
69C22⋊Dic43—42no—
70C4⋊Dic43—22no—
71C4⋊Dic43—22no—
72C4⋊Dic43—22no—
73C4⋊Dic43—22no—
74Dic43⋊C4—42no—
75Dic43⋊C4—42no—
76C4×Dic43—41no—
77C4×Dic43—41no—
78C2×C43⋊C8—42no—
79C2×C43⋊C8—41no—
80Dic172—82no—
81C23×C43—22no—
82C23×C43—41no—
83C23×C43—41no—
84C23×C43#12112yes—
85C23×C43#12111yescharacteristic
86C2×C4×C43—22no—
87C2×C4×C43—24no—
88C2×C4×C43—42no—
89C2×C4×C43—41no—
90C2×C4×C43#12012yes—
91C2×C4×C43#12011yescharacteristic
92C2×C4×C43#12711yescharacteristic
93C2×Dic43—42no—
94C2×Dic43—44no—
95C2×Dic43—41no—
96C2×Dic43—41no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—82no—
101Dic86—44no—
102Dic86—44no—
103C8×C43—44no—
104C8×C43—42no—
105C43⋊C8—81no—
106#9979—431nomaximal, Sylow
107C22×C43—21no—
108C22×C43—21no—
109C22×C43—22no—
110C22×C43—22no—
111C22×C43—22no—
112C22×C43—82no—
113C22×C43#39211yescharacteristic
114C22×C43#47312yes—
115C4×C43—21no—
116C4×C43—22no—
117C4×C43#45812yes—
118Dic43—81no—
119Dic43—82no—
120Dic43—81no—
121Dic43—82no—
122#3189—431no—
123#3095—432no—
124#1818—431no—
125#1472—432no—
126#1293D4311yescharacteristic
127C2×C43—22no—
128C2×C43—42no—
129C2×C43#201711yescharacteristic
130C2×C43#202011yescharacteristic
131C2×C43#202211yescharacteristic
132C2×C22⋊Q8—432no—
133C2×#117—431no—
134#485—864no—
135#484—862no—
136#484—862no—
137#483—862no—
138#467—862no—
139#451—862no—
140#428—862no—
141#419—862no—
142#407C2×D4312yes—
143C2×C22⋊C8—431no—
144C2×C22⋊C8C2×D4311yescharacteristic
145#336—862no—
146#324—864no—
147C43#997911yescharacteristic, complemented, Sylow
148C22×Q8—432no—
149C23×C4C22×D4311yescharacteristic
150C2×Q16—862no—
151C2×M16—22no—
152C22×C8—861no—
153C22×C8D17212yes—
154C22⋊Q8—862no—
155C22⋊Q8—862no—
156C22⋊Q8—862no—
157C22⋊Q8—862no—
158#117—862no—
159#117—862no—
160C2×C4⋊C4—431no—
161C2×C4⋊C4—431no—
162C2×C4⋊C4—432no—
163C2×C4⋊C4—862no—
164C2×C22⋊C4—861no—
165C2×C22⋊C4—862no—
166C2×C42—861no—
167#107—864no—
168#107—862no—
169#106—864no—
170#103—864no—
171#103—864no—
172#103—864no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—862no—
176C22⋊C8D17214yes—
177C24#1062190211yescharacteristic
178C2×Q8—862no—
179C2×Q8—862no—
180C2×Q8—1724no—
181C22×C4—42no—
182C22×C4—862no—
183C22×C4—861no—
184C22×C4—861no—
185C22×C4—862no—
186C22×C4C2×D17211yescharacteristic
187C22×C4C2×D17212yes—
188C22×C4D4×D4312yes—
189C22×C4D4×D4311yescharacteristic
190Q16—3442no—
191M16—44no—
192C2×C8—22no—
193C2×C8—24no—
194C2×C8—42no—
195C2×C8—1722no—
196C2×C8—1721no—
197C4⋊C4—862no—
198C4⋊C4—862no—
199C4⋊C4—862no—
200C4⋊C4—862no—
201C4⋊C4—1722no—
202C4⋊C4—1722no—
203C22⋊C4—1722no—
204C22⋊C4—1722no—
205C22⋊C4—1722no—
206C42—1721no—
207C42—1721no—
208C23—22no—
209C23—41no—
210C23—41no—
211C23#1306330012yes—
212C23#1306330011yescharacteristic
213Q8—1724no—
214Q8—1724no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—3442no—
220C2×C4—1722no—
221C2×C4—1724no—
222C2×C4—1721no—
223C2×C4—1721no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4#1306329512yes—
228C2×C4#1306329511yescharacteristic
229C2×C4#1306332211yescharacteristic
230C8—44no—
231C8—42no—
232C8—3441no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22#1458280911yescharacteristic
240C22#1458317512yes—
241C4—22no—
242C4—21no—
243C4—3441no—
244C4—3442no—
245C4—3441no—
246C4—3442no—
247C4#1458309012yes—
248C2—22no—
249C2—42no—
250C2#1913570011yescharacteristic
251C2#1913571711yescharacteristic
252C2#1913572711yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1293C2
socleC22×C43#392
prime radicalC24×C43#41
hypercenter#1293D43
hypocenterC43#9979
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
147. C43#9979semidirect

Maximal subgroups

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

subgroupindex
#191453702
#191445442
#191346642
#191329602
C43×#12932
#997943