Finite Group Databasebeta

← #24997559

Subgroups — #24997559

Order 11008.

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

normal subgroups only

This group has 468 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#19145940C211yesmaximal, characteristic
2#19144726C212yesmaximal
3#19135534C211yesmaximal, characteristic
4#19133211C212yesmaximal
5C43×#1290C211yesmaximal, characteristic
6#14583456C2212yes—
7C2×C4×Dic86C2211yescharacteristic
8#14583230—22no—
9#14583195—22no—
10#14583185—22no—
11#14583140—22no—
12#14583110—22no—
13#14583110—22no—
14#14583057—22no—
15#14583007—24no—
16C2×#13063236C2211yescharacteristic
17#14582653—22no—
18#14582640—24no—
19C43×#432C2212yes—
20C2×C4⋊C8×C43C2211yescharacteristic
21C22×Dic86D411yescharacteristic
22C2×Dic172—24no—
23C2×Dic172—22no—
24C22×C43⋊C8—21no—
25#13063325D412yes—
26#13063325D412yes—
27#13063317—22no—
28#13063304—22no—
29#13063304—22no—
30C4×Dic86—22no—
31C4×Dic86—22no—
32C4×Dic86—22no—
33C4×Dic86—22no—
34#13063284—22no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×C4×Dic43—21no—
38#13063259—22no—
39#13063257—24no—
40#13063250—24no—
41#13063250—24no—
42#13063250—24no—
43#13063236—22no—
44C22×C8×C43D412yes—
45C2×C42×C43C2311yescharacteristic
46C4⋊C8×C43—22no—
47C4⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49#97×C43D414yes—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43#4111yescharacteristic
53C22×Dic43—21no—
54C22×Dic43—21no—
55C2×Dic86—22no—
56C2×Dic86—22no—
57C2×Dic86—22no—
58C2×Dic86—42no—
59C2×C8×C43—24no—
60C2×C8×C43—22no—
61C2×C8×C43—42no—
62C42×C43C2×D412yes—
63C42×C43C2×D412yes—
64C22⋊Dic43—42no—
65C4⋊Dic43—22no—
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69C4⋊Dic43—22no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72Dic43⋊C4—42no—
73C4×Dic43—41no—
74C4×Dic43—42no—
75C4×Dic43—41no—
76C2×C43⋊C8—22no—
77C2×C43⋊C8—41no—
78C2×C43⋊C8—41no—
79Dic172—48no—
80Dic172—82no—
81C23×C43#12111yescharacteristic
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×C4×C43—21no—
85C2×C4×C43—41no—
86C2×C4×C43#12012yes—
87C2×C4×C43#12011yescharacteristic
88C2×C4×C43#12112yes—
89C2×C4×C43#12711yescharacteristic
90C2×Dic43—22no—
91C2×Dic43—41no—
92C2×Dic43—41no—
93C2×Dic43—41no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97Dic86—24no—
98Dic86—42no—
99Dic86—44no—
100Dic86—42no—
101Dic86—42no—
102C8×C43—44no—
103C8×C43—42no—
104C43⋊C8—42no—
105#10031—431nomaximal, Sylow
106C22×C43—21no—
107C22×C43—21no—
108C22×C43#39211yescharacteristic
109C22×C43#47312yes—
110C4×C43—21no—
111C4×C43—22no—
112C4×C43—22no—
113C4×C43#45511yescharacteristic
114C4×C43#45611yescharacteristic
115Dic43—42no—
116Dic43—82no—
117Dic43—82no—
118Dic43—81no—
119#3249—431no—
120#3113—432no—
121#1985—431no—
122#1531—432no—
123#1290D4311yescharacteristic
124C2×C43—22no—
125C2×C43#200711yescharacteristic
126C2×C43#201011yescharacteristic
127C2×C43#202011yescharacteristic
128#533—432no—
129C2×C4×Q8—431no—
130#483—862no—
131#477—862no—
132#475—862no—
133#467—862no—
134#462—862no—
135#462—862no—
136#451—862no—
137#441—864no—
138#432C2×D4312yes—
139C2×C4⋊C8C2×D4311yescharacteristic
140C2×#97—431no—
141#336—862no—
142#330—864no—
143C43#1003111yescharacteristic, complemented, Sylow
144C22×Q8—431no—
145C2×Q16—862no—
146C2×Q16—864no—
147C22×C8—861no—
148C22×C8D17212yes—
149C4⋊Q8—432no—
150C4⋊Q8—432no—
151#125—862no—
152C22⋊Q8—862no—
153C22⋊Q8—862no—
154C4×Q8—862no—
155C4×Q8—862no—
156C4×Q8—862no—
157C4×Q8—862no—
158#117—862no—
159C2×C4⋊C4—431no—
160C2×C4⋊C4—861no—
161C2×C42—861no—
162C2×C42C22×D4311yescharacteristic
163#107—862no—
164#106—864no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167#103—864no—
168#103—864no—
169#103—864no—
170C22⋊C8—22no—
171#97—862no—
172#97D17214yes—
173C2×Q8—862no—
174C2×Q8—862no—
175C2×Q8—862no—
176C2×Q8—1722no—
177C22×C4—861no—
178C22×C4—861no—
179C22×C4C2×D17211yescharacteristic
180C22×C4D4×D4311yescharacteristic
181C22×C4#1062190211yescharacteristic
182Q16—3442no—
183Q16—1728no—
184C2×C8—24no—
185C2×C8—22no—
186C2×C8—42no—
187C2×C8—862no—
188C2×C8—1721no—
189C2×C8—1721no—
190C4⋊C4—862no—
191C4⋊C4—862no—
192C4⋊C4—862no—
193C4⋊C4—862no—
194C4⋊C4—862no—
195C4⋊C4—1722no—
196C4⋊C4—1722no—
197C4⋊C4—1722no—
198C22⋊C4—1722no—
199C42—1721no—
200C42—1722no—
201C42—1721no—
202C42C2×D17212yes—
203C42D4×D4312yes—
204C23#1306330011yescharacteristic
205Q8—864no—
206Q8—1724no—
207Q8—1722no—
208Q8—1722no—
209Q8—1722no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—862no—
215C2×C4—1721no—
216C2×C4—1722no—
217C2×C4—1722no—
218C2×C4—1722no—
219C2×C4—1721no—
220C2×C4—1721no—
221C2×C4#1306329512yes—
222C2×C4#1306329511yescharacteristic
223C2×C4#1306330012yes—
224C2×C4#1306332211yescharacteristic
225C8—44no—
226C8—42no—
227C8—1722no—
228C22—21no—
229C22—21no—
230C22#1458280911yescharacteristic
231C22#1458317512yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—3442no—
236C4—3442no—
237C4—3441no—
238C4—1722no—
239C4#1458307911yescharacteristic
240C4#1458308411yescharacteristic
241C2—22no—
242C2#1913564411yescharacteristic
243C2#1913566311yescharacteristic
244C2#1913571711yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1290C2
socleC22×C43#392
prime radicalC23×C43#121
hypercenter#1290D43
hypocenterC43#10031
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
143. C43#10031semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191447262
#191355342
#191332112
C43×#12902
#1003143