Finite Group Databasebeta

← #24998829

Subgroups — #24998829

Order 11008.

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

normal subgroups only

This group has 430 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#19145989C211yesmaximal, characteristic
2#19145811C212yesmaximal
3#19135575C211yesmaximal, characteristic
4#19133108C212yesmaximal
5C43×#1307C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583456C2211yescharacteristic
8#14583308—22no—
9#14583268—22no—
10#14583241—24no—
11#14583195—22no—
12#14583185—22no—
13#14583185—22no—
14#14583157—22no—
15#14583110—22no—
16#14582745C2211yescharacteristic
17#14582660—22no—
18#14582637—24no—
19C43×#432C2212yes—
20C43×#423C2211yescharacteristic
21C2×Dic172—22no—
22#13063325D412yes—
23#13063325D412yes—
24#13063325D412yes—
25#13063317—22no—
26#13063317—21no—
27#13063304—22no—
28#13063304—22no—
29#13063304—22no—
30C4×Dic86—22no—
31C4×Dic86—22no—
32C4×Dic86—22no—
33#13063284—21no—
34#13063284—22no—
35C2×C4×Dic43—21no—
36#13063259—24no—
37#13063257—24no—
38#13063257—22no—
39#13063250—24no—
40#13063250—24no—
41#13063250—24no—
42C43⋊#95—22no—
43C2×M16×C43D412yes—
44C2×C42×C43C2311yescharacteristic
45C4⋊C8×C43—22no—
46C4⋊C8×C43—22no—
47C22⋊C8×C43D414yes—
48#97×C43—22no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43C2×D412yes—
51C22×Dic43—41no—
52C2×Dic86—22no—
53C2×Dic86—22no—
54C2×Dic86—22no—
55M16×C43—42no—
56C2×C8×C43—24no—
57C2×C8×C43—22no—
58C42×C43C2×D411yescharacteristic
59C42×C43C2×D412yes—
60C42×C43#4111yescharacteristic
61C22⋊Dic43—41no—
62C22⋊Dic43—42no—
63C4⋊Dic43—22no—
64C4⋊Dic43—22no—
65C4⋊Dic43—22no—
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69Dic43⋊C4—42no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72C4×Dic43—22no—
73C4×Dic43—41no—
74C4×Dic43—41no—
75C4×Dic43—42no—
76Dic172—82no—
77C23×C43#12711yescharacteristic
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—42no—
81C2×C4×C43#12012yes—
82C2×C4×C43#12011yescharacteristic
83C2×C4×C43#12112yes—
84C2×C4×C43#12111yescharacteristic
85C2×Dic43—42no—
86C2×Dic43—42no—
87C2×Dic43—42no—
88C2×Dic43—42no—
89C2×Dic43—82no—
90Dic86—44no—
91Dic86—42no—
92Dic86—42no—
93Dic86—82no—
94C8×C43—44no—
95C8×C43—42no—
96#10217—431nomaximal, Sylow
97C22×C43—21no—
98C22×C43—22no—
99C22×C43#39211yescharacteristic
100C4×C43—21no—
101C4×C43—22no—
102C4×C43—22no—
103C4×C43#45511yescharacteristic
104C4×C43#45611yescharacteristic
105Dic43—82no—
106Dic43—82no—
107Dic43—82no—
108Dic43—82no—
109#3255—431no—
110#3237—432no—
111#1995—431no—
112#1506—432no—
113#1307D4311yescharacteristic
114C2×C43—41no—
115C2×C43#200711yescharacteristic
116C2×C43#200912yes—
117#533—431no—
118#533—432no—
119#501—862no—
120#491—862no—
121#485—864no—
122#477—862no—
123#475—862no—
124#475—862no—
125#470—862no—
126#462—862no—
127#432C2×D4312yes—
128#423C2×D4311yescharacteristic
129#376—431no—
130#339—862no—
131#328—864no—
132C43#1021711yescharacteristic, complemented, Sylow
133C2×Q16—862no—
134C2×M16D17212yes—
135C4⋊Q8—432no—
136C4⋊Q8—432no—
137C4⋊Q8—432no—
138#125—862no—
139#125—861no—
140C22⋊Q8—862no—
141C22⋊Q8—862no—
142C22⋊Q8—862no—
143C4×Q8—862no—
144C4×Q8—862no—
145C4×Q8—862no—
146#117—861no—
147#117—862no—
148C2×C42—861no—
149C2×C42C22×D4311yescharacteristic
150#107—864no—
151#106—862no—
152#106—864no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155#103—864no—
156#103—864no—
157#103—864no—
158C22⋊C8D17214yes—
159#97—22no—
160#95—862no—
161C2×Q8—862no—
162C2×Q8—862no—
163C2×Q8—862no—
164C22×C4—1721no—
165C22×C4C2×D17211yescharacteristic
166C22×C4C2×D17212yes—
167Q16—3442no—
168M16—42no—
169C2×C8—24no—
170C2×C8—22no—
171C4⋊C4—862no—
172C4⋊C4—862no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4—862no—
176C4⋊C4—862no—
177C4⋊C4—1722no—
178C4⋊C4—1722no—
179C4⋊C4—1722no—
180C22⋊C4—1721no—
181C22⋊C4—1722no—
182C42—862no—
183C42—1721no—
184C42—1721no—
185C42—1722no—
186C42D4×D4311yescharacteristic
187C42D4×D4312yes—
188C42#1062190211yescharacteristic
189C23#1306332211yescharacteristic
190Q8—3442no—
191Q8—1724no—
192Q8—1722no—
193Q8—1722no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—3442no—
198C2×C4—1722no—
199C2×C4—1722no—
200C2×C4—1722no—
201C2×C4—1722no—
202C2×C4#1306329512yes—
203C2×C4#1306329511yescharacteristic
204C2×C4#1306330012yes—
205C2×C4#1306330011yescharacteristic
206C8—44no—
207C8—42no—
208C22—21no—
209C22—22no—
210C22#1458280911yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—3442no—
215C4—3442no—
216C4—3442no—
217C4—3442no—
218C4#1458307911yescharacteristic
219C4#1458308411yescharacteristic
220C2—41no—
221C2#1913564411yescharacteristic
222C2#1913565812yes—
subgroupG/H
centerC22#14582809
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1307C2
socleC22×C43#392
prime radicalC23×C43#127
hypercenter#1307D43
hypocenterC43#10217
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
132. C43#10217semidirect

Maximal subgroups

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

subgroupindex
#191459892
#191458112
#191355752
#191331082
C43×#13072
#1021743