Finite Group Databasebeta

← #24998826

Subgroups — #24998826

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#19145809C212yesmaximal
2#19135575C211yesmaximal, characteristic
3#19133107C212yesmaximal
4#19132506C211yesmaximal, characteristic
5C43×#3255C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583309—22no—
8#14583269—22no—
9#14583240—24no—
10#14583191—22no—
11#14583181—22no—
12#14582956C2212yes—
13#14582745C2211yescharacteristic
14#14582660—22no—
15#14582636—24no—
16C43×#533C2212yes—
17C43×#475—22no—
18C43×#470—22no—
19C43×#462—22no—
20C43×#423C2211yescharacteristic
21#13063325D412yes—
22#13063317—21no—
23#13063304—22no—
24C4×Dic86—22no—
25#13063284—21no—
26C2×C4×Dic43—21no—
27#13063258—24no—
28#13063256—24no—
29C4⋊(C43⋊C8)—22no—
30#13063248—24no—
31#13063248—24no—
32C22⋊(C43⋊C8)D414yes—
33#13063236—22no—
34C43⋊#95—22no—
35C2×Q16×C43—22no—
36C2×M16×C43D412yes—
37C4⋊Q8×C43D412yes—
38C4⋊Q8×C43D412yes—
39#125×C43—22no—
40C22⋊Q8×C43—22no—
41C22⋊Q8×C43—22no—
42C4×Q8×C43—22no—
43C4×Q8×C43—22no—
44#117×C43—22no—
45C2×C42×C43C2311yescharacteristic
46#106×C43—22no—
47C4⋊C8×C43—22no—
48#103×C43—24no—
49C2×Q8×C43—22no—
50C2×Q8×C43—22no—
51C22×C4×C43C2×D412yes—
52C22×C4×C43C2×D411yescharacteristic
53C22×Dic43—41no—
54C2×Dic86—22no—
55Q16×C43—82no—
56M16×C43—42no—
57C2×C8×C43—22no—
58C4⋊C4×C43—22no—
59C4⋊C4×C43—22no—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—22no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43—42no—
64C22⋊C4×C43—42no—
65C42×C43—42no—
66C42×C43C2×D411yescharacteristic
67C42×C43C2×D412yes—
68C42×C43#4111yescharacteristic
69C22⋊Dic43—41no—
70C4⋊Dic43—22no—
71C4⋊Dic43—22no—
72Dic43⋊C4—42no—
73C4×Dic43—22no—
74C4×Dic43—41no—
75C4×Dic43—41no—
76C2×C43⋊C8—24no—
77C23×C43#12711yescharacteristic
78Q8×C43—42no—
79Q8×C43—42no—
80Q8×C43—82no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43#12012yes—
87C2×C4×C43#12011yescharacteristic
88C2×C4×C43#12111yescharacteristic
89C2×C4×C43#12112yes—
90C2×Dic43—42no—
91C2×Dic43—42no—
92C2×Dic43—82no—
93Dic86—44no—
94C8×C43—42no—
95C43⋊C8—44no—
96#10217—431nomaximal, Sylow
97C22×C43—21no—
98C22×C43—22no—
99C22×C43#39211yescharacteristic
100C4×C43—21no—
101C4×C43—22no—
102C4×C43—22no—
103C4×C43—82no—
104C4×C43—82no—
105C4×C43#45511yescharacteristic
106C4×C43#45611yescharacteristic
107Dic43—82no—
108Dic43—82no—
109#3255D4311yescharacteristic
110#3237—432no—
111#1995—431no—
112#1506—432no—
113#1307—431no—
114C2×C43—41no—
115C2×C43#200711yescharacteristic
116C2×C43#200912yes—
117#533—431no—
118#533C2×D4312yes—
119#501—862no—
120#491—862no—
121#485—864no—
122#477—862no—
123#475—22no—
124#475—862no—
125#470—22no—
126#462—22no—
127#432—432no—
128#423C2×D4311yescharacteristic
129#376—431no—
130#339—862no—
131#328—864no—
132C43#1021711yescharacteristic, complemented, Sylow
133C2×Q16—22no—
134C2×M16C22⋊D4312yes—
135C4⋊Q8—432no—
136C4⋊Q8C22⋊D4312yes—
137C4⋊Q8C22⋊D4312yes—
138#125—22no—
139#125—861no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—862no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—862no—
146#117—22no—
147#117—861no—
148C2×C42—861no—
149C2×C42C22×D4311yescharacteristic
150#107—864no—
151#106—22no—
152#106—864no—
153C4⋊C8—22no—
154C4⋊C8—862no—
155#103—24no—
156#103—864no—
157#103—864no—
158C22⋊C8—434no—
159#97—862no—
160#95—862no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×Q8—862no—
164C22×C4—1721no—
165C22×C4D4×D4312yes—
166C22×C4C2×C22⋊D4311yescharacteristic
167Q16—82no—
168M16—42no—
169C2×C8—22no—
170C2×C8—864no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—862no—
178C4⋊C4—862no—
179C4⋊C4—1722no—
180C22⋊C4—42no—
181C22⋊C4—1721no—
182C42—42no—
183C42—862no—
184C42—1721no—
185C42—1721no—
186C42D4×D4311yescharacteristic
187C42#1062190011yescharacteristic
188C42C2×C22⋊D4312yes—
189C23#1306332111yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—82no—
193Q8—1724no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—3442no—
200C2×C4—1722no—
201C2×C4—1722no—
202C2×C4#1306329312yes—
203C2×C4#1306329411yescharacteristic
204C2×C4#1306329611yescharacteristic
205C2×C4#1306329712yes—
206C8—42no—
207C8—1724no—
208C22—21no—
209C22—22no—
210C22#1458280711yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—82no—
216C4—3442no—
217C4—3442no—
218C4#1458307711yescharacteristic
219C4#1458308211yescharacteristic
220C2—41no—
221C2#1913564211yescharacteristic
222C2#1913565312yes—
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3255C2
socleC22×C43#392
prime radicalC23×C43#127
hypercenter#3255D43
hypocenterC43#10217
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

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
#191458092
#191355752
#191331072
#191325062
C43×#32552
#1021743