Finite Group Databasebeta

← #24999845

Subgroups — #24999845

Order 11008.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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#19140265C211yesmaximal, characteristic
2#19134692C212yesmaximal
3#19134670C211yesmaximal, characteristic
4#19132449C212yesmaximal
5C43×#1306C211yesmaximal, characteristic
6C2×#13063284C2211yescharacteristic
7#14582822—22no—
8#14582796—22no—
9#14582782—22no—
10#14582762C2211yescharacteristic
11C4×C22⋊Dic43C2212yes—
12#14582665—22no—
13#14582660—22no—
14#14582660—22no—
15C43×#407C2212yes—
16C43×#381C2211yescharacteristic
17#13063284—22no—
18#13063284—22no—
19C2×C4⋊Dic43—22no—
20C2×C4⋊Dic43Q812yes—
21C2×Dic43⋊C4—22no—
22C2×Dic43⋊C4—22no—
23C2×C22⋊Dic43—22no—
24C2×C22⋊Dic43—21no—
25C2×C22⋊Dic43—21no—
26C2×C4×Dic43—21no—
27C2×C4×Dic43D412yes—
28C2×C4×Dic43D412yes—
29C43⋊#95—22no—
30C43⋊#95—22no—
31C43⋊#95—22no—
32C23×C4×C43C2311yescharacteristic
33C2×M16×C43—22no—
34C2×C22⋊C4×C43D412yes—
35C22⋊C8×C43—22no—
36C22⋊C8×C43—22no—
37#95×C43—22no—
38C24×C43C2×D411yescharacteristic
39C22×C4×C43—22no—
40C22×C4×C43—42no—
41C22×C4×C43C2×D412yes—
42C22×C4×C43C2×Q811yescharacteristic
43C22×C4×C43#4111yescharacteristic
44C22×C4×C43#4112yes—
45C22×Dic43—22no—
46C22×Dic43—22no—
47C22×Dic43—22no—
48C22×Dic43—41no—
49M16×C43—42no—
50M16×C43—42no—
51C2×C8×C43—42no—
52C22⋊C4×C43—42no—
53C22⋊Dic43—42no—
54C22⋊Dic43—44no—
55C22⋊Dic43—41no—
56C22⋊Dic43—41no—
57C4⋊Dic43—24no—
58C4⋊Dic43—44no—
59Dic43⋊C4—44no—
60Dic43⋊C4—82no—
61C4×Dic43—42no—
62C4×Dic43—42no—
63C4×Dic43—42no—
64C23×C43—22no—
65C23×C43—42no—
66C23×C43#12011yescharacteristic
67C23×C43C22⋊Q811yescharacteristic
68C23×C43#12411yescharacteristic
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—41no—
72C2×C4×C43—42no—
73C2×C4×C43—41no—
74C2×C4×C43—42no—
75C2×C4×C43—42no—
76C2×C4×C43—42no—
77C2×C4×C43C22⋊Q812yes—
78C2×C4×C43#12412yes—
79C2×Dic43—24no—
80C2×Dic43—42no—
81C2×Dic43—42no—
82C2×Dic43—42no—
83C2×Dic43—42no—
84C2×Dic43—42no—
85C2×Dic43—42no—
86C2×Dic43—82no—
87C2×Dic43—81no—
88C2×Dic43—82no—
89C8×C43—82no—
90#10389—431nomaximal, Sylow
91C22×C43—22no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—22no—
95C22×C43—22no—
96C22×C43—82no—
97C22×C43#39311yescharacteristic
98C22×C43#45812yes—
99C4×C43—22no—
100C4×C43—22no—
101C4×C43—82no—
102Dic43—44no—
103Dic43—82no—
104Dic43—82no—
105Dic43—161no—
106#2608—431no—
107#1826—432no—
108#1820—431no—
109#1306D4311yescharacteristic
110#1284—432no—
111C2×C43—22no—
112C2×C43—41no—
113C2×C43—41no—
114C2×C43#203011yescharacteristic
115C2×C43#203112yes—
116C2×#117—431no—
117#407C2×D4312yes—
118#396—862no—
119#389—862no—
120#387—862no—
121#381—431no—
122#381C2×D4311yescharacteristic
123C4×C22⋊C4—432no—
124#342—862no—
125#339—862no—
126#339—862no—
127C43#1038911yescharacteristic, complemented, Sylow
128C23×C4C22×D4311yescharacteristic
129C2×M16—22no—
130#117—862no—
131#117—862no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—862no—
134C2×C4⋊C4—862no—
135C2×C4⋊C4—862no—
136C2×C22⋊C4—861no—
137C2×C22⋊C4—862no—
138C2×C22⋊C4—861no—
139C2×C22⋊C4D17212yes—
140C2×C42—432no—
141C2×C42—432no—
142C2×C42—861no—
143C22⋊C8—22no—
144C22⋊C8—22no—
145#95—22no—
146#95—862no—
147#95—862no—
148#95—862no—
149C24C2×D17211yescharacteristic
150C22×C4—22no—
151C22×C4—42no—
152C22×C4—862no—
153C22×C4—862no—
154C22×C4—862no—
155C22×C4—1721no—
156C22×C4#1062189812yes—
157C22×C4D4×D4312yes—
158C22×C4#1062190011yescharacteristic
159C22×C4Q8×D4311yescharacteristic
160M16—42no—
161M16—42no—
162C2×C8—42no—
163C4⋊C4—864no—
164C4⋊C4—3442no—
165C4⋊C4—1724no—
166C4⋊C4—1724no—
167C22⋊C4—42no—
168C22⋊C4—1724no—
169C22⋊C4—1722no—
170C22⋊C4—1721no—
171C22⋊C4—1721no—
172C42—1722no—
173C42—1722no—
174C42—1722no—
175C23—22no—
176C23—42no—
177C23#1306329511yescharacteristic
178C23#1306330511yescharacteristic
179C23#1306331311yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—864no—
189C2×C4—3442no—
190C2×C4—3441no—
191C2×C4—3442no—
192C2×C4—1722no—
193C2×C4—1722no—
194C2×C4—1722no—
195C2×C4—1722no—
196C2×C4—1722no—
197C2×C4—1722no—
198C2×C4#1306330312yes—
199C2×C4#1306331112yes—
200C8—82no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1458281211yescharacteristic
208C22#1458309012yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—3442no—
213C4—3442no—
214C4—1724no—
215C4—6881no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#1913576311yescharacteristic
220C2#1913577012yes—
subgroupG/H
centerC22#14582812
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1306C2
socleC22×C43#393
prime radicalC24×C43C2×D4
hypercenter#1306D43
hypocenterC43#10389
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
127. C43#10389semidirect

Maximal subgroups

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

subgroupindex
#191402652
#191346922
#191346702
#191324492
C43×#13062
#1038943