Finite Group Databasebeta

← #24999740

Subgroups — #24999740

Order 11008.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#19137900C211yesmaximal, characteristic
2#19133094C212yesmaximal
3#19132496C212yesmaximal
4#19132424C211yesmaximal, characteristic
5C43×#1995C211yesmaximal, characteristic
6#14582952C2212yes—
7#14582841—22no—
8#14582833—22no—
9C4×Dic43⋊C4—22no—
10C4×C4⋊Dic43C2212yes—
11#14582636—22no—
12#14582636—22no—
13C43×#533C2211yescharacteristic
14C43×#423C2211yescharacteristic
15C43×#376C2211yescharacteristic
16C43×#339—22no—
17C2×C4⋊Dic43—22no—
18C2×Dic43⋊C4—22no—
19C2×Dic43⋊C4—22no—
20C2×C4×Dic43—22no—
21C4⋊(C43⋊C8)—22no—
22C22⋊(C43⋊C8)—22no—
23C4×C43⋊C8—22no—
24C43⋊#95—22no—
25C43⋊#95—22no—
26C43⋊#95D412yes—
27C43⋊#95D412yes—
28C2×M16×C43—21no—
29C4⋊Q8×C43Q812yes—
30#125×C43—21no—
31C22⋊Q8×C43—22no—
32C4×Q8×C43—22no—
33#117×C43—21no—
34C2×C42×C43D412yes—
35C2×C42×C43C2311yescharacteristic
36C4⋊C8×C43—22no—
37#95×C43—22no—
38C2×Q8×C43—22no—
39C22×C4×C43—22no—
40C22×C4×C43C2×D412yes—
41C22×C4×C43C2×D411yescharacteristic
42C22×Dic43—22no—
43C22×Dic43—22no—
44M16×C43—42no—
45C2×C8×C43—41no—
46C4⋊C4×C43—22no—
47C4⋊C4×C43—22no—
48C4⋊C4×C43—42no—
49C22⋊C4×C43—41no—
50C42×C43—22no—
51C42×C43—22no—
52C42×C43—41no—
53C42×C43C2×Q811yescharacteristic
54C42×C43#4111yescharacteristic
55C42×C43#4112yes—
56C4⋊Dic43—44no—
57Dic43⋊C4—44no—
58Dic43⋊C4—44no—
59C4×Dic43—42no—
60C4×Dic43—42no—
61C2×C43⋊C8—42no—
62C23×C43#12011yescharacteristic
63Q8×C43—82no—
64C2×C4×C43—42no—
65C2×C4×C43—42no—
66C2×C4×C43—42no—
67C2×C4×C43—42no—
68C2×C4×C43—42no—
69C2×C4×C43C22⋊Q812yes—
70C2×C4×C43C22⋊Q811yescharacteristic
71C2×C4×C43#12412yes—
72C2×C4×C43#12411yescharacteristic
73C2×C4×C43#13512yes—
74C2×C4×C43#13712yes—
75C2×Dic43—24no—
76C2×Dic43—42no—
77C2×Dic43—42no—
78C2×Dic43—42no—
79C2×Dic43—42no—
80C2×Dic43—42no—
81C8×C43—81no—
82C43⋊C8—82no—
83#10373—431nomaximal, Sylow
84C22×C43—22no—
85C22×C43#39311yescharacteristic
86C22×C43#45212yes—
87C4×C43—22no—
88C4×C43—22no—
89C4×C43—82no—
90C4×C43—82no—
91C4×C43#47912yes—
92C4×C43#48811yescharacteristic
93C4×C43#49111yescharacteristic
94Dic43—44no—
95Dic43—82no—
96#2402—431no—
97#1995D4311yescharacteristic
98#1503—432no—
99#1303—432no—
100#1274—431no—
101C2×C43—22no—
102C2×C43#202611yescharacteristic
103C2×C43#203112yes—
104#533C2×D4311yescharacteristic
105#431—432no—
106#423C2×D4311yescharacteristic
107#400—862no—
108#398—862no—
109C4×C4⋊C4—432no—
110C4×C4⋊C4—862no—
111#376C2×D4311yescharacteristic
112#339—22no—
113#328—862no—
114#328—862no—
115C43#1037311yescharacteristic, complemented, Sylow
116C2×M16—21no—
117C4⋊Q8Dic8612yes—
118#125—21no—
119C22⋊Q8—22no—
120C4×Q8—22no—
121#117—21no—
122C2×C4⋊C4—862no—
123C2×C4⋊C4—862no—
124C2×C4⋊C4—862no—
125C2×C42—862no—
126C2×C42C22⋊D4312yes—
127C2×C42C22×D4311yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—862no—
130C22⋊C8—862no—
131C4×C8—862no—
132#95—22no—
133#95—432no—
134#95—432no—
135#95—862no—
136#95—862no—
137C2×Q8—22no—
138C22×C4—22no—
139C22×C4—862no—
140C22×C4—862no—
141C22×C4D4×D4312yes—
142C22×C4C2×C22⋊D4311yescharacteristic
143M16—42no—
144C2×C8—41no—
145C2×C8—1722no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—42no—
149C4⋊C4—1724no—
150C4⋊C4—1724no—
151C4⋊C4—1724no—
152C22⋊C4—41no—
153C42—22no—
154C42—22no—
155C42—41no—
156C42—1722no—
157C42—1722no—
158C42C2×Dic8611yescharacteristic
159C42#1062189811yescharacteristic
160C42#1062190012yes—
161C23#1306329311yescharacteristic
162Q8—82no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—864no—
169C2×C4—1722no—
170C2×C4—1722no—
171C2×C4—1722no—
172C2×C4—1722no—
173C2×C4—1722no—
174C2×C4#1306330212yes—
175C2×C4#1306330411yescharacteristic
176C2×C4#1306331112yes—
177C2×C4#1306331211yescharacteristic
178C2×C4#1306334512yes—
179C2×C4#1306335612yes—
180C8—81no—
181C8—3442no—
182C22—22no—
183C22#1458281111yescharacteristic
184C22#1458305912yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—82no—
189C4—3442no—
190C4—1724no—
191C4#1458320612yes—
192C4#1458325311yescharacteristic
193C4#1458326711yescharacteristic
194C2—22no—
195C2#1913574611yescharacteristic
196C2#1913576512yes—
subgroupG/H
centerC2×C4#13063312
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1995C2
socleC22×C43#393
prime radicalC23×C43#120
hypercenter#1995D43
hypocenterC43#10373
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
115. C43#10373semidirect

Maximal subgroups

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

subgroupindex
#191379002
#191330942
#191324962
#191324242
C43×#19952
#1037343