Finite Group Databasebeta

← #24999741

Subgroups — #24999741

Order 11008.

364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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#19135576C211yesmaximal, characteristic
3#19133095C212yesmaximal
4#19132497C212yesmaximal
5C43×#1274C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14582923C2211yescharacteristic
8#14582841—22no—
9#14582833—22no—
10C4×Dic43⋊C4—22no—
11C4×C4⋊Dic43C2212yes—
12#14582659—22no—
13#14582637—22no—
14#14582637—22no—
15C43×#431C2212yes—
16C43×#376C2211yescharacteristic
17C2×#10621877—21no—
18#13063325Q812yes—
19#13063317—21no—
20#13063304—22no—
21C4×Dic86—22no—
22#13063284—21no—
23C2×C4⋊Dic43—22no—
24C2×Dic43⋊C4—22no—
25C2×Dic43⋊C4—22no—
26C2×C4×Dic43—22no—
27C4⋊(C43⋊C8)—22no—
28C43⋊#95—22no—
29C43⋊#95—22no—
30C43⋊#95D412yes—
31C43⋊#95D412yes—
32C2×C42×C43D412yes—
33C2×C42×C43C2311yescharacteristic
34C4⋊C8×C43—22no—
35C22⋊C8×C43—22no—
36C4×C8×C43—22no—
37#95×C43—22no—
38C22×C4×C43—22no—
39C22×C4×C43C2×D411yescharacteristic
40C22×C4×C43C2×D412yes—
41C22×Dic43—22no—
42C22×Dic43—22no—
43C2×Dic86—22no—
44C2×C8×C43—42no—
45C42×C43—22no—
46C42×C43—22no—
47C42×C43C2×Q811yescharacteristic
48C42×C43#4112yes—
49C42×C43#4111yescharacteristic
50C22⋊Dic43—41no—
51C4⋊Dic43—22no—
52C4⋊Dic43—22no—
53C4⋊Dic43—44no—
54Dic43⋊C4—44no—
55Dic43⋊C4—44no—
56Dic43⋊C4—42no—
57C4×Dic43—41no—
58C4×Dic43—42no—
59C4×Dic43—42no—
60#10621877—42no—
61C2×C43⋊C8—41no—
62C23×C43#12011yescharacteristic
63C2×C4×C43—42no—
64C2×C4×C43—42no—
65C2×C4×C43—42no—
66C2×C4×C43—42no—
67C2×C4×C43C22⋊Q812yes—
68C2×C4×C43C22⋊Q811yescharacteristic
69C2×C4×C43#12412yes—
70C2×C4×C43#12411yescharacteristic
71C2×C4×C43#13512yes—
72C2×C4×C43#13712yes—
73C2×Dic43—24no—
74C2×Dic43—42no—
75C2×Dic43—42no—
76C2×Dic43—42no—
77C2×Dic43—42no—
78C2×Dic43—42no—
79C2×Dic43—42no—
80Dic86—82no—
81C8×C43—82no—
82C43⋊C8—81no—
83#10373—431nomaximal, Sylow
84C22×C43—22no—
85C22×C43#39311yescharacteristic
86C22×C43#45212yes—
87C4×C43—22no—
88C4×C43—22no—
89C4×C43—82no—
90C4×C43#47912yes—
91C4×C43#48811yescharacteristic
92C4×C43#49111yescharacteristic
93Dic43—44no—
94Dic43—82no—
95Dic43—82no—
96#2402—431no—
97#1995—431no—
98#1503—432no—
99#1303—432no—
100#1274D4311yescharacteristic
101C2×C43—22no—
102C2×C43#202611yescharacteristic
103C2×C43#203112yes—
104#533—431no—
105#431C2×D4312yes—
106#423—431no—
107#400—862no—
108#398—862no—
109C4×C4⋊C4—432no—
110C4×C4⋊C4—862no—
111#376C2×D4311yescharacteristic
112#339—862no—
113#328—862no—
114#328—862no—
115C43#1037311yescharacteristic, complemented, Sylow
116C2×M16—861no—
117C4⋊Q8—432no—
118#125—861no—
119C22⋊Q8—862no—
120C4×Q8—862no—
121#117—861no—
122C2×C4⋊C4—862no—
123C2×C4⋊C4—862no—
124C2×C4⋊C4—862no—
125C2×C42—862no—
126C2×C42D17212yes—
127C2×C42C22×D4311yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—862no—
130C22⋊C8—22no—
131C4×C8—22no—
132#95—22no—
133#95—432no—
134#95—432no—
135#95—862no—
136#95—862no—
137C2×Q8—862no—
138C22×C4—22no—
139C22×C4—862no—
140C22×C4—862no—
141C22×C4C2×D17211yescharacteristic
142C22×C4D4×D4312yes—
143M16—1722no—
144C2×C8—42no—
145C2×C8—1721no—
146C4⋊C4—862no—
147C4⋊C4—862no—
148C4⋊C4—1724no—
149C4⋊C4—1724no—
150C4⋊C4—1724no—
151C4⋊C4—1722no—
152C22⋊C4—1721no—
153C42—22no—
154C42—22no—
155C42—1721no—
156C42—1722no—
157C42—1722no—
158C42#1062189812yes—
159C42#1062190011yescharacteristic
160C42Q8×D4311yescharacteristic
161C23#1306329511yescharacteristic
162Q8—3442no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—864no—
168C2×C4—1722no—
169C2×C4—1722no—
170C2×C4—1722no—
171C2×C4—1722no—
172C2×C4—1722no—
173C2×C4—1722no—
174C2×C4#1306330312yes—
175C2×C4#1306330511yescharacteristic
176C2×C4#1306331112yes—
177C2×C4#1306331311yescharacteristic
178C2×C4#1306334712yes—
179C2×C4#1306335812yes—
180C8—82no—
181C8—3441no—
182C22—22no—
183C22#1458281211yescharacteristic
184C22#1458306312yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—3442no—
189C4—3442no—
190C4—1724no—
191C4#1458320712yes—
192C4#1458325411yescharacteristic
193C4#1458326811yescharacteristic
194C2—22no—
195C2#1913574711yescharacteristic
196C2#1913576612yes—
subgroupG/H
centerC2×C4#13063313
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1274C2
socleC22×C43#393
prime radicalC23×C43#120
hypercenter#1274D43
hypocenterC43#10373
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

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
#191355762
#191330952
#191324972
C43×#12742
#1037343