Finite Group Databasebeta

← #24999321

Subgroups — #24999321

Order 11008.

504 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 113 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#19145746C212yesmaximal
2#19135572C211yesmaximal, characteristic
3#19133280C212yesmaximal
4#19132428C211yesmaximal, characteristic
5C43×#2862C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583302—22no—
8#14583251—22no—
9#14583234—24no—
10#14583191—24no—
11#14582952C2212yes—
12#14582923C2211yescharacteristic
13#14582659—22no—
14#14582645—24no—
15C2×C4⋊Q8×C43C2212yes—
16C43×#391—24no—
17C43×#382—22no—
18C43×C43C2211yescharacteristic
19C2×#10621877—21no—
20#13063325D412yes—
21#13063317—21no—
22#13063304—22no—
23C4×Dic86—22no—
24#13063284—21no—
25#13063258—28no—
26C4⋊(C43⋊C8)—22no—
27C4⋊(C43⋊C8)D414yes—
28#13063248—28no—
29C22⋊(C43⋊C8)—22no—
30C4×C43⋊C8—22no—
31C22×Q8×C43—22no—
32C4⋊Q8×C43—22no—
33C4⋊Q8×C43—22no—
34C4⋊Q8×C43—22no—
35C4⋊Q8×C43—22no—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43D414yes—
38C2×C42×C43—22no—
39C2×C42×C43D412yes—
40C2×C42×C43C2311yescharacteristic
41#95×C43—28no—
42C2×Q8×C43—48no—
43C2×Q8×C43—42no—
44C2×Q8×C43—42no—
45C22×C4×C43—22no—
46C22×C4×C43—24no—
47C22×C4×C43C2×D412yes—
48C22×C4×C43C2×D411yescharacteristic
49C2×Dic86—22no—
50C4⋊C4×C43—24no—
51C4⋊C4×C43—24no—
52C4⋊C4×C43—42no—
53C4⋊C4×C43—42no—
54C42×C43—22no—
55C42×C43—44no—
56C42×C43Q1614yes—
57C42×C43C2×D411yescharacteristic
58C42×C43C2×D412yes—
59C42×C43#4111yescharacteristic
60C22⋊Dic43—41no—
61C4⋊Dic43—22no—
62C4⋊Dic43—22no—
63Dic43⋊C4—42no—
64C4×Dic43—41no—
65#10621877—42no—
66C2×C43⋊C8—24no—
67C2×C43⋊C8—41no—
68C23×C43#12011yescharacteristic
69Q8×C43—84no—
70Q8×C43—84no—
71C2×C4×C43—24no—
72C2×C4×C43—24no—
73C2×C4×C43—44no—
74C2×C4×C43—48no—
75C2×C4×C43—44no—
76C2×C4×C43#12012yes—
77C2×C4×C43#12111yescharacteristic
78C2×C4×C43#12112yes—
79C2×C4×C43#12711yescharacteristic
80C2×C4×C43C2×Q1612yes—
81C2×C4×C43#13712yes—
82C2×Dic43—42no—
83Dic86—44no—
84C43⋊C8—44no—
85C43⋊C8—81no—
86#10295—431nomaximal, Sylow
87C22×C43—22no—
88C22×C43#39211yescharacteristic
89C22×C43#45112yes—
90C4×C43—22no—
91C4×C43—44no—
92C4×C43—84no—
93C4×C43#45414yes—
94C4×C43#46212yes—
95C4×C43#49411yescharacteristic
96C4×C43#49711yescharacteristic
97Dic43—82no—
98#3230—432no—
99#2862D4311yescharacteristic
100#1994—431no—
101#1549—432no—
102#1276—431no—
103C2×C43—22no—
104C2×C43#200312yes—
105C2×C43#201611yescharacteristic
106#533—431no—
107C2×C4⋊Q8C2×D4312yes—
108#500—862no—
109#487—862no—
110#484—864no—
111#477—864no—
112#431—432no—
113#423—431no—
114#391—24no—
115#382—22no—
116C43C2×D4311yescharacteristic
117#339—862no—
118#332—864no—
119C43#1029511yescharacteristic, complemented, Sylow
120C22×Q8—22no—
121C2×M16—861no—
122C4⋊Q8—22no—
123C4⋊Q8—22no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—432no—
127#125—861no—
128C22⋊Q8—862no—
129C4×Q8—862no—
130#117—861no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4C22⋊D4314yes—
133C2×C42—22no—
134C2×C42C22⋊D4312yes—
135C2×C42C22×D4311yescharacteristic
136#107—868no—
137C4⋊C8—434no—
138C4⋊C8—862no—
139#103—868no—
140C22⋊C8—862no—
141C4×C8—862no—
142#95—28no—
143C2×Q8—48no—
144C2×Q8—42no—
145C2×Q8—42no—
146C2×Q8—862no—
147C22×C4—22no—
148C22×C4—24no—
149C22×C4C2×C22⋊D4312yes—
150C22×C4C2×C22⋊D4311yescharacteristic
151M16—1722no—
152C2×C8—864no—
153C2×C8—1721no—
154C4⋊C4—24no—
155C4⋊C4—24no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—862no—
159C4⋊C4—862no—
160C4⋊C4—1722no—
161C22⋊C4—1721no—
162C42—22no—
163C42—44no—
164C42—1721no—
165C42#1062188514yes—
166C42D4×D4311yescharacteristic
167C42D4×D4312yes—
168C42#1062190011yescharacteristic
169C23#1306329411yescharacteristic
170Q8—84no—
171Q8—84no—
172Q8—1724no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—1722no—
179C2×C4#1306329312yes—
180C2×C4#1306329611yescharacteristic
181C2×C4#1306329712yes—
182C2×C4#1306332111yescharacteristic
183C2×C4C2×#1062188512yes—
184C2×C4#1306335612yes—
185C8—3441no—
186C8—1724no—
187C22—22no—
188C22#1458280711yescharacteristic
189C22#1458305512yes—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—3442no—
194C4#1458307114yes—
195C4#1458310612yes—
196C4#1458327811yescharacteristic
197C4#1458329111yescharacteristic
198C2—22no—
199C2#1913561712yes—
200C2#1913569511yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2862C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#2862D43
hypocenterC43#10295
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

Complements

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

NH ≅ G/Ntype
119. C43#10295semidirect

Maximal subgroups

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

subgroupindex
#191457462
#191355722
#191332802
#191324282
C43×#28622
#1029543