Finite Group Databasebeta

← #25006104

Subgroups — #25006104

Order 11008.

270 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 71 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#19143528C211yesmaximal, characteristic
2#19136408C212yesmaximal
3#19132548C211yesmaximal, characteristic
4#19132545C212yesmaximal
5C43×#1328C211yesmaximal, characteristic
6#14583452C411yescharacteristic
7#14583028—22no—
8#14583023—22no—
9#14582925C411yescharacteristic
10#14582922C2211yescharacteristic
11#14582857C2211yescharacteristic
12#14582855C411yescharacteristic
13C2×C8×Dic43C411yescharacteristic
14#14582719—22no—
15#14582681C2212yes—
16#14582676—22no—
17C43×#424C2211yescharacteristic
18C43×#349C2212yes—
19C2×#10621877C2×C411yescharacteristic
20C22×C43⋊C8C2×C411yescharacteristic
21#13063324—21no—
22#13063316—21no—
23#13063302—22no—
24C4×Dic86—22no—
25#13063284C2×C411yescharacteristic
26C2×C4×Dic43C2×C411yescharacteristic
27#13063265—22no—
28Dic43⋊C8—22no—
29Dic43⋊C8—22no—
30#13063236—21no—
31#13063235D412yes—
32C4×C43⋊C8—21no—
33C8×Dic43—21no—
34C8×Dic43—21no—
35C8×Dic43D412yes—
36C2×M16×C43C2311yescharacteristic
37C22×C8×C43C2×C411yescharacteristic
38#117×C43C2×C411yescharacteristic
39M32×C43—22no—
40C4⋊C8×C43—22no—
41C22×C4×C43C22×C411yescharacteristic
42C22×Dic43—21no—
43C2×Dic86—22no—
44M16×C43—41no—
45C2×C8×C43—21no—
46C2×C8×C43—41no—
47C2×C8×C43C2×D412yes—
48C4⋊C4×C43—21no—
49C22⋊C4×C43M1612yes—
50C42×C43—21no—
51C22⋊Dic43—21no—
52C4⋊Dic43—22no—
53C4⋊Dic43—21no—
54Dic43⋊C4—22no—
55Dic43⋊C4—22no—
56C4×Dic43—21no—
57C4×Dic43C22⋊C412yes—
58C4×Dic43M1611yescharacteristic
59C4×Dic43M1611yescharacteristic
60#10621877—41no—
61C2×C43⋊C8—22no—
62C2×C43⋊C8—21no—
63C2×C43⋊C8C22⋊C411yescharacteristic
64C2×C43⋊C8C22⋊C411yescharacteristic
65C16×C43—42no—
66C43⋊C16—42no—
67C23×C43C2×M1611yescharacteristic
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—22no—
71C2×C4×C43C2×C22⋊C411yescharacteristic
72C2×C4×C43C2×M1611yescharacteristic
73C2×Dic43—21no—
74C2×Dic43—21no—
75C2×Dic43—22no—
76C2×Dic43—42no—
77Dic86—44no—
78C8×C43—22no—
79C8×C43—41no—
80C43⋊C8—21no—
81C43⋊C8—41no—
82C43⋊C8#10112yes—
83#11539—431nomaximal, Sylow
84C22×C43—21no—
85C22×C43—41no—
86C22×C43#40711yescharacteristic
87C4×C43—21no—
88C4×C43—42no—
89C4×C43#41011yescharacteristic
90C4×C43C2×#10111yescharacteristic
91Dic43—22no—
92Dic43—42no—
93Dic43—41no—
94#2960—431no—
95#2166—432no—
96#1328—431no—
97#1328D4311yescharacteristic
98#1327—432no—
99C2×C43—21no—
100C2×C43—41no—
101C2×C43#146711yescharacteristic
102#533—431no—
103#446—862no—
104C8×Q8—862no—
105#424—431no—
106#424C2×D4311yescharacteristic
107#423—431no—
108#405—431no—
109#405—431no—
110C2×C4×C8—431no—
111#364—862no—
112#349—432no—
113#349C2×D4312yes—
114#347—862no—
115C43#1153911yescharacteristic, complemented, Sylow
116C2×M16—431no—
117C2×M16C22×D4311yescharacteristic
118C22×C8—431no—
119C22×C8C4×D4311yescharacteristic
120C4⋊Q8—861no—
121#125—861no—
122C22⋊Q8—862no—
123C4×Q8—862no—
124#117—431no—
125#117C4×D4311yescharacteristic
126C2×C42—431no—
127M32—22no—
128M32—862no—
129C4⋊C8—22no—
130C4⋊C8—862no—
131C4⋊C8—862no—
132#97—432no—
133#97—861no—
134C4×C8—432no—
135C4×C8—861no—
136C4×C8—861no—
137C4×C8—861no—
138C2×Q8—862no—
139C22×C4—861no—
140C22×C4C2×C4×D4311yescharacteristic
141M16—41no—
142M16—1721no—
143C2×C8—21no—
144C2×C8—41no—
145C2×C8—431no—
146C2×C8—431no—
147C2×C8—862no—
148C2×C8—861no—
149C2×C8D4×D4312yes—
150C4⋊C4—21no—
151C4⋊C4—862no—
152C4⋊C4—862no—
153C4⋊C4—862no—
154C4⋊C4—861no—
155C22⋊C4—861no—
156C22⋊C4#1062187212yes—
157C42—21no—
158C42—432no—
159C42—431no—
160C42—431no—
161C42—861no—
162C16—42no—
163C16—1722no—
164C23C2×#1062187211yescharacteristic
165Q8—1724no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—861no—
170C2×C4—861no—
171C2×C4—862no—
172C2×C4—1722no—
173C2×C4C22⋊C4×D4311yescharacteristic
174C2×C4M16×D4311yescharacteristic
175C8—22no—
176C8—41no—
177C8—432no—
178C8—861no—
179C8—1721no—
180C22—21no—
181C22—41no—
182C22#1458286111yescharacteristic
183C4—21no—
184C4—42no—
185C4—862no—
186C4—1721no—
187C4—1722no—
188C4#1458287111yescharacteristic
189C4#101×D4311yescharacteristic
190C2—21no—
191C2—41no—
192C2#1913293711yescharacteristic
subgroupG/H
centerC4#14582871
commutatorC22×C4×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1328C2
socleC2×C43#1467
prime radicalC23×C43C2×M16
cosocleC2×M16×C43C23
hypercenter#1328D43
hypocenterC43#11539
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
115. C43#11539semidirect

Maximal subgroups

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

subgroupindex
#191435282
#191364082
#191325482
#191325452
C43×#13282
#1153943