Finite Group Databasebeta

← #24984223

Subgroups — #24984223

Order 11008.

194 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 41 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#19135945C211yesmaximal, characteristic
2#19132539C211yesmaximal, characteristic
3C43×#1295C211yesmaximal, characteristic
4#14583530C411yescharacteristic
5#14582939—21no—
6#14582668C411yescharacteristic
7#14582659—21no—
8#14582625—21no—
9C2×#97×C43—21no—
10C43×#382C2211yescharacteristic
11C2×#10621877—21no—
12#13063324—41no—
13#13063316—41no—
14#13063304—41no—
15#13063284—21no—
16#13063258—41no—
17#13063256—41no—
18C22⋊(C43⋊C8)—41no—
19C22×C8×C43—41no—
20C2×C4⋊C4×C43C2×C411yescharacteristic
21C2×C4⋊C4×C43D411yescharacteristic
22C2×C42×C43D411yescharacteristic
23#97×C43—22no—
24#97×C43—41no—
25#95×C43—41no—
26C22×C4×C43—21no—
27C22×C4×C43—21no—
28C22×C4×C43—21no—
29C22×C4×C43C22⋊C411yescharacteristic
30C2×Dic86—41no—
31C2×C8×C43—42no—
32C2×C8×C43—42no—
33C2×C8×C43—42no—
34C4⋊C4×C43—41no—
35C4⋊C4×C43—41no—
36C42×C43—21no—
37C42×C43SD1611yescharacteristic
38C42×C43Q1611yescharacteristic
39C22⋊Dic43—41no—
40C4⋊Dic43—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43—41no—
43Dic43⋊C4—42no—
44C4×Dic43—41no—
45#10621877—22no—
46#10621877—41no—
47C2×C43⋊C8—41no—
48C2×C43⋊C8—81no—
49C23×C43#9911yescharacteristic
50C2×C4×C43—21no—
51C2×C4×C43—21no—
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—41no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43—41no—
58C2×C4×C43—81no—
59C2×C4×C43—81no—
60C2×C4×C43#10311yescharacteristic
61C2×C4×C43#10411yescharacteristic
62C2×Dic43—41no—
63C2×Dic43—41no—
64Dic86—161no—
65C8×C43—44no—
66C43⋊C8—42no—
67C43⋊C8—161no—
68#7442—431nomaximal, Sylow
69C22×C43—21no—
70C22×C43—21no—
71C22×C43#32811yescharacteristic
72C22×C43AΣL(1,𝔽16)11yescharacteristic
73C22×C43#35611yescharacteristic
74C4×C43—21no—
75C4×C43—21no—
76C4×C43—41no—
77C4×C43—41no—
78C4×C43—81no—
79C4×C43—81no—
80Dic43—81no—
81Dic43—81no—
82#2061—431no—
83#1324—431no—
84#1295D4311yescharacteristic
85C2×C43—21no—
86C2×C43—21no—
87C2×C43#135411yescharacteristic
88C2×C43#140311yescharacteristic
89C2×C43#140411yescharacteristic
90#544—431no—
91#428—861no—
92C2×#97—21no—
93#382C2×D4311yescharacteristic
94#343—431no—
95#339—861no—
96#324—861no—
97C43#744211yescharacteristic, complemented, Sylow
98C2×M16—861no—
99C22×C8—41no—
100C4⋊Q8—1721no—
101#125—1721no—
102C22⋊Q8—1721no—
103#117—861no—
104C2×C4⋊C4C4×D4311yescharacteristic
105C2×C4⋊C4D17211yescharacteristic
106C2×C42C22⋊D4311yescharacteristic
107#107—1721no—
108#106—1721no—
109C22⋊C8—1721no—
110#97—22no—
111#97—41no—
112#95—41no—
113C2×Q8—1721no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4(C2×D43)⋊C411yescharacteristic
118M16—862no—
119M16—1721no—
120C2×C8—42no—
121C2×C8—42no—
122C2×C8—42no—
123C2×C8—3441no—
124C2×C8—1721no—
125C4⋊C4—41no—
126C4⋊C4—41no—
127C4⋊C4—861no—
128C4⋊C4—861no—
129C4⋊C4—1721no—
130C4⋊C4—1722no—
131C22⋊C4—1721no—
132C42—21no—
133C42—1721no—
134C42#1062188311yescharacteristic
135C42#1062188511yescharacteristic
136C23#1306323911yescharacteristic
137Q8—6881no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—1721no—
149C2×C4—1721no—
150C2×C4#1306324811yescharacteristic
151C2×C4#1306325311yescharacteristic
152C8—44no—
153C8—1722no—
154C8—6881no—
155C22—21no—
156C22—21no—
157C22#1458263511yescharacteristic
158C22#1458268711yescharacteristic
159C22#1458269711yescharacteristic
160C4—21no—
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—81no—
166C4—3441no—
167C4—3441no—
168C2—21no—
169C2—21no—
170C2#1913262411yescharacteristic
171C2#1913274411yescharacteristic
172C2#1913274711yescharacteristic
subgroupG/H
centerC22#14582687
commutatorC2×C4⋊C4×C43C2×C4
Frattini#382C2×D43
FittingC43×#1295C2
socleC22×C43AΣL(1,𝔽16)
prime radicalC23×C43#99
cosocleC43×#382C22
hypercenter#1295D43
hypocenterC43#7442
LCSG ▷ C2×C4⋊C4×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1295

Complements

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

NH ≅ G/Ntype
97. C43#7442semidirect

Maximal subgroups

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

subgroupindex
#191359452
#191325392
C43×#12952
#744243