Finite Group Databasebeta

← #24984192

Subgroups — #24984192

Order 11008.

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

normal subgroups only

This group has 206 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#19135756C211yesmaximal, characteristic
2#19132722C211yesmaximal, characteristic
3C43×#1272C211yesmaximal, characteristic
4#14583530C411yescharacteristic
5#14582908—21no—
6C2×#13063244—21no—
7#14582668C411yescharacteristic
8#14582659—21no—
9C43×#391C2211yescharacteristic
10C43×#336—21no—
11C2×#10621877—21no—
12C2×#10621877—41no—
13#13063324—41no—
14#13063316—41no—
15#13063304—41no—
16#13063284—21no—
17#13063249—41no—
18#13063249—41no—
19#13063244—22no—
20#13063244—41no—
21C22×Q8×C43D411yescharacteristic
22C22×C8×C43—41no—
23C2×C4⋊C4×C43C2×C411yescharacteristic
24C2×C42×C43D411yescharacteristic
25#95×C43—41no—
26C2×Q8×C43—21no—
27C2×Q8×C43—41no—
28C2×Q8×C43—41no—
29C2×Q8×C43SD1611yescharacteristic
30C2×Q8×C43Q1611yescharacteristic
31C22×C4×C43—21no—
32C22×C4×C43—21no—
33C22×C4×C43—21no—
34C22×C4×C43C22⋊C411yescharacteristic
35C2×Dic86—41no—
36C2×C8×C43—42no—
37C2×C8×C43—81no—
38C2×C8×C43—81no—
39C4⋊C4×C43—41no—
40C42×C43—41no—
41C22⋊Dic43—41no—
42C4⋊Dic43—21no—
43C4⋊Dic43—21no—
44C4⋊Dic43—41no—
45Dic43⋊C4—42no—
46C4×Dic43—41no—
47#10621877—42no—
48#10621877—41no—
49#10621877—41no—
50#10621877—81no—
51C2×C43⋊C8—41no—
52C2×C43⋊C8—81no—
53C23×C43#9911yescharacteristic
54Q8×C43—41no—
55Q8×C43—41no—
56Q8×C43—81no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—41no—
64C2×C4×C43—41no—
65C2×C4×C43—41no—
66C2×C4×C43—41no—
67C2×C4×C43—41no—
68C2×C4×C43—81no—
69C2×C4×C43#10311yescharacteristic
70C2×C4×C43#10411yescharacteristic
71C2×Dic43—41no—
72C2×Dic43—41no—
73Dic86—161no—
74C8×C43—82no—
75C43⋊C8—81no—
76C43⋊C8—82no—
77#7431—431nomaximal, Sylow
78C22×C43—21no—
79C22×C43—21no—
80C22×C43#32811yescharacteristic
81C22×C43AΣL(1,𝔽16)11yescharacteristic
82C22×C43#35411yescharacteristic
83C4×C43—21no—
84C4×C43—21no—
85C4×C43—41no—
86C4×C43—41no—
87C4×C43—41no—
88C4×C43—41no—
89C4×C43—81no—
90Dic43—81no—
91Dic43—81no—
92#2028—431no—
93#1394—431no—
94#1272D4311yescharacteristic
95C2×C43—21no—
96C2×C43—21no—
97C2×C43#135111yescharacteristic
98C2×C43#140311yescharacteristic
99C2×C43#140511yescharacteristic
100#544—431no—
101#419—861no—
102C2×#101—861no—
103#391C2×D4311yescharacteristic
104#343—431no—
105#339—861no—
106#336—21no—
107C43#743111yescharacteristic, complemented, Sylow
108C22×Q8D17211yescharacteristic
109C2×M16—861no—
110C2×M16—1721no—
111C22×C8—41no—
112C4⋊Q8—1721no—
113#125—1721no—
114C22⋊Q8—1721no—
115#117—861no—
116C2×C4⋊C4C4×D4311yescharacteristic
117C2×C42C22⋊D4311yescharacteristic
118#103—1721no—
119#103—1721no—
120#101—862no—
121#101—1721no—
122#95—41no—
123C2×Q8—21no—
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—1721no—
127C2×Q8#1062187311yescharacteristic
128C2×Q8Dic17211yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4(C2×D43)⋊C411yescharacteristic
133M16—3441no—
134M16—1722no—
135M16—1721no—
136M16—1721no—
137C2×C8—42no—
138C2×C8—81no—
139C2×C8—81no—
140C2×C8—3441no—
141C2×C8—1721no—
142C4⋊C4—41no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C4⋊C4—1721no—
146C4⋊C4—1722no—
147C22⋊C4—1721no—
148C42—41no—
149C42—1721no—
150C23#1306323911yescharacteristic
151Q8—41no—
152Q8—41no—
153Q8—81no—
154Q8—6881no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—81no—
167C2×C4—1721no—
168C2×C4—1721no—
169C2×C4#1306325011yescharacteristic
170C2×C4#1306325111yescharacteristic
171C8—82no—
172C8—3441no—
173C8—3442no—
174C22—21no—
175C22—21no—
176C22#1458263711yescharacteristic
177C22#1458268711yescharacteristic
178C22#1458269311yescharacteristic
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—81no—
186C4—3441no—
187C4—3441no—
188C2—21no—
189C2—21no—
190C2#1913261711yescharacteristic
191C2#1913274411yescharacteristic
192C2#1913275011yescharacteristic
subgroupG/H
centerC22#14582687
commutatorC2×C4⋊C4×C43C2×C4
Frattini#391C2×D43
FittingC43×#1272C2
socleC22×C43AΣL(1,𝔽16)
prime radicalC23×C43#99
cosocleC43×#391C22
hypercenter#1272D43
hypocenterC43#7431
LCSG ▷ C2×C4⋊C4×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1272

Complements

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

NH ≅ G/Ntype
107. C43#7431semidirect

Maximal subgroups

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

subgroupindex
#191357562
#191327222
C43×#12722
#743143