Finite Group Databasebeta

← #24984178

Subgroups — #24984178

Order 11008.

214 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 37 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#19135762C211yesmaximal, characteristic
2#19132525C211yesmaximal, characteristic
3C43×#1306C211yesmaximal, characteristic
4#14583525C411yescharacteristic
5#14582762—21no—
6#14582666C411yescharacteristic
7#14582665—21no—
8#14582623—21no—
9C43×#407—21no—
10C43×#381C2211yescharacteristic
11#13063304—41no—
12#13063302—42no—
13C2×C22⋊Dic43—21no—
14C2×C22⋊Dic43—21no—
15C22⋊(C43⋊C8)—41no—
16C43⋊#95—42no—
17C23×C4×C43D411yescharacteristic
18C2×M16×C43—41no—
19C2×C22⋊C4×C43C2×C411yescharacteristic
20C2×C22⋊C4×C43D411yescharacteristic
21C22⋊C8×C43—22no—
22C22⋊C8×C43—41no—
23#95×C43—41no—
24C24×C43C22⋊C411yescharacteristic
25C22×C4×C43—21no—
26C22×C4×C43—21no—
27C22×C4×C43—21no—
28C22×C4×C43—21no—
29C22×C4×C43—41no—
30C22×C4×C43—41no—
31C22×C4×C43SD1611yescharacteristic
32C22×C4×C43Q1611yescharacteristic
33C22×Dic43—22no—
34C22×Dic43—41no—
35C2×Dic86—41no—
36M16×C43—81no—
37M16×C43—81no—
38C2×C8×C43—42no—
39C22⋊C4×C43—41no—
40C22⋊C4×C43—41no—
41C22⋊Dic43—41no—
42C22⋊Dic43—41no—
43C22⋊Dic43—41no—
44C22⋊Dic43—41no—
45C4⋊Dic43—41no—
46Dic43⋊C4—42no—
47C2×C43⋊C8—81no—
48C23×C43—21no—
49C23×C43—21no—
50C23×C43—81no—
51C23×C43#9911yescharacteristic
52C23×C43#10311yescharacteristic
53C23×C43#10411yescharacteristic
54C2×C4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—41no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43—41no—
61C2×C4×C43—41no—
62C2×C4×C43—81no—
63C2×C4×C43—81no—
64C2×C4×C43—81no—
65C2×Dic43—42no—
66C2×Dic43—82no—
67C2×Dic43—81no—
68C2×Dic43—82no—
69Dic86—161no—
70C8×C43—82no—
71C43⋊C8—161no—
72#7427—431nomaximal, Sylow
73C22×C43—21no—
74C22×C43—21no—
75C22×C43—41no—
76C22×C43—41no—
77C22×C43—41no—
78C22×C43—42no—
79C22×C43—81no—
80C22×C43#32811yescharacteristic
81C22×C43AΣL(1,𝔽16)11yescharacteristic
82C22×C43#35411yescharacteristic
83C4×C43—41no—
84C4×C43—41no—
85C4×C43—81no—
86C4×C43—81no—
87Dic43—82no—
88Dic43—161no—
89#2030—431no—
90#1317—431no—
91#1306D4311yescharacteristic
92C2×C43—21no—
93C2×C43—21no—
94C2×C43—21no—
95C2×C43—41no—
96C2×C43—41no—
97C2×C43#135111yescharacteristic
98#543—431no—
99#407—21no—
100#381—861no—
101#381C2×D4311yescharacteristic
102#342—431no—
103#342—861no—
104#323—861no—
105C43#742711yescharacteristic, complemented, Sylow
106C23×C4C22⋊D4311yescharacteristic
107C2×M16—41no—
108C22⋊Q8—1722no—
109C22⋊Q8—1721no—
110C2×C22⋊C4—861no—
111C2×C22⋊C4—861no—
112C2×C22⋊C4C4×D4311yescharacteristic
113C2×C22⋊C4D17211yescharacteristic
114C22⋊C8—22no—
115C22⋊C8—41no—
116C22⋊C8—1721no—
117#95—41no—
118#95—1722no—
119C24(C2×D43)⋊C411yescharacteristic
120C2×Q8—1721no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—41no—
126C22×C4—41no—
127C22×C4—862no—
128C22×C4—1721no—
129C22×C4#1062188311yescharacteristic
130C22×C4#1062188511yescharacteristic
131M16—81no—
132M16—81no—
133C2×C8—42no—
134C2×C8—3441no—
135C4⋊C4—1722no—
136C4⋊C4—1721no—
137C22⋊C4—41no—
138C22⋊C4—41no—
139C22⋊C4—1721no—
140C22⋊C4—1721no—
141C22⋊C4—1721no—
142C22⋊C4—1721no—
143C23—21no—
144C23—21no—
145C23—81no—
146C23#1306323911yescharacteristic
147C23#1306324811yescharacteristic
148C23#1306325311yescharacteristic
149Q8—6881no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—3442no—
162C2×C4—3441no—
163C2×C4—3442no—
164C2×C4—1722no—
165C8—82no—
166C8—6881no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#1458263511yescharacteristic
175C22#1458268511yescharacteristic
176C22#1458269311yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—3442no—
182C4—6881no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#1913261511yescharacteristic
subgroupG/H
centerC2#19132615
commutatorC2×C22⋊C4×C43C2×C4
Frattini#381C2×D43
FittingC43×#1306C2
socleC2×C43#1351
prime radicalC24×C43C22⋊C4
cosocleC43×#381C22
hypercenter#1306D43
hypocenterC43#7427
LCSG ▷ C2×C22⋊C4×C43 ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1306

Complements

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

NH ≅ G/Ntype
105. C43#7427semidirect

Maximal subgroups

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

subgroupindex
#191357622
#191325252
C43×#13062
#742743