Finite Group Databasebeta

← #25000741

Subgroups — #25000741

Order 11008.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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#19145976C211yesmaximal, characteristic
2#19134735C211yesmaximal, characteristic, complemented
3#19133318C212yesmaximal, complemented
4#19133207C212yesmaximal, complemented
5C43×#1307C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583190—22no—
8#14583152—22no—
9#14583095—22no—
10#14582923C2211yescharacteristic
11C2×#13063236C2211yescharacteristic
12#14582663—22no—
13#14582646—22no—
14#14582642—22no—
15#14582638—24no—
16C43×#432C2212yes—
17C43×#423C2211yescharacteristic
18C2×#10621898—22no—
19C2×D344—22no—
20C2×#10621877—21no—
21C22×C43⋊C8—21no—
22#13063325D412yes—
23#13063322D412yes—
24#13063313—22no—
25#13063299—22no—
26#13063299—22no—
27C4×D172—22no—
28C4×D172—22no—
29#13063257—22no—
30C4⋊(C43⋊C8)—22no—
31#13063247—24no—
32#13063236—21no—
33#13063236D412yes—
34C2×M16×C43D412yes—
35C2×C42×C43C2311yescharacteristic
36C4⋊C8×C43—22no—
37C4⋊C8×C43—22no—
38C22⋊C8×C43—22no—
39#97×C43—22no—
40C22×C4×C43C2×D411yescharacteristic
41C22×C4×C43#4112yes—
42C2×C22⋊D43—42no—
43#10621898—84no—
44C2×D172—22no—
45C2×D172—22no—
46C2×D172—22no—
47C2×C4×D43—42no—
48C2×Dic86—22no—
49M16×C43—42no—
50C2×C8×C43—22no—
51C2×C8×C43—42no—
52C42×C43C2×D412yes—
53C42×C43C2×D411yescharacteristic
54C42×C43#4111yescharacteristic
55(C2×D43)⋊C4—42no—
56(C2×D43)⋊C4—42no—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59#10621877—42no—
60C2×C43⋊C8—22no—
61C2×C43⋊C8—41no—
62C2×C43⋊C8—41no—
63C2×C43⋊C8—41no—
64D344—82no—
65C23×C43#12411yescharacteristic
66C22×D43—42no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—42no—
70C2×C4×C43#12011yescharacteristic
71C2×C4×C43#12112yes—
72C2×C4×C43#12111yescharacteristic
73C2×C4×C43#12312yes—
74C22⋊D43—84no—
75C2×Dic43—42no—
76D172—42no—
77D172—42no—
78D172—82no—
79D172—82no—
80C4×D43—84no—
81Dic86—82no—
82C8×C43—42no—
83C8×C43—82no—
84C43⋊C8—42no—
85C43⋊C8—81no—
86#10525—431nomaximal, Sylow
87C22×C43—22no—
88C22×C43—21no—
89C22×C43#39411yescharacteristic
90C2×D43—82no—
91C2×D43—82no—
92C2×D43—82no—
93C4×C43—22no—
94C4×C43—22no—
95C4×C43—21no—
96C4×C43#45411yescharacteristic
97C4×C43#45511yescharacteristic
98Dic43—82no—
99#3253—431no—
100#1838—431no—
101#1557—432no—
102#1530—432no—
103#1307D4311yescharacteristic, complemented
104C2×C43—41no—
105C2×C43#204011yescharacteristic
106C2×C43#204812yes—
107D43—162no—
108#532—432no—
109#476—862no—
110#469—862no—
111#459—862no—
112#432C2×D4312yes—
113#423—431no—
114#423C2×D4311yescharacteristic
115C2×#97—431no—
116#341—862no—
117#332—862no—
118#331—862no—
119#329—864no—
120C43#1052511yescharacteristic, complemented, Sylow
121C2×#41—862no—
122C2×D8—862no—
123C2×M16—861no—
124C2×M16D17212yes—
125C22×C8—861no—
126C4⋊Q8—432no—
127#127—432no—
128#124—862no—
129#121—862no—
130#121—862no—
131C4×D4—862no—
132C4×D4—862no—
133C2×C42C22×D4311yescharacteristic
134#106—862no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—862no—
138#102—864no—
139C22⋊C8—22no—
140#97—22no—
141#97—432no—
142#97—861no—
143#41—3444no—
144C2×Q8—862no—
145C2×D4—862no—
146C2×D4—862no—
147C2×D4—862no—
148C2×D4—1722no—
149C22×C4—1722no—
150C22×C4C2×D17211yescharacteristic
151C22×C4#1062189812yes—
152D8—3442no—
153M16—42no—
154M16—1722no—
155C2×C8—22no—
156C2×C8—42no—
157C2×C8—862no—
158C2×C8—1721no—
159C2×C8—1721no—
160C2×C8—1721no—
161C4⋊C4—862no—
162C4⋊C4—862no—
163C22⋊C4—1722no—
164C22⋊C4—1722no—
165C42D4×D4312yes—
166C42D4×D4311yescharacteristic
167C42#1062190211yescharacteristic
168C23—1722no—
169C23#1306331311yescharacteristic
170Q8—3442no—
171D4—3442no—
172D4—3442no—
173D4—3444no—
174D4—1722no—
175D4—1722no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—3444no—
180C2×C4—1722no—
181C2×C4#1306329511yescharacteristic
182C2×C4#1306329812yes—
183C2×C4#1306330011yescharacteristic
184C2×C4#1306331012yes—
185C8—42no—
186C8—82no—
187C8—3441no—
188C8—1722no—
189C22—21no—
190C22—22no—
191C22—3442no—
192C22—3442no—
193C22—3442no—
194C22#1458281711yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—3442no—
199C4#1458307411yescharacteristic
200C4#1458307911yescharacteristic
201C2—41no—
202C2—6882no—
203C2#1913582511yescharacteristic
204C2#1913587112yes—
subgroupG/H
centerC22#14582817
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1307C2
socleC22×C43#394
prime radical#19145976C2
hypercenter#1307D43
hypocenterC43#10525
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #19134735C2semidirect
3. #19133318C2semidirect
4. #19133207C2semidirect
5. C43×#1307C2semidirect
103. #1307D43semidirect
120. C43#10525semidirect

Maximal subgroups

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

subgroupindex
#191459762
#191347352
#191333182
#191332072
C43×#13072
#1052543