Finite Group Databasebeta

← #25007782

Subgroups — #25007782

Order 11008.

296 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 75 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#19145245C211yesmaximal, characteristic
2#19136411C211yesmaximal, characteristic, complemented
3#19132627C214yesmaximal, complemented
4C43×#2110C211yesmaximal, characteristic, complemented
5#14583504C412yes—
6#14583301C411yescharacteristic
7#14583276C411yescharacteristic
8#14583264C2212yes—
9#14583152—21no—
10#14583135—21no—
11#14583012—21no—
12C4×D344—21no—
13#14582720—21no—
14#14582681—21no—
15#14582677C2212yes—
16C2×M32×C43—21no—
17C43×#405C2211yescharacteristic
18C43×#347—21no—
19C43×#347C2212yes—
20C2×D344—21no—
21C2×D344—21no—
22#13063322C2×C412yes—
23#13063317C2×C412yes—
24#13063310—42no—
25#13063299—22no—
26#13063298—42no—
27C4×D172—22no—
28#13063265—22no—
29#13063259—21no—
30#13063257—21no—
31#13063247—22no—
32#13063247—22no—
33C2×M16×C43D411yescharacteristic
34C22×C8×C43D411yescharacteristic
35#117×C43C2×C411yescharacteristic
36M32×C43—22no—
37M32×C43—22no—
38C2×C16×C43—22no—
39#97×C43D411yescharacteristic
40#97×C43C2311yescharacteristic
41C4×C8×C43C2×C411yescharacteristic
42C4×C8×C43D411yescharacteristic
43C22×C4×C43C22⋊C411yescharacteristic
44C2×C22⋊D43—42no—
45C2×D172—22no—
46C2×D172—42no—
47C2×C4×D43—42no—
48M16×C43—41no—
49C2×C8×C43—21no—
50C2×C8×C43—21no—
51C2×C8×C43C22⋊C411yescharacteristic
52C2×C8×C43C22⋊C411yescharacteristic
53C2×C8×C43C2×D411yescharacteristic
54C2×C8×C43C2×D411yescharacteristic
55C4⋊C4×C43—21no—
56C22⋊C4×C43—21no—
57C42×C43C22⋊C411yescharacteristic
58C42×C43C22×C411yescharacteristic
59(C2×D43)⋊C4—42no—
60(C2×D43)⋊C4—42no—
61C4⋊Dic43—22no—
62Dic43⋊C4—42no—
63D344—42no—
64D344—41no—
65D344—41no—
66C16×C43—24no—
67C43⋊C16—42no—
68C23×C43#10011yescharacteristic
69C22×D43—42no—
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43#10011yescharacteristic
75C2×C4×C43C2×C22⋊C411yescharacteristic
76C22⋊D43—162no—
77C2×Dic43—42no—
78D172—42no—
79D172—42no—
80D172—162no—
81C4×D43—162no—
82C8×C43—21no—
83C8×C43—21no—
84C8×C43—21no—
85C8×C43#10411yescharacteristic
86C8×C43#10411yescharacteristic
87#11913—431nomaximal, Sylow
88C22×C43—21no—
89C22×C43—41no—
90C22×C43C2×#10011yescharacteristic
91C2×D43—82no—
92C2×D43—82no—
93C2×D43—82no—
94C4×C43—21no—
95C4×C43—41no—
96C4×C43—41no—
97C4×C43C2×#10411yescharacteristic
98C4×C43#42111yescharacteristic
99Dic43—82no—
100#3176—431no—
101#2166—431no—
102#2110D4311yescharacteristic, complemented
103#1355—434no—
104C2×C43—21no—
105C2×C43—41no—
106C2×C43#153011yescharacteristic
107D43—162no—
108#540—432no—
109C2×M32—21no—
110#499—431no—
111#493—431no—
112#490—432no—
113#469—861no—
114#466—861no—
115#442—861no—
116C4×D8—861no—
117#405C2×D4311yescharacteristic
118#364—861no—
119#349—861no—
120#347—21no—
121#347—432no—
122#347C2×D4312yes—
123C43#1191311yescharacteristic, complemented, Sylow
124C2×D8—861no—
125C2×D8—861no—
126C2×M16D17211yescharacteristic
127C22×C8C22⋊D4311yescharacteristic
128#127—432no—
129#125—432no—
130#123—1722no—
131#121—862no—
132#121—1722no—
133C4×D4—862no—
134#117C4×D4311yescharacteristic
135M32—22no—
136M32—22no—
137M32—862no—
138C2×C16—22no—
139#107—861no—
140#106—861no—
141#102—862no—
142#102—862no—
143#97C22⋊D4311yescharacteristic
144#97C22×D4311yescharacteristic
145C4×C8C4×D4311yescharacteristic
146C4×C8D17211yescharacteristic
147C2×D4—862no—
148C2×D4—1722no—
149C2×D4—1722no—
150C22×C4—1722no—
151C22×C4(C2×D43)⋊C411yescharacteristic
152D8—1722no—
153D8—1721no—
154D8—1721no—
155M16—41no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8(C2×D43)⋊C411yescharacteristic
159C2×C8(C2×D43)⋊C411yescharacteristic
160C2×C8C2×D17211yescharacteristic
161C2×C8C2×C22⋊D4311yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—862no—
164C4⋊C4—1722no—
165C22⋊C4—21no—
166C22⋊C4—1722no—
167C22⋊C4—1722no—
168C42(C2×D43)⋊C411yescharacteristic
169C42C2×C4×D4311yescharacteristic
170C16—24no—
171C16—1722no—
172C23—1722no—
173C23#1306324111yescharacteristic
174D4—1722no—
175D4—1722no—
176D4—6882no—
177D4—6882no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—1722no—
183C2×C4—6882no—
184C2×C4#1306324111yescharacteristic
185C2×C4C2×(C2×D43)⋊C411yescharacteristic
186C8—21no—
187C8—21no—
188C8—21no—
189C8#1306325311yescharacteristic
190C8#1306325311yescharacteristic
191C22—21no—
192C22—41no—
193C22—3442no—
194C22—3442no—
195C22—3442no—
196C22C2×#1306324111yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—3442no—
201C4C2×#1306325311yescharacteristic
202C4#1458291511yescharacteristic
203C2—21no—
204C2—41no—
205C2—6882no—
206C2#1913320511yescharacteristic
subgroupG/H
centerC2#19133205
commutatorC42×C43C22×C4
Frattini#97C22×D43
FittingC43×#2110C2
socleC2×C43#1530
prime radical#19145245C2
cosocle#97×C43C23
hypercenter#2110D43
hypocenterC43#11913
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2110

Complements

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

NH ≅ G/Ntype
2. #19136411C2semidirect
3. #19132627C2semidirect
4. C43×#2110C2semidirect
102. #2110D43semidirect
123. C43#11913semidirect

Maximal subgroups

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

subgroupindex
#191452452
#191364112
#191326272
C43×#21102
#1191343