Finite Group Databasebeta

← #24991561

Subgroups — #24991561

Order 11008.

398 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 99 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#19144943C211yesmaximal, characteristic
2#19133260C211yesmaximal, characteristic, complemented
3#19133063C212yesmaximal
4#19132493C212yesmaximal, complemented
5C43×#2987C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7#14583269C412yes—
8#14583265C412yes—
9#14583261—22no—
10#14582952C2212yes—
11#14582893—22no—
12C2×#13063236C2211yescharacteristic
13#14582645—22no—
14#14582626—24no—
15C43×#533C2211yescharacteristic
16C43×#446—24no—
17C43×#433—22no—
18C43×#432C2212yes—
19C2×#10621898—21no—
20C22×C43⋊C8—21no—
21#13063325C2×C411yescharacteristic
22#13063322C2×C411yescharacteristic
23#13063313—21no—
24#13063299—22no—
25C4×D172—22no—
26C4⋊(C43⋊C8)—22no—
27#13063248—24no—
28#13063245—24no—
29C22⋊(C43⋊C8)—22no—
30#13063236—21no—
31#13063236C2×C412yes—
32C4×C43⋊C8—22no—
33C4⋊Q8×C43D412yes—
34#125×C43C2×C412yes—
35C22⋊Q8×C43—22no—
36C4×Q8×C43—22no—
37#117×C43D412yes—
38C2×C42×C43C2311yescharacteristic
39C4⋊C8×C43—24no—
40C4⋊C8×C43D414yes—
41C22⋊C8×C43—22no—
42#97×C43—22no—
43#97×C43—22no—
44C4×C8×C43—22no—
45C2×Q8×C43—22no—
46C22×C4×C43C2×D411yescharacteristic
47C22×C4×C43#4112yes—
48C2×C22⋊D43—41no—
49#10621898—44no—
50C2×D172—21no—
51C2×D172—22no—
52C2×C4×D43—41no—
53C2×Dic86—21no—
54C2×C8×C43—24no—
55C4⋊C4×C43—24no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43C22⋊C414yes—
58C22⋊C4×C43—22no—
59C42×C43—22no—
60C42×C43C22×C411yescharacteristic
61C42×C43C2×D411yescharacteristic
62C42×C43C2×D412yes—
63(C2×D43)⋊C4—42no—
64C4⋊Dic43—22no—
65C2×C43⋊C8—22no—
66C2×C43⋊C8—42no—
67C2×C43⋊C8—42no—
68C23×C43#12311yescharacteristic
69C22×D43—41no—
70Q8×C43—82no—
71C2×C4×C43—22no—
72C2×C4×C43—24no—
73C2×C4×C43—42no—
74C2×C4×C43C2×C22⋊C411yescharacteristic
75C2×C4×C43C4×D412yes—
76C2×C4×C43#12011yescharacteristic
77C2×C4×C43#12112yes—
78C22⋊D43—82no—
79C2×Dic43—41no—
80D172—44no—
81D172—42no—
82C4×D43—82no—
83Dic86—42no—
84C8×C43—44no—
85C43⋊C8—42no—
86C43⋊C8—82no—
87#9008—431nomaximal, Sylow
88C22×C43—22no—
89C22×C43—21no—
90C22×C43#38611yescharacteristic
91C2×D43—82no—
92C2×D43—81no—
93C4×C43—22no—
94C4×C43—22no—
95C4×C43—21no—
96C4×C43—44no—
97C4×C43#45412yes—
98Dic43—81no—
99#3135—431no—
100#2987D4311yescharacteristic, complemented
101#1544—431no—
102#1496—432no—
103#1302—432no—
104C2×C43—41no—
105C2×C43#188112yes—
106C2×C43#188811yescharacteristic
107D43—161no—
108#533C2×D4311yescharacteristic
109#532—431no—
110#491—432no—
111#490—432no—
112#489—862no—
113#446—24no—
114#433—22no—
115#432C2×D4312yes—
116#431—432no—
117#416—862no—
118C2×#97—431no—
119#332—862no—
120D4⋊C8—864no—
121C43#900811yescharacteristic, complemented, Sylow
122C2×#41—861no—
123C22×C8—861no—
124C4⋊Q8—431no—
125C4⋊Q8D17212yes—
126#127—431no—
127#125C4×D4312yes—
128#124—861no—
129C22⋊Q8—22no—
130#121—862no—
131C4×Q8—22no—
132C4×D4—862no—
133#117C22⋊D4312yes—
134C2×C42C22×D4311yescharacteristic
135C4⋊C8—24no—
136C4⋊C8—862no—
137C4⋊C8C22⋊D4314yes—
138#103—864no—
139#102—864no—
140C22⋊C8—22no—
141C22⋊C8—862no—
142#97—22no—
143#97—22no—
144#97—432no—
145#97—861no—
146C4×C8—22no—
147C4×C8—862no—
148#41—1724no—
149C2×Q8—22no—
150C2×Q8—861no—
151C2×D4—861no—
152C2×D4—862no—
153C2×D4—1721no—
154C22×C4—1721no—
155C22×C4#1062189812yes—
156C22×C4C2×C22⋊D4311yescharacteristic
157C2×C8—24no—
158C2×C8—862no—
159C2×C8—1722no—
160C2×C8—1722no—
161C4⋊C4—24no—
162C4⋊C4—22no—
163C4⋊C4—862no—
164C4⋊C4(C2×D43)⋊C414yes—
165C22⋊C4—22no—
166C22⋊C4—1722no—
167C42—22no—
168C42C2×C4×D4311yescharacteristic
169C42C2×D17211yescharacteristic
170C42C2×C22⋊D4312yes—
171C23—1721no—
172C23#1306330811yescharacteristic
173Q8—82no—
174Q8—1722no—
175D4—3442no—
176D4—1722no—
177D4—1724no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—42no—
181C2×C4—3442no—
182C2×C4—1721no—
183C2×C4C2×(C2×D43)⋊C411yescharacteristic
184C2×C4C4×C22⋊D4312yes—
185C2×C4#1306329411yescharacteristic
186C2×C4#1306329912yes—
187C8—44no—
188C8—3442no—
189C8—1722no—
190C22—21no—
191C22—22no—
192C22—3441no—
193C22—3442no—
194C22#1458277811yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—44no—
199C4—3441no—
200C4#1458307212yes—
201C2—41no—
202C2—6881no—
203C2#1913495712yes—
204C2#1913499811yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2987C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2987D43
hypocenterC43#9008
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2987

Complements

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

NH ≅ G/Ntype
2. #19133260C2semidirect
4. #19132493C2semidirect
5. C43×#2987C2semidirect
100. #2987D43semidirect
121. C43#9008semidirect

Maximal subgroups

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

subgroupindex
#191449432
#191332602
#191330632
#191324932
C43×#29872
#900843