Finite Group Databasebeta

← #24991913

Subgroups — #24991913

Order 11008.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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#19145105C211yesmaximal, characteristic
2#19133190C211yesmaximal, characteristic
3#19133015C212yesmaximal
4#19132431C212yesmaximal
5C43×#2986C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583302C412yes—
8#14583298—22no—
9#14583295C412yes—
10#14582935—22no—
11C4×#10621877C2212yes—
12C2×C4×C43⋊C8C2211yescharacteristic
13#14582641—22no—
14#14582629—22no—
15#14582629—22no—
16C43×#533C2211yescharacteristic
17C43×#446—22no—
18C8×Q8×C43—22no—
19C43×#433—22no—
20C43×#431C2212yes—
21C2×#10621877—22no—
22C22×C43⋊C8—21no—
23#13063325C2×C412yes—
24#13063317—21no—
25#13063304—22no—
26C4×Dic86—22no—
27#13063284—21no—
28#13063258—24no—
29#13063256—24no—
30#13063236—22no—
31C4×C43⋊C8—21no—
32C4×C43⋊C8—22no—
33C4×C43⋊C8C2×C411yescharacteristic
34C4×C43⋊C8C2×C411yescharacteristic
35C4⋊Q8×C43C2×C412yes—
36#125×C43D412yes—
37C22⋊Q8×C43—22no—
38C4×Q8×C43—22no—
39#117×C43D412yes—
40C2×C42×C43C2311yescharacteristic
41C4⋊C8×C43—24no—
42C4⋊C8×C43D412yes—
43C4⋊C8×C43D412yes—
44C22⋊C8×C43—22no—
45#97×C43—22no—
46C4×C8×C43—22no—
47C4×C8×C43—22no—
48C2×Q8×C43—22no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43#4112yes—
51C2×Dic86—22no—
52C2×C8×C43—22no—
53C2×C8×C43—22no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—24no—
56C4⋊C4×C43C22⋊C414yes—
57C22⋊C4×C43—22no—
58C42×C43—22no—
59C42×C43C22×C411yescharacteristic
60C42×C43C2×D411yescharacteristic
61C42×C43C2×D412yes—
62C22⋊Dic43—41no—
63C4⋊Dic43—22no—
64C4⋊Dic43—22no—
65Dic43⋊C4—42no—
66C4×Dic43—41no—
67#10621877—24no—
68#10621877—42no—
69C2×C43⋊C8—24no—
70C2×C43⋊C8—21no—
71C2×C43⋊C8—21no—
72C2×C43⋊C8—42no—
73C23×C43#12311yescharacteristic
74Q8×C43—42no—
75Q8×C43—42no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—24no—
80C2×C4×C43C2×C22⋊C411yescharacteristic
81C2×C4×C43C4×D412yes—
82C2×C4×C43#12011yescharacteristic
83C2×C4×C43#12112yes—
84C2×Dic43—42no—
85Dic86—42no—
86Dic86—42no—
87C8×C43—42no—
88C8×C43—42no—
89C43⋊C8—22no—
90C43⋊C8—22no—
91C43⋊C8—44no—
92#9068—431nomaximal, Sylow
93C22×C43—22no—
94C22×C43—21no—
95C22×C43#38611yescharacteristic
96C4×C43—22no—
97C4×C43—21no—
98C4×C43—44no—
99C4×C43#44312yes—
100C4×C43#44412yes—
101C4×C43#45612yes—
102Dic43—82no—
103#3160—431no—
104#2986D4311yescharacteristic
105#1526—431no—
106#1485—432no—
107#1278—432no—
108C2×C43—41no—
109C2×C43#187612yes—
110C2×C43#188611yescharacteristic
111#533—431no—
112#533C2×D4311yescharacteristic
113#500—432no—
114#499—862no—
115#498—432no—
116#446—22no—
117C8×Q8—22no—
118#433—22no—
119#431C2×D4312yes—
120#427—862no—
121C4×M16—432no—
122C2×C4×C8—431no—
123#330—862no—
124Q8⋊C8—862no—
125Q8⋊C8—862no—
126C43#906811yescharacteristic, complemented, Sylow
127C2×M16—862no—
128C22×C8—861no—
129C4⋊Q8—432no—
130C4⋊Q8C4×D4312yes—
131#125—861no—
132#125D17212yes—
133C22⋊Q8—22no—
134C22⋊Q8—862no—
135C4×Q8—22no—
136C4×Q8—862no—
137#117—861no—
138#117C22⋊D4312yes—
139C2×C42C22×D4311yescharacteristic
140#107—864no—
141#106—864no—
142C4⋊C8—24no—
143C4⋊C8C22⋊D4312yes—
144C4⋊C8C22⋊D4312yes—
145C22⋊C8—22no—
146#97—22no—
147#97—862no—
148C4×C8—22no—
149C4×C8—22no—
150C4×C8—431no—
151C4×C8—431no—
152C4×C8—861no—
153C4×C8—862no—
154C2×Q8—22no—
155C2×Q8—862no—
156C22×C4#1062189812yes—
157C22×C4C2×C22⋊D4311yescharacteristic
158M16—864no—
159M16—1722no—
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—864no—
163C2×C8—861no—
164C2×C8—861no—
165C2×C8—1722no—
166C4⋊C4—22no—
167C4⋊C4—24no—
168C4⋊C4—862no—
169C4⋊C4—862no—
170C4⋊C4—1722no—
171C4⋊C4(C2×D43)⋊C414yes—
172C22⋊C4—22no—
173C22⋊C4—1721no—
174C42—22no—
175C42—1721no—
176C42C2×C4×D4311yescharacteristic
177C42C2×D17211yescharacteristic
178C42C2×C22⋊D4312yes—
179C23#1306330811yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—1722no—
183Q8—1722no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—1722no—
189C2×C4C2×(C2×D43)⋊C411yescharacteristic
190C2×C4C4×C22⋊D4312yes—
191C2×C4#1306329411yescharacteristic
192C2×C4#1306329912yes—
193C8—42no—
194C8—42no—
195C8—862no—
196C8—862no—
197C8—1724no—
198C22—21no—
199C22—22no—
200C22#1458277811yescharacteristic
201C4—21no—
202C4—22no—
203C4—44no—
204C4—3442no—
205C4#1458301412yes—
206C4#1458301912yes—
207C4#1458308212yes—
208C2—41no—
209C2#1913492212yes—
210C2#1913498811yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2986C2
socleC22×C43#386
prime radicalC23×C43#123
cosocleC2×C42×C43C23
hypercenter#2986D43
hypocenterC43#9068
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2986

Complements

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

NH ≅ G/Ntype
126. C43#9068semidirect

Maximal subgroups

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

subgroupindex
#191451052
#191331902
#191330152
#191324312
C43×#29862
#906843