Finite Group Databasebeta

← #25001376

Subgroups — #25001376

Order 11008.

310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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#19135427C211yesmaximal, characteristic
2#19133245C212yesmaximal
3#19132492C212yesmaximal, complemented
4#19132424C211yesmaximal, characteristic, complemented
5C43×#1832C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7#14582952C2212yes—
8#14582923C2211yescharacteristic
9C2×#13063253—22no—
10#14582646—22no—
11#14582642—22no—
12C2×C4⋊C8×C43C2212yes—
13C43×#376C2211yescharacteristic
14C43×#336—22no—
15C2×#10621898—21no—
16C2×#10621877—21no—
17#13063325D411yescharacteristic
18#13063322D411yescharacteristic
19#13063313—21no—
20#13063299—22no—
21C4×D172—22no—
22C4⋊(C43⋊C8)—22no—
23C4⋊(C43⋊C8)—22no—
24#13063253—44no—
25C22⋊(C43⋊C8)—22no—
26C4×C43⋊C8—22no—
27C22×C8×C43—22no—
28C2×C42×C43D412yes—
29C2×C42×C43C2311yescharacteristic
30C4⋊C8×C43—22no—
31C4⋊C8×C43—22no—
32#95×C43—22no—
33C22×C4×C43—22no—
34C22×C4×C43C2×D411yescharacteristic
35C22×C4×C43#4112yes—
36C2×C22⋊D43—41no—
37#10621898—42no—
38#10621898—42no—
39C2×D172—21no—
40C2×D172—22no—
41C2×C4×D43—41no—
42C2×Dic86—21no—
43C2×C8×C43—42no—
44C2×C8×C43—42no—
45C2×C8×C43—42no—
46C42×C43—22no—
47C42×C43—22no—
48C42×C43C2×D411yescharacteristic
49C42×C43#4111yescharacteristic
50C42×C43#4112yes—
51(C2×D43)⋊C4—42no—
52C4⋊Dic43—22no—
53#10621877—42no—
54C2×C43⋊C8—42no—
55C2×C43⋊C8—41no—
56C23×C43#12311yescharacteristic
57C22×D43—41no—
58C2×C4×C43—42no—
59C2×C4×C43—44no—
60C2×C4×C43—42no—
61C2×C4×C43#12111yescharacteristic
62C2×C4×C43#12312yes—
63C2×C4×C43#12411yescharacteristic
64C2×C4×C43#12612yes—
65C2×C4×C43#13512yes—
66C2×C4×C43AGL(1,ℤ/8)12yes—
67C22⋊D43—82no—
68C2×Dic43—41no—
69D172—42no—
70D172—82no—
71C4×D43—81no—
72C4×D43—81no—
73Dic86—42no—
74C8×C43—82no—
75C43⋊C8—82no—
76C43⋊C8—81no—
77#10629—431nomaximal, Sylow
78C22×C43—22no—
79C22×C43#39711yescharacteristic
80C22×C43#48212yes—
81C2×D43—81no—
82C2×D43—82no—
83C4×C43—22no—
84C4×C43—22no—
85C4×C43—82no—
86C4×C43#46312yes—
87C4×C43#48811yescharacteristic
88C4×C43#49011yescharacteristic
89Dic43—81no—
90#1963—431no—
91#1832D4311yescharacteristic, complemented
92#1540—432no—
93#1301—432no—
94#1274—431no—
95C2×C43—22no—
96C2×C43#207311yescharacteristic
97C2×C43#208012yes—
98D43—161no—
99#532—431no—
100#431—432no—
101#423—431no—
102C2×C4⋊C8C2×D4312yes—
103C2×#104—862no—
104#376C2×D4311yescharacteristic
105#336—22no—
106#332—862no—
107#331—862no—
108C43#1062911yescharacteristic, complemented, Sylow
109C2×#41—861no—
110C2×M16—861no—
111C22×C8—22no—
112C4⋊Q8—431no—
113#127—431no—
114#124—861no—
115#121—862no—
116C4×D4—862no—
117C2×C42C22⋊D4312yes—
118C2×C42C22×D4311yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—862no—
122C4⋊C8—862no—
123#104—1724no—
124C22⋊C8—862no—
125C4×C8—862no—
126#95—22no—
127#41—1722no—
128#41—1722no—
129C2×Q8—861no—
130C2×D4—861no—
131C2×D4—862no—
132C2×D4—1721no—
133C22×C4—22no—
134C22×C4—1721no—
135C22×C4#1062189812yes—
136C22×C4C2×C22⋊D4311yescharacteristic
137M16—1722no—
138C2×C8—42no—
139C2×C8—42no—
140C2×C8—42no—
141C2×C8—1722no—
142C2×C8—1721no—
143C4⋊C4—862no—
144C22⋊C4—1722no—
145C42—22no—
146C42—22no—
147C42D4×D4311yescharacteristic
148C42#1062190011yescharacteristic
149C42#1062190212yes—
150C23—1721no—
151C23#1306330811yescharacteristic
152Q8—1722no—
153D4—3442no—
154D4—3442no—
155D4—1722no—
156C2×C4—42no—
157C2×C4—44no—
158C2×C4—42no—
159C2×C4—3441no—
160C2×C4—3441no—
161C2×C4—1721no—
162C2×C4#1306329611yescharacteristic
163C2×C4#1306331012yes—
164C2×C4#1306331411yescharacteristic
165C2×C4#1306332012yes—
166C2×C4#1306334512yes—
167C2×C4#1306335012yes—
168C8—82no—
169C8—3442no—
170C8—3441no—
171C22—22no—
172C22—3441no—
173C22—3442no—
174C22#1458282511yescharacteristic
175C22#1458322312yes—
176C4—22no—
177C4—22no—
178C4—82no—
179C4—3441no—
180C4#1458311112yes—
181C4#1458325611yescharacteristic
182C4#1458326511yescharacteristic
183C2—22no—
184C2—6881no—
185C2#1913600911yescharacteristic
186C2#1913604612yes—
subgroupG/H
centerC2×C4#13063314
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1832C2
socleC22×C43#397
prime radical#14583449C22
hypercenter#1832D43
hypocenterC43#10629
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
3. #19132492C2semidirect
4. #19132424C2semidirect
5. C43×#1832C2semidirect
91. #1832D43semidirect
108. C43#10629semidirect

Maximal subgroups

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

subgroupindex
#191354272
#191332452
#191324922
#191324242
C43×#18322
#1062943