Finite Group Databasebeta

← #28391104

Subgroups — #28391104

Order 14464.

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

normal subgroups only

This group has 362 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#20299165C211yesmaximal, characteristic
2#20299073C211yesmaximal, characteristic, complemented
3#20298614C212yesmaximal, complemented
4#20298355C212yesmaximal, complemented
5C2×#100×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2211yescharacteristic
7#16813618C412yescomplemented
8#16813609C412yescomplemented
9#16813593—22no—
10#16813591—22no—
11D4×Dic113—24no—
12#16813581C2211yescharacteristic
13#16813581C2212yes—
14C2×C22⋊Dic113—22no—
15#16813548—24no—
16C22×D4×C113C2211yescharacteristic
17C2×M16×C113C2212yes—
18#100×C113—22no—
19#14268647—22no—
20#14268647—22no—
21C2×Dic226C2×C411yescharacteristic, complemented
22C2×D452C2×C411yescharacteristic, complemented
23C2×C22⋊D113—21no—
24C2×C22⋊D113—24no—
25C22×Dic113—24no—
26C2×C4×D113—21no—
27C4⋊Dic113—22no—
28C4⋊Dic113—21no—
29C22⋊Dic113—24no—
30C22⋊Dic113—24no—
31C22⋊Dic113—22no—
32C22⋊Dic113—21no—
33C4×Dic113C2×C412yescomplemented
34C4×Dic113D414yescomplemented
35C24×C113D412yes—
36C2×D4×C113—22no—
37C2×D4×C113—22no—
38C2×D4×C113C2×C412yes—
39C2×D4×C113D412yes—
40C22×C4×C113C2311yescharacteristic
41M16×C113—22no—
42M16×C113—22no—
43C2×C8×C113—22no—
44C23×C113—22no—
45C23×C113—22no—
46C23×C113—82no—
47C23×C113C22⋊C414yes—
48C23×C113C2×D411yescharacteristic
49C22×D113—21no—
50D4×C113—24no—
51D4×C113—24no—
52C2×C4×C113C22×C411yescharacteristic
53C2×C4×C113C2×D412yes—
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113#4112yes—
56C22⋊D113—41no—
57C22⋊D113—41no—
58C22⋊D113—84no—
59C2×Dic113—22no—
60C2×Dic113—21no—
61C2×Dic113—24no—
62C2×Dic113—84no—
63D452—22no—
64C4×D113—42no—
65Dic226—22no—
66C8×C113—42no—
67C22×C113—24no—
68C22×C113—41no—
69C22×C113—44no—
70C22×C113—44no—
71C22×C113—82no—
72C22×C113C2×C22⋊C411yescharacteristic
73C22×C113#12011yescharacteristic
74C22×C113#12311yescharacteristic
75C2×D113—42no—
76C2×D113—41no—
77C4×C113C4×D412yes—
78C4×C113#12112yes—
79Dic113—44no—
80Dic113—42no—
81Dic113—41no—
82C2×C113—21no—
83C2×C113—21no—
84C2×C113—21no—
85C2×C113—44no—
86C2×C113#38611yescharacteristic
87D113—81no—
88#1911—1131nomaximal, Sylow
89C113#191111yescharacteristic, complemented, Sylow
90#535—1131no—
91#518—1131no—
92#421—1132no—
93C2×#100D11311yescharacteristic, complemented
94H(3,ℤ/4)—1132no—
95C2×#41—1131no—
96C22×D4C2×D11311yescharacteristic
97C2×M16C2×D11312yes—
98#127—1132no—
99#124—1132no—
100#121—2262no—
101#120—2262no—
102C4×D4—2264no—
103#117—1132no—
104#117—1131no—
105C2×C22⋊C4—2262no—
106#104—2264no—
107#100—22no—
108C24D45212yes—
109#41—2262no—
110#41—2262no—
111C2×Q8—1131no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—1131no—
115C2×D4—2264no—
116C2×D4—2261no—
117C2×D4C4×D11312yes—
118C2×D4C22⋊D11312yes—
119C22×C4—2264no—
120C22×C4—2261no—
121C22×C4C22×D11311yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—2262no—
126C4⋊C4—2261no—
127C22⋊C4—2264no—
128C22⋊C4—2264no—
129C22⋊C4—2262no—
130C22⋊C4—2261no—
131C42—1132no—
132C42—1134no—
133C23—22no—
134C23—22no—
135C23—82no—
136C23—2261no—
137C23#1426862414yes—
138C23C2×D45211yescharacteristic
139Q8—2262no—
140D4—24no—
141D4—24no—
142D4—9044no—
143D4—4521no—
144D4—4521no—
145D4—2262no—
146C2×C4—9044no—
147C2×C4—4522no—
148C2×C4—2262no—
149C2×C4—2261no—
150C2×C4—2264no—
151C2×C4C2×C4×D11311yescharacteristic
152C2×C4D4×D11312yes—
153C2×C4C2×C22⋊D11311yescharacteristic
154C2×C4#1426864612yes—
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—4522no—
162C22—4521no—
163C22C2×#1426862411yescharacteristic
164C22#1681359211yescharacteristic
165C22#1681360611yescharacteristic
166C4—4524no—
167C4—4522no—
168C4—4521no—
169C4#1681358212yes—
170C4#1681359412yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—9041no—
176C2#2029847511yescharacteristic
subgroupG/H
centerC2#20298475
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#100×C113C2
socleC2×C113#386
prime radical#20299165C2
cosocleC22×C4×C113C23
hypercenterC2×#100D113
hypocenterC113#1911
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #20299073C2semidirect
3. #20298614C2semidirect
4. #20298355C2semidirect
5. C2×#100×C113C2semidirect
7. #16813618C4semidirect
8. #16813609C4semidirect
21. C2×Dic226C2×C4semidirect
22. C2×D452C2×C4semidirect
33. C4×Dic113C2×C4semidirect
34. C4×Dic113D4semidirect
89. C113#1911semidirect
93. C2×#100D113semidirect

Maximal subgroups

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

subgroupindex
#202991652
#202990732
#202986142
#202983552
C2×#100×C1132
#1911113