Finite Group Databasebeta

← #28391099

Subgroups — #28391099

Order 14464.

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

normal subgroups only

This group has 344 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#20299365C211yesmaximal, characteristic, complemented
2#20299162C211yesmaximal, characteristic
3#20298602C212yesmaximal, complemented
4#20298354C212yesmaximal, complemented
5#410×C113C211yesmaximal, characteristic, complemented
6C22×D452C2211yescharacteristic
7#16813629—24no—
8C2×#14268631—22no—
9C2×#14268631C2212yes—
10#16813618C412yescomplemented
11#16813611C412yescomplemented
12#16813596—22no—
13#16813590—22no—
14#16813581C2211yescharacteristic
15#16813542—24no—
16C2×#41×C113C2211yescharacteristic
17#117×C113C2212yes—
18#99×C113—22no—
19C23×D113—21no—
20C2×D452—22no—
21C2×D452—22no—
22C2×D452—21no—
23C2×D452C2×C412yes—
24C2×C22⋊D113—24no—
25#14268631—24no—
26#14268631—22no—
27#14268631—22no—
28C2×#11744751—24no—
29C2×#11744751D414yescomplemented
30C4⋊Dic113—21no—
31C22⋊Dic113—21no—
32#14268624—24no—
33C4×Dic113C2×C412yes—
34#41×C113—22no—
35#41×C113—22no—
36C2×Q8×C113C2×C411yescharacteristic
37C2×D4×C113C2×C411yescharacteristic
38C2×D4×C113D412yes—
39C22×C4×C113D412yes—
40C22×C4×C113C2311yescharacteristic
41C4⋊C4×C113—22no—
42C22⋊C4×C113—22no—
43C42×C113—22no—
44C23×C113C22⋊C412yes—
45C23×C113C2×D411yescharacteristic
46C22×D113—22no—
47C22×D113—42no—
48C22×D113—82no—
49Q8×C113—22no—
50D4×C113—24no—
51D4×C113—22no—
52C2×C4×C113—22no—
53C2×C4×C113—22no—
54C2×C4×C113—42no—
55C2×C4×C113C22⋊C412yes—
56C2×C4×C113C22×C411yescharacteristic
57C2×C4×C113C2×D412yes—
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113#4112yes—
60C22⋊D113—84no—
61C2×Dic113—22no—
62D452—24no—
63D452—41no—
64D452—41no—
65#11744751—24no—
66C22×C113—22no—
67C22×C113—41no—
68C22×C113—42no—
69C22×C113C2×C22⋊C411yescharacteristic
70C22×C113#12112yes—
71C2×D113—44no—
72C2×D113—42no—
73C2×D113—84no—
74C4×C113—22no—
75C4×C113—82no—
76C4×C113C4×D412yes—
77C4×C113#12011yescharacteristic
78C4×C113#12311yescharacteristic
79Dic113—42no—
80C2×C113—21no—
81C2×C113—22no—
82C2×C113—42no—
83C2×C113#38611yescharacteristic
84D113—82no—
85#1910—1131nomaximal, Sylow
86C113#191011yescharacteristic, complemented, Sylow
87#568—1131no—
88#535—1131no—
89#418—1132no—
90#410D11311yescharacteristic, complemented
91H(3,ℤ/4)—1132no—
92C2×#41C2×D11311yescharacteristic
93C22×D4—1131no—
94#131—2264no—
95C2×M16—1132no—
96C2×M16—2262no—
97#127—1132no—
98#124—1132no—
99#121—2262no—
100#120—2262no—
101#117—1131no—
102#117C2×D11312yes—
103#102—2264no—
104#99—22no—
105C24—2261no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D11311yescharacteristic
109C2×D4—1132no—
110C2×D4—2264no—
111C2×D4—2262no—
112C2×D4—2261no—
113C2×D4—2262no—
114C2×D4C4×D11311yescharacteristic
115C2×D4C22⋊D11312yes—
116C22×C4D45212yes—
117C22×C4C22×D11311yescharacteristic
118M16—2264no—
119M16—2262no—
120M16—2262no—
121C2×C8—1134no—
122C2×C8—2264no—
123C4⋊C4—22no—
124C4⋊C4—2261no—
125C22⋊C4—22no—
126C22⋊C4—2261no—
127C22⋊C4—2264no—
128C42—22no—
129C42—1132no—
130C23—9042no—
131C23—4522no—
132C23—2262no—
133C23#1426862412yes—
134C23C2×C22⋊D11311yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—9044no—
139D4—4521no—
140D4—4521no—
141D4—2264no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—2262no—
146C2×C4#1426862412yes—
147C2×C4C2×C4×D11311yescharacteristic
148C2×C4D4×D11312yes—
149C2×C4C2×D45211yescharacteristic
150C2×C4#1426864612yes—
151C8—2264no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—9044no—
156C22—4524no—
157C22—4522no—
158C22C2×#1426862411yescharacteristic
159C22#1681359412yes—
160C4—22no—
161C4—82no—
162C4—4522no—
163C4#1681358212yes—
164C4#1681359211yescharacteristic
165C4#1681360611yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—9042no—
170C2#2029847511yescharacteristic
subgroupG/H
centerC2#20298475
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#410×C113C2
socleC2×C113#386
prime radical#20299162C2
cosocleC22×C4×C113C23
hypercenter#410D113
hypocenterC113#1910
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #20299365C2semidirect
3. #20298602C2semidirect
4. #20298354C2semidirect
5. #410×C113C2semidirect
10. #16813618C4semidirect
11. #16813611C4semidirect
29. C2×#11744751D4semidirect
86. C113#1910semidirect
90. #410D113semidirect

Maximal subgroups

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

subgroupindex
#202993652
#202991622
#202986022
#202983542
#410×C1132
#1910113