Finite Group Databasebeta

← #28389124

Subgroups — #28389124

Order 14464.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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#20299155C211yesmaximal, characteristic
2#20298655C211yesmaximal, characteristic
3#20298334C214yesmaximal
4#383×C113C211yesmaximal, characteristic
5#16813622C411yescharacteristic, complemented
6#16813622C411yescharacteristic, complemented
7#16813614—21no—
8#16813601—21no—
9#16813601C2212yes—
10C4×Dic226—21no—
11C4×Dic226C412yescomplemented
12#16813581—21no—
13C4⋊#11744751—21no—
14C22⋊#11744751C2212yes—
15#16813533—21no—
16C2×C42×C113C2211yescharacteristic
17#95×C113—21no—
18#95×C113—21no—
19#95×C113C2212yes—
20C2×Dic226—21no—
21C2×Dic226C2×C412yes—
22C2×#11744751—22no—
23C4⋊Dic113—21no—
24C4⋊Dic113—21no—
25C4⋊Dic113—21no—
26C4⋊Dic113C2×C412yes—
27#14268626—22no—
28#14268626—22no—
29C22⋊Dic113—22no—
30C4×Dic113—22no—
31C22×C4×C113—22no—
32C22×C4×C113D411yescharacteristic
33C22×C4×C113D411yescharacteristic
34C22×C4×C113C2311yescharacteristic
35C42×C113C2×C411yescharacteristic
36C42×C113C2×C411yescharacteristic
37C42×C113D411yescharacteristic
38C42×C113D411yescharacteristic
39C23×C113C2×D411yescharacteristic
40C2×C4×C113—22no—
41C2×C4×C113—41no—
42C2×C4×C113—41no—
43C2×C4×C113—42no—
44C2×C4×C113—42no—
45C2×C4×C113—42no—
46C2×C4×C113C22⋊C411yescharacteristic
47C2×C4×C113C22⋊C411yescharacteristic
48C2×C4×C113C22⋊C411yescharacteristic
49C2×C4×C113C22⋊C411yescharacteristic
50C2×C4×C113C22×C411yescharacteristic
51C2×C4×C113C2×D411yescharacteristic
52C2×Dic113—22no—
53C2×Dic113—22no—
54Dic226—42no—
55Dic226—42no—
56#11744751—42no—
57C22×C113—21no—
58C22×C113—21no—
59C22×C113C2×C22⋊C411yescharacteristic
60C22×C113#13712yes—
61C4×C113—21no—
62C4×C113—21no—
63C4×C113—21no—
64C4×C113—21no—
65C4×C113—21no—
66C4×C113—21no—
67C4×C113—82no—
68Dic113—42no—
69Dic113—42no—
70C2×C113—22no—
71C2×C113#41011yescharacteristic
72C2×C113#41911yescharacteristic
73C2×C113#42111yescharacteristic
74#1515—1131nomaximal, Sylow
75C113#151511yescharacteristic, complemented, Sylow
76#533—1131no—
77#432—1131no—
78#383D11311yescharacteristic
79#328—1134no—
80C4⋊Q8—1131no—
81C4⋊Q8—1131no—
82#125—2261no—
83C22⋊Q8—1132no—
84C22⋊Q8—2261no—
85C4×Q8—1132no—
86C4×Q8—2261no—
87#117—2261no—
88C2×C42C2×D11311yescharacteristic
89C4⋊C8—2261no—
90C22⋊C8—1132no—
91#97—2261no—
92#95—21no—
93#95—21no—
94#95C2×D11312yes—
95C2×Q8—1132no—
96C2×Q8—2261no—
97C22×C4—22no—
98C22×C4C22⋊D11311yescharacteristic
99C22×C4C22⋊D11311yescharacteristic
100C22×C4C22×D11311yescharacteristic
101C2×C8—2262no—
102C4⋊C4—1132no—
103C4⋊C4—2261no—
104C4⋊C4—2261no—
105C4⋊C4—2262no—
106C4⋊C4—2261no—
107C4⋊C4—2262no—
108C22⋊C4—2262no—
109C42—2262no—
110C42C4×D11311yescharacteristic
111C42C4×D11311yescharacteristic
112C42D45211yescharacteristic
113C42D45211yescharacteristic
114C23C2×C22⋊D11311yescharacteristic
115Q8—4522no—
116Q8—4522no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4—2262no—
124C2×C4—2262no—
125C2×C4#1426862411yescharacteristic
126C2×C4#1426862411yescharacteristic
127C2×C4#1426862411yescharacteristic
128C2×C4#1426862411yescharacteristic
129C2×C4C2×C4×D11311yescharacteristic
130C2×C4C2×D45211yescharacteristic
131C8—4522no—
132C22—21no—
133C22—21no—
134C22C2×#1426862411yescharacteristic
135C22#1681365212yes—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—82no—
143C4—4522no—
144C4—4522no—
145C2—22no—
146C2#2029857111yescharacteristic
147C2#2029860611yescharacteristic
148C2#2029861611yescharacteristic
subgroupG/H
centerC22C2×#14268624
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#383×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC23×C113C2×D4
cosocleC22×C4×C113C23
hypercenter#383D113
hypocenterC113#1515
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
5. #16813622C4semidirect
6. #16813622C4semidirect
11. C4×Dic226C4semidirect
75. C113#1515semidirect

Maximal subgroups

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

subgroupindex
#202991552
#202986552
#202983342
#383×C1132
#1515113