Finite Group Databasebeta

← #28389710

Subgroups — #28389710

Order 14464.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299305C211yesmaximal, characteristic
2#20298978C211yesmaximal, characteristic, complemented
3#20298894C211yesmaximal, characteristic, complemented
4#20298888C211yesmaximal, characteristic
5#20298346C211yesmaximal, characteristic, complemented
6#20298330C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic
8C2×Dic452—22no—
9#16813622C2211yescharacteristic
10#16813622C2211yescharacteristic
11#16813613—21no—
12#16813601—21no—
13#16813599—22no—
14C4×Dic226C2211yescharacteristic
15D4×Dic113—21no—
16C2×C4⋊Dic113—21no—
17#16813556—21no—
18#16813553—21no—
19C4⋊#11744751C2211yescharacteristic
20#16813547—21no—
21#16813543—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—21no—
26C2×Dic226D411yescharacteristic
27C2×Dic226D412yes—
28C22×Dic113—22no—
29Dic452—44no—
30C2×#11744751—21no—
31C4⋊Dic113—22no—
32C4⋊Dic113—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113D411yescharacteristic
37#14268626—22no—
38#14268626—21no—
39C22⋊Dic113—22no—
40C4×Dic113—21no—
41C2×D4×C113D411yescharacteristic
42C22×C4×C113—21no—
43C2×C8×C113—21no—
44C2×C8×C113—21no—
45C4⋊C4×C113D411yescharacteristic
46C22⋊C4×C113—21no—
47C42×C113C2311yescharacteristic
48C23×C113—21no—
49D4×C113—21no—
50D4×C113Q1612yescomplemented
51C2×C4×C113—21no—
52C2×C4×C113—41no—
53C2×C4×C113—41no—
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—22no—
60C2×Dic113—41no—
61C2×Dic113—82no—
62Dic226—21no—
63Dic226—21no—
64Dic226—42no—
65Dic226—42no—
66C8×C113—22no—
67C8×C113—41no—
68#11744751—41no—
69C22×C113—22no—
70C22×C113—41no—
71C22×C113—41no—
72C22×C113#12011yescharacteristic
73C4×C113—21no—
74C4×C113—41no—
75C4×C113C2×Q1611yescharacteristic
76C4×C113#13511yescharacteristic
77C4×C113#13711yescharacteristic
78C4×C113#13711yescharacteristic
79Dic113—41no—
80Dic113—42no—
81Dic113—41no—
82Dic113—81no—
83C2×C113—42no—
84C2×C113#45111yescharacteristic
85C2×C113#45211yescharacteristic
86C2×C113#45311yescharacteristic
87#1632—1131nomaximal, Sylow
88C113#163211yescharacteristic, complemented, Sylow
89#554—1131no—
90#494—1131no—
91#477—1131no—
92#476—1131no—
93#333—1131no—
94Q8⋊C8—1131no—
95D4⋊C8D11311yescharacteristic
96C2×Q16—2262no—
97C4⋊Q8—1131no—
98C4⋊Q8—1131no—
99#125—2261no—
100C22⋊Q8—2262no—
101C22⋊Q8—2261no—
102C4×Q8—1131no—
103C4×D4—2261no—
104C4×D4C2×D11311yescharacteristic
105C2×C4⋊C4—2261no—
106#107—2261no—
107#106—2261no—
108C4⋊C8—1131no—
109C4⋊C8C2×D11311yescharacteristic
110#103—2261no—
111#102—2261no—
112C4×C8C2×D11311yescharacteristic
113C2×Q8—1132no—
114C2×Q8—1131no—
115C2×Q8—2261no—
116C2×D4D45211yescharacteristic
117C22×C4—21no—
118C22×C4—2262no—
119Q16—4524no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—2261no—
123C4⋊C4—1131no—
124C4⋊C4—2262no—
125C4⋊C4—2262no—
126C4⋊C4—2261no—
127C4⋊C4—2261no—
128C4⋊C4—2261no—
129C4⋊C4—2261no—
130C4⋊C4—2261no—
131C4⋊C4D45211yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2262no—
134C42—2261no—
135C42C22×D11311yescharacteristic
136C23—21no—
137Q8—4522no—
138Q8—4522no—
139Q8—2261no—
140Q8—2261no—
141D4—21no—
142D4Dic45212yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—9042no—
147C2×C4—4521no—
148C2×C4—2261no—
149C2×C4—2261no—
150C2×C4—2262no—
151C2×C4D4×D11311yescharacteristic
152C2×C4D4×D11311yescharacteristic
153C2×C4C2×D45211yescharacteristic
154C8—22no—
155C8—41no—
156C8—4521no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1681359211yescharacteristic
161C4—21no—
162C4—41no—
163C4—9041no—
164C4—4521no—
165C4—4521no—
166C4—4522no—
167C4C2×Dic45211yescharacteristic
168C4#1681364111yescharacteristic
169C4#1681365111yescharacteristic
170C4#1681365511yescharacteristic
171C2—42no—
172C2#2029875611yescharacteristic
173C2#2029876111yescharacteristic
174C2#2029876711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radicalC2×D4×C113D4
hypercenterD4⋊C8D113
hypocenterC113#1632
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20298978C2semidirect
3. #20298894C2semidirect
5. #20298346C2semidirect
6. #20298330C2semidirect
50. D4×C113Q16semidirect
88. C113#1632semidirect
142. D4Dic452semidirect

Maximal subgroups

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

subgroupindex
#202993052
#202989782
#202988942
#202988882
#202983462
#202983302
D4⋊C8×C1132
#1632113