Finite Group Databasebeta

← #28391096

Subgroups — #28391096

Order 14464.

312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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#20299169C211yesmaximal, characteristic
2#20298608C212yesmaximal, complemented
3#20298572C211yesmaximal, characteristic
4#20298355C212yesmaximal, complemented
5#568×C113C211yesmaximal, characteristic
6C22×Dic226C2211yescharacteristic
7#16813620C412yescomplemented
8#16813609C412yescomplemented
9#16813603—22no—
10#16813601—22no—
11#16813581C2212yes—
12#16813581C2211yescharacteristic
13#16813547—24no—
14#16813537—22no—
15C2×#41×C113C2211yescharacteristic
16#131×C113—24no—
17C2×M16×C113—22no—
18C2×M16×C113C2212yes—
19C2×Dic226—22no—
20C2×Dic226—22no—
21C2×Dic226—21no—
22C2×Dic226C2×C412yes—
23C22×Dic113—21no—
24C4⋊Dic113—21no—
25C4⋊Dic113—22no—
26#14268626—24no—
27C22⋊Dic113—24no—
28C22⋊Dic113—21no—
29C22⋊Dic113—22no—
30C4×Dic113—22no—
31C4×Dic113C2×C412yes—
32#41×C113—22no—
33#41×C113—22no—
34C2×Q8×C113C2×C411yescharacteristic
35C2×D4×C113C2×C411yescharacteristic
36C2×D4×C113D412yes—
37C22×C4×C113D412yes—
38C22×C4×C113C2311yescharacteristic
39M16×C113—24no—
40M16×C113—22no—
41M16×C113—22no—
42C2×C8×C113—24no—
43C2×C8×C113D414yes—
44C23×C113C22⋊C412yes—
45C23×C113C2×D411yescharacteristic
46Q8×C113—22no—
47D4×C113—24no—
48D4×C113—22no—
49C2×C4×C113—22no—
50C2×C4×C113—22no—
51C2×C4×C113C22⋊C412yes—
52C2×C4×C113C22×C411yescharacteristic
53C2×C4×C113C2×D412yes—
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113#4112yes—
56C2×Dic113—22no—
57C2×Dic113—22no—
58C2×Dic113—42no—
59C2×Dic113—42no—
60Dic226—24no—
61Dic226—41no—
62Dic226—41no—
63C8×C113—24no—
64C22×C113—22no—
65C22×C113—41no—
66C22×C113—42no—
67C22×C113C2×C22⋊C411yescharacteristic
68C22×C113#12112yes—
69C4×C113—22no—
70C4×C113C4×D412yes—
71C4×C113#12011yescharacteristic
72C4×C113#12311yescharacteristic
73Dic113—42no—
74Dic113—42no—
75Dic113—82no—
76C2×C113—21no—
77C2×C113—22no—
78C2×C113—42no—
79C2×C113#38611yescharacteristic
80#1909—1131nomaximal, Sylow
81C113#190911yescharacteristic, complemented, Sylow
82#568D11311yescharacteristic
83#536—1131no—
84#419—1132no—
85#410—1131no—
86H(3,ℤ/4)—1132no—
87C2×#41C2×D11311yescharacteristic
88C22×Q8—1131no—
89#131—24no—
90C2×M16—22no—
91C2×M16C2×D11312yes—
92C4⋊Q8—1132no—
93#124—1132no—
94#123—2262no—
95C22⋊Q8—2262no—
96#117—1131no—
97#117—1132no—
98#103—2264no—
99#99—2262no—
100#41—22no—
101#41—22no—
102C2×Q8—1132no—
103C2×Q8—2262no—
104C2×Q8—2262no—
105C2×Q8—2261no—
106C2×Q8C4×D11311yescharacteristic
107C2×D4C4×D11311yescharacteristic
108C2×D4D45212yes—
109C22×C4—2261no—
110C22×C4C22⋊D11312yes—
111C22×C4C22×D11311yescharacteristic
112M16—24no—
113M16—22no—
114M16—22no—
115C2×C8—24no—
116C2×C8C22⋊D11314yes—
117C4⋊C4—2262no—
118C4⋊C4—2264no—
119C4⋊C4—2261no—
120C22⋊C4—2262no—
121C22⋊C4—2264no—
122C22⋊C4—2261no—
123C42—1132no—
124C42—2262no—
125C23#1426862412yes—
126C23C2×D45211yescharacteristic
127Q8—22no—
128Q8—4521no—
129Q8—4521no—
130Q8—2264no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—4522no—
136C2×C4—4522no—
137C2×C4—2262no—
138C2×C4—2262no—
139C2×C4#1426862412yes—
140C2×C4C2×C4×D11311yescharacteristic
141C2×C4C2×C22⋊D11312yes—
142C2×C4C2×C22⋊D11311yescharacteristic
143C2×C4#1426864712yes—
144C8—24no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×#1426862411yescharacteristic
149C22#1681359612yes—
150C4—22no—
151C4—9042no—
152C4—4522no—
153C4—4522no—
154C4C4×C22⋊D11312yes—
155C4#1681359111yescharacteristic
156C4#1681360511yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#2029847711yescharacteristic
subgroupG/H
centerC2#20298477
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#568×C113C2
socleC2×C113#386
prime radicalC2×#41×C113C22
cosocleC22×C4×C113C23
hypercenter#568D113
hypocenterC113#1909
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #20298608C2semidirect
4. #20298355C2semidirect
7. #16813620C4semidirect
8. #16813609C4semidirect
81. C113#1909semidirect

Maximal subgroups

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

subgroupindex
#202991692
#202986082
#202985722
#202983552
#568×C1132
#1909113