Finite Group Databasebeta

← #28391323

Subgroups — #28391323

Order 14464.

208 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#16813558C211yesmaximal, characteristic
2#20298625C212yesmaximal
3C2×C8×Dic113C211yesmaximal, characteristic
4#20298357C212yesmaximal
5#427×C113C211yesmaximal, characteristic
6C2×#14268631C2212yes—
7C22×#11744751C2211yescharacteristic
8C2×C4×Dic113C2211yescharacteristic
9#16813558—22no—
10C4⋊#11744751—24no—
11C8×Dic113—22no—
12C22×C8×C113C2211yescharacteristic
13#117×C113C2212yes—
14#107×C113C412yescomplemented
15#106×C113C412yescomplemented
16C22×Dic113—21no—
17#14268631—22no—
18#14268631—22no—
19C2×#11744751—21no—
20C2×#11744751—21no—
21C2×#11744751—22no—
22C2×#11744751D412yes—
23C4×Dic113—21no—
24C4×Dic113Q812yes—
25C22×C4×C113C2311yescharacteristic
26C2×C8×C113C2×C411yescharacteristic
27C2×C8×C113C2×C411yescharacteristic
28C2×C8×C113D412yes—
29C2×C8×C113Q812yes—
30C4⋊C4×C113C2×C414yes—
31C22⋊C4×C113—22no—
32C42×C113—22no—
33C23×C113#4111yescharacteristic
34C2×C4×C113—24no—
35C2×C4×C113C22×C411yescharacteristic
36C2×C4×C113C2×D411yescharacteristic
37C2×C4×C113C2×D411yescharacteristic
38C2×C4×C113C2×Q811yescharacteristic
39C2×C4×C113C2×Q811yescharacteristic
40C2×C4×C113#4111yescharacteristic
41C2×Dic113—24no—
42C2×Dic113—22no—
43C8×C113C4⋊C412yes—
44C8×C113C4⋊C412yes—
45#11744751—22no—
46#11744751—42no—
47C22×C113—22no—
48C22×C113C4×D411yescharacteristic
49C22×C113C22⋊Q811yescharacteristic
50C22×C113#12511yescharacteristic
51C4×C113—44no—
52C4×C113C2×C4⋊C411yescharacteristic
53C4×C113C4×Q811yescharacteristic
54C4×C113#12111yescharacteristic
55C4×C113C4⋊Q811yescharacteristic
56Dic113—24no—
57C2×C113—21no—
58C2×C113—21no—
59C2×C113#38911yescharacteristic
60C2×C113#44312yes—
61#1945—1131nomaximal, Sylow
62C113#194511yescharacteristic, complemented, Sylow
63C2×#108—1131no—
64#427D11311yescharacteristic
65#424—1132no—
66C2×C4×C8—1131no—
67#339—1132no—
68C2×M16—1132no—
69C22×C8—1131no—
70C22×C8C2×D11311yescharacteristic
71#117C2×D11312yes—
72C2×C42—1131no—
73#108—2262no—
74#107Dic11312yescomplemented
75#106Dic11312yescomplemented
76C4⋊C8—2264no—
77C4×C8—2262no—
78C22×C4—2261no—
79C22×C4C22×D11311yescharacteristic
80M16—2262no—
81M16—2262no—
82C2×C8—1132no—
83C2×C8—2262no—
84C2×C8—2261no—
85C2×C8—2261no—
86C2×C8Dic22612yes—
87C2×C8D45212yes—
88C2×C8C2×Dic11311yescharacteristic
89C2×C8C2×Dic11311yescharacteristic
90C4⋊C4C2×Dic11314yes—
91C22⋊C4—22no—
92C42—22no—
93C42—1132no—
94C42—2261no—
95C23#1426864611yescharacteristic
96C2×C4—24no—
97C2×C4—2264no—
98C2×C4—2262no—
99C2×C4C22×Dic11311yescharacteristic
100C2×C4D4×D11311yescharacteristic
101C2×C4C2×D45211yescharacteristic
102C2×C4Q8×D11311yescharacteristic
103C2×C4C2×Dic22611yescharacteristic
104C2×C4#1426864811yescharacteristic
105C8—4522no—
106C8—2262no—
107C8C4⋊Dic11312yes—
108C8C4⋊Dic11312yes—
109C22—22no—
110C22D4×Dic11311yescharacteristic
111C22#1681360211yescharacteristic
112C22#1681361311yescharacteristic
113C4—44no—
114C4—2264no—
115C4C2×C4⋊Dic11311yescharacteristic
116C4Q8×Dic11311yescharacteristic
117C4#1681359711yescharacteristic
118C4#1681362111yescharacteristic
119C2—21no—
120C2—21no—
121C2#2029849711yescharacteristic
122C2#2029871512yes—
subgroupG/H
centerC2×C4D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#427×C113C2
socleC22×C113C4×D4
prime radicalC23×C113#41
cosocleC22×C4×C113C23
hypercenter#427D113
hypocenterC113#1945
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
14. #107×C113C4semidirect
15. #106×C113C4semidirect
62. C113#1945semidirect
74. #107Dic113semidirect
75. #106Dic113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135582
#202986252
C2×C8×Dic1132
#202983572
#427×C1132
#1945113