Finite Group Databasebeta

← #28390791

Subgroups — #28390791

Order 14464.

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

normal subgroups only

This group has 272 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
1#20299076C211yesmaximal, characteristic
2#20298640C212yesmaximal
3#20298505C211yesmaximal, characteristic
4#20298359C212yesmaximal
5C2×#101×C113C211yesmaximal, characteristic
6Q8×Dic113—22no—
7Q8×Dic113—22no—
8#16813581—22no—
9#16813581C2212yes—
10C2×C4⋊Dic113C2211yescharacteristic
11C2×C4×Dic113C2211yescharacteristic
12#16813556—22no—
13#16813554—22no—
14#16813529—22no—
15C22×Q8×C113C2211yescharacteristic
16C2×M16×C113C2212yes—
17#101×C113C414yescomplemented
18C22×Dic113—21no—
19C22×Dic113—21no—
20C4⋊Dic113—22no—
21C4⋊Dic113—22no—
22C4⋊Dic113—22no—
23C4⋊Dic113D412yes—
24C4⋊Dic113D412yes—
25C22⋊Dic113—22no—
26C4×Dic113—24no—
27C4×Dic113—22no—
28C4×Dic113—22no—
29C2×Q8×C113—22no—
30C2×Q8×C113—22no—
31C2×Q8×C113C2×C412yes—
32C2×Q8×C113Q812yes—
33C22×C4×C113D412yes—
34C22×C4×C113C2311yescharacteristic
35M16×C113—22no—
36M16×C113C2×C414yes—
37C2×C8×C113—22no—
38C23×C113C2×D411yescharacteristic
39Q8×C113—24no—
40Q8×C113—24no—
41C2×C4×C113—22no—
42C2×C4×C113—22no—
43C2×C4×C113C4⋊C414yes—
44C2×C4×C113C22×C411yescharacteristic
45C2×C4×C113C2×D412yes—
46C2×C4×C113C2×Q811yescharacteristic
47C2×C4×C113#4112yes—
48C2×Dic113—22no—
49C2×Dic113—22no—
50C2×Dic113—22no—
51C2×Dic113—41no—
52C2×Dic113—41no—
53C2×Dic113—42no—
54C2×Dic113—41no—
55C8×C113—24no—
56C22×C113—21no—
57C22×C113—21no—
58C22×C113C2×C4⋊C411yescharacteristic
59C22×C113#12011yescharacteristic
60C22×C113#12311yescharacteristic
61C4×C113—24no—
62C4×C113C4×D412yes—
63C4×C113C22⋊Q812yes—
64Dic113—42no—
65Dic113—42no—
66Dic113—42no—
67Dic113—81no—
68C2×C113—21no—
69C2×C113—21no—
70C2×C113#38511yescharacteristic
71C2×C113#45411yescharacteristic
72C2×C113#45611yescharacteristic
73#1857—1131nomaximal, Sylow
74C113#185711yescharacteristic, complemented, Sylow
75#519—1131no—
76#428—1132no—
77C2×#101D11311yescharacteristic
78#391—1131no—
79#339—1132no—
80C22×Q8C2×D11311yescharacteristic
81C2×M16C2×D11312yes—
82C4×Q8—2262no—
83C4×Q8—2262no—
84#117—1132no—
85#117—2262no—
86C2×C4⋊C4—1131no—
87C2×C42—1131no—
88#107—2262no—
89#106—2262no—
90#101Dic11314yescomplemented
91#95—2262no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8Dic22612yes—
95C2×Q8C2×Dic11312yes—
96C22×C4—2261no—
97C22×C4—2261no—
98C22×C4D45212yes—
99C22×C4C22×D11311yescharacteristic
100M16—22no—
101M16C2×Dic11314yes—
102C2×C8—22no—
103C4⋊C4—1132no—
104C4⋊C4—1132no—
105C4⋊C4—2262no—
106C4⋊C4—2262no—
107C4⋊C4—2262no—
108C22⋊C4—2262no—
109C42—2264no—
110C42—2262no—
111C42—2262no—
112C23C2×D45211yescharacteristic
113Q8—24no—
114Q8—24no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—4522no—
118C2×C4—4521no—
119C2×C4—4521no—
120C2×C4—4521no—
121C2×C4—2262no—
122C2×C4—2262no—
123C2×C4—2262no—
124C2×C4C4⋊Dic11314yes—
125C2×C4C22×Dic11311yescharacteristic
126C2×C4D4×D11312yes—
127C2×C4C2×Dic22611yescharacteristic
128C2×C4#1426864612yes—
129C8—24no—
130C22—21no—
131C22—21no—
132C22C2×C4⋊Dic11311yescharacteristic
133C22#1681359211yescharacteristic
134C22#1681360611yescharacteristic
135C4—24no—
136C4—9041no—
137C4—4522no—
138C4—4522no—
139C4—4522no—
140C4D4×Dic11312yes—
141C4#1681359912yes—
142C2—21no—
143C2—21no—
144C2#2029847311yescharacteristic
145C2#2029877311yescharacteristic
146C2#2029878311yescharacteristic
subgroupG/H
centerC22#16813592
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#101×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
cosocleC22×C4×C113C23
hypercenterC2×#101D113
hypocenterC113#1857
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
17. #101×C113C4semidirect
74. C113#1857semidirect
90. #101Dic113semidirect

Maximal subgroups

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

subgroupindex
#202990762
#202986402
#202985052
#202983592
C2×#101×C1132
#1857113