Finite Group Databasebeta

← #28391736

Subgroups — #28391736

Order 14464.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#20299229C211yesmaximal, characteristic
2#20298608C212yesmaximal
3#20298503C211yesmaximal, characteristic
4#20298359C212yesmaximal
5#343×C113C211yesmaximal, characteristic
6C22×Dic226C2211yescharacteristic
7#16813621—22no—
8#16813613—22no—
9#16813601—22no—
10#16813581C2212yes—
11C2×C4×Dic113C2211yescharacteristic
12#16813547—22no—
13#16813547—22no—
14#16813529—22no—
15C2×M16×C113C2212yes—
16C2×C4⋊C4×C113C2211yescharacteristic
17C2×Dic226—22no—
18C2×Dic226—22no—
19C2×Dic226—21no—
20C2×Dic226—22no—
21C2×Dic226Q812yescomplemented
22C22×Dic113—21no—
23C22×Dic113—21no—
24C4⋊Dic113—22no—
25C4⋊Dic113D412yes—
26C4⋊Dic113D412yes—
27#14268626—24no—
28C22⋊Dic113—22no—
29C4×Dic113—22no—
30C4×Dic113—22no—
31C22×C4×C113D412yes—
32C22×C4×C113C2311yescharacteristic
33M16×C113—22no—
34M16×C113—22no—
35C2×C8×C113—22no—
36C4⋊C4×C113—22no—
37C23×C113C2×D411yescharacteristic
38C2×C4×C113—22no—
39C2×C4×C113—42no—
40C2×C4×C113C2×D412yes—
41C2×C4×C113C2×Q811yescharacteristic
42C2×C4×C113#4111yescharacteristic
43C2×C4×C113#4112yes—
44C2×Dic113—22no—
45C2×Dic113—22no—
46C2×Dic113—22no—
47C2×Dic113—22no—
48C2×Dic113—41no—
49C2×Dic113—41no—
50C2×Dic113—41no—
51C2×Dic113—41no—
52Dic226—24no—
53Dic226—42no—
54Dic226—82no—
55C8×C113—42no—
56C22×C113—21no—
57C22×C113—21no—
58C22×C113#12011yescharacteristic
59C22×C113C22⋊Q811yescharacteristic
60C22×C113#12411yescharacteristic
61C4×C113—42no—
62C4×C113C22⋊Q812yes—
63C4×C113#12412yes—
64Dic113—42no—
65Dic113—42no—
66Dic113—42no—
67Dic113—42no—
68C2×C113—21no—
69C2×C113—21no—
70C2×C113#39311yescharacteristic
71C2×C113#45511yescharacteristic
72C2×C113#45611yescharacteristic
73#2028—1131nomaximal, Sylow
74C113#202811yescharacteristic, complemented, Sylow
75#544—1131no—
76#419—1132no—
77#391—1131no—
78#343D11311yescharacteristic
79#339—1132no—
80C22×Q8—1131no—
81C2×M16C2×D11312yes—
82C4⋊Q8—2262no—
83#125—2262no—
84C22⋊Q8—2262no—
85#117—1132no—
86C2×C4⋊C4C2×D11311yescharacteristic
87C2×C42—1131no—
88#103—2262no—
89#103—2262no—
90#95—2262no—
91C2×Q8—1132no—
92C2×Q8—2262no—
93C2×Q8—2262no—
94C2×Q8—2262no—
95C2×Q8—2261no—
96C22×C4—2261no—
97C22×C4—2261no—
98C22×C4D45212yes—
99C22×C4C22×D11311yescharacteristic
100M16—22no—
101M16—22no—
102C2×C8—22no—
103C4⋊C4—22no—
104C4⋊C4—1132no—
105C4⋊C4—1132no—
106C4⋊C4—2262no—
107C4⋊C4—2264no—
108C22⋊C4—2262no—
109C42—2262no—
110C42—2262no—
111C23C2×D45211yescharacteristic
112Q8—9042no—
113Q8—4522no—
114Q8—2264no—
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—4521no—
118C2×C4—4521no—
119C2×C4—4521no—
120C2×C4—4521no—
121C2×C4—2262no—
122C2×C4—2262no—
123C2×C4—2262no—
124C2×C4—2262no—
125C2×C4D4×D11312yes—
126C2×C4Q8×D11311yescharacteristic
127C2×C4#1426864611yescharacteristic
128C2×C4#1426864712yes—
129C8—42no—
130C22—21no—
131C22—21no—
132C22#1681359211yescharacteristic
133C22#1681360211yescharacteristic
134C22#1681361011yescharacteristic
135C4—42no—
136C4—4522no—
137C4—4522no—
138C4—4522no—
139C4—4522no—
140C4#1681360012yes—
141C4#1681360812yes—
142C2—21no—
143C2—21no—
144C2#2029851111yescharacteristic
145C2#2029877811yescharacteristic
146C2#2029878311yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#343×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#343D113
hypocenterC113#2028
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
21. C2×Dic226Q8semidirect
74. C113#2028semidirect

Maximal subgroups

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

subgroupindex
#202992292
#202986082
#202985032
#202983592
#343×C1132
#2028113