Finite Group Databasebeta

← #28391732

Subgroups — #28391732

Order 14464.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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#20298606C212yesmaximal
2#20298503C211yesmaximal, characteristic
3#20298367C211yesmaximal, characteristic
4#20298357C212yesmaximal
5#544×C113C211yesmaximal, characteristic
6C22×Dic226C2211yescharacteristic
7C2×#14268631C2212yes—
8C2×C4×Dic113C2211yescharacteristic
9#16813545—22no—
10#16813545—22no—
11#16813529—22no—
12C4⋊Q8×C113—22no—
13#125×C113—22no—
14C22⋊Q8×C113—22no—
15#117×C113C2212yes—
16C2×C4⋊C4×C113C2211yescharacteristic
17C2×Dic226—22no—
18C2×Dic226—22no—
19C2×Dic226—21no—
20C2×Dic226Q812yescomplemented
21C22×Dic113—21no—
22C22×Dic113—21no—
23#14268631—22no—
24#14268631—22no—
25C2×#11744751—22no—
26C4×Dic113—22no—
27C2×Q8×C113—22no—
28C22×C4×C113D412yes—
29C22×C4×C113C2311yescharacteristic
30C4⋊C4×C113—22no—
31C4⋊C4×C113—24no—
32C4⋊C4×C113—22no—
33C4⋊C4×C113D412yes—
34C4⋊C4×C113D412yes—
35C22⋊C4×C113—22no—
36C42×C113—22no—
37C23×C113C2×D411yescharacteristic
38Q8×C113—82no—
39C2×C4×C113—22no—
40C2×C4×C113—22no—
41C2×C4×C113—22no—
42C2×C4×C113—42no—
43C2×C4×C113C2×D412yes—
44C2×C4×C113C2×Q811yescharacteristic
45C2×C4×C113#4112yes—
46C2×C4×C113#4111yescharacteristic
47C2×Dic113—22no—
48C2×Dic113—22no—
49C2×Dic113—41no—
50C2×Dic113—41no—
51C2×Dic113—41no—
52C2×Dic113—41no—
53Dic226—24no—
54Dic226—42no—
55#11744751—42no—
56C22×C113—21no—
57C22×C113—21no—
58C22×C113#12011yescharacteristic
59C22×C113C22⋊Q811yescharacteristic
60C22×C113#12411yescharacteristic
61C4×C113—42no—
62C4×C113—42no—
63C4×C113—42no—
64C4×C113C22⋊Q812yes—
65C4×C113#12412yes—
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#544D11311yescharacteristic
76#419—1132no—
77#391—1131no—
78#343—1131no—
79#339—1132no—
80C22×Q8—1131no—
81C2×M16—1132no—
82C4⋊Q8—22no—
83#125—22no—
84C22⋊Q8—22no—
85#117C2×D11312yes—
86C2×C4⋊C4C2×D11311yescharacteristic
87C2×C42—1131no—
88#103—2262no—
89#103—2262no—
90#95—2262no—
91C2×Q8—22no—
92C2×Q8—1132no—
93C2×Q8—2262no—
94C2×Q8—2262no—
95C2×Q8—2261no—
96C22×C4—2261no—
97C22×C4—2261no—
98C22×C4C22⋊D11312yes—
99C22×C4C22×D11311yescharacteristic
100M16—2262no—
101M16—2262no—
102C2×C8—2262no—
103C4⋊C4—22no—
104C4⋊C4—24no—
105C4⋊C4—22no—
106C4⋊C4C22⋊D11312yes—
107C4⋊C4C22⋊D11312yes—
108C22⋊C4—22no—
109C42—22no—
110C42—2262no—
111C23C2×C22⋊D11311yescharacteristic
112Q8—82no—
113Q8—4522no—
114Q8—2264no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—4521no—
120C2×C4—4521no—
121C2×C4—4521no—
122C2×C4—4521no—
123C2×C4—2262no—
124C2×C4—2262no—
125C2×C4C2×C22⋊D11312yes—
126C2×C4Q8×D11311yescharacteristic
127C2×C4#1426864812yes—
128C2×C4#1426864811yescharacteristic
129C8—4522no—
130C22—21no—
131C22—21no—
132C22#1681359111yescharacteristic
133C22#1681359811yescharacteristic
134C22#1681361111yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—4522no—
139C4—4522no—
140C4#1681359812yes—
141C4#1681361112yes—
142C2—21no—
143C2—21no—
144C2#2029850911yescharacteristic
145C2#2029877611yescharacteristic
146C2#2029878111yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#544×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#544D113
hypocenterC113#2028
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. 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
#202986062
#202985032
#202983672
#202983572
#544×C1132
#2028113