Finite Group Databasebeta

← #28389618

Subgroups — #28389618

Order 14464.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#20298934C212yesmaximal
3#20298537C211yesmaximal, characteristic
4#20298336C212yesmaximal
5#324×C113C211yesmaximal, characteristic
6#16813621—22no—
7#16813613—22no—
8#16813601—21no—
9#16813601C2212yes—
10#16813581—21no—
11C2×C4⋊Dic113C2211yescharacteristic
12#16813556—22no—
13#16813547—22no—
14#16813529—21no—
15#16813529—21no—
16#16813529C2211yescharacteristic
17C2×C4⋊C4×C113C2211yescharacteristic
18C22⋊C8×C113C2212yes—
19C2×Dic226—21no—
20C2×Dic226D412yes—
21C22×Dic113—21no—
22C22×Dic113—21no—
23C4⋊Dic113—21no—
24C4⋊Dic113—21no—
25C4⋊Dic113—21no—
26C4⋊Dic113—22no—
27C4⋊Dic113D412yes—
28#14268626—22no—
29#14268626—22no—
30C22⋊Dic113—22no—
31C4×Dic113—22no—
32C22×C4×C113D411yescharacteristic
33C22×C4×C113D411yescharacteristic
34C22×C4×C113C2311yescharacteristic
35C2×C8×C113—22no—
36C4⋊C4×C113—22no—
37C23×C113C2×D411yescharacteristic
38C2×C4×C113—21no—
39C2×C4×C113—21no—
40C2×C4×C113—21no—
41C2×C4×C113—41no—
42C2×C4×C113—41no—
43C2×C4×C113Q1612yes—
44C2×C4×C113C2×D412yes—
45C2×Dic113—22no—
46C2×Dic113—22no—
47C2×Dic113—41no—
48C2×Dic113—41no—
49C2×Dic113—42no—
50C2×Dic113—41no—
51C2×Dic113—41no—
52Dic226—42no—
53Dic226—81no—
54C8×C113—42no—
55C22×C113—21no—
56C22×C113—21no—
57C22×C113#12011yescharacteristic
58C22×C113C2×Q1611yescharacteristic
59C22×C113#13711yescharacteristic
60C4×C113—22no—
61C4×C113—22no—
62C4×C113—41no—
63Dic113—42no—
64Dic113—42no—
65Dic113—81no—
66Dic113—81no—
67C2×C113—21no—
68C2×C113—21no—
69C2×C113#45111yescharacteristic
70C2×C113#45411yescharacteristic
71C2×C113#45811yescharacteristic
72#1617—1131nomaximal, Sylow
73C113#161711yescharacteristic, complemented, Sylow
74#544—1131no—
75#484—1132no—
76#400—1131no—
77#328—1132no—
78#324D11311yescharacteristic
79C4⋊Q8—2262no—
80#125—2262no—
81C22⋊Q8—1132no—
82C22⋊Q8—2261no—
83#117—2261no—
84C2×C4⋊C4—1131no—
85C2×C4⋊C4C2×D11311yescharacteristic
86#107—2262no—
87#103—2262no—
88C22⋊C8C2×D11312yes—
89#95—1131no—
90#95—2261no—
91#95—2261no—
92C2×Q8—1132no—
93C2×Q8—2261no—
94C22×C4—2261no—
95C22×C4—2261no—
96C22×C4D45211yescharacteristic
97C22×C4D45211yescharacteristic
98C22×C4C22×D11311yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—1132no—
102C4⋊C4—2261no—
103C4⋊C4—2261no—
104C4⋊C4—2261no—
105C4⋊C4—2262no—
106C4⋊C4—2262no—
107C4⋊C4—2262no—
108C22⋊C4—2262no—
109C42—2262no—
110C23C2×D45211yescharacteristic
111Q8—9041no—
112Q8—4522no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—4521no—
119C2×C4—4521no—
120C2×C4—4522no—
121C2×C4—4521no—
122C2×C4—4521no—
123C2×C4—2262no—
124C2×C4—2262no—
125C2×C4Dic45212yes—
126C2×C4D4×D11312yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1681359211yescharacteristic
131C22C2×Dic45211yescharacteristic
132C22#1681365511yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—9041no—
137C4—9041no—
138C4—4522no—
139C4—4522no—
140C2—21no—
141C2—21no—
142C2#2029875611yescharacteristic
143C2#2029877311yescharacteristic
144C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#324D113
hypocenterC113#1617
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
73. C113#1617semidirect

Maximal subgroups

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

subgroupindex
#202992292
#202989342
#202985372
#202983362
#324×C1132
#1617113