Finite Group Databasebeta

← #28389564

Subgroups — #28389564

Order 14464.

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

normal subgroups only

This group has 228 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#20299224C211yesmaximal, characteristic
2#20298928C212yesmaximal, complemented
3#20298334C212yesmaximal, complemented
4#20298322C211yesmaximal, characteristic
5#397×C113C211yesmaximal, characteristic
6#16813601—21no—
7#16813601C2212yes—
8#16813599—22no—
9#16813599—22no—
10C2×C22⋊Dic113—21no—
11#16813553—22no—
12#16813545—22no—
13C22⋊#11744751C2212yes—
14C2×C4⋊C4×C113C2211yescharacteristic
15C2×C22⋊C4×C113—21no—
16C2×C22⋊C4×C113C2211yescharacteristic
17#95×C113—21no—
18#95×C113C2211yescharacteristic
19C2×Dic226—21no—
20C2×Dic226D412yes—
21C22×Dic113—21no—
22C22×Dic113—21no—
23C2×#11744751—22no—
24C4⋊Dic113—21no—
25C4⋊Dic113D412yes—
26#14268626—22no—
27#14268626—22no—
28C22⋊Dic113—22no—
29C22⋊Dic113—22no—
30C24×C113D411yescharacteristic
31C22×C4×C113—21no—
32C22×C4×C113—21no—
33C22×C4×C113D411yescharacteristic
34C22×C4×C113C2311yescharacteristic
35C4⋊C4×C113—22no—
36C22⋊C4×C113—22no—
37C22⋊C4×C113—42no—
38C23×C113—21no—
39C23×C113—21no—
40C23×C113—41no—
41C23×C113—41no—
42C23×C113SD1612yes—
43C23×C113C2×D411yescharacteristic
44C2×C4×C113—21no—
45C2×C4×C113—41no—
46C2×C4×C113—41no—
47C2×C4×C113—41no—
48C2×C4×C113—41no—
49C2×C4×C113—41no—
50C2×C4×C113—41no—
51C2×C4×C113—41no—
52C2×C4×C113—41no—
53C2×C4×C113C2×D412yes—
54C2×Dic113—22no—
55C2×Dic113—22no—
56C2×Dic113—81no—
57C2×Dic113—81no—
58Dic226—42no—
59Dic226—81no—
60#11744751—42no—
61C22×C113—21no—
62C22×C113—21no—
63C22×C113—22no—
64C22×C113—42no—
65C22×C113—41no—
66C22×C113—41no—
67C22×C113—81no—
68C22×C113#12011yescharacteristic
69C22×C113C2×SD1611yescharacteristic
70C22×C113#13711yescharacteristic
71C4×C113—22no—
72C4×C113—41no—
73C4×C113—81no—
74C4×C113—81no—
75Dic113—42no—
76Dic113—42no—
77C2×C113—21no—
78C2×C113—21no—
79C2×C113—42no—
80C2×C113#44811yescharacteristic
81C2×C113#45511yescharacteristic
82C2×C113#45811yescharacteristic
83#1608—1131nomaximal, Sylow
84C113#160811yescharacteristic, complemented, Sylow
85#543—1131no—
86#483—1132no—
87#397D11311yescharacteristic
88#328—1132no—
89#323—1131no—
90C22⋊Q8—1132no—
91C22⋊Q8—2262no—
92C22⋊Q8—2262no—
93C22⋊Q8—2261no—
94C2×C4⋊C4C2×D11311yescharacteristic
95C2×C22⋊C4—21no—
96C2×C22⋊C4—2261no—
97C2×C22⋊C4C2×D11311yescharacteristic
98#106—2262no—
99#103—2262no—
100C22⋊C8—1132no—
101#95—21no—
102#95C2×D11311yescharacteristic
103C24C22⋊D11311yescharacteristic
104C2×Q8—1132no—
105C2×Q8—2261no—
106C22×C4—21no—
107C22×C4—21no—
108C22×C4—2261no—
109C22×C4—2261no—
110C22×C4C22⋊D11311yescharacteristic
111C22×C4C22×D11311yescharacteristic
112C2×C8—2262no—
113C4⋊C4—22no—
114C4⋊C4—1132no—
115C4⋊C4—2262no—
116C4⋊C4—2261no—
117C4⋊C4—2262no—
118C22⋊C4—22no—
119C22⋊C4—42no—
120C22⋊C4—2262no—
121C22⋊C4—2262no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1426863512yes—
127C23C2×C22⋊D11311yescharacteristic
128Q8—9041no—
129Q8—4522no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—9041no—
140C2×C4—9041no—
141C2×C4—2262no—
142C2×C4—2262no—
143C2×C4D4×D11312yes—
144C8—4522no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#1681359011yescharacteristic
153C22C2×#1426863511yescharacteristic
154C22#1681365211yescharacteristic
155C4—22no—
156C4—41no—
157C4—81no—
158C4—81no—
159C4—4522no—
160C4—4522no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#2029873611yescharacteristic
165C2#2029877511yescharacteristic
166C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#397×C113C2
socleC22×C113#120
prime radicalC24×C113D4
hypercenter#397D113
hypocenterC113#1608
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #20298928C2semidirect
3. #20298334C2semidirect
84. C113#1608semidirect

Maximal subgroups

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

subgroupindex
#202992242
#202989282
#202983342
#202983222
#397×C1132
#1608113