Finite Group Databasebeta

← #28390764

Subgroups — #28390764

Order 14464.

360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C22×C4⋊Dic113C211yesmaximal, characteristic
2C2×#16813556C212yesmaximal, complemented
3#20298458C211yesmaximal, characteristic
4#20298361C212yesmaximal, complemented
5C2×C22⋊C8×C113C211yesmaximal, characteristic
6C23×Dic113—21no—
7C2×C4⋊Dic113—24no—
8C2×C4⋊Dic113—21no—
9C2×C4⋊Dic113C2211yescharacteristic
10C2×C4⋊Dic113C2211yescharacteristic
11C2×C4⋊Dic113C2212yes—
12C2×C22⋊Dic113—21no—
13#16813556—24no—
14#16813529—21no—
15C23×C4×C113C2211yescharacteristic
16C22×C8×C113C2212yes—
17C22⋊C8×C113C414yescomplemented
18C22×Dic113—24no—
19C22×Dic113—22no—
20C22×Dic113—21no—
21C22×Dic113—21no—
22C22×Dic113—42no—
23C22×Dic113—42no—
24C4⋊Dic113—24no—
25C4⋊Dic113—22no—
26C4⋊Dic113—22no—
27C4⋊Dic113—22no—
28C4⋊Dic113D414yes—
29C22⋊Dic113—42no—
30C24×C113D411yescharacteristic
31C22×C4×C113—22no—
32C22×C4×C113—22no—
33C22×C4×C113C2×C412yes—
34C22×C4×C113D411yescharacteristic
35C22×C4×C113Q812yes—
36C22×C4×C113C2311yescharacteristic
37C2×C8×C113—22no—
38C2×C8×C113—22no—
39C2×C8×C113C2×C414yescomplemented
40C23×C113—21no—
41C23×C113—21no—
42C23×C113—21no—
43C23×C113—21no—
44C23×C113C4⋊C412yes—
45C23×C113D812yes—
46C23×C113Q1612yes—
47C23×C113C2×D411yescharacteristic
48C2×C4×C113—21no—
49C2×C4×C113—21no—
50C2×C4×C113—24no—
51C2×C4×C113—24no—
52C2×C4×C113C4⋊C412yes—
53C2×C4×C113C22×C411yescharacteristic
54C2×C4×C113C2×D412yes—
55C2×C4×C113C2×Q811yescharacteristic
56C2×C4×C113#4112yes—
57C2×Dic113—24no—
58C2×Dic113—48no—
59C2×Dic113—42no—
60C2×Dic113—42no—
61C2×Dic113—41no—
62C2×Dic113—41no—
63C2×Dic113—41no—
64C2×Dic113—41no—
65C2×Dic113—41no—
66C2×Dic113—41no—
67C8×C113—24no—
68C22×C113—22no—
69C22×C113—22no—
70C22×C113—22no—
71C22×C113—22no—
72C22×C113—22no—
73C22×C113—22no—
74C22×C113#10714yescomplemented
75C22×C113C2×C4⋊C411yescharacteristic
76C22×C113#12011yescharacteristic
77C22×C113#12311yescharacteristic
78C22×C113C2×D811yescharacteristic
79C22×C113C2×Q1611yescharacteristic
80C22×C113AGL(1,ℤ/8)11yescharacteristic
81C22×C113#13711yescharacteristic
82C4×C113—22no—
83C4×C113C4×D412yes—
84C4×C113C22⋊Q812yes—
85Dic113—44no—
86Dic113—81no—
87Dic113—81no—
88C2×C113—24no—
89C2×C113#38511yescharacteristic
90C2×C113C2×#10711yescharacteristic
91C2×C113#42811yescharacteristic
92C2×C113#44711yescharacteristic
93C2×C113#45111yescharacteristic
94C2×C113#48011yescharacteristic
95C2×C113#48411yescharacteristic
96#1852—1131nomaximal, Sylow
97C113#185211yescharacteristic, complemented, Sylow
98C22×C4⋊C4—1131no—
99C2×#107—1132no—
100C2×C22⋊C8D11311yescharacteristic
101#380—1131no—
102#340—1132no—
103C23×C4—2261no—
104C23×C4C2×D11311yescharacteristic
105C22×C8C2×D11312yes—
106C2×C4⋊C4—1132no—
107C2×C4⋊C4—1131no—
108C2×C4⋊C4—1131no—
109C2×C4⋊C4—2264no—
110C2×C4⋊C4—2261no—
111C2×C22⋊C4—2261no—
112#107—2264no—
113C22⋊C8Dic11314yescomplemented
114#95—2261no—
115C24D45211yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—4522no—
119C22×C4—4522no—
120C22×C4—2261no—
121C22×C4—2261no—
122C22×C4—2264no—
123C22×C4—2262no—
124C22×C4Dic22612yes—
125C22×C4D45211yescharacteristic
126C22×C4C2×Dic11312yes—
127C22×C4C22×D11311yescharacteristic
128C2×C8—22no—
129C2×C8—22no—
130C2×C8C2×Dic11314yescomplemented
131C4⋊C4—1134no—
132C4⋊C4—2264no—
133C4⋊C4—2262no—
134C4⋊C4—2262no—
135C4⋊C4—2262no—
136C22⋊C4—4522no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23C4⋊Dic11312yes—
142C23D90412yes—
143C23Dic45212yes—
144C23C2×D45211yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—4521no—
150C2×C4—4521no—
151C2×C4—4521no—
152C2×C4—4521no—
153C2×C4—4521no—
154C2×C4—4521no—
155C2×C4—4528no—
156C2×C4—4522no—
157C2×C4—4522no—
158C2×C4—2264no—
159C2×C4C4⋊Dic11312yes—
160C2×C4C22×Dic11311yescharacteristic
161C2×C4D4×D11312yes—
162C2×C4C2×Dic22611yescharacteristic
163C2×C4#1426864612yes—
164C8—24no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#1681355614yescomplemented
172C22C2×C4⋊Dic11311yescharacteristic
173C22#1681359211yescharacteristic
174C22#1681360611yescharacteristic
175C22C2×D90411yescharacteristic
176C22C2×Dic45211yescharacteristic
177C22#1681365011yescharacteristic
178C22#1681365511yescharacteristic
179C4—22no—
180C4—9041no—
181C4—9041no—
182C4—4524no—
183C4D4×Dic11312yes—
184C4#1681359912yes—
185C2—24no—
186C2#2029847311yescharacteristic
187C2C2×#1681355611yescharacteristic
188C2#2029864011yescharacteristic
189C2#2029873411yescharacteristic
190C2#2029875611yescharacteristic
191C2#2029891211yescharacteristic
192C2#2029893411yescharacteristic
subgroupG/H
centerC23C2×D452
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×C22⋊C8×C113C2
socleC23×C113C2×D4
prime radicalC24×C113D4
cosocleC22×C4×C113C23
hypercenterC2×C22⋊C8D113
hypocenterC113#1852
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#16813556C2semidirect
4. #20298361C2semidirect
17. C22⋊C8×C113C4semidirect
39. C2×C8×C113C2×C4semidirect
74. C22×C113#107semidirect
97. C113#1852semidirect
113. C22⋊C8Dic113semidirect
130. C2×C8C2×Dic113semidirect
171. C22#16813556semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic1132
C2×#168135562
#202984582
#202983612
C2×C22⋊C8×C1132
#1852113