Finite Group Databasebeta

← #28391008

Subgroups — #28391008

Order 14464.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14268631C211yesmaximal, characteristic
2C2×#16813546C212yesmaximal, complemented
3#20298458C211yesmaximal, characteristic
4#20298360C212yesmaximal, complemented
5C2×C22⋊Q8×C113C211yesmaximal, characteristic
6C2×#14268631—24no—
7C2×#14268631—22no—
8C22×#11744751C2212yes—
9C2×C4⋊Dic113C2212yes—
10C2×C22⋊Dic113—21no—
11#16813546—24no—
12#16813529—21no—
13C22×Q8×C113C2211yescharacteristic
14C23×C4×C113C2211yescharacteristic
15C22⋊Q8×C113—22no—
16C22⋊Q8×C113C414yescomplemented
17C2×C4⋊C4×C113—21no—
18C2×C4⋊C4×C113C2211yescharacteristic
19C2×C22⋊C4×C113—21no—
20C22×Dic113—22no—
21#14268631—28no—
22C2×#11744751—22no—
23C2×#11744751—22no—
24C2×#11744751D414yes—
25C4⋊Dic113—22no—
26C4⋊Dic113—22no—
27C22⋊Dic113—42no—
28C24×C113D411yescharacteristic
29C2×Q8×C113—21no—
30C2×Q8×C113—22no—
31C2×Q8×C113—22no—
32C2×Q8×C113C2×C412yes—
33C22×C4×C113—22no—
34C22×C4×C113—22no—
35C22×C4×C113—21no—
36C22×C4×C113—21no—
37C22×C4×C113C2×C412yes—
38C22×C4×C113D411yescharacteristic
39C22×C4×C113D412yes—
40C22×C4×C113C2311yescharacteristic
41C4⋊C4×C113—24no—
42C4⋊C4×C113—21no—
43C4⋊C4×C113C2×C412yes—
44C22⋊C4×C113—24no—
45C23×C113—22no—
46C23×C113—21no—
47C23×C113—21no—
48C23×C113—22no—
49C23×C113C22⋊C412yes—
50C23×C113C2×D411yescharacteristic
51Q8×C113—24no—
52Q8×C113—41no—
53Q8×C113—41no—
54C2×C4×C113—22no—
55C2×C4×C113—24no—
56C2×C4×C113—22no—
57C2×C4×C113—22no—
58C2×C4×C113—22no—
59C2×C4×C113—22no—
60C2×C4×C113—42no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113C22⋊C412yes—
64C2×C4×C113C22×C411yescharacteristic
65C2×C4×C113C2×D412yes—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113#4112yes—
68C2×Dic113—42no—
69C2×Dic113—42no—
70C2×Dic113—42no—
71#11744751—24no—
72C22×C113—22no—
73C22×C113—22no—
74C22×C113—22no—
75C22×C113—42no—
76C22×C113—42no—
77C22×C113C2×C22⋊C411yescharacteristic
78C22×C113#12112yes—
79C22×C113AGL(1,ℤ/8)11yescharacteristic
80C22×C113#13711yescharacteristic
81C22×C113#13712yes—
82C4×C113—22no—
83C4×C113—42no—
84C4×C113—42no—
85C4×C113C4×D412yes—
86C4×C113#12011yescharacteristic
87C4×C113#12311yescharacteristic
88Dic113—82no—
89C2×C113—42no—
90C2×C113#38611yescharacteristic
91C2×C113#41711yescharacteristic
92C2×C113#41911yescharacteristic
93C2×C113#46812yes—
94C2×C113#47012yes—
95#1894—1131nomaximal, Sylow
96C113#189411yescharacteristic, complemented, Sylow
97C22×M16—1131no—
98C2×C22⋊Q8D11311yescharacteristic
99C2×#103—1132no—
100#380—1131no—
101#340—1132no—
102C22×Q8C2×D11311yescharacteristic
103C23×C4C2×D11311yescharacteristic
104C2×M16—2264no—
105C2×M16—2262no—
106C22×C8—1132no—
107C22⋊Q8—22no—
108C22⋊Q8Dic11314yescomplemented
109C2×C4⋊C4—21no—
110C2×C4⋊C4—1132no—
111C2×C4⋊C4C2×D11311yescharacteristic
112C2×C22⋊C4—21no—
113C2×C22⋊C4—2261no—
114#103—2264no—
115#95—2261no—
116C24C22⋊D11311yescharacteristic
117C2×Q8—21no—
118C2×Q8—22no—
119C2×Q8—22no—
120C2×Q8C2×Dic11312yes—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—2262no—
126C22×C4C2×Dic11312yes—
127C22×C4C22⋊D11311yescharacteristic
128C22×C4C22⋊D11312yes—
129C22×C4C22×D11311yescharacteristic
130M16—2268no—
131C2×C8—1134no—
132C2×C8—2262no—
133C2×C8—2262no—
134C4⋊C4—24no—
135C4⋊C4—21no—
136C4⋊C4—2262no—
137C4⋊C4—2262no—
138C4⋊C4C2×Dic11312yes—
139C22⋊C4—24no—
140C22⋊C4—4522no—
141C23—22no—
142C23—21no—
143C23—21no—
144C23—22no—
145C23C22⋊Dic11312yes—
146C23C2×C22⋊D11311yescharacteristic
147Q8—24no—
148Q8—41no—
149Q8—41no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—4522no—
160C2×C4—4522no—
161C2×C4—4522no—
162C2×C4C22⋊Dic11312yes—
163C2×C4C22×Dic11311yescharacteristic
164C2×C4D4×D11312yes—
165C2×C4C2×C22⋊D11311yescharacteristic
166C2×C4#1426864612yes—
167C8—2264no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22C2×C22⋊Dic11311yescharacteristic
174C22#1681359412yes—
175C22#1681364711yescharacteristic
176C22#1681365211yescharacteristic
177C22#1681365312yes—
178C4—22no—
179C4—42no—
180C4—42no—
181C4—9042no—
182C4D4×Dic11312yes—
183C4#1681359011yescharacteristic
184C4#1681360311yescharacteristic
185C2—42no—
186C2#2029847811yescharacteristic
187C2#2029859911yescharacteristic
188C2#2029860711yescharacteristic
189C2#2029884612yes—
190C2#2029885412yes—
subgroupG/H
centerC23C2×C22⋊D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×C22⋊Q8×C113C2
socleC23×C113C2×D4
prime radicalC24×C113D4
cosocleC22×C4×C113C23
hypercenterC2×C22⋊Q8D113
hypocenterC113#1894
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#16813546C2semidirect
4. #20298360C2semidirect
16. C22⋊Q8×C113C4semidirect
96. C113#1894semidirect
108. C22⋊Q8Dic113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686312
C2×#168135462
#202984582
#202983602
C2×C22⋊Q8×C1132
#1894113