Finite Group Databasebeta

← #28390894

Subgroups — #28390894

Order 14464.

412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C2×#16813596C211yesmaximal, characteristic
2C2×#16813581C211yesmaximal, characteristic, complemented
3C2×#16813544C212yesmaximal, complemented
4#20298361C212yesmaximal, complemented
5C2×C22⋊C8×C113C211yesmaximal, characteristic, complemented
6C22×D452C2211yescharacteristic
7C22×C22⋊D113—21no—
8#16813596—22no—
9#16813596C414yescomplemented
10#16813581—24no—
11C2×C4⋊Dic113C2211yescharacteristic
12C2×C4⋊Dic113C2212yes—
13C2×C22⋊Dic113—21no—
14C2×#14268624—21no—
15C2×C4×Dic113—21no—
16#16813544—24no—
17C23×C4×C113C2211yescharacteristic
18C22×C8×C113C2212yes—
19C22⋊C8×C113—22no—
20C23×D113—21no—
21C2×D452—22no—
22C2×D452—22no—
23C2×D452—21no—
24C2×D452C2×C412yes—
25C2×C22⋊D113—24no—
26C2×C22⋊D113—44no—
27C22×Dic113—22no—
28C22×Dic113—21no—
29C4⋊Dic113—22no—
30C4⋊Dic113—21no—
31C4⋊Dic113C2×C412yes—
32C4⋊Dic113D414yescomplemented
33C22⋊Dic113—24no—
34#14268624—24no—
35C4×Dic113—24no—
36C24×C113D411yescharacteristic
37C22×C4×C113—22no—
38C22×C4×C113—22no—
39C22×C4×C113C2×C412yes—
40C22×C4×C113D411yescharacteristic
41C22×C4×C113D412yes—
42C22×C4×C113C2311yescharacteristic
43C2×C8×C113—22no—
44C2×C8×C113—22no—
45C2×C8×C113—22no—
46C23×C113—21no—
47C23×C113—21no—
48C23×C113—22no—
49C23×C113—22no—
50C23×C113C22⋊C412yes—
51C23×C113C2×D411yescharacteristic
52C22×D113—22no—
53C22×D113—41no—
54C22×D113—41no—
55C22×D113—42no—
56C22×D113—42no—
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113—24no—
60C2×C4×C113—24no—
61C2×C4×C113C22⋊C412yes—
62C2×C4×C113C22×C411yescharacteristic
63C2×C4×C113C2×D412yes—
64C2×C4×C113C2×D411yescharacteristic
65C2×C4×C113#4112yes—
66C22⋊D113—48no—
67C2×Dic113—22no—
68C2×Dic113—24no—
69C2×Dic113—42no—
70C2×Dic113—42no—
71C2×Dic113—42no—
72D452—24no—
73D452—42no—
74C8×C113—42no—
75C22×C113—22no—
76C22×C113—22no—
77C22×C113—22no—
78C22×C113—42no—
79C22×C113—42no—
80C22×C113C2×C22⋊C411yescharacteristic
81C22×C113#12011yescharacteristic
82C22×C113#12311yescharacteristic
83C22×C113#13512yes—
84C22×C113AGL(1,ℤ/8)12yes—
85C2×D113—42no—
86C2×D113—42no—
87C2×D113—42no—
88C2×D113—82no—
89C2×D113—82no—
90C4×C113—22no—
91C4×C113C4×D412yes—
92C4×C113#12112yes—
93Dic113—42no—
94Dic113—44no—
95C2×C113—42no—
96C2×C113#38611yescharacteristic
97C2×C113#41611yescharacteristic
98C2×C113#41811yescharacteristic
99C2×C113#44912yes—
100C2×C113#48212yes—
101D113—82no—
102#1875—1131nomaximal, Sylow
103C113#187511yescharacteristic, complemented, Sylow
104C2×#121—1131no—
105C2×#117—1131no—
106C2×#102—1132no—
107C2×C22⋊C8D11311yescharacteristic, complemented
108#340—1132no—
109C22×D4—1131no—
110C22×D4—2261no—
111C23×C4C2×D11311yescharacteristic
112C22×C8C2×D11312yes—
113#121—1134no—
114#121—2262no—
115#117—2264no—
116C2×C4⋊C4—1132no—
117C2×C4⋊C4—1131no—
118C2×C22⋊C4—2261no—
119C2×C22⋊C4—2261no—
120C2×C42—2261no—
121#102—2264no—
122C22⋊C8—22no—
123C24—2261no—
124C24D45211yescharacteristic
125C2×D4—1132no—
126C2×D4—4524no—
127C2×D4—2264no—
128C2×D4—2262no—
129C2×D4—2261no—
130C2×D4—2262no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—2262no—
134C22×C4—2261no—
135C22×C4C4×D11312yes—
136C22×C4D45211yescharacteristic
137C22×C4C22⋊D11312yes—
138C22×C4C22×D11311yescharacteristic
139C2×C8—22no—
140C2×C8—22no—
141C2×C8—22no—
142C4⋊C4—1132no—
143C4⋊C4—1134no—
144C4⋊C4—2262no—
145C4⋊C4—2261no—
146C22⋊C4—2264no—
147C22⋊C4—2264no—
148C42—2264no—
149C23—21no—
150C23—21no—
151C23—22no—
152C23—22no—
153C23—4521no—
154C23—4521no—
155C23—4522no—
156C23—4522no—
157C23—2262no—
158C23#1426862412yes—
159C23C2×D45211yescharacteristic
160D4—4528no—
161D4—4522no—
162D4—2264no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—4522no—
168C2×C4—4522no—
169C2×C4—4522no—
170C2×C4—2262no—
171C2×C4—2264no—
172C2×C4#1426862412yes—
173C2×C4C2×C4×D11311yescharacteristic
174C2×C4D4×D11312yes—
175C2×C4C2×C22⋊D11311yescharacteristic
176C2×C4#1426864612yes—
177C8—42no—
178C22—22no—
179C22—22no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—9042no—
184C22—9042no—
185C22—4522no—
186C22—4522no—
187C22—4522no—
188C22C2×#1426862411yescharacteristic
189C22#1681359211yescharacteristic
190C22#1681360611yescharacteristic
191C22#1681364412yes—
192C22#1681365012yes—
193C4—22no—
194C4—4522no—
195C4—4524no—
196C4#1681358212yes—
197C4#1681359412yes—
198C2—42no—
199C2—9042no—
200C2#2029847511yescharacteristic
201C2#2029859511yescharacteristic
202C2#2029860411yescharacteristic
203C2#2029874512yes—
204C2#2029892312yes—
subgroupG/H
centerC23C2×D452
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×C22⋊C8×C113C2
socleC23×C113C2×D4
prime radicalC2×#16813596C2
cosocleC22×C4×C113C23
hypercenterC2×C22⋊C8D113
hypocenterC113#1875
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×#16813581C2semidirect
3. C2×#16813544C2semidirect
4. #20298361C2semidirect
5. C2×C22⋊C8×C113C2semidirect
9. #16813596C4semidirect
32. C4⋊Dic113D4semidirect
103. C113#1875semidirect
107. C2×C22⋊C8D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135962
C2×#168135812
C2×#168135442
#202983612
C2×C22⋊C8×C1132
#1875113