Finite Group Databasebeta

← #28391003

Subgroups — #28391003

Order 14464.

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

normal subgroups only

This group has 432 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
1C23×#11744751C211yesmaximal, characteristic, complemented
2C2×#16813543C212yesmaximal, complemented
3#20298458C211yesmaximal, characteristic, complemented
4#20298360C212yesmaximal, complemented
5C2×#121×C113C211yesmaximal, characteristic
6C22×#11744751—24no—
7C22×#11744751—22no—
8C22×#11744751C2212yes—
9C2×C4⋊Dic113C2212yes—
10C2×C22⋊Dic113—21no—
11#16813543—24no—
12#16813529—21no—
13C22×D4×C113—21no—
14C22×D4×C113C2211yescharacteristic
15C23×C4×C113C2211yescharacteristic
16#121×C113—22no—
17#121×C113C414yescomplemented
18C2×C4⋊C4×C113C2211yescharacteristic
19C2×C22⋊C4×C113—21no—
20C22×Dic113—22no—
21C2×#11744751—28no—
22C2×#11744751—22no—
23C2×#11744751—22no—
24C2×#11744751D414yescomplemented
25C4⋊Dic113—22no—
26C4⋊Dic113—22no—
27C22⋊Dic113—42no—
28C24×C113—21no—
29C24×C113D411yescharacteristic
30C2×D4×C113—24no—
31C2×D4×C113—22no—
32C2×D4×C113—21no—
33C2×D4×C113—22no—
34C2×D4×C113—42no—
35C2×D4×C113—42no—
36C2×D4×C113C2×C412yes—
37C22×C4×C113—22no—
38C22×C4×C113—22no—
39C22×C4×C113—21no—
40C22×C4×C113C2×C412yes—
41C22×C4×C113D411yescharacteristic
42C22×C4×C113D412yes—
43C22×C4×C113C2311yescharacteristic
44C4⋊C4×C113—21no—
45C4⋊C4×C113C2×C412yes—
46C22⋊C4×C113—24no—
47C23×C113—22no—
48C23×C113—22no—
49C23×C113—22no—
50C23×C113—42no—
51C23×C113—41no—
52C23×C113—41no—
53C23×C113—42no—
54C23×C113C22⋊C412yes—
55C23×C113D812yes—
56C23×C113SD1612yes—
57C23×C113C2×D411yescharacteristic
58D4×C113—24no—
59D4×C113—48no—
60D4×C113—41no—
61D4×C113—41no—
62C2×C4×C113—22no—
63C2×C4×C113—24no—
64C2×C4×C113—22no—
65C2×C4×C113—22no—
66C2×C4×C113—22no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113C22⋊C412yes—
70C2×C4×C113C22×C411yescharacteristic
71C2×C4×C113C2×D412yes—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113#4112yes—
74C2×Dic113—42no—
75C2×Dic113—42no—
76C2×Dic113—42no—
77#11744751—24no—
78C22×C113—22no—
79C22×C113—22no—
80C22×C113—24no—
81C22×C113—24no—
82C22×C113—42no—
83C22×C113—42no—
84C22×C113—42no—
85C22×C113—82no—
86C22×C113—82no—
87C22×C113#10214yescomplemented
88C22×C113C2×C22⋊C411yescharacteristic
89C22×C113#12112yes—
90C22×C113C2×D811yescharacteristic
91C22×C113C2×SD1611yescharacteristic
92C22×C113#13512yes—
93C4×C113—22no—
94C4×C113—42no—
95C4×C113C4×D412yes—
96C4×C113#12011yescharacteristic
97C4×C113#12311yescharacteristic
98Dic113—82no—
99C2×C113—24no—
100C2×C113—82no—
101C2×C113#38611yescharacteristic
102C2×C113C2×#10211yescharacteristic
103C2×C113#41611yescharacteristic
104C2×C113#46512yes—
105C2×C113#46612yes—
106#1893—1131nomaximal, Sylow
107C113#189311yescharacteristic, complemented, Sylow
108C23×C8—1131no—
109C2×#121D11311yescharacteristic
110C2×#102—1132no—
111#380—1131no—
112#340—1132no—
113C22×D4—21no—
114C22×D4C2×D11311yescharacteristic
115C23×C4C2×D11311yescharacteristic
116C22×C8—1132no—
117C22×C8—2264no—
118C22×C8—2262no—
119#121—22no—
120#121Dic11314yescomplemented
121C2×C4⋊C4—1132no—
122C2×C4⋊C4C2×D11311yescharacteristic
123C2×C22⋊C4—21no—
124C2×C22⋊C4—2261no—
125#102—2264no—
126#95—2261no—
127C24—21no—
128C24C22⋊D11311yescharacteristic
129C2×D4—24no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—22no—
133C2×D4—42no—
134C2×D4—42no—
135C2×D4C2×Dic11312yes—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—2262no—
140C22×C4C2×Dic11312yes—
141C22×C4C22⋊D11311yescharacteristic
142C22×C4C22⋊D11312yes—
143C22×C4C22×D11311yescharacteristic
144C2×C8—1134no—
145C2×C8—2268no—
146C2×C8—2262no—
147C2×C8—2262no—
148C4⋊C4—21no—
149C4⋊C4—2262no—
150C4⋊C4—2262no—
151C4⋊C4C2×Dic11312yes—
152C22⋊C4—24no—
153C22⋊C4—4522no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—42no—
158C23—41no—
159C23—41no—
160C23—42no—
161C23C22⋊Dic11312yes—
162C23#1426863212yes—
163C23#1426863512yes—
164C23C2×C22⋊D11311yescharacteristic
165D4—24no—
166D4—48no—
167D4—41no—
168D4—41no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—4522no—
177C2×C4—4522no—
178C2×C4—4522no—
179C2×C4C22⋊Dic11312yes—
180C2×C4C22×Dic11311yescharacteristic
181C2×C4D4×D11312yes—
182C2×C4C2×C22⋊D11311yescharacteristic
183C2×C4#1426864612yes—
184C8—2264no—
185C22—24no—
186C22—24no—
187C22—22no—
188C22—22no—
189C22—42no—
190C22—42no—
191C22—42no—
192C22—82no—
193C22—82no—
194C22#1681354314yescomplemented
195C22C2×C22⋊Dic11311yescharacteristic
196C22#1681359412yes—
197C22C2×#1426863211yescharacteristic
198C22C2×#1426863511yescharacteristic
199C22#1681364212yes—
200C4—22no—
201C4—42no—
202C4—9042no—
203C4D4×Dic11312yes—
204C4#1681359011yescharacteristic
205C4#1681360311yescharacteristic
206C2—24no—
207C2—82no—
208C2#2029847811yescharacteristic
209C2C2×#1681354311yescharacteristic
210C2#2029859411yescharacteristic
211C2#2029882512yes—
212C2#2029883212yes—
subgroupG/H
centerC23C2×C22⋊D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting, prime radicalC2×#121×C113C2
socleC23×C113C2×D4
cosocleC22×C4×C113C23
hypercenterC2×#121D113
hypocenterC113#1893
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C23×#11744751C2semidirect
2. C2×#16813543C2semidirect
3. #20298458C2semidirect
4. #20298360C2semidirect
17. #121×C113C4semidirect
24. C2×#11744751D4semidirect
87. C22×C113#102semidirect
107. C113#1893semidirect
120. #121Dic113semidirect
194. C22#16813543semidirect

Maximal subgroups

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

subgroupindex
C23×#117447512
C2×#168135432
#202984582
#202983602
C2×#121×C1132
#1893113