Finite Group Databasebeta

← #26110662

Subgroups — #26110662

Order 12032.

396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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#20244358C211yesmaximal, characteristic
2#20243521C212yesmaximal
3C2×#15688865C211yesmaximal, characteristic
4#20241269C212yesmaximal
5C47×#2382C211yesmaximal, characteristic
6C2×#13093935C2211yescharacteristic
7C2×#13093935C2212yes—
8#15688993C2211yescharacteristic
9#15688885—22no—
10#15688885—22no—
11#15688885—22no—
12#15688865C414yescomplemented
13C2×#125×C47C2211yescharacteristic
14C47×#389—22no—
15C47×#387—22no—
16C47×#387—22no—
17C47×#382C2212yes—
18C22×C47⋊C8—21no—
19C22×C47⋊C8—22no—
20C2×C4⋊Dic47—21no—
21C2×C4⋊Dic47—22no—
22#13093935—22no—
23#13093935—22no—
24#13093935C2×C414yes—
25#125×C47—22no—
26#125×C47C2×C412yes—
27#125×C47Q812yes—
28C2×C4⋊C4×C47—22no—
29C2×C4⋊C4×C47—22no—
30C2×C4⋊C4×C47D412yes—
31C2×C4⋊C4×C47D412yes—
32C2×C4⋊C4×C47D412yes—
33C2×C42×C47—22no—
34C2×C42×C47C2311yescharacteristic
35#95×C47—22no—
36#95×C47—22no—
37#95×C47—22no—
38#95×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47C2×D411yescharacteristic
43C22×C4×C47C2×D412yes—
44C22×Dic47—41no—
45C4⋊C4×C47—24no—
46C4⋊C4×C47—24no—
47C4⋊C4×C47—22no—
48C4⋊C4×C47—42no—
49C4⋊C4×C47—42no—
50C4⋊C4×C47—82no—
51C4⋊C4×C47C4⋊C414yes—
52C42×C47—82no—
53C42×C47C22×C411yescharacteristic
54C42×C47C2×Q811yescharacteristic
55C42×C47#4112yes—
56C4⋊Dic47—42no—
57C4⋊Dic47—44no—
58C2×C47⋊C8—22no—
59C2×C47⋊C8—24no—
60C2×C47⋊C8—41no—
61C2×C47⋊C8—42no—
62C2×C47⋊C8—42no—
63C2×C47⋊C8—41no—
64C23×C47#12011yescharacteristic
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—24no—
70C2×C4×C47—42no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47C2×C4⋊C411yescharacteristic
79C2×C4×C47C4×D412yes—
80C2×C4×C47C22⋊Q812yes—
81C2×C4×C47#12311yescharacteristic
82C2×Dic47—81no—
83C2×Dic47—82no—
84C47⋊C8—42no—
85C47⋊C8—44no—
86#8915—471nomaximal, Sylow
87C22×C47#38511yescharacteristic
88C22×C47#45411yescharacteristic
89C22×C47#45412yes—
90C22×C47#45512yes—
91C22×C47#45611yescharacteristic
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—22no—
95C4×C47—22no—
96C4×C47—44no—
97C4×C47—82no—
98C4×C47—82no—
99Dic47—161no—
100#2382D4711yescharacteristic
101#1992—471no—
102#1836—472no—
103C2×#330—471no—
104#1295—472no—
105C2×C47#165811yescharacteristic
106C2×C47#166211yescharacteristic
107C2×C47#166412yes—
108C2×C47#185711yescharacteristic
109C2×C47#186012yes—
110C2×#125C2×D4711yescharacteristic
111C2×#97—472no—
112C2×#97—471no—
113#389—22no—
114#387—22no—
115#387—22no—
116#384—471no—
117#382C2×D4712yes—
118#340—942no—
119#340—942no—
120#340—942no—
121#330—474no—
122C47#891511yescharacteristic, complemented, Sylow
123C22×C8—941no—
124C22×C8—942no—
125#125—22no—
126#125Dic9412yes—
127#125C4×D4712yes—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—941no—
131C2×C4⋊C4—942no—
132C2×C4⋊C4C22⋊D4712yes—
133C2×C4⋊C4C22⋊D4712yes—
134C2×C4⋊C4C22⋊D4712yes—
135C2×C42—22no—
136C2×C42C22×D4711yescharacteristic
137#97—474no—
138#97—942no—
139#97—942no—
140#95—22no—
141#95—22no—
142#95—22no—
143#95—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—1881no—
148C22×C4C2×C22⋊D4711yescharacteristic
149C22×C4C2×C22⋊D4712yes—
150C2×C8—942no—
151C2×C8—944no—
152C2×C8—1881no—
153C2×C8—1882no—
154C2×C8—1882no—
155C2×C8—1881no—
156C4⋊C4—24no—
157C4⋊C4—24no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—82no—
162C4⋊C4—1882no—
163C4⋊C4—1884no—
164C4⋊C4Dic47⋊C414yes—
165C42—82no—
166C42C2×Dic9411yescharacteristic
167C42C2×C4×D4711yescharacteristic
168C42#1062535012yes—
169C23#1309399311yescharacteristic
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—3761no—
184C2×C4—3762no—
185C2×C4C2×Dic47⋊C411yescharacteristic
186C2×C4C4×C22⋊D4712yes—
187C2×C4#1309400312yes—
188C2×C4#1309400711yescharacteristic
189C8—1882no—
190C8—1884no—
191C22#1568899611yescharacteristic
192C22#1568929611yescharacteristic
193C22#1568929612yes—
194C22#1568930112yes—
195C22#1568930611yescharacteristic
196C4—21no—
197C4—21no—
198C4—22no—
199C4—22no—
200C4—44no—
201C4—82no—
202C4—82no—
203C4—7521no—
204C2#2024269011yescharacteristic
205C2#2024271111yescharacteristic
206C2#2024272212yes—
207C2#2024360311yescharacteristic
208C2#2024362112yes—
subgroupG/H
centerC23#13093993
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2382C2
socle, prime radicalC23×C47#120
cosocleC2×C42×C47C23
hypercenter#2382D47
hypocenterC47#8915
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2382

Complements

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

NH ≅ G/Ntype
12. #15688865C4semidirect
122. C47#8915semidirect

Maximal subgroups

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

subgroupindex
#202443582
#202435212
C2×#156888652
#202412692
C47×#23822
#891547