Finite Group Databasebeta

← #26110652

Subgroups — #26110652

Order 12032.

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

normal subgroups only

This group has 428 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#20243557C212yesmaximal
3C2×#15688865C211yesmaximal, characteristic
4#20241269C212yesmaximal
5C47×#2382C211yesmaximal, characteristic
6C2×#13093957—22no—
7C2×#13093955—22no—
8C2×#13093935C2211yescharacteristic
9C2×#13093935C2212yes—
10#15688993C2211yescharacteristic
11#15688885—22no—
12#15688865C414yescomplemented
13C2×#125×C47C2211yescharacteristic
14C47×#389—22no—
15C47×#387—22no—
16C47×#387—22no—
17C47×#382C2212yes—
18C22×C47⋊C8—22no—
19C22×C47⋊C8—21no—
20C2×C4⋊Dic47—21no—
21C2×C4⋊Dic47—22no—
22#13093957—44no—
23#13093955—44no—
24#13093935—22no—
25#13093935—22no—
26#13093935C2×C414yes—
27#125×C47—22no—
28#125×C47C2×C412yes—
29#125×C47Q812yes—
30C2×C4⋊C4×C47—22no—
31C2×C4⋊C4×C47—22no—
32C2×C4⋊C4×C47D412yes—
33C2×C4⋊C4×C47D412yes—
34C2×C4⋊C4×C47D412yes—
35C2×C42×C47—22no—
36C2×C42×C47C2311yescharacteristic
37#95×C47—22no—
38#95×C47—22no—
39#95×C47—22no—
40#95×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47—22no—
44C22×C4×C47C2×D411yescharacteristic
45C22×C4×C47C2×D412yes—
46C22×Dic47—41no—
47C4⋊C4×C47—24no—
48C4⋊C4×C47—24no—
49C4⋊C4×C47—22no—
50C4⋊C4×C47—42no—
51C4⋊C4×C47—42no—
52C4⋊C4×C47—82no—
53C4⋊C4×C47C4⋊C414yes—
54C42×C47—82no—
55C42×C47C22×C411yescharacteristic
56C42×C47C2×Q811yescharacteristic
57C42×C47#4112yes—
58C4⋊Dic47—42no—
59C4⋊Dic47—42no—
60C4⋊Dic47—42no—
61C2×C47⋊C8—24no—
62C2×C47⋊C8—24no—
63C2×C47⋊C8—24no—
64C2×C47⋊C8—22no—
65C2×C47⋊C8—41no—
66C2×C47⋊C8—41no—
67C23×C47#12011yescharacteristic
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—24no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—42no—
81C2×C4×C47C2×C4⋊C411yescharacteristic
82C2×C4×C47C4×D412yes—
83C2×C4×C47C22⋊Q812yes—
84C2×C4×C47#12311yescharacteristic
85C2×Dic47—82no—
86C2×Dic47—81no—
87C47⋊C8—28no—
88C47⋊C8—42no—
89#8913—471nomaximal, Sylow
90C22×C47#38511yescharacteristic
91C22×C47#45312yes—
92C22×C47#45411yescharacteristic
93C22×C47#45611yescharacteristic
94C22×C47#45612yes—
95C4×C47—21no—
96C4×C47—21no—
97C4×C47—22no—
98C4×C47—22no—
99C4×C47—44no—
100C4×C47—82no—
101C4×C47—82no—
102Dic47—161no—
103#2382D4711yescharacteristic
104#1992—471no—
105#1847—472no—
106C2×#330—471no—
107#1295—472no—
108C2×C47#165611yescharacteristic
109C2×C47#166012yes—
110C2×C47#166311yescharacteristic
111C2×C47#185711yescharacteristic
112C2×C47#185912yes—
113C2×#125C2×D4711yescharacteristic
114C2×#107—942no—
115C2×#106—942no—
116C2×#97—472no—
117C2×#97—471no—
118#389—22no—
119#387—22no—
120#387—22no—
121#384—471no—
122#382C2×D4712yes—
123#340—942no—
124#330—474no—
125C47#891311yescharacteristic, complemented, Sylow
126C22×C8—942no—
127C22×C8—941no—
128#125—22no—
129#125Dic9412yes—
130#125C4×D4712yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—941no—
134C2×C4⋊C4—942no—
135C2×C4⋊C4C22⋊D4712yes—
136C2×C4⋊C4C22⋊D4712yes—
137C2×C4⋊C4C22⋊D4712yes—
138C2×C42—22no—
139C2×C42C22×D4711yescharacteristic
140#107—1884no—
141#106—1884no—
142#97—474no—
143#97—942no—
144#97—942no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—1881no—
153C22×C4C2×C22⋊D4711yescharacteristic
154C22×C4C2×C22⋊D4712yes—
155C2×C8—944no—
156C2×C8—944no—
157C2×C8—944no—
158C2×C8—942no—
159C2×C8—1881no—
160C2×C8—1881no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—82no—
167C4⋊C4—1882no—
168C4⋊C4—1882no—
169C4⋊C4—1882no—
170C4⋊C4Dic47⋊C414yes—
171C42—82no—
172C42C2×Dic9411yescharacteristic
173C42C2×C4×D4711yescharacteristic
174C42#1062535012yes—
175C23#1309399311yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—3762no—
190C2×C4—3761no—
191C2×C4C2×Dic47⋊C411yescharacteristic
192C2×C4C4×C22⋊D4712yes—
193C2×C4#1309400312yes—
194C2×C4#1309400711yescharacteristic
195C8—948no—
196C8—1882no—
197C22#1568899611yescharacteristic
198C22#1568929112yes—
199C22#1568929611yescharacteristic
200C22#1568930611yescharacteristic
201C22#1568930612yes—
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—82no—
208C4—82no—
209C4—7521no—
210C2#2024268111yescharacteristic
211C2#2024269912yes—
212C2#2024271611yescharacteristic
213C2#2024360311yescharacteristic
214C2#2024361412yes—
subgroupG/H
centerC23#13093993
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2382C2
socle, prime radicalC23×C47#120
cosocleC2×C42×C47C23
hypercenter#2382D47
hypocenterC47#8913
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
125. C47#8913semidirect

Maximal subgroups

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

subgroupindex
#202443582
#202435572
C2×#156888652
#202412692
C47×#23822
#891347