Finite Group Databasebeta

← #26120350

Subgroups — #26120350

Order 12032.

388 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 81 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#20243507C211yesmaximal, characteristic, complemented
2#20242083C212yesmaximal, complemented
3#20241896C212yesmaximal, complemented
4#20241258C211yesmaximal, characteristic, complemented
5C47×#3245C211yesmaximal, characteristic
6#15689180C2212yes—
7C2×C4⋊(C47⋊C8)C2211yescharacteristic
8#15688969C2211yescharacteristic
9#15688877—22no—
10#15688872—22no—
11#15688867—22no—
12#15688857—24no—
13C47×#532C2212yes—
14C47×#474—22no—
15C47×#466—22no—
16C47×#459—22no—
17C2×C4⋊C8×C47C2211yescharacteristic
18C22×C47⋊C8—21no—
19C2×C4×Dic47—21no—
20C4⋊(C47⋊C8)—22no—
21C4⋊(C47⋊C8)—22no—
22C22⋊(C47⋊C8)—22no—
23#13093935—22no—
24C47⋊#95—21no—
25C47⋊#95D412yes—
26C2×#41×C47—22no—
27C2×D8×C47—22no—
28C22×C8×C47D412yes—
29C4⋊Q8×C47D412yes—
30#127×C47D412yes—
31#124×C47—22no—
32#121×C47—22no—
33#121×C47—22no—
34C4×D4×C47—22no—
35C4×D4×C47—22no—
36C2×C42×C47C2311yescharacteristic
37#107×C47—22no—
38C4⋊C8×C47—22no—
39#102×C47—24no—
40#41×C47—84no—
41C2×Q8×C47—22no—
42C2×D4×C47—22no—
43C2×D4×C47—22no—
44C2×D4×C47—22no—
45C2×D4×C47—42no—
46C22×C4×C47—42no—
47C22×C4×C47C2×D411yescharacteristic
48C22×C4×C47C2×D411yescharacteristic
49C22×C4×C47#4111yescharacteristic
50C22×Dic47—22no—
51D8×C47—82no—
52C2×C8×C47—22no—
53C2×C8×C47—42no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47—22no—
56C22⋊C4×C47—42no—
57C22⋊C4×C47—42no—
58C42×C47C2×D412yes—
59C42×C47#4112yes—
60C4×Dic47—41no—
61C4×Dic47—41no—
62C2×C47⋊C8—42no—
63C2×C47⋊C8—41no—
64C2×C47⋊C8—42no—
65C23×C47—42no—
66C23×C47#12111yescharacteristic
67Q8×C47—82no—
68D4×C47—42no—
69D4×C47—42no—
70D4×C47—82no—
71D4×C47—82no—
72D4×C47—84no—
73C2×C4×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—41no—
77C2×C4×C47—42no—
78C2×C4×C47—84no—
79C2×C4×C47#12011yescharacteristic
80C2×C4×C47#12112yes—
81C2×C4×C47#12312yes—
82C2×C4×C47#12411yescharacteristic
83C2×Dic47—42no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C8×C47—42no—
87C47⋊C8—82no—
88C47⋊C8—81no—
89#10513—471nomaximal, Sylow
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—82no—
93C22×C47—82no—
94C22×C47—82no—
95C22×C47#39411yescharacteristic
96C22×C47#47212yes—
97C4×C47—22no—
98C4×C47—21no—
99C4×C47—22no—
100C4×C47—82no—
101C4×C47#45411yescharacteristic
102C4×C47#45511yescharacteristic
103Dic47—82no—
104#3245D4711yescharacteristic
105#1832—471no—
106#1551—472no—
107#1505—472no—
108#1290—471no—
109C2×C47—22no—
110C2×C47—162no—
111C2×C47#204011yescharacteristic
112C2×C47#204511yescharacteristic
113C2×C47#205311yescharacteristic
114#532C2×D4712yes—
115#474—22no—
116#466—22no—
117#459—22no—
118#432—472no—
119C2×C4⋊C8—471no—
120C2×C4⋊C8C2×D4711yescharacteristic
121#376—471no—
122#336—942no—
123#333—942no—
124#331—942no—
125#327—944no—
126C47#1051311yescharacteristic, complemented, Sylow
127C2×#41—22no—
128C2×D8—22no—
129C22×C8—941no—
130C22×C8C22⋊D4712yes—
131C4⋊Q8C22⋊D4712yes—
132#127C22⋊D4712yes—
133#124—22no—
134#121—22no—
135#121—22no—
136C4×D4—22no—
137C4×D4—22no—
138C2×C42—941no—
139C2×C42C22×D4711yescharacteristic
140#107—22no—
141C4⋊C8—22no—
142C4⋊C8—942no—
143C4⋊C8—942no—
144#102—24no—
145C22⋊C8—942no—
146#97—942no—
147#95—472no—
148#95—941no—
149#41—84no—
150C2×Q8—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—42no—
155C22×C4—42no—
156C22×C4—942no—
157C22×C4D4×D4711yescharacteristic
158C22×C4#1062535211yescharacteristic
159C22×C4C2×C22⋊D4711yescharacteristic
160D8—82no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—1882no—
164C2×C8—1881no—
165C2×C8—1882no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42—1881no—
171C42—1881no—
172C42#1062535212yes—
173C42C2×C22⋊D4712yes—
174C23—42no—
175C23#1309399511yescharacteristic
176Q8—82no—
177D4—42no—
178D4—42no—
179D4—82no—
180D4—82no—
181D4—84no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—84no—
188C2×C4—1882no—
189C2×C4—1882no—
190C2×C4—1882no—
191C2×C4#1309399311yescharacteristic
192C2×C4#1309399612yes—
193C2×C4#1309400512yes—
194C2×C4#1309401111yescharacteristic
195C8—42no—
196C8—3762no—
197C8—3761no—
198C22—21no—
199C22—21no—
200C22—82no—
201C22—82no—
202C22—82no—
203C22#1568903711yescharacteristic
204C22#1568939012yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—3762no—
210C4#1568929611yescharacteristic
211C4#1568930111yescharacteristic
212C2—22no—
213C2—162no—
214C2#2024461411yescharacteristic
215C2#2024464111yescharacteristic
216C2#2024469111yescharacteristic
subgroupG/H
centerC22#15689037
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3245C2
socleC22×C47#394
hypercenter#3245D47
hypocenterC47#10513
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #20243507C2semidirect
2. #20242083C2semidirect
3. #20241896C2semidirect
4. #20241258C2semidirect
126. C47#10513semidirect

Maximal subgroups

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

subgroupindex
#202435072
#202420832
#202418962
#202412582
C47×#32452
#1051347