Finite Group Databasebeta

← #26120353

Subgroups — #26120353

Order 12032.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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#20254698C211yesmaximal, characteristic
2#20242081C212yesmaximal, complemented
3#20241895C212yesmaximal, complemented
4#20241258C211yesmaximal, characteristic, complemented
5C47×#1832C211yesmaximal, characteristic, complemented
6#15689673C2212yes—
7#15689404—22no—
8#15689359—22no—
9#15689319—22no—
10#15689180C2212yes—
11#15688871—22no—
12#15688866—22no—
13#15688856—24no—
14C2×C4⋊C8×C47C2211yescharacteristic
15C2×C4⋊C8×C47C2211yescharacteristic
16C47×#376C2211yescharacteristic
17C47×#336—22no—
18C2×#10625350—22no—
19C2×D376—22no—
20#13094024D412yes—
21#13094021D412yes—
22#13094012—22no—
23#13093998—22no—
24#13093998—22no—
25C4×D188—22no—
26C4×D188—22no—
27#13093958—22no—
28C4⋊(C47⋊C8)—22no—
29#13093946—24no—
30C22⋊(C47⋊C8)—22no—
31#13093935—22no—
32C22×C8×C47—21no—
33C22×C8×C47D412yes—
34C2×C42×C47—21no—
35C2×C42×C47C2311yescharacteristic
36C4⋊C8×C47—22no—
37C4⋊C8×C47—22no—
38#95×C47—21no—
39#95×C47D412yes—
40C22×C4×C47—22no—
41C22×C4×C47C2×D411yescharacteristic
42C22×C4×C47C2×D411yescharacteristic
43C22×C4×C47#4111yescharacteristic
44C2×C22⋊D47—42no—
45#10625350—84no—
46C2×D188—22no—
47C2×D188—22no—
48C2×D188—22no—
49C2×C4×D47—42no—
50C2×Dic94—22no—
51C2×C8×C47—22no—
52C2×C8×C47—42no—
53C2×C8×C47—42no—
54C2×C8×C47—41no—
55C42×C47—41no—
56C42×C47—41no—
57C42×C47C2×D412yes—
58C42×C47#4112yes—
59(C2×D47)⋊C4—42no—
60(C2×D47)⋊C4—42no—
61C4⋊Dic47—22no—
62C4⋊Dic47—22no—
63C2×C47⋊C8—42no—
64D376—82no—
65C23×C47#12111yescharacteristic
66C22×D47—42no—
67C2×C4×C47—22no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—41no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47—42no—
74C2×C4×C47#12011yescharacteristic
75C2×C4×C47#12112yes—
76C2×C4×C47#12312yes—
77C2×C4×C47#12411yescharacteristic
78C22⋊D47—84no—
79C2×Dic47—42no—
80D188—42no—
81D188—42no—
82D188—82no—
83D188—82no—
84C4×D47—84no—
85Dic94—82no—
86C8×C47—42no—
87C8×C47—81no—
88C47⋊C8—82no—
89#10513—471nomaximal, Sylow
90C22×C47—21no—
91C22×C47—21no—
92C22×C47#39411yescharacteristic
93C22×C47#47212yes—
94C2×D47—82no—
95C2×D47—82no—
96C2×D47—82no—
97C4×C47—22no—
98C4×C47—21no—
99C4×C47—22no—
100C4×C47—82no—
101C4×C47#45411yescharacteristic
102C4×C47#45511yescharacteristic
103Dic47—82no—
104#3245—471no—
105#1832D4711yescharacteristic, complemented
106#1551—472no—
107#1505—472no—
108#1290—471no—
109C2×C47—22no—
110C2×C47#204011yescharacteristic
111C2×C47#204511yescharacteristic
112C2×C47#205311yescharacteristic
113D47—162no—
114#532—472no—
115#474—942no—
116#466—942no—
117#459—942no—
118#432—472no—
119C2×C4⋊C8C2×D4711yescharacteristic
120C2×C4⋊C8C2×D4711yescharacteristic
121#376C2×D4711yescharacteristic
122#336—22no—
123#333—942no—
124#331—942no—
125#327—944no—
126C47#1051311yescharacteristic, complemented, Sylow
127C2×#41—942no—
128C2×D8—942no—
129C22×C8—21no—
130C22×C8C22⋊D4712yes—
131C4⋊Q8—472no—
132#127—472no—
133#124—942no—
134#121—942no—
135#121—942no—
136C4×D4—942no—
137C4×D4—942no—
138C2×C42—21no—
139C2×C42C22×D4711yescharacteristic
140#107—942no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—942no—
144#102—944no—
145C22⋊C8—942no—
146#97—942no—
147#95—21no—
148#95D18812yes—
149#41—3764no—
150C2×Q8—942no—
151C2×D4—942no—
152C2×D4—942no—
153C2×D4—942no—
154C2×D4—1882no—
155C22×C4—22no—
156C22×C4—1882no—
157C22×C4C2×D18811yescharacteristic
158C22×C4#1062535011yescharacteristic
159C22×C4C2×C22⋊D4711yescharacteristic
160D8—3762no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—41no—
165C2×C8—1882no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C22⋊C4—1882no—
169C22⋊C4—1882no—
170C42—41no—
171C42—41no—
172C42D4×D4712yes—
173C42#1062535412yes—
174C23—1882no—
175C23#1309399811yescharacteristic
176Q8—3762no—
177D4—3762no—
178D4—3762no—
179D4—3764no—
180D4—1882no—
181D4—1882no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—3764no—
190C2×C4—1882no—
191C2×C4#1309399211yescharacteristic
192C2×C4#1309399912yes—
193C2×C4#1309400912yes—
194C2×C4#1309401311yescharacteristic
195C8—42no—
196C8—81no—
197C8—3762no—
198C22—21no—
199C22—21no—
200C22—3762no—
201C22—3762no—
202C22—3762no—
203C22#1568904011yescharacteristic
204C22#1568939312yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—3762no—
210C4#1568929511yescharacteristic
211C4#1568930011yescharacteristic
212C2—22no—
213C2—7522no—
214C2#2024461711yescharacteristic
215C2#2024464411yescharacteristic
216C2#2024469411yescharacteristic
subgroupG/H
centerC22#15689040
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1832C2
socleC22×C47#394
prime radical#20254698C2
hypercenter#1832D47
hypocenterC47#10513
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
2. #20242081C2semidirect
3. #20241895C2semidirect
4. #20241258C2semidirect
5. C47×#1832C2semidirect
105. #1832D47semidirect
126. C47#10513semidirect

Maximal subgroups

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

subgroupindex
#202546982
#202420812
#202418952
#202412582
C47×#18322
#1051347