Finite Group Databasebeta

← #20244432

Subgroups — #20244432

Order 6016.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#13094052C212yesmaximal, complemented
2#15689704C211yesmaximal, characteristic, complemented
3C2×#13093950C212yesmaximal, complemented
4#15689024C211yesmaximal, characteristic, complemented
5C47×#343C211yesmaximal, characteristic, complemented
6C2×#10625350C2212yes—
7C22×D188C2211yescharacteristic
8#13094052—24no—
9#13094052—24no—
10C2×#10625325—22no—
11C2×D376—22no—
12#13094004—22no—
13#13093999—22no—
14#13093998—22no—
15C2×(C2×D47)⋊C4—22no—
16C2×C4×Dic47C2211yescharacteristic
17#13093950—24no—
18C2×M16×C47C2212yes—
19C2×C4⋊C4×C47C2211yescharacteristic
20C23×D47—21no—
21C22×C4×C47D412yes—
22C22×C4×C47C2311yescharacteristic
23C2×C22⋊D47—22no—
24C22×Dic47—21no—
25#10625350—22no—
26#10625350—22no—
27#10625350—22no—
28#10625350—22no—
29C2×D188—22no—
30C2×D188—22no—
31C2×D188—21no—
32C2×D188—22no—
33C2×D188D412yes—
34C2×D188D412yescomplemented
35C2×C4×D47—22no—
36C2×Dic94D412yes—
37M16×C47—22no—
38M16×C47D414yescomplemented
39C2×C8×C47—22no—
40C4⋊C4×C47—22no—
41(C2×D47)⋊C4—24no—
42(C2×D47)⋊C4—44no—
43C4⋊Dic47—22no—
44C4×Dic47—22no—
45D376—28no—
46#10625325—28no—
47C23×C47C2×D411yescharacteristic
48C22×D47—22no—
49C22×D47—22no—
50C22×D47—42no—
51C22×D47—42no—
52C22×D47—41no—
53C22×D47—41no—
54C2×C4×C47—22no—
55C2×C4×C47—42no—
56C2×C4×C47C2×D412yes—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D412yes—
59C2×C4×C47#4111yescharacteristic
60C22⋊D47—42no—
61C22⋊D47—42no—
62C2×Dic47—22no—
63C2×Dic47—22no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66D188—24no—
67D188—22no—
68D188—22no—
69D188—42no—
70D188—82no—
71C4×D47—42no—
72C4×D47—42no—
73Dic94—22no—
74Dic94—22no—
75C8×C47—24no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47#12011yescharacteristic
79C22×C47#12111yescharacteristic
80C22×C47#12711yescharacteristic
81C2×D47—44no—
82C2×D47—42no—
83C2×D47—42no—
84C2×D47—42no—
85C2×D47—42no—
86C2×D47—82no—
87C2×D47—81no—
88C2×D47—81no—
89C4×C47—42no—
90C4×C47#12012yes—
91C4×C47#12112yes—
92Dic47—42no—
93Dic47—42no—
94#2006—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—21no—
97C2×C47#39211yescharacteristic
98C2×C47#45311yescharacteristic
99C2×C47#45411yescharacteristic
100D47—82no—
101D47—82no—
102C2×AGL(1,ℤ/8)—472no—
103#537—471no—
104C2×#104—472no—
105#390—471no—
106#343D4711yescharacteristic, complemented
107C47#200611yescharacteristic, complemented, Sylow
108C2×#41—472no—
109C22×D4—471no—
110AGL(1,ℤ/8)—944no—
111AGL(1,ℤ/8)—944no—
112C2×SD16—942no—
113C2×D8—942no—
114C2×M16C2×D4712yes—
115C22⋊Q8—942no—
116#121—942no—
117#121—942no—
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C22⋊C4—942no—
120C2×C42—471no—
121#104—944no—
122C24—941no—
123#41—942no—
124#41—942no—
125#41—942no—
126#41—942no—
127C2×Q8—472no—
128C2×D4—472no—
129C2×D4—472no—
130C2×D4—942no—
131C2×D4—942no—
132C2×D4—942no—
133C2×D4—942no—
134C2×D4—941no—
135C22×C4—941no—
136C22×C4—942no—
137C22×C4D18812yes—
138C22×C4C22×D4711yescharacteristic
139SD16—948no—
140D8—948no—
141M16—22no—
142M16D18814yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—942no—
146C22⋊C4—944no—
147C22⋊C4—1884no—
148C42—942no—
149C23—942no—
150C23—942no—
151C23—1882no—
152C23—1882no—
153C23—1881no—
154C23—1881no—
155C23C2×D18811yescharacteristic
156Q8—942no—
157Q8—942no—
158D4—942no—
159D4—944no—
160D4—942no—
161D4—3762no—
162D4—1882no—
163D4—1882no—
164D4—1882no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—1881no—
170C2×C4—1881no—
171C2×C4—1882no—
172C2×C4—1882no—
173C2×C4C2×D18812yes—
174C2×C4D4×D4711yescharacteristic
175C2×C4D4×D4712yes—
176C2×C4#1062535411yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—3762no—
181C22—3761no—
182C22—3761no—
183C22—1884no—
184C22—1882no—
185C22—1882no—
186C22—1882no—
187C22—1882no—
188C22#1309399411yescharacteristic
189C22#1309399911yescharacteristic
190C22#1309402111yescharacteristic
191C4—42no—
192C4—1882no—
193C4—1882no—
194C4#1309399412yes—
195C4#1309399912yes—
196C2—21no—
197C2—21no—
198C2—3762no—
199C2—3762no—
200C2#1568903311yescharacteristic
201C2#1568929311yescharacteristic
202C2#1568929811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#343C2
socleC22×C47#120
hypercenter#343D47
hypocenterC47#2006
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#13094052C2semidirect
2. #15689704C2semidirect
3. C2×#13093950C2semidirect
4. #15689024C2semidirect
5. C47×#343C2semidirect
34. C2×D188D4semidirect
38. M16×C47D4semidirect
106. #343D47semidirect
107. C47#2006semidirect
142. M16D188semidirect