Finite Group Databasebeta

← #15767063

Subgroups — #15767063

Order 3328.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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#13126217C211yesmaximal, characteristic
2#13114976C211yesmaximal, characteristic, complemented
3#13113559C212yesmaximal, complemented
4#13113448C212yesmaximal, complemented
5C13×#1307C211yesmaximal, characteristic, complemented
6#11719182C2212yes—
7C13×#432C2212yes—
8C13×#423C2211yescharacteristic
9#11718796—22no—
10#11718585C2211yescharacteristic
11C2×#88043C2211yescharacteristic
12#11718504—22no—
13#11718503—22no—
14#11718150—22no—
15#11718077—22no—
16#11718074—22no—
17#11718056—24no—
18C2×#6127—22no—
19C2×C13×M16D412yes—
20C2×C42×C13C2311yescharacteristic
21#88184—22no—
22#88184—22no—
23C2×#6099—21no—
24C22×#1055—21no—
25C2×D104—22no—
26#88129—22no—
27#88128D412yes—
28C4×D52—22no—
29C4×D52—22no—
30#88123D412yes—
31C13×C4⋊C8—22no—
32C13×C4⋊C8—22no—
33C13×C22⋊C8—22no—
34C13×#97—22no—
35#88061—24no—
36#88057—22no—
37C4⋊#1055—22no—
38#88043—21no—
39#88043D412yes—
40#10525—131nomaximal, Sylow
41C22×C4×C13C2×D411yescharacteristic
42C22×C4×C13#4112yes—
43C2×C22⋊D13—42no—
44#6127—84no—
45C2×D52—22no—
46C2×D52—22no—
47C2×D52—22no—
48C2×C4×D13—42no—
49C2×Dic26—22no—
50C13×M16—42no—
51C2×C8×C13—22no—
52C2×C8×C13—42no—
53C42×C13C2×D412yes—
54C42×C13C2×D411yescharacteristic
55C42×C13#4111yescharacteristic
56#6103—42no—
57#6103—42no—
58C4⋊Dic13—22no—
59C4⋊Dic13—22no—
60#6099—42no—
61C2×#1055—22no—
62C2×#1055—41no—
63C2×#1055—41no—
64C2×#1055—41no—
65D104—82no—
66#3253—131no—
67#1838—131no—
68#1557—132no—
69#1530—132no—
70#1307D1311yescharacteristic, complemented
71C23×C13#12411yescharacteristic
72C22×D13—42no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—42no—
76C2×C4×C13#12011yescharacteristic
77C2×C4×C13#12112yes—
78C2×C4×C13#12111yescharacteristic
79C2×C4×C13#12312yes—
80C22⋊D13—84no—
81C2×Dic13—42no—
82D52—42no—
83D52—42no—
84D52—82no—
85D52—82no—
86C4×D13—84no—
87Dic26—82no—
88C8×C13—42no—
89C8×C13—82no—
90#1055—42no—
91#1055—81no—
92#532—132no—
93#476—262no—
94#469—262no—
95#459—262no—
96#432C2×D1312yes—
97#423—131no—
98#423C2×D1311yescharacteristic
99C2×#97—131no—
100#341—262no—
101#332—262no—
102#331—262no—
103#329—264no—
104C22×C13—22no—
105C22×C13—21no—
106C22×C13#39411yescharacteristic
107C2×D13—82no—
108C2×D13—82no—
109C2×D13—82no—
110C4×C13—22no—
111C4×C13—22no—
112C4×C13—21no—
113C4×C13#45411yescharacteristic
114C4×C13#45511yescharacteristic
115Dic13—82no—
116C2×#41—262no—
117C2×D8—262no—
118C2×M16—261no—
119C2×M16D5212yes—
120C22×C8—261no—
121C4⋊Q8—132no—
122#127—132no—
123#124—262no—
124#121—262no—
125#121—262no—
126C4×D4—262no—
127C4×D4—262no—
128C2×C42C22×D1311yescharacteristic
129#106—262no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—262no—
133#102—264no—
134C22⋊C8—22no—
135#97—22no—
136#97—132no—
137#97—261no—
138C2×C13—41no—
139C2×C13#204011yescharacteristic
140C2×C13#204812yes—
141D13—162no—
142#41—1044no—
143C2×Q8—262no—
144C2×D4—262no—
145C2×D4—262no—
146C2×D4—262no—
147C2×D4—522no—
148C22×C4—522no—
149C22×C4C2×D5211yescharacteristic
150C22×C4#612712yes—
151D8—1042no—
152M16—42no—
153M16—522no—
154C2×C8—22no—
155C2×C8—42no—
156C2×C8—262no—
157C2×C8—521no—
158C2×C8—521no—
159C2×C8—521no—
160C4⋊C4—262no—
161C4⋊C4—262no—
162C22⋊C4—522no—
163C22⋊C4—522no—
164C42D4×D1312yes—
165C42D4×D1311yescharacteristic
166C42#613111yescharacteristic
167C13#1052511yescharacteristic, complemented, Sylow
168C23—522no—
169C23#8812911yescharacteristic
170Q8—1042no—
171D4—522no—
172D4—522no—
173D4—1042no—
174D4—1042no—
175D4—1044no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—522no—
180C2×C4—1044no—
181C2×C4#8813611yescharacteristic
182C2×C4#8813812yes—
183C2×C4#8814812yes—
184C2×C4#8814911yescharacteristic
185C8—42no—
186C8—82no—
187C8—522no—
188C8—1041no—
189C22—21no—
190C22—22no—
191C22—1042no—
192C22—1042no—
193C22—1042no—
194C22#1171833311yescharacteristic
195C4—21no—
196C4—22no—
197C4—22no—
198C4—1042no—
199C4#1171840711yescharacteristic
200C4#1171841411yescharacteristic
201C2—41no—
202C2—2082no—
203C2#1311606611yescharacteristic
204C2#1311611212yes—
subgroupG/H
centerC22#11718333
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1307C2
socleC22×C13#394
prime radical#13126217C2
hypercenter#1307D13
hypocenterC13#10525
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #13114976C2semidirect
3. #13113559C2semidirect
4. #13113448C2semidirect
5. C13×#1307C2semidirect
70. #1307D13semidirect
167. C13#10525semidirect

Maximal subgroups

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

subgroupindex
#131262172
#131149762
#131135592
#131134482
C13×#13072
#1052513