Finite Group Databasebeta

← #15767057

Subgroups — #15767057

Order 3328.

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

normal subgroups only

This group has 386 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
1#13126217C211yesmaximal, characteristic
2#13113556C212yesmaximal, complemented
3#13113446C212yesmaximal, complemented
4#13112747C211yesmaximal, characteristic, complemented
5C13×#1849C211yesmaximal, characteristic, complemented
6#11719182C2212yes—
7C2×C13×#108—22no—
8C13×#423C2211yescharacteristic
9C13×#423C2211yescharacteristic
10C2×C13×#97C2211yescharacteristic
11#11718796—22no—
12#11718587C2212yes—
13#11718504—22no—
14#11718503—22no—
15#11718078—22no—
16#11718077—22no—
17#11718056—24no—
18C2×#6127—22no—
19C2×C13×M16—21no—
20C2×C13×M16D412yes—
21C22×C8×C13—21no—
22C2×C42×C13C2311yescharacteristic
23#88184—22no—
24#88184—22no—
25C2×D104—22no—
26#88129—22no—
27#88128D412yes—
28C4×D52—22no—
29C4×D52—22no—
30#88123D412yes—
31C13×#108—44no—
32C13×C4⋊C8—22no—
33C13×C4⋊C8—22no—
34C13×#97—21no—
35C13×#97D412yes—
36C22⋊#1055—22no—
37#88061—24no—
38#88057—22no—
39C4⋊#1055—22no—
40#88043—22no—
41#10524—131nomaximal, Sylow
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13#4112yes—
44C2×C22⋊D13—42no—
45#6127—84no—
46C2×D52—22no—
47C2×D52—22no—
48C2×D52—22no—
49C2×C4×D13—42no—
50C2×Dic26—22no—
51C13×M16—42no—
52C13×M16—42no—
53C2×C8×C13—22no—
54C2×C8×C13—22no—
55C2×C8×C13—22no—
56C2×C8×C13—22no—
57C2×C8×C13—41no—
58C42×C13C2×D411yescharacteristic
59C42×C13C2×D412yes—
60C42×C13#4111yescharacteristic
61#6103—42no—
62#6103—42no—
63C4⋊Dic13—22no—
64C4⋊Dic13—22no—
65C2×#1055—42no—
66D104—82no—
67#3253—131no—
68#1849D1311yescharacteristic, complemented
69#1557—132no—
70#1530—132no—
71#1307—131no—
72C23×C13#12411yescharacteristic
73C22×D13—42no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—42no—
77C2×C4×C13#12011yescharacteristic
78C2×C4×C13#12112yes—
79C2×C4×C13#12111yescharacteristic
80C2×C4×C13#12312yes—
81C22⋊D13—84no—
82C2×Dic13—42no—
83D52—42no—
84D52—42no—
85D52—82no—
86D52—82no—
87C4×D13—84no—
88Dic26—82no—
89C8×C13—24no—
90C8×C13—42no—
91C8×C13—81no—
92#1055—82no—
93#532—132no—
94#476—262no—
95#469—262no—
96#459—262no—
97#432—132no—
98C2×#108—22no—
99#423C2×D1311yescharacteristic
100#423C2×D1311yescharacteristic
101C2×#97C2×D1311yescharacteristic
102#332—262no—
103#331—262no—
104#329—264no—
105C22×C13—22no—
106C22×C13—21no—
107C22×C13#39411yescharacteristic
108C2×D13—82no—
109C2×D13—82no—
110C2×D13—82no—
111C4×C13—22no—
112C4×C13—22no—
113C4×C13—21no—
114C4×C13#45311yescharacteristic
115C4×C13#45611yescharacteristic
116Dic13—82no—
117C2×#41—262no—
118C2×D8—262no—
119C2×M16—21no—
120C2×M16C22⋊D1312yes—
121C22×C8—21no—
122C4⋊Q8—132no—
123#127—132no—
124#124—262no—
125#121—262no—
126#121—262no—
127C4×D4—262no—
128C4×D4—262no—
129C2×C42C22×D1311yescharacteristic
130#108—44no—
131#106—262no—
132C4⋊C8—22no—
133C4⋊C8—22no—
134C4⋊C8—262no—
135#102—264no—
136C22⋊C8—262no—
137#97—21no—
138#97—262no—
139#97D5212yes—
140C2×C13—41no—
141C2×C13#203911yescharacteristic
142C2×C13#204812yes—
143D13—162no—
144#41—1044no—
145C2×Q8—262no—
146C2×D4—262no—
147C2×D4—262no—
148C2×D4—262no—
149C2×D4—522no—
150C22×C4—522no—
151C22×C4#613112yes—
152C22×C4C2×C22⋊D1311yescharacteristic
153D8—1042no—
154M16—42no—
155M16—42no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—22no—
160C2×C8—41no—
161C2×C8—522no—
162C4⋊C4—262no—
163C4⋊C4—262no—
164C22⋊C4—522no—
165C22⋊C4—522no—
166C42C2×D5211yescharacteristic
167C42#612711yescharacteristic
168C42D4×D1312yes—
169C13#1052411yescharacteristic, complemented, Sylow
170C23—522no—
171C23#8820111yescharacteristic
172Q8—1042no—
173D4—522no—
174D4—522no—
175D4—1042no—
176D4—1042no—
177D4—1044no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—522no—
182C2×C4—1044no—
183C2×C4#8814812yes—
184C2×C4#8814912yes—
185C2×C4#8818411yescharacteristic
186C2×C4#8819111yescharacteristic
187C8—24no—
188C8—42no—
189C8—81no—
190C8—1042no—
191C22—21no—
192C22—22no—
193C22—1042no—
194C22—1042no—
195C22—1042no—
196C22#1171865211yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—1042no—
201C4#1171873811yescharacteristic
202C4#1171875611yescharacteristic
203C2—41no—
204C2—2082no—
205C2#1311606011yescharacteristic
206C2#1311611112yes—
subgroupG/H
centerC22#11718652
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1849C2
socleC22×C13#394
prime radical#13126217C2
hypercenter#1849D13
hypocenterC13#10524
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1849

Complements

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

NH ≅ G/Ntype
2. #13113556C2semidirect
3. #13113446C2semidirect
4. #13112747C2semidirect
5. C13×#1849C2semidirect
68. #1849D13semidirect
169. C13#10524semidirect

Maximal subgroups

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

subgroupindex
#131262172
#131135562
#131134462
#131127472
C13×#18492
#1052413