Finite Group Databasebeta

← #15766994

Subgroups — #15766994

Order 3328.

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#13126146C211yesmaximal, characteristic
2#13113529C212yesmaximal, complemented
3#13113343C212yesmaximal, complemented
4#13112706C211yesmaximal, characteristic, complemented
5C13×#1832C211yesmaximal, characteristic, complemented
6#11719182C2212yes—
7C2×C13×C4⋊C8C2211yescharacteristic
8C2×C13×C4⋊C8C2211yescharacteristic
9C13×#376C2211yescharacteristic
10#11718776—22no—
11#11718587C2212yes—
12#11718507—22no—
13#11718504—22no—
14C13×#336—22no—
15#11718077—22no—
16#11718073—22no—
17#11718043—24no—
18C2×#6127—22no—
19C22×C8×C13—21no—
20C22×C8×C13D412yes—
21C2×C42×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×C4⋊C8—22no—
32C13×C4⋊C8—22no—
33C13×#95—21no—
34C13×#95D412yes—
35C22⋊#1055—22no—
36#88061—24no—
37#88058—22no—
38C4⋊#1055—22no—
39#88043—22no—
40#10513—131nomaximal, Sylow
41C22×C4×C13—22no—
42C22×C4×C13C2×D411yescharacteristic
43C22×C4×C13C2×D411yescharacteristic
44C22×C4×C13#4111yescharacteristic
45C2×C22⋊D13—42no—
46#6127—84no—
47C2×D52—22no—
48C2×D52—22no—
49C2×D52—22no—
50C2×C4×D13—42no—
51C2×Dic26—22no—
52C2×C8×C13—22no—
53C2×C8×C13—42no—
54C2×C8×C13—42no—
55C2×C8×C13—41no—
56C42×C13—41no—
57C42×C13—41no—
58C42×C13C2×D412yes—
59C42×C13#4112yes—
60#6103—42no—
61#6103—42no—
62C4⋊Dic13—22no—
63C4⋊Dic13—22no—
64C2×#1055—42no—
65D104—82no—
66#3245—131no—
67#1832D1311yescharacteristic, complemented
68#1551—132no—
69#1505—132no—
70#1290—131no—
71C23×C13#12111yescharacteristic
72C22×D13—42no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—41no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13#12011yescharacteristic
81C2×C4×C13#12112yes—
82C2×C4×C13#12312yes—
83C2×C4×C13#12411yescharacteristic
84C22⋊D13—84no—
85C2×Dic13—42no—
86D52—42no—
87D52—42no—
88D52—82no—
89D52—82no—
90C4×D13—84no—
91Dic26—82no—
92C8×C13—42no—
93C8×C13—81no—
94#1055—82no—
95#532—132no—
96#474—262no—
97#466—262no—
98#459—262no—
99#432—132no—
100C2×C4⋊C8C2×D1311yescharacteristic
101C2×C4⋊C8C2×D1311yescharacteristic
102#376C2×D1311yescharacteristic
103#336—22no—
104#333—262no—
105#331—262no—
106#327—264no—
107C22×C13—21no—
108C22×C13—21no—
109C22×C13#39411yescharacteristic
110C22×C13#47212yes—
111C2×D13—82no—
112C2×D13—82no—
113C2×D13—82no—
114C4×C13—22no—
115C4×C13—21no—
116C4×C13—22no—
117C4×C13—82no—
118C4×C13#45411yescharacteristic
119C4×C13#45511yescharacteristic
120Dic13—82no—
121C2×#41—262no—
122C2×D8—262no—
123C22×C8—21no—
124C22×C8C22⋊D1312yes—
125C4⋊Q8—132no—
126#127—132no—
127#124—262no—
128#121—262no—
129#121—262no—
130C4×D4—262no—
131C4×D4—262no—
132C2×C42—21no—
133C2×C42C22×D1311yescharacteristic
134#107—262no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—262no—
138#102—264no—
139C22⋊C8—262no—
140#97—262no—
141#95—21no—
142#95D5212yes—
143C2×C13—22no—
144C2×C13#204011yescharacteristic
145C2×C13#204511yescharacteristic
146C2×C13#205311yescharacteristic
147D13—162no—
148#41—1044no—
149C2×Q8—262no—
150C2×D4—262no—
151C2×D4—262no—
152C2×D4—262no—
153C2×D4—522no—
154C22×C4—22no—
155C22×C4—522no—
156C22×C4C2×D5211yescharacteristic
157C22×C4#612711yescharacteristic
158C22×C4C2×C22⋊D1311yescharacteristic
159D8—1042no—
160C2×C8—22no—
161C2×C8—42no—
162C2×C8—42no—
163C2×C8—41no—
164C2×C8—522no—
165C4⋊C4—262no—
166C4⋊C4—262no—
167C22⋊C4—522no—
168C22⋊C4—522no—
169C42—41no—
170C42—41no—
171C42D4×D1312yes—
172C42#613112yes—
173C13#1051311yescharacteristic, complemented, Sylow
174C23—522no—
175C23#8818411yescharacteristic
176Q8—1042no—
177D4—522no—
178D4—522no—
179D4—1042no—
180D4—1042no—
181D4—1044no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—522no—
190C2×C4—1044no—
191C2×C4#8814812yes—
192C2×C4#8814912yes—
193C2×C4#8819111yescharacteristic
194C2×C4#8820111yescharacteristic
195C8—42no—
196C8—81no—
197C8—1042no—
198C22—21no—
199C22—21no—
200C22—1042no—
201C22—1042no—
202C22—1042no—
203C22#1171865211yescharacteristic
204C22#1171880312yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—82no—
209C4—1042no—
210C4#1171872211yescharacteristic
211C4#1171872311yescharacteristic
212C2—22no—
213C2—2082no—
214C2#1311606511yescharacteristic
215C2#1311609211yescharacteristic
216C2#1311614211yescharacteristic
subgroupG/H
centerC22#11718652
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1832C2
socleC22×C13#394
prime radical#13126146C2
hypercenter#1832D13
hypocenterC13#10513
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1832

Complements

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

NH ≅ G/Ntype
2. #13113529C2semidirect
3. #13113343C2semidirect
4. #13112706C2semidirect
5. C13×#1832C2semidirect
67. #1832D13semidirect
173. C13#10513semidirect

Maximal subgroups

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

subgroupindex
#131261462
#131135292
#131133432
#131127062
C13×#18322
#1051313