Finite Group Databasebeta

← #15757881

Subgroups — #15757881

Order 3328.

398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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#13125184C211yesmaximal, characteristic
2#13123942C211yesmaximal, characteristic, complemented
3#13113306C212yesmaximal
4#13112736C212yesmaximal, complemented
5C13×#1544C211yesmaximal, characteristic, complemented
6C13×#533C2211yescharacteristic
7#11719182C2211yescharacteristic
8C13×#431C2212yes—
9#11718750—22no—
10#11718730C412yes—
11#11718728C412yes—
12#11718685—24no—
13#11718663—22no—
14#11718661—22no—
15#11718587C2212yes—
16C2×#88043C2211yescharacteristic
17C13×#332—22no—
18#11718051—24no—
19C2×#6127—21no—
20C13×C4⋊Q8D412yes—
21C13×#125C2×C412yes—
22C13×C22⋊Q8—22no—
23C4×Q8×C13—22no—
24C13×#117D412yes—
25C2×C42×C13C2311yescharacteristic
26#88184—22no—
27C22×#1055—21no—
28#88129—21no—
29#88128C2×C411yescharacteristic
30C4×D52—22no—
31#88123C2×C411yescharacteristic
32C13×C4⋊C8—22no—
33C13×C22⋊C8—22no—
34C4×C8×C13—22no—
35C22⋊#1055—22no—
36#88050—24no—
37#88049—24no—
38C4⋊#1055—24no—
39C4⋊#1055D414yes—
40#88043—22no—
41#88043—22no—
42#88043—21no—
43#88043C2×C412yes—
44C4×#1055—22no—
45#9008—131nomaximal, Sylow
46C2×Q8×C13—22no—
47C22×C4×C13C2×D411yescharacteristic
48C22×C4×C13#4112yes—
49C2×C22⋊D13—41no—
50#6127—44no—
51C2×D52—21no—
52C2×D52—22no—
53C2×C4×D13—41no—
54C2×Dic26—21no—
55C2×C8×C13—42no—
56C13×C4⋊C4—24no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4C22⋊C414yes—
59C13×C22⋊C4—22no—
60C42×C13—22no—
61C42×C13C22×C411yescharacteristic
62C42×C13C2×D412yes—
63C42×C13C2×D411yescharacteristic
64#6103—42no—
65C4⋊Dic13—22no—
66C2×#1055—22no—
67C2×#1055—24no—
68C2×#1055—42no—
69#3135—131no—
70#2987—131no—
71#1544D1311yescharacteristic, complemented
72#1496—132no—
73#1302—132no—
74C23×C13#12311yescharacteristic
75C22×D13—41no—
76Q8×C13—82no—
77C2×C4×C13—22no—
78C2×C4×C13—24no—
79C2×C4×C13—42no—
80C2×C4×C13C2×C22⋊C411yescharacteristic
81C2×C4×C13C4×D412yes—
82C2×C4×C13#12011yescharacteristic
83C2×C4×C13#12112yes—
84C22⋊D13—82no—
85C2×Dic13—41no—
86D52—44no—
87D52—42no—
88C4×D13—82no—
89Dic26—42no—
90C8×C13—82no—
91#1055—42no—
92#1055—44no—
93#533C2×D1311yescharacteristic
94#532—131no—
95#491—132no—
96#490—132no—
97#489—262no—
98#446—264no—
99#433—262no—
100#432—132no—
101#431C2×D1312yes—
102#416—262no—
103C2×#97—131no—
104#332—22no—
105D4⋊C8—264no—
106C22×C13—22no—
107C22×C13—21no—
108C22×C13#38611yescharacteristic
109C2×D13—82no—
110C2×D13—81no—
111C4×C13—22no—
112C4×C13—22no—
113C4×C13—21no—
114C4×C13—44no—
115C4×C13#45412yes—
116Dic13—81no—
117C2×#41—261no—
118C22×C8—261no—
119C4⋊Q8—131no—
120C4⋊Q8C22⋊D1312yes—
121#127—131no—
122#125C4×D1312yes—
123#124—261no—
124C22⋊Q8—22no—
125#121—262no—
126C4×Q8—22no—
127C4×D4—262no—
128#117D5212yes—
129C2×C42C22×D1311yescharacteristic
130C4⋊C8—22no—
131C4⋊C8—134no—
132C4⋊C8—264no—
133#103—264no—
134#102—264no—
135C22⋊C8—22no—
136C22⋊C8—262no—
137#97—132no—
138#97—262no—
139#97—262no—
140#97—261no—
141C4×C8—22no—
142C4×C8—262no—
143C2×C13—41no—
144C2×C13#188112yes—
145C2×C13#188811yescharacteristic
146D13—161no—
147#41—524no—
148C2×Q8—22no—
149C2×Q8—261no—
150C2×D4—262no—
151C2×D4—261no—
152C2×D4—521no—
153C22×C4—521no—
154C22×C4C2×D5211yescharacteristic
155C22×C4#612912yes—
156C2×C8—42no—
157C2×C8—264no—
158C2×C8—262no—
159C2×C8—522no—
160C4⋊C4—24no—
161C4⋊C4—22no—
162C4⋊C4—262no—
163C4⋊C4#610314yes—
164C22⋊C4—22no—
165C22⋊C4—522no—
166C42—22no—
167C42C2×C4×D1311yescharacteristic
168C42D4×D1312yes—
169C42C2×C22⋊D1311yescharacteristic
170C13#900811yescharacteristic, complemented, Sylow
171C23—521no—
172C23#8814011yescharacteristic
173Q8—82no—
174Q8—522no—
175D4—524no—
176D4—522no—
177D4—1042no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—42no—
181C2×C4—521no—
182C2×C4—1042no—
183C2×C4#8813512yes—
184C2×C4#8813611yescharacteristic
185C2×C4C2×#610311yescharacteristic
186C2×C4#8819312yes—
187C8—82no—
188C8—522no—
189C8—524no—
190C22—22no—
191C22—21no—
192C22—1042no—
193C22—1041no—
194C22#1171861911yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—44no—
199C4—1041no—
200C4#1171841412yes—
201C2—41no—
202C2—2081no—
203C2#1311519612yes—
204C2#1311523711yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1544C2
socleC22×C13#386
prime radical#11719182C22
cosocleC2×C42×C13C23
hypercenter#1544D13
hypocenterC13#9008
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
2. #13123942C2semidirect
4. #13112736C2semidirect
5. C13×#1544C2semidirect
71. #1544D13semidirect
170. C13#9008semidirect

Maximal subgroups

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

subgroupindex
#131251842
#131239422
#131133062
#131127362
C13×#15442
#900813