Finite Group Databasebeta

← #15760449

Subgroups — #15760449

Order 3328.

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

normal subgroups only

This group has 436 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#13125212C211yesmaximal, characteristic
2#13123942C211yesmaximal, characteristic, complemented
3#13113549C212yesmaximal
4#13112709C212yesmaximal, complemented
5C13×#1537C211yesmaximal, characteristic, complemented
6C13×#533C2211yescharacteristic
7C2×#88128C2211yescharacteristic
8C13×#432C2212yes—
9#11718749C414yes—
10#11718728—22no—
11#11718685—24no—
12#11718662—22no—
13#11718661—22no—
14#11718587C2212yes—
15C4×#6099C2211yescharacteristic
16C13×#330—22no—
17#11718077—24no—
18C22×D52—21no—
19C22×D52—22no—
20C13×C4⋊Q8C2×C412yes—
21C13×#125D412yes—
22C13×C22⋊Q8—22no—
23C4×Q8×C13—22no—
24C13×#117D412yes—
25C2×C42×C13C2311yescharacteristic
26C2×#6099—21no—
27#88128—21no—
28#88128—22no—
29#88128C2×C412yes—
30C13×C4⋊C8—22no—
31C13×C22⋊C8—22no—
32C13×#97—22no—
33C22⋊#1055—22no—
34#88049—28no—
35C4⋊#1055—24no—
36C4⋊#1055D414yes—
37#88043—22no—
38#88043—22no—
39#88043—21no—
40C4×#1055—22no—
41C4×#1055C2×C412yes—
42#9424—131nomaximal, Sylow
43C23×D13—41no—
44C2×Q8×C13—22no—
45C22×C4×C13C2×D411yescharacteristic
46C22×C4×C13#4112yes—
47C2×D52—22no—
48C2×D52—24no—
49C2×D52—44no—
50C2×D52—41no—
51C2×D52—42no—
52C2×D52—84no—
53C2×C8×C13—42no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—24no—
56C13×C4⋊C4C22⋊C414yes—
57C13×C22⋊C4—22no—
58C42×C13—22no—
59C42×C13C22×C411yescharacteristic
60C42×C13C2×D412yes—
61C42×C13C2×D411yescharacteristic
62#6099—42no—
63C2×#1055—22no—
64C2×#1055—24no—
65#3138—131no—
66#2987—131no—
67#1555—132no—
68#1537D1311yescharacteristic, complemented
69#1291—132no—
70C23×C13#12311yescharacteristic
71C22×D13—42no—
72C22×D13—82no—
73C22×D13—84no—
74Q8×C13—82no—
75C2×C4×C13—22no—
76C2×C4×C13—24no—
77C2×C4×C13—42no—
78C2×C4×C13C2×C22⋊C411yescharacteristic
79C2×C4×C13C4×D412yes—
80C2×C4×C13#12011yescharacteristic
81C2×C4×C13#12112yes—
82D52—44no—
83D52—84no—
84D52—84no—
85D52—82no—
86C8×C13—82no—
87#1055—42no—
88#1055—44no—
89#533C2×D1311yescharacteristic
90C2×#127—131no—
91#490—262no—
92#486—134no—
93#446—264no—
94#433—262no—
95#432—132no—
96#432C2×D1312yes—
97#418—262no—
98C4×M16—131no—
99#331—264no—
100#330—22no—
101C22×C13—21no—
102C22×C13—22no—
103C22×C13#38611yescharacteristic
104C2×D13—82no—
105C2×D13—84no—
106C2×D13—164no—
107C4×C13—21no—
108C4×C13—22no—
109C4×C13—22no—
110C4×C13—44no—
111C4×C13#45412yes—
112C22×D4—261no—
113C22×D4—262no—
114C2×M16—261no—
115C4⋊Q8C4×D1312yes—
116#127—132no—
117#127—262no—
118#127—261no—
119#125C22⋊D1312yes—
120C22⋊Q8—22no—
121C4×Q8—22no—
122#117D5212yes—
123C2×C42C22×D1311yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—134no—
126C4⋊C8—264no—
127#102—268no—
128C22⋊C8—22no—
129C22⋊C8—262no—
130#97—22no—
131#97—262no—
132#97—262no—
133#97—261no—
134C4×C8—132no—
135C4×C8—262no—
136C2×C13—41no—
137C2×C13#188811yescharacteristic
138C2×C13#190312yes—
139D13—162no—
140C24—521no—
141C2×Q8—22no—
142C2×D4—264no—
143C2×D4—262no—
144C2×D4—524no—
145C2×D4—521no—
146C2×D4—522no—
147C2×D4—1044no—
148C22×C4C2×D5211yescharacteristic
149C22×C4#612912yes—
150M16—522no—
151C2×C8—42no—
152C2×C8—264no—
153C2×C8—262no—
154C4⋊C4—22no—
155C4⋊C4—24no—
156C4⋊C4#610314yes—
157C22⋊C4—22no—
158C42—22no—
159C42C2×C4×D1311yescharacteristic
160C42D4×D1312yes—
161C42C2×C22⋊D1311yescharacteristic
162C13#942411yescharacteristic, complemented, Sylow
163C23—522no—
164C23—1042no—
165C23—1044no—
166C23#8814011yescharacteristic
167Q8—82no—
168D4—524no—
169D4—1044no—
170D4—1044no—
171D4—1042no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—42no—
175C2×C4#8813512yes—
176C2×C4#8813611yescharacteristic
177C2×C4C2×#610311yescharacteristic
178C2×C4#8819312yes—
179C8—82no—
180C8—522no—
181C8—524no—
182C22—21no—
183C22—22no—
184C22—1042no—
185C22—1044no—
186C22—2084no—
187C22#1171861911yescharacteristic
188C4—21no—
189C4—22no—
190C4—22no—
191C4—44no—
192C4#1171841412yes—
193C2—41no—
194C2—2082no—
195C2#1311523711yescharacteristic
196C2#1311531412yes—
subgroupG/H
centerC22#11718619
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1537C2
socleC22×C13#386
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#1537D13
hypocenterC13#9424
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
2. #13123942C2semidirect
4. #13112709C2semidirect
5. C13×#1537C2semidirect
68. #1537D13semidirect
162. C13#9424semidirect

Maximal subgroups

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

subgroupindex
#131252122
#131239422
#131135492
#131127092
C13×#15372
#942413