Finite Group Databasebeta

← #15760456

Subgroups — #15760456

Order 3328.

534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 99 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#13125210C211yesmaximal, characteristic
2#13113550C211yesmaximal, characteristic
3#13113386C212yesmaximal, complemented
4#13112700C212yesmaximal, complemented
5C13×#2380C211yesmaximal, characteristic
6C2×C13×#127C2211yescharacteristic
7#11719175C2211yescharacteristic
8C13×#386—22no—
9C13×#386—24no—
10C13×#383C2212yes—
11#11718876—22no—
12#11718732—22no—
13#11718731C414yescomplemented
14#11718587C2212yes—
15C4×#6099C2211yescharacteristic
16#11718136—22no—
17#11718044—24no—
18C22×D4×C13—22no—
19C22×D4×C13D412yes—
20C23×C4×C13—22no—
21C13×#127—22no—
22C13×#127C2×C412yes—
23C13×#127D412yes—
24C2×C13×C22⋊C4—24no—
25C2×C13×C22⋊C4—22no—
26C2×C42×C13C2311yescharacteristic
27#88180—21no—
28#88178—22no—
29C2×#6099—21no—
30#88124—21no—
31#88123C2×C412yescomplemented
32C4×Dic26—22no—
33C13×#95—22no—
34C13×#95—22no—
35C13×#95D414yes—
36#88072—28no—
37C22⋊#1055—22no—
38C4⋊#1055—22no—
39#88043—21no—
40#88043—22no—
41C4×#1055C2×C412yescomplemented
42#9425—131nomaximal, Sylow
43C24×C13—22no—
44C2×D4×C13—24no—
45C2×D4×C13—24no—
46C2×D4×C13—22no—
47C2×D4×C13—42no—
48C2×D4×C13—42no—
49C2×D4×C13—82no—
50C2×D4×C13—82no—
51C2×D4×C13C22⋊C414yes—
52C22×C4×C13—24no—
53C22×C4×C13—84no—
54C22×C4×C13—82no—
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D412yes—
57C2×Dic26—22no—
58C13×C22⋊C4—84no—
59C13×C22⋊C4—82no—
60C42×C13C22×C411yescharacteristic
61C42×C13C2×D411yescharacteristic
62C42×C13#4112yes—
63C22⋊Dic13—41no—
64C4⋊Dic13—22no—
65C4⋊Dic13—22no—
66#6101—42no—
67C4×Dic13—41no—
68#6099—42no—
69C2×#1055—22no—
70C2×#1055—42no—
71#3138—131no—
72#2380D1311yescharacteristic
73#1555—131no—
74#1515—132no—
75#1288—132no—
76C23×C13—24no—
77C23×C13—44no—
78C23×C13—44no—
79C23×C13—42no—
80C23×C13—42no—
81C23×C13#12011yescharacteristic
82D4×C13—44no—
83D4×C13—82no—
84D4×C13—84no—
85D4×C13—84no—
86C2×C4×C13—22no—
87C2×C4×C13—42no—
88C2×C4×C13—48no—
89C2×C4×C13—44no—
90C2×C4×C13—88no—
91C2×C4×C13C2×C22⋊C411yescharacteristic
92C2×C4×C13C4×D412yes—
93C2×C4×C13#12112yes—
94C2×C4×C13#12311yescharacteristic
95C2×Dic13—42no—
96Dic26—82no—
97#1055—42no—
98#1055—82no—
99#533—131no—
100C2×#127C2×D1311yescharacteristic
101#490—262no—
102#486—134no—
103#432—132no—
104#418—262no—
105C4×M16—131no—
106#386—22no—
107#386—24no—
108#383C2×D1312yes—
109#331—262no—
110#328—264no—
111C22×C13—22no—
112C22×C13—44no—
113C22×C13—48no—
114C22×C13—82no—
115C22×C13—82no—
116C22×C13—84no—
117C22×C13#38611yescharacteristic
118C22×C13#45512yes—
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—84no—
124Dic13—82no—
125C22×D4—22no—
126C22×D4C22⋊D1312yes—
127C23×C4—22no—
128C2×M16—261no—
129C4⋊Q8—132no—
130#127—22no—
131#127C4×D1312yes—
132#127D5212yes—
133#125—261no—
134C22⋊Q8—262no—
135C4×Q8—262no—
136#117—261no—
137C2×C22⋊C4—24no—
138C2×C22⋊C4—22no—
139C2×C42C22×D1311yescharacteristic
140C4⋊C8—262no—
141#102—268no—
142C22⋊C8—262no—
143#97—261no—
144#97—262no—
145C4×C8—132no—
146#95—22no—
147#95—22no—
148#95C22⋊D1314yes—
149C2×C13—22no—
150C2×C13—84no—
151C2×C13#188511yescharacteristic
152C2×C13#190412yes—
153C24—22no—
154C2×Q8—262no—
155C2×D4—24no—
156C2×D4—22no—
157C2×D4—24no—
158C2×D4—42no—
159C2×D4—42no—
160C2×D4—82no—
161C2×D4—82no—
162C2×D4#610314yes—
163C22×C4—24no—
164C22×C4—84no—
165C22×C4—82no—
166C22×C4C2×C22⋊D1311yescharacteristic
167C22×C4C2×C22⋊D1312yes—
168M16—522no—
169C2×C8—262no—
170C2×C8—522no—
171C4⋊C4—262no—
172C4⋊C4—262no—
173C4⋊C4—522no—
174C22⋊C4—84no—
175C22⋊C4—82no—
176C22⋊C4—521no—
177C42—521no—
178C42C2×C4×D1311yescharacteristic
179C42C2×D5211yescharacteristic
180C42#612712yes—
181C13#942511yescharacteristic, complemented, Sylow
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#8820711yescharacteristic
188Q8—1042no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—48no—
196C2×C4—44no—
197C2×C4—88no—
198C2×C4—522no—
199C2×C4C2×#610311yescharacteristic
200C2×C4C4×C22⋊D1312yes—
201C2×C4#8818311yescharacteristic
202C2×C4#8818412yes—
203C8—522no—
204C8—1042no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22#1171887411yescharacteristic
212C22#1171890312yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—84no—
218C4—1042no—
219C2—22no—
220C2—84no—
221C2#1311522411yescharacteristic
222C2#1311532312yes—
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2380C2
socleC22×C13#386
prime radicalC2×C13×#127C22
cosocleC2×C42×C13C23
hypercenter#2380D13
hypocenterC13#9425
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2380

Complements

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

NH ≅ G/Ntype
3. #13113386C2semidirect
4. #13112700C2semidirect
13. #11718731C4semidirect
31. #88123C2×C4semidirect
41. C4×#1055C2×C4semidirect
181. C13#9425semidirect

Maximal subgroups

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

subgroupindex
#131252102
#131135502
#131133862
#131127002
C13×#23802
#942513