Finite Group Databasebeta

← #15760533

Subgroups — #15760533

Order 3328.

452 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 107 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#13113574C211yesmaximal, characteristic, complemented
3#13113503C212yesmaximal
4#13112727C212yesmaximal, complemented
5C13×#2986C211yesmaximal, characteristic, complemented
6C13×#533C2211yescharacteristic
7C2×#88128C2211yescharacteristic
8C13×#446—22no—
9C8×Q8×C13—22no—
10C13×#433—22no—
11C13×#431C2212yes—
12#11718749—22no—
13#11718728C414yes—
14#11718662—22no—
15#11718585C2212yes—
16C4×#6099C2211yescharacteristic
17#11718139—22no—
18#11718077—22no—
19#11718077—22no—
20C22×D52—21no—
21C22×D52—22no—
22C13×C4⋊Q8D412yes—
23C13×#125C2×C412yes—
24C13×C22⋊Q8—22no—
25C4×Q8×C13—22no—
26C13×#117D412yes—
27C2×C42×C13C2311yescharacteristic
28C2×#6099—21no—
29C2×#6099—22no—
30#88128—21no—
31#88128—22no—
32#88128C2×C412yes—
33C13×C4⋊C8—24no—
34C13×C4⋊C8D412yes—
35C13×C4⋊C8D412yes—
36C13×C22⋊C8—22no—
37C13×#97—22no—
38C4×C8×C13—22no—
39C4×C8×C13—22no—
40#88049—28no—
41C4⋊#1055—22no—
42C4⋊#1055—22no—
43#88043C2×C412yes—
44C4×#1055—21no—
45#9438—131nomaximal, Sylow
46C23×D13—41no—
47C2×Q8×C13—22no—
48C22×C4×C13C2×D411yescharacteristic
49C22×C4×C13#4112yes—
50C2×D52—22no—
51C2×D52—24no—
52C2×D52—44no—
53C2×D52—41no—
54C2×D52—42no—
55C2×D52—82no—
56C2×D52—82no—
57C2×C8×C13—22no—
58C2×C8×C13—22no—
59C13×C4⋊C4—24no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4C22⋊C414yes—
62C13×C22⋊C4—22no—
63C42×C13—22no—
64C42×C13C22×C411yescharacteristic
65C42×C13C2×D411yescharacteristic
66C42×C13C2×D412yes—
67#6099—42no—
68#6099—82no—
69C2×#1055—22no—
70C2×#1055—42no—
71#3138—131no—
72#2986D1311yescharacteristic, complemented
73#1561—131no—
74#1545—132no—
75#1299—132no—
76C23×C13#12311yescharacteristic
77C22×D13—42no—
78C22×D13—82no—
79C22×D13—84no—
80Q8×C13—42no—
81Q8×C13—42no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—24no—
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13C4×D412yes—
88C2×C4×C13#12011yescharacteristic
89C2×C4×C13#12112yes—
90D52—44no—
91D52—84no—
92D52—82no—
93D52—82no—
94D52—82no—
95C8×C13—42no—
96C8×C13—42no—
97#1055—42no—
98#1055—82no—
99#533C2×D1311yescharacteristic
100C2×#127—131no—
101#490—134no—
102#486—262no—
103#446—22no—
104C8×Q8—22no—
105#433—22no—
106#431C2×D1312yes—
107#423—132no—
108#418—262no—
109C4×M16—131no—
110#332—262no—
111#331—262no—
112#331—262no—
113C22×C13—21no—
114C22×C13—22no—
115C22×C13#38611yescharacteristic
116C2×D13—82no—
117C2×D13—84no—
118C2×D13—164no—
119C4×C13—21no—
120C4×C13—22no—
121C4×C13—44no—
122C4×C13#45412yes—
123C4×C13#47112yes—
124C4×C13#47212yes—
125C22×D4—262no—
126C22×D4—261no—
127C2×M16—261no—
128C2×M16—262no—
129C4⋊Q8D5212yes—
130#127—132no—
131#127—261no—
132#127—262no—
133#125C4×D1312yes—
134C22⋊Q8—22no—
135C4×Q8—22no—
136#117C22⋊D1312yes—
137C2×C42C22×D1311yescharacteristic
138C4⋊C8—24no—
139C4⋊C8—262no—
140C4⋊C8—262no—
141C4⋊C8C22⋊D1312yes—
142C4⋊C8C22⋊D1312yes—
143#102—268no—
144C22⋊C8—22no—
145#97—22no—
146#97—132no—
147C4×C8—22no—
148C4×C8—22no—
149C4×C8—261no—
150C2×C13—41no—
151C2×C13#188811yescharacteristic
152C2×C13#190712yes—
153D13—162no—
154C24—521no—
155C2×Q8—22no—
156C2×D4—262no—
157C2×D4—264no—
158C2×D4—524no—
159C2×D4—522no—
160C2×D4—521no—
161C2×D4—1042no—
162C2×D4—1042no—
163C22×C4#612712yes—
164C22×C4C2×C22⋊D1311yescharacteristic
165M16—522no—
166M16—1042no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—262no—
170C2×C8—522no—
171C4⋊C4—24no—
172C4⋊C4—22no—
173C4⋊C4#610314yes—
174C22⋊C4—22no—
175C42—22no—
176C42C2×C4×D1311yescharacteristic
177C42C2×D5211yescharacteristic
178C42C2×C22⋊D1312yes—
179C13#943811yescharacteristic, complemented, Sylow
180C23—522no—
181C23—1042no—
182C23—1044no—
183C23#8818311yescharacteristic
184Q8—42no—
185Q8—42no—
186D4—524no—
187D4—1044no—
188D4—1042no—
189D4—1042no—
190D4—1042no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4C2×#610311yescharacteristic
196C2×C4C4×C22⋊D1312yes—
197C2×C4#8818412yes—
198C2×C4#8820711yescharacteristic
199C8—42no—
200C8—42no—
201C8—522no—
202C8—1042no—
203C22—21no—
204C22—22no—
205C22—1042no—
206C22—1044no—
207C22—2084no—
208C22#1171887411yescharacteristic
209C4—21no—
210C4—22no—
211C4—44no—
212C4#1171880212yes—
213C4#1171880312yes—
214C4#1171890612yes—
215C2—41no—
216C2—2082no—
217C2#1311523911yescharacteristic
218C2#1311534412yes—
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2986C2
socleC22×C13#386
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#2986D13
hypocenterC13#9438
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2986

Complements

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

NH ≅ G/Ntype
2. #13113574C2semidirect
4. #13112727C2semidirect
5. C13×#2986C2semidirect
72. #2986D13semidirect
179. C13#9438semidirect

Maximal subgroups

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

subgroupindex
#131252122
#131135742
#131135032
#131127272
C13×#29862
#943813