Finite Group Databasebeta

← #15774433

Subgroups — #15774433

Order 3328.

292 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 69 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#13125483C211yesmaximal, characteristic
2#13116651C211yesmaximal, characteristic, complemented
3#13116600C211yesmaximal, characteristic, complemented
4#13112898C211yesmaximal, characteristic, complemented
5#13112896C211yesmaximal, characteristic, complemented
6#13112873C211yesmaximal, characteristic, complemented
7C13×#1357C211yesmaximal, characteristic, complemented
8#11719424C412yes—
9C13×#493C2211yescharacteristic
10#11718820—21no—
11#11718818—21no—
12#11718813—21no—
13D8×Dic13—21no—
14#11718732C412yes—
15D13×M32—21no—
16#11718350C2211yescharacteristic
17#11718344C2211yescharacteristic
18C13×#364C2211yescharacteristic
19C13×#364C2211yescharacteristic
20#11718106—21no—
21#11718104—21no—
22#11718103—21no—
23#11718055C2211yescharacteristic
24#11718055C2211yescharacteristic
25C2×C13×D8—21no—
26C2×C13×D8—21no—
27C13×#127C2×C412yes—
28#88193—42no—
29#88192—22no—
30#88189—42no—
31D4×Dic13—22no—
32C2×#6094D411yescharacteristic
33C2×C8×D13D411yescharacteristic
34#88126C2×C411yescharacteristic
35#88124C2×C412yes—
36C13×M32—21no—
37C13×M32—21no—
38C4×C8×C13C2311yescharacteristic
39#88072—22no—
40#88072—22no—
41#88058—21no—
42#88057—21no—
43#88055D411yescharacteristic
44C8×Dic13D411yescharacteristic
45#88052—21no—
46#88052—21no—
47#88043C2×C411yescharacteristic
48#88038—41no—
49C16×D13—41no—
50#11989—131nomaximal, Sylow
51C2×D4×C13—22no—
52C2×D4×C13—42no—
53C2×C22⋊D13—42no—
54C22×Dic13—42no—
55C2×C4×D13C22⋊C411yescharacteristic
56C13×D8—41no—
57C13×D8—41no—
58C13×D8—41no—
59C13×D8—41no—
60C2×C8×C13C2×D411yescharacteristic
61C2×C8×C13C2×D411yescharacteristic
62C42×C13C22×C411yescharacteristic
63C22⋊Dic13—42no—
64C22⋊Dic13—42no—
65#6103—21no—
66C4⋊Dic13—22no—
67#6101—21no—
68#6101—42no—
69C4×Dic13C22⋊C411yescharacteristic
70C2×#1055C22⋊C411yescharacteristic
71C2×#1055C22⋊C411yescharacteristic
72#6094—21no—
73#6094—21no—
74C8×D13—21no—
75C8×D13—21no—
76C13×C16—41no—
77C13×C16—41no—
78#6090—41no—
79#6090—41no—
80#3176—131no—
81#2166—131no—
82#2153—131no—
83#1366—131no—
84#1366—131no—
85#1357—131no—
86#1357D1311yescharacteristic, complemented
87C23×C13—42no—
88C22×D13#10011yescharacteristic
89D4×C13—42no—
90D4×C13—42no—
91D4×C13—162no—
92C2×C4×C13—21no—
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C22⋊D13—162no—
95C2×Dic13—21no—
96C2×Dic13—42no—
97C2×Dic13—162no—
98C2×Dic13#10011yescharacteristic
99C4×D13—21no—
100C4×D13—21no—
101C8×C13#13511yescharacteristic
102C8×C13#13511yescharacteristic
103C8×C13AGL(1,ℤ/8)11yescharacteristic
104C8×C13#13711yescharacteristic
105#1055—21no—
106#1055—21no—
107#540—132no—
108C2×M32—261no—
109#499—131no—
110#493C2×D1311yescharacteristic
111#490—132no—
112#469—261no—
113#466—261no—
114#442—261no—
115C4×D8—261no—
116#405—131no—
117#364—131no—
118#364—131no—
119#364—261no—
120#364C2×D1311yescharacteristic
121#364C2×D1311yescharacteristic
122#349—261no—
123#347—261no—
124C22×C13—82no—
125C22×C13—82no—
126C22×C13—82no—
127C22×C13C2×#10011yescharacteristic
128C2×D13—21no—
129C2×D13—41no—
130C4×C13—41no—
131C4×C13#41611yescharacteristic
132C4×C13#41711yescharacteristic
133Dic13—21no—
134Dic13—41no—
135Dic13—82no—
136C2×D8—21no—
137C2×D8—21no—
138C2×M16—131no—
139C22×C8—131no—
140#127C4×D1312yes—
141#125—132no—
142#123—522no—
143#121—262no—
144#121—522no—
145C4×D4—262no—
146#117—131no—
147M32—21no—
148M32—21no—
149M32—261no—
150M32—261no—
151M32—521no—
152C2×C16—521no—
153#107—261no—
154#106—261no—
155#102—262no—
156#102—262no—
157#97—131no—
158#97—131no—
159C4×C8—131no—
160C4×C8C22×D1311yescharacteristic
161C2×C13—21no—
162C2×C13—162no—
163C2×C13#155111yescharacteristic
164D13—41no—
165C2×D4—22no—
166C2×D4—42no—
167C2×D4—522no—
168C22×C4—131no—
169C22×C4—522no—
170D8—41no—
171D8—41no—
172D8—41no—
173D8—41no—
174M16—261no—
175M16—261no—
176C2×C8—131no—
177C2×C8—131no—
178C2×C8—261no—
179C2×C8—261no—
180C2×C8D4×D1311yescharacteristic
181C2×C8D4×D1311yescharacteristic
182C4⋊C4—261no—
183C4⋊C4—262no—
184C4⋊C4—522no—
185C22⋊C4—261no—
186C22⋊C4—522no—
187C22⋊C4—522no—
188C42—131no—
189C42C2×C4×D1311yescharacteristic
190C16—41no—
191C16—41no—
192C16—521no—
193C16—521no—
194C13#1198911yescharacteristic, complemented, Sylow
195C23—42no—
196C23—131no—
197D4—42no—
198D4—42no—
199D4—162no—
200D4—2082no—
201C2×C4—21no—
202C2×C4—131no—
203C2×C4—261no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—522no—
207C2×C4—2082no—
208C2×C4C22⋊C4×D1311yescharacteristic
209C8—261no—
210C8—261no—
211C8#8816511yescharacteristic
212C8#8816611yescharacteristic
213C8#8816911yescharacteristic
214C8#8817011yescharacteristic
215C22—82no—
216C22—82no—
217C22—82no—
218C22—261no—
219C22—521no—
220C22D13×#10011yescharacteristic
221C4—41no—
222C4—261no—
223C4—521no—
224C4—1042no—
225C4#1171843211yescharacteristic
226C4#1171843311yescharacteristic
227C2—21no—
228C2—162no—
229C2—521no—
230C2#1311352811yescharacteristic
subgroupG/H
centerC2#13113528
commutatorC42×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1357C2
socleC2×C13#1551
prime radical#13125483C2
cosocleC4×C8×C13C23
hypercenter#1357D13
hypocenterC13#11989
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1357

Complements

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

NH ≅ G/Ntype
2. #13116651C2semidirect
3. #13116600C2semidirect
4. #13112898C2semidirect
5. #13112896C2semidirect
6. #13112873C2semidirect
7. C13×#1357C2semidirect
86. #1357D13semidirect
194. C13#11989semidirect

Maximal subgroups

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

subgroupindex
#131254832
#131166512
#131166002
#131128982
#131128962
#131128732
C13×#13572
#1198913