Finite Group Databasebeta

← #15774438

Subgroups — #15774438

Order 3328.

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

normal subgroups only

This group has 268 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#13125492C211yesmaximal, characteristic
2#13116651C211yesmaximal, characteristic
3#13116600C211yesmaximal, characteristic
4#13112898C211yesmaximal, characteristic, complemented
5#13112896C211yesmaximal, characteristic, complemented
6#13112875C211yesmaximal, characteristic, complemented
7C13×#1358C211yesmaximal, characteristic, complemented
8#11719436C412yes—
9C13×#494C2211yescharacteristic
10#11718850—21no—
11#11718849—21no—
12#11718845—21no—
13Q16×Dic13—21no—
14#11718743C412yes—
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×Q16—21no—
26C2×C13×Q16—21no—
27C13×C4⋊Q8C2×C412yes—
28#88200—22no—
29Q8×Dic13—22no—
30C2×#6094D411yescharacteristic
31C2×C8×D13D411yescharacteristic
32#88152—42no—
33#88143—42no—
34#88126C2×C411yescharacteristic
35#88124C2×C412yes—
36C13×M32—21no—
37C13×M32—21no—
38C4×C8×C13C2311yescharacteristic
39#88075—22no—
40#88075—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#11990—131nomaximal, Sylow
51C2×Q8×C13—22no—
52C2×C4×D13C22⋊C411yescharacteristic
53C13×Q16—41no—
54C13×Q16—41no—
55C13×Q16—41no—
56C13×Q16—41no—
57C2×C8×C13C2×D411yescharacteristic
58C2×C8×C13C2×D411yescharacteristic
59C13×C4⋊C4—42no—
60C42×C13C22×C411yescharacteristic
61#6103—21no—
62#6103—42no—
63C4⋊Dic13—22no—
64C4⋊Dic13—42no—
65#6101—21no—
66#6101—42no—
67#6101—42no—
68C4×Dic13—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#3177—131no—
81#2166—131no—
82#2153—131no—
83#1366—131no—
84#1366—131no—
85#1358—131no—
86#1358D1311yescharacteristic, complemented
87C22×D13#10011yescharacteristic
88Q8×C13—42no—
89Q8×C13—42no—
90C2×C4×C13—21no—
91C2×C4×C13—42no—
92C2×C4×C13C2×C22⋊C411yescharacteristic
93C2×Dic13—21no—
94C2×Dic13—42no—
95C2×Dic13#10011yescharacteristic
96C4×D13—21no—
97C4×D13—21no—
98C8×C13#13511yescharacteristic
99C8×C13#13511yescharacteristic
100C8×C13AGL(1,ℤ/8)11yescharacteristic
101C8×C13#13711yescharacteristic
102#1055—21no—
103#1055—21no—
104#541—132no—
105C2×M32—261no—
106#499—131no—
107#494C2×D1311yescharacteristic
108#491—132no—
109#470—261no—
110#467—261no—
111#441—261no—
112C4×Q16—261no—
113#405—131no—
114#364—131no—
115#364—131no—
116#364—261no—
117#364C2×D1311yescharacteristic
118#364C2×D1311yescharacteristic
119#349—261no—
120#347—261no—
121C22×C13C2×#10011yescharacteristic
122C2×D13—21no—
123C2×D13—41no—
124C4×C13—41no—
125C4×C13—82no—
126C4×C13#41611yescharacteristic
127C4×C13#41711yescharacteristic
128Dic13—21no—
129Dic13—41no—
130Dic13—82no—
131C2×Q16—21no—
132C2×Q16—21no—
133C2×M16—131no—
134C22×C8—131no—
135C4⋊Q8C4×D1312yes—
136#126—522no—
137#125—132no—
138#125—522no—
139C22⋊Q8—262no—
140C4×Q8—262no—
141#117—131no—
142M32—21no—
143M32—21no—
144M32—261no—
145M32—261no—
146M32—521no—
147C2×C16—521no—
148#107—261no—
149#106—261no—
150#103—262no—
151#103—262no—
152#97—131no—
153#97—131no—
154C4×C8—131no—
155C4×C8C22×D1311yescharacteristic
156C2×C13—21no—
157C2×C13#155111yescharacteristic
158D13—41no—
159C2×Q8—22no—
160C22×C4—131no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16—41no—
165M16—261no—
166M16—261no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—261no—
170C2×C8—261no—
171C2×C8D4×D1311yescharacteristic
172C2×C8D4×D1311yescharacteristic
173C4⋊C4—42no—
174C4⋊C4—261no—
175C4⋊C4—262no—
176C4⋊C4—522no—
177C4⋊C4—522no—
178C4⋊C4—522no—
179C22⋊C4—261no—
180C22⋊C4—522no—
181C42—131no—
182C42—522no—
183C42C2×C4×D1311yescharacteristic
184C16—41no—
185C16—41no—
186C16—521no—
187C16—521no—
188C13#1199011yescharacteristic, complemented, Sylow
189C23—131no—
190Q8—42no—
191Q8—42no—
192C2×C4—21no—
193C2×C4—42no—
194C2×C4—131no—
195C2×C4—261no—
196C2×C4—261no—
197C2×C4—261no—
198C2×C4—522no—
199C2×C4C22⋊C4×D1311yescharacteristic
200C8—261no—
201C8—261no—
202C8#8816511yescharacteristic
203C8#8816611yescharacteristic
204C8#8816911yescharacteristic
205C8#8817011yescharacteristic
206C22—261no—
207C22—521no—
208C22D13×#10011yescharacteristic
209C4—41no—
210C4—82no—
211C4—261no—
212C4—521no—
213C4—1042no—
214C4#1171843211yescharacteristic
215C4#1171843311yescharacteristic
216C2—21no—
217C2—521no—
218C2#1311352811yescharacteristic
subgroupG/H
centerC2#13113528
commutatorC42×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#1358C2
socleC2×C13#1551
prime radicalC22×D13#100
cosocleC4×C8×C13C23
hypercenter#1358D13
hypocenterC13#11990
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
4. #13112898C2semidirect
5. #13112896C2semidirect
6. #13112875C2semidirect
7. C13×#1358C2semidirect
86. #1358D13semidirect
188. C13#11990semidirect

Maximal subgroups

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

subgroupindex
#131254922
#131166512
#131166002
#131128982
#131128962
#131128752
C13×#13582
#1199013