Finite Group Databasebeta

← #15773463

Subgroups — #15773463

Order 3328.

316 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 75 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#13125486C211yesmaximal, characteristic
2#13114591C211yesmaximal, characteristic, complemented
3#13112828C212yesmaximal, complemented
4#13112822C212yesmaximal, complemented
5C13×#2166C211yesmaximal, characteristic, complemented
6#11719240—21no—
7C13×#405C2211yescharacteristic
8#11718796C2212yes—
9#11718776—21no—
10#11718762—21no—
11#11718374—21no—
12#11718372C412yescomplemented
13#11718356C411yescharacteristic, complemented
14C4×D104—21no—
15#11718344C411yescharacteristic, complemented
16C13×#364—21no—
17C13×#349C2212yes—
18C13×#347—21no—
19#11718152C2211yescharacteristic
20#11718149C2211yescharacteristic
21#11718123—21no—
22C2×C13×M16C2311yescharacteristic
23C22×C8×C13D411yescharacteristic
24C13×#117D411yescharacteristic
25#88184—22no—
26#88180—21no—
27C2×#6099—21no—
28C2×D104—21no—
29C2×D104C2×C412yes—
30#88148—42no—
31#88138—42no—
32#88128—21no—
33C4×D52—22no—
34#88124—21no—
35C13×M32—22no—
36C13×#97C2×C411yescharacteristic
37C13×#97D411yescharacteristic
38C4×C8×C13C2×C411yescharacteristic
39C4×C8×C13D411yescharacteristic
40#88061—22no—
41#88061—22no—
42#88058—21no—
43#88057C2×C412yes—
44#88055—22no—
45C8×Dic13—22no—
46#11770—131nomaximal, Sylow
47C22×C4×C13C2×D411yescharacteristic
48C2×C22⋊D13—42no—
49C2×D52—22no—
50C2×D52—42no—
51C2×C4×D13—42no—
52C13×M16—41no—
53C2×C8×C13—21no—
54C2×C8×C13—21no—
55C2×C8×C13C22⋊C411yescharacteristic
56C2×C8×C13C22⋊C411yescharacteristic
57C2×C8×C13C22×C411yescharacteristic
58C2×C8×C13C2×D411yescharacteristic
59C13×C4⋊C4—21no—
60C13×C22⋊C4—21no—
61C42×C13C22⋊C411yescharacteristic
62C42×C13C22⋊C411yescharacteristic
63C22⋊Dic13—41no—
64#6103—42no—
65#6103—42no—
66C4⋊Dic13—22no—
67C4⋊Dic13—41no—
68#6101—42no—
69C4×Dic13—22no—
70#6099—41no—
71#6099—41no—
72C2×#1055—22no—
73D104—42no—
74D104—41no—
75D104—41no—
76C13×C16—42no—
77#3176—131no—
78#2166D1311yescharacteristic, complemented
79#1747—131no—
80#1341—132no—
81#1339—132no—
82C23×C13AGL(1,ℤ/8)11yescharacteristic
83C22×D13—42no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
90C22⋊D13—162no—
91C2×Dic13—42no—
92C2×Dic13—42no—
93D52—42no—
94D52—42no—
95D52—162no—
96C4×D13—162no—
97C8×C13—21no—
98C8×C13—21no—
99C8×C13—21no—
100C8×C13#10411yescharacteristic
101C8×C13#10411yescharacteristic
102#1055—42no—
103#540—261no—
104#499—131no—
105#493—131no—
106#490—261no—
107#469—132no—
108#466—261no—
109#442—132no—
110C4×D8—261no—
111#405—261no—
112#405C2×D1311yescharacteristic
113#364—21no—
114#349C2×D1312yes—
115#347—21no—
116#338—131no—
117H(3,ℤ/4)—131no—
118H(3,ℤ/4)—261no—
119C22×C13—21no—
120C22×C13—41no—
121C22×C13#41811yescharacteristic
122C2×D13—82no—
123C2×D13—82no—
124C2×D13—82no—
125C4×C13—21no—
126C4×C13—41no—
127C4×C13—41no—
128C4×C13#41011yescharacteristic
129C4×C13C2×#10411yescharacteristic
130Dic13—82no—
131Dic13—82no—
132C2×D8—132no—
133C2×D8—261no—
134C2×M16—261no—
135C2×M16C22×D1311yescharacteristic
136C22×C8D5211yescharacteristic
137#127—261no—
138#125—261no—
139#123—522no—
140#121—262no—
141#121—522no—
142C4×D4—262no—
143#117—261no—
144#117D5211yescharacteristic
145M32—22no—
146#107—261no—
147#106—132no—
148#102—262no—
149#102—262no—
150#97—262no—
151#97C4×D1311yescharacteristic
152#97C22⋊D1311yescharacteristic
153C4×C8—262no—
154C4×C8C4×D1311yescharacteristic
155C4×C8C22⋊D1311yescharacteristic
156C2×C13—21no—
157C2×C13—41no—
158C2×C13#150511yescharacteristic
159D13—162no—
160C2×D4—262no—
161C2×D4—522no—
162C2×D4—522no—
163C22×C4—522no—
164C22×C4C2×D5211yescharacteristic
165D8—522no—
166D8—521no—
167D8—521no—
168M16—41no—
169M16—521no—
170M16—521no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—262no—
174C2×C8#610311yescharacteristic
175C2×C8#610311yescharacteristic
176C2×C8C2×C4×D1311yescharacteristic
177C2×C8C2×C22⋊D1311yescharacteristic
178C4⋊C4—21no—
179C4⋊C4—262no—
180C4⋊C4—521no—
181C4⋊C4—522no—
182C22⋊C4—21no—
183C22⋊C4—522no—
184C22⋊C4—521no—
185C22⋊C4—522no—
186C42—262no—
187C42#610311yescharacteristic
188C42#610311yescharacteristic
189C16—42no—
190C13#1177011yescharacteristic, complemented, Sylow
191C23—522no—
192C23#8816211yescharacteristic
193D4—522no—
194D4—522no—
195D4—2082no—
196D4—2082no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—2082no—
204C2×C4#8816211yescharacteristic
205C2×C4C2×#610311yescharacteristic
206C8—21no—
207C8—21no—
208C8—21no—
209C8—522no—
210C8#8806511yescharacteristic
211C8#8806511yescharacteristic
212C22—21no—
213C22—41no—
214C22—1042no—
215C22—1042no—
216C22—1042no—
217C22#1171879211yescharacteristic
218C4—21no—
219C4—41no—
220C4—41no—
221C4—1042no—
222C4—1042no—
223C4#1171866711yescharacteristic
224C4C2×#8806511yescharacteristic
225C2—21no—
226C2—41no—
227C2—2082no—
228C2#1311334511yescharacteristic
subgroupG/H
centerC2#13113345
commutatorC2×C8×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2166C2
socleC2×C13#1505
prime radical#13125486C2
cosocleC2×C13×M16C23
hypercenter#2166D13
hypocenterC13#11770
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #13114591C2semidirect
3. #13112828C2semidirect
4. #13112822C2semidirect
5. C13×#2166C2semidirect
12. #11718372C4semidirect
13. #11718356C4semidirect
15. #11718344C4semidirect
78. #2166D13semidirect
190. C13#11770semidirect

Maximal subgroups

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

subgroupindex
#131254862
#131145912
#131128282
#131128222
C13×#21662
#1177013