Finite Group Databasebeta

← #15773460

Subgroups — #15773460

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#13116652C211yesmaximal, characteristic, complemented
3#13112826C212yesmaximal, complemented
4#13112820C212yesmaximal, complemented
5C13×#1747C211yesmaximal, characteristic, complemented
6#11719240—21no—
7C13×#405—21no—
8C13×#405C2211yescharacteristic
9#11718796C2212yes—
10#11718776—21no—
11#11718374—21no—
12#11718372C412yescomplemented
13#11718356C411yescharacteristic, complemented
14C4×D104—21no—
15#11718344C411yescharacteristic, complemented
16C13×#338C2211yescharacteristic
17C13×H(3,ℤ/4)—21no—
18C13×H(3,ℤ/4)C2211yescharacteristic
19#11718145C2212yes—
20#11718058—21no—
21#11718055—21no—
22C2×C13×M16—21no—
23C2×C13×M16C2311yescharacteristic
24C22×C8×C13D411yescharacteristic
25C13×#117—21no—
26C13×#117D411yescharacteristic
27#88184—22no—
28C2×D104—21no—
29C2×D104C2×C412yes—
30#88148—42no—
31#88138—42no—
32#88128—21no—
33C4×D52—22no—
34#88124—21no—
35C13×#97—22no—
36C13×#97C2×C411yescharacteristic
37C13×#97D411yescharacteristic
38C4×C8×C13—22no—
39C4×C8×C13C2×C411yescharacteristic
40C4×C8×C13D411yescharacteristic
41#88061—22no—
42#88061—22no—
43#88058—21no—
44#88057C2×C412yes—
45#88052—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—
53C13×M16—41no—
54C13×M16—41no—
55C2×C8×C13—21no—
56C2×C8×C13—21no—
57C2×C8×C13—22no—
58C2×C8×C13C22⋊C411yescharacteristic
59C2×C8×C13C22⋊C411yescharacteristic
60C2×C8×C13C22×C411yescharacteristic
61C2×C8×C13C2×D411yescharacteristic
62C13×C4⋊C4—21no—
63C13×C4⋊C4—41no—
64C13×C22⋊C4—21no—
65C13×C22⋊C4—41no—
66C42×C13—22no—
67C42×C13C22⋊C411yescharacteristic
68C42×C13C22⋊C411yescharacteristic
69#6103—42no—
70#6103—42no—
71C4⋊Dic13—22no—
72#6101—42no—
73D104—42no—
74D104—41no—
75D104—41no—
76#6090—42no—
77#3176—131no—
78#2166—131no—
79#1747D1311yescharacteristic, complemented
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×C13—42no—
89C2×C4×C13C2×C22⋊C411yescharacteristic
90C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
91C22⋊D13—162no—
92C2×Dic13—42no—
93D52—42no—
94D52—42no—
95D52—162no—
96C4×D13—162no—
97C8×C13—21no—
98C8×C13—21no—
99C8×C13—21no—
100C8×C13—42no—
101C8×C13#10411yescharacteristic
102C8×C13#10411yescharacteristic
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—21no—
112#405C2×D1311yescharacteristic
113#364—261no—
114#349—132no—
115#347—261no—
116#338C2×D1311yescharacteristic
117H(3,ℤ/4)—21no—
118H(3,ℤ/4)C2×D1311yescharacteristic
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—82no—
129C4×C13#41011yescharacteristic
130C4×C13C2×#10411yescharacteristic
131Dic13—82no—
132C2×D8—132no—
133C2×D8—261no—
134C2×M16—21no—
135C2×M16C22×D1311yescharacteristic
136C22×C8C22⋊D1311yescharacteristic
137#127—261no—
138#125—261no—
139#123—522no—
140#121—262no—
141#121—522no—
142C4×D4—262no—
143#117—21no—
144#117C22⋊D1311yescharacteristic
145M32—262no—
146#107—261no—
147#106—132no—
148#102—262no—
149#102—262no—
150#97—22no—
151#97C4×D1311yescharacteristic
152#97D5211yescharacteristic
153C4×C8—22no—
154C4×C8C4×D1311yescharacteristic
155C4×C8D5211yescharacteristic
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×C22⋊D1311yescharacteristic
165D8—522no—
166D8—521no—
167D8—521no—
168M16—41no—
169M16—41no—
170M16—41no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—22no—
174C2×C8#610311yescharacteristic
175C2×C8#610311yescharacteristic
176C2×C8C2×C4×D1311yescharacteristic
177C2×C8C2×D5211yescharacteristic
178C4⋊C4—21no—
179C4⋊C4—41no—
180C4⋊C4—262no—
181C4⋊C4—522no—
182C22⋊C4—21no—
183C22⋊C4—41no—
184C22⋊C4—522no—
185C22⋊C4—522no—
186C42—22no—
187C42#610311yescharacteristic
188C42#610311yescharacteristic
189C16—522no—
190C13#1177011yescharacteristic, complemented, Sylow
191C23—522no—
192C23#8820311yescharacteristic
193D4—522no—
194D4—522no—
195D4—2082no—
196D4—2082no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—522no—
203C2×C4—2082no—
204C2×C4C2×#610311yescharacteristic
205C2×C4#8820311yescharacteristic
206C8—21no—
207C8—21no—
208C8—21no—
209C8—42no—
210C8#8804511yescharacteristic
211C8#8804511yescharacteristic
212C22—21no—
213C22—41no—
214C22—1042no—
215C22—1042no—
216C22—1042no—
217C22#1171866211yescharacteristic
218C4—21no—
219C4—41no—
220C4—41no—
221C4—82no—
222C4—1042no—
223C4C2×#8804511yescharacteristic
224C4#1171866711yescharacteristic
225C2—21no—
226C2—41no—
227C2—2082no—
228C2#1311334311yescharacteristic
subgroupG/H
centerC2#13113343
commutatorC2×C8×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1747C2
socleC2×C13#1505
prime radical#13125486C2
cosocleC2×C13×M16C23
hypercenter#1747D13
hypocenterC13#11770
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #1747

Complements

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

NH ≅ G/Ntype
2. #13116652C2semidirect
3. #13112826C2semidirect
4. #13112820C2semidirect
5. C13×#1747C2semidirect
12. #11718372C4semidirect
13. #11718356C4semidirect
15. #11718344C4semidirect
79. #1747D13semidirect
190. C13#11770semidirect

Maximal subgroups

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

subgroupindex
#131254862
#131166522
#131128262
#131128202
C13×#17472
#1177013