Finite Group Databasebeta

← #13113849

Subgroups — #13113849

Order 1664.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#11719349C211yesmaximal, characteristic
2C13×#483C211yesmaximal, characteristic, complemented
3#11718654C211yesmaximal, characteristic, complemented
4#11718628C211yesmaximal, characteristic, complemented
5#11718130C211yesmaximal, characteristic, complemented
6#11718062C211yesmaximal, characteristic, complemented
7#11718060C211yesmaximal, characteristic, complemented
8C13×C22⋊Q8C2211yescharacteristic
9C2×C13×C4⋊C4C2211yescharacteristic
10#88201—21no—
11#88184C2211yescharacteristic
12C2×#6103—21no—
13C2×#6103C2211yescharacteristic
14#88152—21no—
15#88149—21no—
16#88148—21no—
17#88136—21no—
18#88135—21no—
19C13×#106—21no—
20C13×#103—21no—
21C13×C22⋊C8C2211yescharacteristic
22#88071—21no—
23#88071C2211yescharacteristic
24C22⋊#1055C2211yescharacteristic
25#88049—21no—
26#88047—21no—
27C23×D13D411yescharacteristic
28C2×Q8×C13D411yescharacteristic
29C22×C4×C13—21no—
30C22×C4×C13C2311yescharacteristic
31C2×C22⋊D13—21no—
32C22×Dic13—21no—
33C22×Dic13D411yescharacteristic
34C2×D52—21no—
35C2×D52—21no—
36C2×D52D411yescharacteristic
37C2×C4×D13—21no—
38C2×C8×C13—21no—
39C13×C4⋊C4—21no—
40C13×C4⋊C4—21no—
41C13×C4⋊C4—21no—
42C13×C4⋊C4D411yescharacteristic
43C13×C22⋊C4—21no—
44#6103—21no—
45#6103—21no—
46#6103—21no—
47#6103—21no—
48#6103—21no—
49#6103—21no—
50#6103—42no—
51C4⋊Dic13D411yescharacteristic
52#6101—21no—
53C4×Dic13—21no—
54C2×#1055—21no—
55#1612—131nomaximal, Sylow
56C23×C13C2×D411yescharacteristic
57C22×D13—21no—
58C22×D13—21no—
59C22×D13—21no—
60C22×D13—21no—
61C22×D13—41no—
62C22×D13—41no—
63Q8×C13—41no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13—41no—
70C2×C4×C13C2×D411yescharacteristic
71C2×C4×C13C2×D411yescharacteristic
72C22⋊D13—41no—
73C22⋊D13—41no—
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—41no—
77C2×Dic13—41no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80D52—41no—
81D52—81no—
82D52—81no—
83C4×D13—81no—
84C8×C13—41no—
85#1055—41no—
86#538—131no—
87#483D1311yescharacteristic, complemented
88#480—131no—
89#397—131no—
90#328—131no—
91#327—131no—
92#323—131no—
93C22×C13—21no—
94C22×C13—21no—
95C22×C13#12011yescharacteristic
96C22×C13#13511yescharacteristic
97C22×C13AGL(1,ℤ/8)11yescharacteristic
98C2×D13—42no—
99C2×D13—41no—
100C2×D13—41no—
101C2×D13—41no—
102C2×D13—41no—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13—81no—
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—41no—
109C4×C13—41no—
110C4×C13—81no—
111Dic13—41no—
112Dic13—41no—
113Dic13—81no—
114#126—261no—
115#124—261no—
116#123—261no—
117C22⋊Q8C2×D1311yescharacteristic
118#121—131no—
119#121—261no—
120#120—261no—
121C4×D4—261no—
122C2×C4⋊C4C2×D1311yescharacteristic
123C2×C22⋊C4—131no—
124C2×C22⋊C4—261no—
125#107—261no—
126#106—21no—
127#103—21no—
128#102—261no—
129C22⋊C8—131no—
130C22⋊C8C2×D1311yescharacteristic
131#95—131no—
132#95—261no—
133C2×C13—21no—
134C2×C13—21no—
135C2×C13#44911yescharacteristic
136C2×C13#45511yescharacteristic
137C2×C13#45811yescharacteristic
138D13—81no—
139D13—81no—
140C24—131no—
141C2×Q8C22⋊D1311yescharacteristic
142C2×D4—131no—
143C2×D4—261no—
144C2×D4—261no—
145C2×D4—261no—
146C22×C4—21no—
147C22×C4—131no—
148C22×C4—261no—
149C22×C4—261no—
150C22×C4C22×D1311yescharacteristic
151C2×C8—21no—
152C2×C8—261no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—131no—
157C4⋊C4—261no—
158C4⋊C4C22⋊D1311yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—261no—
161C22⋊C4—261no—
162C22⋊C4—261no—
163C22⋊C4—261no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—522no—
167C42—261no—
168C13#161211yescharacteristic, complemented, Sylow
169C23—261no—
170C23—261no—
171C23—261no—
172C23—261no—
173C23—521no—
174C23—521no—
175C23D4×D1311yescharacteristic
176Q8—41no—
177D4—521no—
178D4—521no—
179D4—521no—
180D4—1041no—
181D4—1041no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—261no—
189C2×C4—261no—
190C2×C4—521no—
191C2×C4—521no—
192C2×C4—521no—
193C2×C4—521no—
194C2×C4—1041no—
195C2×C4D4×D1311yescharacteristic
196C2×C4C2×C22⋊D1311yescharacteristic
197C8—41no—
198C8—521no—
199C22—21no—
200C22—21no—
201C22—522no—
202C22—521no—
203C22—521no—
204C22—521no—
205C22—521no—
206C22—521no—
207C22—521no—
208C22—1041no—
209C22#8816811yescharacteristic
210C22#8817011yescharacteristic
211C22#8819111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—521no—
218C4—521no—
219C4—1041no—
220C2—21no—
221C2—21no—
222C2—1041no—
223C2—1041no—
224C2#1171871411yescharacteristic
225C2#1171883311yescharacteristic
226C2#1171886311yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#483C2
socleC22×C13#120
prime radical#11719349C2
hypercenter#483D13
hypocenterC13#1612
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C13×#483C2semidirect
3. #11718654C2semidirect
4. #11718628C2semidirect
5. #11718130C2semidirect
6. #11718062C2semidirect
7. #11718060C2semidirect
87. #483D13semidirect
168. C13#1612semidirect

Maximal subgroups

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

subgroupindex
#117193492
C13×#4832
#117186542
#117186282
#117181302
#117180622
#117180602
#161213