Finite Group Databasebeta

← #13113847

Subgroups — #13113847

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#11719322C211yesmaximal, characteristic
2C13×#480C211yesmaximal, characteristic, complemented
3#11718654C211yesmaximal, characteristic, complemented
4#11718632C211yesmaximal, characteristic, complemented
5#11718129C211yesmaximal, characteristic, complemented
6#11718060C211yesmaximal, characteristic, complemented
7#11718059C211yesmaximal, characteristic, complemented
8C13×#121C2211yescharacteristic
9C2×C13×C4⋊C4C2211yescharacteristic
10#88193—21no—
11#88191—21no—
12D4×Dic13—21no—
13C2×#6103—21no—
14C2×#6103C2211yescharacteristic
15#88178C2211yescharacteristic
16#88152—21no—
17#88140—21no—
18#88139—21no—
19C13×#107—21no—
20C13×#102—21no—
21C13×C22⋊C8C2211yescharacteristic
22#88071—21no—
23#88071C2211yescharacteristic
24C22⋊#1055C2211yescharacteristic
25#88050—21no—
26#88048—21no—
27C23×D13D411yescharacteristic
28C2×D4×C13—21no—
29C2×D4×C13D411yescharacteristic
30C22×C4×C13—21no—
31C22×C4×C13C2311yescharacteristic
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C22×Dic13—21no—
35C22×Dic13—21no—
36C22×Dic13D411yescharacteristic
37C2×Dic26D411yescharacteristic
38C2×C8×C13—21no—
39C13×C4⋊C4—21no—
40C13×C4⋊C4—21no—
41C13×C4⋊C4D411yescharacteristic
42C13×C22⋊C4—21no—
43C22⋊Dic13—21no—
44C22⋊Dic13—21no—
45#6103—21no—
46#6103—21no—
47#6103—21no—
48#6103—21no—
49#6103—42no—
50C4⋊Dic13—21no—
51C4⋊Dic13D411yescharacteristic
52#6101—21no—
53C4×Dic13—21no—
54C2×#1055—21no—
55#1612—131nomaximal, Sylow
56C23×C13—21no—
57C23×C13C2×D411yescharacteristic
58C22×D13—21no—
59C22×D13—21no—
60C22×D13—21no—
61C22×D13—41no—
62C22×D13—41no—
63D4×C13—41no—
64D4×C13—41no—
65D4×C13—41no—
66C2×C4×C13—21no—
67C2×C4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×D411yescharacteristic
73C22⋊D13—81no—
74C22⋊D13—81no—
75C2×Dic13—21no—
76C2×Dic13—21no—
77C2×Dic13—21no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—41no—
82C2×Dic13—81no—
83Dic26—41no—
84C8×C13—41no—
85#1055—41no—
86#538—131no—
87#483—131no—
88#480D1311yescharacteristic, complemented
89#397—131no—
90#328—131no—
91#327—131no—
92#323—131no—
93C22×C13—21no—
94C22×C13—21no—
95C22×C13—41no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13#12011yescharacteristic
99C22×C13#13511yescharacteristic
100C22×C13AGL(1,ℤ/8)11yescharacteristic
101C2×D13—42no—
102C2×D13—41no—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13—81no—
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—41no—
109C4×C13—81no—
110Dic13—41no—
111Dic13—41no—
112Dic13—41no—
113Dic13—81no—
114#126—261no—
115#124—261no—
116#123—261no—
117C22⋊Q8—131no—
118#121—261no—
119#121C2×D1311yescharacteristic
120#120—261no—
121C4×D4—261no—
122C2×C4⋊C4C2×D1311yescharacteristic
123C2×C22⋊C4—131no—
124C2×C22⋊C4—261no—
125#107—21no—
126#106—261no—
127#103—261no—
128#102—21no—
129C22⋊C8—131no—
130C22⋊C8C2×D1311yescharacteristic
131#95—131no—
132#95—261no—
133C2×C13—21no—
134C2×C13—21no—
135C2×C13—81no—
136C2×C13#44911yescharacteristic
137C2×C13#45511yescharacteristic
138C2×C13#45811yescharacteristic
139D13—81no—
140C24—131no—
141C2×Q8—131no—
142C2×D4—21no—
143C2×D4—261no—
144C2×D4—261no—
145C2×D4C22⋊D1311yescharacteristic
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—131no—
156C4⋊C4—261no—
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—21no—
170C23—261no—
171C23—261no—
172C23—261no—
173C23—521no—
174C23—521no—
175C23D4×D1311yescharacteristic
176Q8—521no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—1041no—
181D4—1041no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—261no—
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—41no—
202C22—41no—
203C22—41no—
204C22—522no—
205C22—521no—
206C22—521no—
207C22—521no—
208C22—1041no—
209C22#8816511yescharacteristic
210C22#8816611yescharacteristic
211C22#8819111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—521no—
217C4—521no—
218C4—521no—
219C4—1041no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—1041no—
224C2#1171871411yescharacteristic
225C2#1171881911yescharacteristic
226C2#1171886311yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#480C2
socleC22×C13#120
prime radical#11719322C2
hypercenter#480D13
hypocenterC13#1612
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C13×#480C2semidirect
3. #11718654C2semidirect
4. #11718632C2semidirect
5. #11718129C2semidirect
6. #11718060C2semidirect
7. #11718059C2semidirect
88. #480D13semidirect
168. C13#1612semidirect

Maximal subgroups

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

subgroupindex
#117193222
C13×#4802
#117186542
#117186322
#117181292
#117180602
#117180592
#161213