Finite Group Databasebeta

← #13113848

Subgroups — #13113848

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#11719199C211yesmaximal, characteristic
2C13×#397C211yesmaximal, characteristic, complemented
3#11718632C211yesmaximal, characteristic, complemented
4#11718628C211yesmaximal, characteristic, complemented
5#11718117C211yesmaximal, characteristic, complemented
6#11718044C211yesmaximal, characteristic, complemented
7#11718043C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊C4C2211yescharacteristic
9C2×C13×C22⋊C4—21no—
10C2×C13×C22⋊C4C2211yescharacteristic
11#88207—21no—
12#88184C2211yescharacteristic
13C4×C22⋊D13—21no—
14#88178C2211yescharacteristic
15#88139—21no—
16#88138—21no—
17#88137—21no—
18#88133—21no—
19C13×#95—21no—
20C13×#95C2211yescharacteristic
21C22⋊#1055C2211yescharacteristic
22C22⋊#1055C2211yescharacteristic
23#88050—21no—
24#88049—21no—
25#88048—21no—
26#88047—21no—
27C24×C13D411yescharacteristic
28C22×C4×C13—21no—
29C22×C4×C13—21no—
30C22×C4×C13D411yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C2×C22⋊D13—21no—
35C2×D52D411yescharacteristic
36C2×C4×D13—21no—
37C2×Dic26D411yescharacteristic
38C13×C4⋊C4—21no—
39C13×C4⋊C4—21no—
40C13×C22⋊C4—21no—
41C13×C22⋊C4—21no—
42C13×C22⋊C4—42no—
43C22⋊Dic13—21no—
44C22⋊Dic13—21no—
45C22⋊Dic13—21no—
46#6103—21no—
47#6103—21no—
48C4⋊Dic13D411yescharacteristic
49C4⋊Dic13D411yescharacteristic
50#6101—21no—
51#6101—21no—
52C4×Dic13—21no—
53C2×#1055—21no—
54C2×#1055—21no—
55#1612—131nomaximal, Sylow
56C23×C13—21no—
57C23×C13—21no—
58C23×C13—21no—
59C23×C13—41no—
60C23×C13—41no—
61C23×C13C2×D411yescharacteristic
62C22×D13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13—41no—
70C2×C4×C13—41no—
71C2×C4×C13—41no—
72C2×C4×C13C2×D411yescharacteristic
73C2×C4×C13C2×D411yescharacteristic
74C22⋊D13—41no—
75C22⋊D13—41no—
76C22⋊D13—81no—
77C22⋊D13—81no—
78C2×Dic13—21no—
79C2×Dic13—21no—
80C2×Dic13—21no—
81D52—41no—
82C4×D13—81no—
83Dic26—41no—
84#1055—41no—
85#1055—41no—
86#538—131no—
87#483—131no—
88#480—131no—
89#397D1311yescharacteristic, complemented
90#328—131no—
91#327—131no—
92#323—131no—
93C22×C13—21no—
94C22×C13—21no—
95C22×C13—42no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13—41no—
99C22×C13—81no—
100C22×C13#12011yescharacteristic
101C22×C13#13511yescharacteristic
102C22×C13AGL(1,ℤ/8)11yescharacteristic
103C2×D13—41no—
104C2×D13—41no—
105C2×D13—41no—
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—41no—
109C4×C13—81no—
110C4×C13—81no—
111Dic13—41no—
112Dic13—41no—
113Dic13—41no—
114#126—261no—
115#124—261no—
116#123—261no—
117C22⋊Q8—131no—
118#121—131no—
119#121—261no—
120#120—261no—
121C4×D4—261no—
122C2×C4⋊C4C2×D1311yescharacteristic
123C2×C22⋊C4—21no—
124C2×C22⋊C4C2×D1311yescharacteristic
125#107—261no—
126#106—261no—
127#103—261no—
128#102—261no—
129C22⋊C8—131no—
130C22⋊C8—131no—
131#95—21no—
132#95C2×D1311yescharacteristic
133C2×C13—21no—
134C2×C13—21no—
135C2×C13—81no—
136C2×C13#44911yescharacteristic
137C2×C13#45511yescharacteristic
138C2×C13#45811yescharacteristic
139D13—81no—
140C24C22⋊D1311yescharacteristic
141C2×Q8—131no—
142C2×D4—131no—
143C2×D4—261no—
144C2×D4—261no—
145C2×D4—261no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—261no—
149C22×C4C22⋊D1311yescharacteristic
150C22×C4C22×D1311yescharacteristic
151C2×C8—261no—
152C2×C8—261no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—131no—
156C4⋊C4—131no—
157C4⋊C4—261no—
158C4⋊C4—261no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—42no—
162C22⋊C4—261no—
163C22⋊C4—261no—
164C22⋊C4—261no—
165C22⋊C4—261no—
166C22⋊C4—261no—
167C42—261no—
168C13#161211yescharacteristic, complemented, Sylow
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—261no—
175C23C2×C22⋊D1311yescharacteristic
176Q8—521no—
177D4—521no—
178D4—521no—
179D4—521no—
180D4—1041no—
181D4—1041no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—261no—
192C2×C4—261no—
193C2×C4—261no—
194C2×C4—1041no—
195C2×C4D4×D1311yescharacteristic
196C2×C4D4×D1311yescharacteristic
197C8—521no—
198C8—521no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—521no—
207C22—521no—
208C22—521no—
209C22#8818611yescharacteristic
210C22#8819111yescharacteristic
211C22#8820411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—521no—
218C4—521no—
219C4—521no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—1041no—
224C2#1171869811yescharacteristic
225C2#1171871411yescharacteristic
226C2#1171872211yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#397C2
socleC22×C13#120
prime radical#11719199C2
hypercenter#397D13
hypocenterC13#1612
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C13×#397C2semidirect
3. #11718632C2semidirect
4. #11718628C2semidirect
5. #11718117C2semidirect
6. #11718044C2semidirect
7. #11718043C2semidirect
89. #397D13semidirect
168. C13#1612semidirect

Maximal subgroups

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

subgroupindex
#117191992
C13×#3972
#117186322
#117186282
#117181172
#117180442
#117180432
#161213