Finite Group Databasebeta

← #13123116

Subgroups — #13123116

Order 1664.

1224 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 209 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
1C24×Dic13C211yesmaximal, characteristic, complemented
2C2×C13×#120C211yesmaximal, characteristic, complemented
3C2×#88207C211yesmaximal, characteristic, complemented
4C2×#88193C213yesmaximal, complemented
5#11718881C213yesmaximal, complemented
6#11718619C213yesmaximal, complemented
7#11718603C213yesmaximal, complemented
8C25×C13C2211yescharacteristic
9C22×D4×C13C2213yes—
10C22×C22⋊D13C2213yes—
11C22×C22⋊D13C2211yescharacteristic, complemented
12C23×Dic13—212no—
13C23×Dic13C2213yes—
14C23×Dic13C2213yes—
15C13×#120—24no—
16C2×C13×C22⋊C4C2213yes—
17#88207—24no—
18C2×C22⋊Dic13C2213yes—
19C2×C22⋊Dic13C2213yescomplemented
20#88193—212no—
21C2×#6103C2213yescomplemented
22C2×#6101C2213yescomplemented
23#88071C2216yescomplemented
24C24×C13—26no—
25C24×C13—26no—
26C24×C13D414yescomplemented
27C24×C13C2311yescharacteristic
28C24×C13C2313yes—
29C23×D13C2311yescharacteristic
30C2×D4×C13—26no—
31C2×D4×C13—26no—
32C2×D4×C13—26no—
33C22×C4×C13C2313yes—
34C2×C22⋊D13—26no—
35C2×C22⋊D13—26no—
36C2×C22⋊D13—26no—
37C2×C22⋊D13—26no—
38C22×Dic13—232no—
39C22×Dic13—26no—
40C22×Dic13—212no—
41C22×Dic13—212no—
42C22×Dic13D4112yescomplemented
43C22×Dic13C2313yes—
44C22×Dic13C2313yes—
45C22×Dic13C2311yescharacteristic
46C13×C22⋊C4—26no—
47C22⋊Dic13—26no—
48C22⋊Dic13—26no—
49#6103—26no—
50#6101—26no—
51#2847—131nomaximal, Sylow
52C23×C13—28no—
53C23×C13—224no—
54C23×C13—224no—
55C23×C13—26no—
56C23×C13—26no—
57C23×C13—23no—
58C23×C13—21no—
59C23×C13—23no—
60C23×C13C2×D416yes—
61C23×C13C2×D416yes—
62C23×C13#4116yes—
63C23×C13C2411yescharacteristic
64C22×D13—23no—
65C22×D13—21no—
66C22×D13—23no—
67D4×C13—412no—
68C2×C4×C13—23no—
69C2×C4×C13—23no—
70C2×C4×C13—23no—
71C22⋊D13—412no—
72C22⋊D13—44no—
73C2×Dic13—224no—
74C2×Dic13—26no—
75C2×Dic13—224no—
76C2×Dic13—23no—
77C2×Dic13—23no—
78C2×Dic13—23no—
79C2×Dic13C2×D416yes—
80C2×Dic13C2×D416yes—
81C24×C4—131no—
82C2×#121—133no—
83C2×#120—131no—
84C2×#120D1311yescharacteristic, complemented
85#386—133no—
86#386—133no—
87#380—133no—
88C22×C13—232no—
89C22×C13—26no—
90C22×C13—212no—
91C22×C13—26no—
92C22×C13—212no—
93C22×C13—41no—
94C22×C13—43no—
95C22×C13—43no—
96C22×C13#121112yescomplemented
97C22×C13C22×D413yes—
98C22×C13C22×D411yescharacteristic
99C22×C13C2×#4113yes—
100C2×D13—41no—
101C2×D13—43no—
102C2×D13—43no—
103C4×C13—43no—
104Dic13—26no—
105Dic13—43no—
106Dic13#12014yescomplemented
107C25C2×D1311yescharacteristic
108C22×D4—133no—
109C22×D4—131no—
110C22×D4C2×D1313yes—
111C23×C4—133no—
112C23×C4—133no—
113C23×C4—2612no—
114#121—2612no—
115#120—24no—
116#120—264no—
117C2×C4⋊C4—133no—
118C2×C22⋊C4—133no—
119C2×C22⋊C4—133no—
120C2×C22⋊C4—133no—
121C2×C22⋊C4C2×D1313yes—
122#95—136no—
123C2×C13—212no—
124C2×C13—81no—
125C2×C13C2×#12011yescharacteristic
126C2×C13C2×#12113yes—
127C2×C13#52513yes—
128D13—81no—
129C24—26no—
130C24—26no—
131C24—131no—
132C24C22⋊D1314yescomplemented
133C24C22×D1311yescharacteristic
134C24C22×D1313yes—
135C2×D4—26no—
136C2×D4—26no—
137C2×D4—26no—
138C2×D4—266no—
139C2×D4—266no—
140C2×D4—266no—
141C2×D4—266no—
142C22×C4—131no—
143C22×C4—1312no—
144C22×C4—133no—
145C22×C4—133no—
146C22×C4—2612no—
147C22×C4—2612no—
148C22×C4—2632no—
149C22×C4—266no—
150C22×C4C22×D1313yes—
151C4⋊C4—266no—
152C22⋊C4—26no—
153C22⋊C4—266no—
154C22⋊C4—266no—
155C22⋊C4—266no—
156C13#284711yescharacteristic, complemented, Sylow
157C23—28no—
158C23—224no—
159C23—224no—
160C23—26no—
161C23—26no—
162C23—23no—
163C23—23no—
164C23—21no—
165C23—263no—
166C23—263no—
167C23—261no—
168C23D4×D1316yes—
169C23#612916yes—
170C23C2×C22⋊D1316yes—
171C23C23×D1311yescharacteristic
172D4—412no—
173D4—524no—
174D4—5212no—
175C2×C4—23no—
176C2×C4—23no—
177C2×C4—23no—
178C2×C4—136no—
179C2×C4—136no—
180C2×C4—2624no—
181C2×C4—2624no—
182C2×C4—266no—
183C2×C4—263no—
184C2×C4—263no—
185C2×C4—263no—
186C22—232no—
187C22—212no—
188C22—26no—
189C22—212no—
190C22—26no—
191C22—43no—
192C22—43no—
193C22—41no—
194C22—523no—
195C22—523no—
196C22—521no—
197C22#88193112yescomplemented
198C22C2×D4×D1313yes—
199C22C2×#612913yes—
200C22C22×C22⋊D1311yescharacteristic
201C4—43no—
202C4—134no—
203C4—266no—
204C4—523no—
205C2—212no—
206C2—81no—
207C2—1041no—
208C2#1171929113yes—
209C2D13×#12011yescharacteristic
210C2C2×#8819313yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#120C2
hypercenterC2×#120D13
hypocenterC13#2847
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C24×Dic13C2semidirect
2. C2×C13×#120C2semidirect
3. C2×#88207C2semidirect
4. C2×#88193C2semidirect
5. #11718881C2semidirect
6. #11718619C2semidirect
7. #11718603C2semidirect
11. C22×C22⋊D13C22semidirect
19. C2×C22⋊Dic13C22semidirect
21. C2×#6103C22semidirect
22. C2×#6101C22semidirect
23. #88071C22semidirect
26. C24×C13D4semidirect
42. C22×Dic13D4semidirect
84. C2×#120D13semidirect
96. C22×C13#121semidirect
106. Dic13#120semidirect
132. C24C22⋊D13semidirect
156. C13#2847semidirect
197. C22#88193semidirect

Maximal subgroups

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

subgroupindex
C24×Dic132
C2×C13×#1202
C2×#882072
C2×#881932
#117188812
#117186192
#117186032
#284713