Finite Group Databasebeta

← #13122864

Subgroups — #13122864

Order 1664.

528 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×C13×#121C211yesmaximal, characteristic
2C2×#88178C211yesmaximal, characteristic, complemented
3#11718883C214yesmaximal, complemented
4#11718883C212yesmaximal, complemented
5#11718872C211yesmaximal, characteristic, complemented
6#11718641C212yesmaximal, complemented
7#11718610C212yesmaximal, complemented
8#11718608C212yesmaximal, complemented
9C22×D4×C13C2212yes—
10C22×D4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C13×#121—24no—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2214yes—
18C2×C22⋊Dic13C2214yes—
19C2×C22⋊Dic13C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21#88178—24no—
22C2×#6101C2212yes—
23C2×#6101C2214yes—
24#88071C2212yes—
25#88071C2214yes—
26#88071C2212yes—
27C24×C13C2312yes—
28C24×C13C2311yescharacteristic
29C2×D4×C13—24no—
30C2×D4×C13—22no—
31C2×D4×C13—42no—
32C2×D4×C13—44no—
33C22×C4×C13—42no—
34C22×C4×C13D414yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2314yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C2×Dic26—22no—
42C2×Dic26—42no—
43C13×C4⋊C4—22no—
44C13×C22⋊C4—24no—
45C22⋊Dic13—24no—
46C22⋊Dic13—44no—
47C22⋊Dic13—42no—
48C22⋊Dic13—44no—
49C4⋊Dic13—22no—
50#6101—24no—
51#6101—44no—
52#2816—131nomaximal, Sylow
53C23×C13—22no—
54C23×C13—22no—
55C23×C13—22no—
56C23×C13—22no—
57C23×C13—24no—
58C23×C13—24no—
59C23×C13—24no—
60C23×C13C2×D412yes—
61C23×C13C2411yescharacteristic
62D4×C13—44no—
63D4×C13—48no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—24no—
68C2×C4×C13—44no—
69C2×C4×C13C2×D412yes—
70C2×C4×C13C2×D412yes—
71C2×Dic13—22no—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—24no—
75C2×Dic13—22no—
76C2×Dic13—24no—
77C2×Dic13—24no—
78C2×Dic13—24no—
79Dic26—44no—
80C2×C22⋊Q8—131no—
81C2×#121D1311yescharacteristic
82#399—132no—
83#398—132no—
84#394—132no—
85#394—134no—
86#393—132no—
87#381—131no—
88C22×C13—22no—
89C22×C13—22no—
90C22×C13—22no—
91C22×C13—44no—
92C22×C13—42no—
93C22×C13—42no—
94C22×C13—42no—
95C22×C13—48no—
96C22×C13C22×D411yescharacteristic
97C22×C13H(5,𝔽2)12yes—
98C22×C13H(5,𝔽2)12yes—
99C22×C132−1+412yes—
100C4×C13—22no—
101C4×C13—22no—
102C4×C13—42no—
103Dic13—42no—
104Dic13—42no—
105Dic13—44no—
106C22×Q8—131no—
107C22×D4C2×D1312yes—
108C22×D4C2×D1311yescharacteristic
109C23×C4C2×D1311yescharacteristic
110C22⋊Q8—264no—
111#121—24no—
112C2×C4⋊C4—132no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4—134no—
115C2×C4⋊C4C2×D1311yescharacteristic
116C2×C22⋊C4—132no—
117C2×C22⋊C4—132no—
118C2×C22⋊C4—134no—
119C2×C22⋊C4—134no—
120C2×C22⋊C4C2×D1312yes—
121#95—132no—
122#95—132no—
123#95—134no—
124C2×C13—42no—
125C2×C13—82no—
126C2×C13#53411yescharacteristic
127C2×C13#53511yescharacteristic
128C2×C13#53611yescharacteristic
129C2×C13#56214yes—
130C24C22×D1312yes—
131C24C22×D1311yescharacteristic
132C2×Q8—262no—
133C2×Q8—522no—
134C2×D4—24no—
135C2×D4—22no—
136C2×D4—42no—
137C2×D4—44no—
138C22×C4—42no—
139C22×C4—134no—
140C22×C4—132no—
141C22×C4—132no—
142C22×C4C22⋊D1314yes—
143C22×C4C22×D1312yes—
144C22×C4C22×D1311yescharacteristic
145C22×C4C22×D1311yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—264no—
148C4⋊C4—262no—
149C4⋊C4—524no—
150C22⋊C4—24no—
151C22⋊C4—264no—
152C22⋊C4—522no—
153C22⋊C4—524no—
154C22⋊C4—524no—
155C13#281611yescharacteristic, complemented, Sylow
156C23—22no—
157C23—22no—
158C23—22no—
159C23—24no—
160C23—24no—
161C23—24no—
162C23—22no—
163C23C2×C22⋊D1312yes—
164C23C23×D1311yescharacteristic
165Q8—524no—
166D4—44no—
167D4—48no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—44no—
173C2×C4—262no—
174C2×C4—264no—
175C2×C4—264no—
176C2×C4—264no—
177C2×C4—262no—
178C2×C4—264no—
179C2×C4—262no—
180C2×C4—262no—
181C2×C4C2×C22⋊D1312yes—
182C2×C4C2×C22⋊D1312yes—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—44no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—48no—
191C22#8825112yes—
192C22#8825112yes—
193C22#8825712yes—
194C22C22×C22⋊D1311yescharacteristic
195C4—22no—
196C4—22no—
197C4—42no—
198C4—522no—
199C4—522no—
200C4—524no—
201C2—42no—
202C2—82no—
203C2#1171932614yes—
204C2#1171950911yescharacteristic
205C2#1171951011yescharacteristic
206C2#1171953011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2816
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#88178C2semidirect
3. #11718883C2semidirect
4. #11718883C2semidirect
5. #11718872C2semidirect
6. #11718641C2semidirect
7. #11718610C2semidirect
8. #11718608C2semidirect
155. C13#2816semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881782
#117188832
#117188722
#117186412
#117186102
#117186082
#281613