Finite Group Databasebeta

← #13122894

Subgroups — #13122894

Order 1664.

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

normal subgroups only

This group has 430 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×#126C211yesmaximal, characteristic
2C2×#88123C211yesmaximal, characteristic, complemented
3#11718647C212yesmaximal, complemented
4#11718644C212yesmaximal, complemented
5#11718640C212yesmaximal, complemented
6#11718614C212yesmaximal
7#11718610C212yesmaximal
8#11718608C212yesmaximal
9#11718598C211yesmaximal, characteristic, complemented
10C22×Dic26C2212yes—
11C13×#126—24no—
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C42×C13C2211yescharacteristic
19C2×C22⋊Dic13C2214yes—
20C2×C4⋊Dic13C2212yes—
21C2×C4⋊Dic13C2212yes—
22C2×#6101C2214yes—
23#88123—24no—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2214yes—
28#88071C2214yes—
29C24×C13C2311yescharacteristic
30C22×C4×C13C2311yescharacteristic
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2311yescharacteristic
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2314yes—
37C22×Dic13C2314yes—
38C2×Dic26—24no—
39C2×Dic26—44no—
40C13×C4⋊C4—22no—
41C13×C4⋊C4—22no—
42C13×C4⋊C4—22no—
43C13×C22⋊C4—22no—
44C13×C22⋊C4—22no—
45C13×C22⋊C4—22no—
46C42×C13D414yes—
47C22⋊Dic13—44no—
48C4⋊Dic13—24no—
49C4⋊Dic13—24no—
50#6101—44no—
51#2821—131nomaximal, Sylow
52C23×C13—21no—
53C23×C13—22no—
54C23×C13—22no—
55C23×C13—22no—
56C23×C13C2411yescharacteristic
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13C2×D412yes—
67C2×C4×C13C2×D412yes—
68C2×C4×C13C2×D412yes—
69C2×Dic13—24no—
70C2×Dic13—24no—
71C2×Dic13—24no—
72C2×Dic13—24no—
73C2×Dic13—24no—
74C2×Dic13—24no—
75Dic26—48no—
76C2×C4⋊Q8—131no—
77C2×#126D1311yescharacteristic
78#400—132no—
79#399—132no—
80#398—132no—
81#397—132no—
82#395—132no—
83#393—132no—
84#383—131no—
85C22×C13—41no—
86C22×C13—41no—
87C22×C13—41no—
88C22×C13—44no—
89C22×C13C22×D411yescharacteristic
90C22×C13H(5,𝔽2)12yes—
91C22×C132−1+412yes—
92C22×C132−1+412yes—
93C4×C13—22no—
94C4×C13—22no—
95C4×C13—22no—
96C4×C13—41no—
97C4×C13—41no—
98C4×C13—41no—
99Dic13—44no—
100Dic13—44no—
101C22×Q8—132no—
102C4⋊Q8—264no—
103#126—24no—
104C2×C4⋊C4—132no—
105C2×C4⋊C4—132no—
106C2×C4⋊C4—134no—
107C2×C4⋊C4C2×D1311yescharacteristic
108C2×C4⋊C4C2×D1311yescharacteristic
109C2×C4⋊C4C2×D1311yescharacteristic
110C2×C22⋊C4—134no—
111C2×C22⋊C4C2×D1311yescharacteristic
112C2×C22⋊C4C2×D1311yescharacteristic
113C2×C22⋊C4C2×D1311yescharacteristic
114C2×C42C2×D1311yescharacteristic
115#95—132no—
116#95—132no—
117#95—132no—
118#95—134no—
119#95—134no—
120C2×C13—81no—
121C2×C13#53511yescharacteristic
122C2×C13#53611yescharacteristic
123C2×C13#53611yescharacteristic
124C2×C13#56314yes—
125C24C22×D1311yescharacteristic
126C2×Q8—264no—
127C2×Q8—524no—
128C22×C4—134no—
129C22×C4—134no—
130C22×C4C22×D1311yescharacteristic
131C22×C4C22×D1311yescharacteristic
132C22×C4C22×D1311yescharacteristic
133C22×C4C22×D1311yescharacteristic
134C22×C4C22×D1311yescharacteristic
135C22×C4C22×D1311yescharacteristic
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—22no—
139C4⋊C4—264no—
140C4⋊C4—264no—
141C4⋊C4—524no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C22⋊C4—524no—
146C42C22⋊D1314yes—
147C13#282111yescharacteristic, complemented, Sylow
148C23—22no—
149C23—22no—
150C23—22no—
151C23—21no—
152C23C23×D1311yescharacteristic
153Q8—528no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—264no—
164C2×C4—264no—
165C2×C4—264no—
166C2×C4—264no—
167C2×C4—264no—
168C2×C4—264no—
169C2×C4C2×C22⋊D1312yes—
170C2×C4C2×C22⋊D1312yes—
171C2×C4C2×C22⋊D1312yes—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—44no—
176C22#8825612yes—
177C22#8825712yes—
178C22#8825712yes—
179C22C22×C22⋊D1311yescharacteristic
180C4—22no—
181C4—22no—
182C4—22no—
183C4—41no—
184C4—41no—
185C4—41no—
186C4—524no—
187C4—524no—
188C2—81no—
189C2#1171941714yes—
190C2#1171953011yescharacteristic
191C2#1171953011yescharacteristic
192C2#1171953511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#126C2
prime radicalC24×C13C23
hypercenterC2×#126D13
hypocenterC13#2821
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. C2×#88123C2semidirect
3. #11718647C2semidirect
4. #11718644C2semidirect
5. #11718640C2semidirect
9. #11718598C2semidirect
147. C13#2821semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1262
C2×#881232
#117186472
#117186442
#117186402
#117186142
#117186102
#117186082
#117185982
#282113