Finite Group Databasebeta

← #13122897

Subgroups — #13122897

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×#88130C211yesmaximal, characteristic
2C2×#88123C211yesmaximal, characteristic, complemented
3C13×#383C211yesmaximal, characteristic, complemented
4#11718338C212yesmaximal
5#11718335C212yesmaximal
6#11718334C212yesmaximal
7#11718322C212yesmaximal, complemented
8#11718320C212yesmaximal, complemented
9#11718317C212yesmaximal, complemented
10C22×Dic26C2212yes—
11C2×C42×C13C2211yescharacteristic
12C2×#6103C2211yescharacteristic
13C2×#6103C2211yescharacteristic
14C2×#6103C2211yescharacteristic
15C2×#6103C2214yes—
16C2×C4⋊Dic13C2212yes—
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2214yes—
19C2×#6101C2211yescharacteristic
20C2×#6101C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22#88130—24no—
23#88123—24no—
24C13×#95C2212yes—
25C13×#95C2212yes—
26C13×#95C2212yes—
27#88071C2214yes—
28#88071C2214yes—
29C23×D13C2311yescharacteristic
30C22×C4×C13C2314yes—
31C22×C4×C13C2311yescharacteristic
32C22×C4×C13C2311yescharacteristic
33C22×C4×C13C2311yescharacteristic
34C22×Dic13C2311yescharacteristic
35C22×Dic13C2311yescharacteristic
36C22×Dic13C2314yes—
37C22×Dic13C2311yescharacteristic
38C2×Dic26—24no—
39C2×Dic26—44no—
40C42×C13D414yes—
41#6103—22no—
42#6103—22no—
43#6103—22no—
44#6103—44no—
45C4⋊Dic13—24no—
46C4⋊Dic13—24no—
47C4⋊Dic13—44no—
48#6101—22no—
49#6101—22no—
50#6101—22no—
51#2821—131nomaximal, Sylow
52C23×C13C2411yescharacteristic
53C22×D13—21no—
54C22×D13—22no—
55C22×D13—22no—
56C22×D13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—22no—
60C2×C4×C13—24no—
61C2×C4×C13—24no—
62C2×C4×C13—24no—
63C2×C4×C13C2×D412yes—
64C2×C4×C13C2×D412yes—
65C2×C4×C13C2×D412yes—
66C2×Dic13—21no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—24no—
70C2×Dic13—22no—
71C2×Dic13—24no—
72C2×Dic13—24no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75Dic26—48no—
76C2×C4⋊Q8—131no—
77C2×#126—131no—
78#400—132no—
79#399—132no—
80#398—132no—
81#397—132no—
82#395—132no—
83#393—132no—
84#383D1311yescharacteristic, complemented
85C22×C13C22×D411yescharacteristic
86C22×C13H(5,𝔽2)12yes—
87C22×C132−1+412yes—
88C22×C132−1+412yes—
89C2×D13—41no—
90C2×D13—41no—
91C2×D13—41no—
92C2×D13—44no—
93C4×C13—22no—
94C4×C13—22no—
95C4×C13—22no—
96C4×C13—44no—
97Dic13—44no—
98Dic13—41no—
99Dic13—41no—
100Dic13—41no—
101C22×Q8—132no—
102C4⋊Q8—264no—
103#126—264no—
104C2×C4⋊C4—131no—
105C2×C4⋊C4—131no—
106C2×C4⋊C4—131no—
107C2×C4⋊C4—132no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—134no—
110C2×C22⋊C4—131no—
111C2×C22⋊C4—131no—
112C2×C22⋊C4—131no—
113C2×C22⋊C4—134no—
114C2×C42C2×D1311yescharacteristic
115#95—134no—
116#95—134no—
117#95C2×D1312yes—
118#95C2×D1312yes—
119#95C2×D1312yes—
120C2×C13#53511yescharacteristic
121C2×C13#53611yescharacteristic
122C2×C13#53611yescharacteristic
123C2×C13#56314yes—
124D13—81no—
125C24—131no—
126C2×Q8—264no—
127C2×Q8—524no—
128C22×C4—131no—
129C22×C4—131no—
130C22×C4—134no—
131C22×C4—131no—
132C22×C4C22×D1314yes—
133C22×C4C22×D1311yescharacteristic
134C22×C4C22×D1311yescharacteristic
135C22×C4C22×D1311yescharacteristic
136C4⋊C4—262no—
137C4⋊C4—262no—
138C4⋊C4—262no—
139C4⋊C4—264no—
140C4⋊C4—264no—
141C4⋊C4—524no—
142C22⋊C4—262no—
143C22⋊C4—262no—
144C22⋊C4—262no—
145C22⋊C4—524no—
146C42D5214yes—
147C13#282111yescharacteristic, complemented, Sylow
148C23—261no—
149C23—262no—
150C23—262no—
151C23—262no—
152C23C23×D1311yescharacteristic
153Q8—528no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—261no—
161C2×C4—261no—
162C2×C4—261no—
163C2×C4—264no—
164C2×C4—264no—
165C2×C4—262no—
166C2×C4—264no—
167C2×C4—262no—
168C2×C4—262no—
169C2×C4C2×D5212yes—
170C2×C4C2×D5212yes—
171C2×C4C2×D5212yes—
172C22—521no—
173C22—521no—
174C22—521no—
175C22—524no—
176C22C22×D5211yescharacteristic
177C22#8825612yes—
178C22#8825712yes—
179C22#8825712yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—44no—
184C4—521no—
185C4—524no—
186C4—521no—
187C4—521no—
188C2—1041no—
189C2#1171923011yescharacteristic
190C2#1171923111yescharacteristic
191C2#1171923111yescharacteristic
192C2#1171941714yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#383C2
prime radicalC23×D13C23
hypercenter#383D13
hypocenterC13#2821
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
2. C2×#88123C2semidirect
3. C13×#383C2semidirect
7. #11718322C2semidirect
8. #11718320C2semidirect
9. #11718317C2semidirect
84. #383D13semidirect
147. C13#2821semidirect

Maximal subgroups

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

subgroupindex
C2×#881302
C2×#881232
C13×#3832
#117183382
#117183352
#117183342
#117183222
#117183202
#117183172
#282113