Finite Group Databasebeta

← #13120939

Subgroups — #13120939

Order 1664.

804 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 153 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×#88149C213yesmaximal, complemented
2C2×#88138C213yesmaximal, complemented
3C13×#399C211yesmaximal, characteristic, complemented
4#11718653C213yesmaximal, complemented
5#11718621C213yesmaximal, complemented
6#11718332C211yesmaximal, characteristic, complemented
7D13×#95C211yesmaximal, characteristic, complemented
8C22×C22⋊D13C2211yescharacteristic
9C22×C22⋊D13C2213yes—
10C22×D52C2213yes—
11C22×D52C2213yes—
12C22×C4×D13C2213yes—
13C2×C13×C4⋊C4C2213yes—
14C2×C13×C22⋊C4C2213yes—
15C2×#6103C2213yes—
16C2×#6103C2216yes—
17C2×#6101C2213yes—
18#88149—212no—
19#88138—212no—
20C13×#95C2211yescharacteristic
21#88071C2213yes—
22C24×C13C2311yescharacteristic
23C23×D13C2313yes—
24C23×D13C2311yescharacteristic
25C22×C4×C13C2313yes—
26C22×C4×C13C2313yes—
27C2×C22⋊D13—26no—
28C2×C22⋊D13—26no—
29C2×C22⋊D13—46no—
30C22×Dic13C2311yescharacteristic
31C22×Dic13C2313yes—
32C2×D52—26no—
33C2×D52—212no—
34C2×D52—26no—
35C2×D52—46no—
36C2×C4×D13—46no—
37C2×C4×D13D4112yescomplemented
38C13×C4⋊C4—26no—
39C13×C22⋊C4—26no—
40#6103—26no—
41#6103—212no—
42#6101—26no—
43#2656—131nomaximal, Sylow
44C23×C13—23no—
45C23×C13—23no—
46C23×C13—21no—
47C23×C13C2411yescharacteristic
48C22×D13—23no—
49C22×D13—21no—
50C22×D13—26no—
51C22×D13—23no—
52C22×D13—23no—
53C22×D13—26no—
54C22×D13—23no—
55C22×D13C2×D416yes—
56C2×C4×C13—26no—
57C2×C4×C13—23no—
58C2×C4×C13—26no—
59C2×C4×C13C2×D416yes—
60C22⋊D13—412no—
61C22⋊D13—44no—
62C2×Dic13—26no—
63C2×Dic13—23no—
64C2×Dic13C2×D416yes—
65D52—412no—
66D52—412no—
67C4×D13—412no—
68C2×#121—133no—
69C2×#121—133no—
70#399—133no—
71#399D1311yescharacteristic, complemented
72#392—133no—
73#392—131no—
74C2×#95—131no—
75C22×C13—41no—
76C22×C13—43no—
77C22×C13—43no—
78C22×C13C22×D413yes—
79C22×C13H(5,𝔽2)13yes—
80C22×C132−1+411yescharacteristic
81C2×D13—26no—
82C2×D13—26no—
83C2×D13—43no—
84C2×D13—46no—
85C2×D13—43no—
86C2×D13—46no—
87C2×D13—43no—
88C2×D13#12714yes—
89C4×C13—26no—
90C4×C13—43no—
91Dic13—26no—
92Dic13—41no—
93C22×D4—131no—
94C22×D4—133no—
95C22×D4—133no—
96C22×D4—133no—
97C23×C4—133no—
98#121—2612no—
99#121—2612no—
100C2×C4⋊C4—133no—
101C2×C4⋊C4C2×D1313yes—
102C2×C22⋊C4—136no—
103C2×C22⋊C4—133no—
104C2×C22⋊C4C2×D1313yes—
105#95—133no—
106#95C2×D1311yescharacteristic
107C2×C13—81no—
108C2×C13C2×#12711yescharacteristic
109C2×C13#53413yes—
110C2×C13#53713yes—
111D13—24no—
112D13—83no—
113C24—131no—
114C24—133no—
115C24C22×D1311yescharacteristic
116C2×D4—266no—
117C2×D4—2612no—
118C2×D4—266no—
119C2×D4—266no—
120C2×D4—266no—
121C2×D4—526no—
122C2×D4—526no—
123C22×C4—133no—
124C22×C4—1312no—
125C22×C4—131no—
126C22×C4—526no—
127C22×C4C22×D1313yes—
128C22×C4C22×D1313yes—
129C4⋊C4—26no—
130C4⋊C4—266no—
131C22⋊C4—26no—
132C22⋊C4—2612no—
133C22⋊C4—266no—
134C13#265611yescharacteristic, complemented, Sylow
135C23—23no—
136C23—21no—
137C23—23no—
138C23—136no—
139C23—261no—
140C23—263no—
141C23—266no—
142C23—263no—
143C23—263no—
144C23—263no—
145C23—266no—
146C23C23×D1311yescharacteristic
147D4—5212no—
148D4—5212no—
149D4—5212no—
150D4—524no—
151C2×C4—26no—
152C2×C4—23no—
153C2×C4—26no—
154C2×C4—136no—
155C2×C4—266no—
156C2×C4—263no—
157C2×C4—5212no—
158C2×C4D4×D1316yes—
159C22—43no—
160C22—43no—
161C22—41no—
162C22—134no—
163C22—266no—
164C22—266no—
165C22—526no—
166C22—523no—
167C22—526no—
168C22—523no—
169C22—523no—
170C22C2×D4×D1313yes—
171C22#8825411yescharacteristic
172C22#8825613yes—
173C4—26no—
174C4—43no—
175C4—266no—
176C4—521no—
177C2—81no—
178C2—264no—
179C2—1043no—
180C2#1171933413yes—
181C2#1171935813yes—
182C2D13×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#399C2
hypercenter#399D13
hypocenterC13#2656
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#88149C2semidirect
2. C2×#88138C2semidirect
3. C13×#399C2semidirect
4. #11718653C2semidirect
5. #11718621C2semidirect
6. #11718332C2semidirect
7. D13×#95C2semidirect
37. C2×C4×D13D4semidirect
71. #399D13semidirect
134. C13#2656semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
C2×#881382
C13×#3992
#117186532
#117186212
#117183322
D13×#952
#265613