Finite Group Databasebeta

← #13116060

Subgroups — #13116060

Order 1664.

306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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
1#11719215C211yesmaximal, characteristic
2C13×#384C211yesmaximal, characteristic, complemented
3#11718627C212yesmaximal, complemented
4C2×#88045C212yesmaximal, complemented
5#11718122C211yesmaximal, characteristic, complemented
6C2×#6127C2212yes—
7C2×C13×C4⋊C4—22no—
8C2×C13×C4⋊C4C2211yescharacteristic
9C2×C13×C4⋊C4C2211yescharacteristic
10C2×C42×C13C2211yescharacteristic
11#88184—22no—
12C2×#6099C2212yes—
13#88151—22no—
14#88149—22no—
15#88050—22no—
16#88049—22no—
17#88045—24no—
18C22×C4×C13—21no—
19C22×C4×C13—21no—
20C22×C4×C13D412yes—
21C22×C4×C13C2311yescharacteristic
22C2×C22⋊D13—22no—
23#6127—22no—
24#6127—22no—
25#6127—22no—
26#6127—22no—
27C2×D52—22no—
28C2×D52D412yes—
29C2×C4×D13—22no—
30C2×Dic26D412yes—
31C13×C4⋊C4—22no—
32C13×C4⋊C4—22no—
33C13×C4⋊C4—44no—
34C42×C13—21no—
35C42×C13D412yescomplemented
36#6103—24no—
37C4⋊Dic13—22no—
38#6099—22no—
39#6099—22no—
40C2×#1055—22no—
41#2039—131nomaximal, Sylow
42C23×C13C2×D411yescharacteristic
43C22×D13—22no—
44C2×C4×C13—22no—
45C2×C4×C13—22no—
46C2×C4×C13—22no—
47C2×C4×C13—22no—
48C2×C4×C13—42no—
49C2×C4×C13—42no—
50C2×C4×C13—41no—
51C2×C4×C13C2×D411yescharacteristic
52C2×C4×C13C2×D412yes—
53C2×C4×C13#4112yes—
54C2×C4×C13#4111yescharacteristic
55C22⋊D13—42no—
56C22⋊D13—42no—
57C2×Dic13—22no—
58D52—22no—
59D52—22no—
60D52—82no—
61C4×D13—42no—
62C4×D13—42no—
63Dic26—22no—
64Dic26—22no—
65#1055—42no—
66#537—131no—
67C2×#104—132no—
68#417—132no—
69#384D1311yescharacteristic, complemented
70#343—131no—
71C22×C13—21no—
72C22×C13—21no—
73C22×C13#12011yescharacteristic
74C22×C13#12111yescharacteristic
75C22×C13#12411yescharacteristic
76C2×D13—42no—
77C2×D13—42no—
78C2×D13—42no—
79C4×C13—24no—
80C4×C13—42no—
81C4×C13—81no—
82C4×C13#12112yes—
83C4×C13#12312yes—
84Dic13—42no—
85C2×#41—132no—
86C2×M16—132no—
87C22⋊Q8—262no—
88#121—262no—
89#121—262no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4C2×D1311yescharacteristic
92C2×C4⋊C4C2×D1311yescharacteristic
93C2×C42C2×D1311yescharacteristic
94#104—264no—
95#103—262no—
96#102—262no—
97C2×C13—21no—
98C2×C13—21no—
99C2×C13#39411yescharacteristic
100C2×C13#45311yescharacteristic
101C2×C13#45611yescharacteristic
102D13—82no—
103#41—262no—
104#41—262no—
105#41—262no—
106#41—262no—
107C2×Q8—132no—
108C2×D4—132no—
109C2×D4—262no—
110C2×D4—262no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—262no—
114C22×C4C22⋊D1312yes—
115C22×C4C22×D1311yescharacteristic
116M16—262no—
117M16—262no—
118C2×C8—262no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—44no—
122C4⋊C4—262no—
123C22⋊C4—264no—
124C42—21no—
125C42D5212yescomplemented
126C13#203911yescharacteristic, complemented, Sylow
127C23—262no—
128C23C2×C22⋊D1311yescharacteristic
129Q8—262no—
130Q8—262no—
131D4—262no—
132D4—262no—
133D4—522no—
134D4—522no—
135D4—1042no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—262no—
144C2×C4—522no—
145C2×C4—522no—
146C2×C4C2×D5211yescharacteristic
147C2×C4#612711yescharacteristic
148C2×C4D4×D1312yes—
149C2×C4#613112yes—
150C8—522no—
151C22—21no—
152C22—21no—
153C22—522no—
154C22—522no—
155C22—522no—
156C22#8818411yescharacteristic
157C22#8819111yescharacteristic
158C22#8820111yescharacteristic
159C4—24no—
160C4—42no—
161C4—81no—
162C4—522no—
163C4#8814812yes—
164C4#8814912yes—
165C2—21no—
166C2—21no—
167C2—1042no—
168C2#1171865211yescharacteristic
169C2#1171873811yescharacteristic
170C2#1171875611yescharacteristic
subgroupG/H
centerC22#88191
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#384C2
socleC22×C13#120
prime radical#11719215C2
hypercenter#384D13
hypocenterC13#2039
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C13×#384C2semidirect
3. #11718627C2semidirect
4. C2×#88045C2semidirect
5. #11718122C2semidirect
35. C42×C13D4semidirect
69. #384D13semidirect
125. C42D52semidirect
126. C13#2039semidirect

Maximal subgroups

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

subgroupindex
#117192152
C13×#3842
#117186272
C2×#880452
#117181222
#203913