Finite Group Databasebeta

← #13115217

Subgroups — #13115217

Order 1664.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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#11719537C211yesmaximal, characteristic
2#11719524C211yesmaximal, characteristic, complemented
3C13×#410C211yesmaximal, characteristic, complemented
4#11718666C212yesmaximal, complemented
5#11718124C212yesmaximal, complemented
6C2×C13×#41C2211yescharacteristic
7C2×#6127C2211yescharacteristic
8C13×#117C2212yes—
9#88202—24no—
10#88201C411yescharacteristic, complemented
11#88198C411yescharacteristic, complemented
12#88194C411yescharacteristic, complemented
13#88193—22no—
14#88190C411yescharacteristic, complemented
15C4×C22⋊D13—22no—
16C2×C4×Dic13C2211yescharacteristic
17C2×#6099—22no—
18C2×#6099C2212yes—
19C13×#99—22no—
20#88045—24no—
21C13×#41—22no—
22C13×#41—22no—
23C2×Q8×C13C2×C411yescharacteristic
24C2×D4×C13C2×C411yescharacteristic
25C2×D4×C13D412yes—
26C22×C4×C13D412yes—
27C22×C4×C13C2311yescharacteristic
28C2×C22⋊D13—22no—
29C2×C22⋊D13—21no—
30C22×Dic13—21no—
31#6127—22no—
32#6127—22no—
33C2×D52C2×C411yescharacteristic
34C2×C4×D13—21no—
35C2×Dic26C2×C411yescharacteristic
36C13×C4⋊C4—22no—
37C13×C22⋊C4—22no—
38C42×C13—22no—
39C22⋊Dic13—22no—
40#6103—22no—
41#6101—22no—
42C4×Dic13—21no—
43C4×Dic13C2×C411yescharacteristic
44C4×Dic13C2×C411yescharacteristic
45#6099—24no—
46#6099—22no—
47#6099D414yescomplemented
48C2×#1055—24no—
49C2×#1055—22no—
50#1884—131nomaximal, Sylow
51C23×C13C22⋊C412yes—
52C23×C13C2×D411yescharacteristic
53C22×D13—21no—
54Q8×C13—22no—
55D4×C13—24no—
56D4×C13—22no—
57C2×C4×C13—22no—
58C2×C4×C13—22no—
59C2×C4×C13—42no—
60C2×C4×C13C22⋊C412yes—
61C2×C4×C13C22×C411yescharacteristic
62C2×C4×C13C2×D412yes—
63C2×C4×C13C2×D411yescharacteristic
64C2×C4×C13#4112yes—
65C22⋊D13—44no—
66C22⋊D13—42no—
67C2×Dic13—21no—
68C2×Dic13—21no—
69C2×Dic13—21no—
70C2×Dic13—42no—
71D52—22no—
72C4×D13—41no—
73C4×D13—41no—
74Dic26—22no—
75#1055—24no—
76#568—131no—
77#532—131no—
78#421—132no—
79#410D1311yescharacteristic, complemented
80#339—132no—
81C22×C13—22no—
82C22×C13—41no—
83C22×C13—42no—
84C22×C13C2×C22⋊C411yescharacteristic
85C22×C13#12112yes—
86C2×D13—42no—
87C2×D13—41no—
88C4×C13—22no—
89C4×C13—82no—
90C4×C13C4×D412yes—
91C4×C13#12011yescharacteristic
92C4×C13#12311yescharacteristic
93Dic13—22no—
94Dic13—41no—
95Dic13—41no—
96C2×#41—131no—
97C2×#41C2×D1311yescharacteristic
98#131—264no—
99C2×M16—132no—
100C2×M16—262no—
101C4⋊Q8—131no—
102#127—131no—
103#124—131no—
104#124—131no—
105#121—262no—
106C4×D4—262no—
107#117C2×D1312yes—
108C2×C42—131no—
109#104—264no—
110#99—22no—
111C2×C13—21no—
112C2×C13—22no—
113C2×C13—42no—
114C2×C13#38611yescharacteristic
115D13—81no—
116#41—22no—
117#41—22no—
118#41—262no—
119#41—262no—
120C2×Q8—131no—
121C2×Q8C4×D1311yescharacteristic
122C2×D4—131no—
123C2×D4—262no—
124C2×D4—261no—
125C2×D4C4×D1311yescharacteristic
126C2×D4C22⋊D1312yes—
127C22×C4—261no—
128C22×C4—261no—
129C22×C4D5212yes—
130C22×C4C22×D1311yescharacteristic
131M16—134no—
132M16—264no—
133M16—262no—
134C2×C8—264no—
135C2×C8—262no—
136C4⋊C4—22no—
137C4⋊C4—262no—
138C22⋊C4—22no—
139C22⋊C4—262no—
140C22⋊C4—262no—
141C42—22no—
142C42—131no—
143C42—131no—
144C42—261no—
145C13#188411yescharacteristic, complemented, Sylow
146C23—261no—
147C23#610312yes—
148C23C2×C22⋊D1311yescharacteristic
149Q8—22no—
150Q8—262no—
151D4—24no—
152D4—22no—
153D4—262no—
154D4—524no—
155D4—522no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—261no—
160C2×C4—261no—
161C2×C4—261no—
162C2×C4—522no—
163C2×C4—521no—
164C2×C4—521no—
165C2×C4#610312yes—
166C2×C4C2×C4×D1311yescharacteristic
167C2×C4C2×D5211yescharacteristic
168C2×C4D4×D1312yes—
169C2×C4#612912yes—
170C8—264no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—522no—
175C22—521no—
176C22C2×#610311yescharacteristic
177C22#8819312yes—
178C4—22no—
179C4—82no—
180C4—262no—
181C4—521no—
182C4—521no—
183C4#8813512yes—
184C4#8813611yescharacteristic
185C4#8814011yescharacteristic
186C2—22no—
187C2—21no—
188C2—42no—
189C2—1041no—
190C2#1171861911yescharacteristic
subgroupG/H
centerC4#88136
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#410C2
socleC2×C13#386
prime radical#11719537C2
cosocleC22×C4×C13C23
hypercenter#410D13
hypocenterC13#1884
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #11719524C2semidirect
3. C13×#410C2semidirect
4. #11718666C2semidirect
5. #11718124C2semidirect
10. #88201C4semidirect
11. #88198C4semidirect
12. #88194C4semidirect
14. #88190C4semidirect
47. #6099D4semidirect
79. #410D13semidirect
145. C13#1884semidirect

Maximal subgroups

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

subgroupindex
#117195372
#117195242
C13×#4102
#117186662
#117181242
#188413