Finite Group Databasebeta

← #13130881

Subgroups — #13130881

Order 1664.

362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 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#11719623C211yesmaximal, characteristic, complemented
2#11719379C211yesmaximal, characteristic
3#11719155C212yesmaximal, complemented
4D13⋊#100C211yesmaximal, characteristic, complemented
5#11718235C212yesmaximal, complemented
6C2×#6131C2211yescharacteristic
7C2×D4×D13C2211yescharacteristic
8C2×C22⋊#261—22no—
9D4×#261—24no—
10#88237C2212yes—
11D13⋊M16C2212yes—
12C13×#124C411yescharacteristic, complemented
13#88201C411yescharacteristic, complemented
14#88194C411yescharacteristic, complemented
15#88138—22no—
16#88136—22no—
17#88128C411yescharacteristic, complemented
18#88126C2211yescharacteristic
19#88121—22no—
20#88118—24no—
21C23×D13D412yes—
22C22×#261—24no—
23C2×Q8×C13C2×C411yescharacteristic, complemented
24C2×D4×C13C2×C411yescharacteristic
25C2×C22⋊D13—22no—
26C2×C22⋊D13D412yes—
27#6131—22no—
28#6131—22no—
29D4×D13—22no—
30D4×D13—22no—
31C2×D52—21no—
32C2×D52—22no—
33C2×D52C2×C411yescharacteristic
34C2×D52C2×C411yescharacteristic, complemented
35C2×C4×D13—21no—
36C2×C4×D13C2311yescharacteristic
37C22⋊#261—24no—
38C22⋊#261—22no—
39#6122—22no—
40C4⋊#261—22no—
41C4×#261D414yescomplemented
42#6118—22no—
43D13⋊C8—22no—
44C13×C22⋊C4—22no—
45C42×C13C2×C411yescharacteristic, complemented
46#6103—22no—
47#6103—21no—
48#6101—21no—
49C4×Dic13C2×C411yescharacteristic, complemented
50#1911—131nomaximal, Sylow
51C23×C13C22⋊C412yes—
52C22×D13—22no—
53C22×D13—22no—
54C22×D13—21no—
55C22×D13—82no—
56C22×D13C22⋊C412yes—
57C22×D13C2×D411yescharacteristic
58C2×#261—24no—
59C2×#261—84no—
60Q8×C13—22no—
61D4×C13—22no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13C22×C411yescharacteristic
65C22⋊D13—24no—
66C22⋊D13—82no—
67C2×Dic13—21no—
68C2×Dic13C2×D411yescharacteristic
69D52—22no—
70D52—22no—
71D52—41no—
72D52—41no—
73D52—82no—
74C4×D13—42no—
75C4×D13C2×D412yes—
76C4×D13#4112yes—
77#1057—42no—
78#535—131no—
79#518—131no—
80#421—132no—
81C2×#100—131no—
82H(3,ℤ/4)—132no—
83C22×C13—22no—
84C22×C13—42no—
85C22×C13C2×C22⋊C411yescharacteristic
86C2×D13—22no—
87C2×D13—41no—
88C2×D13—44no—
89C2×D13—42no—
90C2×D13—42no—
91C2×D13—41no—
92C2×D13—82no—
93C2×D13#12011yescharacteristic
94C2×D13#12311yescharacteristic
95#261—44no—
96C4×C13—41no—
97C4×C13—41no—
98C4×C13C4×D412yes—
99Dic13—41no—
100Dic13#12112yes—
101C2×#41—131no—
102C22×D4—131no—
103C2×M16—132no—
104#127—131no—
105#127—131no—
106#124—131no—
107#124#26111yescharacteristic, complemented
108#121—262no—
109#120—262no—
110C4×D4—264no—
111#117—132no—
112#117—131no—
113C2×C22⋊C4—262no—
114#104—264no—
115#100—262no—
116C2×C13—21no—
117C2×C13—42no—
118C2×C13#38611yescharacteristic
119D13—21no—
120D13—21no—
121D13—42no—
122D13—81no—
123C24—132no—
124#41—262no—
125#41—262no—
126C2×Q8C2×#26111yescharacteristic, complemented
127C2×D4—132no—
128C2×D4—131no—
129C2×D4—131no—
130C2×D4—261no—
131C2×D4—262no—
132C2×D4—262no—
133C2×D4—262no—
134C2×D4—262no—
135C2×D4C2×#26111yescharacteristic
136C22×C4—131no—
137C22×C4—261no—
138C22×C4—264no—
139M16—262no—
140M16—262no—
141C2×C8—262no—
142C4⋊C4—261no—
143C4⋊C4—262no—
144C22⋊C4—22no—
145C22⋊C4—261no—
146C22⋊C4—262no—
147C22⋊C4—262no—
148C22⋊C4—264no—
149C42—134no—
150C42—131no—
151C42C2×#26111yescharacteristic, complemented
152C13#191111yescharacteristic, complemented, Sylow
153C23—131no—
154C23—132no—
155C23—262no—
156C23—262no—
157C23—261no—
158C23—1042no—
159C23C22⋊#26112yes—
160Q8—22no—
161D4—22no—
162D4—264no—
163D4—262no—
164D4—262no—
165D4—521no—
166D4—521no—
167D4—1042no—
168D4—1042no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—131no—
172C2×C4—132no—
173C2×C4—132no—
174C2×C4—264no—
175C2×C4—261no—
176C2×C4—522no—
177C2×C4—1044no—
178C2×C4C22×#26111yescharacteristic
179C8—522no—
180C22—22no—
181C22—42no—
182C22—131no—
183C22—131no—
184C22—262no—
185C22—521no—
186C22—522no—
187C22—522no—
188C22—524no—
189C22—521no—
190C22—1042no—
191C22C2×C22⋊#26111yescharacteristic
192C4—41no—
193C4—41no—
194C4—132no—
195C4—521no—
196C4—524no—
197C4D4×#26112yes—
198C2—21no—
199C2—42no—
200C2—261no—
201C2—261no—
202C2—522no—
203C2—1041no—
204C2#1171915011yescharacteristic
subgroupG/H
centerC2#11719150
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC2×C13#386
prime radical#11719379C2
cosocleC2×C4×D13C23
hypercenter#124#261
hypocenterC13#1911
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #11719623C2semidirect
3. #11719155C2semidirect
4. D13⋊#100C2semidirect
5. #11718235C2semidirect
12. C13×#124C4semidirect
13. #88201C4semidirect
14. #88194C4semidirect
17. #88128C4semidirect
23. C2×Q8×C13C2×C4semidirect
34. C2×D52C2×C4semidirect
41. C4×#261D4semidirect
45. C42×C13C2×C4semidirect
49. C4×Dic13C2×C4semidirect
107. #124#261semidirect
126. C2×Q8C2×#261semidirect
151. C42C2×#261semidirect
152. C13#1911semidirect

Maximal subgroups

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

subgroupindex
#117196232
#117193792
#117191552
D13⋊#1002
#117182352
#191113