Finite Group Databasebeta

← #13130233

Subgroups — #13130233

Order 1664.

346 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 64 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×#88149C211yesmaximal, characteristic
2C4×C22⋊#261C211yesmaximal, characteristic, complemented
3#11719127C211yesmaximal, characteristic, complemented
4#11718240C214yesmaximal, complemented
5C22×D52—21no—
6C22×D52C411yescharacteristic, complemented
7C22×C4×D13C2211yescharacteristic
8C2×C22⋊#261—21no—
9C2×C4×#261—21no—
10C2×#6118—21no—
11C2×C13×C4⋊C4C411yescharacteristic, complemented
12C2×#6103—21no—
13#88149—21no—
14#88149—21no—
15#88149C412yescomplemented
16#88149C2212yes—
17C22⋊#1057—21no—
18(C2×#261)⋊C4C2212yescomplemented
19#88111C2212yescomplemented
20C23×D13—21no—
21C23×D13D411yescharacteristic
22C22×#261—22no—
23C22×C4×C13—21no—
24C22×C4×C13C2×C411yescharacteristic
25C22×Dic13D411yescharacteristic
26C2×D52—22no—
27C2×D52—22no—
28C2×D52—21no—
29C2×D52—44no—
30C2×D52—42no—
31C2×D52C2×C412yes—
32C2×C4×D13—42no—
33C2×C4×D13C2×C411yescharacteristic
34C2×C4×D13D411yescharacteristic
35C2×C4×D13D411yescharacteristic
36C2×C4×D13C2311yescharacteristic
37C22⋊#261—24no—
38C2×#1057—22no—
39C4×#261—42no—
40#6118—42no—
41C13×C4⋊C4—21no—
42C13×C4⋊C4C2×C412yes—
43#6103—22no—
44#6103—22no—
45#1507—131nomaximal, Sylow
46C23×C13C22⋊C411yescharacteristic
47C22×D13—22no—
48C22×D13—22no—
49C22×D13—22no—
50C22×D13—41no—
51C22×D13—42no—
52C22×D13—42no—
53C22×D13—42no—
54C22×D13C22⋊C411yescharacteristic
55C22×D13C2×D411yescharacteristic
56C2×#261—24no—
57C2×#261—42no—
58C2×#261—42no—
59C2×C4×C13—22no—
60C2×C4×C13—22no—
61C2×C4×C13—42no—
62C2×C4×C13C22⋊C411yescharacteristic
63C2×C4×C13C22×C411yescharacteristic
64C2×Dic13—41no—
65C2×Dic13C22⋊C411yescharacteristic
66C2×Dic13C2×D411yescharacteristic
67D52—42no—
68D52—44no—
69D52—44no—
70D52—42no—
71C4×D13—22no—
72C4×D13—22no—
73C4×D13—41no—
74C4×D13—41no—
75#1057—42no—
76C2×#121—131no—
77#407—131no—
78C4×C22⋊C4—131no—
79#327—134no—
80C22×C13—21no—
81C22×C13—21no—
82C22×C13#10412yes—
83C22×C13C2×C22⋊C411yescharacteristic
84C2×D13—21no—
85C2×D13—21no—
86C2×D13—21no—
87C2×D13—21no—
88C2×D13—21no—
89C2×D13—44no—
90C2×D13—42no—
91C2×D13—42no—
92C2×D13—42no—
93C2×D13—84no—
94C2×D13AGL(1,ℤ/8)12yes—
95#261—44no—
96C4×C13—21no—
97C4×C13—42no—
98C4×C13#9912yes—
99Dic13—21no—
100Dic13—21no—
101C22×D4—131no—
102C22×D4—261no—
103C23×C4—131no—
104C2×M16—261no—
105#121—132no—
106#121—132no—
107#121—261no—
108#121—261no—
109C2×C4⋊C4#26111yescharacteristic, complemented
110C2×C22⋊C4—261no—
111C2×C22⋊C4—261no—
112C2×C42—261no—
113C22⋊C8—132no—
114C22⋊C8—261no—
115#95—132no—
116C2×C13—22no—
117C2×C13C2×#9911yescharacteristic
118C2×C13#41811yescharacteristic
119C2×C13C2×#10411yescharacteristic
120D13—22no—
121D13—41no—
122D13—82no—
123C24—131no—
124C24—261no—
125C2×D4—132no—
126C2×D4—262no—
127C2×D4—262no—
128C2×D4—261no—
129C2×D4—522no—
130C2×D4—524no—
131C22×C4—21no—
132C22×C4—131no—
133C22×C4—131no—
134C22×C4—131no—
135C22×C4—131no—
136C22×C4—131no—
137C22×C4—262no—
138C22×C4—522no—
139C22×C4C2×#26111yescharacteristic
140M16—522no—
141C2×C8—262no—
142C4⋊C4—21no—
143C4⋊C4C2×#26112yes—
144C22⋊C4—262no—
145C22⋊C4—262no—
146C22⋊C4—264no—
147C42—522no—
148C13#150711yescharacteristic, complemented, Sylow
149C23—131no—
150C23—131no—
151C23—262no—
152C23—262no—
153C23—262no—
154C23—521no—
155C23—522no—
156C23—522no—
157C23—522no—
158C23C22⋊#26111yescharacteristic
159D4—522no—
160D4—524no—
161D4—524no—
162D4—522no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—131no—
167C2×C4—131no—
168C2×C4—262no—
169C2×C4—262no—
170C2×C4—264no—
171C2×C4—521no—
172C2×C4—521no—
173C2×C4—521no—
174C2×C4—522no—
175C2×C4—522no—
176C2×C4C22⋊#26111yescharacteristic
177C2×C4C22×#26111yescharacteristic
178C8—522no—
179C22—21no—
180C22—21no—
181C22—132no—
182C22—261no—
183C22—261no—
184C22—261no—
185C22—261no—
186C22—261no—
187C22—524no—
188C22—522no—
189C22—522no—
190C22—522no—
191C22—1044no—
192C22#8811812yes—
193C22C2×C22⋊#26111yescharacteristic
194C4—21no—
195C4—42no—
196C4—261no—
197C4—261no—
198C4—524no—
199C4#8810712yes—
200C2—22no—
201C2—262no—
202C2—521no—
203C2—1042no—
204C2C2×#8810711yescharacteristic
205C2#1171913811yescharacteristic
206C2C2×#8811811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC2×C13×C4⋊C4C4
socleC22×C13C2×C22⋊C4
prime radicalC2×#88149C2
cosocleC2×C4×D13C23
hypercenterC2×C4⋊C4#261
hypocenterC13#1507
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#261C2semidirect
3. #11719127C2semidirect
4. #11718240C2semidirect
6. C22×D52C4semidirect
11. C2×C13×C4⋊C4C4semidirect
15. #88149C4semidirect
18. (C2×#261)⋊C4C22semidirect
19. #88111C22semidirect
109. C2×C4⋊C4#261semidirect
148. C13#1507semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
C4×C22⋊#2612
#117191272
#117182402
#150713