Finite Group Databasebeta

← #13130999

Subgroups — #13130999

Order 1664.

336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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#11719430C211yesmaximal, characteristic
2C2×#88118C214yesmaximal, complemented
3C4×C4⋊#261C211yesmaximal, characteristic, complemented
4C4×#6118C211yesmaximal, characteristic, complemented
5C2×#6131C2212yes—
6C2×C4⋊#261—21no—
7C2×C4×#261C2212yes—
8C2×#6118C2212yes—
9C13×C4⋊Q8C411yescharacteristic, complemented
10#88201C412yescomplemented
11#88149—21no—
12#88149—21no—
13#88147—21no—
14#88147—21no—
15#88128C411yescharacteristic, complemented
16C42×D13C2211yescharacteristic
17#88118—28no—
18(C2×#261)⋊C4—21no—
19#88110—21no—
20C4×#1057—21no—
21C22×#261—22no—
22C2×Q8×C13C2×C412yes—
23#6131—24no—
24#6131—24no—
25C2×D52—22no—
26C2×D52—21no—
27C2×D52—21no—
28C2×D52C2×C412yes—
29C2×C4×D13—22no—
30C2×C4×D13D411yescharacteristic
31C2×C4×D13D411yescharacteristic
32C2×C4×D13C2311yescharacteristic
33C2×#1057—22no—
34C4⋊#261—24no—
35C4×#261—24no—
36#6118—22no—
37#6118D414yescomplemented
38C13×C4⋊C4—21no—
39C13×C4⋊C4—21no—
40C42×C13C2×C411yescharacteristic
41#6103—22no—
42#6103—22no—
43C4×Dic13C2×C411yescharacteristic
44C4×Dic13D411yescharacteristic
45C4×Dic13D411yescharacteristic
46#1980—131nomaximal, Sylow
47C22×D13—22no—
48C22×D13C2×D411yescharacteristic
49C2×#261—24no—
50C2×#261—42no—
51C2×#261—42no—
52Q8×C13—24no—
53C2×C4×C13—22no—
54C2×C4×C13C22⋊C411yescharacteristic
55C2×C4×C13C22⋊C411yescharacteristic
56C2×C4×C13C22×C411yescharacteristic
57C2×Dic13C22⋊C411yescharacteristic
58C2×Dic13C22⋊C411yescharacteristic
59C2×Dic13C2×D411yescharacteristic
60D52—24no—
61D52—42no—
62D52—42no—
63D52—42no—
64D52—42no—
65C4×D13—22no—
66C4×D13—41no—
67C4×D13—44no—
68C4×D13C2×D412yes—
69C4×D13#4112yes—
70#1057—24no—
71#532—131no—
72C2×#104—134no—
73C4×M16—131no—
74C4×C4⋊C4—131no—
75C22×C13C2×C22⋊C411yescharacteristic
76C2×D13—21no—
77C2×D13—21no—
78C2×D13—42no—
79C2×D13—42no—
80C2×D13—42no—
81C2×D13#12411yescharacteristic
82C2×D13#12711yescharacteristic
83#261—44no—
84C4×C13—21no—
85C4×C13—42no—
86C4×C13#10412yescomplemented
87C4×C13C4×D412yes—
88Dic13—21no—
89Dic13—21no—
90Dic13#12112yes—
91C2×#41—132no—
92C2×M16—132no—
93C4⋊Q8#26111yescharacteristic, complemented
94#127—131no—
95#124—132no—
96#121—261no—
97#121—261no—
98C4×D4—261no—
99C4×D4—261no—
100C2×C4⋊C4—261no—
101C2×C42—131no—
102C2×C42—132no—
103#104—268no—
104#97—261no—
105C4×C8—261no—
106#95—261no—
107C2×C13#39011yescharacteristic
108C2×C13C2×#10411yescharacteristic
109C2×C13#42111yescharacteristic
110D13—21no—
111D13—21no—
112D13—82no—
113#41—264no—
114#41—264no—
115C2×Q8C2×#26112yes—
116C2×D4—132no—
117C2×D4—262no—
118C2×D4—261no—
119C2×D4—261no—
120C22×C4—131no—
121C22×C4—131no—
122C22×C4—131no—
123C22×C4—262no—
124C22×C4—262no—
125M16—134no—
126M16—262no—
127C2×C8—262no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—264no—
131C22⋊C4—262no—
132C22⋊C4—262no—
133C42—131no—
134C42—131no—
135C42—131no—
136C42—264no—
137C42C2×#26111yescharacteristic
138C13#198011yescharacteristic, complemented, Sylow
139C23—131no—
140C23—262no—
141Q8—24no—
142D4—264no—
143D4—522no—
144D4—522no—
145D4—522no—
146D4—522no—
147C2×C4—22no—
148C2×C4—131no—
149C2×C4—132no—
150C2×C4—132no—
151C2×C4—131no—
152C2×C4—131no—
153C2×C4—262no—
154C2×C4—264no—
155C2×C4—521no—
156C2×C4—524no—
157C2×C4—522no—
158C2×C4—522no—
159C2×C4C22⋊#26111yescharacteristic
160C2×C4C22⋊#26111yescharacteristic
161C2×C4C22×#26111yescharacteristic
162C8—264no—
163C22—131no—
164C22—131no—
165C22—261no—
166C22—261no—
167C22—522no—
168C22—522no—
169C22—522no—
170C22C2×C22⋊#26111yescharacteristic
171C4—21no—
172C4—42no—
173C4—132no—
174C4—261no—
175C4—261no—
176C4—524no—
177C4#8811812yescomplemented
178C4D4×#26112yes—
179C2—261no—
180C2—261no—
181C2—1042no—
182C2#1171915111yescharacteristic
183C2C2×#8811811yescharacteristic
184C2#1171915511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radical#11719430C2
cosocleC2×C4×D13C23
hypercenterC4⋊Q8#261
hypocenterC13#1980
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#88118C2semidirect
3. C4×C4⋊#261C2semidirect
4. C4×#6118C2semidirect
9. C13×C4⋊Q8C4semidirect
10. #88201C4semidirect
15. #88128C4semidirect
37. #6118D4semidirect
86. C4×C13#104semidirect
93. C4⋊Q8#261semidirect
138. C13#1980semidirect
177. C4#88118semidirect

Maximal subgroups

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

subgroupindex
#117194302
C2×#881182
C4×C4⋊#2612
C4×#61182
#198013