Finite Group Databasebeta

← #16784484

Subgroups — #16784484

Order 3328.

290 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 92 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#13130950C212yesmaximal
2#13130394C211yesmaximal, characteristic
3#13130046C211yesmaximal, characteristic
4#13129728C212yesmaximal
5D13×#334C211yesmaximal, characteristic
6C2×#88104—22no—
7#11719052C2212yes—
8#11719051C2211yescharacteristic
9C4×#6118C2211yescharacteristic
10D13×C4⋊C8C2212yes—
11C4×C8×D13C2211yescharacteristic
12#11718268—22no—
13#11718254—21no—
14#11718254—21no—
15#1057⋊C8—21no—
16#11718251—21no—
17C13×#334C411yescharacteristic
18#11718072C412yes—
19#11718049C411yescharacteristic
20C2×#6118—22no—
21C2×#6118D411yescharacteristic
22C2×#6118D411yescharacteristic
23C2×C8×D13—22no—
24C2×C8×D13Q811yescharacteristic
25C2×C8×D13Q811yescharacteristic
26C42×D13C2311yescharacteristic
27#88111Q812yes—
28#88110—21no—
29C4⋊#1057—22no—
30C4⋊#1057—21no—
31C4⋊#1057—22no—
32C4×#1057—21no—
33C4×#1057—21no—
34#88104—44no—
35C13×C4⋊C8C2×C412yes—
36C4×C8×C13C2×C411yescharacteristic
37#88054—22no—
38C8×Dic13D411yescharacteristic
39C8×Dic13D411yescharacteristic
40C4⋊#1055C2×C412yes—
41C4×#1055C2×C411yescharacteristic
42#9626—131nomaximal, Sylow
43C2×C4×D13C2×D411yescharacteristic
44C2×C4×D13C2×Q811yescharacteristic
45C2×C4×D13C2×Q811yescharacteristic
46C2×#1057—21no—
47C2×#1057—21no—
48C2×#1057—22no—
49C2×#1057—42no—
50#6118—22no—
51#6118—22no—
52#6118—42no—
53#6118—42no—
54C2×C8×C13—22no—
55C2×C8×C13C4⋊C411yescharacteristic
56C2×C8×C13C4⋊C411yescharacteristic
57C42×C13C22×C411yescharacteristic
58C4×Dic13C2×D411yescharacteristic
59C4×Dic13#4111yescharacteristic
60C4×Dic13#4111yescharacteristic
61C2×#1055—22no—
62C2×#1055C4⋊C411yescharacteristic
63C2×#1055C4⋊C411yescharacteristic
64C8×D13—22no—
65C8×D13—41no—
66C8×D13—42no—
67C8×D13—42no—
68#1950—132no—
69#1567—131no—
70C2×#334—131no—
71#1451—131no—
72#1301—132no—
73C22×D13C4⋊Q811yescharacteristic
74C2×C4×C13C2×C4⋊C411yescharacteristic
75C2×C4×C13C4×D411yescharacteristic
76C2×C4×C13C4×Q811yescharacteristic
77C2×Dic13#12111yescharacteristic
78C2×Dic13C22⋊Q811yescharacteristic
79C2×Dic13#12511yescharacteristic
80C4×D13—21no—
81C4×D13—21no—
82C4×D13—41no—
83C4×D13AGL(1,ℤ/8)12yes—
84C4×D13#13712yes—
85#1057—42no—
86#1057—41no—
87#1057—41no—
88#1057—82no—
89C8×C13—21no—
90C8×C13—42no—
91C8×C13#10812yescomplemented
92#1055—21no—
93#1055—21no—
94#1055—42no—
95#431—131no—
96C2×#108—262no—
97#423—132no—
98C2×C4⋊C8—132no—
99C4×M16—131no—
100C2×C4×C8—131no—
101#341—262no—
102#335—261no—
103#335—261no—
104#334—132no—
105#334—131no—
106#334#26111yescharacteristic
107#322—261no—
108#322—261no—
109C22×C13#38911yescharacteristic
110C2×D13—21no—
111C2×D13—21no—
112C2×D13#50112yes—
113C4×C13—21no—
114C4×C13C2×#10811yescharacteristic
115C4×C13#43011yescharacteristic
116C4×C13#44012yes—
117Dic13—21no—
118Dic13—21no—
119Dic13#46911yescharacteristic
120Dic13#47011yescharacteristic
121C2×M16—131no—
122C2×M16—131no—
123C2×M16—262no—
124C22×C8—131no—
125C22×C8—131no—
126C22×C8—262no—
127C2×C42—131no—
128#108—524no—
129C4⋊C8—132no—
130C4⋊C8—262no—
131C4⋊C8—261no—
132C4⋊C8—262no—
133C4⋊C8—262no—
134C4⋊C8C2×#26112yes—
135C22⋊C8—132no—
136#97—261no—
137C4×C8—131no—
138C4×C8—131no—
139C4×C8—131no—
140C4×C8—261no—
141C4×C8—261no—
142C4×C8C2×#26111yescharacteristic
143C2×C13#194411yescharacteristic
144C2×C13#195011yescharacteristic
145C2×C13#195311yescharacteristic
146D13—22no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—131no—
150M16—262no—
151M16—262no—
152M16—522no—
153M16—522no—
154C2×C8—22no—
155C2×C8—131no—
156C2×C8—131no—
157C2×C8—262no—
158C2×C8—261no—
159C2×C8—261no—
160C2×C8—262no—
161C2×C8—262no—
162C2×C8—521no—
163C2×C8—522no—
164C2×C8—522no—
165C2×C8—522no—
166C2×C8C4⋊#26111yescharacteristic
167C2×C8C4⋊#26111yescharacteristic
168C42—131no—
169C42—131no—
170C42—131no—
171C42C22×#26111yescharacteristic
172C13#962611yescharacteristic, complemented, Sylow
173C23—131no—
174C2×C4—131no—
175C2×C4—132no—
176C2×C4—132no—
177C2×C4—131no—
178C2×C4—131no—
179C2×C4—261no—
180C2×C4—261no—
181C2×C4—521no—
182C2×C4C2×C4⋊#26111yescharacteristic
183C2×C4D4×#26111yescharacteristic
184C2×C4Q8×#26111yescharacteristic
185C8—21no—
186C8—42no—
187C8—261no—
188C8—261no—
189C8—521no—
190C8—521no—
191C8—522no—
192C8—522no—
193C8—1042no—
194C8#8810412yescomplemented
195C22—132no—
196C22—261no—
197C22—261no—
198C22#1171908311yescharacteristic
199C4—21no—
200C4—131no—
201C4—131no—
202C4—261no—
203C4—261no—
204C4C2×#8810411yescharacteristic
205C4#1171910011yescharacteristic
206C4#1171910612yes—
207C2—262no—
208C2#1313094211yescharacteristic
209C2#1313095011yescharacteristic
210C2#1313095611yescharacteristic
subgroupG/H
centerC22#11719083
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#334C4
socleC22×C13#389
prime radicalC22×D13C4⋊Q8
cosocleC42×D13C23
hypercenter#334#261
hypocenterC13#9626
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
91. C8×C13#108semidirect
172. C13#9626semidirect
194. C8#88104semidirect

Maximal subgroups

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

subgroupindex
#131309502
#131303942
#131300462
#131297282
D13×#3342
#962613