Finite Group Databasebeta

← #16782445

Subgroups — #16782445

Order 3328.

322 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 116 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#13130775C211yesmaximal, characteristic
2#13130760C211yesmaximal, characteristic
3#13130395C211yesmaximal, characteristic
4#13130394C211yesmaximal, characteristic
5#13130391C211yesmaximal, characteristic
6#13130391C211yesmaximal, characteristic
7D13×#322C211yesmaximal, characteristic
8C2×#88103—22no—
9#11719052C2211yescharacteristic
10#11719052C2211yescharacteristic
11#11719052C2211yescharacteristic
12#11719052C2211yescharacteristic
13C4×C8×D13C2211yescharacteristic
14C4×C8×D13C2211yescharacteristic
15C4×C8×D13C2211yescharacteristic
16#11718268—22no—
17#11718256—22no—
18#11718254—22no—
19#11718253—22no—
20#11718253—22no—
21C13×#322C411yescharacteristic
22#11718047C411yescharacteristic
23#11718046C411yescharacteristic
24#11718046C411yescharacteristic
25C2×#6118—21no—
26C2×#6118—21no—
27C2×#6118—21no—
28C2×#6118—21no—
29C2×C8×D13D412yes—
30C2×C8×D13Q812yes—
31C2×C8×D13Q812yes—
32C42×D13C2311yescharacteristic
33C4⋊#1057—21no—
34C4⋊#1057—21no—
35C4⋊#1057—21no—
36C4⋊#1057—21no—
37C4⋊#1057—21no—
38C4⋊#1057—21no—
39C4⋊#1057—21no—
40C4⋊#1057—21no—
41#88103—44no—
42C4×C8×C13C2×C411yescharacteristic
43C4×C8×C13C2×C411yescharacteristic
44C4×C8×C13C2×C411yescharacteristic
45C8×Dic13D412yes—
46C8×Dic13D412yes—
47C8×Dic13Q812yes—
48C4×#1055C2×C411yescharacteristic
49C4×#1055C2×C411yescharacteristic
50C4×#1055C2×C411yescharacteristic
51#8828—131nomaximal, Sylow
52C2×C4×D13C2×D411yescharacteristic
53C2×C4×D13C2×Q811yescharacteristic
54C2×C4×D13C2×Q811yescharacteristic
55C2×#1057—41no—
56C2×#1057—41no—
57C2×#1057—41no—
58C2×#1057—41no—
59#6118—42no—
60#6118—42no—
61#6118—42no—
62#6118—42no—
63C2×C8×C13C4⋊C412yes—
64C2×C8×C13C4⋊C412yes—
65C2×C8×C13C4⋊C412yes—
66C42×C13C22×C411yescharacteristic
67C4×Dic13C2×D411yescharacteristic
68C4×Dic13C2×D411yescharacteristic
69C4×Dic13C2×Q811yescharacteristic
70C2×#1055C4⋊C412yes—
71C2×#1055C4⋊C412yes—
72C2×#1055C4⋊C412yes—
73C8×D13—22no—
74C8×D13—22no—
75C8×D13—24no—
76C8×D13—42no—
77#1848—131no—
78#1837—131no—
79#1567—131no—
80#1567—131no—
81#1566—131no—
82#1566—131no—
83C2×#322—131no—
84C22×D13C4⋊Q811yescharacteristic
85C2×C4×C13C2×C4⋊C411yescharacteristic
86C2×C4×C13C2×C4⋊C411yescharacteristic
87C2×C4×C13C2×C4⋊C411yescharacteristic
88C2×Dic13#12711yescharacteristic
89C2×Dic13C4⋊Q811yescharacteristic
90C2×Dic13C4⋊Q811yescharacteristic
91C4×D13—22no—
92C4×D13—22no—
93C4×D13AGL(1,ℤ/8)12yes—
94C4×D13#13712yes—
95#1057—81no—
96#1057—81no—
97#1057—81no—
98#1057—81no—
99C8×C13—22no—
100C8×C13—22no—
101C8×C13#10814yescomplemented
102#1055—22no—
103#1055—22no—
104#1055—22no—
105C2×#108—262no—
106#423—131no—
107#423—131no—
108#423—131no—
109#423—131no—
110C2×C4×C8—131no—
111C2×C4×C8—131no—
112C2×C4×C8—131no—
113#341—262no—
114#335—262no—
115#335—262no—
116#334—262no—
117#334—262no—
118#322—131no—
119#322—131no—
120#322—131no—
121#322#26111yescharacteristic
122C22×C13#38411yescharacteristic
123C2×D13—21no—
124C2×D13—21no—
125C2×D13#50112yes—
126C4×C13#42812yes—
127C4×C13C2×#10812yes—
128C4×C13#43012yes—
129Dic13—21no—
130Dic13—21no—
131Dic13#49611yescharacteristic
132Dic13#49711yescharacteristic
133C2×M16—261no—
134C2×M16—261no—
135C2×M16—261no—
136C2×M16—261no—
137C22×C8—132no—
138C22×C8—132no—
139C22×C8—132no—
140C2×C42—131no—
141#108—524no—
142C4⋊C8—261no—
143C4⋊C8—261no—
144C4⋊C8—261no—
145C4⋊C8—261no—
146C4⋊C8—261no—
147C4⋊C8—261no—
148C4⋊C8—261no—
149C4⋊C8—261no—
150C4×C8—132no—
151C4×C8—132no—
152C4×C8—132no—
153C4×C8—131no—
154C4×C8—131no—
155C4×C8—131no—
156C4×C8C2×#26111yescharacteristic
157C4×C8C2×#26111yescharacteristic
158C4×C8C2×#26111yescharacteristic
159C2×C13#184711yescharacteristic
160C2×C13#184811yescharacteristic
161C2×C13#184911yescharacteristic
162D13—22no—
163C22×C4—131no—
164C22×C4—131no—
165C22×C4—131no—
166M16—522no—
167M16—522no—
168M16—522no—
169M16—522no—
170C2×C8—132no—
171C2×C8—132no—
172C2×C8—132no—
173C2×C8—262no—
174C2×C8—262no—
175C2×C8—264no—
176C2×C8—522no—
177C2×C8—521no—
178C2×C8—521no—
179C2×C8—521no—
180C2×C8—521no—
181C2×C8C4⋊#26112yes—
182C2×C8C4⋊#26112yes—
183C2×C8C4⋊#26112yes—
184C42—131no—
185C42—131no—
186C42—131no—
187C42C22×#26111yescharacteristic
188C13#882811yescharacteristic, complemented, Sylow
189C23—131no—
190C2×C4—131no—
191C2×C4—132no—
192C2×C4—132no—
193C2×C4—131no—
194C2×C4—131no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4C2×C4⋊#26111yescharacteristic
198C2×C4C2×C4⋊#26111yescharacteristic
199C2×C4C2×C4⋊#26111yescharacteristic
200C8—22no—
201C8—22no—
202C8—262no—
203C8—262no—
204C8—262no—
205C8—1041no—
206C8—1041no—
207C8—1041no—
208C8—1041no—
209C8#8810314yescomplemented
210C22—132no—
211C22—261no—
212C22—261no—
213C22#1171905911yescharacteristic
214C4—131no—
215C4—131no—
216C4—261no—
217C4—261no—
218C4C2×#8810312yes—
219C4#1171909812yes—
220C4#1171910012yes—
221C2—262no—
222C2#1313077411yescharacteristic
223C2#1313077511yescharacteristic
224C2#1313077811yescharacteristic
subgroupG/H
centerC22#11719059
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#322C4
socleC22×C13#384
prime radicalC22×D13C4⋊Q8
cosocleC42×D13C23
hypercenter#322#261
hypocenterC13#8828
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #322

Complements

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

NH ≅ G/Ntype
101. C8×C13#108semidirect
188. C13#8828semidirect
209. C8#88103semidirect

Maximal subgroups

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

subgroupindex
#131307752
#131307602
#131303952
#131303942
#131303912
D13×#3222
#882813