Finite Group Databasebeta

← #16782435

Subgroups — #16782435

Order 3328.

354 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 140 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#13130775C212yesmaximal
2#13130395C212yesmaximal
3#13130394C212yesmaximal
4C82×D13C211yesmaximal, characteristic
5C2×#88103—24no—
6#11719052C2214yes—
7C4×C8×D13C2211yescharacteristic
8C4×C8×D13C2211yescharacteristic
9C4×C8×D13C2211yescharacteristic
10#11718256—24no—
11#11718254—24no—
12C82×C13C411yescharacteristic
13C8×#1055C411yescharacteristic
14C8×#1055C411yescharacteristic
15C8×#1055C411yescharacteristic
16C2×#6118—24no—
17C2×C8×D13D412yes—
18C2×C8×D13Q812yes—
19C2×C8×D13Q812yes—
20C42×D13C2311yescharacteristic
21C4⋊#1057—24no—
22C4⋊#1057—24no—
23#88103—48no—
24C4×C8×C13C2×C411yescharacteristic
25C4×C8×C13C2×C411yescharacteristic
26C4×C8×C13C2×C411yescharacteristic
27C8×Dic13D412yes—
28C8×Dic13D412yes—
29C8×Dic13Q812yes—
30C4×#1055C2×C411yescharacteristic
31C4×#1055C2×C411yescharacteristic
32C4×#1055C2×C411yescharacteristic
33#8823—131nomaximal, Sylow
34C2×C4×D13C2×D411yescharacteristic
35C2×C4×D13C2×Q811yescharacteristic
36C2×C4×D13C2×Q811yescharacteristic
37C2×#1057—44no—
38#6118—48no—
39C2×C8×C13C4⋊C412yes—
40C2×C8×C13C4⋊C412yes—
41C2×C8×C13C4⋊C412yes—
42C42×C13C22×C411yescharacteristic
43C4×Dic13C2×D411yescharacteristic
44C4×Dic13C2×D411yescharacteristic
45C4×Dic13C2×Q811yescharacteristic
46C2×#1055C4⋊C412yes—
47C2×#1055C4⋊C412yes—
48C2×#1055C4⋊C412yes—
49C8×D13—24no—
50C8×D13—24no—
51C8×D13D814yes—
52C8×D13Q1614yes—
53#1848—132no—
54#1567—132no—
55#1567—132no—
56C2×C82—131no—
57C22×D13C4⋊Q811yescharacteristic
58C2×C4×C13C2×C4⋊C411yescharacteristic
59C2×C4×C13C2×C4⋊C411yescharacteristic
60C2×C4×C13C2×C4⋊C411yescharacteristic
61C2×Dic13#12711yescharacteristic
62C2×Dic13C4⋊Q811yescharacteristic
63C2×Dic13C4⋊Q811yescharacteristic
64C4×D13—22no—
65C4×D13—22no—
66C4×D13C2×D812yes—
67C4×D13C2×Q1612yes—
68#1057—84no—
69C8×C13—22no—
70C8×C13#10714yes—
71C8×C13#10814yescomplemented
72#1055—22no—
73#1055#10714yes—
74#1055#10814yescomplemented
75C2×#108—264no—
76#423—134no—
77C2×C4×C8—131no—
78C2×C4×C8—131no—
79C2×C4×C8—131no—
80#335—264no—
81#335—264no—
82C82—131no—
83C82—131no—
84C82—131no—
85C82#26111yescharacteristic
86C22×C13#38411yescharacteristic
87C2×D13—21no—
88C2×D13—21no—
89C2×D13#50012yes—
90C4×C13C2×#10712yes—
91C4×C13C2×#10812yes—
92C4×C13C2×#10812yes—
93Dic13—21no—
94Dic13—21no—
95Dic13#49311yescharacteristic
96Dic13#49411yescharacteristic
97C2×M16—264no—
98C22×C8—132no—
99C22×C8—132no—
100C22×C8—132no—
101C2×C42—131no—
102#108—528no—
103C4⋊C8—264no—
104C4⋊C8—264no—
105C4×C8—132no—
106C4×C8—132no—
107C4×C8—132no—
108C4×C8—131no—
109C4×C8—131no—
110C4×C8—131no—
111C4×C8C2×#26111yescharacteristic
112C4×C8C2×#26111yescharacteristic
113C4×C8C2×#26111yescharacteristic
114C2×C13#184511yescharacteristic
115C2×C13#184811yescharacteristic
116C2×C13#184811yescharacteristic
117D13—22no—
118C22×C4—131no—
119C22×C4—131no—
120C22×C4—131no—
121M16—528no—
122C2×C8—132no—
123C2×C8—132no—
124C2×C8—134no—
125C2×C8—134no—
126C2×C8—132no—
127C2×C8—264no—
128C2×C8—264no—
129C2×C8—524no—
130C2×C8C4⋊#26112yes—
131C2×C8C4⋊#26112yes—
132C2×C8C4⋊#26112yes—
133C42—131no—
134C42—131no—
135C42—131no—
136C42C22×#26111yescharacteristic
137C13#882311yescharacteristic, complemented, Sylow
138C23—131no—
139C2×C4—131no—
140C2×C4—132no—
141C2×C4—132no—
142C2×C4—131no—
143C2×C4—131no—
144C2×C4—262no—
145C2×C4—262no—
146C2×C4C2×C4⋊#26111yescharacteristic
147C2×C4C2×C4⋊#26111yescharacteristic
148C2×C4C2×C4⋊#26111yescharacteristic
149C8—22no—
150C8—134no—
151C8—134no—
152C8—262no—
153C8—1044no—
154C8#8810214yes—
155C8#8810314yescomplemented
156C22—132no—
157C22—261no—
158C22—261no—
159C22#1171905911yescharacteristic
160C4—131no—
161C4—131no—
162C4—261no—
163C4—261no—
164C4C2×#8810212yes—
165C4C2×#8810312yes—
166C4D13⋊#10812yes—
167C2—262no—
168C2#1313077211yescharacteristic
169C2#1313077511yescharacteristic
170C2#1313077611yescharacteristic
subgroupG/H
centerC22#11719059
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC82×C13C4
socleC22×C13#384
prime radicalC22×D13C4⋊Q8
cosocleC42×D13C23
hypercenterC82#261
hypocenterC13#8823
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C82

Complements

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

NH ≅ G/Ntype
71. C8×C13#108semidirect
74. #1055#108semidirect
137. C13#8823semidirect
155. C8#88103semidirect

Maximal subgroups

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

subgroupindex
#131307752
#131303952
#131303942
C82×D132
#882313