Finite Group Databasebeta

← #15756724

Subgroups — #15756724

Order 3328.

322 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 139 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#13114974C211yesmaximal, characteristic
2#13113594C212yesmaximal
3#13113591C212yesmaximal
4C2×C8×#1055C211yesmaximal, characteristic
5C13×#1837C211yesmaximal, characteristic
6C13×#423C2212yes—
7C2×C4×C8×C13C2211yescharacteristic
8#11718585C2212yes—
9C2×C4×#1055C2211yescharacteristic
10C2×C4×#1055C2211yescharacteristic
11C13×#341—22no—
12#11718144—22no—
13#11718072—24no—
14#11718071—24no—
15C8×#1055C411yescharacteristic
16C8×#1055C411yescharacteristic
17C8×#1055C411yescharacteristic
18C8×#1055C411yescharacteristic
19C2×C13×M16—22no—
20C22×C8×C13D412yes—
21C2×C42×C13C2311yescharacteristic
22C2×#6099—22no—
23C22×#1055Q812yes—
24C22×#1055Q812yes—
25C13×C4⋊C8—22no—
26C13×C4⋊C8—22no—
27C4×C8×C13C2×C411yescharacteristic
28C4×C8×C13C2×C411yescharacteristic
29C4×C8×C13Q812yes—
30C4⋊#1055—22no—
31C4⋊#1055—22no—
32C4×#1055C2×C411yescharacteristic
33C4×#1055C2×C411yescharacteristic
34C4×#1055C2×C411yescharacteristic
35C4×#1055C2×C411yescharacteristic
36C4×#1055D412yes—
37C4×#1055D412yes—
38#8824—131nomaximal, Sylow
39C22×C4×C13C2×D411yescharacteristic
40C22×C4×C13C2×Q811yescharacteristic
41C22×C4×C13C2×Q811yescharacteristic
42C13×M16—44no—
43C2×C8×C13—24no—
44C2×C8×C13—42no—
45C2×C8×C13C4⋊C412yes—
46C2×C8×C13C4⋊C412yes—
47C42×C13C22×C411yescharacteristic
48C42×C13C2×D411yescharacteristic
49C42×C13C2×D411yescharacteristic
50C42×C13C2×Q811yescharacteristic
51#6099—44no—
52C2×#1055—24no—
53C2×#1055—24no—
54C2×#1055—42no—
55C2×#1055C4⋊C412yes—
56C2×#1055C4⋊C412yes—
57C2×#1055C4⋊C412yes—
58C2×#1055C4⋊C412yes—
59#1837—131no—
60#1837D1311yescharacteristic
61#1567—132no—
62#1566—132no—
63C2×C82—131no—
64C23×C13C4⋊Q811yescharacteristic
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13C2×C4⋊C411yescharacteristic
68C2×C4×C13C2×C4⋊C411yescharacteristic
69C2×C4×C13C2×C4⋊C411yescharacteristic
70C2×C4×C13#12711yescharacteristic
71C2×C4×C13C4⋊Q811yescharacteristic
72C2×C4×C13C4⋊Q811yescharacteristic
73C2×C4×C13#13514yes—
74C8×C13—22no—
75C8×C13—22no—
76C8×C13—82no—
77#1055—22no—
78#1055—22no—
79#1055—82no—
80#1055#10814yes—
81#1055#10814yes—
82#423—132no—
83#423C2×D1312yes—
84C2×C4×C8—131no—
85C2×C4×C8—131no—
86C2×C4×C8C2×D1311yescharacteristic
87#341—22no—
88#341—262no—
89#335—264no—
90#334—264no—
91C82—131no—
92C82—131no—
93C82—131no—
94C82—131no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13#38411yescharacteristic
98C22×C13#49912yes—
99C4×C13—21no—
100C4×C13—21no—
101C4×C13#42712yes—
102C4×C13C2×#10812yes—
103C4×C13C2×#10812yes—
104C4×C13#49512yes—
105C2×M16—22no—
106C2×M16—262no—
107C22×C8—132no—
108C22×C8—132no—
109C22×C8C22⋊D1312yes—
110C2×C42C22×D1311yescharacteristic
111C4⋊C8—22no—
112C4⋊C8—22no—
113C4⋊C8—262no—
114C4⋊C8—262no—
115C4×C8—131no—
116C4×C8—131no—
117C4×C8—131no—
118C4×C8—131no—
119C4×C8—132no—
120C4×C8—132no—
121C4×C8Dic2612yes—
122C4×C8C4×D1311yescharacteristic
123C4×C8C4×D1311yescharacteristic
124C2×C13—22no—
125C2×C13#184611yescharacteristic
126C2×C13#184811yescharacteristic
127C2×C13#184811yescharacteristic
128C22×C4Q8×D1311yescharacteristic
129C22×C4Q8×D1311yescharacteristic
130C22×C4C2×C22⋊D1311yescharacteristic
131M16—44no—
132M16—524no—
133C2×C8—24no—
134C2×C8—42no—
135C2×C8—132no—
136C2×C8—132no—
137C2×C8—132no—
138C2×C8—132no—
139C2×C8—264no—
140C2×C8—264no—
141C2×C8—522no—
142C2×C8#610112yes—
143C2×C8#610112yes—
144C42C2×Dic2611yescharacteristic
145C42C2×C4×D1311yescharacteristic
146C42D4×D1311yescharacteristic
147C42D4×D1311yescharacteristic
148C13#882411yescharacteristic, complemented, Sylow
149C23#8819811yescharacteristic
150C2×C4—22no—
151C2×C4—22no—
152C2×C4#8814211yescharacteristic
153C2×C4#8814211yescharacteristic
154C2×C4C4⋊C4×D1311yescharacteristic
155C2×C4C4⋊C4×D1311yescharacteristic
156C2×C4C2×#610111yescharacteristic
157C2×C4#8819411yescharacteristic
158C2×C4#8820414yes—
159C8—22no—
160C8—22no—
161C8—82no—
162C8—134no—
163C8—134no—
164C8—262no—
165C8—262no—
166C8—1042no—
167C22—21no—
168C22—21no—
169C22#1171863711yescharacteristic
170C22#1171872512yes—
171C4—21no—
172C4—21no—
173C4D13×#10812yes—
174C4D13×#10812yes—
175C4#1171865912yes—
176C4#1171872012yes—
177C2—22no—
178C2#1311499811yescharacteristic
179C2#1311500611yescharacteristic
180C2#1311500611yescharacteristic
subgroupG/H
centerC2×C4#88194
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1837C2
socleC22×C13#384
prime radicalC23×C13C4⋊Q8
cosocleC2×C42×C13C23
hypercenter#1837D13
hypocenterC13#8824
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1837

Complements

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

NH ≅ G/Ntype
148. C13#8824semidirect

Maximal subgroups

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

subgroupindex
#131149742
#131135942
#131135912
C2×C8×#10552
C13×#18372
#882413