Finite Group Databasebeta

← #16778268

Subgroups — #16778268

Order 3328.

444 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 126 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#13130550C212yesmaximal
2#13129654C214yesmaximal
3#125×Dic13C211yesmaximal, characteristic
4C2×C13×#125C411yescharacteristic
5C2×C4×#1057—22no—
6#11718646C2212yes—
7#11718642—22no—
8C4⋊C4×Dic13—22no—
9C4⋊C4×Dic13C412yes—
10#11718597C411yescharacteristic
11C42×Dic13C2211yescharacteristic
12#11718290—22no—
13#11718290C2214yes—
14C22×#1057—24no—
15C13×#125—22no—
16C13×#125C814yescomplemented
17C2×C13×C4⋊C4—22no—
18C2×C13×C4⋊C4C2×C412yes—
19C2×C42×C13C2×C411yescharacteristic
20C2×C4⋊Dic13—22no—
21C2×C4⋊Dic13C2×C412yes—
22C2×C4×Dic13—22no—
23C2×C4×Dic13C2×C411yescharacteristic
24C2×C4×Dic13D412yes—
25C2×C4×Dic13D412yes—
26C2×C4×Dic13C2311yescharacteristic
27C4×#1057—28no—
28#88071—22no—
29#88071—22no—
30#88071—22no—
31#7568—131nomaximal, Sylow
32C22×C4×C13—22no—
33C22×C4×C13C22⋊C412yes—
34C22×C4×C13C22×C411yescharacteristic
35C22×Dic13—22no—
36C22×Dic13C22⋊C411yescharacteristic
37C22×Dic13C22⋊C411yescharacteristic
38C22×Dic13C2×D412yes—
39C2×#1057—28no—
40C2×#1057—44no—
41C2×#1057—44no—
42C13×C4⋊C4—28no—
43C13×C4⋊C4—22no—
44C13×C4⋊C4C2×C814yes—
45C42×C13C2×C812yes—
46C42×C13M1612yes—
47C4⋊Dic13—44no—
48C4⋊Dic13—42no—
49C4×Dic13—22no—
50C4×Dic13—24no—
51C4×Dic13—24no—
52C4×Dic13—41no—
53C4×Dic13—44no—
54C4×#125—131no—
55#1744—132no—
56#1271—134no—
57C23×C13C2×C22⋊C411yescharacteristic
58C2×C4×C13—21no—
59C2×C4×C13—21no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—24no—
63C2×C4×C13—42no—
64C2×C4×C13—42no—
65C2×C4×C13C22⋊C814yes—
66C2×C4×C13C22×C811yescharacteristic
67C2×C4×C13C2×M1611yescharacteristic
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—21no—
71C2×Dic13—22no—
72C2×Dic13—42no—
73C2×Dic13—42no—
74C2×Dic13—42no—
75C2×Dic13#10112yes—
76C2×Dic13#10414yes—
77C2×Dic13#13514yes—
78#1057—48no—
79C2×#125#26111yescharacteristic
80C2×C4×C8—262no—
81#389—132no—
82#387—262no—
83#382—131no—
84C4×C4⋊C4—132no—
85C4×C4⋊C4—262no—
86C43—131no—
87#336—134no—
88#336—262no—
89C22×C13C2×C22⋊C811yescharacteristic
90C22×C13#41011yescharacteristic
91C22×C13C2×#10111yescharacteristic
92C22×C13#41612yes—
93C22×C13C2×#10412yes—
94C4×C13—21no—
95C4×C13—21no—
96C4×C13—24no—
97C4×C13—44no—
98Dic13—24no—
99Dic13—41no—
100Dic13—82no—
101Dic13#33014yes—
102C22×C8—264no—
103#125—22no—
104#125#105714yescomplemented
105C2×C4⋊C4—22no—
106C2×C4⋊C4—132no—
107C2×C4⋊C4—262no—
108C2×C4⋊C4C2×#26112yes—
109C2×C42—132no—
110C2×C42—132no—
111C2×C42—131no—
112C2×C42—131no—
113C2×C42—262no—
114C2×C42C2×#26111yescharacteristic
115C4×C8—268no—
116#95—262no—
117#95—262no—
118#95—262no—
119C2×C13#146111yescharacteristic
120C2×C13#147612yes—
121C2×C13#150012yes—
122C2×C13C2×#33011yescharacteristic
123C2×C13#154411yescharacteristic
124C22×C4—22no—
125C22×C4—131no—
126C22×C4—132no—
127C22×C4—131no—
128C22×C4—262no—
129C22×C4C22⋊#26112yes—
130C22×C4C22×#26111yescharacteristic
131C2×C8—268no—
132C2×C8—524no—
133C2×C8—524no—
134C4⋊C4—28no—
135C4⋊C4—22no—
136C4⋊C4—522no—
137C4⋊C4—524no—
138C4⋊C4C2×#105714yes—
139C42—264no—
140C42—262no—
141C42—264no—
142C42—521no—
143C42—524no—
144C42C2×#105712yes—
145C42#612212yes—
146C13#756811yescharacteristic, complemented, Sylow
147C23C2×C22⋊#26111yescharacteristic
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—24no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—132no—
156C2×C4—134no—
157C2×C4—134no—
158C2×C4—262no—
159C2×C4—262no—
160C2×C4—261no—
161C2×C4—262no—
162C2×C4—522no—
163C2×C4—522no—
164C2×C4—522no—
165C2×C4C22⋊#105714yes—
166C2×C4C22×#105711yescharacteristic
167C2×C4C2×#612211yescharacteristic
168C8—528no—
169C22#1171915611yescharacteristic
170C22D13⋊#10111yescharacteristic
171C22D13⋊#10412yes—
172C22#1171916512yes—
173C22C2×C22⋊#105711yescharacteristic
174C4—21no—
175C4—21no—
176C4—24no—
177C4—44no—
178C4—134no—
179C4—264no—
180C4—521no—
181C4—1042no—
182C2#1313007911yescharacteristic
183C2#1313012712yes—
184C2#1313021012yes—
185C2D13⋊#33011yescharacteristic
186C2#1313034211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#125C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#125#261
hypocenterC13#7568
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
16. C13×#125C8semidirect
104. #125#1057semidirect
146. C13#7568semidirect

Maximal subgroups

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

subgroupindex
#131305502
#131296542
#125×Dic132
#756813