Finite Group Databasebeta

← #16778508

Subgroups — #16778508

Order 3328.

436 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 102 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#13130621C212yesmaximal
2#13129654C214yesmaximal
3#125×Dic13C211yesmaximal, characteristic
4C2×C13×#125C411yescharacteristic
5C2×#88112—22no—
6C2×#88110—22no—
7#11718646C2212yes—
8#11718642—22no—
9C4⋊C4×Dic13—22no—
10C4⋊C4×Dic13C412yes—
11#11718597C411yescharacteristic
12C42×Dic13C2211yescharacteristic
13#11718290C2214yes—
14C22×#1057—24no—
15C13×#125—24no—
16C2×C13×C4⋊C4—22no—
17C2×C13×C4⋊C4C2×C412yes—
18C2×C42×C13C2×C411yescharacteristic
19C2×C4⋊Dic13—22no—
20C2×C4⋊Dic13C2×C412yes—
21C2×C4×Dic13—22no—
22C2×C4×Dic13C2×C411yescharacteristic
23C2×C4×Dic13D412yes—
24C2×C4×Dic13D412yes—
25C2×C4×Dic13C2311yescharacteristic
26#88112—28no—
27#88110—44no—
28#88071—22no—
29#88071—22no—
30#88071—22no—
31#7636—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⋊C4M1614yes—
45C42×C13—22no—
46C4⋊Dic13—42no—
47C4⋊Dic13—42no—
48C4⋊Dic13—42no—
49C4×Dic13—22no—
50C4×Dic13—24no—
51C4×Dic13—22no—
52C4×Dic13—22no—
53C4×Dic13—41no—
54C4×Dic13—44no—
55C4×#125—131no—
56#1767—132no—
57#1271—134no—
58C23×C13C2×C22⋊C411yescharacteristic
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—22no—
62C2×C4×C13—24no—
63C2×C4×C13—22no—
64C2×C4×C13—22no—
65C2×C4×C13—42no—
66C2×C4×C13—42no—
67C2×C4×C13C2×M1612yes—
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×Dic13AGL(1,ℤ/8)12yes—
78C2×Dic13#13712yes—
79#1057—48no—
80C2×#125#26111yescharacteristic
81C2×C4⋊C8—262no—
82C2×#97—262no—
83#389—132no—
84#387—262no—
85#382—131no—
86C4×C4⋊C4—132no—
87C4×C4⋊C4—262no—
88C43—131no—
89#336—134no—
90C22×C13#40711yescharacteristic
91C22×C13#41011yescharacteristic
92C22×C13C2×#10111yescharacteristic
93C22×C13#41712yes—
94C22×C13C2×#10412yes—
95C4×C13—22no—
96C4×C13—42no—
97C4×C13—44no—
98Dic13—22no—
99Dic13—22no—
100Dic13—41no—
101Dic13—82no—
102Dic13#33014yes—
103C22×C8—264no—
104#125—24no—
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#97—524no—
117#95—262no—
118#95—262no—
119#95—262no—
120C2×C13#146711yescharacteristic
121C2×C13#148912yes—
122C2×C13#150912yes—
123C2×C13C2×#33011yescharacteristic
124C2×C13#156111yescharacteristic
125C22×C4—22no—
126C22×C4—131no—
127C22×C4—132no—
128C22×C4—131no—
129C22×C4—262no—
130C22×C4C22⋊#26112yes—
131C22×C4C22×#26111yescharacteristic
132C2×C8—268no—
133C2×C8—524no—
134C2×C8—524no—
135C4⋊C4—28no—
136C4⋊C4—22no—
137C4⋊C4—522no—
138C4⋊C4—522no—
139C4⋊C4—522no—
140C4⋊C4#612214yes—
141C42—22no—
142C42—262no—
143C42—264no—
144C42—262no—
145C42—262no—
146C42—521no—
147C42—524no—
148C13#763611yescharacteristic, complemented, Sylow
149C23C2×C22⋊#26111yescharacteristic
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—132no—
159C2×C4—134no—
160C2×C4—132no—
161C2×C4—132no—
162C2×C4—262no—
163C2×C4—262no—
164C2×C4—261no—
165C2×C4—262no—
166C2×C4—522no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4C2×#612212yes—
170C8—528no—
171C22#1171915611yescharacteristic
172C22D13⋊#10111yescharacteristic
173C22D13⋊#10412yes—
174C22#1171916412yes—
175C22#1171916911yescharacteristic
176C4—22no—
177C4—42no—
178C4—44no—
179C4—134no—
180C4—262no—
181C4—262no—
182C4—521no—
183C4—1042no—
184C2#1313009911yescharacteristic
185C2#1313017112yes—
186C2#1313023912yes—
187C2D13⋊#33011yescharacteristic
188C2#1313037611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#125C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#125#261
hypocenterC13#7636
LCSG ▷ C22×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
148. C13#7636semidirect

Maximal subgroups

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

subgroupindex
#131306212
#131296542
#125×Dic132
#763613