Finite Group Databasebeta

← #16779818

Subgroups — #16779818

Order 3328.

698 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 176 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
1C2×#11719053C212yesmaximal
2#13129714C214yesmaximal, complemented
3#13117242C211yesmaximal, characteristic
4C22×#6118—22no—
5C2×#88146C412yes—
6C2×C42×D13C2211yescharacteristic
7C2×#88112—22no—
8C2×#88112C2214yes—
9#11719053—24no—
10#11719053C418yescomplemented
11C13×#382C411yescharacteristic
12#11718637C2212yes—
13#11718597C411yescharacteristic
14#11718328—22no—
15#11718310—22no—
16C22×C4×D13C2×C411yescharacteristic
17C22×C4×D13D412yes—
18C22×#1057—24no—
19C2×#6118—28no—
20C2×#6118—48no—
21C2×C13×C4⋊C4C2×C412yes—
22C2×C42×C13C2×C411yescharacteristic
23C2×#6103—22no—
24C2×C4⋊Dic13C2×C412yes—
25C2×#6101—24no—
26C2×C4×Dic13—22no—
27C2×C4×Dic13D412yes—
28C2×C4×Dic13C2311yescharacteristic
29#88146—44no—
30C42×D13C2×C414yes—
31C42×D13D412yes—
32C42×D13Q812yes—
33#88112—28no—
34#88112—24no—
35#88112C2×C418yes—
36C13×#95—22no—
37#88071—22no—
38#8041—131nomaximal, Sylow
39C23×D13C22⋊C411yescharacteristic
40C22×C4×C13—22no—
41C22×C4×C13C22⋊C412yes—
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13C22⋊C411yescharacteristic
45C22×Dic13C2×D412yes—
46C2×C4×D13—22no—
47C2×C4×D13—22no—
48C2×C4×D13—24no—
49C2×C4×D13—24no—
50C2×C4×D13C4212yes—
51C2×C4×D13C22⋊C414yes—
52C2×C4×D13C4⋊C412yes—
53C2×C4×D13C4⋊C414yes—
54C2×#1057—28no—
55C2×#1057—48no—
56#6118—416no—
57C13×C4⋊C4—42no—
58C42×C13C4212yes—
59C42×C13C4⋊C412yes—
60#6103—44no—
61C4⋊Dic13—42no—
62#6101—44no—
63#6101—44no—
64C4×Dic13—44no—
65C4×Dic13C22⋊C414yes—
66C4×Dic13C4⋊C414yes—
67C4×Dic13C22×C412yes—
68C4×Dic13C2×D411yescharacteristic
69C4×Dic13C2×Q811yescharacteristic
70C2×#423—132no—
71#2285—131no—
72#1296—134no—
73C23×C13C2×C22⋊C411yescharacteristic
74C22×D13—21no—
75C22×D13—21no—
76C22×D13—24no—
77C22×D13#9512yes—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—24no—
81C2×C4×C13—42no—
82C2×C4×C13—44no—
83C2×C4×C13#9514yes—
84C2×C4×C13C2×C4211yescharacteristic
85C2×C4×C13C2×C4⋊C411yescharacteristic
86C2×Dic13—42no—
87C2×Dic13—44no—
88C2×Dic13#9512yes—
89C2×Dic13#10012yes—
90C2×Dic13#10112yes—
91C2×Dic13C2×C22⋊C412yes—
92C2×Dic13C2×C4⋊C412yes—
93C2×Dic13AGL(1,ℤ/8)14yes—
94C2×Dic13#13714yes—
95C4×D13—24no—
96C4×D13—24no—
97C4×D13—24no—
98C4×D13—24no—
99C4×D13—28no—
100#1057—48no—
101C22×M16—262no—
102C2×#117—132no—
103C22×C42—131no—
104#423—138no—
105#423—264no—
106C2×C4⋊C8—134no—
107C2×C4⋊C8—262no—
108#384—132no—
109#382—131no—
110#382#26111yescharacteristic
111#380—262no—
112C4×C4⋊C4—262no—
113C22×C13C2×#9511yescharacteristic
114C22×C13C2×#10011yescharacteristic
115C22×C13C2×#10111yescharacteristic
116C22×C13#41714yes—
117C2×D13—24no—
118C2×D13—22no—
119C2×D13—42no—
120C2×D13—42no—
121C4×C13—24no—
122C4×C13—21no—
123C4×C13—21no—
124C4×C13—82no—
125Dic13—82no—
126Dic13#34314yes—
127Dic13#41812yes—
128Dic13#41912yes—
129Dic13#42814yes—
130C23×C4—132no—
131C23×C4—131no—
132C2×M16—268no—
133C2×M16—528no—
134C22×C8—264no—
135#117—524no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—264no—
138C2×C4⋊C4C2×#26112yes—
139C2×C22⋊C4—262no—
140C2×C42—132no—
141C2×C42—131no—
142C2×C42—134no—
143C2×C42—132no—
144C2×C42—132no—
145C2×C42—262no—
146C2×C42C2×#26111yescharacteristic
147C4⋊C8—138no—
148C4⋊C8—264no—
149C4⋊C8—268no—
150#95—22no—
151#95—262no—
152C2×C13#156012yes—
153C2×C13#156112yes—
154C2×C13#173612yes—
155C2×C13C2×#34311yescharacteristic
156D13—42no—
157C24—131no—
158C22×C4—22no—
159C22×C4—131no—
160C22×C4—132no—
161C22×C4—134no—
162C22×C4—134no—
163C22×C4—132no—
164C22×C4—132no—
165C22×C4—262no—
166C22×C4—264no—
167C22×C4—262no—
168C22×C4—264no—
169C22×C4—262no—
170C22×C4C22⋊#26112yes—
171C22×C4C22×#26111yescharacteristic
172M16—5216no—
173C2×C8—268no—
174C2×C8—528no—
175C4⋊C4—42no—
176C4⋊C4—522no—
177C4⋊C4—524no—
178C4⋊C4—524no—
179C22⋊C4—524no—
180C42—134no—
181C42—134no—
182C42—132no—
183C42—131no—
184C42—131no—
185C42—524no—
186C42C4×#26112yes—
187C42C4⋊#26112yes—
188C13#804111yescharacteristic, complemented, Sylow
189C23—132no—
190C23—261no—
191C23—261no—
192C23—264no—
193C23C2×C22⋊#26111yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—24no—
197C2×C4—42no—
198C2×C4—44no—
199C2×C4—132no—
200C2×C4—132no—
201C2×C4—132no—
202C2×C4—132no—
203C2×C4—132no—
204C2×C4—134no—
205C2×C4—134no—
206C2×C4—264no—
207C2×C4—264no—
208C2×C4—268no—
209C2×C4—264no—
210C2×C4—264no—
211C2×C4—522no—
212C2×C4—524no—
213C2×C4(C2×#261)⋊C414yes—
214C2×C4C2×C4×#26111yescharacteristic
215C2×C4C2×C4⋊#26111yescharacteristic
216C8—528no—
217C22—264no—
218C22—262no—
219C22—522no—
220C22—522no—
221C22C2×(C2×#261)⋊C411yescharacteristic
222C22D13⋊#10011yescharacteristic
223C22D13⋊#10111yescharacteristic
224C22#1171916414yes—
225C4—24no—
226C4—21no—
227C4—21no—
228C4—82no—
229C4—132no—
230C4—132no—
231C4—134no—
232C4—134no—
233C4—1042no—
234C2—522no—
235C2#1313037412yes—
236C2#1313037612yes—
237C2#1313052512yes—
238C2#1313053911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#382C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#382#261
hypocenterC13#8041
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #13129714C2semidirect
10. #11719053C4semidirect
188. C13#8041semidirect

Maximal subgroups

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

subgroupindex
C2×#117190532
#131297142
#131172422
#804113