Finite Group Databasebeta

← #16779769

Subgroups — #16779769

Order 3328.

830 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 200 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×#11719047C212yesmaximal
2#13129712C214yesmaximal, complemented
3D13×#382C211yesmaximal, characteristic
4C22×D13⋊C8—22no—
5C2×C4⋊C4×D13C412yes—
6C2×C42×D13C2211yescharacteristic
7C2×#88110—22no—
8C2×#88110C2214yes—
9#11719047—24no—
10#11719047C418yescomplemented
11C13×#382C411yescharacteristic
12#11718638C2212yes—
13#11718597C411yescharacteristic
14D13×#95—22no—
15#11718311—22no—
16C22×C4×D13—22no—
17C22×C4×D13C2×C411yescharacteristic
18C22×C4×D13D412yes—
19C22×#1057—24no—
20C2×D13⋊C8—216no—
21C2×D13⋊C8—28no—
22C2×C13×C4⋊C4C2×C412yes—
23C2×C42×C13C2×C411yescharacteristic
24C2×C4⋊Dic13C2×C412yes—
25C2×#6101—22no—
26C2×C4×Dic13D412yes—
27C2×C4×Dic13C2311yescharacteristic
28C4⋊C4×D13—44no—
29C42×D13C2×C414yes—
30C42×D13D412yes—
31C42×D13Q812yes—
32#88110—28no—
33#88110—24no—
34#88110C2×C418yescomplemented
35C13×#95—22no—
36#88071—22no—
37#88071—24no—
38C2×#1295—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—28no—
49C2×C4×D13—44no—
50C2×C4×D13—48no—
51C2×C4×D13C4212yes—
52C2×C4×D13C22⋊C414yes—
53C2×C4×D13C4⋊C412yes—
54C2×C4×D13C4⋊C414yes—
55C2×#1057—216no—
56C2×#1057—28no—
57D13⋊C8—232no—
58C13×C4⋊C4—42no—
59C42×C13C4212yes—
60C42×C13C4⋊C412yes—
61C4⋊Dic13—42no—
62#6101—44no—
63C4×Dic13C22⋊C414yes—
64C4×Dic13C4⋊C414yes—
65C4×Dic13C22×C412yes—
66C4×Dic13C2×D411yescharacteristic
67C4×Dic13C2×Q811yescharacteristic
68C22×#97—132no—
69C2×#382—131no—
70#1295—134no—
71C23×C13C2×C22⋊C411yescharacteristic
72C22×D13#9512yes—
73C22×D13#10012yes—
74C22×D13#10112yes—
75C22×D13#10418yes—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—24no—
79C2×C4×C13—42no—
80C2×C4×C13—44no—
81C2×C4×C13#9514yes—
82C2×C4×C13C2×C4211yescharacteristic
83C2×C4×C13C2×C4⋊C411yescharacteristic
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—24no—
87C2×Dic13—42no—
88C2×Dic13—44no—
89C2×Dic13#9512yes—
90C2×Dic13C2×C22⋊C412yes—
91C2×Dic13C2×C4⋊C412yes—
92C4×D13—28no—
93C4×D13—28no—
94C4×D13—24no—
95C4×D13—24no—
96C4×D13—88no—
97#1057—216no—
98C23×C8—262no—
99C22×C4⋊C4—132no—
100C22×C42—131no—
101C2×#97—134no—
102C2×#97—138no—
103C2×#97—264no—
104C2×#97—262no—
105#382—132no—
106#382—131no—
107#382—262no—
108#382#26111yescharacteristic
109C2×#95—262no—
110C22×C13C2×#9511yescharacteristic
111C22×C13C2×#10011yescharacteristic
112C22×C13C2×#10111yescharacteristic
113C22×C13C2×#10414yes—
114C2×D13#32918yes—
115C2×D13#33018yes—
116C2×D13#33918yes—
117C2×D13#34314yes—
118C4×C13—24no—
119C4×C13—21no—
120C4×C13—21no—
121C4×C13—82no—
122Dic13—22no—
123Dic13—22no—
124Dic13—22no—
125Dic13—82no—
126C23×C4—132no—
127C23×C4—131no—
128C23×C4—262no—
129C22×C8—268no—
130C22×C8—264no—
131C22×C8—2616no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—262no—
134C2×C4⋊C4—524no—
135C2×C4⋊C4C2×#26112yes—
136C2×C42—132no—
137C2×C42—131no—
138C2×C42—134no—
139C2×C42—132no—
140C2×C42—132no—
141C2×C42C2×#26111yescharacteristic
142#97—138no—
143#97—268no—
144#97—264no—
145#95—22no—
146#95—264no—
147#95—262no—
148C2×C13C2×#32912yes—
149C2×C13C2×#33012yes—
150C2×C13C2×#33912yes—
151C2×C13C2×#34311yescharacteristic
152D13#129518yescomplemented
153C24—131no—
154C22×C4—22no—
155C22×C4—132no—
156C22×C4—131no—
157C22×C4—134no—
158C22×C4—134no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4—262no—
162C22×C4—268no—
163C22×C4—262no—
164C22×C4—262no—
165C22×C4—524no—
166C22×C4—528no—
167C22×C4C22⋊#26112yes—
168C22×C4C22×#26111yescharacteristic
169C2×C8—268no—
170C2×C8—2632no—
171C2×C8—2616no—
172C4⋊C4—42no—
173C4⋊C4—522no—
174C4⋊C4—524no—
175C42—134no—
176C42—134no—
177C42—132no—
178C42—131no—
179C42—131no—
180C42C4×#26112yes—
181C42C4⋊#26112yes—
182C13C2×#129511yescharacteristic, complemented, Sylow
183C23—132no—
184C23—132no—
185C23—132no—
186C23—138no—
187C23C2×C22⋊#26111yescharacteristic
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—24no—
191C2×C4—42no—
192C2×C4—44no—
193C2×C4—132no—
194C2×C4—132no—
195C2×C4—132no—
196C2×C4—268no—
197C2×C4—268no—
198C2×C4—264no—
199C2×C4—264no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—264no—
203C2×C4—522no—
204C2×C4—524no—
205C2×C4—1048no—
206C2×C4(C2×#261)⋊C414yes—
207C2×C4C2×C4×#26111yescharacteristic
208C2×C4C2×C4⋊#26111yescharacteristic
209C8—2616no—
210C22—138no—
211C22—138no—
212C22—134no—
213C22—138no—
214C22C2×(C2×#261)⋊C411yescharacteristic
215C22D13⋊#10011yescharacteristic
216C22D13⋊#10111yescharacteristic
217C22D13⋊#10414yes—
218C4—24no—
219C4—21no—
220C4—21no—
221C4—82no—
222C4—262no—
223C4—262no—
224C4—262no—
225C4—1042no—
226C2—138no—
227C2D13⋊#32912yes—
228C2D13⋊#33012yes—
229C2#1313051212yes—
230C2#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
hypocenterC13C2×#1295
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. #13129712C2semidirect
10. #11719047C4semidirect
34. #88110C2×C4semidirect
152. D13#1295semidirect
182. C13C2×#1295semidirect

Maximal subgroups

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

subgroupindex
C2×#117190472
#131297122
D13×#3822
C2×#129513