Finite Group Databasebeta

← #15779179

Subgroups — #15779179

Order 3328.

786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114751C212yesmaximal
2#13112961C214yesmaximal, complemented
3C13×#2309C211yesmaximal, characteristic
4C23×D4×C13C2211yescharacteristic
5C2×C13×#117C411yescharacteristic, complemented
6C2×C13×#117C411yescharacteristic, complemented
7C13×#390—22no—
8C13×#390C412yescomplemented
9C13×#390C2212yes—
10C13×#379—22no—
11#11718908—22no—
12C2×#88074—22no—
13C2×#88074C2214yes—
14C25×C13D412yes—
15C22×D4×C13—24no—
16C22×D4×C13—42no—
17C22×D4×C13—42no—
18C22×D4×C13C2×C411yescharacteristic
19C22×D4×C13D412yes—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C13×#117—42no—
23C13×#117—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C13×C22⋊C4—21no—
27C2×C13×C22⋊C4—21no—
28C2×C13×C22⋊C4—24no—
29C2×C13×C22⋊C4—24no—
30C2×C42×C13—21no—
31C2×C42×C13C2×C412yes—
32C2×C22⋊Dic13—24no—
33C2×C22⋊Dic13—44no—
34#88074—28no—
35#88074—44no—
36#12858—131nomaximal, Sylow
37C24×C13—24no—
38C24×C13—24no—
39C24×C13—42no—
40C24×C13—84no—
41C24×C13C22⋊C412yes—
42C24×C13C22⋊C411yescharacteristic
43C24×C13C2×D412yes—
44C2×D4×C13—24no—
45C2×D4×C13—24no—
46C2×D4×C13—22no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13—42no—
50C2×D4×C13—41no—
51C2×D4×C13—41no—
52C2×D4×C13—416no—
53C2×D4×C13#4114yes—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—44no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C13×C22⋊C4—42no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—84no—
67C13×C22⋊C4—84no—
68C42×C13—42no—
69C42×C13—42no—
70C22⋊Dic13—44no—
71C22⋊Dic13—44no—
72C22⋊Dic13—88no—
73#2309D1311yescharacteristic
74#1781—132no—
75#1393—134no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—22no—
83C23×C13—42no—
84C23×C13—48no—
85C23×C13—44no—
86C23×C13—44no—
87C23×C13—48no—
88C23×C13—84no—
89C23×C13—88no—
90C23×C13—88no—
91C23×C13#9912yes—
92C23×C13C2×C22⋊C411yescharacteristic
93C23×C13#12314yes—
94D4×C13—44no—
95D4×C13—48no—
96D4×C13—44no—
97C2×C4×C13—28no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—44no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13#9912yes—
108C2×C4×C13#11712yes—
109C2×Dic13—84no—
110C2×Dic13—88no—
111C23×D4C2×D1311yescharacteristic
112C2×#117Dic1311yescharacteristic, complemented
113C2×#117Dic1311yescharacteristic, complemented
114C2×#99—134no—
115C2×#99—262no—
116#390—22no—
117#390Dic1312yescomplemented
118#390C2×D1312yes—
119#379—22no—
120#379—262no—
121C22×C13—22no—
122C22×C13—24no—
123C22×C13—22no—
124C22×C13—24no—
125C22×C13—44no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—44no—
129C22×C13—44no—
130C22×C13—42no—
131C22×C13—44no—
132C22×C13—82no—
133C22×C13—82no—
134C22×C13—816no—
135C22×C13#38111yescharacteristic
136C22×C13C2×#9911yescharacteristic
137C22×C13C2×#9911yescharacteristic
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—82no—
141C4×C13—82no—
142Dic13—164no—
143C25C22⋊D1312yes—
144C22×D4—24no—
145C22×D4—42no—
146C22×D4—42no—
147C22×D4C2×Dic1311yescharacteristic
148C22×D4C22⋊D1312yes—
149C22×D4C22×D1311yescharacteristic
150C23×C4C2×Dic1311yescharacteristic
151#117—42no—
152#117—42no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4C2×Dic1312yes—
155C2×C22⋊C4—21no—
156C2×C22⋊C4—21no—
157C2×C22⋊C4—24no—
158C2×C22⋊C4—24no—
159C2×C22⋊C4—264no—
160C2×C22⋊C4—524no—
161C2×C42—21no—
162C2×C42C2×Dic1312yes—
163#99—268no—
164#99—524no—
165C2×C13—21no—
166C2×C13—21no—
167C2×C13—44no—
168C2×C13—42no—
169C2×C13—82no—
170C2×C13#181911yescharacteristic
171C2×C13#212712yes—
172C24—24no—
173C24—24no—
174C24—42no—
175C24—84no—
176C24C22⋊Dic1312yes—
177C24C22⋊Dic1311yescharacteristic
178C24C2×C22⋊D1312yes—
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—22no—
182C2×D4—41no—
183C2×D4—41no—
184C2×D4—42no—
185C2×D4—41no—
186C2×D4—41no—
187C2×D4—416no—
188C2×D4#612714yes—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—524no—
195C22×C4C22⋊Dic1311yescharacteristic
196C22×C4C22×Dic1311yescharacteristic
197C4⋊C4—42no—
198C4⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C22⋊C4—84no—
202C22⋊C4—84no—
203C22⋊C4—524no—
204C22⋊C4—524no—
205C22⋊C4—1048no—
206C42—42no—
207C42—42no—
208C13#1285811yescharacteristic, complemented, Sylow
209C23—21no—
210C23—21no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23—42no—
217C23—48no—
218C23—44no—
219C23—44no—
220C23—48no—
221C23—84no—
222C23—88no—
223C23—88no—
224C23#8807412yes—
225C23#8818314yes—
226C23C2×C22⋊Dic1311yescharacteristic
227D4—44no—
228D4—48no—
229D4—44no—
230C2×C4—28no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—44no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—1044no—
241C2×C4—1048no—
242C2×C4#8807412yes—
243C2×C4#8818012yes—
244C22—22no—
245C22—22no—
246C22—24no—
247C22—24no—
248C22—44no—
249C22—42no—
250C22—42no—
251C22—44no—
252C22—44no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—82no—
257C22—816no—
258C22#1171887211yescharacteristic
259C22C2×#8807411yescharacteristic
260C22C2×#8807411yescharacteristic
261C4—22no—
262C4—22no—
263C4—82no—
264C4—82no—
265C4—2084no—
266C2—21no—
267C2—21no—
268C2—44no—
269C2—42no—
270C2—82no—
271C2#1311491011yescharacteristic
272C2#1311650512yes—
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2309C2
socleC22×C13C2×#99
prime radicalC23×D4×C13C22
cosocleC22×D4×C13C23
hypercenter#2309D13
hypocenterC13#12858
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #13112961C2semidirect
5. C2×C13×#117C4semidirect
6. C2×C13×#117C4semidirect
8. C13×#390C4semidirect
112. C2×#117Dic13semidirect
113. C2×#117Dic13semidirect
117. #390Dic13semidirect
208. C13#12858semidirect

Maximal subgroups

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

subgroupindex
#131147512
#131129612
C13×#23092
#1285813