Finite Group Databasebeta

← #16782144

Subgroups — #16782144

Order 3328.

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

normal subgroups only

This group has 540 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#13130691C211yesmaximal, characteristic
2C4×#88111C211yesmaximal, characteristic
3#13129672C214yesmaximal, complemented
4#13117241C211yesmaximal, characteristic
5C2×#88146—21no—
6C2×C42×D13C2211yescharacteristic
7C2×#88111—21no—
8C2×#88111—21no—
9C2×C4⋊#1057C2212yes—
10C2×C4×#1057C2212yes—
11C13×#384C411yescharacteristic
12#11718648—21no—
13#11718648C412yes—
14#11718638—21no—
15C4⋊C4×Dic13—21no—
16C4⋊C4×Dic13C2212yes—
17#11718596C411yescharacteristic
18#11718290—21no—
19#11718290—21no—
20C22×C4×D13C2×C411yescharacteristic
21C22×C4×D13D411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C42×C13C2×C411yescharacteristic
29C2×#6103—22no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C412yes—
33C2×C4×Dic13—22no—
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13C2311yescharacteristic
37#88146—42no—
38#88146—42no—
39C42×D13—24no—
40#88111—24no—
41#88111—42no—
42C4⋊#1057—24no—
43C4×#1057—24no—
44#88071—22no—
45#88071—22no—
46#8709—131nomaximal, Sylow
47C23×D13C22⋊C411yescharacteristic
48C22×C4×C13—22no—
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22⋊C411yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C22×Dic13—22no—
53C22×Dic13C22⋊C411yescharacteristic
54C22×Dic13C2×D411yescharacteristic
55C22×Dic13C2×D411yescharacteristic
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C4×D13—22no—
59C2×C4×D13—22no—
60C2×C4×D13—22no—
61C2×C4×D13—22no—
62C2×C4×D13—22no—
63C2×C4×D13—41no—
64C2×C4×D13D812yes—
65C2×C4×D13SD1612yes—
66C2×#1057—24no—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C42×C13—22no—
76#6103—44no—
77C4⋊Dic13—24no—
78C4⋊Dic13—42no—
79C4⋊Dic13—42no—
80C4×Dic13—22no—
81C4×Dic13—22no—
82C4×Dic13—42no—
83C4×Dic13—42no—
84C4×Dic13#4114yes—
85#2285—131no—
86#1797—131no—
87C4×C22⋊C8—131no—
88#1279—134no—
89C23×C13C2×C22⋊C411yescharacteristic
90C22×D13—21no—
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—21no—
94C22×D13—21no—
95C22×D13—21no—
96C22×D13#10212yes—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13#10212yes—
105C2×C4×C13#10412yes—
106C2×C4×C13#11712yes—
107C2×C4×C13#13112yes—
108C2×C4×C13#13112yes—
109C2×Dic13—21no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13#12312yes—
118C2×Dic13#12312yes—
119C2×Dic13C2×D811yescharacteristic
120C2×Dic13C2×SD1611yescharacteristic
121C2×Dic13#13712yes—
122C4×D13—24no—
123C4×D13—24no—
124C4×D13—44no—
125C4×D13—44no—
126#1057—44no—
127#1057—82no—
128C2×#117—261no—
129C22×C42—131no—
130C2×C4⋊C8—132no—
131C2×C22⋊C8—261no—
132C2×C22⋊C8—261no—
133C2×C4×C8—132no—
134#384—131no—
135#384#26111yescharacteristic
136#382—261no—
137#380—132no—
138#380—261no—
139C4×C4⋊C4—132no—
140C4×C4⋊C4—261no—
141#336—261no—
142#336—261no—
143C22×C13#38111yescharacteristic
144C22×C13#40811yescharacteristic
145C22×C13#40811yescharacteristic
146C22×C13C2×#10211yescharacteristic
147C22×C13#41911yescharacteristic
148C22×C13C2×#10411yescharacteristic
149C22×C13#42111yescharacteristic
150C2×D13—22no—
151C2×D13—22no—
152C2×D13—22no—
153C2×D13—41no—
154C2×D13—41no—
155C2×D13—41no—
156C2×D13—41no—
157C4×C13—22no—
158C4×C13—22no—
159C4×C13—82no—
160C4×C13#43314yes—
161Dic13—22no—
162Dic13—41no—
163Dic13—82no—
164Dic13#48012yes—
165Dic13#48312yes—
166C23×C4—131no—
167C23×C4—131no—
168C23×C4—131no—
169C22×C8—262no—
170C22×C8—262no—
171#117—522no—
172#117—522no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—132no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4C2×#26112yes—
179C2×C22⋊C4—262no—
180C2×C42—131no—
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—264no—
184C2×C42—262no—
185C2×C42C2×#26111yescharacteristic
186C4⋊C8—264no—
187C22⋊C8—264no—
188C22⋊C8—522no—
189C4×C8—264no—
190#95—262no—
191#95—262no—
192C2×C13#148011yescharacteristic
193C2×C13#148511yescharacteristic
194C2×C13#149211yescharacteristic
195C2×C13#149711yescharacteristic
196C2×C13#181811yescharacteristic
197C2×C13#182311yescharacteristic
198C2×C13#182611yescharacteristic
199D13—42no—
200C24—131no—
201C22×C4—22no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—132no—
205C22×C4—132no—
206C22×C4—131no—
207C22×C4—262no—
208C22×C4—262no—
209C22×C4—262no—
210C22×C4—262no—
211C22×C4—262no—
212C22×C4—262no—
213C22×C4—262no—
214C22×C4—262no—
215C22×C4—521no—
216C22×C4C22⋊#26111yescharacteristic
217C22×C4C22⋊#26111yescharacteristic
218C22×C4C22×#26111yescharacteristic
219C2×C8—264no—
220C2×C8—522no—
221C2×C8—522no—
222C2×C8—522no—
223C2×C8—522no—
224C2×C8—522no—
225C4⋊C4—24no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—264no—
229C4⋊C4—522no—
230C4⋊C4—522no—
231C22⋊C4—524no—
232C42—22no—
233C42—134no—
234C42—262no—
235C42—262no—
236C42—522no—
237C42—522no—
238C13#870911yescharacteristic, complemented, Sylow
239C23—132no—
240C23—261no—
241C23—261no—
242C23—261no—
243C23—261no—
244C23—261no—
245C23—261no—
246C23C2×C22⋊#26111yescharacteristic
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—132no—
255C2×C4—131no—
256C2×C4—131no—
257C2×C4—132no—
258C2×C4—132no—
259C2×C4—264no—
260C2×C4—264no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—524no—
267C2×C4—524no—
268C2×C4—522no—
269C2×C4—522no—
270C2×C4—522no—
271C2×C4#8811512yes—
272C2×C4#8811812yes—
273C2×C4#8823712yes—
274C2×C4#8823812yes—
275C2×C4#8824012yes—
276C8—524no—
277C8—1042no—
278C22—262no—
279C22—262no—
280C22—262no—
281C22—521no—
282C22—521no—
283C22—521no—
284C22—521no—
285C22#1171913511yescharacteristic
286C22C2×#8811511yescharacteristic
287C22#1171914011yescharacteristic
288C22#1171914711yescharacteristic
289C22#1171915311yescharacteristic
290C22C2×#8811811yescharacteristic
291C22#1171915911yescharacteristic
292C4—22no—
293C4—22no—
294C4—82no—
295C4—132no—
296C4—132no—
297C4—262no—
298C4—521no—
299C4—1042no—
300C4#1171907714yes—
301C2—522no—
302C2#1313014211yescharacteristic
303C2#1313015911yescharacteristic
304C2#1313018311yescharacteristic
305C2#1313020011yescharacteristic
306C2#1313073011yescharacteristic
307C2#1313073911yescharacteristic
308C2#1313074311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#8709
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #13129672C2semidirect
238. C13#8709semidirect

Maximal subgroups

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

subgroupindex
#131306912
C4×#881112
#131296722
#131172412
#870913