Finite Group Databasebeta

← #15756255

Subgroups — #15756255

Order 3328.

530 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11718597C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic
3#13112678C214yesmaximal
4C13×#1817C211yesmaximal, characteristic
5C22×C42×C13C2211yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8C2×C13×C22⋊C8C2212yes—
9C2×#88071C412yes—
10C2×#88071C2212yes—
11C2×C22⋊#1055C2212yes—
12#11718597—21no—
13#11718597—21no—
14#11718597—21no—
15#11718597—21no—
16C13×#336—21no—
17C13×#336—21no—
18#11718116—21no—
19#11718116—21no—
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13C2×C412yes—
24C23×Dic13C2×C412yes—
25C22×C8×C13—22no—
26C2×C42×C13—24no—
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—42no—
36C2×C4⋊Dic13—42no—
37C22×#1055—22no—
38C13×C22⋊C8—24no—
39#88071—22no—
40#88071—22no—
41#88071—22no—
42#88071—22no—
43C22⋊#1055—24no—
44#8703—131nomaximal, Sylow
45C24×C13C22×C411yescharacteristic
46C22×C4×C13—22no—
47C22×C4×C13—22no—
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13#4114yes—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—24no—
64C22×Dic13—24no—
65C22×Dic13—42no—
66C22×Dic13—42no—
67C22×Dic13—42no—
68C22×Dic13—42no—
69C2×C8×C13—42no—
70C2×C8×C13—42no—
71C2×C8×C13—42no—
72C42×C13—22no—
73C42×C13—22no—
74C42×C13—22no—
75C42×C13—22no—
76C4⋊Dic13—42no—
77C4⋊Dic13—42no—
78C4⋊Dic13—42no—
79C4⋊Dic13—42no—
80C2×#1055—42no—
81C2×#1055—42no—
82C2×#1055—42no—
83C2×#382—131no—
84#1817—131no—
85#1817D1311yescharacteristic
86#1280—134no—
87C23×C13—21no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13C2×C22⋊C411yescharacteristic
92C23×C13#11712yes—
93C23×C13#13112yes—
94C23×C13#13112yes—
95C2×C4×C13—28no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—44no—
111C2×C4×C13—44no—
112C2×C4×C13#10012yes—
113C2×C4×C13#10112yes—
114C2×C4×C13#12312yes—
115C2×C4×C13#12312yes—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—84no—
123C2×Dic13—84no—
124C8×C13—82no—
125#1055—82no—
126C22×C4⋊C4—131no—
127C22×C4⋊C4—131no—
128C22×C42C2×D1311yescharacteristic
129C2×C22⋊C8—132no—
130C2×C22⋊C8C2×D1312yes—
131#382—261no—
132#382—261no—
133#382—261no—
134#382—261no—
135C2×#95—132no—
136C2×#95—132no—
137#336—21no—
138#336—21no—
139#336—261no—
140#336—261no—
141C22×C13—22no—
142C22×C13—22no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—22no—
147C22×C13#38111yescharacteristic
148C22×C13#40811yescharacteristic
149C22×C13#40811yescharacteristic
150C22×C13#41011yescharacteristic
151C22×C13#41011yescharacteristic
152C22×C13C2×#10011yescharacteristic
153C22×C13C2×#10111yescharacteristic
154C22×C13#43314yes—
155C4×C13—22no—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—22no—
159C4×C13—41no—
160C4×C13—41no—
161Dic13—82no—
162Dic13—82no—
163C23×C4—132no—
164C23×C4—132no—
165C23×C4C4×D1311yescharacteristic
166C23×C4C4×D1311yescharacteristic
167C23×C4C22×D1311yescharacteristic
168C22×C8—22no—
169C22×C8—262no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—261no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—522no—
175C2×C4⋊C4—522no—
176C2×C42—24no—
177C2×C42D5211yescharacteristic
178C2×C42D5211yescharacteristic
179C2×C42C22⋊D1311yescharacteristic
180C2×C42C22⋊D1311yescharacteristic
181C22⋊C8—24no—
182C22⋊C8—264no—
183#95—262no—
184#95—262no—
185#95—262no—
186#95—262no—
187C2×C13—24no—
188C2×C13#146911yescharacteristic
189C2×C13#146911yescharacteristic
190C2×C13#147011yescharacteristic
191C2×C13#147011yescharacteristic
192C2×C13#181811yescharacteristic
193C2×C13#182011yescharacteristic
194C2×C13#182111yescharacteristic
195C24C2×C4×D1311yescharacteristic
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—264no—
207C22×C4—264no—
208C22×C4—522no—
209C22×C4—522no—
210C22×C4—522no—
211C22×C4—522no—
212C22×C4#610311yescharacteristic
213C22×C4#610311yescharacteristic
214C22×C4#610311yescharacteristic
215C22×C4#610311yescharacteristic
216C22×C4C2×D5211yescharacteristic
217C22×C4#612914yes—
218C22×C4C2×C22⋊D1311yescharacteristic
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—522no—
223C2×C8—522no—
224C2×C8—522no—
225C4⋊C4—522no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C4⋊C4—522no—
229C42—22no—
230C42—22no—
231C42—22no—
232C42—22no—
233C13#870311yescharacteristic, complemented, Sylow
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23#8813112yes—
239C23#8815512yes—
240C23#8816112yes—
241C23C2×#610311yescharacteristic
242C2×C4—28no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—522no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—1044no—
266C2×C4—1044no—
267C2×C4#8806312yes—
268C2×C4#8806412yes—
269C2×C4#8814012yes—
270C2×C4#8818912yes—
271C8—82no—
272C8—1042no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22#1171838114yes—
280C22#1171860411yescharacteristic
281C22#1171866711yescharacteristic
282C22#1171866711yescharacteristic
283C22#1171877111yescharacteristic
284C22#1171879011yescharacteristic
285C22C2×#8806311yescharacteristic
286C22C2×#8806411yescharacteristic
287C4—22no—
288C4—22no—
289C4—22no—
290C4—22no—
291C4—41no—
292C4—41no—
293C4—1042no—
294C4—1042no—
295C2—24no—
296C2#1311318711yescharacteristic
297C2#1311318911yescharacteristic
298C2#1311319111yescharacteristic
299C2#1311319311yescharacteristic
300C2#1311490511yescharacteristic
301C2#1311491111yescharacteristic
302C2#1311491411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1817C2
socleC23×C13C2×C22⋊C4
cosocleC23×C4×C13C23
hypercenter#1817D13
hypocenterC13#8703
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
233. C13#8703semidirect

Maximal subgroups

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

subgroupindex
C2×#117185972
#131149042
#131126782
C13×#18172
#870313