Finite Group Databasebeta

← #15756256

Subgroups — #15756256

Order 3328.

530 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 119 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×#11718311C211yesmaximal, characteristic
2#13114902C212yesmaximal
3#13112679C211yesmaximal, characteristic
4#13112678C212yesmaximal
5C13×#1280C211yesmaximal, characteristic
6C22×#6101C412yes—
7C22×C4×Dic13C2211yescharacteristic
8C2×C13×C22⋊C8C2212yes—
9C2×C13×#95C2211yescharacteristic
10C2×#88071C412yes—
11C2×#88071C2211yescharacteristic
12C2×C22⋊#1055C2212yes—
13#11718311—22no—
14#11718311—22no—
15#11718142—22no—
16#11718142—22no—
17C23×C4×C13C2×C412yes—
18C23×C4×C13C2311yescharacteristic
19C23×Dic13C2×C411yescharacteristic
20C23×Dic13C2×C411yescharacteristic
21C23×Dic13C2×C412yes—
22C22×C8×C13—22no—
23C2×#6101—22no—
24C2×#6101—22no—
25C2×#6101—44no—
26C2×C4×Dic13—22no—
27C2×C4×Dic13—21no—
28C2×C4×Dic13—21no—
29C2×C4×Dic13D412yes—
30C2×C4×Dic13D412yes—
31C22×#1055—22no—
32C13×C22⋊C8—22no—
33C13×C22⋊C8—22no—
34C13×#95—22no—
35#88071—22no—
36#88071—24no—
37C22⋊#1055—22no—
38C22⋊#1055—22no—
39#8703—131nomaximal, Sylow
40C24×C13C22×C411yescharacteristic
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—42no—
45C22×C4×C13—42no—
46C22×C4×C13—42no—
47C22×C4×C13C2×D412yes—
48C22×C4×C13#4112yes—
49C22×C4×C13#4111yescharacteristic
50C22×C4×C13#4111yescharacteristic
51C22×Dic13—21no—
52C22×Dic13—21no—
53C22×Dic13—22no—
54C22×Dic13—22no—
55C22×Dic13—21no—
56C22×Dic13—21no—
57C22×Dic13—22no—
58C22×Dic13—22no—
59C22×Dic13—22no—
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—42no—
63C22×Dic13—42no—
64C22×Dic13C22⋊C412yes—
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C2×C8×C13—44no—
68C2×C8×C13—42no—
69#6101—44no—
70#6101—44no—
71C4×Dic13—22no—
72C4×Dic13—22no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75C2×#1055—44no—
76C2×#1055—42no—
77C2×#382—131no—
78#1817—132no—
79#1280—132no—
80#1280—131no—
81#1280D1311yescharacteristic
82C23×C13—22no—
83C23×C13—21no—
84C23×C13—21no—
85C23×C13C2×C22⋊C411yescharacteristic
86C23×C13#11711yescharacteristic
87C23×C13#11711yescharacteristic
88C23×C13#13112yes—
89C23×C13#13112yes—
90C2×C4×C13—24no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—82no—
98C2×C4×C13—82no—
99C2×C4×C13#12312yes—
100C2×C4×C13#12312yes—
101C2×Dic13—24no—
102C2×Dic13—24no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—24no—
109C2×Dic13—42no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114C2×Dic13—42no—
115C2×Dic13—82no—
116C2×Dic13—82no—
117C2×Dic13#10012yes—
118C2×Dic13#10112yes—
119C8×C13—82no—
120#1055—82no—
121C22×C4⋊C4—132no—
122C22×C42—131no—
123C2×C22⋊C8—132no—
124C2×C22⋊C8C2×D1312yes—
125#382—262no—
126#382—262no—
127C2×#95—132no—
128C2×#95—131no—
129C2×#95C2×D1311yescharacteristic
130#336—262no—
131#336—262no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13—22no—
137C22×C13—22no—
138C22×C13—22no—
139C22×C13—22no—
140C22×C13#38111yescharacteristic
141C22×C13#40812yes—
142C22×C13#41012yes—
143C22×C13C2×#10011yescharacteristic
144C22×C13C2×#10111yescharacteristic
145C22×C13#43312yes—
146C22×C13#43311yescharacteristic
147C22×C13#43311yescharacteristic
148C4×C13—22no—
149C4×C13—22no—
150C4×C13—82no—
151Dic13—22no—
152Dic13—22no—
153Dic13—42no—
154Dic13—82no—
155C23×C4—131no—
156C23×C4—131no—
157C23×C4—132no—
158C23×C4C4×D1312yes—
159C23×C4C22×D1311yescharacteristic
160C22×C8—22no—
161C22×C8—262no—
162C2×C4⋊C4—262no—
163C2×C4⋊C4—262no—
164C2×C4⋊C4—524no—
165C2×C42—132no—
166C2×C42—132no—
167C2×C42—262no—
168C2×C42—261no—
169C2×C42—261no—
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—262no—
173C22⋊C8—262no—
174#95—22no—
175#95—264no—
176#95—262no—
177C2×C13—22no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13#146912yes—
181C2×C13#147012yes—
182C2×C13#181811yescharacteristic
183C2×C13#182011yescharacteristic
184C2×C13#182111yescharacteristic
185C24C2×C4×D1311yescharacteristic
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—132no—
195C22×C4—262no—
196C22×C4—262no—
197C22×C4—261no—
198C22×C4—261no—
199C22×C4—261no—
200C22×C4—261no—
201C22×C4—262no—
202C22×C4—262no—
203C22×C4—262no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—522no—
207C22×C4—522no—
208C22×C4#612712yes—
209C22×C4D4×D1312yes—
210C22×C4#612911yescharacteristic
211C22×C4#613111yescharacteristic
212C2×C8—44no—
213C2×C8—42no—
214C2×C8—524no—
215C2×C8—522no—
216C4⋊C4—524no—
217C4⋊C4—524no—
218C42—262no—
219C42—262no—
220C42—262no—
221C42—262no—
222C13#870311yescharacteristic, complemented, Sylow
223C23—22no—
224C23—21no—
225C23—21no—
226C23#8812611yescharacteristic
227C23C22⋊C4×D1311yescharacteristic
228C23#8814611yescharacteristic
229C23#8815512yes—
230C23#8816112yes—
231C2×C4—24no—
232C2×C4—42no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—132no—
241C2×C4—132no—
242C2×C4—264no—
243C2×C4—264no—
244C2×C4—261no—
245C2×C4—261no—
246C2×C4—261no—
247C2×C4—261no—
248C2×C4—262no—
249C2×C4—264no—
250C2×C4—522no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—1042no—
257C2×C4—1042no—
258C2×C4#8813712yes—
259C2×C4#8814812yes—
260C8—82no—
261C8—1042no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22#1171832511yescharacteristic
271C22#1171835111yescharacteristic
272C22#1171837011yescharacteristic
273C22#1171838812yes—
274C22#1171840112yes—
275C22D13×#10011yescharacteristic
276C22D13×#10111yescharacteristic
277C22#1171850112yes—
278C4—22no—
279C4—22no—
280C4—82no—
281C4—262no—
282C4—262no—
283C4—522no—
284C4—1042no—
285C2—22no—
286C2—21no—
287C2—21no—
288C2#1311318612yes—
289C2#1311319012yes—
290C2#1311490611yescharacteristic
291C2#1311491211yescharacteristic
292C2#1311491511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1280C2
socleC23×C13C2×C22⋊C4
cosocleC23×C4×C13C23
hypercenter#1280D13
hypocenterC13#8703
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
222. C13#8703semidirect

Maximal subgroups

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

subgroupindex
C2×#117183112
#131149022
#131126792
#131126782
C13×#12802
#870313