Finite Group Databasebeta

← #15760873

Subgroups — #15760873

Order 3328.

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

normal subgroups only

This group has 682 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#13118201C211yesmaximal, characteristic
2#13114759C212yesmaximal, complemented
3#13113174C211yesmaximal, characteristic
4#13112741C212yesmaximal, complemented
5C13×#2975C211yesmaximal, characteristic
6C23×Dic26C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C2×#88178—21no—
9C13×#436—24no—
10C13×#431—21no—
11C13×#407—21no—
12C13×#407C2212yes—
13#11718881C412yes—
14#11718873C2211yescharacteristic
15#11718868C2212yes—
16C2×#88064—24no—
17#11718640—21no—
18#11718608—21no—
19#11718607C412yes—
20#11718590—21no—
21#11718120—21no—
22#11718117—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13C2×C412yes—
27C22×Dic26—21no—
28C22×Dic26—22no—
29C22×Dic26—21no—
30C22×Dic26—22no—
31C22×Dic26—44no—
32C2×C13×M16—22no—
33C2×C13×M16D414yes—
34C4×D4×C13—22no—
35C4×D4×C13—22no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C22⋊Dic13—22no—
41C2×C22⋊Dic13C2×C412yes—
42C2×C4⋊Dic13—21no—
43#88178—44no—
44C2×#6101—22no—
45C2×#6099—22no—
46C13×C4⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—22no—
50C4×C8×C13—22no—
51#88071—22no—
52#88071—22no—
53#88071—21no—
54C22⋊#1055—22no—
55C22⋊#1055—22no—
56#88064—48no—
57#9506—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C22×C411yescharacteristic
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—41no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4112yes—
74C22×Dic13—22no—
75C22×Dic13—24no—
76C22×Dic13—22no—
77C22×Dic13—44no—
78C2×Dic26—28no—
79C2×Dic26—24no—
80C2×Dic26—44no—
81C2×Dic26—48no—
82C2×Dic26—44no—
83C2×Dic26—42no—
84C2×Dic26—41no—
85C2×Dic26—42no—
86C2×Dic26—41no—
87C13×M16—44no—
88C13×M16—82no—
89C2×C8×C13—24no—
90C13×C4⋊C4—22no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—22no—
93C42×C13—21no—
94C42×C13—21no—
95C22⋊Dic13—44no—
96C22⋊Dic13—42no—
97C4⋊Dic13—42no—
98#6101—44no—
99#6099—44no—
100C2×#1055—42no—
101#2975D1311yescharacteristic
102#2409—131no—
103#1784—132no—
104#1465—131no—
105#1305—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13C4×D412yes—
117D4×C13—44no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—24no—
121C2×C4×C13—22no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—81no—
130C2×C4×C13#10112yescomplemented
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12112yes—
133C2×C4×C13#12311yescharacteristic
134C2×Dic13—24no—
135C2×Dic13—28no—
136C2×Dic13—42no—
137C2×Dic13—44no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142Dic26—48no—
143Dic26—44no—
144Dic26—44no—
145C8×C13—44no—
146#1055—82no—
147C23×Q8—131no—
148C2×C22⋊Q8—261no—
149C2×C4×D4C2×D1311yescharacteristic
150#436—24no—
151#431—21no—
152C2×#101—264no—
153#407—21no—
154#407—132no—
155#407C2×D1312yes—
156#395—261no—
157#393—261no—
158#391—261no—
159#386—132no—
160#385—132no—
161#380—131no—
162#324—261no—
163#323—261no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—81no—
176C22×C13#38611yescharacteristic
177C22×C13C2×#10111yescharacteristic
178C22×C13#41311yescharacteristic
179C4×C13—22no—
180C4×C13—21no—
181C4×C13—22no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13B(4,𝔽2)12yes—
185Dic13—44no—
186Dic13—82no—
187C22×Q8—261no—
188C22×Q8—262no—
189C22×Q8—261no—
190C22×Q8—262no—
191C22×Q8—524no—
192C22×D4C4×D1311yescharacteristic
193C23×C4—132no—
194C23×C4C22⋊D1311yescharacteristic
195C23×C4C22×D1311yescharacteristic
196C2×M16—22no—
197C2×M16—262no—
198C2×M16C22⋊D1314yes—
199C22⋊Q8—524no—
200C4×D4—22no—
201C4×D4—22no—
202C2×C4⋊C4—262no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4D5211yescharacteristic
205C2×C22⋊C4—132no—
206C2×C22⋊C4—262no—
207C2×C22⋊C4C4×D1311yescharacteristic
208C2×C22⋊C4D5211yescharacteristic
209C2×C42C22⋊D1311yescharacteristic
210C4⋊C8—22no—
211#101—528no—
212C22⋊C8—22no—
213C22⋊C8—22no—
214C22⋊C8—22no—
215C22⋊C8—262no—
216C22⋊C8—262no—
217C4×C8—22no—
218#95—262no—
219#95—262no—
220#95—261no—
221C2×C13—21no—
222C2×C13—21no—
223C2×C13—42no—
224C2×C13—81no—
225C2×C13#188911yescharacteristic
226C2×C13#190111yescharacteristic
227C2×C13#191511yescharacteristic
228C24#610311yescharacteristic
229C24C2×C4×D1311yescharacteristic
230C2×Q8—268no—
231C2×Q8—264no—
232C2×Q8—522no—
233C2×Q8—524no—
234C2×Q8—524no—
235C2×Q8—528no—
236C2×Q8—521no—
237C2×Q8—522no—
238C2×Q8—521no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—41no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—262no—
247C22×C4—264no—
248C22×C4—262no—
249C22×C4—524no—
250C22×C4#610311yescharacteristic
251C22×C4#610311yescharacteristic
252C22×C4#610311yescharacteristic
253C22×C4C2×D5211yescharacteristic
254C22×C4#612712yes—
255C22×C4C2×C22⋊D1311yescharacteristic
256C22×C4C2×C22⋊D1312yes—
257M16—44no—
258M16—82no—
259M16—524no—
260C2×C8—24no—
261C2×C8—522no—
262C4⋊C4—22no—
263C4⋊C4—522no—
264C4⋊C4—524no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—524no—
268C22⋊C4—522no—
269C42—21no—
270C42—21no—
271C13#950611yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23C2×#610311yescharacteristic
282C23C4×C22⋊D1312yes—
283Q8—528no—
284Q8—524no—
285Q8—524no—
286D4—44no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—81no—
299C2×C4—264no—
300C2×C4—268no—
301C2×C4—522no—
302C2×C4—524no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—522no—
306C2×C4—522no—
307C2×C4#8806412yescomplemented
308C2×C4#8818311yescharacteristic
309C2×C4#8818412yes—
310C2×C4#8820711yescharacteristic
311C8—44no—
312C8—1042no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22#1171879311yescharacteristic
326C22C2×#8806411yescharacteristic
327C22#1171887411yescharacteristic
328C4—22no—
329C4—21no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—524no—
334C4—1042no—
335C4#1171890512yes—
336C2—21no—
337C2—21no—
338C2—42no—
339C2—81no—
340C2#1311524411yescharacteristic
341C2#1311530411yescharacteristic
342C2#1311538811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2975C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#2975D13
hypocenterC13#9506
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #13114759C2semidirect
4. #13112741C2semidirect
130. C2×C4×C13#101semidirect
271. C13#9506semidirect
307. C2×C4#88064semidirect

Maximal subgroups

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

subgroupindex
#131182012
#131147592
#131131742
#131127412
C13×#29752
#950613