Finite Group Databasebeta

← #15760883

Subgroups — #15760883

Order 3328.

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

normal subgroups only

This group has 542 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#13119144C211yesmaximal, characteristic
2#13114914C212yesmaximal, complemented
3#13113174C211yesmaximal, characteristic
4#13112741C212yesmaximal, complemented
5C13×#2975C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189C412yes—
8C22×C4⋊Dic13C2211yescharacteristic
9C13×#436—24no—
10C13×#431—21no—
11C13×#407—21no—
12C13×#407C2212yes—
13#11718873—21no—
14#11718873C2211yescharacteristic
15#11718868C2212yes—
16#11718644—21no—
17#11718614—21no—
18#11718604C412yes—
19#11718589—21no—
20#11718146—24no—
21#11718120—21no—
22#11718117—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13C2×C412yes—
27C2×C13×M16—22no—
28C2×C13×M16D414yes—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13C2×C412yes—
37#88189—44no—
38C2×C4⋊Dic13—22no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—22no—
43C2×#6101—22no—
44C2×#6099—22no—
45C13×C4⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49C4×C8×C13—22no—
50#88071—22no—
51#88071—22no—
52#88071—21no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55#9508—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C22×C411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D412yes—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4112yes—
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—24no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C13×M16—44no—
78C13×M16—82no—
79C2×C8×C13—24no—
80C13×C4⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C42×C13—21no—
84C42×C13—21no—
85C22⋊Dic13—44no—
86C22⋊Dic13—42no—
87C4⋊Dic13—42no—
88C4⋊Dic13—41no—
89C4⋊Dic13—42no—
90C4⋊Dic13—41no—
91#6101—44no—
92#6099—44no—
93C2×#1055—42no—
94#2975D1311yescharacteristic
95#2486—131no—
96#1821—132no—
97#1465—131no—
98#1305—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109C23×C13C4×D412yes—
110D4×C13—44no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—24no—
114C2×C4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—81no—
123C2×C4×C13#10012yes—
124C2×C4×C13#12011yescharacteristic
125C2×C4×C13#12112yes—
126C2×C4×C13#12311yescharacteristic
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—84no—
134C8×C13—44no—
135#1055—82no—
136C2×#123—132no—
137C2×C4×D4C2×D1311yescharacteristic
138C22×C4⋊C4—131no—
139#436—24no—
140#431—21no—
141#407—21no—
142#407—132no—
143#407C2×D1312yes—
144#398—261no—
145#397—261no—
146#389—261no—
147#381—132no—
148#380—131no—
149#380—261no—
150#343—264no—
151#324—261no—
152#323—261no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—81no—
165C22×C13#38611yescharacteristic
166C22×C13C2×#10011yescharacteristic
167C22×C13#41311yescharacteristic
168C4×C13—22no—
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13#45812yes—
174Dic13—82no—
175Dic13—82no—
176C22×D4C4×D1311yescharacteristic
177C23×C4—132no—
178C23×C4C22⋊D1311yescharacteristic
179C23×C4C22×D1311yescharacteristic
180C2×M16—22no—
181C2×M16—262no—
182C2×M16C22⋊D1314yes—
183#123—524no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—262no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4D5211yescharacteristic
193C2×C22⋊C4—132no—
194C2×C22⋊C4—262no—
195C2×C22⋊C4C4×D1311yescharacteristic
196C2×C22⋊C4D5211yescharacteristic
197C2×C42C22⋊D1311yescharacteristic
198C4⋊C8—22no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201C22⋊C8—22no—
202C22⋊C8—262no—
203C22⋊C8—262no—
204C4×C8—22no—
205#95—262no—
206#95—262no—
207#95—261no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—42no—
211C2×C13—81no—
212C2×C13#189011yescharacteristic
213C2×C13#190011yescharacteristic
214C2×C13#191511yescharacteristic
215C24#610311yescharacteristic
216C24C2×C4×D1311yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—41no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—262no—
225C22×C4—262no—
226C22×C4—264no—
227C22×C4—522no—
228C22×C4—522no—
229C22×C4#610311yescharacteristic
230C22×C4#610311yescharacteristic
231C22×C4#610311yescharacteristic
232C22×C4C2×D5211yescharacteristic
233C22×C4#612712yes—
234C22×C4C2×C22⋊D1311yescharacteristic
235C22×C4C2×C22⋊D1312yes—
236M16—44no—
237M16—82no—
238M16—524no—
239C2×C8—24no—
240C2×C8—522no—
241C4⋊C4—22no—
242C4⋊C4—522no—
243C4⋊C4—521no—
244C4⋊C4—522no—
245C4⋊C4—521no—
246C4⋊C4—524no—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—524no—
250C22⋊C4—522no—
251C42—21no—
252C42—21no—
253C13#950811yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23C2×#610311yescharacteristic
264C23C4×C22⋊D1312yes—
265D4—44no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—522no—
283C2×C4—522no—
284C2×C4—1044no—
285C2×C4#8806312yes—
286C2×C4#8818311yescharacteristic
287C2×C4#8818412yes—
288C2×C4#8820711yescharacteristic
289C8—44no—
290C8—1042no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#8806311yescharacteristic
304C22#1171879311yescharacteristic
305C22#1171887411yescharacteristic
306C4—22no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—41no—
311C4—1042no—
312C4—1042no—
313C4#1171890412yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—81no—
318C2#1311524911yescharacteristic
319C2#1311529911yescharacteristic
320C2#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#9508
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. #13114914C2semidirect
4. #13112741C2semidirect
253. C13#9508semidirect

Maximal subgroups

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

subgroupindex
#131191442
#131149142
#131131742
#131127412
C13×#29752
#950813