Finite Group Databasebeta

← #15760854

Subgroups — #15760854

Order 3328.

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

normal subgroups only

This group has 660 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#13117434C211yesmaximal, characteristic
2#13114910C212yesmaximal
3#13114910C211yesmaximal, characteristic
4#13112740C212yesmaximal
5C13×#2483C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C22×C13×C22⋊C4C2211yescharacteristic
8C13×#397—22no—
9C13×#385—21no—
10C13×#385C412yescomplemented
11C13×#381—21no—
12C13×#381C412yescomplemented
13C13×#379C2211yescharacteristic
14#11718908C2212yes—
15#11718908C2212yes—
16#11718873—21no—
17C4×C22⋊Dic13—21no—
18#11718612—24no—
19#11718118—22no—
20#11718118—24no—
21C25×C13C2311yescharacteristic
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C2×C13×C4⋊C4—22no—
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—21no—
30C2×C13×C22⋊C4—21no—
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4C2×C412yes—
36C2×C13×C22⋊C4C2×C412yes—
37C2×C13×C22⋊C4D412yes—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—22no—
40C2×C22⋊Dic13—22no—
41C2×C22⋊Dic13—22no—
42C2×C22⋊Dic13—22no—
43C2×C22⋊Dic13D414yes—
44C2×C4⋊Dic13—22no—
45C2×C4×Dic13—22no—
46C13×#95—22no—
47C13×#95—22no—
48C13×#95—22no—
49#88071—22no—
50#88071—22no—
51#9502—131nomaximal, Sylow
52C24×C13—42no—
53C24×C13—42no—
54C24×C13—81no—
55C24×C13C22×C411yescharacteristic
56C24×C13C2×D412yes—
57C24×C13C2×D411yescharacteristic
58C24×C13C2×D411yescharacteristic
59C24×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—81no—
72C22×C4×C13—81no—
73C22×C4×C13C22⋊C412yes—
74C22×C4×C13C22⋊C412yes—
75C22×Dic13—24no—
76C22×Dic13—42no—
77C13×C4⋊C4—82no—
78C13×C22⋊C4—24no—
79C13×C22⋊C4—24no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—81no—
86C22⋊Dic13—44no—
87C22⋊Dic13—44no—
88C22⋊Dic13—44no—
89C22⋊Dic13—44no—
90C22⋊Dic13—82no—
91C22⋊Dic13—82no—
92C4⋊Dic13—82no—
93C4×Dic13—82no—
94#2483D1311yescharacteristic
95#2312—131no—
96#1819—132no—
97#1819—131no—
98#1304—132no—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—22no—
102C23×C13—22no—
103C23×C13—24no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—42no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—88no—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13C4×D412yes—
117C23×C13#12011yescharacteristic
118C23×C13#12112yes—
119C23×C13#12311yescharacteristic
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—82no—
136C2×C4×C13—82no—
137C2×Dic13—44no—
138C2×Dic13—44no—
139C2×Dic13—44no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142C2×Dic13—82no—
143C22×C22⋊C4C2×D1311yescharacteristic
144C22×C22⋊C4C2×D1311yescharacteristic
145#397—22no—
146#388—264no—
147#385—21no—
148#385Dic1312yescomplemented
149#381—21no—
150#381Dic1312yescomplemented
151#380—261no—
152#379—132no—
153#379—132no—
154#379C2×D1311yescharacteristic
155C4×C22⋊C4—261no—
156#342—264no—
157#342—262no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—21no—
164C22×C13—22no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—21no—
171C22×C13—44no—
172C22×C13—44no—
173C22×C13—84no—
174C22×C13—82no—
175C22×C13—84no—
176C22×C13#38611yescharacteristic
177C22×C13#41012yes—
178C22×C13#45812yes—
179C4×C13—42no—
180C4×C13—42no—
181C4×C13—82no—
182C4×C13—81no—
183C4×C13—81no—
184Dic13—84no—
185Dic13—162no—
186C25C22×D1311yescharacteristic
187C23×C4C2×Dic1311yescharacteristic
188C23×C4C2×Dic1311yescharacteristic
189C23×C4C22⋊D1311yescharacteristic
190C23×C4C22⋊D1311yescharacteristic
191C2×C4⋊C4—22no—
192C2×C4⋊C4—262no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—134no—
202C2×C22⋊C4—262no—
203C2×C22⋊C4—262no—
204C2×C22⋊C4—262no—
205C2×C22⋊C4—262no—
206C2×C22⋊C4—262no—
207C2×C22⋊C4C2×Dic1312yes—
208C2×C22⋊C4C2×Dic1312yes—
209C2×C22⋊C4C22⋊D1312yes—
210C2×C42—262no—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—262no—
215#95—262no—
216C2×C13—22no—
217C2×C13—22no—
218C2×C13—42no—
219C2×C13—41no—
220C2×C13—42no—
221C2×C13#189011yescharacteristic
222C2×C13#189911yescharacteristic
223C2×C13#191311yescharacteristic
224C24—42no—
225C24—42no—
226C24—81no—
227C24D4×D1312yes—
228C24#612912yes—
229C24C22×Dic1311yescharacteristic
230C24C2×C22⋊D1311yescharacteristic
231C24C2×C22⋊D1311yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—81no—
244C22×C4—81no—
245C22×C4—264no—
246C22×C4—522no—
247C22×C4C22⋊Dic1312yes—
248C22×C4C22⋊Dic1312yes—
249C4⋊C4—82no—
250C4⋊C4—1042no—
251C22⋊C4—24no—
252C22⋊C4—24no—
253C22⋊C4—42no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—81no—
259C22⋊C4—524no—
260C22⋊C4—524no—
261C22⋊C4—524no—
262C22⋊C4—524no—
263C22⋊C4—1042no—
264C22⋊C4—1042no—
265C42—1042no—
266C13#950211yescharacteristic, complemented, Sylow
267C23—22no—
268C23—22no—
269C23—22no—
270C23—24no—
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—42no—
277C23—42no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—41no—
282C23—88no—
283C23D4×Dic1312yes—
284C23#8818911yescharacteristic
285C23#8819111yescharacteristic
286C23#8819312yes—
287C23C2×C22⋊Dic1311yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4—524no—
306C2×C4—524no—
307C2×C4—524no—
308C2×C4—1042no—
309C2×C4—1042no—
310C2×C4—1042no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—22no—
324C22—44no—
325C22—44no—
326C22—82no—
327C22—84no—
328C22—84no—
329C22#1171871412yes—
330C22#1171888111yescharacteristic
331C22#1171890112yes—
332C4—42no—
333C4—42no—
334C4—82no—
335C4—81no—
336C4—81no—
337C4—1044no—
338C4—2082no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—41no—
343C2—42no—
344C2#1311525011yescharacteristic
345C2#1311529511yescharacteristic
346C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC24×C13C22×C4
FrattiniC25C22×D13
FittingC13×#2483C2
socleC22×C13#386
prime radical, cosocleC25×C13C23
hypercenter#2483D13
hypocenterC13#9502
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ #2483

Complements

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

NH ≅ G/Ntype
10. C13×#385C4semidirect
12. C13×#381C4semidirect
148. #385Dic13semidirect
150. #381Dic13semidirect
266. C13#9502semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131149102
#131127402
C13×#24832
#950213