Finite Group Databasebeta

← #15760808

Subgroups — #15760808

Order 3328.

458 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 99 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#13120413C211yesmaximal, characteristic
2#13113284C212yesmaximal, complemented
3#13113170C211yesmaximal, characteristic
4#13112701C212yesmaximal, complemented
5C13×#2921C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C13×#433—24no—
9C13×#423—21no—
10C13×#407—21no—
11C4×C13×M16C2212yes—
12#11718871—21no—
13#11718644C411yescharacteristic
14#11718640C411yescharacteristic
15#11718639—21no—
16#11718614C411yescharacteristic
17#11718608C411yescharacteristic
18#11718605—21no—
19#11718598C2211yescharacteristic
20#11718594—21no—
21#11718587C2212yes—
22#11718120—21no—
23#11718117—21no—
24#11718048—24no—
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C2×C13×M16—22no—
28C13×#117—22no—
29C13×#117—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C4×Dic26—22no—
44C4×Dic26—22no—
45C13×C4⋊C8—24no—
46C13×C22⋊C8—24no—
47C13×#97—22no—
48C4×C8×C13D414yes—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071C2×C411yescharacteristic
56#88071C2×C411yescharacteristic
57C22⋊#1055—22no—
58C4⋊#1055—22no—
59#88043—22no—
60#9493—131nomaximal, Sylow
61C24×C13C22⋊C411yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C2×Dic26—22no—
77C2×Dic26—42no—
78C13×M16—42no—
79C13×M16—42no—
80C2×C8×C13—24no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13C2×D412yes—
88C42×C13#4112yes—
89C22⋊Dic13—42no—
90C22⋊Dic13—42no—
91C4⋊Dic13—22no—
92#6101—42no—
93#6101—42no—
94#6101—41no—
95#6101—41no—
96C4×Dic13—42no—
97C2×#1055—42no—
98#2921D1311yescharacteristic
99#2599—131no—
100#1491—132no—
101#1464—131no—
102#1288—132no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13#12112yes—
125C2×C4×C13#12311yescharacteristic
126C2×Dic13—22no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138Dic26—24no—
139Dic26—42no—
140C8×C13—44no—
141#1055—82no—
142C2×C4×Q8—131no—
143C2×#117C2×D1311yescharacteristic
144#433—24no—
145#432—132no—
146#423—21no—
147#407—21no—
148C4×M16C2×D1312yes—
149#398—131no—
150#397—131no—
151#395—131no—
152#393—131no—
153#388—261no—
154#387—261no—
155#387—261no—
156#385—261no—
157#383—131no—
158Q8⋊C8—264no—
159#324—261no—
160#323—261no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—42no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—81no—
168C22×C13#38611yescharacteristic
169C22×C13#42111yescharacteristic
170C22×C13#42111yescharacteristic
171C4×C13—22no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—22no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178Dic13—42no—
179Dic13—81no—
180Dic13—81no—
181Dic13—81no—
182C22×Q8—131no—
183C23×C4C22⋊D1311yescharacteristic
184C2×M16—22no—
185C4×Q8—262no—
186C4×Q8—262no—
187#117—22no—
188#117—22no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4C4×D1311yescharacteristic
194C2×C4⋊C4D5211yescharacteristic
195C2×C22⋊C4—261no—
196C2×C22⋊C4—261no—
197C2×C22⋊C4C4×D1311yescharacteristic
198C2×C22⋊C4D5211yescharacteristic
199C2×C42—261no—
200C2×C42C22⋊D1311yescharacteristic
201C2×C42C22×D1311yescharacteristic
202C4⋊C8—24no—
203C4⋊C8—262no—
204C22⋊C8—24no—
205C22⋊C8—262no—
206#97—22no—
207#97—262no—
208C4×C8C22⋊D1314yes—
209#95—131no—
210#95—131no—
211#95—261no—
212#95—261no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217C2×C13—21no—
218C2×C13—21no—
219C2×C13—81no—
220C2×C13#189111yescharacteristic
221C2×C13#189711yescharacteristic
222C2×C13#190911yescharacteristic
223C24#610311yescharacteristic
224C2×Q8—262no—
225C2×Q8—522no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4#610311yescharacteristic
235C22×C4#610311yescharacteristic
236C22×C4#610311yescharacteristic
237C22×C4C2×C4×D1311yescharacteristic
238C22×C4C2×D5211yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240M16—42no—
241M16—42no—
242C2×C8—24no—
243C2×C8—522no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—262no—
247C4⋊C4—522no—
248C4⋊C4—522no—
249C4⋊C4—521no—
250C4⋊C4—521no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—522no—
254C22⋊C4—522no—
255C42—21no—
256C42—21no—
257C42—522no—
258C42#612712yes—
259C42C2×C22⋊D1312yes—
260C13#949311yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×#610311yescharacteristic
267Q8—264no—
268Q8—522no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—262no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4C4×C22⋊D1312yes—
295C2×C4#8818311yescharacteristic
296C2×C4#8818412yes—
297C2×C4#8820711yescharacteristic
298C8—44no—
299C8—1042no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#1171866611yescharacteristic
308C22#1171866611yescharacteristic
309C22#1171887411yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—522no—
318C4—1041no—
319C4—1041no—
320C4—1041no—
321C2—21no—
322C2—21no—
323C2—81no—
324C2#1311525411yescharacteristic
325C2#1311528411yescharacteristic
326C2#1311535811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2921C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2921D13
hypocenterC13#9493
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #13113284C2semidirect
4. #13112701C2semidirect
260. C13#9493semidirect

Maximal subgroups

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

subgroupindex
#131204132
#131132842
#131131702
#131127012
C13×#29212
#949313