Finite Group Databasebeta

← #15760911

Subgroups — #15760911

Order 3328.

478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 95 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#13123474C211yesmaximal, characteristic
2#13119119C211yesmaximal, characteristic
3#13113165C212yesmaximal
4#13112745C212yesmaximal
5C13×#1822C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C22×#6101C2211yescharacteristic
8C13×#407C2212yes—
9#11718872C2211yescharacteristic
10#11718868C2212yes—
11#11718661—24no—
12#11718643—21no—
13#11718641—21no—
14#11718607C411yescharacteristic
15#11718607C411yescharacteristic
16#11718604C411yescharacteristic
17#11718604C411yescharacteristic
18#11718594—21no—
19#11718594—21no—
20#11718585—21no—
21C4×#6099—21no—
22C13×#343—21no—
23C13×#343—21no—
24#11718061—24no—
25C23×C4×C13C2311yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C2×C13×M16—22no—
29C13×#117—22no—
30C13×#117—22no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C22⋊Dic13C2×C411yescharacteristic
38C2×C22⋊Dic13C2×C411yescharacteristic
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—22no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—22no—
45C2×#6099—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56C22⋊#1055—22no—
57C22⋊#1055D414yes—
58C4⋊#1055—24no—
59#88043—22no—
60C4×#1055—22no—
61#9514—131nomaximal, Sylow
62C24×C13C22×C411yescharacteristic
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D412yes—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13#4112yes—
73C22×Dic13—21no—
74C22×Dic13—22no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—22no—
79C22×Dic13—42no—
80C22×Dic13—41no—
81C22×Dic13—41no—
82C13×M16—42no—
83C13×M16—42no—
84C2×C8×C13—42no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C22⋊C4—22no—
88C13×C22⋊C4—22no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95#6101—42no—
96#6101—42no—
97#6101—41no—
98#6101—42no—
99#6101—41no—
100#6099—42no—
101#6099—42no—
102C2×#1055—24no—
103#2921—131no—
104#2484—131no—
105#1822D1311yescharacteristic
106#1463—132no—
107#1306—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13C2×C22⋊C411yescharacteristic
113C23×C13C4×D412yes—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12112yes—
130C2×C4×C13#12311yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—24no—
133C2×Dic13—41no—
134C2×Dic13—42no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—82no—
146C8×C13—82no—
147#1055—44no—
148C2×#117C2×D1311yescharacteristic
149C22×C4⋊C4—131no—
150#433—264no—
151#423—261no—
152#407—132no—
153#407C2×D1312yes—
154C4×M16—261no—
155#400—261no—
156#398—261no—
157#387—261no—
158#387—261no—
159#385—131no—
160#385—131no—
161#381—131no—
162#381—131no—
163#381—131no—
164#343—21no—
165#343—21no—
166#324—264no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—42no—
173C22×C13—42no—
174C22×C13#38611yescharacteristic
175C22×C13#41011yescharacteristic
176C22×C13#41011yescharacteristic
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184Dic13—42no—
185Dic13—81no—
186Dic13—81no—
187Dic13—81no—
188C23×C4—131no—
189C23×C4—131no—
190C23×C4C22×D1311yescharacteristic
191C2×M16—22no—
192C2×M16—262no—
193#117—22no—
194#117—22no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—262no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4C22⋊D1311yescharacteristic
202C2×C4⋊C4C22⋊D1311yescharacteristic
203C2×C22⋊C4—131no—
204C2×C22⋊C4—131no—
205C2×C22⋊C4C4×D1311yescharacteristic
206C2×C22⋊C4C4×D1311yescharacteristic
207C2×C42D5211yescharacteristic
208C2×C42D5211yescharacteristic
209C4⋊C8—264no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212C22⋊C8—134no—
213C22⋊C8—262no—
214#97—262no—
215C4×C8—262no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—42no—
227C2×C13#189111yescharacteristic
228C2×C13#189911yescharacteristic
229C2×C13#191511yescharacteristic
230C24C2×C4×D1311yescharacteristic
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—262no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—262no—
239C22×C4—522no—
240C22×C4—521no—
241C22×C4—521no—
242C22×C4#610311yescharacteristic
243C22×C4#610311yescharacteristic
244C22×C4#610311yescharacteristic
245C22×C4#610311yescharacteristic
246C22×C4C2×D5211yescharacteristic
247C22×C4D4×D1312yes—
248C22×C4#612912yes—
249C22×C4C2×C22⋊D1311yescharacteristic
250M16—42no—
251M16—42no—
252M16—522no—
253M16—522no—
254C2×C8—42no—
255C2×C8—264no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—522no—
259C4⋊C4—522no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—522no—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—521no—
266C22⋊C4—521no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C13#951411yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#8813512yes—
277C23C2×#610311yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—262no—
293C2×C4—264no—
294C2×C4—521no—
295C2×C4—522no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—1042no—
307C2×C4#8813611yescharacteristic
308C2×C4#8814011yescharacteristic
309C2×C4#8819312yes—
310C8—82no—
311C8—524no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1171861911yescharacteristic
320C22#1171866711yescharacteristic
321C22#1171866711yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—522no—
330C4—1041no—
331C4—1041no—
332C4—1041no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1311525211yescharacteristic
337C2#1311529211yescharacteristic
338C2#1311538611yescharacteristic
subgroupG/H
centerC22#11718619
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1822C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#1822D13
hypocenterC13#9514
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
271. C13#9514semidirect

Maximal subgroups

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

subgroupindex
#131234742
#131191192
#131131652
#131127452
C13×#18222
#951413