Finite Group Databasebeta

← #15760914

Subgroups — #15760914

Order 3328.

478 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 103 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#13114919C211yesmaximal, characteristic
3#13113166C212yesmaximal
4#13112744C212yesmaximal
5C13×#2484C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#400—21no—
9C13×#398—21no—
10C13×#387—21no—
11C13×#387—21no—
12C13×#385C411yescharacteristic
13C13×#385C411yescharacteristic
14C13×#381C411yescharacteristic
15C13×#381C411yescharacteristic
16C13×#381C2211yescharacteristic
17#11718868C2212yes—
18#11718868C2212yes—
19#11718661—24no—
20#11718585—21no—
21C4×#6099—21no—
22#11718122—21no—
23#11718122—21no—
24#11718120—24no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C13×#117—22no—
29C13×#117—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×#6099—22no—
45C2×#6099—22no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C22⋊#1055—22no—
55C22⋊#1055—22no—
56C22⋊#1055—22no—
57C22⋊#1055D414yes—
58C4⋊#1055—24no—
59#88043—22no—
60C4×#1055—22no—
61#9514—131nomaximal, Sylow
62C24×C13C22×C411yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13—42no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C2×D412yes—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4112yes—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97#6099—42no—
98#6099—42no—
99#6099—42no—
100#6099—42no—
101C2×#1055—24no—
102C2×#1055—42no—
103#2921—131no—
104#2484D1311yescharacteristic
105#1822—131no—
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—22no—
119C2×C4×C13—24no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—82no—
143C2×C4×C13#12011yescharacteristic
144C2×C4×C13#12112yes—
145C2×C4×C13#12311yescharacteristic
146#1055—44no—
147#1055—82no—
148C2×#117C2×D1311yescharacteristic
149C22×C4⋊C4C2×D1311yescharacteristic
150#433—264no—
151#423—261no—
152#407—132no—
153#407—132no—
154C4×M16—261no—
155#400—21no—
156#398—21no—
157#387—21no—
158#387—21no—
159#385Dic1311yescharacteristic
160#385Dic1311yescharacteristic
161#381Dic1311yescharacteristic
162#381Dic1311yescharacteristic
163#381C2×D1311yescharacteristic
164#343—261no—
165#343—261no—
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—42no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—81no—
186C4×C13—81no—
187C4×C13—81no—
188C23×C4C2×Dic1311yescharacteristic
189C23×C4C2×Dic1311yescharacteristic
190C23×C4C22×D1311yescharacteristic
191C2×M16—262no—
192C2×M16—262no—
193#117—22no—
194#117—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C22⋊D1311yescharacteristic
202C2×C4⋊C4C22⋊D1311yescharacteristic
203C2×C22⋊C4C2×Dic1311yescharacteristic
204C2×C22⋊C4C2×Dic1311yescharacteristic
205C2×C22⋊C4C2×Dic1311yescharacteristic
206C2×C22⋊C4C2×Dic1311yescharacteristic
207C2×C42C22⋊D1311yescharacteristic
208C2×C42C22⋊D1311yescharacteristic
209C4⋊C8—264no—
210C22⋊C8—134no—
211C22⋊C8—262no—
212C22⋊C8—262no—
213C22⋊C8—262no—
214#97—262no—
215C4×C8—262no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—42no—
227C2×C13#189111yescharacteristic
228C2×C13#189911yescharacteristic
229C2×C13#191511yescharacteristic
230C24C22×Dic1311yescharacteristic
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—42no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4C22⋊Dic1311yescharacteristic
245C22×C4C22⋊Dic1311yescharacteristic
246C22×C4D4×D1312yes—
247C22×C4#612912yes—
248C22×C4C2×C22⋊D1311yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250M16—522no—
251M16—522no—
252M16—522no—
253M16—522no—
254C2×C8—264no—
255C2×C8—522no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C13#951411yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23D4×Dic1312yes—
277C23C2×C22⋊Dic1311yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4#8818911yescharacteristic
308C2×C4#8819111yescharacteristic
309C2×C4#8819312yes—
310C8—524no—
311C8—1042no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1171888111yescharacteristic
320C22#1171890111yescharacteristic
321C22#1171890111yescharacteristic
322C4—21no—
323C4—22no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1311525511yescharacteristic
337C2#1311529511yescharacteristic
338C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2484C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#2484D13
hypocenterC13#9514
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

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
#131149192
#131131662
#131127442
C13×#24842
#951413