Finite Group Databasebeta

← #15758469

Subgroups — #15758469

Order 3328.

560 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 119 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#13117501C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3C2×#11718061C212yesmaximal, complemented
4#13112682C212yesmaximal, complemented
5C13×#2973C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189C411yescharacteristic
8C22×#6101C2211yescharacteristic
9C13×#435—24no—
10C13×#432—21no—
11C13×#407—21no—
12C2×C13×C22⋊C8C2212yes—
13#11718881C411yescharacteristic
14#11718871—21no—
15C4×C22⋊Dic13C2211yescharacteristic
16C2×C22⋊#1055C2212yes—
17#11718633—21no—
18#11718607C411yescharacteristic
19#11718606—21no—
20#11718604C411yescharacteristic
21#11718594—21no—
22#11718120—21no—
23#11718117—21no—
24#11718061—24no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C2×C13×M16—22no—
31C22×C8×C13—22no—
32C4×D4×C13—22no—
33C4×D4×C13—22no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13C2×C411yescharacteristic
41C2×C22⋊Dic13C2×C411yescharacteristic
42#88189—22no—
43#88189—22no—
44C2×#6101—21no—
45C2×#6101—22no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6101—22no—
49C2×#6101—21no—
50C2×C4×Dic13—21no—
51C22×#1055—22no—
52C13×C4⋊C8—22no—
53C13×C22⋊C8—22no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8D414yes—
56C13×#97—22no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62C22⋊#1055—22no—
63C22⋊#1055—22no—
64#9110—131nomaximal, Sylow
65C24×C13C22⋊C411yescharacteristic
66C24×C13C22×C411yescharacteristic
67C2×D4×C13—22no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—22no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D412yes—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4112yes—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—22no—
85C22×Dic13—21no—
86C22×Dic13—22no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—22no—
90C22×Dic13—81no—
91C22×Dic13M1612yescomplemented
92C13×M16—82no—
93C2×C8×C13—24no—
94C2×C8×C13—82no—
95C13×C4⋊C4—22no—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C42×C13—21no—
99C42×C13—21no—
100C22⋊Dic13—24no—
101C22⋊Dic13—21no—
102C22⋊Dic13—22no—
103C22⋊Dic13—81no—
104C22⋊Dic13M1612yescomplemented
105#6101—24no—
106#6101—41no—
107#6101—42no—
108#6101—41no—
109#6101—81no—
110C4×Dic13—81no—
111C2×#1055—42no—
112C2×#1055—82no—
113#2973D1311yescharacteristic
114#2322—131no—
115#1459—131no—
116C2×#324—132no—
117#1282—132no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13C4×D412yes—
127C23×C13C2×M1611yescharacteristic
128C23×C13C2×M1611yescharacteristic
129C23×C13#13112yes—
130D4×C13—42no—
131D4×C13—42no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—81no—
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13#12112yes—
147C2×C4×C13#12311yescharacteristic
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—24no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—42no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—82no—
163C8×C13—44no—
164#1055—82no—
165C2×#123—131no—
166C2×C4×D4C2×D1311yescharacteristic
167C22×C4⋊C4—131no—
168#435—24no—
169#432—21no—
170#407—21no—
171C2×C22⋊C8—132no—
172C2×C22⋊C8C2×D1312yes—
173#389—261no—
174#388—261no—
175#387—261no—
176#386—131no—
177#385—131no—
178#385—261no—
179#381—131no—
180C4×C22⋊C4—131no—
181#324—261no—
182#324—264no—
183#323—261no—
184C22×C13—21no—
185C22×C13—22no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—81no—
196C22×C13#38611yescharacteristic
197C22×C13#40711yescharacteristic
198C22×C13#40811yescharacteristic
199C22×C13#43512yes—
200C22×C13#43612yes—
201C4×C13—22no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—41no—
207Dic13—42no—
208Dic13—42no—
209Dic13—81no—
210Dic13—81no—
211C22×D4C4×D1311yescharacteristic
212C23×C4—131no—
213C23×C4—131no—
214C23×C4C22⋊D1311yescharacteristic
215C23×C4C22×D1311yescharacteristic
216C2×M16—22no—
217C22×C8—22no—
218C22×C8—262no—
219#123—262no—
220#123—262no—
221C4×D4—22no—
222C4×D4—22no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—262no—
226C2×C4⋊C4—262no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4D5211yescharacteristic
230C2×C22⋊C4—131no—
231C2×C22⋊C4—131no—
232C2×C22⋊C4—261no—
233C2×C22⋊C4—261no—
234C2×C22⋊C4C4×D1311yescharacteristic
235C2×C22⋊C4D5211yescharacteristic
236C2×C42—261no—
237C2×C42C22⋊D1311yescharacteristic
238C4⋊C8—22no—
239C22⋊C8—22no—
240C22⋊C8—22no—
241C22⋊C8—262no—
242C22⋊C8—262no—
243C22⋊C8C22⋊D1314yes—
244#97—22no—
245#95—261no—
246#95—261no—
247#95—261no—
248#95—261no—
249#95—261no—
250C2×C13—21no—
251C2×C13—21no—
252C2×C13—22no—
253C2×C13—22no—
254C2×C13—81no—
255C2×C13#187011yescharacteristic
256C2×C13#191311yescharacteristic
257C2×C13#191511yescharacteristic
258C24#610311yescharacteristic
259C24C2×C4×D1311yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—22no—
263C2×D4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—81no—
267C22×C4—81no—
268C22×C4—132no—
269C22×C4—261no—
270C22×C4—262no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—262no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4—262no—
277C22×C4—1041no—
278C22×C4#610311yescharacteristic
279C22×C4#610311yescharacteristic
280C22×C4#610311yescharacteristic
281C22×C4C2×D5211yescharacteristic
282C22×C4#612712yes—
283C22×C4C2×C22⋊D1311yescharacteristic
284C22×C4C2×C22⋊D1312yes—
285M16—82no—
286C2×C8—24no—
287C2×C8—82no—
288C2×C8—522no—
289C2×C8—1042no—
290C4⋊C4—22no—
291C4⋊C4—264no—
292C4⋊C4—521no—
293C4⋊C4—522no—
294C4⋊C4—521no—
295C4⋊C4—1041no—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—132no—
299C22⋊C4—264no—
300C22⋊C4—261no—
301C22⋊C4—262no—
302C22⋊C4—1041no—
303C42—21no—
304C42—21no—
305C42—1041no—
306C13#911011yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23M16×D1311yescharacteristic
315C23M16×D1311yescharacteristic
316C23#8816112yes—
317C23C2×#610311yescharacteristic
318C23C4×C22⋊D1312yes—
319D4—42no—
320D4—42no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—262no—
335C2×C4—262no—
336C2×C4—264no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—522no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—521no—
347C2×C4—521no—
348C2×C4—1042no—
349C2×C4#8818311yescharacteristic
350C2×C4#8818412yes—
351C2×C4#8820711yescharacteristic
352C8—44no—
353C8—1042no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—42no—
361C22—42no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—81no—
366C22#1171878711yescharacteristic
367C22#1171878812yes—
368C22#1171878912yes—
369C22#1171879011yescharacteristic
370C22#1171887411yescharacteristic
371C4—21no—
372C4—22no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—522no—
378C4—522no—
379C4—1041no—
380C4—1041no—
381C2—21no—
382C2—21no—
383C2—22no—
384C2—22no—
385C2—81no—
386C2#1311513311yescharacteristic
387C2#1311537811yescharacteristic
388C2#1311538811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2973C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#2973D13
hypocenterC13#9110
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
3. C2×#11718061C2semidirect
4. #13112682C2semidirect
91. C22×Dic13M16semidirect
104. C22⋊Dic13M16semidirect
306. C13#9110semidirect

Maximal subgroups

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

subgroupindex
#131175012
#131131542
C2×#117180612
#131126822
C13×#29732
#911013