Finite Group Databasebeta

← #15760386

Subgroups — #15760386

Order 3328.

552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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#13120317C211yesmaximal, characteristic
2#13117436C211yesmaximal, characteristic, complemented
3#13113352C211yesmaximal, characteristic
4#13113165C211yesmaximal, characteristic, complemented
5#13112722C211yesmaximal, characteristic, complemented
6#13112721C211yesmaximal, characteristic, complemented
7C13×#1507C211yesmaximal, characteristic
8C2×C13×#121C2211yescharacteristic
9C22×#6101C2211yescharacteristic
10C13×#407C2211yescharacteristic
11C4×C13×C22⋊C4C2211yescharacteristic
12#11718883C412yescomplemented
13#11718881—21no—
14#11718881—21no—
15C4×C22⋊Dic13C2211yescharacteristic
16C4×C22⋊Dic13C2211yescharacteristic
17#11718868C2211yescharacteristic
18#11718643C412yescomplemented
19#11718606—22no—
20#11718604—21no—
21#11718603—21no—
22#11718594—22no—
23#11718313—22no—
24C13×#327—22no—
25#11718129—22no—
26#11718061—22no—
27C22×D4×C13—21no—
28C22×D4×C13C2×C411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C23×Dic13D411yescharacteristic
31C23×Dic13D411yescharacteristic
32C2×C13×M16—21no—
33C13×#121—21no—
34C13×#121—21no—
35C13×#121—21no—
36C13×#121—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13—21no—
41C2×C22⋊Dic13—21no—
42C2×C22⋊Dic13—21no—
43C2×C22⋊Dic13—22no—
44C2×C22⋊Dic13—22no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6101—21no—
49C2×#6101—22no—
50C2×#6101C2×C412yes—
51C2×#6101D412yes—
52C2×C4×Dic13—21no—
53C2×C4×Dic13—21no—
54C2×#6099—21no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×#95D412yes—
58#88071—22no—
59#88071—24no—
60#88071—22no—
61#88071—22no—
62#88071C2×C412yes—
63#88071D412yes—
64C22⋊#1055—21no—
65C22⋊#1055—21no—
66#9414—131nomaximal, Sylow
67C24×C13—21no—
68C24×C13C2×D411yescharacteristic
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—44no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—81no—
75C22×C4×C13—21no—
76C22×C4×C13—22no—
77C22×C4×C13—81no—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13#4111yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—22no—
89C22×Dic13—22no—
90C22×Dic13—42no—
91C22×Dic13—81no—
92C22×Dic13C22⋊C412yes—
93C22×Dic13C22⋊C412yes—
94C13×M16—81no—
95C2×C8×C13—41no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C42×C13—81no—
102C22⋊Dic13—44no—
103C22⋊Dic13—42no—
104C22⋊Dic13—42no—
105C22⋊Dic13—82no—
106#6101—22no—
107#6101—22no—
108#6101—22no—
109#6101—22no—
110#6101—82no—
111C4×Dic13—81no—
112C4×Dic13—81no—
113#6099—81no—
114C2×#1055—41no—
115#2591—131no—
116#2313—131no—
117#1507—131no—
118#1507D1311yescharacteristic
119#1463—131no—
120#1297—131no—
121#1297—131no—
122C23×C13—22no—
123C23×C13—22no—
124C23×C13—41no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—41no—
128C23×C13—42no—
129C23×C13C2×C22⋊C411yescharacteristic
130C23×C13#12011yescharacteristic
131C23×C13#12311yescharacteristic
132D4×C13—81no—
133D4×C13—81no—
134D4×C13—82no—
135D4×C13—82no—
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—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—41no—
146C2×C4×C13—42no—
147C2×C4×C13C4×D411yescharacteristic
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13—42no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—81no—
166C8×C13—81no—
167#1055—81no—
168C2×#121C2×D1311yescharacteristic
169C22×C4⋊C4—131no—
170#407—131no—
171#407C2×D1311yescharacteristic
172#400—132no—
173#394—132no—
174#388—262no—
175#387—262no—
176#387—262no—
177#386—261no—
178#386—261no—
179#381—261no—
180#380—261no—
181C4×C22⋊C4—131no—
182C4×C22⋊C4—131no—
183C4×C22⋊C4C2×D1311yescharacteristic
184#327—22no—
185#327—262no—
186#324—262no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—44no—
195C22×C13—84no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13#38611yescharacteristic
200C22×C13#42112yes—
201C22×C13#45412yes—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—82no—
207C4×C13—81no—
208Dic13—42no—
209Dic13—42no—
210Dic13—82no—
211Dic13—82no—
212C22×D4—21no—
213C22×D4C4×D1311yescharacteristic
214C23×C4—131no—
215C23×C4—131no—
216C23×C4C22×D1311yescharacteristic
217C2×M16—21no—
218C2×M16—261no—
219#121—21no—
220#121—21no—
221#121—21no—
222#121—21no—
223C2×C4⋊C4—132no—
224C2×C4⋊C4—132no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—261no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4—262no—
230C2×C4⋊C4C4×D1311yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—262no—
234C2×C22⋊C4—261no—
235C2×C22⋊C4—261no—
236C2×C22⋊C4—262no—
237C2×C42—21no—
238C2×C42—261no—
239C2×C42—261no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—261no—
243C22⋊C8—261no—
244#95—132no—
245#95—132no—
246#95—262no—
247#95—262no—
248#95—262no—
249#95—264no—
250#95C22⋊D1312yes—
251C2×C13—22no—
252C2×C13—22no—
253C2×C13—41no—
254C2×C13—161no—
255C2×C13#188811yescharacteristic
256C2×C13#189711yescharacteristic
257C2×C13#191311yescharacteristic
258C24—21no—
259C24D4×D1311yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—44no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—81no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—81no—
269C22×C4—132no—
270C22×C4—132no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4—262no—
276C22×C4—262no—
277C22×C4—522no—
278C22×C4—1041no—
279C22×C4C2×C4×D1311yescharacteristic
280C22×C4#612711yescharacteristic
281C22×C4D4×D1311yescharacteristic
282C22×C4D4×D1311yescharacteristic
283C22×C4#612911yescharacteristic
284C22×C4C2×C22⋊D1311yescharacteristic
285M16—81no—
286M16—1041no—
287C2×C8—41no—
288C2×C8—521no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—1042no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—524no—
300C22⋊C4—522no—
301C22⋊C4—522no—
302C22⋊C4—1042no—
303C42—81no—
304C42—1041no—
305C42—1041no—
306C13#941411yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—41no—
310C23—42no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23C22⋊C4×D1311yescharacteristic
315C23#8813711yescharacteristic
316C23#8819111yescharacteristic
317D4—81no—
318D4—81no—
319D4—82no—
320D4—82no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—262no—
333C2×C4—262no—
334C2×C4—262no—
335C2×C4—262no—
336C2×C4—522no—
337C2×C4—522no—
338C2×C4—522no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—1041no—
347C2×C4#8813511yescharacteristic
348C2×C4#8813811yescharacteristic
349C2×C4C4×C22⋊D1311yescharacteristic
350C2×C4#8819211yescharacteristic
351C8—81no—
352C8—1041no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—84no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22#1171848212yes—
366C22#1171861711yescharacteristic
367C22#1171886212yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—81no—
374C4—522no—
375C4—522no—
376C4—1042no—
377C4—1042no—
378C2—22no—
379C2—22no—
380C2—41no—
381C2—161no—
382C2#1311523611yescharacteristic
383C2#1311528111yescharacteristic
384C2#1311537511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1507C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#1507D13
hypocenterC13#9414
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #13117436C2semidirect
4. #13113165C2semidirect
5. #13112722C2semidirect
6. #13112721C2semidirect
12. #11718883C4semidirect
18. #11718643C4semidirect
306. C13#9414semidirect

Maximal subgroups

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

subgroupindex
#131203172
#131174362
#131133522
#131131652
#131127222
#131127212
C13×#15072
#941413