Finite Group Databasebeta

← #15760574

Subgroups — #15760574

Order 3328.

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

normal subgroups only

This group has 516 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, complemented
2#13114913C211yesmaximal, characteristic, complemented
3#13113365C212yesmaximal
4#13112689C212yesmaximal, complemented
5C13×#2500C211yesmaximal, characteristic
6C2×C13×#121C2211yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#394—21no—
9C13×#394—21no—
10C13×#390C411yescharacteristic, complemented
11C13×#390C411yescharacteristic, complemented
12C13×#388—21no—
13C13×#388—21no—
14C13×#384C411yescharacteristic, complemented
15C13×#382C411yescharacteristic, complemented
16C4×C13×C22⋊C4C2211yescharacteristic
17#11718872C2212yes—
18#11718868C2212yes—
19#11718661—24no—
20#11718585—21no—
21C4×#6099—21no—
22#11718129—24no—
23#11718118—21no—
24#11718118—21no—
25C22×D4×C13—21no—
26C22×D4×C13C2×C411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C13×#121—22no—
29C13×#121—22no—
30C13×#117—22no—
31C13×#117—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C42×C13C2×C411yescharacteristic
46C2×C42×C13C2×C411yescharacteristic
47C2×C42×C13D411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C22⋊Dic13—22no—
50C2×#6099—22no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54#88071—22no—
55#88071—22no—
56C22⋊#1055—22no—
57C22⋊#1055D414yes—
58C4⋊#1055—24no—
59#88043—22no—
60C4×#1055—22no—
61#9446—131nomaximal, Sylow
62C24×C13—21no—
63C24×C13C2×D411yescharacteristic
64C2×D4×C13—22no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C2×D4×C13—42no—
68C2×D4×C13—81no—
69C2×D4×C13—81no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13#4112yes—
83C22×Dic13—42no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—81no—
88C13×C4⋊C4—81no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—81no—
97C13×C22⋊C4—81no—
98C42×C13—21no—
99C42×C13—21no—
100C42×C13—21no—
101C42×C13—21no—
102C42×C13—41no—
103C42×C13—41no—
104C22⋊Dic13—42no—
105C22⋊Dic13—42no—
106#6099—42no—
107#6099—42no—
108C2×#1055—24no—
109#2921—131no—
110#2500D1311yescharacteristic
111#1820—131no—
112#1510—132no—
113#1284—132no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13#12112yes—
127D4×C13—82no—
128D4×C13—84no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—22no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13C4×D412yes—
153C2×C4×C13#12011yescharacteristic
154C2×C4×C13#12311yescharacteristic
155C2×Dic13—82no—
156C2×Dic13—82no—
157C2×Dic13—82no—
158#1055—44no—
159C2×#121C2×D1311yescharacteristic
160C2×#117C2×D1311yescharacteristic
161#433—264no—
162#423—261no—
163#407—132no—
164C4×M16—261no—
165#394—21no—
166#394—21no—
167#390Dic1311yescharacteristic, complemented
168#390Dic1311yescharacteristic, complemented
169#388—21no—
170#388—21no—
171#384Dic1311yescharacteristic, complemented
172#382Dic1311yescharacteristic, complemented
173#381—132no—
174C4×C22⋊C4C2×D1311yescharacteristic
175#342—261no—
176#342—261no—
177#327—264no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13#38611yescharacteristic
193C22×C13#41011yescharacteristic
194C22×C13#41011yescharacteristic
195C4×C13—21no—
196C4×C13—22no—
197C4×C13—21no—
198C4×C13—42no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—81no—
204C4×C13—81no—
205Dic13—162no—
206C22×D4—21no—
207C22×D4C2×Dic1311yescharacteristic
208C23×C4C22×D1311yescharacteristic
209C2×M16—262no—
210#121—22no—
211#121—22no—
212#117—22no—
213#117—22no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C2×Dic1311yescharacteristic
217C2×C4⋊C4C2×Dic1311yescharacteristic
218C2×C4⋊C4C2×Dic1311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—262no—
226C2×C22⋊C4C22⋊D1311yescharacteristic
227C2×C22⋊C4C22⋊D1311yescharacteristic
228C2×C42C2×Dic1311yescharacteristic
229C2×C42C2×Dic1311yescharacteristic
230C2×C42C22⋊D1311yescharacteristic
231C2×C42C22⋊D1311yescharacteristic
232C4⋊C8—264no—
233C22⋊C8—134no—
234C22⋊C8—262no—
235#97—262no—
236C4×C8—262no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—262no—
241#95—262no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—42no—
245C2×C13—161no—
246C2×C13#188411yescharacteristic
247C2×C13#189911yescharacteristic
248C2×C13#191011yescharacteristic
249C24—21no—
250C24C2×C22⋊D1311yescharacteristic
251C2×D4—22no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—42no—
255C2×D4—81no—
256C2×D4—81no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—522no—
263C22×C4C22⋊Dic1311yescharacteristic
264C22×C4C22⋊Dic1311yescharacteristic
265C22×C4C22⋊Dic1311yescharacteristic
266C22×C4C22⋊Dic1311yescharacteristic
267C22×C4D4×D1312yes—
268C22×C4#612912yes—
269C22×C4C22×Dic1311yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271M16—522no—
272M16—522no—
273C2×C8—264no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—81no—
287C22⋊C4—81no—
288C22⋊C4—522no—
289C22⋊C4—522no—
290C42—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—41no—
295C42—41no—
296C13#944611yescharacteristic, complemented, Sylow
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23#8819312yes—
309C23C2×C22⋊Dic1311yescharacteristic
310D4—82no—
311D4—84no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—1042no—
336C2×C4—1042no—
337C2×C4—1042no—
338C2×C4D4×Dic1312yes—
339C2×C4#8818911yescharacteristic
340C2×C4#8819111yescharacteristic
341C8—524no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22#1171888111yescharacteristic
357C22#1171890111yescharacteristic
358C22#1171890111yescharacteristic
359C4—21no—
360C4—22no—
361C4—21no—
362C4—42no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—81no—
368C4—81no—
369C4—2082no—
370C2—21no—
371C2—21no—
372C2—42no—
373C2—161no—
374C2#1311522011yescharacteristic
375C2#1311529511yescharacteristic
376C2#1311536411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2500C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2500D13
hypocenterC13#9446
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2500

Complements

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

NH ≅ G/Ntype
1. #13123474C2semidirect
2. #13114913C2semidirect
4. #13112689C2semidirect
10. C13×#390C4semidirect
11. C13×#390C4semidirect
14. C13×#384C4semidirect
15. C13×#382C4semidirect
167. #390Dic13semidirect
168. #390Dic13semidirect
171. #384Dic13semidirect
172. #382Dic13semidirect
296. C13#9446semidirect

Maximal subgroups

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

subgroupindex
#131234742
#131149132
#131133652
#131126892
C13×#25002
#944613