Finite Group Databasebeta

← #15773380

Subgroups — #15773380

Order 3328.

500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114569C211yesmaximal, characteristic, complemented
2#13113170C211yesmaximal, characteristic, complemented
3#13112860C212yesmaximal, complemented
4#13112833C212yesmaximal
5C13×#2598C211yesmaximal, characteristic
6C2×C4×D4×C13C411yescharacteristic, complemented
7C2×C13×#117C2211yescharacteristic
8C2×#88180—21no—
9C13×#400C411yescharacteristic, complemented
10C13×#399C2211yescharacteristic
11C13×#394C411yescharacteristic, complemented
12C13×#392C2211yescharacteristic
13C13×#388—21no—
14C13×#386—21no—
15C13×#386—21no—
16C13×#385—21no—
17C13×#383C411yescharacteristic, complemented
18#11718587—21no—
19#11718120—21no—
20#11718118—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13—21no—
26C23×C4×C13D411yescharacteristic
27C4×D4×C13—41no—
28C4×D4×C13—41no—
29C13×#117—41no—
30C13×#117—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C13×C22⋊C4C2311yescharacteristic
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C22⋊Dic13—22no—
45#88180—24no—
46#88180—42no—
47C2×C4⋊Dic13—41no—
48C2×C4×Dic13—41no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95C2×C411yescharacteristic
54C13×#95C2×C411yescharacteristic
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57#88043—41no—
58#11754—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13C2×D411yescharacteristic
61C2×D4×C13—41no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—81no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—22no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—42no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—42no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—81no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—81no—
96C13×C22⋊C4—81no—
97C42×C13—21no—
98C42×C13—21no—
99C42×C13—21no—
100C42×C13—21no—
101C22⋊Dic13—24no—
102C22⋊Dic13—42no—
103C4⋊Dic13—44no—
104C4×Dic13—44no—
105C2×#1055—42no—
106#2598D1311yescharacteristic
107#1740—131no—
108#1464—131no—
109#1352—132no—
110#1343—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—22no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13C2×C22⋊C411yescharacteristic
123C23×C13AGL(1,ℤ/8)11yescharacteristic
124C23×C13#13711yescharacteristic
125D4×C13—42no—
126D4×C13—42no—
127D4×C13—82no—
128D4×C13—82no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
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×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—84no—
155C2×C4×C13#9911yescharacteristic
156C2×C4×C13#9911yescharacteristic
157C2×C4×C13#10412yes—
158C2×Dic13—44no—
159C2×Dic13—82no—
160C2×Dic13—82no—
161#1055—82no—
162C2×C4×D4Dic1311yescharacteristic, complemented
163C2×#117—261no—
164C2×#117C2×D1311yescharacteristic
165#432—261no—
166#400Dic1311yescharacteristic, complemented
167#399C2×D1311yescharacteristic
168#394Dic1311yescharacteristic, complemented
169#392C2×D1311yescharacteristic
170#388—21no—
171#386—21no—
172#386—21no—
173#385—21no—
174#383Dic1311yescharacteristic, complemented
175#342—132no—
176#342—261no—
177#324—261no—
178#323—132no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—42no—
190C22×C13—81no—
191C22×C13—81no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13C2×#9911yescharacteristic
196C22×C13#41711yescharacteristic
197C22×C13C2×#10411yescharacteristic
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—22no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—81no—
206C4×C13—81no—
207C4×C13—81no—
208Dic13—84no—
209C22×D4—21no—
210C22×D4C2×Dic1311yescharacteristic
211C23×C4—21no—
212C23×C4C22⋊D1311yescharacteristic
213C4×D4—41no—
214C4×D4—41no—
215#117—41no—
216#117—41no—
217#117—264no—
218#117—522no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—521no—
221C2×C4⋊C4C2×Dic1311yescharacteristic
222C2×C4⋊C4C2×Dic1311yescharacteristic
223C2×C4⋊C4C22⋊D1311yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—262no—
230C2×C22⋊C4C22⋊D1311yescharacteristic
231C2×C22⋊C4C22×D1311yescharacteristic
232C2×C42—521no—
233C2×C42C2×Dic1311yescharacteristic
234C2×C42C22⋊D1311yescharacteristic
235C4⋊C8—521no—
236C22⋊C8—262no—
237#97—521no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95C2×Dic1311yescharacteristic
243#95C2×Dic1311yescharacteristic
244C2×C13—21no—
245C2×C13—21no—
246C2×C13—41no—
247C2×C13—41no—
248C2×C13—82no—
249C2×C13#150411yescharacteristic
250C2×C13#212011yescharacteristic
251C2×C13#212811yescharacteristic
252C24—21no—
253C24C2×C22⋊D1311yescharacteristic
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—81no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—81no—
270C22×C4—81no—
271C22×C4—522no—
272C22×C4C22⋊Dic1311yescharacteristic
273C22×C4C22⋊Dic1311yescharacteristic
274C22×C4C22⋊Dic1311yescharacteristic
275C22×C4C22⋊Dic1311yescharacteristic
276C22×C4C22×Dic1311yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278C2×C8—522no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—524no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—264no—
293C22⋊C4—522no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—524no—
299C13#1175411yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—22no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23#8820311yescharacteristic
312C23#8820511yescharacteristic
313C23C2×C22⋊Dic1311yescharacteristic
314D4—42no—
315D4—42no—
316D4—82no—
317D4—82no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—84no—
344C2×C4—524no—
345C2×C4—1042no—
346C2×C4—1042no—
347C2×C4#8807411yescharacteristic
348C2×C4#8807411yescharacteristic
349C2×C4#8807712yes—
350C8—1042no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—42no—
358C22—42no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22C2×#8807411yescharacteristic
368C22#1171889311yescharacteristic
369C22C2×#8807711yescharacteristic
370C4—21no—
371C4—21no—
372C4—22no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—1044no—
381C2—21no—
382C2—21no—
383C2—41no—
384C2—41no—
385C2—82no—
386C2#1311334011yescharacteristic
387C2#1311647711yescharacteristic
388C2#1311650811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2598C2
socleC22×C13C2×#99
prime radicalC13×#392C22
cosocleC2×C13×C22⋊C4C23
hypercenter#2598D13
hypocenterC13#11754
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2598

Complements

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

NH ≅ G/Ntype
1. #13114569C2semidirect
2. #13113170C2semidirect
3. #13112860C2semidirect
6. C2×C4×D4×C13C4semidirect
9. C13×#400C4semidirect
11. C13×#394C4semidirect
17. C13×#383C4semidirect
162. C2×C4×D4Dic13semidirect
166. #400Dic13semidirect
168. #394Dic13semidirect
174. #383Dic13semidirect
299. C13#11754semidirect

Maximal subgroups

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

subgroupindex
#131145692
#131131702
#131128602
#131128332
C13×#25982
#1175413