Finite Group Databasebeta

← #15758669

Subgroups — #15758669

Order 3328.

1088 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 147 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#13123118C211yesmaximal, characteristic
2#13114746C211yesmaximal, characteristic, complemented
3C2×#11718043C212yesmaximal, complemented
4#13112715C212yesmaximal, complemented
5C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
6C24×C4×C13C2211yescharacteristic
7C22×C13×C22⋊C4—21no—
8C22×C42×C13—21no—
9C2×#88207—21no—
10C2×#88184C412yescomplemented
11C2×#88184C2211yescharacteristic
12C4×C13×C22⋊C4—24no—
13C2×C13×#95C2212yes—
14#11718874—21no—
15#11718874—22no—
16#11718873C412yescomplemented
17#11718873C2211yescharacteristic
18C2×C22⋊#1055—22no—
19C2×C22⋊#1055C2212yes—
20#11718043—24no—
21C25×C13D411yescharacteristic
22C23×C4×C13—22no—
23C23×C4×C13—22no—
24C23×C4×C13—22no—
25C23×C4×C13—44no—
26C23×C4×C13C2×C412yes—
27C23×C4×C13D412yes—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C22×C22⋊D13—22no—
31C22×C22⋊D13—21no—
32C22×D52C2×C411yescharacteristic
33C2×C13×C22⋊C4—24no—
34C2×C13×C22⋊C4—28no—
35C2×C42×C13—24no—
36C2×C42×C13—44no—
37#88207—44no—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—21no—
40#88184—22no—
41#88184—22no—
42#88184—44no—
43C2×#6103—22no—
44C2×#6103—21no—
45C2×C4⋊Dic13C2×C411yescharacteristic
46C2×C4⋊Dic13C2×C412yes—
47C22×#1055—22no—
48C13×#95—22no—
49C13×#95D414yescomplemented
50#88071—22no—
51#88071—21no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54C22⋊#1055—44no—
55#9150—131nomaximal, Sylow
56C24×C13—24no—
57C24×C13—21no—
58C24×C13—21no—
59C24×C13—22no—
60C24×C13—22no—
61C24×C13—42no—
62C24×C13C22⋊C412yes—
63C24×C13C2×D411yescharacteristic
64C23×D13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—24no—
68C22×C4×C13—28no—
69C22×C4×C13—24no—
70C22×C4×C13—24no—
71C22×C4×C13—24no—
72C22×C4×C13—24no—
73C22×C4×C13—24no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13—48no—
78C22×C4×C13—48no—
79C22×C4×C13—44no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13C22⋊C412yes—
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D412yes—
86C22×C4×C13#4112yes—
87C2×C22⋊D13—44no—
88C2×C22⋊D13—44no—
89C2×C22⋊D13—44no—
90C2×C22⋊D13—41no—
91C2×C22⋊D13—41no—
92C2×C22⋊D13—42no—
93C2×C22⋊D13—42no—
94C22×Dic13—21no—
95C22×Dic13—22no—
96C2×D52—22no—
97C2×D52—42no—
98C13×C22⋊C4—216no—
99C42×C13—48no—
100C22⋊Dic13—44no—
101C22⋊Dic13—42no—
102#6103—44no—
103#6103—42no—
104C4⋊Dic13—22no—
105C4⋊Dic13—42no—
106C2×#1055—44no—
107C2×#1055—42no—
108#2847—131no—
109C2×C4×C22⋊C4D1311yescharacteristic, complemented
110#1779—131no—
111C2×#327—132no—
112#1294—132no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—24no—
116C23×C13—24no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—48no—
124C23×C13—48no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13#10414yes—
130C23×C13C2×C22⋊C411yescharacteristic
131C23×C13#12011yescharacteristic
132C23×C13#12311yescharacteristic
133C23×C13#13512yes—
134C23×C13AGL(1,ℤ/8)12yes—
135C22×D13—41no—
136C22×D13—42no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—42no—
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—28no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—48no—
150C2×C4×C13—48no—
151C2×C4×C13—44no—
152C2×C4×C13—48no—
153C2×C4×C13—48no—
154C2×C4×C13—44no—
155C2×C4×C13#9914yes—
156C2×C4×C13C4×D412yes—
157C2×C4×C13#12112yes—
158C22⋊D13—88no—
159C22⋊D13—82no—
160C22⋊D13—82no—
161C2×Dic13—41no—
162C2×Dic13—42no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—42no—
166C2×Dic13—42no—
167D52—82no—
168#1055—82no—
169C24×C4C2×D1311yescharacteristic
170C2×#121—131no—
171C2×#121—132no—
172C2×#120—261no—
173C22×C22⋊C4—21no—
174C22×C42—21no—
175C2×C22⋊C8—132no—
176C2×C22⋊C8—262no—
177#386—262no—
178#386—261no—
179#380—132no—
180#380—131no—
181C4×C22⋊C4—24no—
182C2×#95C2×D1312yes—
183#327—264no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—24no—
189C22×C13—24no—
190C22×C13—24no—
191C22×C13—24no—
192C22×C13—24no—
193C22×C13—48no—
194C22×C13—48no—
195C22×C13—42no—
196C22×C13—42no—
197C22×C13—42no—
198C22×C13—42no—
199C22×C13#38611yescharacteristic
200C22×C13C2×#9912yes—
201C22×C13#41611yescharacteristic
202C22×C13#41811yescharacteristic
203C22×C13C2×#10412yes—
204C22×C13#44912yes—
205C22×C13#48212yes—
206C2×D13—81no—
207C2×D13—81no—
208C2×D13—81no—
209C2×D13—82no—
210C2×D13—82no—
211C4×C13—22no—
212C4×C13—22no—
213C4×C13—24no—
214C4×C13—48no—
215Dic13—81no—
216Dic13—82no—
217C25C22⋊D1311yescharacteristic
218C22×D4—131no—
219C22×D4—262no—
220C22×D4—261no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—44no—
225C23×C4C4×D1312yes—
226C23×C4D5212yes—
227C23×C4C22⋊D1311yescharacteristic
228C23×C4C22×D1311yescharacteristic
229C22×C8—262no—
230#121—262no—
231#121—262no—
232#121—524no—
233#120—524no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—132no—
236C2×C22⋊C4—24no—
237C2×C22⋊C4—28no—
238C2×C22⋊C4—262no—
239C2×C22⋊C4—261no—
240C2×C22⋊C4—262no—
241C2×C22⋊C4—261no—
242C2×C42—24no—
243C2×C42—44no—
244C22⋊C8—262no—
245C22⋊C8—262no—
246C22⋊C8—524no—
247#95—22no—
248#95—262no—
249#95—261no—
250#95C22⋊D1314yescomplemented
251C2×C13—22no—
252C2×C13—22no—
253C2×C13—44no—
254C2×C13#150112yes—
255C2×C13#150712yes—
256C2×C13#187511yescharacteristic
257C2×C13#189611yescharacteristic
258C2×C13#189811yescharacteristic
259D13—161no—
260C24—21no—
261C24—21no—
262C24—24no—
263C24—22no—
264C24—22no—
265C24—42no—
266C24—261no—
267C24#610312yes—
268C24C2×C22⋊D1311yescharacteristic
269C2×D4—262no—
270C2×D4—522no—
271C2×D4—524no—
272C2×D4—524no—
273C2×D4—521no—
274C2×D4—522no—
275C2×D4—522no—
276C2×D4—521no—
277C2×D4—524no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—24no—
281C22×C4—28no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—48no—
291C22×C4—48no—
292C22×C4—44no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—261no—
296C22×C4—262no—
297C22×C4#610312yes—
298C22×C4C2×C4×D1311yescharacteristic
299C22×C4C2×D5211yescharacteristic
300C22×C4#612712yes—
301C22×C4C2×C22⋊D1312yes—
302C2×C8—524no—
303C2×C8—522no—
304C4⋊C4—262no—
305C4⋊C4—522no—
306C22⋊C4—216no—
307C22⋊C4—524no—
308C22⋊C4—522no—
309C22⋊C4—522no—
310C22⋊C4—524no—
311C42—48no—
312C13#915011yescharacteristic, complemented, Sylow
313C23—22no—
314C23—22no—
315C23—24no—
316C23—24no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—48no—
324C23—48no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23—521no—
330C23—521no—
331C23—522no—
332C23—522no—
333C23—521no—
334C23#8804514yes—
335C23C2×#610311yescharacteristic
336C23#8818311yescharacteristic
337C23#8820312yes—
338C23#8820412yes—
339C23#8820711yescharacteristic
340D4—1042no—
341D4—1048no—
342D4—1042no—
343D4—1042no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—28no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—48no—
354C2×C4—48no—
355C2×C4—44no—
356C2×C4—48no—
357C2×C4—48no—
358C2×C4—44no—
359C2×C4—522no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—521no—
365C2×C4#8804614yes—
366C2×C4C4×C22⋊D1312yes—
367C2×C4#8818412yes—
368C8—1042no—
369C22—24no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—24no—
375C22—24no—
376C22—24no—
377C22—24no—
378C22—48no—
379C22—48no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—1042no—
385C22—1041no—
386C22—1041no—
387C22—1041no—
388C22—1042no—
389C22C2×#8804512yes—
390C22C2×#8804612yes—
391C22#1171866211yescharacteristic
392C22#1171866311yescharacteristic
393C22#1171866412yes—
394C22#1171887411yescharacteristic
395C22#1171889912yes—
396C4—22no—
397C4—24no—
398C4—22no—
399C4—48no—
400C4—1042no—
401C4—1041no—
402C2—22no—
403C2—22no—
404C2—44no—
405C2—2081no—
406C2#1311332512yes—
407C2#1311335112yes—
408C2#1311515811yescharacteristic
409C2#1311527911yescharacteristic
410C2#1311528911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C4×C13×C22⋊C4C2
socleC23×C13C2×C22⋊C4
prime radical#13123118C2
cosocleC23×C4×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#9150
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13114746C2semidirect
3. C2×#11718043C2semidirect
4. #13112715C2semidirect
5. C2×C4×C13×C22⋊C4C2semidirect
10. C2×#88184C4semidirect
16. #11718873C4semidirect
49. C13×#95D4semidirect
109. C2×C4×C22⋊C4D13semidirect
250. #95C22⋊D13semidirect
312. C13#9150semidirect

Maximal subgroups

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

subgroupindex
#131231182
#131147462
C2×#117180432
#131127152
C2×C4×C13×C22⋊C42
#915013