Finite Group Databasebeta

← #15760704

Subgroups — #15760704

Order 3328.

912 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 912 conjugacy classes of subgroups — too many to draw. Only its 123 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#13123865C211yesmaximal, characteristic, complemented
2#13114824C211yesmaximal, characteristic, complemented
3#13114767C212yesmaximal, complemented
4#13112703C212yesmaximal, complemented
5C13×#2408C211yesmaximal, characteristic
6C23×D4×C13C2211yescharacteristic
7C2×C13×#121—21no—
8C2×C13×#120—21no—
9C2×C4×D4×C13C2211yescharacteristic
10C13×#394C412yescomplemented
11C13×#392C412yescomplemented
12C13×#390—21no—
13C13×#380C2211yescharacteristic
14C13×#379—21no—
15C2×#88074—21no—
16C2×#88072—24no—
17#11718873C2212yes—
18#11718868—21no—
19C2×C22⋊#1055C2212yes—
20#11718672—24no—
21#11718587—21no—
22#11718118—21no—
23C25×C13—21no—
24C22×D4×C13—22no—
25C22×D4×C13—22no—
26C22×D4×C13—21no—
27C22×D4×C13—22no—
28C22×D4×C13—44no—
29C22×D4×C13C2×C412yes—
30C22×D4×C13D411yescharacteristic
31C23×C4×C13D411yescharacteristic
32C23×C4×C13C2311yescharacteristic
33C13×#121—44no—
34C13×#120—44no—
35C4×D4×C13—22no—
36C4×D4×C13—22no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—22no—
43C2×C13×C22⋊C4C2×C411yescharacteristic
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C22⋊Dic13—22no—
47C2×C4⋊Dic13—22no—
48C2×#6099—22no—
49C22×#1055D414yescomplemented
50C13×#95C2×C412yes—
51#88074—42no—
52#88072—48no—
53#88071—22no—
54C22⋊#1055—22no—
55C22⋊#1055—22no—
56C22⋊#1055—22no—
57C4⋊#1055—22no—
58#88043—22no—
59#9472—131nomaximal, Sylow
60C24×C13—22no—
61C24×C13—44no—
62C24×C13—42no—
63C24×C13—42no—
64C24×C13—41no—
65C24×C13—41no—
66C24×C13—82no—
67C24×C13C22⋊C411yescharacteristic
68C24×C13C2×D411yescharacteristic
69C2×D4×C13—28no—
70C2×D4×C13—24no—
71C2×D4×C13—22no—
72C2×D4×C13—21no—
73C2×D4×C13—22no—
74C2×D4×C13—21no—
75C2×D4×C13—24no—
76C2×D4×C13—44no—
77C2×D4×C13—42no—
78C2×D4×C13—44no—
79C2×D4×C13—48no—
80C2×D4×C13—44no—
81C2×D4×C13—44no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—82no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—22no—
88C22×C4×C13—42no—
89C22×C4×C13—42no—
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C22×C411yescharacteristic
94C22×C4×C13C2×D412yes—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13#4112yes—
97C22×Dic13—42no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—42no—
100C13×C22⋊C4—22no—
101C13×C22⋊C4—22no—
102C13×C22⋊C4—44no—
103C13×C22⋊C4—44no—
104C13×C22⋊C4—42no—
105C13×C22⋊C4—82no—
106C42×C13—21no—
107C42×C13—21no—
108C22⋊Dic13—42no—
109C22⋊Dic13—42no—
110C4⋊Dic13—44no—
111#6099—82no—
112C2×#1055—24no—
113C2×#1055—44no—
114#2973—131no—
115#2408D1311yescharacteristic
116#1799—131no—
117#1786—132no—
118#1289—132no—
119C23×C13—24no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—42no—
128C23×C13—48no—
129C23×C13—42no—
130C23×C13—42no—
131C23×C13—42no—
132C23×C13—42no—
133C23×C13—42no—
134C23×C13—84no—
135C23×C13—88no—
136C23×C13—84no—
137C23×C13—84no—
138C23×C13—82no—
139C23×C13—82no—
140C23×C13C2×C22⋊C411yescharacteristic
141C23×C13#12112yes—
142C23×C13AGL(1,ℤ/8)11yescharacteristic
143C23×C13AGL(1,ℤ/8)12yes—
144C23×C13#13711yescharacteristic
145D4×C13—28no—
146D4×C13—44no—
147D4×C13—44no—
148D4×C13—42no—
149D4×C13—42no—
150D4×C13—44no—
151D4×C13—88no—
152C2×C4×C13—24no—
153C2×C4×C13—22no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—81no—
168C2×C4×C13C4×D412yes—
169C2×C4×C13#12011yescharacteristic
170C2×C4×C13#12311yescharacteristic
171C2×Dic13—82no—
172C2×Dic13—82no—
173C2×Dic13—82no—
174#1055—44no—
175C23×D4C2×D1311yescharacteristic
176C2×#121—21no—
177C2×#120—21no—
178C2×C4×D4C2×D1311yescharacteristic
179#435—264no—
180#432—261no—
181C2×#102—264no—
182C2×#99—261no—
183#407—261no—
184C2×C22⋊C8—132no—
185#394Dic1312yescomplemented
186#392Dic1312yescomplemented
187#390—21no—
188#380—132no—
189#380C2×D1311yescharacteristic
190#379—21no—
191#342—261no—
192C22×C13—22no—
193C22×C13—21no—
194C22×C13—22no—
195C22×C13—21no—
196C22×C13—42no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—42no—
200C22×C13—44no—
201C22×C13—44no—
202C22×C13—41no—
203C22×C13—44no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—81no—
207C22×C13—82no—
208C22×C13—82no—
209C22×C13—88no—
210C22×C13—88no—
211C22×C13—82no—
212C22×C13—82no—
213C22×C13#38611yescharacteristic
214C22×C13#41711yescharacteristic
215C22×C13#41811yescharacteristic
216C22×C13#46812yes—
217C22×C13#46912yes—
218C4×C13—21no—
219C4×C13—22no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—82no—
224C4×C13B(4,𝔽2)12yes—
225Dic13—162no—
226C25—21no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—44no—
232C22×D4C2×Dic1312yes—
233C22×D4C22⋊D1311yescharacteristic
234C23×C4C22⋊D1311yescharacteristic
235C23×C4C22×D1311yescharacteristic
236C2×M16—262no—
237C22×C8—134no—
238#121—44no—
239#120—44no—
240C4×D4—22no—
241C4×D4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—262no—
244C2×C4⋊C4C2×Dic1311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—262no—
250C2×C22⋊C4C2×Dic1311yescharacteristic
251C2×C22⋊C4C22⋊D1311yescharacteristic
252C2×C42C22⋊D1311yescharacteristic
253C4⋊C8—262no—
254#102—528no—
255#99—522no—
256C22⋊C8—262no—
257C22⋊C8—262no—
258C22⋊C8—262no—
259#97—262no—
260#95—262no—
261#95C2×Dic1312yes—
262C2×C13—22no—
263C2×C13—21no—
264C2×C13—21no—
265C2×C13—22no—
266C2×C13—81no—
267C2×C13—84no—
268C2×C13#188911yescharacteristic
269C2×C13#189511yescharacteristic
270C2×C13#191011yescharacteristic
271C24—22no—
272C24—44no—
273C24—42no—
274C24—42no—
275C24—41no—
276C24—41no—
277C24—82no—
278C24C22⋊Dic1311yescharacteristic
279C24C2×C22⋊D1311yescharacteristic
280C2×D4—28no—
281C2×D4—24no—
282C2×D4—22no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—24no—
287C2×D4—42no—
288C2×D4—44no—
289C2×D4—44no—
290C2×D4—48no—
291C2×D4—44no—
292C2×D4—44no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—82no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—522no—
302C22×C4C22⋊Dic1311yescharacteristic
303C22×C4C22⋊Dic1311yescharacteristic
304C22×C4C22⋊Dic1311yescharacteristic
305C22×C4D4×D1312yes—
306C22×C4#612912yes—
307C22×C4C22×Dic1311yescharacteristic
308C22×C4C2×C22⋊D1311yescharacteristic
309M16—1042no—
310C2×C8—264no—
311C2×C8—524no—
312C4⋊C4—22no—
313C4⋊C4—42no—
314C4⋊C4—524no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—44no—
318C22⋊C4—44no—
319C22⋊C4—42no—
320C22⋊C4—82no—
321C22⋊C4—522no—
322C22⋊C4—522no—
323C42—21no—
324C42—21no—
325C13#947211yescharacteristic, complemented, Sylow
326C23—24no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23—48no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—42no—
341C23—84no—
342C23—88no—
343C23—84no—
344C23—84no—
345C23—82no—
346C23—82no—
347C23#8818612yes—
348C23#8819312yes—
349C23#8820311yescharacteristic
350C23#8820511yescharacteristic
351C23C2×C22⋊Dic1311yescharacteristic
352D4—28no—
353D4—44no—
354D4—44no—
355D4—42no—
356D4—42no—
357D4—44no—
358D4—88no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—81no—
375C2×C4—1042no—
376C2×C4—1042no—
377C2×C4—1042no—
378C2×C4D4×Dic1312yes—
379C2×C4#8818911yescharacteristic
380C2×C4#8819111yescharacteristic
381C8—524no—
382C22—21no—
383C22—22no—
384C22—21no—
385C22—22no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—42no—
390C22—44no—
391C22—44no—
392C22—41no—
393C22—44no—
394C22—41no—
395C22—41no—
396C22—81no—
397C22—82no—
398C22—82no—
399C22—88no—
400C22—88no—
401C22—82no—
402C22—82no—
403C22#1171870012yes—
404C22#1171870312yes—
405C22#1171887611yescharacteristic
406C22#1171888111yescharacteristic
407C22#1171889311yescharacteristic
408C4—21no—
409C4—22no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—82no—
414C4—2082no—
415C4#1171869312yes—
416C2—21no—
417C2—22no—
418C2—21no—
419C2—22no—
420C2—81no—
421C2—84no—
422C2#1311524511yescharacteristic
423C2#1311527511yescharacteristic
424C2#1311536411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#2408C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#2408D13
hypocenterC13#9472
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. #13123865C2semidirect
2. #13114824C2semidirect
3. #13114767C2semidirect
4. #13112703C2semidirect
10. C13×#394C4semidirect
11. C13×#392C4semidirect
49. C22×#1055D4semidirect
185. #394Dic13semidirect
186. #392Dic13semidirect
325. C13#9472semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131148242
#131147672
#131127032
C13×#24082
#947213