Finite Group Databasebeta

← #15754850

Subgroups — #15754850

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115760C211yesmaximal, characteristic, complemented
2#13114856C211yesmaximal, characteristic, complemented
3#13113517C211yesmaximal, characteristic, complemented
4#13113513C211yesmaximal, characteristic, complemented
5#13113331C211yesmaximal, characteristic, complemented
6#13113223C211yesmaximal, characteristic, complemented
7C13×#3511C211yesmaximal, characteristic
8C13×#556—21no—
9C13×#555C412yescomplemented
10C13×#554C412yescomplemented
11C13×#553—22no—
12C13×#548—22no—
13C13×#547—21no—
14C13×#542—22no—
15C13×#537—21no—
16C13×#533—21no—
17C13×#532—21no—
18C13×#532C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C13×#520—21no—
21C4×C13×#41C2211yescharacteristic
22C2×#88077—21no—
23C2×#88075—22no—
24C4×C4⋊Dic13C2211yescharacteristic
25#11718586C2211yescharacteristic
26#11718585C2211yescharacteristic
27C2×C4⋊#1055C2211yescharacteristic
28#11718139—21no—
29#11718138—22no—
30#11718136—21no—
31#11718129—22no—
32Q8⋊#1055—21no—
33D4⋊#1055—21no—
34#11718124—21no—
35C2×C13×#41—22no—
36C2×C13×#41—21no—
37C2×C13×#41D411yescharacteristic
38C22×Q8×C13D412yes—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8C2×C412yes—
42C13×C4⋊Q8D412yes—
43C13×C4⋊Q8D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#126—24no—
46C13×#125—22no—
47C13×#124—22no—
48C13×#124—24no—
49C13×#124—21no—
50C13×#123—24no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—24no—
55C13×#121—22no—
56C13×#121—24no—
57C13×#121—22no—
58C13×#121—22no—
59C13×#121—21no—
60C13×#121D412yes—
61C4×Q8×C13—22no—
62C4×Q8×C13—22no—
63C4×Q8×C13C2×C411yescharacteristic
64C4×Q8×C13D411yescharacteristic
65C4×D4×C13—22no—
66C4×D4×C13—24no—
67C4×D4×C13—22no—
68C4×D4×C13—21no—
69C4×D4×C13—21no—
70C4×D4×C13—21no—
71C4×D4×C13C2×C411yescharacteristic
72C4×D4×C13C2×C412yes—
73C4×D4×C13D411yescharacteristic
74C13×#117—22no—
75C13×#117—22no—
76C13×#117—21no—
77C13×#117D411yescharacteristic
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—22no—
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C4⋊Dic13—21no—
84C2×C4×Dic13—21no—
85C2×#6099—21no—
86C22×#1055—21no—
87#88077—42no—
88#88075—44no—
89#88071—21no—
90C22⋊#1055—21no—
91C4⋊#1055—21no—
92C4⋊#1055—21no—
93C4⋊#1055—21no—
94C4⋊#1055—21no—
95C4⋊#1055—21no—
96C4×#1055—21no—
97#8423—131nomaximal, Sylow
98C13×#41—21no—
99C13×#41—21no—
100C13×#41—21no—
101C13×#41—21no—
102C13×#41—41no—
103C13×#41—41no—
104C13×#41—41no—
105C13×#41—41no—
106C13×#41—82no—
107C13×#41—82no—
108C2×Q8×C13—21no—
109C2×Q8×C13—22no—
110C2×Q8×C13—42no—
111C2×Q8×C13—42no—
112C2×Q8×C13C22⋊C411yescharacteristic
113C2×Q8×C13C22⋊C414yes—
114C2×D4×C13—21no—
115C2×D4×C13—22no—
116C2×D4×C13—24no—
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13C22⋊C411yescharacteristic
120C2×D4×C13C22⋊C412yes—
121C22×C4×C13—24no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×Dic13—41no—
131C13×C4⋊C4—24no—
132C13×C4⋊C4—24no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4—22no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4—21no—
139C13×C4⋊C4—21no—
140C13×C4⋊C4C22⋊C411yescharacteristic
141C13×C4⋊C4C22⋊C411yescharacteristic
142C13×C4⋊C4C22⋊C412yes—
143C13×C22⋊C4—24no—
144C13×C22⋊C4—24no—
145C13×C22⋊C4—24no—
146C13×C22⋊C4—21no—
147C13×C22⋊C4—21no—
148C13×C22⋊C4—22no—
149C13×C22⋊C4—21no—
150C13×C22⋊C4—22no—
151C42×C13—24no—
152C42×C13—21no—
153C42×C13—21no—
154C42×C13—21no—
155C42×C13C22×C411yescharacteristic
156C42×C13C2×D411yescharacteristic
157C42×C13C2×D411yescharacteristic
158C42×C13C2×D411yescharacteristic
159C4⋊Dic13—22no—
160C4⋊Dic13—41no—
161C4×Dic13—41no—
162C4×Dic13—41no—
163#6099—41no—
164#6099—41no—
165C2×#1055—42no—
166C2×#1055—41no—
167C2×#1055—41no—
168C2×#1055—41no—
169#3511D1311yescharacteristic
170#1981—131no—
171#1806—131no—
172#1548—131no—
173#1547—131no—
174#1502—131no—
175#1477—131no—
176C23×C13—21no—
177C23×C13—22no—
178C23×C13#12011yescharacteristic
179Q8×C13—21no—
180Q8×C13—21no—
181Q8×C13—44no—
182Q8×C13—41no—
183Q8×C13—41no—
184Q8×C13—42no—
185Q8×C13—42no—
186D4×C13—21no—
187D4×C13—21no—
188D4×C13—42no—
189D4×C13—41no—
190D4×C13—42no—
191D4×C13—41no—
192D4×C13—42no—
193D4×C13—41no—
194D4×C13—41no—
195D4×C13—41no—
196D4×C13—41no—
197D4×C13—84no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—22no—
203C2×C4×C13—21no—
204C2×C4×C13—24no—
205C2×C4×C13—41no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—82no—
214C2×C4×C13—84no—
215C2×C4×C13C2×C22⋊C411yescharacteristic
216C2×C4×C13C2×C22⋊C411yescharacteristic
217C2×C4×C13C2×C22⋊C411yescharacteristic
218C2×C4×C13#12011yescharacteristic
219C2×C4×C13#12011yescharacteristic
220C2×C4×C13#12011yescharacteristic
221C2×C4×C13#13511yescharacteristic
222C2×C4×C13#13511yescharacteristic
223C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
224C2×C4×C13#13711yescharacteristic
225C2×Dic13—42no—
226C2×Dic13—81no—
227C2×Dic13—81no—
228#1055—81no—
229#1055—81no—
230#1055—81no—
231#556—21no—
232#555Dic1312yescomplemented
233#554Dic1312yescomplemented
234#553—22no—
235#548—22no—
236#547—21no—
237#542—22no—
238#537—21no—
239#533—21no—
240#532—21no—
241#532C2×D1311yescharacteristic
242C2×C4⋊Q8C2×D1311yescharacteristic
243#520—21no—
244C4×#41C2×D1311yescharacteristic
245#431—131no—
246#423—131no—
247C2×C4⋊C8—131no—
248C2×#104—261no—
249C2×#103—262no—
250C4×C4⋊C4—131no—
251#339—261no—
252#333—262no—
253#332—261no—
254#331—261no—
255#327—262no—
256Q8⋊C8—261no—
257D4⋊C8—261no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—41no—
261C22×C13—42no—
262C22×C13—41no—
263C22×C13—42no—
264C22×C13—41no—
265C22×C13—42no—
266C22×C13#37911yescharacteristic
267C22×C13#44911yescharacteristic
268C22×C13#45211yescharacteristic
269C4×C13—21no—
270C4×C13—21no—
271C4×C13—21no—
272C4×C13—41no—
273C4×C13—44no—
274C4×C13—41no—
275C4×C13—41no—
276C4×C13—42no—
277C4×C13#41611yescharacteristic
278C4×C13#41711yescharacteristic
279C4×C13#44911yescharacteristic
280C4×C13#45211yescharacteristic
281C4×C13#45311yescharacteristic
282C4×C13#45511yescharacteristic
283Dic13—82no—
284C2×#41—22no—
285C2×#41—21no—
286C2×#41C22⋊D1311yescharacteristic
287C22×Q8C22⋊D1312yes—
288C2×M16—261no—
289C22×C8—261no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8C2×Dic1312yes—
293C4⋊Q8C22⋊D1312yes—
294C4⋊Q8C22⋊D1311yescharacteristic
295#127C22⋊D1311yescharacteristic
296#126—24no—
297#125—22no—
298#124—22no—
299#124—24no—
300#124—21no—
301#123—24no—
302C22⋊Q8—22no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306#121—22no—
307#121—24no—
308#121—22no—
309#121—22no—
310#121—21no—
311#121C22⋊D1312yes—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8C2×Dic1311yescharacteristic
315C4×Q8C22⋊D1311yescharacteristic
316C4×D4—22no—
317C4×D4—24no—
318C4×D4—22no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4C2×Dic1311yescharacteristic
323C4×D4C2×Dic1312yes—
324C4×D4C22⋊D1311yescharacteristic
325#117—22no—
326#117—22no—
327#117—21no—
328#117C22⋊D1311yescharacteristic
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—261no—
333C2×C42—21no—
334C2×C42—261no—
335C2×C42C22×D1311yescharacteristic
336C4⋊C8—261no—
337C4⋊C8—261no—
338C4⋊C8—261no—
339C4⋊C8—261no—
340C4⋊C8—261no—
341#104—522no—
342#103—524no—
343C22⋊C8—261no—
344C4×C8—261no—
345#95—261no—
346C2×C13—21no—
347C2×C13—21no—
348C2×C13—81no—
349C2×C13—82no—
350C2×C13#178811yescharacteristic
351C2×C13#179211yescharacteristic
352C2×C13#179611yescharacteristic
353#41—21no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—41no—
358#41—41no—
359#41—41no—
360#41—41no—
361#41—82no—
362#41—82no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8C22⋊Dic1311yescharacteristic
368C2×Q8C22⋊Dic1314yes—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4C22⋊Dic1311yescharacteristic
375C2×D4C22⋊Dic1312yes—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—521no—
383C22×C4C2×C22⋊D1311yescharacteristic
384C22×C4C2×C22⋊D1311yescharacteristic
385C22×C4C2×C22⋊D1311yescharacteristic
386M16—521no—
387M16—521no—
388C2×C8—522no—
389C2×C8—521no—
390C2×C8—521no—
391C2×C8—521no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—262no—
402C4⋊C4—521no—
403C4⋊C4C22⋊Dic1311yescharacteristic
404C4⋊C4C22⋊Dic1311yescharacteristic
405C4⋊C4C22⋊Dic1312yes—
406C22⋊C4—24no—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—22no—
412C22⋊C4—21no—
413C22⋊C4—22no—
414C42—24no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42—521no—
419C42—521no—
420C42C22×Dic1311yescharacteristic
421C42C2×C22⋊D1311yescharacteristic
422C42C2×C22⋊D1311yescharacteristic
423C42C2×C22⋊D1311yescharacteristic
424C13#842311yescharacteristic, complemented, Sylow
425C23—21no—
426C23—22no—
427C23#8820711yescharacteristic
428Q8—21no—
429Q8—21no—
430Q8—44no—
431Q8—41no—
432Q8—41no—
433Q8—42no—
434Q8—42no—
435D4—21no—
436D4—21no—
437D4—42no—
438D4—41no—
439D4—42no—
440D4—41no—
441D4—42no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—84no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—82no—
463C2×C4—84no—
464C2×C4—522no—
465C2×C4—1041no—
466C2×C4—1041no—
467C2×C4#8820311yescharacteristic
468C2×C4#8820411yescharacteristic
469C2×C4#8820411yescharacteristic
470C2×C4#8820511yescharacteristic
471C2×C4C2×C22⋊Dic1311yescharacteristic
472C2×C4C2×C22⋊Dic1311yescharacteristic
473C2×C4C2×C22⋊Dic1311yescharacteristic
474C2×C4#8820711yescharacteristic
475C2×C4#8820711yescharacteristic
476C2×C4#8820711yescharacteristic
477C8—1041no—
478C8—1041no—
479C8—1041no—
480C22—21no—
481C22—21no—
482C22—41no—
483C22—42no—
484C22—41no—
485C22—42no—
486C22—41no—
487C22—42no—
488C22#1171889911yescharacteristic
489C22#1171890011yescharacteristic
490C22#1171890811yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—41no—
495C4—42no—
496C4—41no—
497C4—44no—
498C4—41no—
499C4—1042no—
500C4#1171889311yescharacteristic
501C4#1171889411yescharacteristic
502C4#1171889911yescharacteristic
503C4#1171890011yescharacteristic
504C4#1171890211yescharacteristic
505C4#1171890311yescharacteristic
506C2—21no—
507C2—21no—
508C2—81no—
509C2—82no—
510C2#1311477611yescharacteristic
511C2#1311479011yescharacteristic
512C2#1311481111yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3511C2
socleC22×C13#379
cosocleC2×C42×C13C23
hypercenter#3511D13
hypocenterC13#8423
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13115760C2semidirect
2. #13114856C2semidirect
3. #13113517C2semidirect
4. #13113513C2semidirect
5. #13113331C2semidirect
6. #13113223C2semidirect
9. C13×#555C4semidirect
10. C13×#554C4semidirect
232. #555Dic13semidirect
233. #554Dic13semidirect
424. C13#8423semidirect

Maximal subgroups

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

subgroupindex
#131157602
#131148562
#131135172
#131135132
#131133312
#131132232
C13×#35112
#842313