Finite Group Databasebeta

← #15753805

Subgroups — #15753805

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic13C211yesmaximal, characteristic
2#13114600C211yesmaximal, characteristic, complemented
3C2×#11718129C211yesmaximal, characteristic
4#13113061C211yesmaximal, characteristic, complemented
5#13112716C211yesmaximal, characteristic, complemented
6#13112715C211yesmaximal, characteristic, complemented
7C2×C13×#327C211yesmaximal, characteristic
8C2×C13×#121C2211yescharacteristic
9C2×D4×Dic13—21no—
10C2×D4×Dic13C411yescharacteristic, complemented
11C22×C4×Dic13C2211yescharacteristic
12C2×C13×C22⋊C8C2211yescharacteristic
13C2×C13×#95C2211yescharacteristic
14#11718882C411yescharacteristic, complemented
15#11718881—21no—
16#11718873C2211yescharacteristic
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88071C2211yescharacteristic
20C2×C22⋊#1055C2211yescharacteristic
21C2×#88055—21no—
22#11718646C411yescharacteristic, complemented
23C4⋊C4×Dic13C411yescharacteristic, complemented
24#11718612—21no—
25C22⋊C4×Dic13—21no—
26C13×#327C414yescomplemented
27#11718142—21no—
28#11718129C414yescomplemented
29C22×D4×C13—21no—
30C22×D4×C13C2×C411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13C2311yescharacteristic
33C23×Dic13—21no—
34C23×Dic13—21no—
35C23×Dic13D411yescharacteristic
36C23×Dic13D411yescharacteristic
37C22×C8×C13—21no—
38C13×#121—21no—
39C13×#121—21no—
40C13×#121C2×C412yes—
41C13×#121C2×C412yes—
42C2×C13×C4⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C22⋊Dic13—21no—
45C2×C22⋊Dic13—21no—
46C2×C22⋊Dic13—21no—
47C2×C22⋊Dic13—21no—
48D4×Dic13—42no—
49D4×Dic13—42no—
50D4×Dic13—42no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13C2×C411yescharacteristic
53C2×C4⋊Dic13C2×C411yescharacteristic
54C2×C4×Dic13—21no—
55C2×C4×Dic13—42no—
56C2×C4×Dic13C2×C411yescharacteristic
57C2×C4×Dic13C2×C411yescharacteristic
58C2×C4×Dic13D411yescharacteristic
59C2×C4×Dic13D411yescharacteristic
60C22×#1055—21no—
61C13×C22⋊C8—21no—
62C13×C22⋊C8C2×C412yescomplemented
63C13×#95—21no—
64C13×#95C2×C412yescomplemented
65#88071—21no—
66#88071—21no—
67#88071—21no—
68#88071—21no—
69#88071—42no—
70#88071—42no—
71#88071C2×C412yescomplemented
72C22⋊#1055—21no—
73C22⋊#1055C2×C412yescomplemented
74#88055—42no—
75#8216—131nomaximal, Sylow
76C24×C13—21no—
77C24×C13C2×D411yescharacteristic
78C2×D4×C13—22no—
79C2×D4×C13—22no—
80C2×D4×C13—21no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13C4212yes—
88C22×C4×C13—21no—
89C22×C4×C13—22no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C22×C411yescharacteristic
100C22×C4×C13C22×C411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C22×Dic13—21no—
105C22×Dic13—21no—
106C22×Dic13—21no—
107C22×Dic13—21no—
108C22×Dic13—22no—
109C22×Dic13—21no—
110C22×Dic13—21no—
111C22×Dic13—22no—
112C22×Dic13—41no—
113C22×Dic13—41no—
114C22×Dic13—41no—
115C22×Dic13—42no—
116C22×Dic13—42no—
117C22×Dic13—41no—
118C22×Dic13—41no—
119C22×Dic13—41no—
120C22×Dic13—41no—
121C22×Dic13—41no—
122C22×Dic13—41no—
123C22×Dic13—42no—
124C22×Dic13C22⋊C411yescharacteristic
125C22×Dic13C22⋊C411yescharacteristic
126C22×Dic13C22⋊C411yescharacteristic
127C22×Dic13C22⋊C411yescharacteristic
128C2×C8×C13—22no—
129C2×C8×C13—41no—
130C2×C8×C13—41no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4C4212yes—
133C13×C22⋊C4—22no—
134C13×C22⋊C4—22no—
135C22⋊Dic13—42no—
136C22⋊Dic13—42no—
137C22⋊Dic13—42no—
138C22⋊Dic13—41no—
139C22⋊Dic13—41no—
140C4⋊Dic13—42no—
141C4⋊Dic13—41no—
142C4⋊Dic13—41no—
143C4×Dic13—22no—
144C4×Dic13—22no—
145C4×Dic13—41no—
146C4×Dic13—41no—
147C4×Dic13—42no—
148C2×#1055—22no—
149C2×#1055—41no—
150C2×#1055—41no—
151C4×#121—131no—
152#1749—131no—
153C2×#327—131no—
154C2×#327D1311yescharacteristic
155#1434—131no—
156#1294—131no—
157#1294—131no—
158C23×C13—21no—
159C23×C13—21no—
160C23×C13—21no—
161C23×C13—21no—
162C23×C13—22no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13C2×C22⋊C411yescharacteristic
170C23×C13C4×D411yescharacteristic
171C23×C13C4×D411yescharacteristic
172C23×C13AGL(1,ℤ/8)11yescharacteristic
173C23×C13AGL(1,ℤ/8)11yescharacteristic
174C23×C13AGL(1,ℤ/8)11yescharacteristic
175C23×C13#13711yescharacteristic
176D4×C13—42no—
177D4×C13—42no—
178D4×C13—42no—
179D4×C13—42no—
180D4×C13—42no—
181D4×C13—42no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—22no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—81no—
197C2×C4×C13—81no—
198C2×C4×C13—81no—
199C2×C4×C13—81no—
200C2×C4×C13C2×C4211yescharacteristic
201C2×C4×C13#11711yescharacteristic
202C2×C4×C13C4×D411yescharacteristic
203C2×C4×C13C4×D411yescharacteristic
204C2×Dic13—21no—
205C2×Dic13—21no—
206C2×Dic13—21no—
207C2×Dic13—21no—
208C2×Dic13—21no—
209C2×Dic13—21no—
210C2×Dic13—21no—
211C2×Dic13—21no—
212C2×Dic13—21no—
213C2×Dic13—21no—
214C2×Dic13—21no—
215C2×Dic13—42no—
216C2×Dic13—42no—
217C2×Dic13—42no—
218C2×Dic13—42no—
219C2×Dic13—42no—
220C2×Dic13—42no—
221C2×Dic13—41no—
222C2×Dic13—41no—
223C2×Dic13—41no—
224C2×Dic13—41no—
225C2×Dic13—41no—
226C2×Dic13—41no—
227C2×Dic13—42no—
228C2×Dic13—84no—
229C2×Dic13—81no—
230C2×Dic13—81no—
231C2×Dic13—81no—
232C2×Dic13—81no—
233C2×Dic13#9912yes—
234C8×C13—42no—
235#1055—42no—
236C2×#121C2×D1311yescharacteristic
237C2×C4×D4—131no—
238C2×C4×D4—261no—
239C22×C42—131no—
240C2×C22⋊C8—131no—
241C2×C22⋊C8C2×D1311yescharacteristic
242C2×#97—261no—
243#390—131no—
244#389—131no—
245#388—261no—
246#386—261no—
247#380—131no—
248C4×C4⋊C4—131no—
249C4×C22⋊C4—261no—
250C2×#95—131no—
251C2×#95—261no—
252C2×#95—261no—
253C2×#95C2×D1311yescharacteristic
254#336—261no—
255#327—134no—
256#327Dic1314yescomplemented
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13—42no—
272C22×C13—81no—
273C22×C13—81no—
274C22×C13—81no—
275C22×C13—81no—
276C22×C13C4×C22⋊C411yescharacteristic
277C22×C13C2×#9911yescharacteristic
278C22×C13#41011yescharacteristic
279C22×C13#41711yescharacteristic
280C22×C13#41811yescharacteristic
281C22×C13#42111yescharacteristic
282C22×C13#42111yescharacteristic
283C22×C13#44011yescharacteristic
284C22×C13#44011yescharacteristic
285C22×C13#44211yescharacteristic
286C22×C13#44211yescharacteristic
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—42no—
292C4×C13—82no—
293Dic13—22no—
294Dic13—41no—
295Dic13—41no—
296Dic13—41no—
297Dic13—82no—
298Dic13—81no—
299Dic13—81no—
300C22×D4—21no—
301C22×D4C4×D1311yescharacteristic
302C23×C4—21no—
303C23×C4—131no—
304C23×C4—131no—
305C23×C4—261no—
306C23×C4—261no—
307C23×C4C22×D1311yescharacteristic
308C22×C8—21no—
309C22×C8—261no—
310#121—21no—
311#121—21no—
312#121C4×D1312yes—
313#121C2×Dic1312yes—
314C4×D4—522no—
315C4×D4—522no—
316C4×D4—522no—
317C2×C4⋊C4—131no—
318C2×C4⋊C4—131no—
319C2×C4⋊C4—261no—
320C2×C4⋊C4C4×D1311yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—261no—
323C2×C22⋊C4—261no—
324C2×C22⋊C4—261no—
325C2×C22⋊C4—261no—
326C2×C42—131no—
327C2×C42—131no—
328C2×C42—131no—
329C2×C42—131no—
330C2×C42—261no—
331C2×C42—522no—
332C22⋊C8—21no—
333C22⋊C8—132no—
334C22⋊C8—261no—
335C22⋊C8C2×Dic1312yescomplemented
336#97—522no—
337#95—21no—
338#95—132no—
339#95—261no—
340#95—261no—
341#95—261no—
342#95—261no—
343#95—522no—
344#95—522no—
345#95C2×Dic1312yescomplemented
346C2×C13—21no—
347C2×C13—21no—
348C2×C13—21no—
349C2×C13—21no—
350C2×C13—82no—
351C2×C13#151011yescharacteristic
352C2×C13#151211yescharacteristic
353C2×C13#151311yescharacteristic
354C2×C13#151411yescharacteristic
355C2×C13C4×#9911yescharacteristic
356C2×C13#175911yescharacteristic
357C2×C13#176211yescharacteristic
358C24—21no—
359C24D4×D1311yescharacteristic
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4C4×Dic1312yes—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—131no—
381C22×C4—131no—
382C22×C4—131no—
383C22×C4—131no—
384C22×C4—262no—
385C22×C4—261no—
386C22×C4—261no—
387C22×C4—261no—
388C22×C4—261no—
389C22×C4—261no—
390C22×C4—261no—
391C22×C4—262no—
392C22×C4—522no—
393C22×C4—521no—
394C22×C4—521no—
395C22×C4—521no—
396C22×C4—522no—
397C22×C4—522no—
398C22×C4—521no—
399C22×C4—521no—
400C22×C4—521no—
401C22×C4—521no—
402C22×C4—521no—
403C22×C4—521no—
404C22×C4C2×C4×D1311yescharacteristic
405C22×C4C2×C4×D1311yescharacteristic
406C22×C4D4×D1311yescharacteristic
407C22×C4#612911yescharacteristic
408C22×C4#612911yescharacteristic
409C22×C4C22×Dic1311yescharacteristic
410C2×C8—22no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—262no—
414C2×C8—521no—
415C2×C8—521no—
416C4⋊C4—21no—
417C4⋊C4—521no—
418C4⋊C4—521no—
419C4⋊C4—522no—
420C4⋊C4C4×Dic1312yes—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—522no—
424C22⋊C4—522no—
425C22⋊C4—522no—
426C22⋊C4—521no—
427C22⋊C4—521no—
428C42—262no—
429C42—262no—
430C42—521no—
431C42—521no—
432C42—522no—
433C13#821611yescharacteristic, complemented, Sylow
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23C22⋊C4×D1311yescharacteristic
446C23#8813511yescharacteristic
447C23#8816511yescharacteristic
448C23#8816511yescharacteristic
449C23#8816811yescharacteristic
450C23#8816911yescharacteristic
451C23D4×Dic1311yescharacteristic
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—132no—
477C2×C4—261no—
478C2×C4—261no—
479C2×C4—261no—
480C2×C4—261no—
481C2×C4—261no—
482C2×C4—261no—
483C2×C4—261no—
484C2×C4—261no—
485C2×C4—261no—
486C2×C4—261no—
487C2×C4—261no—
488C2×C4—522no—
489C2×C4—522no—
490C2×C4—522no—
491C2×C4—522no—
492C2×C4—522no—
493C2×C4—522no—
494C2×C4—521no—
495C2×C4—521no—
496C2×C4—521no—
497C2×C4—521no—
498C2×C4—522no—
499C2×C4—521no—
500C2×C4—521no—
501C2×C4—1044no—
502C2×C4—1041no—
503C2×C4—1041no—
504C2×C4—1041no—
505C2×C4—1041no—
506C2×C4#8813111yescharacteristic
507C2×C4#8813511yescharacteristic
508C2×C4C2×C4×Dic1311yescharacteristic
509C2×C4D4×Dic1311yescharacteristic
510C8—42no—
511C8—522no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22#1171840111yescharacteristic
532C22D13×#9911yescharacteristic
533C22#1171841811yescharacteristic
534C22#1171843111yescharacteristic
535C22#1171843211yescharacteristic
536C22#1171844611yescharacteristic
537C22#1171848211yescharacteristic
538C22#1171848211yescharacteristic
539C22C22⋊C4×Dic1311yescharacteristic
540C22#1171881311yescharacteristic
541C22#1171882511yescharacteristic
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—82no—
548C4—262no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4—1042no—
553C4—1041no—
554C4—1041no—
555C2—21no—
556C2—21no—
557C2—21no—
558C2—21no—
559C2—82no—
560C2#1311336311yescharacteristic
561C2#1311337111yescharacteristic
562C2#1311337611yescharacteristic
563C2#1311338111yescharacteristic
564C2#99×Dic1311yescharacteristic
565C2#1311464811yescharacteristic
566C2#1311466311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#327C2
socleC23×C13C2×C22⋊C4
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenterC2×#327D13
hypocenterC13#8216
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #13114600C2semidirect
4. #13113061C2semidirect
5. #13112716C2semidirect
6. #13112715C2semidirect
10. C2×D4×Dic13C4semidirect
14. #11718882C4semidirect
22. #11718646C4semidirect
23. C4⋊C4×Dic13C4semidirect
26. C13×#327C4semidirect
28. #11718129C4semidirect
62. C13×C22⋊C8C2×C4semidirect
64. C13×#95C2×C4semidirect
71. #88071C2×C4semidirect
73. C22⋊#1055C2×C4semidirect
256. #327Dic13semidirect
335. C22⋊C8C2×Dic13semidirect
345. #95C2×Dic13semidirect
433. C13#8216semidirect

Maximal subgroups

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

subgroupindex
#121×Dic132
#131146002
C2×#117181292
#131130612
#131127162
#131127152
C2×C13×#3272
#821613