Finite Group Databasebeta

← #15789997

Subgroups — #15789997

Order 3328.

1282 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
1C2×#11718646C211yesmaximal, characteristic
2C2×#11718642C211yesmaximal, characteristic
3#13113104C211yesmaximal, characteristic
4#13113101C212yesmaximal
5#13113101C211yesmaximal, characteristic
6#13113089C211yesmaximal, characteristic
7#13113089C212yesmaximal
8#13113065C212yesmaximal
9#13113061C212yesmaximal
10#95×Dic13C211yesmaximal, characteristic
11C2×C13×#398C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4⋊Dic13C2212yes—
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2212yes—
21C13×#398C418yescomplemented
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2212yes—
24C2×#88071C2211yescharacteristic
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718646—24no—
37#11718642—24no—
38C23×C4×C13C2312yes—
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×Dic13C2311yescharacteristic
44C23×Dic13C2312yes—
45C23×Dic13C2311yescharacteristic
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4C2×C414yes—
56C2×C13×C4⋊C4C2×C414yes—
57C2×C13×C4⋊C4C2×C418yes—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—24no—
60C2×C4⋊Dic13—22no—
61C2×C4⋊Dic13—24no—
62C2×C4⋊Dic13—42no—
63C2×C4⋊Dic13—42no—
64C2×C4⋊Dic13—42no—
65C2×C4⋊Dic13—42no—
66C2×C4⋊Dic13—42no—
67C2×C4⋊Dic13—42no—
68C2×C4×Dic13—42no—
69C2×C4×Dic13—42no—
70C2×C4×Dic13—42no—
71C2×C4×Dic13D414yes—
72C2×C4×Dic13Q818yes—
73C13×#95C2×C418yes—
74C13×#95C2×C414yes—
75#88071—22no—
76#88071—22no—
77#88071—24no—
78#88071—24no—
79#88071—22no—
80#88071—22no—
81#88071—22no—
82#88071—24no—
83#88071—42no—
84#88071—42no—
85#88071—42no—
86#88071—42no—
87#14328—131nomaximal, Sylow
88C24×C13C2411yescharacteristic
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13C22×C412yes—
112C22×C4×C13C22×C414yes—
113C22×C4×C13C22×C412yes—
114C22×C4×C13C22×C412yes—
115C22×C4×C13C22×C414yes—
116C22×C4×C13C2×D412yes—
117C22×C4×C13C2×Q814yes—
118C22×C4×C13#4112yes—
119C22×C4×C13#4114yes—
120C22×Dic13—22no—
121C22×Dic13—21no—
122C22×Dic13—21no—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13—21no—
150C22×Dic13C2×D412yes—
151C22×Dic13C2×D412yes—
152C22×Dic13C2×Q814yes—
153C22×Dic13C2×Q814yes—
154C13×C4⋊C4—28no—
155C13×C4⋊C4—28no—
156C13×C4⋊C4—48no—
157C4⋊Dic13—44no—
158C4⋊Dic13—48no—
159C4⋊Dic13—44no—
160C4⋊Dic13—48no—
161C4×Dic13—44no—
162C4×Dic13—48no—
163C2×#398D1311yescharacteristic
164C2×#389—131no—
165C2×#387—131no—
166#1445—131no—
167#1444—131no—
168#1444—132no—
169#1441—131no—
170#1441—132no—
171C4⋊#95—132no—
172#1434—132no—
173C4×#95—131no—
174C23×C13C23×C411yescharacteristic
175C23×C13C22×D411yescharacteristic
176C23×C13C22×Q812yes—
177C23×C13C2×#4111yescharacteristic
178C23×C13C2×#4112yes—
179C23×C13H(5,𝔽2)11yescharacteristic
180C23×C13H(5,𝔽2)11yescharacteristic
181C23×C13H(5,𝔽2)12yes—
182C23×C13H(5,𝔽2)11yescharacteristic
183C23×C132−1+412yes—
184C23×C132−1+411yescharacteristic
185C2×C4×C13—24no—
186C2×C4×C13—24no—
187C2×C4×C13—24no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—24no—
191C2×C4×C13—24no—
192C2×C4×C13—24no—
193C2×C4×C13—24no—
194C2×C4×C13—24no—
195C2×C4×C13—22no—
196C2×C4×C13—22no—
197C2×C4×C13—24no—
198C2×C4×C13—22no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—22no—
202C2×C4×C13—24no—
203C2×C4×C13—41no—
204C2×C4×C13—42no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—41no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13C4×D414yes—
215C2×C4×C13C4×Q818yes—
216C2×Dic13—22no—
217C2×Dic13—22no—
218C2×Dic13—24no—
219C2×Dic13—24no—
220C2×Dic13—22no—
221C2×Dic13—24no—
222C2×Dic13—22no—
223C2×Dic13—22no—
224C2×Dic13—24no—
225C2×Dic13—24no—
226C2×Dic13—42no—
227C2×Dic13—42no—
228C2×Dic13—42no—
229C2×Dic13—42no—
230C2×Dic13—42no—
231C2×Dic13—42no—
232C2×Dic13—41no—
233C2×Dic13—42no—
234C2×Dic13—41no—
235C2×Dic13—41no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13—41no—
239C2×Dic13—41no—
240C2×Dic13—41no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13C4⋊Q814yes—
250C22×C4⋊C4—132no—
251C22×C4⋊C4—132no—
252C22×C4⋊C4—131no—
253C22×C4⋊C4—131no—
254C22×C4⋊C4C2×D1311yescharacteristic
255C22×C4⋊C4C2×D1311yescharacteristic
256C22×C4⋊C4C2×D1312yes—
257C22×C42—132no—
258C22×C42—131no—
259#398Dic1318yescomplemented
260#389—264no—
261#387—264no—
262C2×#95—132no—
263C2×#95—131no—
264C2×#95—131no—
265C2×#95—132no—
266C2×#95—132no—
267C2×#95—131no—
268C2×#95—131no—
269C2×#95—131no—
270C2×#95—132no—
271C2×#95—132no—
272C2×#95—132no—
273C2×#95—132no—
274C2×#95C2×D1311yescharacteristic
275C2×#95C2×D1312yes—
276C22×C13C2×C4×D411yescharacteristic
277C22×C13C2×C4×Q812yes—
278C22×C13#51811yescharacteristic
279C22×C13#52012yes—
280C22×C13#52011yescharacteristic
281C22×C13C2×C4⋊Q811yescharacteristic
282C22×C13#53211yescharacteristic
283C22×C13#53312yes—
284C22×C13#53411yescharacteristic
285C22×C13#53511yescharacteristic
286C22×C13#53611yescharacteristic
287C22×C13#53711yescharacteristic
288C22×C13#53812yes—
289C22×C13#53912yes—
290C22×C13#53912yes—
291C22×C13#54011yescharacteristic
292C22×C13#54012yes—
293C22×C13#54112yes—
294C22×C13#54211yescharacteristic
295C22×C13#54312yes—
296C22×C13#54412yes—
297C22×C13#54412yes—
298C22×C13#54412yes—
299C4×C13—24no—
300C4×C13—28no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—44no—
304Dic13—24no—
305Dic13—42no—
306Dic13—44no—
307Dic13—82no—
308Dic13—81no—
309Dic13—81no—
310C23×C4—131no—
311C23×C4—131no—
312C23×C4—132no—
313C23×C4—131no—
314C23×C4—132no—
315C23×C4—131no—
316C23×C4C22×D1312yes—
317C23×C4C22×D1311yescharacteristic
318C23×C4C22×D1311yescharacteristic
319C23×C4C22×D1311yescharacteristic
320C23×C4C22×D1312yes—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—262no—
328C2×C4⋊C4—264no—
329C2×C4⋊C4—262no—
330C2×C4⋊C4—264no—
331C2×C4⋊C4—522no—
332C2×C4⋊C4—522no—
333C2×C4⋊C4—522no—
334C2×C4⋊C4—522no—
335C2×C4⋊C4—522no—
336C2×C4⋊C4—522no—
337C2×C4⋊C4C2×Dic1314yes—
338C2×C4⋊C4C2×Dic1314yes—
339C2×C4⋊C4C2×Dic1318yes—
340C2×C42—134no—
341C2×C42—138no—
342C2×C42—522no—
343C2×C42—522no—
344C2×C42—522no—
345#95—262no—
346#95—262no—
347#95—262no—
348#95—264no—
349#95—262no—
350#95—262no—
351#95—264no—
352#95—264no—
353#95—522no—
354#95—522no—
355#95—522no—
356#95—522no—
357#95C2×Dic1318yes—
358#95C2×Dic1314yes—
359C2×C13C4×C4⋊Q811yescharacteristic
360C2×C13#232211yescharacteristic
361C2×C13#232411yescharacteristic
362C2×C13#232912yes—
363C2×C13#233012yes—
364C2×C13#265911yescharacteristic
365C2×C13#266011yescharacteristic
366C2×C13#266111yescharacteristic
367C2×C13#266411yescharacteristic
368C2×C13#266612yes—
369C2×C13#266712yes—
370C24C23×D1311yescharacteristic
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—132no—
394C22×C4—134no—
395C22×C4—132no—
396C22×C4—134no—
397C22×C4—261no—
398C22×C4—262no—
399C22×C4—261no—
400C22×C4—262no—
401C22×C4—262no—
402C22×C4—261no—
403C22×C4—262no—
404C22×C4—262no—
405C22×C4—262no—
406C22×C4—262no—
407C22×C4—262no—
408C22×C4—261no—
409C22×C4—262no—
410C22×C4—261no—
411C22×C4—261no—
412C22×C4—262no—
413C22×C4—261no—
414C22×C4—262no—
415C22×C4—261no—
416C22×C4—262no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—261no—
421C22×C4—262no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—261no—
426C22×C4—262no—
427C22×C4D4×D1312yes—
428C22×C4#612912yes—
429C22×C4Q8×D1314yes—
430C22×C4#613114yes—
431C22×C4C22×Dic1312yes—
432C22×C4C22×Dic1314yes—
433C22×C4C22×Dic1312yes—
434C22×C4C22×Dic1312yes—
435C22×C4C22×Dic1314yes—
436C4⋊C4—28no—
437C4⋊C4—28no—
438C4⋊C4—48no—
439C4⋊C4—528no—
440C4⋊C4—524no—
441C4⋊C4—528no—
442C4⋊C4—524no—
443C42—528no—
444C42—524no—
445C13#1432811yescharacteristic, complemented, Sylow
446C23C2×D4×D1311yescharacteristic
447C23C2×#612911yescharacteristic
448C23#8825111yescharacteristic
449C23#8825111yescharacteristic
450C23C2×Q8×D1312yes—
451C23C2×#613112yes—
452C23#8825611yescharacteristic
453C23#8825612yes—
454C23#8825711yescharacteristic
455C23#8825712yes—
456C23C23×Dic1311yescharacteristic
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—134no—
487C2×C4—262no—
488C2×C4—264no—
489C2×C4—262no—
490C2×C4—264no—
491C2×C4—262no—
492C2×C4—264no—
493C2×C4—262no—
494C2×C4—264no—
495C2×C4—262no—
496C2×C4—264no—
497C2×C4—522no—
498C2×C4—522no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—522no—
502C2×C4—522no—
503C2×C4—521no—
504C2×C4—522no—
505C2×C4—521no—
506C2×C4—522no—
507C2×C4—521no—
508C2×C4—521no—
509C2×C4—522no—
510C2×C4—522no—
511C2×C4—522no—
512C2×C4—522no—
513C2×C4—521no—
514C2×C4—522no—
515C2×C4—521no—
516C2×C4—522no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4D4×Dic1314yes—
521C2×C4Q8×Dic1318yes—
522C22#1171930811yescharacteristic
523C22#1171931211yescharacteristic
524C22#1171931311yescharacteristic
525C22#1171932411yescharacteristic
526C22#1171932812yes—
527C22#1171933912yes—
528C22#1171934912yes—
529C22#1171935012yes—
530C22#1171935311yescharacteristic
531C22#1171935811yescharacteristic
532C22#1171937012yes—
533C22#1171939412yes—
534C22#1171939412yes—
535C22#1171940212yes—
536C22#1171940312yes—
537C22D13×C4⋊Q811yescharacteristic
538C22#1171943011yescharacteristic
539C22#1171943312yes—
540C22C2×D4×Dic1311yescharacteristic
541C22#1171950311yescharacteristic
542C22C2×Q8×Dic1312yes—
543C22#1171953212yes—
544C22#1171953211yescharacteristic
545C4—24no—
546C4—28no—
547C4—42no—
548C4—42no—
549C4—44no—
550C4—264no—
551C4—524no—
552C4—522no—
553C4—1042no—
554C4—1041no—
555C4—1041no—
556C2C4⋊Q8×Dic1311yescharacteristic
557C2#1311750811yescharacteristic
558C2#1311753111yescharacteristic
559C2#1311757112yes—
560C2#1311757812yes—
561C2#1312095111yescharacteristic
562C2#1312095911yescharacteristic
563C2#1312096911yescharacteristic
564C2#1312100211yescharacteristic
565C2#1312102412yes—
566C2#1312103512yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#398C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#398D13
hypocenterC13#14328
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
21. C13×#398C4semidirect
259. #398Dic13semidirect
445. C13#14328semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117186422
#131131042
#131131012
#131130892
#131130652
#131130612
#95×Dic132
C2×C13×#3982
#1432813