Finite Group Databasebeta

← #15799643

Subgroups — #15799643

Order 3328.

1566 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718318C212yesmaximal
2C2×#11718645C212yesmaximal
3C2×#11718308C211yesmaximal, characteristic
4C2×#11718637C211yesmaximal, characteristic
5C2×#11718637C212yesmaximal
6#13113101C211yesmaximal, characteristic
7#13113100C211yesmaximal, characteristic
8#13113099C211yesmaximal, characteristic
9#13113064C212yesmaximal
10#95×Dic13C211yesmaximal, characteristic
11C13×#1444C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2212yes—
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2212yes—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×#6101C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×#6101C2212yes—
22C22×#6101C2212yes—
23C22×#6101C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2212yes—
26C2×C13×#95C2211yescharacteristic
27C2×C13×#95C2212yes—
28C2×C13×#95C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35#11718645—28no—
36#11718637—28no—
37#11718637—24no—
38#11718318—28no—
39#11718308—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—24no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4—42no—
56C2×C4⋊Dic13—24no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—24no—
60C2×C4⋊Dic13—24no—
61C2×C4⋊Dic13—42no—
62C2×C4⋊Dic13—42no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—24no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101—24no—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101—24no—
74C2×#6101—24no—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—42no—
80C2×#6101—42no—
81C2×#6101D414yes—
82C2×C4×Dic13—24no—
83C2×C4×Dic13—24no—
84C2×C4×Dic13—24no—
85C2×C4×Dic13D414yes—
86C2×C4×Dic13Q818yes—
87C13×#95—22no—
88C13×#95—24no—
89C13×#95Q814yes—
90#88071—22no—
91#88071—24no—
92#88071—24no—
93#88071—24no—
94#88071D418yes—
95#88071Q814yes—
96#15145—131nomaximal, Sylow
97C24×C13C2411yescharacteristic
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×D414yes—
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2×Q814yes—
124C22×C4×C13C2×Q812yes—
125C22×C4×C13C2×Q812yes—
126C22×C4×C13C2×Q814yes—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—22no—
134C22×Dic13—21no—
135C22×Dic13—22no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13C2×D412yes—
151C22×Dic13C2×D414yes—
152C22×Dic13C2×D412yes—
153C22×Dic13C2×D414yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D412yes—
156C22×Dic13C2×Q814yes—
157C22×Dic13C2×Q814yes—
158C22×Dic13C2×Q814yes—
159C22×Dic13#4112yes—
160C22×Dic13#4114yes—
161C13×C4⋊C4—48no—
162C13×C4⋊C4—44no—
163C4⋊Dic13—48no—
164C4⋊Dic13—44no—
165C4⋊Dic13—44no—
166#6101—28no—
167#6101—48no—
168#6101—48no—
169#6101—48no—
170#6101—44no—
171#6101—44no—
172#6101—48no—
173C4×Dic13—216no—
174C4×Dic13—28no—
175C2×#398—132no—
176C2×#398—132no—
177C2×#389—131no—
178C2×#384—132no—
179C2×#384—131no—
180#1444—131no—
181#1444—131no—
182#1444—131no—
183#1444D1311yescharacteristic
184C4⋊#95—132no—
185C4×#95—131no—
186C23×C13C22×D411yescharacteristic
187C23×C13C22×D411yescharacteristic
188C23×C13C22×D412yes—
189C23×C13C22×Q812yes—
190C23×C13C22×Q811yescharacteristic
191C23×C13C22×Q811yescharacteristic
192C23×C13C2×#4111yescharacteristic
193C23×C13C2×#4112yes—
194C23×C13H(5,𝔽2)12yes—
195C23×C132−1+411yescharacteristic
196C23×C132−1+411yescharacteristic
197C2×C4×C13—24no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—24no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—22no—
208C2×C4×C13—24no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13C4⋊Q818yes—
225C2×C4×C13C4⋊Q814yes—
226C2×Dic13—24no—
227C2×Dic13—22no—
228C2×Dic13—22no—
229C2×Dic13—24no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—22no—
237C2×Dic13—24no—
238C2×Dic13—41no—
239C2×Dic13—41no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—41no—
243C2×Dic13—42no—
244C2×Dic13—41no—
245C2×Dic13—42no—
246C2×Dic13—41no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13#12114yes—
254C2×Dic13C22⋊Q818yes—
255C2×Dic13#12314yes—
256C2×Dic13#12518yes—
257C2×Dic13#12714yes—
258C2×Dic13C4⋊Q818yes—
259C2×Dic13C4⋊Q814yes—
260C22×C4⋊C4—131no—
261C22×C4⋊C4—132no—
262C22×C4⋊C4—131no—
263C22×C4⋊C4—131no—
264C22×C4⋊C4—132no—
265C22×C4⋊C4—131no—
266C22×C4⋊C4—132no—
267C22×C4⋊C4—132no—
268C22×C4⋊C4—132no—
269C22×C4⋊C4—131no—
270C22×C4⋊C4C2×D1312yes—
271C22×C4⋊C4C2×D1311yescharacteristic
272C22×C42—132no—
273C22×C42—131no—
274#398—268no—
275#398—268no—
276#389—264no—
277#384—264no—
278#384—268no—
279C2×#95—132no—
280C2×#95—131no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—131no—
285C2×#95C2×D1312yes—
286C2×#95C2×D1311yescharacteristic
287C2×#95C2×D1311yescharacteristic
288C22×C13C2×#12111yescharacteristic
289C22×C13C2×C22⋊Q812yes—
290C22×C13C2×#12311yescharacteristic
291C22×C13C2×#12512yes—
292C22×C13C2×#12711yescharacteristic
293C22×C13C2×C4⋊Q811yescharacteristic
294C22×C13C2×C4⋊Q812yes—
295C22×C13C2×C4⋊Q812yes—
296C22×C13C2×C4⋊Q811yescharacteristic
297C22×C13#53511yescharacteristic
298C22×C13#53611yescharacteristic
299C22×C13#54412yes—
300C22×C13#54412yes—
301C22×C13D4212yes—
302C22×C13#54712yes—
303C22×C13#54712yes—
304C22×C13D4×Q811yescharacteristic
305C22×C13D4×Q811yescharacteristic
306C22×C13#55012yes—
307C22×C13#55412yes—
308C22×C13#55412yes—
309C22×C13#55711yescharacteristic
310C22×C13#55711yescharacteristic
311C4×C13—28no—
312C4×C13—24no—
313C4×C13—42no—
314C4×C13—81no—
315C4×C13—82no—
316Dic13—28no—
317Dic13—24no—
318Dic13—42no—
319Dic13—81no—
320Dic13—82no—
321Dic13#39818yescomplemented
322C23×C4—131no—
323C23×C4—131no—
324C23×C4—132no—
325C23×C4—131no—
326C23×C4—132no—
327C23×C4—131no—
328C23×C4C22×D1312yes—
329C23×C4C22×D1311yescharacteristic
330C23×C4C22×D1311yescharacteristic
331C23×C4C22×D1312yes—
332C23×C4C22×D1311yescharacteristic
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—134no—
339C2×C4⋊C4—262no—
340C2×C4⋊C4—262no—
341C2×C4⋊C4—264no—
342C2×C4⋊C4—264no—
343C2×C4⋊C4—264no—
344C2×C4⋊C4—264no—
345C2×C4⋊C4—264no—
346C2×C4⋊C4—264no—
347C2×C4⋊C4—262no—
348C2×C4⋊C4—262no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—264no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—264no—
354C2×C4⋊C4—264no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—264no—
357C2×C4⋊C4—264no—
358C2×C4⋊C4—262no—
359C2×C4⋊C4—264no—
360C2×C4⋊C4—522no—
361C2×C4⋊C4—522no—
362C2×C4⋊C4—522no—
363C2×C4⋊C4—522no—
364C2×C42—134no—
365C2×C42—138no—
366C2×C42—264no—
367C2×C42—264no—
368C2×C42—264no—
369#95—22no—
370#95—24no—
371#95—138no—
372#95—134no—
373#95—264no—
374#95—264no—
375#95—262no—
376#95—264no—
377#95Dic2614yes—
378C2×C13C2×#39811yescharacteristic
379C2×C13#244012yes—
380C2×C13#244012yes—
381C2×C13#250111yescharacteristic
382C2×C13#250211yescharacteristic
383C2×C13#254111yescharacteristic
384C2×C13#254611yescharacteristic
385C2×C13#255212yes—
386C2×C13#255212yes—
387C2×C13#266011yescharacteristic
388C2×C13#286811yescharacteristic
389C24C23×D1311yescharacteristic
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—132no—
413C22×C4—132no—
414C22×C4—134no—
415C22×C4—134no—
416C22×C4—132no—
417C22×C4—134no—
418C22×C4—134no—
419C22×C4—132no—
420C22×C4—134no—
421C22×C4—134no—
422C22×C4—132no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—261no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—261no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—261no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—261no—
446C22×C4C2×Dic2614yes—
447C22×C4C2×Dic2612yes—
448C22×C4D4×D1312yes—
449C22×C4D4×D1314yes—
450C22×C4D4×D1312yes—
451C22×C4Q8×D1312yes—
452C22×C4Q8×D1314yes—
453C4⋊C4—48no—
454C4⋊C4—44no—
455C4⋊C4—268no—
456C4⋊C4—528no—
457C4⋊C4—528no—
458C4⋊C4—524no—
459C4⋊C4—528no—
460C4⋊C4—524no—
461C4⋊C4—524no—
462C4⋊C4—528no—
463C4⋊C4—524no—
464C4⋊C4—528no—
465C42—2616no—
466C42—268no—
467C13#1514511yescharacteristic, complemented, Sylow
468C23C22×Dic2611yescharacteristic
469C23C2×D4×D1312yes—
470C23C2×D4×D1311yescharacteristic
471C23C2×D4×D1311yescharacteristic
472C23#8825112yes—
473C23C2×Q8×D1311yescharacteristic
474C23C2×Q8×D1312yes—
475C23#8825411yescharacteristic
476C23#41×D1312yes—
477C23#41×D1311yescharacteristic
478C23#8825711yescharacteristic
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—134no—
507C2×C4—134no—
508C2×C4—138no—
509C2×C4—134no—
510C2×C4—138no—
511C2×C4—138no—
512C2×C4—134no—
513C2×C4—264no—
514C2×C4—264no—
515C2×C4—264no—
516C2×C4—264no—
517C2×C4—262no—
518C2×C4—264no—
519C2×C4—264no—
520C2×C4—264no—
521C2×C4—262no—
522C2×C4—264no—
523C2×C4—264no—
524C2×C4—262no—
525C2×C4—521no—
526C2×C4—522no—
527C2×C4—521no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—521no—
535C2×C4—522no—
536C2×C4—521no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—521no—
540C2×C4#8814218yes—
541C2×C4#8814214yes—
542C22C2×#8814212yes—
543C22C2×#8814211yescharacteristic
544C22D4×Dic2611yescharacteristic
545C22#1171924412yes—
546C22#1171927411yescharacteristic
547C22#1171929512yes—
548C22#1171929711yescharacteristic
549C22#1171930412yes—
550C22D13×#12111yescharacteristic
551C22#1171932812yes—
552C22D13×C22⋊Q812yes—
553C22#1171933311yescharacteristic
554C22#1171933612yes—
555C22#1171934112yes—
556C22D13×#12311yescharacteristic
557C22#1171936012yes—
558C22#1171939011yescharacteristic
559C22D13×#12512yes—
560C22D13×#12711yescharacteristic
561C22D13×C4⋊Q812yes—
562C22D13×C4⋊Q811yescharacteristic
563C22#1171943211yescharacteristic
564C22#1171943412yes—
565C4—28no—
566C4—24no—
567C4—42no—
568C4—82no—
569C4—81no—
570C4—138no—
571C4—268no—
572C4—264no—
573C4—522no—
574C4—1042no—
575C4—1041no—
576C2D13×#39811yescharacteristic
577C2#1311853112yes—
578C2#1311853712yes—
579C2#1311930211yescharacteristic
580C2#1311931211yescharacteristic
581C2#1311977711yescharacteristic
582C2#1311982311yescharacteristic
583C2#1311986612yes—
584C2#1311987312yes—
585C2#1312095411yescharacteristic
586C2#1312323311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, prime radical, cosocleC24×C13C24
FittingC13×#1444C2
hypercenter#1444D13
hypocenterC13#15145
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
321. Dic13#398semidirect
467. C13#15145semidirect

Maximal subgroups

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

subgroupindex
C2×#117183182
C2×#117186452
C2×#117183082
C2×#117186372
#131131012
#131131002
#131130992
#131130642
#95×Dic132
C13×#14442
#1514513