Finite Group Databasebeta

← #15784807

Subgroups — #15784807

Order 3328.

2438 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88131C211yesmaximal, characteristic
2C23×#6101C211yesmaximal, characteristic
3C2×#11718872C211yesmaximal, characteristic
4C2×#11718604C211yesmaximal, characteristic
5#13113087C214yesmaximal, complemented
6#13113067C214yesmaximal, complemented
7#13113058C211yesmaximal, characteristic
8#13113058C211yesmaximal, characteristic
9C2×C13×#381C211yesmaximal, characteristic
10C24×C4×C13C2211yescharacteristic
11C24×Dic13C2211yescharacteristic
12C24×Dic13C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C22⋊Dic13C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×#6101—24no—
18C22×#6101—24no—
19C22×#6101C418yescomplemented
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C22×#6101C2212yes—
23C22×C4×Dic13C2212yes—
24C2×#88131—24no—
25C2×#88131—24no—
26C2×#88131—24no—
27C13×#381—24no—
28C2×C13×#95C2214yes—
29#11718872—24no—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2214yes—
33C2×#88071C2214yes—
34C2×#88071C2214yes—
35#11718604—24no—
36C25×C13C2311yescharacteristic
37C23×C4×C13—22no—
38C23×C4×C13—22no—
39C23×C4×C13—22no—
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13C2×C414yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×Dic13—22no—
48C23×Dic13—22no—
49C23×Dic13—22no—
50C23×Dic13—22no—
51C23×Dic13—22no—
52C23×Dic13—22no—
53C23×Dic13—28no—
54C23×Dic13C2×C414yes—
55C23×Dic13C2×C414yes—
56C23×Dic13D414yes—
57C23×Dic13D414yes—
58C23×Dic13C2312yes—
59C23×Dic13C2312yes—
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2312yes—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—22no—
65C2×C13×C22⋊C4—22no—
66C2×C13×C22⋊C4—22no—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4D414yes—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—22no—
73C2×C22⋊Dic13—22no—
74C2×C22⋊Dic13D414yes—
75C2×#6101—24no—
76C2×#6101—232no—
77C2×#6101—24no—
78C2×#6101—24no—
79C2×#6101—24no—
80C2×#6101—24no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101C2×C418yes—
84C2×#6101C2×C418yes—
85C2×C4×Dic13—24no—
86C2×C4×Dic13—24no—
87C2×C4×Dic13—24no—
88#88131—232no—
89C13×#95—28no—
90#88071—24no—
91#88071—24no—
92#88071—28no—
93#88071—28no—
94#88071—28no—
95#13870—131nomaximal, Sylow
96C24×C13—24no—
97C24×C13—24no—
98C24×C13C22×C412yes—
99C24×C13C2×D412yes—
100C24×C13C2×D412yes—
101C24×C13C2×D412yes—
102C24×C13C2×D412yes—
103C24×C13#4112yes—
104C24×C13#4112yes—
105C24×C13C2411yescharacteristic
106C22×C4×C13—28no—
107C22×C4×C13—28no—
108C22×C4×C13—28no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—24no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—24no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—24no—
122C22×C4×C13—22no—
123C22×C4×C13—24no—
124C22×C4×C13—44no—
125C22×C4×C13—44no—
126C22×C4×C13—44no—
127C22×C4×C13—44no—
128C22×C4×C13C22×C414yes—
129C22×C4×C13C2×D414yes—
130C22×Dic13—216no—
131C22×Dic13—216no—
132C22×Dic13—28no—
133C22×Dic13—28no—
134C22×Dic13—28no—
135C22×Dic13—28no—
136C22×Dic13—28no—
137C22×Dic13—28no—
138C22×Dic13—28no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—24no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—216no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—24no—
158C22×Dic13—22no—
159C22×Dic13—24no—
160C22×Dic13C22⋊C4116yes—
161C22×Dic13C22×C412yes—
162C22×Dic13C22×C412yes—
163C22×Dic13C22×C414yes—
164C22×Dic13C2×D414yes—
165C22×Dic13C2×D412yes—
166C22×Dic13C2×D412yes—
167C22×Dic13C2×D412yes—
168C22×Dic13C2×D412yes—
169C22×Dic13#4118yes—
170C13×C22⋊C4—28no—
171C13×C22⋊C4—44no—
172C22⋊Dic13—28no—
173C22⋊Dic13—44no—
174#6101—216no—
175#6101—216no—
176#6101—216no—
177C4×Dic13—216no—
178C22×#117—131no—
179C23×C4⋊C4—131no—
180C2×#381—131no—
181C2×#381—131no—
182C2×#381D1311yescharacteristic
183#1441—134no—
184#1436—134no—
185C22⋊#95—131no—
186C22⋊#95—131no—
187C23×C13—24no—
188C23×C13—24no—
189C23×C13—24no—
190C23×C13—24no—
191C23×C13—24no—
192C23×C13—24no—
193C23×C13—28no—
194C23×C13—28no—
195C23×C13—28no—
196C23×C13—28no—
197C23×C13C2×C22⋊C414yes—
198C23×C13C4×D414yes—
199C23×C13C4×D414yes—
200C23×C13#12014yes—
201C23×C13#12114yes—
202C23×C13#12114yes—
203C23×C13#12314yes—
204C23×C13C23×C411yescharacteristic
205C23×C13C22×D411yescharacteristic
206C23×C13C22×D411yescharacteristic
207C23×C13C22×D411yescharacteristic
208C23×C13C22×D411yescharacteristic
209C23×C13C2×#4114yes—
210C23×C13C2×#4111yescharacteristic
211C23×C13C2×#4111yescharacteristic
212C23×C132−1+414yes—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—28no—
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×C13—44no—
225C2×C4×C13—416no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—44no—
230C2×C4×C13—44no—
231C2×Dic13—232no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—28no—
247C2×Dic13—28no—
248C2×Dic13—232no—
249C2×Dic13—24no—
250C2×Dic13—28no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—44no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—44no—
258C2×Dic13—44no—
259C2×Dic13C2×C22⋊C414yes—
260C2×Dic13C2×C22⋊C414yes—
261C2×Dic13#11718yescomplemented
262C24×C4—131no—
263C24×C4—131no—
264C24×C4C2×D1311yescharacteristic
265C2×#117—264no—
266C2×#117—264no—
267C2×#117—264no—
268C22×C4⋊C4—138no—
269C22×C4⋊C4—132no—
270C22×C4⋊C4—132no—
271C22×C4⋊C4—132no—
272C22×C4⋊C4—264no—
273C22×C4⋊C4—264no—
274C22×C22⋊C4—131no—
275C22×C22⋊C4—131no—
276C22×C22⋊C4C2×D1311yescharacteristic
277C22×C22⋊C4C2×D1311yescharacteristic
278C22×C42—132no—
279#381—24no—
280#381—264no—
281#381—264no—
282C2×#95—134no—
283C2×#95—134no—
284C2×#95—132no—
285C2×#95—134no—
286C2×#95—132no—
287C2×#95C2×D1314yes—
288C22×C13—24no—
289C22×C13—28no—
290C22×C13—28no—
291C22×C13—28no—
292C22×C13—28no—
293C22×C13—28no—
294C22×C13—28no—
295C22×C13—24no—
296C22×C13#38618yes—
297C22×C13C22×C22⋊C411yescharacteristic
298C22×C13C2×#11712yes—
299C22×C13C2×C4×D411yescharacteristic
300C22×C13C2×C4×D411yescharacteristic
301C22×C13#51912yes—
302C22×C13C2×#12011yescharacteristic
303C22×C13C2×#12111yescharacteristic
304C22×C13C2×#12111yescharacteristic
305C22×C13C2×#12311yescharacteristic
306C22×C13#52512yes—
307C22×C13#52512yes—
308C22×C13#53612yes—
309C22×C13#53612yes—
310C22×C13#54714yes—
311C22×C13#54714yes—
312C22×C13#55214yes—
313C22×C13#55214yes—
314C4×C13—44no—
315C4×C13—44no—
316C4×C13—82no—
317Dic13—28no—
318Dic13—24no—
319Dic13—24no—
320Dic13—44no—
321Dic13—82no—
322C25C22×D1311yescharacteristic
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—134no—
330C23×C4—134no—
331C23×C4—134no—
332C23×C4—131no—
333C23×C4—132no—
334C23×C4—131no—
335C23×C4—134no—
336C23×C4—132no—
337C23×C4—132no—
338C23×C4—268no—
339C23×C4—262no—
340C23×C4—262no—
341C23×C4—262no—
342C23×C4—262no—
343C23×C4—262no—
344C23×C4—262no—
345C23×C4C4×D1314yes—
346C23×C4C22×D1312yes—
347C23×C4C22×D1312yes—
348C23×C4C22×D1312yes—
349#117—2632no—
350C2×C4⋊C4—138no—
351C2×C4⋊C4—138no—
352C2×C4⋊C4—2632no—
353C2×C4⋊C4—264no—
354C2×C4⋊C4—264no—
355C2×C4⋊C4—264no—
356C2×C4⋊C4—264no—
357C2×C4⋊C4—264no—
358C2×C4⋊C4—264no—
359C2×C4⋊C4—264no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—134no—
366C2×C22⋊C4—262no—
367C2×C22⋊C4—262no—
368C2×C22⋊C4—262no—
369C2×C22⋊C4—262no—
370C2×C22⋊C4—262no—
371C2×C22⋊C4C22⋊D1314yes—
372C2×C42—264no—
373C2×C42—264no—
374C2×C42—264no—
375#95—28no—
376#95—268no—
377#95—268no—
378#95—268no—
379#95—264no—
380#95—264no—
381C2×C13—28no—
382C2×C13#228011yescharacteristic
383C2×C13C2×#38611yescharacteristic
384C2×C13#231011yescharacteristic
385C2×C13#234412yes—
386C2×C13#234412yes—
387C2×C13#240612yes—
388C2×C13#241312yes—
389C2×C13#241312yes—
390C2×C13#248412yes—
391C24—24no—
392C24—24no—
393C24C2×C4×D1312yes—
394C24#612712yes—
395C24D4×D1312yes—
396C24D4×D1312yes—
397C24D4×D1312yes—
398C24#612912yes—
399C24C2×C22⋊D1312yes—
400C24C23×D1311yescharacteristic
401C22×C4—28no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—1316no—
424C22×C4—132no—
425C22×C4—132no—
426C22×C4—134no—
427C22×C4—132no—
428C22×C4—132no—
429C22×C4—132no—
430C22×C4—132no—
431C22×C4—138no—
432C22×C4—134no—
433C22×C4—2616no—
434C22×C4—2616no—
435C22×C4—2616no—
436C22×C4—268no—
437C22×C4—268no—
438C22×C4—268no—
439C22×C4—268no—
440C22×C4—268no—
441C22×C4—268no—
442C22×C4—268no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—264no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—262no—
455C22×C4—264no—
456C22×C4—264no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4C2×C4×D1314yes—
464C22×C4C2×C22⋊D1314yes—
465C4⋊C4—2616no—
466C4⋊C4—2616no—
467C4⋊C4—2616no—
468C22⋊C4—28no—
469C22⋊C4—44no—
470C22⋊C4—268no—
471C22⋊C4—524no—
472C42—2616no—
473C13#1387011yescharacteristic, complemented, Sylow
474C23—24no—
475C23—24no—
476C23—28no—
477C23—28no—
478C23—24no—
479C23—24no—
480C23—28no—
481C23—28no—
482C23—24no—
483C23—24no—
484C23C22⋊C4×D1314yes—
485C23#8813514yes—
486C23#8813714yes—
487C23#8813814yes—
488C23C4×C22⋊D1314yes—
489C23#8819114yes—
490C23#8819214yes—
491C23C22×C4×D1311yescharacteristic
492C23C2×#612711yescharacteristic
493C23C2×D4×D1311yescharacteristic
494C23C2×D4×D1311yescharacteristic
495C23C2×D4×D1311yescharacteristic
496C23C2×#612911yescharacteristic
497C23#41×D1314yes—
498C23#8825714yes—
499C23C22×C22⋊D1311yescharacteristic
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—28no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—416no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—134no—
519C2×C4—134no—
520C2×C4—138no—
521C2×C4—2632no—
522C2×C4—264no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—264no—
530C2×C4—262no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—268no—
537C2×C4—268no—
538C2×C4—2632no—
539C2×C4—264no—
540C2×C4—268no—
541C2×C4—524no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—524no—
546C2×C4—522no—
547C2×C4—524no—
548C2×C4—522no—
549C22—28no—
550C22—28no—
551C22—28no—
552C22—24no—
553C22—28no—
554C22—28no—
555C22—28no—
556C22—24no—
557C22#1171861718yes—
558C22C2×C22⋊C4×D1311yescharacteristic
559C22C2×#8813511yescharacteristic
560C22C2×#8813711yescharacteristic
561C22C2×#8813811yescharacteristic
562C22#1171922112yes—
563C22D13×#11712yes—
564C22#1171923614yes—
565C22#1171935312yes—
566C22#1171935312yes—
567C22#1171935514yes—
568C22#1171936014yes—
569C22#1171936112yes—
570C22#1171936112yes—
571C22C2×C4×C22⋊D1311yescharacteristic
572C22C2×#8819111yescharacteristic
573C22C2×#8819211yescharacteristic
574C22#1171952914yes—
575C4—44no—
576C4—44no—
577C4—82no—
578C4—268no—
579C4—264no—
580C4—264no—
581C4—524no—
582C4—1042no—
583C2—28no—
584C2#1311721611yescharacteristic
585C2C2×#1171861711yescharacteristic
586C2#1311742111yescharacteristic
587C2#1311770012yes—
588C2#1311770612yes—
589C2#1311816812yes—
590C2#1311823912yes—
591C2#1311824512yes—
592C2#1311912012yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#381C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#381D13
hypocenterC13#13870
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
5. #13113087C2semidirect
6. #13113067C2semidirect
19. C22×#6101C4semidirect
261. C2×Dic13#117semidirect
473. C13#13870semidirect

Maximal subgroups

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

subgroupindex
C22×#881312
C23×#61012
C2×#117188722
C2×#117186042
#131130872
#131130672
#131130582
C2×C13×#3812
#1387013