Finite Group Databasebeta

← #15789522

Subgroups — #15789522

Order 3328.

1502 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88143C211yesmaximal, characteristic
2C2×#11718637C211yesmaximal, characteristic
3C2×#11718309C211yesmaximal, characteristic
4#13113090C211yesmaximal, characteristic
5#13113089C211yesmaximal, characteristic
6#13113088C212yesmaximal
7#13113087C212yesmaximal
8#13113086C211yesmaximal, characteristic
9#13113064C212yesmaximal
10#13113064C212yesmaximal
11C13×#1441C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C22×#6101C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×#6101C2211yescharacteristic
21C22×#6101C2212yes—
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C2×#88143—24no—
25C2×#88143—24no—
26C2×#88143C418yescomplemented
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718637—24no—
39#11718309—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—42no—
55C2×C13×C4⋊C4C2×C414yes—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—42no—
60C2×C4⋊Dic13C2×C414yes—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—22no—
69C2×#6101—24no—
70C2×#6101—24no—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101—42no—
74C2×#6101—42no—
75C2×#6101C2×C414yes—
76C2×#6101C2×C414yes—
77C2×#6101C2×C414yes—
78C2×#6101C2×C414yes—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13C2×C414yes—
82C2×C4×Dic13D414yes—
83C2×C4×Dic13D414yes—
84C2×C4×Dic13Q818yes—
85#88143—232no—
86C13×#95—22no—
87C13×#95—42no—
88C13×#95—42no—
89#88071—22no—
90#88071—24no—
91#88071—42no—
92#88071—42no—
93#88071—42no—
94#88071—42no—
95#88071—42no—
96#88071—42no—
97#14283—131nomaximal, Sylow
98C24×C13C2411yescharacteristic
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13C22×C412yes—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13C2×D412yes—
129C22×C4×C13C2×Q814yes—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C22×Dic13—21no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13C22×C412yes—
158C22×Dic13C22×C412yes—
159C22×Dic13C22×C412yes—
160C22×Dic13C22×C412yes—
161C22×Dic13C2×D412yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×D412yes—
164C22×Dic13C2×D412yes—
165C22×Dic13C2×Q814yes—
166C22×Dic13C2×Q814yes—
167C22×Dic13#4114yes—
168C13×C4⋊C4—28no—
169C13×C4⋊C4—44no—
170C4⋊Dic13—28no—
171C4⋊Dic13—44no—
172#6101—28no—
173#6101—28no—
174#6101—28no—
175#6101—28no—
176#6101—48no—
177#6101—48no—
178C4×Dic13—216no—
179C4×Dic13C22⋊C4116yes—
180C22×#125—131no—
181C2×#384—131no—
182C2×#376—131no—
183#1441—132no—
184#1441—131no—
185#1441—132no—
186#1441—131no—
187#1441—131no—
188#1441D1311yescharacteristic
189C4⋊#95—132no—
190C4⋊#95—132no—
191C23×C13C23×C411yescharacteristic
192C23×C13C22×D411yescharacteristic
193C23×C13C22×D411yescharacteristic
194C23×C13C22×Q812yes—
195C23×C13C2×#4112yes—
196C23×C13H(5,𝔽2)11yescharacteristic
197C23×C13H(5,𝔽2)12yes—
198C23×C13H(5,𝔽2)11yescharacteristic
199C23×C132−1+411yescharacteristic
200C23×C132−1+411yescharacteristic
201C23×C132−1+412yes—
202C2×C4×C13—24no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—24no—
206C2×C4×C13—22no—
207C2×C4×C13—22no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13C2×C22⋊C414yes—
233C2×Dic13—22no—
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—24no—
244C2×Dic13—24no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—41no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—42no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13C2×C22⋊C414yes—
266C2×Dic13C2×C22⋊C414yes—
267C2×Dic13C4×Q818yes—
268C2×Dic13C22⋊Q818yes—
269C2×Dic13#12414yes—
270C2×Dic13C4⋊Q814yes—
271C2×#125—138no—
272C2×#125—264no—
273C2×#125—264no—
274C22×C4⋊C4—131no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4—131no—
277C22×C4⋊C4—131no—
278C22×C4⋊C4—131no—
279C22×C4⋊C4—132no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C4⋊C4C2×D1311yescharacteristic
284C22×C42—131no—
285C22×C42—132no—
286#384—264no—
287#376—264no—
288C2×#95—132no—
289C2×#95—131no—
290C2×#95—132no—
291C2×#95—132no—
292C2×#95—132no—
293C2×#95—132no—
294C2×#95—132no—
295C2×#95—132no—
296C2×#95C2×D1311yescharacteristic
297C2×#95C2×D1312yes—
298C2×#95C2×D1312yes—
299C22×C13C22×C22⋊C411yescharacteristic
300C22×C13C2×C4×Q812yes—
301C22×C13#52011yescharacteristic
302C22×C13#52011yescharacteristic
303C22×C13#52012yes—
304C22×C13C2×C22⋊Q812yes—
305C22×C13C2×#12411yescharacteristic
306C22×C13C2×C4⋊Q811yescharacteristic
307C22×C13#53511yescharacteristic
308C22×C13#53511yescharacteristic
309C22×C13#53611yescharacteristic
310C22×C13#53611yescharacteristic
311C22×C13#53712yes—
312C22×C13#53711yescharacteristic
313C22×C13#53711yescharacteristic
314C22×C13#54012yes—
315C22×C13#54012yes—
316C22×C13#54112yes—
317C22×C13#54112yes—
318C22×C13#54412yes—
319C22×C13#54412yes—
320C22×C13#54412yes—
321C22×C13#54412yes—
322C4×C13—24no—
323C4×C13—42no—
324C4×C13—42no—
325C4×C13—44no—
326C4×C13—82no—
327Dic13—24no—
328Dic13—42no—
329Dic13—42no—
330Dic13—44no—
331Dic13—82no—
332Dic13#39118yes—
333C23×C4—131no—
334C23×C4—131no—
335C23×C4—131no—
336C23×C4—131no—
337C23×C4—132no—
338C23×C4—132no—
339C23×C4C22×D1312yes—
340C23×C4C22×D1311yescharacteristic
341C23×C4C22×D1311yescharacteristic
342C23×C4C22×D1312yes—
343C23×C4C22×D1311yescharacteristic
344#125—2632no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—134no—
350C2×C4⋊C4—134no—
351C2×C4⋊C4—134no—
352C2×C4⋊C4—134no—
353C2×C4⋊C4—134no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—262no—
357C2×C4⋊C4—262no—
358C2×C4⋊C4—262no—
359C2×C4⋊C4—262no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—262no—
363C2×C4⋊C4—262no—
364C2×C4⋊C4—264no—
365C2×C4⋊C4—264no—
366C2×C4⋊C4—264no—
367C2×C4⋊C4—264no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—522no—
370C2×C4⋊C4—522no—
371C2×C4⋊C4—522no—
372C2×C4⋊C4C4×D1314yes—
373C2×C42—134no—
374C2×C42—134no—
375C2×C42—134no—
376C2×C42—138no—
377C2×C42—264no—
378C2×C42—264no—
379#95—22no—
380#95—42no—
381#95—42no—
382#95—264no—
383#95—262no—
384#95—522no—
385#95—522no—
386#95—522no—
387#95—522no—
388#95—522no—
389#95—522no—
390C2×C13C2×#39111yescharacteristic
391C2×C13#231111yescharacteristic
392C2×C13#231111yescharacteristic
393C2×C13#233012yes—
394C2×C13#233012yes—
395C2×C13#262912yes—
396C2×C13#262912yes—
397C2×C13#264111yescharacteristic
398C2×C13#264211yescharacteristic
399C2×C13#266011yescharacteristic
400C2×C13#266011yescharacteristic
401C24C23×D1311yescharacteristic
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—132no—
428C22×C4—132no—
429C22×C4—132no—
430C22×C4—134no—
431C22×C4—134no—
432C22×C4—132no—
433C22×C4—132no—
434C22×C4—132no—
435C22×C4—132no—
436C22×C4—132no—
437C22×C4—134no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—262no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—262no—
448C22×C4—261no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—261no—
452C22×C4—262no—
453C22×C4—261no—
454C22×C4—262no—
455C22×C4—261no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4C2×C4×D1312yes—
466C22×C4C2×C4×D1312yes—
467C22×C4C2×C4×D1312yes—
468C22×C4D4×D1312yes—
469C22×C4D4×D1312yes—
470C22×C4Q8×D1314yes—
471C4⋊C4—28no—
472C4⋊C4—44no—
473C4⋊C4—268no—
474C4⋊C4—268no—
475C4⋊C4—268no—
476C4⋊C4—268no—
477C4⋊C4—268no—
478C4⋊C4—524no—
479C4⋊C4—528no—
480C4⋊C4—528no—
481C42—1316no—
482C42—2616no—
483C13#1428311yescharacteristic, complemented, Sylow
484C23C22×C4×D1311yescharacteristic
485C23C2×D4×D1311yescharacteristic
486C23C2×D4×D1311yescharacteristic
487C23#8825112yes—
488C23#8825111yescharacteristic
489C23C2×Q8×D1312yes—
490C23#8825411yescharacteristic
491C23#41×D1312yes—
492C23#8825611yescharacteristic
493C23#8825711yescharacteristic
494C23#8825712yes—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—134no—
526C2×C4—134no—
527C2×C4—138no—
528C2×C4—138no—
529C2×C4—134no—
530C2×C4—134no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—262no—
537C2×C4—264no—
538C2×C4—262no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—264no—
543C2×C4—264no—
544C2×C4—264no—
545C2×C4—521no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—522no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4C22⋊C4×D1314yes—
564C22C2×C22⋊C4×D1311yescharacteristic
565C22#1171920911yescharacteristic
566C22#1171922811yescharacteristic
567C22#1171925112yes—
568C22C4×Q8×D1312yes—
569C22#1171929711yescharacteristic
570C22#1171930212yes—
571C22#1171931211yescharacteristic
572C22#1171931311yescharacteristic
573C22#1171932012yes—
574C22#1171932812yes—
575C22#1171932812yes—
576C22D13×C22⋊Q812yes—
577C22#1171933311yescharacteristic
578C22#1171933411yescharacteristic
579C22#1171935311yescharacteristic
580C22#1171936812yes—
581C22D13×#12411yescharacteristic
582C22#1171939412yes—
583C22#1171940112yes—
584C22#1171940612yes—
585C22D13×C4⋊Q811yescharacteristic
586C22#1171943412yes—
587C4—24no—
588C4—44no—
589C4—42no—
590C4—42no—
591C4—82no—
592C4—138no—
593C4—264no—
594C4—524no—
595C4—522no—
596C4—522no—
597C4—1042no—
598C2D13×#39111yescharacteristic
599C2#1311742311yescharacteristic
600C2#1311742511yescharacteristic
601C2#1311757212yes—
602C2#1311757412yes—
603C2#1312066512yes—
604C2#1312066812yes—
605C2#1312077811yescharacteristic
606C2#1312078311yescharacteristic
607C2#1312095411yescharacteristic
608C2#1312095911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#14283
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
26. C2×#88143C4semidirect
483. C13#14283semidirect

Maximal subgroups

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

subgroupindex
C22×#881432
C2×#117186372
C2×#117183092
#131130902
#131130892
#131130882
#131130872
#131130862
#131130642
C13×#14412
#1428313