Finite Group Databasebeta

← #15897231

Subgroups — #15897231

Order 3328.

1198 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718745C211yesmaximal, characteristic, complemented
2C2×#11718744C211yesmaximal, characteristic, complemented
3C4×#88184C211yesmaximal, characteristic
4#13116029C212yesmaximal, complemented
5#13115837C212yesmaximal
6#13115785C211yesmaximal, characteristic, complemented
7#13115760C211yesmaximal, characteristic, complemented
8#13115191C212yesmaximal, complemented
9#13115104C212yesmaximal, complemented
10#13114816C211yesmaximal, characteristic, complemented
11C2×C13×#533C211yesmaximal, characteristic, complemented
12C13×#533—24no—
13C13×#533—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#125—21no—
17C2×C13×C22⋊Q8—21no—
18C2×C13×C22⋊Q8C2212yes—
19C2×C4×Q8×C13—21no—
20C2×C4×Q8×C13C2212yes—
21C2×C13×#117—21no—
22C22×C42×C13C2211yescharacteristic
23C22×#6106C2212yes—
24C2×#88184C2211yescharacteristic
25C2×C4×C22⋊D13—21no—
26C2×C4×D52C2211yescharacteristic
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30#11718874—21no—
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2212yes—
33#11718745—24no—
34#11718744—24no—
35C2×#88049C2212yes—
36C2×#88048C2212yes—
37#11718601—21no—
38#11718600C2211yescharacteristic
39C4×#6103—21no—
40C4×C4⋊Dic13C2211yescharacteristic
41#11718589C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13C2312yes—
49C23×C4×C13D411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C22×C22⋊D13—21no—
53C22×D52C2311yescharacteristic
54C22×C4×D13—21no—
55C13×C4⋊Q8—22no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8D414yescomplemented
58C13×C4⋊Q8D414yescomplemented
59C13×#125—28no—
60C13×C22⋊Q8—28no—
61C13×C22⋊Q8—24no—
62C13×C22⋊Q8—24no—
63C4×Q8×C13—28no—
64C4×Q8×C13—24no—
65C4×Q8×C13—24no—
66C13×#117—28no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C22⋊C4—22no—
74C2×C42×C13—22no—
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13D411yescharacteristic
78C2×C42×C13D411yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C22⋊Dic13—21no—
82C2×#6106—24no—
83C2×#6106—24no—
84C2×#6106—42no—
85#88184—22no—
86#88184—22no—
87C4×C22⋊D13—44no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×#6101—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2312yes—
98C22×#1055C2312yes—
99C4×D52—22no—
100C4×D52—22no—
101#88075—24no—
102#88075—24no—
103#88075—42no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107C22⋊#1055—42no—
108#88049—24no—
109#88048—24no—
110C4⋊#1055—22no—
111C4⋊#1055—22no—
112#24151—131nomaximal, Sylow
113C24×C13C2×D411yescharacteristic
114C23×D13—21no—
115C2×Q8×C13—24no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13—42no—
122C2×Q8×C13—42no—
123C2×Q8×C13C2×D414yes—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—41no—
136C22×C4×C13—41no—
137C22×C4×C13SD1614yescomplemented
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2411yescharacteristic
144C2×C22⋊D13—24no—
145C2×C22⋊D13—42no—
146C2×C22⋊D13—42no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52#4112yes—
156C2×C4×D13—42no—
157C2×C4×D13—42no—
158C2×C4×D13—42no—
159C13×C4⋊C4—28no—
160C13×C4⋊C4—28no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4C2×D414yes—
166C13×C22⋊C4—28no—
167C42×C13—28no—
168C42×C13—22no—
169C42×C13—22no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13C2×D412yes—
173C42×C13C2×D412yes—
174C22⋊Dic13—42no—
175#6106—48no—
176#6103—24no—
177#6103—42no—
178#6103—42no—
179#6103—42no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13#4112yes—
186#6101—42no—
187C4×Dic13—42no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#1055—22no—
194C2×#533D1311yescharacteristic, complemented
195C2×#476—131no—
196C2×#461—131no—
197C4×#121—131no—
198#2035—132no—
199#2000—132no—
200#1987—131no—
201#1981—131no—
202#1880—132no—
203#1865—132no—
204#1797—131no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13C2×SD1612yes—
212C23×C13C22×D411yescharacteristic
213C22×D13—22no—
214C22×D13—41no—
215C22×D13—41no—
216C22×D13—41no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220Q8×C13—24no—
221Q8×C13—24no—
222Q8×C13—48no—
223Q8×C13—42no—
224Q8×C13—42no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—28no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—44no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13#12012yes—
248C2×C4×C13#12012yes—
249C2×C4×C13C2×SD1612yes—
250C2×C4×C13C2×SD1612yes—
251C2×C4×C13#13712yes—
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13H(5,𝔽2)11yescharacteristic
257C2×C4×C132−1+411yescharacteristic
258C22⋊D13—48no—
259C2×Dic13—22no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268D52—22no—
269D52—22no—
270D52—41no—
271D52—41no—
272C4×D13—84no—
273#1055—42no—
274#1055—42no—
275C22×SD16—132no—
276#533—24no—
277#533—24no—
278C2×C4⋊Q8C2×D1311yescharacteristic
279C2×C4⋊Q8C2×D1311yescharacteristic
280C2×#125—21no—
281C2×C22⋊Q8—21no—
282C2×C22⋊Q8C2×D1312yes—
283C2×#121—131no—
284C2×C4×Q8—21no—
285C2×C4×Q8C2×D1312yes—
286C2×C4×D4—131no—
287C2×C4×D4—261no—
288C2×#117—21no—
289C22×C42C2×D1311yescharacteristic
290#476—264no—
291#461—264no—
292C2×#106—132no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8—131no—
295C2×#103—132no—
296C2×#103—132no—
297C2×#103—132no—
298C2×#102—132no—
299C2×C22⋊C8—132no—
300#390—131no—
301#389—131no—
302#388—261no—
303#386—261no—
304#380—131no—
305C4×C4⋊C4—131no—
306C4×C22⋊C4—261no—
307#340—132no—
308#340—132no—
309#336—132no—
310C22×C13—22no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—41no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13C2×#12011yescharacteristic
318C22×C13#52511yescharacteristic
319C22×C13#53711yescharacteristic
320C22×C13C22×SD1611yescharacteristic
321C22×C13C2×#13711yescharacteristic
322C22×C13#57511yescharacteristic
323C22×C13#57511yescharacteristic
324C2×D13—42no—
325C2×D13—42no—
326C2×D13—42no—
327C2×D13—81no—
328C2×D13—81no—
329C2×D13—81no—
330C2×D13—81no—
331C4×C13—22no—
332C4×C13—22no—
333C4×C13—41no—
334C4×C13—44no—
335C4×C13—41no—
336C4×C13—44no—
337C4×C13#44814yes—
338C4×C13#54611yescharacteristic
339C4×C13#54711yescharacteristic
340C4×C13#54811yescharacteristic
341C4×C13#55011yescharacteristic
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345C22×Q8—21no—
346C22×Q8C22×D1312yes—
347C22×D4—131no—
348C22×D4—261no—
349C23×C4—261no—
350C23×C4C22⋊D1311yescharacteristic
351C23×C4C22⋊D1311yescharacteristic
352C23×C4C22×D1311yescharacteristic
353C2×SD16—264no—
354C2×SD16—264no—
355C2×SD16—522no—
356C22×C8—132no—
357C22×C8—132no—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4⋊Q8C22⋊D1314yescomplemented
361C4⋊Q8C22⋊D1314yescomplemented
362#125—28no—
363C22⋊Q8—28no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366#121—262no—
367#121—262no—
368C4×Q8—28no—
369C4×Q8—24no—
370C4×Q8—24no—
371C4×D4—262no—
372C4×D4—262no—
373C4×D4—524no—
374#117—28no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22×D1312yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—261no—
395C2×C42C22⋊D1311yescharacteristic
396C2×C42C22⋊D1311yescharacteristic
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399#106—264no—
400C4⋊C8—262no—
401C4⋊C8—262no—
402#103—264no—
403#103—264no—
404#103—522no—
405#102—264no—
406C22⋊C8—522no—
407#95—261no—
408#95—261no—
409#95—261no—
410C2×C13—42no—
411C2×C13#240711yescharacteristic
412C2×C13C2×#44811yescharacteristic
413C2×C13#300511yescharacteristic
414C2×C13#310111yescharacteristic
415C2×C13#311611yescharacteristic
416C2×C13#324611yescharacteristic
417C2×C13#325211yescharacteristic
418D13—82no—
419C24—261no—
420C24C2×C22⋊D1311yescharacteristic
421C2×Q8—24no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8C2×C22⋊D1314yes—
430C2×D4—132no—
431C2×D4—264no—
432C2×D4—261no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C2×D4—261no—
437C2×D4—522no—
438C2×D4—522no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—522no—
456C22×C4—522no—
457C22×C4—522no—
458C22×C4#610614yescomplemented
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C23×D1311yescharacteristic
465SD16—528no—
466C2×C8—262no—
467C2×C8—262no—
468C2×C8—262no—
469C2×C8—262no—
470C2×C8—262no—
471C2×C8—262no—
472C4⋊C4—28no—
473C4⋊C4—28no—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—132no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—522no—
485C4⋊C4C2×C22⋊D1314yes—
486C22⋊C4—28no—
487C22⋊C4—264no—
488C22⋊C4—522no—
489C22⋊C4—522no—
490C22⋊C4—522no—
491C22⋊C4—522no—
492C42—28no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—522no—
498C42C2×C22⋊D1312yes—
499C42C2×C22⋊D1312yes—
500C13#2415111yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—262no—
508C23—521no—
509C23—521no—
510C23—521no—
511C23—521no—
512C23—521no—
513C23—521no—
514C23C2×#610612yes—
515C23C22×C22⋊D1311yescharacteristic
516Q8—24no—
517Q8—24no—
518Q8—48no—
519Q8—42no—
520Q8—42no—
521D4—262no—
522D4—262no—
523D4—528no—
524D4—521no—
525D4—521no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—262no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—1044no—
558C2×C4C2×#610612yes—
559C2×C4C2×#610612yes—
560C2×C4#8819612yes—
561C2×C4#8820712yes—
562C2×C4#8820712yes—
563C2×C4#41×D1311yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C2×C4#8825611yescharacteristic
566C2×C4#8825711yescharacteristic
567C2×C4C22×C22⋊D1311yescharacteristic
568C2×C4C22×C22⋊D1311yescharacteristic
569C8—522no—
570C8—522no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—522no—
579C22—522no—
580C22—522no—
581C22—1041no—
582C22—1041no—
583C22—1041no—
584C22—1041no—
585C22C22×#610611yescharacteristic
586C22C2×#8819611yescharacteristic
587C22#1171952711yescharacteristic
588C22#1171952711yescharacteristic
589C22#1171953311yescharacteristic
590C22#1171953811yescharacteristic
591C22C2×#8820711yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—44no—
596C4—41no—
597C4—44no—
598C4—522no—
599C4—1041no—
600C4—1041no—
601C4#1171888814yes—
602C4#1171952911yescharacteristic
603C4#1171953411yescharacteristic
604C4#1171953611yescharacteristic
605C4#1171953911yescharacteristic
606C2—42no—
607C2—1042no—
608C2#1311817511yescharacteristic
609C2C2×#1171888811yescharacteristic
610C2#1312407811yescharacteristic
611C2#1312484011yescharacteristic
612C2#1312499211yescharacteristic
613C2#1312614811yescharacteristic
614C2#1312620311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#533C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#533D13
hypocenterC13#24151
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×#11718745C2semidirect
2. C2×#11718744C2semidirect
4. #13116029C2semidirect
6. #13115785C2semidirect
7. #13115760C2semidirect
8. #13115191C2semidirect
9. #13115104C2semidirect
10. #13114816C2semidirect
11. C2×C13×#533C2semidirect
57. C13×C4⋊Q8D4semidirect
58. C13×C4⋊Q8D4semidirect
137. C22×C4×C13SD16semidirect
194. C2×#533D13semidirect
360. C4⋊Q8C22⋊D13semidirect
361. C4⋊Q8C22⋊D13semidirect
458. C22×C4#6106semidirect
500. C13#24151semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
C2×#117187442
C4×#881842
#131160292
#131158372
#131157852
#131157602
#131151912
#131151042
#131148162
C2×C13×#5332
#2415113