Finite Group Databasebeta

← #16798759

Subgroups — #16798759

Order 3328.

898 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131317C211yesmaximal, characteristic
2#13131273C211yesmaximal, characteristic
3#13130900C212yesmaximal, complemented
4#13130899C212yesmaximal, complemented
5#13130898C212yesmaximal, complemented
6#13130897C212yesmaximal, complemented
7#13130525C211yesmaximal, characteristic
8#13130525C211yesmaximal, characteristic
9C2×#11718265C211yesmaximal, characteristic
10#13130501C211yesmaximal, characteristic
11D13×#427C211yesmaximal, characteristic
12C2×#88237C2211yescharacteristic
13C22×C4⋊#261C2211yescharacteristic
14C22×C4⋊#261C2211yescharacteristic
15C2×D13⋊M16C2211yescharacteristic
16C22×C8×D13C2211yescharacteristic
17D13×#117C2211yescharacteristic
18D13×#117C2211yescharacteristic
19#11719083C2212yes—
20#11719083C2212yes—
21C4⋊C4×#261C2212yes—
22C4⋊C4×#261C2212yes—
23#11719070—22no—
24C22⋊C4×#261—22no—
25#11719060—21no—
26#11719059—21no—
27C4×C4⋊#261—21no—
28C4×C4⋊#261—21no—
29C13×#427C411yescharacteristic, complemented
30#11718767C411yescharacteristic, complemented
31#11718659C411yescharacteristic, complemented
32#11718659C411yescharacteristic, complemented
33#11718541C411yescharacteristic, complemented
34#11718541C411yescharacteristic, complemented
35D13×#107C2211yescharacteristic
36D13×#107C2211yescharacteristic
37#11718521C411yescharacteristic, complemented
38#11718521C411yescharacteristic, complemented
39D13×#106C2211yescharacteristic
40D13×#106C2211yescharacteristic
41#11718265C2212yes—
42#11718265C2212yes—
43(C2×#261)⋊C8C2212yes—
44(C2×#261)⋊C8C2212yes—
45#11718246C2212yes—
46#11718246C2212yes—
47#11718246C2212yes—
48#11718246C2212yes—
49C23×#261—21no—
50C23×#261—21no—
51C22×C4×D13C2311yescharacteristic
52C2×C22⋊#261D412yes—
53C2×#6122—21no—
54#88237—22no—
55#88237—22no—
56C2×C4⋊#261—21no—
57C2×C4⋊#261—22no—
58C2×C4⋊#261—22no—
59C2×C4⋊#261—22no—
60C2×C4⋊#261—21no—
61C2×C4⋊#261—22no—
62C2×C4⋊#261—22no—
63C2×C4⋊#261D411yescharacteristic
64C2×C4⋊#261D411yescharacteristic
65C2×C4⋊#261Q814yes—
66C2×C4⋊#261C2312yes—
67C2×C4⋊#261C2312yes—
68C2×C4×#261—22no—
69C2×C4×#261—22no—
70C2×C4×#261C2312yes—
71D13⋊M16—22no—
72D13⋊M16—22no—
73C2×#6118—21no—
74C2×D13⋊C8C2312yes—
75C22×C8×C13C2×C411yescharacteristic
76C13×#117C2×C411yescharacteristic
77C13×#117C2×C411yescharacteristic
78#88180C2×C411yescharacteristic
79#88180C2×C411yescharacteristic
80C22×#1055C2×C411yescharacteristic
81C2×C8×D13—22no—
82C2×C8×D13—22no—
83C2×C8×D13C2×C411yescharacteristic
84C2×C8×D13C2×C411yescharacteristic
85C2×C8×D13C2311yescharacteristic
86C2×C8×D13C2311yescharacteristic
87#88146C2×C411yescharacteristic
88#88146C2×C411yescharacteristic
89#88146C2×C411yescharacteristic
90#88146C2×C411yescharacteristic
91C4⋊C4×D13C2311yescharacteristic
92C4⋊C4×D13C2311yescharacteristic
93C4⋊C4×D13C2311yescharacteristic
94C4⋊C4×D13C2311yescharacteristic
95C22⋊C4×D13—21no—
96C22⋊C4×D13—21no—
97#88131—21no—
98#88131—21no—
99#88126—21no—
100#88126—21no—
101C42×D13—21no—
102C42×D13—21no—
103(C2×#261)⋊C4—22no—
104(C2×#261)⋊C4—22no—
105(C2×#261)⋊C4—22no—
106(C2×#261)⋊C4—22no—
107C13×#107C2×C411yescharacteristic, complemented
108C13×#107C2×C411yescharacteristic, complemented
109C13×#106C2×C411yescharacteristic, complemented
110C13×#106C2×C411yescharacteristic, complemented
111#88058C2×C411yescharacteristic, complemented
112#88058C2×C411yescharacteristic, complemented
113#88057C2×C411yescharacteristic, complemented
114#88057C2×C411yescharacteristic, complemented
115#88048C2×C411yescharacteristic, complemented
116#88048C2×C411yescharacteristic, complemented
117#88048C2×C411yescharacteristic, complemented
118#88048C2×C411yescharacteristic, complemented
119#88047C2×C411yescharacteristic, complemented
120#88047C2×C411yescharacteristic, complemented
121#88047C2×C411yescharacteristic, complemented
122#88047C2×C411yescharacteristic, complemented
123#21039—131nomaximal, Sylow
124C23×D13C2×D411yescharacteristic
125C22×#261—22no—
126C22×#261—24no—
127C22×#261—22no—
128C22×#261—42no—
129C22×#261—81no—
130C22×#261—81no—
131C22×#261—81no—
132C22×#261—81no—
133C22×#261C2×D412yes—
134C22×#261C2×D412yes—
135C22×C4×C13C22×C411yescharacteristic
136C22×Dic13#4111yescharacteristic
137C2×C4×D13—21no—
138C2×C4×D13—21no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13C22×C411yescharacteristic
142C2×C4×D13C2×D411yescharacteristic
143C2×C4×D13C2×Q812yes—
144C2×C4×D13#4112yes—
145C2×C4×D13#4112yes—
146C2×C4×D13#4112yes—
147C2×C4×D13#4111yescharacteristic
148C2×C4×D13C2411yescharacteristic
149C22⋊#261—24no—
150#6122—42no—
151C2×#1057—22no—
152C4⋊#261—24no—
153C4⋊#261—22no—
154C4⋊#261—22no—
155C4⋊#261—22no—
156C4⋊#261—22no—
157C4⋊#261—22no—
158C4⋊#261—42no—
159C4⋊#261—82no—
160C4⋊#261—82no—
161C4⋊#261C2×Q814yes—
162C4×#261—22no—
163C4×#261—22no—
164C4×#261—82no—
165C4×#261—82no—
166#6118—42no—
167D13⋊C8—22no—
168D13⋊C8—22no—
169C2×C8×C13—22no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C13×C4⋊C4C22×C411yescharacteristic
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C42×C13—21no—
179C42×C13—21no—
180C22⋊Dic13—21no—
181C22⋊Dic13—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C2×#1055—22no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C8×D13—22no—
204C8×D13—22no—
205C8×D13—21no—
206C8×D13—21no—
207C8×D13—21no—
208C8×D13—21no—
209C2×#427—131no—
210#2317—131no—
211#2274—131no—
212#1921—132no—
213#1920—132no—
214#1919—132no—
215#1918—132no—
216#1736—131no—
217#1736—131no—
218C2×#340—131no—
219#1729—131no—
220C23×C13C4×D411yescharacteristic
221C22×D13—21no—
222C22×D13—21no—
223C22×D13—21no—
224C22×D13—21no—
225C22×D13C4×D411yescharacteristic
226C22×D13C22⋊Q812yes—
227C22×D13#12312yes—
228C22×D13C22×D411yescharacteristic
229C2×#261—24no—
230C2×#261—22no—
231C2×#261—22no—
232C2×#261—22no—
233C2×#261—22no—
234C2×#261—22no—
235C2×#261—22no—
236C2×#261—42no—
237C2×#261—42no—
238C2×#261—42no—
239C2×#261—42no—
240C2×#261—42no—
241C2×#261—84no—
242C2×#261—84no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13#11712yes—
248C2×C4×C13C4×D411yescharacteristic
249C2×C4×C13C4×Q812yes—
250C2×C4×C13C23×C411yescharacteristic
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13C4×D411yescharacteristic
256C2×Dic13#12512yes—
257C2×Dic13#12612yes—
258C2×Dic13C2×#4111yescharacteristic
259C4×D13—41no—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13#11712yes—
268C4×D13C4×Q812yes—
269C4×D13C22⋊Q812yes—
270C4×D13#12312yes—
271C4×D13#12512yes—
272C4×D13#12612yes—
273C4×D13C22×Q811yescharacteristic
274C4×D13C2×#4111yescharacteristic
275C4×D13C2×#4111yescharacteristic
276C4×D13C2×#4111yescharacteristic
277#1057—42no—
278C8×C13—21no—
279C8×C13—21no—
280#1055—21no—
281#1055—21no—
282C22×M16—131no—
283C23×C8—131no—
284C2×#117—131no—
285C2×#117—131no—
286C2×#117—131no—
287C22×C4⋊C4—131no—
288C22×C4⋊C4—131no—
289#427—131no—
290#427—131no—
291#427—131no—
292#427—131no—
293#427—131no—
294#427—131no—
295#427—131no—
296#427#26111yescharacteristic, complemented
297C2×#107—131no—
298C2×#107—131no—
299C2×#106—131no—
300C2×#106—131no—
301#389—132no—
302#389—132no—
303#385—262no—
304#384—261no—
305#382—261no—
306C4×C4⋊C4—132no—
307C4×C4⋊C4—132no—
308C4×C4⋊C4—261no—
309C4×C4⋊C4—261no—
310C4×C22⋊C4—262no—
311#340—132no—
312#340—132no—
313#340—132no—
314#340—132no—
315#340—132no—
316#340—132no—
317#336—132no—
318#336—132no—
319C22×C13—21no—
320C22×C13—21no—
321C22×C13#38712yes—
322C22×C13C2×C4×D411yescharacteristic
323C2×D13—21no—
324C2×D13—21no—
325C2×D13—22no—
326C2×D13—22no—
327C2×D13—22no—
328C2×D13—22no—
329C2×D13#38712yes—
330C2×D13C2×C22⋊Q811yescharacteristic
331C2×D13C2×#12311yescharacteristic
332C2×D13#57611yescharacteristic
333C2×D13#57711yescharacteristic
334C2×D13#57711yescharacteristic
335C2×D13#57811yescharacteristic
336#261—44no—
337#261—42no—
338#261—42no—
339#261—82no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13#38712yes—
345C4×C13C2×#11711yescharacteristic
346C4×C13C2×C4×Q811yescharacteristic
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350Dic13—41no—
351Dic13#38712yes—
352Dic13C2×#12511yescharacteristic
353Dic13C2×#12611yescharacteristic
354C23×C4—131no—
355C23×C4—261no—
356C23×C4—261no—
357C2×M16—261no—
358C2×M16—262no—
359C2×M16—262no—
360C2×M16—261no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8—131no—
365C22×C8—131no—
366C22×C8—132no—
367C22×C8—262no—
368C22×C8—262no—
369C22×C8C2×#26111yescharacteristic
370#117—131no—
371#117—131no—
372#117—131no—
373#117—131no—
374#117—131no—
375#117—131no—
376#117—261no—
377#117—261no—
378#117—261no—
379#117—261no—
380#117—262no—
381#117—262no—
382#117C2×#26111yescharacteristic
383#117C2×#26111yescharacteristic
384C2×C4⋊C4—132no—
385C2×C4⋊C4—134no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—132no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—262no—
395C2×C4⋊C4—262no—
396C2×C4⋊C4—262no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—262no—
399C2×C4⋊C4—262no—
400C2×C22⋊C4—132no—
401C2×C22⋊C4—261no—
402C2×C22⋊C4—261no—
403C2×C42—132no—
404C2×C42—261no—
405C2×C42—261no—
406C2×C42—262no—
407C2×C42—262no—
408#107—131no—
409#107—131no—
410#107—131no—
411#107—131no—
412#107—131no—
413#107—131no—
414#107C2×#26111yescharacteristic, complemented
415#107C2×#26111yescharacteristic, complemented
416#106—131no—
417#106—131no—
418#106—131no—
419#106—131no—
420#106—131no—
421#106—131no—
422#106C2×#26111yescharacteristic, complemented
423#106C2×#26111yescharacteristic, complemented
424#95—262no—
425#95—262no—
426#95—262no—
427#95—262no—
428C2×C13—22no—
429C2×C13C2×#38711yescharacteristic
430C2×C13#295111yescharacteristic
431C2×C13#295211yescharacteristic
432D13—22no—
433D13#308111yescharacteristic
434D13#308211yescharacteristic
435D13#309611yescharacteristic
436D13#309711yescharacteristic
437C24—131no—
438C22×C4—131no—
439C22×C4—132no—
440C22×C4—132no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—132no—
444C22×C4—132no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—132no—
448C22×C4—132no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—262no—
454C22×C4—264no—
455C22×C4—262no—
456C22×C4—522no—
457C22×C4—1041no—
458C22×C4—1041no—
459C22×C4—1041no—
460C22×C4—1041no—
461C22×C4C22×#26111yescharacteristic
462M16—522no—
463M16—522no—
464C2×C8—22no—
465C2×C8—131no—
466C2×C8—131no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—262no—
472C2×C8—262no—
473C2×C8—262no—
474C2×C8—262no—
475C2×C8—262no—
476C2×C8—262no—
477C2×C8C22×#26111yescharacteristic
478C2×C8C22×#26111yescharacteristic
479C4⋊C4—134no—
480C4⋊C4—131no—
481C4⋊C4—131no—
482C4⋊C4—131no—
483C4⋊C4—131no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—264no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4—262no—
493C4⋊C4—262no—
494C4⋊C4—522no—
495C4⋊C4—1042no—
496C4⋊C4—1042no—
497C4⋊C4C22×#26111yescharacteristic
498C4⋊C4C22×#26111yescharacteristic
499C4⋊C4C22×#26111yescharacteristic
500C4⋊C4C22×#26111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—264no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C42—21no—
511C42—21no—
512C42—261no—
513C42—261no—
514C42—261no—
515C42—261no—
516C42—262no—
517C42—262no—
518C42—261no—
519C42—261no—
520C42—1042no—
521C42—1042no—
522C13#2103911yescharacteristic, complemented, Sylow
523C23—131no—
524C23—132no—
525C23—132no—
526C23—131no—
527C23—261no—
528C23—261no—
529C23—261no—
530C23—261no—
531C23D4×#26111yescharacteristic
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—131no—
539C2×C4—131no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—132no—
544C2×C4—131no—
545C2×C4—131no—
546C2×C4—132no—
547C2×C4—131no—
548C2×C4—131no—
549C2×C4—132no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—262no—
554C2×C4—264no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—261no—
560C2×C4—261no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4—1044no—
575C2×C4—1044no—
576C2×C4#8823712yes—
577C2×C4D4×#26111yescharacteristic
578C2×C4Q8×#26112yes—
579C2×C4C23×#26111yescharacteristic
580C8—21no—
581C8—21no—
582C8—261no—
583C8—261no—
584C8—522no—
585C22—21no—
586C22—21no—
587C22—131no—
588C22—131no—
589C22—131no—
590C22—131no—
591C22—131no—
592C22—131no—
593C22—132no—
594C22—262no—
595C22—262no—
596C22—262no—
597C22—262no—
598C22—261no—
599C22—261no—
600C22#1171908212yes—
601C22C2×D4×#26111yescharacteristic
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—131no—
607C4—131no—
608C4—132no—
609C4—522no—
610C4—522no—
611C4—524no—
612C4—521no—
613C4—521no—
614C4—521no—
615C4—521no—
616C4—1042no—
617C4#1171908212yes—
618C4C2×#8823711yescharacteristic
619C4C2×Q8×#26111yescharacteristic
620C2—22no—
621C2—131no—
622C2—131no—
623C2—131no—
624C2—131no—
625C2—262no—
626C2C2×#1171908211yescharacteristic
627C2#1313159811yescharacteristic
628C2#1313159911yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#427C4
socleC22×C13C2×C4×D4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenter#427#261
hypocenterC13#21039
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
3. #13130900C2semidirect
4. #13130899C2semidirect
5. #13130898C2semidirect
6. #13130897C2semidirect
29. C13×#427C4semidirect
30. #11718767C4semidirect
31. #11718659C4semidirect
32. #11718659C4semidirect
33. #11718541C4semidirect
34. #11718541C4semidirect
37. #11718521C4semidirect
38. #11718521C4semidirect
107. C13×#107C2×C4semidirect
108. C13×#107C2×C4semidirect
109. C13×#106C2×C4semidirect
110. C13×#106C2×C4semidirect
111. #88058C2×C4semidirect
112. #88058C2×C4semidirect
113. #88057C2×C4semidirect
114. #88057C2×C4semidirect
115. #88048C2×C4semidirect
116. #88048C2×C4semidirect
117. #88048C2×C4semidirect
118. #88048C2×C4semidirect
119. #88047C2×C4semidirect
120. #88047C2×C4semidirect
121. #88047C2×C4semidirect
122. #88047C2×C4semidirect
296. #427#261semidirect
414. #107C2×#261semidirect
415. #107C2×#261semidirect
422. #106C2×#261semidirect
423. #106C2×#261semidirect
522. C13#21039semidirect

Maximal subgroups

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

subgroupindex
#131313172
#131312732
#131309002
#131308992
#131308982
#131308972
#131305252
C2×#117182652
#131305012
D13×#4272
#2103913