Finite Group Databasebeta

← #15903911

Subgroups — #15903911

Order 3328.

778 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×#11718724C211yesmaximal, characteristic, complemented
2C2×C4×#6105C211yesmaximal, characteristic
3#13117799C211yesmaximal, characteristic, complemented
4#13116255C211yesmaximal, characteristic, complemented
5#13116245C211yesmaximal, characteristic, complemented
6#13116153C211yesmaximal, characteristic
7#13116153C211yesmaximal, characteristic
8#13115802C211yesmaximal, characteristic, complemented
9#13115602C211yesmaximal, characteristic, complemented
10#13115597C211yesmaximal, characteristic, complemented
11#13115555C211yesmaximal, characteristic, complemented
12#13115460C211yesmaximal, characteristic
13#13115453C211yesmaximal, characteristic
14#13114846C211yesmaximal, characteristic
15C13×#2566C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C22×#6105C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C13×#396—21no—
21C13×#396—21no—
22C13×#390C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#385—21no—
25C13×#385—21no—
26C13×#384C2211yescharacteristic
27C13×#382C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32#11718724—24no—
33C4×#6105—24no—
34#11718639—21no—
35#11718639—21no—
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42#11718597C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718312—21no—
52#11718309—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C22×Dic26C2311yescharacteristic
64C13×#125—22no—
65C13×#125—22no—
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×#6105—22no—
86C2×#6105—22no—
87C2×#6105—22no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C4×Dic26—22no—
100C4×Dic26D414yes—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95D411yescharacteristic
104C13×#95D411yescharacteristic
105#88072—22no—
106#88072—22no—
107#88072—22no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88050—22no—
117#88050—22no—
118#88050—22no—
119#88048—22no—
120#88048—22no—
121#88047—22no—
122C4⋊#1055—22no—
123C4⋊#1055—22no—
124C4⋊#1055—22no—
125C4×#1055—22no—
126#24685—131nomaximal, Sylow
127C24×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13#4112yes—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—42no—
138C22×C4×C13—81no—
139C22×C4×C13—81no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C2×D412yes—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—81no—
168C13×C4⋊C4—81no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—42no—
172C13×C22⋊C4—81no—
173C13×C22⋊C4—81no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13C2×D412yes—
179C42×C13#4112yes—
180#6105—28no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C2×D412yes—
187#6101—24no—
188C4×Dic13—24no—
189C4×Dic13—42no—
190C4×Dic13—42no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055#4112yes—
203C2×#479—131no—
204C2×C4×SD16—131no—
205#2566D1311yescharacteristic
206#2356—131no—
207#2074—131no—
208#2072—131no—
209#2055—131no—
210#2055—131no—
211#1991—131no—
212#1949—131no—
213#1948—131no—
214#1939—131no—
215#1926—131no—
216#1925—131no—
217#1804—131no—
218C23×C13—22no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13C22×D411yescharacteristic
226D4×C13—22no—
227D4×C13—22no—
228D4×C13—41no—
229D4×C13—41no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—84no—
255C2×C4×C13#12112yes—
256C2×C4×C13#12112yes—
257C2×C4×C13#13512yes—
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C132−1+411yescharacteristic
263C2×C4×C132−1+411yescharacteristic
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276Dic26—22no—
277Dic26—22no—
278Dic26—41no—
279Dic26—41no—
280#1055—22no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284C22×SD16—131no—
285C2×#125C2×D1311yescharacteristic
286C2×C4×Q8—131no—
287C2×C4×D4C2×D1311yescharacteristic
288#479—264no—
289C4×SD16—264no—
290C2×#107—131no—
291C2×#106—131no—
292C2×#106—131no—
293C2×C4⋊C8—131no—
294C2×C4⋊C8—131no—
295C2×C4⋊C8—131no—
296C2×#103—131no—
297C2×#103—131no—
298C2×#103—131no—
299C2×#102—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×C4×C8—131no—
303#396—21no—
304#396—21no—
305#391—131no—
306#391—131no—
307#390C2×D1311yescharacteristic
308#390C2×D1311yescharacteristic
309#387—261no—
310#387—261no—
311#385—21no—
312#385—21no—
313#384C2×D1311yescharacteristic
314#383—261no—
315#382—131no—
316#382C2×D1311yescharacteristic
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C4⋊C4C2×D1311yescharacteristic
320#376—261no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#336—131no—
328#336—131no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—81no—
333C22×C13—81no—
334C22×C13—81no—
335C22×C13—81no—
336C22×C13C2×#12111yescharacteristic
337C22×C13#54711yescharacteristic
338C22×C13#54811yescharacteristic
339C22×C13C2×#13511yescharacteristic
340C22×C13#57511yescharacteristic
341C22×C13#57711yescharacteristic
342C22×C13#57711yescharacteristic
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13—81no—
350C4×C13—81no—
351C4×C13—81no—
352C4×C13#52511yescharacteristic
353C4×C13#53611yescharacteristic
354C4×C13#55211yescharacteristic
355C4×C13#55611yescharacteristic
356Dic13—42no—
357Dic13—42no—
358Dic13—81no—
359Dic13—81no—
360C22×Q8—131no—
361C22×D4C22×D1311yescharacteristic
362C23×C4—21no—
363C2×SD16—262no—
364C2×SD16—262no—
365C2×SD16—262no—
366C22×C8—131no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370#125—22no—
371#125—22no—
372C4×Q8—134no—
373C4×Q8—262no—
374C4×D4—22no—
375C4×D4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22⋊D1311yescharacteristic
385C2×C4⋊C4C22⋊D1311yescharacteristic
386C2×C4⋊C4C22×D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—261no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400#107—262no—
401#106—262no—
402#106—262no—
403C4⋊C8—262no—
404C4⋊C8—262no—
405C4⋊C8—262no—
406#103—262no—
407#103—262no—
408#103—262no—
409#102—262no—
410#102—262no—
411#102—262no—
412C4×C8—262no—
413#95—21no—
414#95—21no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95C22⋊D1311yescharacteristic
424#95C22⋊D1311yescharacteristic
425C2×C13—82no—
426C2×C13#241511yescharacteristic
427C2×C13#303511yescharacteristic
428C2×C13#304311yescharacteristic
429C2×C13#333711yescharacteristic
430C2×C13#335111yescharacteristic
431C2×C13#336011yescharacteristic
432C2×C13#337611yescharacteristic
433C24—21no—
434C2×Q8—132no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8—261no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4#613112yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—81no—
451C22×C4—81no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C23×D1311yescharacteristic
463SD16—268no—
464C2×C8—132no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—132no—
489C4⋊C4—264no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—81no—
499C22⋊C4—81no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—264no—
505C42—522no—
506C42—522no—
507C42D4×D1312yes—
508C42#612912yes—
509C13#2468511yescharacteristic, complemented, Sylow
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23C22×C22⋊D1311yescharacteristic
518Q8—262no—
519Q8—262no—
520Q8—521no—
521Q8—521no—
522D4—22no—
523D4—22no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—84no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4#8819212yes—
564C2×C4#8819212yes—
565C2×C4#8820412yes—
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4C2×#612911yescharacteristic
568C2×C4C2×#613111yescharacteristic
569C2×C4#8825411yescharacteristic
570C2×C4#41×D1311yescharacteristic
571C2×C4#8825711yescharacteristic
572C8—262no—
573C8—521no—
574C8—521no—
575C8—521no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22C2×#8819211yescharacteristic
584C22#1171952211yescharacteristic
585C22C2×#8820411yescharacteristic
586C22#1171952711yescharacteristic
587C22#1171952911yescharacteristic
588C22#1171954111yescharacteristic
589C22#1171954111yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—522no—
600C4—522no—
601C4—1041no—
602C4—1041no—
603C4#1171933211yescharacteristic
604C4#1171933311yescharacteristic
605C4#1171934611yescharacteristic
606C4#1171934711yescharacteristic
607C2—82no—
608C2#1311826111yescharacteristic
609C2#1312428511yescharacteristic
610C2#1312435311yescharacteristic
611C2#1312720911yescharacteristic
612C2#1312739011yescharacteristic
613C2#1312748511yescharacteristic
614C2#1312766311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2566C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2566D13
hypocenterC13#24685
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2566

Complements

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

NH ≅ G/Ntype
1. C2×#11718724C2semidirect
3. #13117799C2semidirect
4. #13116255C2semidirect
5. #13116245C2semidirect
8. #13115802C2semidirect
9. #13115602C2semidirect
10. #13115597C2semidirect
11. #13115555C2semidirect
509. C13#24685semidirect

Maximal subgroups

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

subgroupindex
C2×#117187242
C2×C4×#61052
#131177992
#131162552
#131162452
#131161532
#131158022
#131156022
#131155972
#131155552
#131154602
#131154532
#131148462
C13×#25662
#2468513