Finite Group Databasebeta

← #15892928

Subgroups — #15892928

Order 3328.

796 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
1C22⋊Q8×Dic13C211yesmaximal, characteristic
2#13117238C211yesmaximal, characteristic
3#13116397C211yesmaximal, characteristic, complemented
4#13116377C211yesmaximal, characteristic, complemented
5#13116315C211yesmaximal, characteristic, complemented
6#13116272C211yesmaximal, characteristic
7#13116269C211yesmaximal, characteristic
8#13116247C211yesmaximal, characteristic, complemented
9#13116029C211yesmaximal, characteristic
10#106×Dic13C211yesmaximal, characteristic, complemented
11#13114724C211yesmaximal, characteristic, complemented
12#103×Dic13C211yesmaximal, characteristic, complemented
13#103×Dic13C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic13C211yesmaximal, characteristic
15C13×#2035C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C2×#88131—21no—
20C2×C13×#106C2211yescharacteristic
21C2×C13×#103C2211yescharacteristic
22C2×C13×#103C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24C13×#380C2211yescharacteristic
25#11718891C2211yescharacteristic
26C2×#88075C2211yescharacteristic
27C2×#88075C2211yescharacteristic
28#11718873C2211yescharacteristic
29#11718873C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34#11718646C2211yescharacteristic
35#11718642—21no—
36#11718637C2211yescharacteristic
37#11718637C2211yescharacteristic
38C4⋊C4×Dic13—21no—
39C4⋊C4×Dic13C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44#11718611—21no—
45#11718603—21no—
46C22⋊C4×Dic13—21no—
47#11718311—21no—
48#11718310—21no—
49C13×#340C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13D411yescharacteristic
62C23×Dic13D411yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75Q8×Dic13—22no—
76Q8×Dic13—22no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13D411yescharacteristic
94C2×C4×Dic13D411yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88131—44no—
100C13×#106—22no—
101C13×#103—22no—
102C13×#103—22no—
103C13×C22⋊C8—22no—
104C13×#95—21no—
105#88075—22no—
106#88075—22no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115C22⋊#1055—22no—
116#88057—22no—
117C8×Dic13—22no—
118C8×Dic13—22no—
119#88048—22no—
120#88048—22no—
121#23756—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C2×Q8×C13—21no—
124C2×Q8×C13—21no—
125C2×Q8×C13—21no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13#4112yes—
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—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—41no—
150C22×Dic13SD1614yes—
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13#4112yes—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4#4112yes—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—42no—
170C22⋊Dic13—42no—
171C22⋊Dic13—42no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—42no—
181C4⋊Dic13—42no—
182#6101—42no—
183#6101—42no—
184#6101—42no—
185#6101—42no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—22no—
189C4×Dic13—22no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C4×Dic13—42no—
193C4×Dic13—42no—
194C4×Dic13#4112yes—
195C4×Dic13#4112yes—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055#4112yes—
202C4×C22⋊Q8—131no—
203#2285—131no—
204#2099—131no—
205#2096—131no—
206#2084—131no—
207#2077—131no—
208#2077—131no—
209#2072—131no—
210#2035—131no—
211#2035D1311yescharacteristic
212C4×#106—131no—
213C4×#106—131no—
214C4×#103—131no—
215C4×#103—131no—
216C4×C22⋊C8—131no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13C2×SD1612yes—
224C23×C13C22×D411yescharacteristic
225Q8×C13—22no—
226Q8×C13—22no—
227Q8×C13—41no—
228Q8×C13—41no—
229C2×C4×C13—21no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—28no—
261C2×Dic13—44no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
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#12312yes—
275C2×Dic13#12312yes—
276C2×Dic13C2×SD1612yes—
277C2×Dic13C2×SD1612yes—
278C2×Dic13#13512yes—
279C2×Dic13#13712yes—
280C8×C13—22no—
281C8×C13—41no—
282#1055—22no—
283#1055—41no—
284C2×C22⋊Q8C2×D1311yescharacteristic
285C2×C4×Q8—131no—
286C2×#117—261no—
287C22×C42—131no—
288C2×#106—131no—
289C2×#106—131no—
290C2×#106—131no—
291C2×#106C2×D1311yescharacteristic
292C2×#103—131no—
293C2×#103—131no—
294C2×#103C2×D1311yescharacteristic
295C2×#103C2×D1311yescharacteristic
296C2×C22⋊C8—131no—
297C2×C22⋊C8C2×D1311yescharacteristic
298C2×C4×C8—131no—
299C2×C4×C8—131no—
300#391—131no—
301#389—131no—
302#387—261no—
303#385—261no—
304#384—131no—
305#384—131no—
306#382—261no—
307#380—131no—
308#380—131no—
309#380—261no—
310#380C2×D1311yescharacteristic
311C4×C4⋊C4—131no—
312C4×C4⋊C4—131no—
313C4×C4⋊C4—131no—
314C4×C4⋊C4—261no—
315C4×C4⋊C4—261no—
316C4×C22⋊C4—261no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340C2×D1311yescharacteristic
325#336—131no—
326#336—131no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13—22no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13C2×#12311yescharacteristic
335C22×C13#52511yescharacteristic
336C22×C13#53211yescharacteristic
337C22×C13C22×SD1611yescharacteristic
338C22×C13C2×#13511yescharacteristic
339C22×C13C2×#13711yescharacteristic
340C22×C13#57511yescharacteristic
341C4×C13—42no—
342C4×C13—41no—
343C4×C13—42no—
344C4×C13—81no—
345C4×C13—81no—
346C4×C13#52911yescharacteristic
347C4×C13#52911yescharacteristic
348C4×C13#52911yescharacteristic
349C4×C13#52911yescharacteristic
350Dic13—22no—
351Dic13—22no—
352Dic13—22no—
353Dic13—81no—
354Dic13—81no—
355Dic13—81no—
356Dic13—81no—
357Dic13#48314yes—
358C22×Q8C22×D1311yescharacteristic
359C23×C4—131no—
360C23×C4—131no—
361C23×C4C22×D1311yescharacteristic
362C22×C8—131no—
363C22×C8—131no—
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C4×Q8—262no—
369C4×Q8—262no—
370#117—524no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C4⋊C4C22×D1311yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—261no—
388C2×C22⋊C4—261no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—262no—
394C2×C42—262no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—261no—
399#106—22no—
400#106—262no—
401#106—262no—
402#106—262no—
403#103—22no—
404#103—22no—
405#103—262no—
406#103—262no—
407C22⋊C8—22no—
408C22⋊C8—262no—
409C4×C8—262no—
410C4×C8—262no—
411#95—21no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420C2×C13—42no—
421C2×C13#239511yescharacteristic
422C2×C13C2×#48311yescharacteristic
423C2×C13#309111yescharacteristic
424C2×C13#310311yescharacteristic
425C2×C13#310711yescharacteristic
426C2×C13#316711yescharacteristic
427C2×C13#317211yescharacteristic
428C24D4×D1311yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8#612912yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—131no—
446C22×C4—134no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—521no—
459C22×C4D4×D1311yescharacteristic
460C22×C4C23×D1311yescharacteristic
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—132no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8#612912yes—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—522no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4—522no—
491C4⋊C4—522no—
492C4⋊C4—522no—
493C4⋊C4#612912yes—
494C22⋊C4—24no—
495C22⋊C4—42no—
496C22⋊C4—522no—
497C22⋊C4—522no—
498C42—132no—
499C42—132no—
500C42—262no—
501C42—262no—
502C42—261no—
503C42—261no—
504C42—522no—
505C42—522no—
506C42—522no—
507C42—522no—
508C13#2375611yescharacteristic, complemented, Sylow
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23SD16×D1312yes—
516C23C2×D4×D1311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—132no—
544C2×C4—132no—
545C2×C4—132no—
546C2×C4—268no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—524no—
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—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4C2×#612911yescharacteristic
567C2×C4C2×#612911yescharacteristic
568C2×C4C2×#612911yescharacteristic
569C2×C4#41×D1311yescharacteristic
570C2×C4#41×D1311yescharacteristic
571C2×C4#41×D1311yescharacteristic
572C8—22no—
573C8—41no—
574C8—262no—
575C8—521no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22#1171929111yescharacteristic
584C22#1171930111yescharacteristic
585C22D13×#12311yescharacteristic
586C22C2×SD16×D1311yescharacteristic
587C22D13×#13511yescharacteristic
588C22D13×#13711yescharacteristic
589C22#1171948211yescharacteristic
590C4—42no—
591C4—41no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4—134no—
596C4—262no—
597C4—262no—
598C4—262no—
599C4—1041no—
600C4—1041no—
601C4—1041no—
602C4—1041no—
603C4#1171930511yescharacteristic
604C4#1171930511yescharacteristic
605C4#1171935411yescharacteristic
606C4#1171938511yescharacteristic
607C2—42no—
608C2#1311809211yescharacteristic
609C2D13×#48311yescharacteristic
610C2#1312475411yescharacteristic
611C2#1312486211yescharacteristic
612C2#1312490011yescharacteristic
613C2#1312539011yescharacteristic
614C2#1312543711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2035C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2035D13
hypocenterC13#23756
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
3. #13116397C2semidirect
4. #13116377C2semidirect
5. #13116315C2semidirect
8. #13116247C2semidirect
10. #106×Dic13C2semidirect
11. #13114724C2semidirect
12. #103×Dic13C2semidirect
13. #103×Dic13C2semidirect
508. C13#23756semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×Dic132
#131172382
#131163972
#131163772
#131163152
#131162722
#131162692
#131162472
#131160292
#106×Dic132
#131147242
#103×Dic132
C22⋊C8×Dic132
C13×#20352
#2375613