Finite Group Databasebeta

← #15870532

Subgroups — #15870532

Order 3328.

948 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718532C211yesmaximal, characteristic
2#13117395C211yesmaximal, characteristic, complemented
3C4×#88147C211yesmaximal, characteristic
4#13115792C211yesmaximal, characteristic, complemented
5#13115603C211yesmaximal, characteristic, complemented
6#13115428C211yesmaximal, characteristic, complemented
7#13115100C211yesmaximal, characteristic
8#13115082C211yesmaximal, characteristic
9#13114845C211yesmaximal, characteristic
10#13114728C211yesmaximal, characteristic, complemented
11#106×Dic13C211yesmaximal, characteristic, complemented
12#13114684C211yesmaximal, characteristic, complemented
13#13114650C211yesmaximal, characteristic
14#13114650C211yesmaximal, characteristic
15C13×#1919C211yesmaximal, characteristic, complemented
16C2×#88147C2211yescharacteristic
17C2×#88147C2211yescharacteristic
18C2×#88144C2211yescharacteristic
19C2×C4×D52C2211yescharacteristic
20C2×C42×D13—21no—
21C2×C13×#106C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24C2×#88061C2211yescharacteristic
25C2×#88061C2211yescharacteristic
26C2×#88057C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30C2×C8×Dic13C2211yescharacteristic
31#11718639—21no—
32#11718638C2211yescharacteristic
33C4⋊C4×Dic13—21no—
34C4⋊C4×Dic13C2211yescharacteristic
35C4⋊C4×Dic13C2211yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C4×#6103—21no—
43C42×Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45#11718532C418yescomplemented
46#11718327—21no—
47#11718327—21no—
48#11718314—21no—
49#11718310—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52C13×#340C2211yescharacteristic
53C13×#336C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C42×C13—21no—
72C2×C42×C13C2311yescharacteristic
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×#6101—21no—
81C2×#6101—21no—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13D411yescharacteristic
87C2×C4×Dic13D411yescharacteristic
88C2×C4×Dic13D411yescharacteristic
89C2×C4×Dic13D411yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91C2×C4×Dic13C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94#88147—22no—
95#88147—22no—
96#88147C2×C414yes—
97#88147Q814yes—
98#88144—22no—
99#88144C2×C414yescomplemented
100C4×D52—22no—
101C4×D52—22no—
102C42×D13—44no—
103C13×#106C2×C414yescomplemented
104C13×#95—21no—
105C13×#95—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88061—22no—
114#88061C2×C414yes—
115#88057—22no—
116#88054—22no—
117#88054C2×C414yescomplemented
118C8×Dic13—22no—
119C8×Dic13—22no—
120#88049—22no—
121#88049C2×C414yes—
122#88047—22no—
123#88047C2×C414yescomplemented
124C4×#478—131nomaximal, Sylow
125C23×D13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13C2×D411yescharacteristic
137C22×Dic13C2×D411yescharacteristic
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52C22×C412yes—
144C2×D52C2×Q812yes—
145C2×D52#4112yes—
146C2×C4×D13—24no—
147C2×C4×D13—24no—
148C2×C4×D13—24no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13—42no—
154C2×C4×D13—42no—
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13C22×C412yes—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4C22×C412yes—
168C13×C4⋊C4C22×C412yes—
169C13×C4⋊C4C2×Q812yes—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—42no—
173#6103—24no—
174#6103—24no—
175#6103—24no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—24no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13C22×C412yes—
182C4⋊Dic13#4112yes—
183#6101—24no—
184#6101—42no—
185C4×Dic13—22no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—41no—
189C4×Dic13—42no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C4×Dic13—42no—
193C4×Dic13C22×C412yes—
194C4×Dic13C2×Q812yes—
195C4×Dic13#4112yes—
196C4×Dic13#4112yes—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C22×C412yes—
203C2×#478—131no—
204C4×#125—131no—
205C42×D4—131no—
206#1989—131no—
207#1949—131no—
208#1921—131no—
209#1919D1311yescharacteristic, complemented
210#1864—131no—
211#1862—131no—
212#1804—131no—
213C4×#107—131no—
214C4×#106—131no—
215C4×C4⋊C8—131no—
216C4×#102—131no—
217C4×#102—131no—
218C23×C13C22×D411yescharacteristic
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—21no—
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#13512yes—
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×Q811yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13C4×D412yes—
266C2×Dic13C4×D412yes—
267C2×Dic13C22⋊Q812yes—
268C2×Dic13C22⋊Q812yes—
269C2×Dic13#13512yes—
270C2×Dic13AGL(1,ℤ/8)12yes—
271D52—22no—
272D52—22no—
273D52—22no—
274D52C4×Q814yes—
275C4×D13—48no—
276C4×D13—48no—
277C4×D13—48no—
278C8×C13—22no—
279C8×C13—41no—
280#1055—22no—
281#1055—41no—
282C2×#125—131no—
283C2×C4×D4—131no—
284C2×C4×D4—131no—
285C2×C4×D4—131no—
286C22×C42—261no—
287#478—138no—
288C2×#107—131no—
289C2×#107—131no—
290C2×#106—131no—
291C2×#106C2×D1311yescharacteristic
292C2×C4⋊C8—131no—
293C2×C4⋊C8—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#102—131no—
298C2×C4×C8—131no—
299C2×C4×C8—131no—
300#389—131no—
301#389C2×D1311yescharacteristic
302#387—261no—
303#387—261no—
304#382—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—261no—
310C4×C4⋊C4—261no—
311C4×C4⋊C4C2×D1311yescharacteristic
312C4×C22⋊C4—261no—
313C4×C22⋊C4—261no—
314C4×C22⋊C4—261no—
315C43—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340C2×D1311yescharacteristic
322#340C2×D1311yescharacteristic
323#340C2×D1311yescharacteristic
324#336—131no—
325#336C2×D1311yescharacteristic
326C22×C13C2×C4×D411yescharacteristic
327C22×C13C2×C22⋊Q811yescharacteristic
328C22×C13#52511yescharacteristic
329C22×C13C2×#13511yescharacteristic
330C22×C13C2×#13511yescharacteristic
331C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C13#57511yescharacteristic
333C2×D13—24no—
334C2×D13—42no—
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—42no—
338C2×D13—42no—
339C2×D13—42no—
340C4×C13—22no—
341C4×C13—42no—
342C4×C13—41no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13—81no—
346C4×C13C2×C4×Q811yescharacteristic
347C4×C13C4×#4111yescharacteristic
348C4×C13#52911yescharacteristic
349C4×C13#53311yescharacteristic
350Dic13—22no—
351Dic13—22no—
352Dic13—22no—
353Dic13—42no—
354Dic13—42no—
355Dic13—81no—
356Dic13#47814yescomplemented
357C22×D4—131no—
358C23×C4—261no—
359C23×C4—261no—
360C23×C4—261no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8C22×D1311yescharacteristic
364C22×C8C22×D1311yescharacteristic
365#125—134no—
366#125—262no—
367C4×D4—134no—
368C4×D4—134no—
369C4×D4—262no—
370C4×D4—262no—
371C4×D4—262no—
372C4×D4—262no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—21no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—261no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—524no—
399C2×C42C22×D1311yescharacteristic
400#107—134no—
401#107—262no—
402#106—262no—
403#106C4×D1314yescomplemented
404C4⋊C8—134no—
405C4⋊C8—262no—
406#102—134no—
407#102—134no—
408#102—262no—
409#102—262no—
410C4×C8—262no—
411C4×C8—262no—
412#95—21no—
413#95—21no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421C2×C13C4×C22⋊Q811yescharacteristic
422C2×C13C4×#13511yescharacteristic
423C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C13C2×#47811yescharacteristic
425C2×C13#307611yescharacteristic
426C2×C13#310211yescharacteristic
427C2×C13#310511yescharacteristic
428D13—44no—
429C24—261no—
430C2×D4—132no—
431C2×D4—132no—
432C2×D4—132no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—264no—
445C22×C4—264no—
446C22×C4—264no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—522no—
451C22×C4—522no—
452C22×C4—522no—
453C22×C4—522no—
454C22×C4—522no—
455C22×C4—522no—
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—132no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8C2×C4×D1312yes—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—42no—
477C4⋊C4—132no—
478C4⋊C4—132no—
479C4⋊C4—264no—
480C4⋊C4—264no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—522no—
486C4⋊C4C2×C4×D1312yes—
487C4⋊C4C2×C4×D1312yes—
488C4⋊C4Q8×D1312yes—
489C22⋊C4—264no—
490C22⋊C4—264no—
491C22⋊C4—264no—
492C42—21no—
493C42—21no—
494C42—42no—
495C42—132no—
496C42—132no—
497C42—132no—
498C42—132no—
499C42—262no—
500C42—262no—
501C42—262no—
502C42—521no—
503C42—522no—
504C42—522no—
505C42—522no—
506C42—522no—
507C13C4×#47811yescharacteristic, complemented, Sylow
508C23—262no—
509C23—262no—
510C23—262no—
511C23—521no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23C2×D4×D1311yescharacteristic
516D4—134no—
517D4—262no—
518D4—262no—
519D4—262no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
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—132no—
538C2×C4—132no—
539C2×C4—132no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—132no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—528no—
552C2×C4—528no—
553C2×C4—528no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4#8817012yes—
562C2×C4C22×C4×D1311yescharacteristic
563C2×C4C2×Q8×D1311yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C2×C4#41×D1311yescharacteristic
566C2×C4#41×D1311yescharacteristic
567C2×C4#41×D1311yescharacteristic
568C8—22no—
569C8—41no—
570C8—262no—
571C8—521no—
572C22—264no—
573C22—522no—
574C22—522no—
575C22—522no—
576C22—522no—
577C22—522no—
578C22—522no—
579C22C4×D4×D1311yescharacteristic
580C22D13×C22⋊Q811yescharacteristic
581C22#1171936111yescharacteristic
582C22C2×#8817011yescharacteristic
583C22D13×#13511yescharacteristic
584C22D13×AGL(1,ℤ/8)11yescharacteristic
585C22#1171948211yescharacteristic
586C4—22no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—41no—
591C4—81no—
592C4—134no—
593C4—262no—
594C4—262no—
595C4—262no—
596C4—522no—
597C4—522no—
598C4—1041no—
599C4#1171922711yescharacteristic
600C4C4×Q8×D1311yescharacteristic
601C4#1171939311yescharacteristic
602C4#1171941111yescharacteristic
603C2—524no—
604C2#1311737011yescharacteristic
605C2C4×#8817011yescharacteristic
606C2#1312364111yescharacteristic
607C2D13×#47811yescharacteristic
608C2#1312461911yescharacteristic
609C2#1312485711yescharacteristic
610C2#1312488011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1919C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1919D13
hypocenterC13C4×#478
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
2. #13117395C2semidirect
4. #13115792C2semidirect
5. #13115603C2semidirect
6. #13115428C2semidirect
10. #13114728C2semidirect
11. #106×Dic13C2semidirect
12. #13114684C2semidirect
15. C13×#1919C2semidirect
45. #11718532C4semidirect
99. #88144C2×C4semidirect
103. C13×#106C2×C4semidirect
117. #88054C2×C4semidirect
123. #88047C2×C4semidirect
209. #1919D13semidirect
356. Dic13#478semidirect
403. #106C4×D13semidirect
507. C13C4×#478semidirect

Maximal subgroups

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

subgroupindex
C2×#117185322
#131173952
C4×#881472
#131157922
#131156032
#131154282
#131151002
#131150822
#131148452
#131147282
#106×Dic132
#131146842
#131146502
C13×#19192
C4×#47813