Finite Group Databasebeta

← #15870601

Subgroups — #15870601

Order 3328.

936 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×#11718508C211yesmaximal, characteristic
2C4×#88124C211yesmaximal, characteristic, complemented
3C42×D52C211yesmaximal, characteristic
4#13115791C211yesmaximal, characteristic, complemented
5#13115606C211yesmaximal, characteristic, complemented
6#13115422C211yesmaximal, characteristic, complemented
7#13115408C211yesmaximal, characteristic, complemented
8#13115100C211yesmaximal, characteristic
9#13115086C211yesmaximal, characteristic
10#13114847C211yesmaximal, characteristic
11#13114733C211yesmaximal, characteristic, complemented
12#13114733C211yesmaximal, characteristic, complemented
13#13114662C211yesmaximal, characteristic
14#13114662C211yesmaximal, characteristic
15C13×#1767C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C2×C42×D13—21no—
20C2×#88124C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×#97C2211yescharacteristic
24C2×C13×#97C2211yescharacteristic
25C43×C13C2211yescharacteristic
26C2×#88061C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88061C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88058C2211yescharacteristic
32C2×#88057C2211yescharacteristic
33C2×#88057C2211yescharacteristic
34C4×#6103—21no—
35C4×#6103—21no—
36C4×#6103—21no—
37#11718597C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40C4×C4⋊Dic13C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42C4×C4⋊Dic13C2211yescharacteristic
43#11718594—21no—
44#11718594—21no—
45C4×#6101—21no—
46C4×#6101—21no—
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49#11718508C418yescomplemented
50C13×#336C2211yescharacteristic
51C13×#336C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C2×C42×C13D411yescharacteristic
69C2×C42×C13D411yescharacteristic
70C2×C42×C13D411yescharacteristic
71C2×C42×C13D411yescharacteristic
72C2×C42×C13C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×#6103—21no—
76C2×#6103—21no—
77C2×#6103—21no—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C4×D52—22no—
95C4×D52—22no—
96C4×D52—22no—
97C4×D52—22no—
98C4×D52C2×C414yes—
99C4×D52Q814yes—
100C42×D13—44no—
101#88124—22no—
102#88124C2×C414yescomplemented
103C13×C4⋊C8—22no—
104C13×C4⋊C8C2×C414yescomplemented
105C13×#97—22no—
106C13×#97—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—
115#88071—21no—
116#88061—22no—
117#88061—22no—
118#88061C2×C414yes—
119#88061C2×C414yes—
120#88058—22no—
121#88058C2×C414yescomplemented
122#88057—22no—
123#88057C2×C414yescomplemented
124#21617—131nomaximal, Sylow
125C23×D13—21no—
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
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×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13C22×C412yes—
166C2×C8×C13C22×C412yes—
167C42×C13—22no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—41no—
171C42×C13—41no—
172C42×C13—41no—
173C42×C13C22×C412yes—
174C42×C13C2×Q812yes—
175C42×C13#4112yes—
176C42×C13#4112yes—
177#6103—24no—
178#6103—24no—
179#6103—24no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13C22×C412yes—
190C4⋊Dic13C22×C412yes—
191C4⋊Dic13C22×C412yes—
192C4⋊Dic13C2×Q812yes—
193C4⋊Dic13#4112yes—
194#6101—24no—
195#6101—24no—
196#6101—42no—
197#6101—42no—
198C4×Dic13—42no—
199C4×Dic13—42no—
200C4×Dic13—42no—
201C4×Dic13—42no—
202C4×Dic13—42no—
203C2×#478—131no—
204C4×#125—131no—
205C42×D4—131no—
206#1989—131no—
207#1949—131no—
208#1920—131no—
209#1918—131no—
210#1864—131no—
211#1862—131no—
212#1804—131no—
213#1776—131no—
214#1776—131no—
215#1767D1311yescharacteristic, complemented
216#1762—131no—
217#1762—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—21no—
229C2×C4×C13—21no—
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×C13C4×D412yes—
240C2×C4×C13C4×D412yes—
241C2×C4×C13C22⋊Q812yes—
242C2×C4×C13C22⋊Q812yes—
243C2×C4×C13AGL(1,ℤ/8)12yes—
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—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
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—
271D52—22no—
272D52—22no—
273D52—22no—
274D52C4×Q814yes—
275C4×D13—48no—
276C4×D13—48no—
277C4×D13—48no—
278C8×C13—22no—
279C8×C13—22no—
280C8×C13—41no—
281C8×C13—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×#106—131no—
292C2×C4⋊C8C2×D1311yescharacteristic
293C2×C4⋊C8C2×D1311yescharacteristic
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#102—131no—
298C2×#97C2×D1311yescharacteristic
299C2×#97C2×D1311yescharacteristic
300#389—131no—
301#389—131no—
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—131no—
310C4×C4⋊C4—261no—
311C4×C4⋊C4—261no—
312C4×C22⋊C4—261no—
313C4×C22⋊C4—261no—
314C4×C22⋊C4—261no—
315C43C2×D1311yescharacteristic
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#336C2×D1311yescharacteristic
325#336C2×D1311yescharacteristic
326C22×C13C2×C4×D411yescharacteristic
327C22×C13C2×C22⋊Q811yescharacteristic
328C22×C13#52511yescharacteristic
329C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C13#57511yescharacteristic
331C22×C13#57511yescharacteristic
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—22no—
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—41no—
346C4×C13C2×C4×Q811yescharacteristic
347C4×C13C4×#4111yescharacteristic
348C4×C13#52911yescharacteristic
349C4×C13#53311yescharacteristic
350Dic13—42no—
351Dic13—42no—
352Dic13—42no—
353Dic13—42no—
354Dic13—42no—
355Dic13—81no—
356Dic13—81no—
357C22×D4—131no—
358C23×C4—261no—
359C23×C4—261no—
360C23×C4—261no—
361C22×C8C22×D1311yescharacteristic
362C22×C8C22×D1311yescharacteristic
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—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—261no—
388C2×C42—261no—
389C2×C42—261no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42—524no—
393C2×C42D5211yescharacteristic
394C2×C42D5211yescharacteristic
395C2×C42D5211yescharacteristic
396C2×C42D5211yescharacteristic
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400#107—134no—
401#107—262no—
402#106—134no—
403#106—262no—
404C4⋊C8—22no—
405C4⋊C8C4×D1314yescomplemented
406#102—134no—
407#102—134no—
408#102—262no—
409#102—262no—
410#97—22no—
411#97—22no—
412#95—261no—
413#95—261no—
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×C13#294311yescharacteristic
423C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C13#307711yescharacteristic
425C2×C13#308011yescharacteristic
426C2×C13#311111yescharacteristic
427C2×C13#311411yescharacteristic
428D13—44no—
429C24—261no—
430C2×D4—132no—
431C2×D4—132no—
432C2×D4—132no—
433C2×D4—261no—
434C2×D4—261no—
435C2×D4—261no—
436C22×C4—264no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—264no—
443C22×C4—264no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—522no—
447C22×C4—522no—
448C22×C4—522no—
449C22×C4—522no—
450C22×C4—522no—
451C22×C4—522no—
452C22×C4C2×D5211yescharacteristic
453C22×C4C2×D5211yescharacteristic
454C22×C4C2×D5211yescharacteristic
455C22×C4C2×D5211yescharacteristic
456C22×C4C2×D5211yescharacteristic
457C22×C4C2×D5211yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8C2×C4×D1312yes—
470C2×C8C2×C4×D1312yes—
471C4⋊C4—132no—
472C4⋊C4—132no—
473C4⋊C4—132no—
474C4⋊C4—132no—
475C4⋊C4—132no—
476C4⋊C4—264no—
477C4⋊C4—264no—
478C4⋊C4—261no—
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—
489C22⋊C4—264no—
490C22⋊C4—264no—
491C22⋊C4—264no—
492C42—22no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42—41no—
497C42—41no—
498C42—522no—
499C42—522no—
500C42—522no—
501C42—522no—
502C42—522no—
503C42C2×C4×D1312yes—
504C42#612712yes—
505C42#612912yes—
506C42Q8×D1312yes—
507C13#2161711yescharacteristic, complemented, Sylow
508C23—262no—
509C23—262no—
510C23—262no—
511C23—521no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23C22×D5211yescharacteristic
516D4—134no—
517D4—262no—
518D4—262no—
519D4—262no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—262no—
536C2×C4—262no—
537C2×C4—262no—
538C2×C4—528no—
539C2×C4—528no—
540C2×C4—528no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
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×C4C4×D5212yes—
558C2×C4C4×D5212yes—
559C2×C4#8815112yes—
560C2×C4#8815112yes—
561C2×C4#8816212yes—
562C2×C4C22×C4×D1311yescharacteristic
563C2×C4C2×#612711yescharacteristic
564C2×C4C2×#612911yescharacteristic
565C2×C4C2×Q8×D1311yescharacteristic
566C2×C4#41×D1311yescharacteristic
567C2×C4#41×D1311yescharacteristic
568C8—22no—
569C8—22no—
570C8—41no—
571C8—41no—
572C22—264no—
573C22—522no—
574C22—522no—
575C22—522no—
576C22—522no—
577C22—522no—
578C22—522no—
579C22C2×C4×D5211yescharacteristic
580C22C2×#8815111yescharacteristic
581C22#1171922911yescharacteristic
582C22C2×#8816211yescharacteristic
583C22#1171945311yescharacteristic
584C22#1171945311yescharacteristic
585C22#1171945311yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—22no—
591C4—41no—
592C4—522no—
593C4—522no—
594C4—522no—
595C4—522no—
596C4—522no—
597C4—1041no—
598C4—1041no—
599C4C4×#612911yescharacteristic
600C4#1171926211yescharacteristic
601C4C4×Q8×D1311yescharacteristic
602C4#1171928311yescharacteristic
603C2—524no—
604C2C4×#8815111yescharacteristic
605C2#1312363811yescharacteristic
606C2C4×#8816211yescharacteristic
607C2#1312463511yescharacteristic
608C2#1312465911yescharacteristic
609C2#1312494711yescharacteristic
610C2#1312497611yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1767C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1767D13
hypocenterC13#21617
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. C4×#88124C2semidirect
4. #13115791C2semidirect
5. #13115606C2semidirect
6. #13115422C2semidirect
7. #13115408C2semidirect
11. #13114733C2semidirect
12. #13114733C2semidirect
15. C13×#1767C2semidirect
49. #11718508C4semidirect
102. #88124C2×C4semidirect
104. C13×C4⋊C8C2×C4semidirect
121. #88058C2×C4semidirect
123. #88057C2×C4semidirect
215. #1767D13semidirect
405. C4⋊C8C4×D13semidirect
507. C13#21617semidirect

Maximal subgroups

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

subgroupindex
C2×#117185082
C4×#881242
C42×D522
#131157912
#131156062
#131154222
#131154082
#131151002
#131150862
#131148472
#131147332
#131146622
C13×#17672
#2161713