Finite Group Databasebeta

← #15914587

Subgroups — #15914587

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718725C211yesmaximal, characteristic, complemented
2#13120032C211yesmaximal, characteristic
3#13117936C211yesmaximal, characteristic, complemented
4#13116320C211yesmaximal, characteristic, complemented
5#13116315C211yesmaximal, characteristic, complemented
6#13116220C211yesmaximal, characteristic
7#13116220C211yesmaximal, characteristic
8#13115791C211yesmaximal, characteristic, complemented
9#13115605C211yesmaximal, characteristic, complemented
10#13115591C211yesmaximal, characteristic, complemented
11#13115552C211yesmaximal, characteristic, complemented
12#13115466C211yesmaximal, characteristic
13#13115466C211yesmaximal, characteristic
14C4×#88072C211yesmaximal, characteristic
15C2×C13×#478C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×#88124C2211yescharacteristic
19C13×#478—24no—
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24C2×C13×#102C2211yescharacteristic
25#11718882C2211yescharacteristic
26#11718882C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29#11718871—21no—
30#11718871—21no—
31C2×#88054C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33#11718725—24no—
34#11718646—21no—
35#11718646C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718642—21no—
38#11718642—21no—
39#11718638C2211yescharacteristic
40#11718637C2211yescharacteristic
41C4⋊C4×Dic13—21no—
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718609—21no—
49#11718609—21no—
50C4×C4⋊Dic13C2211yescharacteristic
51C4×C4⋊Dic13C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718142C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×#125—22no—
66C13×#125D414yes—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13D411yescharacteristic
83C2×C4⋊Dic13D411yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88124—22no—
100#88124—22no—
101C13×#107—22no—
102C13×#106—22no—
103C13×C4⋊C8—22no—
104C13×#102—22no—
105C13×#102—22no—
106#88072—22no—
107#88072Q814yes—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071D411yescharacteristic
116#88071D411yescharacteristic
117#88054—22no—
118#88054—22no—
119#88048—22no—
120#88048—22no—
121#88047—22no—
122#88047—22no—
123C4×#1055—22no—
124#25457—131nomaximal, Sylow
125C24×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13C2×Q812yes—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—42no—
136C22×C4×C13—81no—
137C22×C4×C13—81no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C22×Dic13C2×D411yescharacteristic
148C22×Dic13C2×D411yescharacteristic
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4C2×D412yes—
162C13×C4⋊C4C2×D412yes—
163C13×C22⋊C4—42no—
164C42×C13C2×D412yes—
165C42×C13#4112yes—
166C22⋊Dic13—42no—
167C22⋊Dic13—42no—
168C22⋊Dic13—81no—
169C22⋊Dic13—81no—
170C4⋊Dic13—21no—
171C4⋊Dic13—22no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—41no—
179C4⋊Dic13—42no—
180C4⋊Dic13—81no—
181C4⋊Dic13C2×Q812yes—
182#6101—42no—
183#6101—42no—
184#6101—81no—
185#6101—81no—
186C4×Dic13—21no—
187C4×Dic13—21no—
188C4×Dic13—21no—
189C4×Dic13—21no—
190C4×Dic13—42no—
191C4×Dic13—81no—
192C4×Dic13—81no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055C2×Q812yes—
198C2×#1055#4112yes—
199C2×#499—131no—
200C2×#478D1311yescharacteristic
201#2566—131no—
202#2370—131no—
203#2085—131no—
204#2084—131no—
205#2067—131no—
206#2067—131no—
207#1989—131no—
208#1949—131no—
209#1947—131no—
210#1939—131no—
211#1926—131no—
212#1926—131no—
213C4×#102—131no—
214C23×C13—22no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—41no—
220C23×C13—41no—
221C23×C13C22×D411yescharacteristic
222D4×C13—22no—
223D4×C13—22no—
224D4×C13—41no—
225D4×C13—41no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—84no—
240C2×C4×C13#12112yes—
241C2×C4×C13#12112yes—
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C22×Q811yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C132−1+411yescharacteristic
247C2×C4×C132−1+411yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—22no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
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—
271C2×Dic13#13512yes—
272C8×C13—41no—
273C8×C13—41no—
274#1055—22no—
275#1055—22no—
276C2×#125—131no—
277C2×#125C2×D1311yescharacteristic
278C2×C4×D4C2×D1311yescharacteristic
279#499—264no—
280#478—24no—
281C2×#107—131no—
282C2×#107—131no—
283C2×#107C2×D1311yescharacteristic
284C2×#106—131no—
285C2×#106—131no—
286C2×#106C2×D1311yescharacteristic
287C2×C4⋊C8—131no—
288C2×C4⋊C8—131no—
289C2×C4⋊C8C2×D1311yescharacteristic
290C2×#102—131no—
291C2×#102—131no—
292C2×#102C2×D1311yescharacteristic
293C2×#102C2×D1311yescharacteristic
294C2×C4×C8—131no—
295#396—261no—
296#396—261no—
297#390—131no—
298#390—131no—
299#389—131no—
300#389—131no—
301#389—261no—
302#387—261no—
303#387—261no—
304#385—261no—
305#385—261no—
306#384—131no—
307#382—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4—131no—
311C4×C4⋊C4—131no—
312C4×C4⋊C4—261no—
313#340—131no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#336—131no—
320#336—131no—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—81no—
325C22×C13—81no—
326C22×C13—81no—
327C22×C13—81no—
328C22×C13C2×#12111yescharacteristic
329C22×C13#54711yescharacteristic
330C22×C13D4×Q811yescharacteristic
331C22×C13C2×#13511yescharacteristic
332C22×C13#57511yescharacteristic
333C22×C13#57611yescharacteristic
334C22×C13#57711yescharacteristic
335C4×C13—22no—
336C4×C13—22no—
337C4×C13—42no—
338C4×C13—42no—
339C4×C13—81no—
340C4×C13#53311yescharacteristic
341C4×C13#54111yescharacteristic
342C4×C13#54811yescharacteristic
343C4×C13D4×Q811yescharacteristic
344Dic13—22no—
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348Dic13—42no—
349Dic13—81no—
350Dic13—81no—
351Dic13—81no—
352C22×D4C22×D1311yescharacteristic
353C23×C4—21no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8C22×D1311yescharacteristic
357C22×C8C22×D1311yescharacteristic
358#125—22no—
359#125—262no—
360#125—262no—
361#125C22⋊D1314yes—
362C4×D4—22no—
363C4×D4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—261no—
389C2×C42—261no—
390C2×C42—261no—
391C2×C42C22×D1311yescharacteristic
392#107—22no—
393#107—262no—
394#107—262no—
395#106—22no—
396#106—262no—
397#106—262no—
398C4⋊C8—22no—
399C4⋊C8—262no—
400C4⋊C8—262no—
401#102—22no—
402#102—22no—
403#102—134no—
404#102—262no—
405C4×C8—262no—
406#95—131no—
407#95—131no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415C2×C13—82no—
416C2×C13#242911yescharacteristic
417C2×C13#303511yescharacteristic
418C2×C13#304511yescharacteristic
419C2×C13#333911yescharacteristic
420C2×C13#335111yescharacteristic
421C2×C13#338111yescharacteristic
422C2×C13#338911yescharacteristic
423C24—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4Q8×D1312yes—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—42no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4D4×D1311yescharacteristic
445C22×C4D4×D1311yescharacteristic
446C22×C4C23×D1311yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—132no—
454C2×C8—132no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—132no—
466C4⋊C4—262no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—521no—
475C4⋊C4—522no—
476C4⋊C4—522no—
477C4⋊C4—522no—
478C4⋊C4—1041no—
479C4⋊C4—1041no—
480C4⋊C4—1041no—
481C4⋊C4C2×C22⋊D1312yes—
482C4⋊C4C2×C22⋊D1312yes—
483C22⋊C4—42no—
484C22⋊C4—522no—
485C22⋊C4—522no—
486C22⋊C4—1041no—
487C22⋊C4—1041no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—261no—
492C42—522no—
493C42—1041no—
494C42—1041no—
495C42#612912yes—
496C42C2×C22⋊D1312yes—
497C13#2545711yescharacteristic, complemented, Sylow
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23C2×D4×D1311yescharacteristic
506D4—22no—
507D4—22no—
508D4—41no—
509D4—41no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—84no—
524C2×C4—132no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—262no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4#8819312yes—
549C2×C4#8819312yes—
550C2×C4C2×#612911yescharacteristic
551C2×C4C2×Q8×D1311yescharacteristic
552C2×C4#8825411yescharacteristic
553C2×C4#41×D1311yescharacteristic
554C2×C4#8825711yescharacteristic
555C2×C4C22×C22⋊D1311yescharacteristic
556C8—41no—
557C8—41no—
558C8—262no—
559C8—262no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22#1171933611yescharacteristic
568C22#1171933711yescharacteristic
569C22D13×#13511yescharacteristic
570C22#1171947311yescharacteristic
571C22#1171947911yescharacteristic
572C22#1171948011yescharacteristic
573C22C2×#8819311yescharacteristic
574C4—22no—
575C4—22no—
576C4—42no—
577C4—42no—
578C4—81no—
579C4—262no—
580C4—521no—
581C4—522no—
582C4—521no—
583C4—521no—
584C4—1041no—
585C4—1041no—
586C4—1041no—
587C4#1171932711yescharacteristic
588C4#1171933011yescharacteristic
589C4Q8×C22⋊D1311yescharacteristic
590C4#1171953611yescharacteristic
591C2—82no—
592C2#1311843711yescharacteristic
593C2#1312428711yescharacteristic
594C2#1312437911yescharacteristic
595C2#1312723511yescharacteristic
596C2#1312740311yescharacteristic
597C2#1312770611yescharacteristic
598C2#1312779411yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#478C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterC2×#478D13
hypocenterC13#25457
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#11718725C2semidirect
3. #13117936C2semidirect
4. #13116320C2semidirect
5. #13116315C2semidirect
8. #13115791C2semidirect
9. #13115605C2semidirect
10. #13115591C2semidirect
11. #13115552C2semidirect
497. C13#25457semidirect

Maximal subgroups

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

subgroupindex
C2×#117187252
#131200322
#131179362
#131163202
#131163152
#131162202
#131157912
#131156052
#131155912
#131155522
#131154662
C4×#880722
C2×C13×#4782
#2545713