Finite Group Databasebeta

← #15920678

Subgroups — #15920678

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118561C211yesmaximal, characteristic
2#13117707C211yesmaximal, characteristic
3#13116406C211yesmaximal, characteristic, complemented
4#13116335C211yesmaximal, characteristic, complemented
5#13116333C211yesmaximal, characteristic, complemented
6#13116176C211yesmaximal, characteristic, complemented
7#13115792C211yesmaximal, characteristic, complemented
8#13115605C211yesmaximal, characteristic, complemented
9#13115426C211yesmaximal, characteristic, complemented
10#13115416C211yesmaximal, characteristic, complemented
11#13115023C211yesmaximal, characteristic
12#13115014C211yesmaximal, characteristic
13#13114920C211yesmaximal, characteristic
14C2×#11718143C211yesmaximal, characteristic
15C13×#1807C211yesmaximal, characteristic
16C23×C8×C13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C2×#88144C2211yescharacteristic
20C2×#88131—21no—
21C2×C13×#106C2211yescharacteristic
22C2×C13×#106C2211yescharacteristic
23C13×#380C2211yescharacteristic
24C13×#380C2211yescharacteristic
25C4×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊#1055C2211yescharacteristic
27C2×#88054C2211yescharacteristic
28C2×#88054C2211yescharacteristic
29#11718646C2211yescharacteristic
30#11718638C2211yescharacteristic
31C4⋊C4×Dic13C2211yescharacteristic
32C4⋊C4×Dic13C2211yescharacteristic
33#11718634C2211yescharacteristic
34#11718634C2211yescharacteristic
35#11718634C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38#11718611—21no—
39#11718604—21no—
40#11718603—21no—
41#11718322—21no—
42#11718321—21no—
43#11718315—21no—
44#11718315—21no—
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47#11718143C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C23×Dic13—21no—
62C22×C8×C13—22no—
63C22×C8×C13—22no—
64C22×C8×C13—41no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C13×C22⋊C4—21no—
73C2×C22⋊Dic13D411yescharacteristic
74C2×C22⋊Dic13D411yescharacteristic
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—41no—
82C2×C4⋊Dic13Q814yes—
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88144—22no—
98#88144—41no—
99#88131—44no—
100C13×#106—22no—
101C13×#106—41no—
102C13×#95—21no—
103C13×#95—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071D411yescharacteristic
113#88071D411yescharacteristic
114C22⋊#1055—22no—
115#88054—22no—
116#88054—41no—
117#88047—22no—
118#88047—41no—
119#25998—131nomaximal, Sylow
120C24×C13C2×D411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×Q812yes—
131C22×C4×C13#4112yes—
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—24no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—42no—
139C22×Dic13—42no—
140C22×Dic13—42no—
141C22×Dic13—42no—
142C22×Dic13—81no—
143C22×Dic13C2×D411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—44no—
153C2×C8×C13#4112yes—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C22⋊C4—42no—
163C13×C22⋊C4—42no—
164C22⋊Dic13—22no—
165C22⋊Dic13—22no—
166C4⋊Dic13—24no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—21no—
172C4⋊Dic13—42no—
173C4⋊Dic13—42no—
174C4⋊Dic13—81no—
175C4⋊Dic13C2×Q812yes—
176C4⋊Dic13C2×Q812yes—
177C4⋊Dic13#4112yes—
178#6101—42no—
179#6101—42no—
180#6101—42no—
181#6101—81no—
182C4×Dic13—21no—
183C4×Dic13—21no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—42no—
187C4×Dic13—42no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194#2442—131no—
195#2344—131no—
196#2101—131no—
197#2088—131no—
198#2087—131no—
199#2059—131no—
200#1989—131no—
201#1949—131no—
202#1921—131no—
203#1919—131no—
204#1852—131no—
205#1850—131no—
206#1823—131no—
207#1807D1311yescharacteristic
208C2×#340—131no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13C22⋊Q812yes—
214C23×C13#13512yes—
215C23×C13AGL(1,ℤ/8)12yes—
216C23×C13C22×D411yescharacteristic
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13C22⋊Q812yes—
236C2×C4×C13C22×Q811yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13H(5,𝔽2)11yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—22no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—48no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—84no—
268C8×C13—22no—
269C8×C13—41no—
270#1055—41no—
271#1055—41no—
272C23×C8C2×D1311yescharacteristic
273C2×#125—131no—
274C2×#117—261no—
275C22×C4⋊C4—131no—
276C22×C4⋊C4—131no—
277C2×#107—131no—
278C2×#107—131no—
279C2×#106C2×D1311yescharacteristic
280C2×#106C2×D1311yescharacteristic
281C2×C4⋊C8—131no—
282C2×C4⋊C8—131no—
283C2×C22⋊C8—131no—
284#400—261no—
285#398—261no—
286#389—131no—
287#389—131no—
288#389—131no—
289#389—131no—
290#387—261no—
291#387—261no—
292#385—261no—
293#382—131no—
294#381—261no—
295#380—261no—
296#380C2×D1311yescharacteristic
297#380C2×D1311yescharacteristic
298C4×C4⋊C4—131no—
299C4×C4⋊C4—131no—
300C4×C22⋊C4—131no—
301#340—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340—131no—
309#340—131no—
310#340—131no—
311#340C2×D1311yescharacteristic
312#340C2×D1311yescharacteristic
313#336—131no—
314#336—131no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—22no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13#47814yes—
322C22×C13C2×C22⋊Q811yescharacteristic
323C22×C13#54611yescharacteristic
324C22×C13#54711yescharacteristic
325C22×C13C2×#13511yescharacteristic
326C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C13#57711yescharacteristic
328C22×C13#57811yescharacteristic
329C4×C13—22no—
330C4×C13—81no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13#53311yescharacteristic
335C4×C13#54411yescharacteristic
336C4×C13#55111yescharacteristic
337C4×C13#55211yescharacteristic
338Dic13—42no—
339Dic13—42no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344Dic13—42no—
345Dic13—81no—
346C23×C4—261no—
347C23×C4—261no—
348C23×C4C22×D1311yescharacteristic
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—41no—
352C22×C8—131no—
353C22×C8—131no—
354C22×C8C22×D1311yescharacteristic
355C22×C8C22×D1311yescharacteristic
356#125—262no—
357#125—521no—
358#117—524no—
359C2×C4⋊C4—134no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—262no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—521no—
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—131no—
382C2×C22⋊C4—131no—
383C2×C42—131no—
384C2×C42—131no—
385C2×C42—261no—
386C2×C42—261no—
387#107—262no—
388#107—521no—
389#106—22no—
390#106—41no—
391C4⋊C8—262no—
392C4⋊C8—521no—
393C22⋊C8—262no—
394#95—21no—
395#95—21no—
396#95—131no—
397#95—131no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405#95—261no—
406C2×C13—24no—
407C2×C13#243811yescharacteristic
408C2×C13C2×#47811yescharacteristic
409C2×C13#308211yescharacteristic
410C2×C13#330011yescharacteristic
411C2×C13#330611yescharacteristic
412C2×C13#333711yescharacteristic
413C2×C13#334311yescharacteristic
414C24D4×D1311yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—264no—
428C22×C4—261no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—522no—
433C22×C4—522no—
434C22×C4—522no—
435C22×C4—522no—
436C22×C4—1041no—
437C22×C4#612712yes—
438C22×C4D4×D1311yescharacteristic
439C22×C4Q8×D1312yes—
440C22×C4C23×D1311yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—44no—
447C2×C8—261no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8#612912yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—132no—
463C4⋊C4—132no—
464C4⋊C4—132no—
465C4⋊C4—264no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—522no—
472C4⋊C4—522no—
473C4⋊C4—522no—
474C4⋊C4—522no—
475C4⋊C4—522no—
476C4⋊C4—1041no—
477C4⋊C4—1041no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—262no—
481C22⋊C4—262no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42—522no—
487C42—522no—
488C13#2599811yescharacteristic, complemented, Sylow
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23#8815012yes—
494C23#8816812yes—
495C23#8817012yes—
496C23C2×D4×D1311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—262no—
520C2×C4—262no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—262no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—528no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—1044no—
541C2×C4#8815012yes—
542C2×C4C2×#612711yescharacteristic
543C2×C4C2×#612911yescharacteristic
544C2×C4#8825111yescharacteristic
545C2×C4C2×Q8×D1311yescharacteristic
546C2×C4#41×D1311yescharacteristic
547C2×C4#8825711yescharacteristic
548C8—22no—
549C8—41no—
550C8—521no—
551C8—521no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22#1171853214yes—
559C22C2×#8815011yescharacteristic
560C22#1171931511yescharacteristic
561C22#1171931611yescharacteristic
562C22C2×#8816811yescharacteristic
563C22C2×#8817011yescharacteristic
564C22#1171947511yescharacteristic
565C22#1171947611yescharacteristic
566C4—22no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—521no—
572C4—521no—
573C4—521no—
574C4—521no—
575C4—522no—
576C4—522no—
577C4—522no—
578C4—1041no—
579C4#1171920011yescharacteristic
580C4#1171923611yescharacteristic
581C4#1171932711yescharacteristic
582C4#1171932811yescharacteristic
583C2—24no—
584C2#1311851811yescharacteristic
585C2C2×#1171853211yescharacteristic
586C2#1312468111yescharacteristic
587C2#1312672911yescharacteristic
588C2#1312680311yescharacteristic
589C2#1312722111yescharacteristic
590C2#1312728211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1807C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#1807D13
hypocenterC13#25998
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
3. #13116406C2semidirect
4. #13116335C2semidirect
5. #13116333C2semidirect
6. #13116176C2semidirect
7. #13115792C2semidirect
8. #13115605C2semidirect
9. #13115426C2semidirect
10. #13115416C2semidirect
488. C13#25998semidirect

Maximal subgroups

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

subgroupindex
#131185612
#131177072
#131164062
#131163352
#131163332
#131161762
#131157922
#131156052
#131154262
#131154162
#131150232
#131150142
#131149202
C2×#117181432
C13×#18072
#2599813