Finite Group Databasebeta

← #15831273

Subgroups — #15831273

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2D13×#431C211yesmaximal, characteristic
3D13×#423C211yesmaximal, characteristic
4#13113523C214yesmaximal, complemented
5#13113522C211yesmaximal, characteristic, complemented
6#13113520C211yesmaximal, characteristic, complemented
7#13113517C211yesmaximal, characteristic, complemented
8#13113490C214yesmaximal, complemented
9C13×#1548C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×#88200C412yes—
12C2×Q8×Dic13C412yes—
13C2×M16×D13—21no—
14#11719433—21no—
15#11719433—21no—
16#11719433—21no—
17#11719433—21no—
18#11719433C412yes—
19#11719433C412yes—
20#11719433C2212yes—
21#11719433C2212yes—
22C2×#88151—21no—
23C2×#88146—21no—
24C2×#88144—21no—
25C2×#88141—21no—
26C2×C42×D13C2211yescharacteristic
27C2×#88123C2211yescharacteristic
28C13×#431C2211yescharacteristic
29C13×#423C2211yescharacteristic
30#11718779—21no—
31#11718586C2211yescharacteristic
32#11718585C2211yescharacteristic
33#11718498—21no—
34#11718498C2212yes—
35#11718494C2212yes—
36D13×C4⋊C8—21no—
37D13×C4⋊C8C2212yes—
38D13×C4⋊C8C2212yes—
39D13×C22⋊C8—21no—
40#11718379—21no—
41#11718346—21no—
42C4×C8×D13—21no—
43C13×#333C2214yescomplemented
44#11718138C2214yescomplemented
45#11718078C2214yescomplemented
46#11718074C2214yescomplemented
47C22×Q8×C13C2×C412yes—
48C22×C4×D13C2×C411yescharacteristic
49C22×C4×D13D411yescharacteristic
50C22×C4×D13D411yescharacteristic
51C22×Dic26—21no—
52C2×C13×M16—21no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8C2×C412yes—
56C13×C4⋊Q8C2312yes—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C42×C13C2311yescharacteristic
60#88200—22no—
61#88200—22no—
62#88200C2×C414yes—
63#88200C2×C414yes—
64Q8×Dic13—22no—
65Q8×Dic13—22no—
66Q8×Dic13C2×C414yes—
67Q8×Dic13C2×C414yes—
68C2×#6103—22no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13C2×C412yes—
72C2×#6101—22no—
73C2×C4×Dic13—22no—
74C2×C4×Dic13C2×C411yescharacteristic
75C2×C4×Dic13D411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77C2×#6099—21no—
78M16×D13—44no—
79C2×#6094—22no—
80C2×C8×D13—22no—
81C2×C8×D13—22no—
82#88151—22no—
83#88151—22no—
84#88151—22no—
85#88151—22no—
86#88146—22no—
87#88146—22no—
88#88146—22no—
89#88146—22no—
90#88144—22no—
91#88144—22no—
92#88144—22no—
93#88144—22no—
94#88141—22no—
95#88141—22no—
96#88141—22no—
97#88141—22no—
98C42×D13C2×C411yescharacteristic
99C42×D13C2×C411yescharacteristic
100C42×D13D411yescharacteristic
101C42×D13D411yescharacteristic
102C42×D13D411yescharacteristic
103C42×D13D411yescharacteristic
104C42×D13C2311yescharacteristic
105C42×D13C2311yescharacteristic
106#88123—21no—
107#88123—21no—
108#88123C2×C412yes—
109#88123C2312yes—
110C13×C4⋊C8—21no—
111C13×C4⋊C8C2312yes—
112C13×C4⋊C8C2312yes—
113C13×C22⋊C8—21no—
114C4×C8×C13—21no—
115C22⋊#1055—21no—
116#88060—22no—
117#88054—22no—
118#88054—22no—
119#88054—22no—
120C8×Dic13—22no—
121C4⋊#1055—21no—
122C4⋊#1055C2312yes—
123C4⋊#1055C2312yes—
124C4×#1055—21no—
125#17708—131nomaximal, Sylow
126C23×D13C22⋊C411yescharacteristic
127C2×Q8×C13—22no—
128C2×Q8×C13—44no—
129C2×Q8×C13C22×C414yes—
130C22×C4×C13—22no—
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×Dic13—22no—
135C22×Dic13C22⋊C411yescharacteristic
136C22×Dic13C22⋊C411yescharacteristic
137C22×Dic13C22⋊C411yescharacteristic
138C2×C4×D13—42no—
139C2×C4×D13—42no—
140C2×C4×D13C22⋊C411yescharacteristic
141C2×C4×D13C22⋊C411yescharacteristic
142C2×C4×D13C22⋊C411yescharacteristic
143C2×C4×D13C22⋊C411yescharacteristic
144C2×C4×D13C22⋊C411yescharacteristic
145C2×C4×D13C22⋊C411yescharacteristic
146C2×C4×D13SD1614yes—
147C2×C4×D13Q1614yes—
148C2×C4×D13C22×C411yescharacteristic
149C2×C4×D13C22×C411yescharacteristic
150C2×C4×D13C2×D411yescharacteristic
151C2×C4×D13C2×D411yescharacteristic
152C2×C4×D13C2×D411yescharacteristic
153C2×C4×D13C2×D411yescharacteristic
154C2×Dic26—22no—
155C2×Dic26—22no—
156C2×Dic26—44no—
157C13×M16—42no—
158C2×C8×C13—22no—
159C2×C8×C13—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C42×C13C22×C411yescharacteristic
165C42×C13C2×D411yescharacteristic
166C42×C13C2×D411yescharacteristic
167C42×C13C2411yescharacteristic
168#6103—24no—
169#6103—24no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—24no—
174C4⋊Dic13—24no—
175C4⋊Dic13C22×C414yes—
176#6101—24no—
177#6101—24no—
178C4×Dic13—24no—
179C4×Dic13—24no—
180C4×Dic13C22⋊C411yescharacteristic
181C4×Dic13C22⋊C411yescharacteristic
182C4×Dic13C22⋊C411yescharacteristic
183C4×Dic13C22⋊C411yescharacteristic
184C4×Dic13C22⋊C411yescharacteristic
185C4×Dic13C22⋊C411yescharacteristic
186C4×Dic13C22×C411yescharacteristic
187C4×Dic13C22×C411yescharacteristic
188C4×Dic13C2×D411yescharacteristic
189C4×Dic13C2×D411yescharacteristic
190C4×Dic13C2×D411yescharacteristic
191C4×Dic13C2×D411yescharacteristic
192#6099—42no—
193C2×#1055—22no—
194C2×#1055—22no—
195#6094—44no—
196C8×D13—44no—
197C8×D13—44no—
198C2×#533—131no—
199C2×#431—131no—
200C2×#423—131no—
201#1550—134no—
202#1549—131no—
203#1549—131no—
204#1548—131no—
205#1548D1311yescharacteristic, complemented
206#1542—134no—
207C23×C13C2×C22⋊C411yescharacteristic
208C22×D13—41no—
209C22×D13—41no—
210C22×D13#10314yes—
211C22×D13C2×C22⋊C411yescharacteristic
212C22×D13C2×C22⋊C411yescharacteristic
213Q8×C13—44no—
214Q8×C13—44no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—24no—
218C2×C4×C13—44no—
219C2×C4×C13C2×C22⋊C411yescharacteristic
220C2×C4×C13C2×C22⋊C411yescharacteristic
221C2×C4×C13C2×C22⋊C411yescharacteristic
222C2×C4×C13C2×SD1612yes—
223C2×C4×C13C2×Q1612yes—
224C2×C4×C13C23×C411yescharacteristic
225C2×C4×C13C22×D411yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C2×Dic13—24no—
228C2×Dic13—41no—
229C2×Dic13—41no—
230C2×Dic13—44no—
231C2×Dic13#10314yes—
232C2×Dic13C2×C22⋊C411yescharacteristic
233C2×Dic13C2×C22⋊C411yescharacteristic
234C2×Dic13C2×C22⋊C411yescharacteristic
235C2×Dic13C2×C22⋊C411yescharacteristic
236C2×Dic13C2×C22⋊C411yescharacteristic
237C2×Dic13C2×C22⋊C411yescharacteristic
238C4×D13—22no—
239C4×D13—22no—
240C4×D13—22no—
241C4×D13—22no—
242C4×D13—41no—
243C4×D13—41no—
244C4×D13—41no—
245C4×D13—41no—
246C4×D13#10314yes—
247C4×D13#10314yes—
248C4×D13C2×SD1612yes—
249C4×D13C2×SD1612yes—
250C4×D13C2×Q1612yes—
251C4×D13C2×Q1612yes—
252Dic26—44no—
253Dic26—44no—
254C8×C13—42no—
255C8×C13—42no—
256#1055—42no—
257#1055—42no—
258C22×M16—261no—
259#533—132no—
260#533—132no—
261#533—132no—
262#533—132no—
263#533—261no—
264#533—261no—
265#533—261no—
266#533—261no—
267C2×C4⋊Q8—131no—
268C2×C4⋊Q8C2×D1311yescharacteristic
269C2×#125—261no—
270C2×C22⋊Q8—132no—
271C2×C22⋊Q8—261no—
272C2×C4×Q8—132no—
273C2×C4×Q8—261no—
274C2×#117—261no—
275C22×C42—131no—
276#431—131no—
277#431—132no—
278#431—261no—
279#431—261no—
280#431C2×D1311yescharacteristic
281#423—131no—
282#423—132no—
283#423—261no—
284#423—261no—
285#423C2×D1311yescharacteristic
286C2×C4⋊C8—132no—
287C2×C4⋊C8—132no—
288C2×C4⋊C8—261no—
289C2×C22⋊C8—261no—
290C2×C4×C8—261no—
291#333—134no—
292#333C2×D1314yescomplemented
293#332—134no—
294#332—134no—
295C22×C13—21no—
296C22×C13—21no—
297C22×C13C2×#10312yes—
298C22×C13C22×C22⋊C411yescharacteristic
299C2×D13—21no—
300C2×D13—21no—
301C2×D13—21no—
302C2×D13—21no—
303C2×D13—44no—
304C2×D13C2×#10312yes—
305C2×D13C2×#10312yes—
306C4×C13—21no—
307C4×C13—21no—
308C4×C13—44no—
309C4×C13#41312yes—
310C4×C13C2×#10312yes—
311C4×C13C22×SD1611yescharacteristic
312C4×C13C22×Q1611yescharacteristic
313C4×C13#57512yes—
314Dic13—21no—
315Dic13—21no—
316Dic13—21no—
317Dic13—21no—
318Dic13—44no—
319Dic13C2×#10312yes—
320Dic13C2×#10312yes—
321C22×Q8—261no—
322C22×Q8C4×D1312yes—
323C23×C4—131no—
324C23×C4—131no—
325C23×C4—131no—
326C2×M16—21no—
327C2×M16—262no—
328C2×M16—261no—
329C2×M16—524no—
330C22×C8—262no—
331C22×C8—262no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—132no—
335C4⋊Q8—132no—
336C4⋊Q8—261no—
337C4⋊Q8—261no—
338C4⋊Q8C4×D1312yes—
339C4⋊Q8C22×D1312yes—
340#125—262no—
341#125—262no—
342#125—262no—
343#125—262no—
344C22⋊Q8—134no—
345C22⋊Q8—134no—
346C22⋊Q8—262no—
347C22⋊Q8—262no—
348C22⋊Q8—262no—
349C22⋊Q8—262no—
350C22⋊Q8—262no—
351C22⋊Q8—262no—
352C4×Q8—134no—
353C4×Q8—134no—
354C4×Q8—262no—
355C4×Q8—262no—
356C4×Q8—262no—
357C4×Q8—262no—
358C4×Q8—262no—
359C4×Q8—262no—
360#117—262no—
361#117—262no—
362#117—262no—
363#117—262no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—132no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—261no—
370C2×C22⋊C4—262no—
371C2×C42—131no—
372C2×C42—131no—
373C2×C42—131no—
374C2×C42—131no—
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—131no—
382C2×C42—262no—
383C2×C42C22×D1311yescharacteristic
384C4⋊C8—21no—
385C4⋊C8—132no—
386C4⋊C8—132no—
387C4⋊C8—262no—
388C4⋊C8—262no—
389C4⋊C8—262no—
390C4⋊C8—261no—
391C4⋊C8C22×D1312yes—
392C4⋊C8C22×D1312yes—
393C22⋊C8—21no—
394C22⋊C8—262no—
395C22⋊C8—261no—
396C4×C8—21no—
397C4×C8—262no—
398C4×C8—261no—
399C2×C13—22no—
400C2×C13C2×#41311yescharacteristic
401C2×C13C22×#10311yescharacteristic
402C2×C13#289611yescharacteristic
403D13—22no—
404D13—22no—
405C24—131no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—262no—
409C2×Q8—262no—
410C2×Q8—524no—
411C2×Q8C2×C4×D1314yes—
412C22×C4—22no—
413C22×C4—131no—
414C22×C4—131no—
415C22×C4—131no—
416C22×C4—134no—
417C22×C4—134no—
418C22×C4—131no—
419C22×C4—131no—
420C22×C4—131no—
421C22×C4—131no—
422C22×C4—131no—
423C22×C4—131no—
424C22×C4—131no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—262no—
431C22×C4—522no—
432C22×C4—522no—
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4D4×D1311yescharacteristic
435C22×C4D4×D1311yescharacteristic
436M16—42no—
437M16—524no—
438M16—522no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—262no—
442C2×C8—262no—
443C2×C8—524no—
444C2×C8—524no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—134no—
450C4⋊C4—264no—
451C4⋊C4—264no—
452C4⋊C4—264no—
453C4⋊C4—264no—
454C4⋊C4—262no—
455C4⋊C4—262no—
456C4⋊C4—262no—
457C22⋊C4—264no—
458C22⋊C4—264no—
459C42—131no—
460C42—131no—
461C42—131no—
462C42—131no—
463C42—131no—
464C42—131no—
465C42—131no—
466C42—131no—
467C42—131no—
468C42—131no—
469C42—131no—
470C42—131no—
471C42—264no—
472C42—264no—
473C42C2×C4×D1311yescharacteristic
474C42D4×D1311yescharacteristic
475C42D4×D1311yescharacteristic
476C42C23×D1311yescharacteristic
477C13#1770811yescharacteristic, complemented, Sylow
478C23—131no—
479C23—131no—
480C23—134no—
481C23—521no—
482C23—521no—
483C23C22⋊C4×D1311yescharacteristic
484Q8—44no—
485Q8—44no—
486Q8—524no—
487Q8—524no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—44no—
492C2×C4—131no—
493C2×C4—131no—
494C2×C4—134no—
495C2×C4—132no—
496C2×C4—132no—
497C2×C4—132no—
498C2×C4—132no—
499C2×C4—134no—
500C2×C4—134no—
501C2×C4—131no—
502C2×C4—131no—
503C2×C4—131no—
504C2×C4—131no—
505C2×C4—262no—
506C2×C4—262no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—264no—
510C2×C4—521no—
511C2×C4—521no—
512C2×C4—521no—
513C2×C4—521no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4—524no—
517C2×C4C22⋊C4×D1311yescharacteristic
518C2×C4C22⋊C4×D1311yescharacteristic
519C2×C4C22⋊C4×D1311yescharacteristic
520C2×C4SD16×D1312yes—
521C2×C4Q16×D1312yes—
522C2×C4C22×C4×D1311yescharacteristic
523C2×C4C2×D4×D1311yescharacteristic
524C2×C4C2×D4×D1311yescharacteristic
525C8—42no—
526C8—42no—
527C8—522no—
528C8—522no—
529C22—21no—
530C22—21no—
531C22—132no—
532C22—132no—
533C22—261no—
534C22—261no—
535C22—261no—
536C22—261no—
537C22—524no—
538C22D13×#10312yes—
539C22C2×C22⋊C4×D1311yescharacteristic
540C4—21no—
541C4—21no—
542C4—44no—
543C4—132no—
544C4—132no—
545C4—261no—
546C4—261no—
547C4—261no—
548C4—261no—
549C4—524no—
550C4#1171840612yes—
551C4D13×#10312yes—
552C4C2×SD16×D1311yescharacteristic
553C4C2×Q16×D1311yescharacteristic
554C4#1171948212yes—
555C2—22no—
556C2—262no—
557C2—262no—
558C2C2×#1171840611yescharacteristic
559C2C2×D13×#10311yescharacteristic
560C2#1312335411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1548C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC42×C13C24
hypercenter#1548D13
hypocenterC13#17708
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
4. #13113523C2semidirect
5. #13113522C2semidirect
6. #13113520C2semidirect
7. #13113517C2semidirect
8. #13113490C2semidirect
9. C13×#1548C2semidirect
43. C13×#333C22semidirect
44. #11718138C22semidirect
45. #11718078C22semidirect
46. #11718074C22semidirect
205. #1548D13semidirect
292. #333C2×D13semidirect
477. C13#17708semidirect

Maximal subgroups

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

subgroupindex
C2×#117194332
D13×#4312
D13×#4232
#131135232
#131135222
#131135202
#131135172
#131134902
C13×#15482
#1770813