Finite Group Databasebeta

← #16735292

Subgroups — #16735292

Order 3328.

1690 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128241C211yesmaximal, characteristic, complemented
2#13126128C218yesmaximal, complemented
3#13126113C218yesmaximal, complemented
4#13125378C212yesmaximal, complemented
5#13125222C212yesmaximal, complemented
6#13124780C212yesmaximal, complemented
7#13124772C212yesmaximal
8#13124641C212yesmaximal, complemented
9#13124633C212yesmaximal, complemented
10#13123474C211yesmaximal, characteristic, complemented
11C2×C13×#542C211yesmaximal, characteristic
12C13×#542—24no—
13C13×#542C2218yes—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#126—21no—
16C2×C13×#124—21no—
17C2×C13×#124C2211yescharacteristic
18C2×C13×#123—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#117C2211yescharacteristic
25C2×#88180C2212yes—
26#11719224C2214yescomplemented
27#11719224C2214yescomplemented
28#11719222—24no—
29#11719205—21no—
30#11719205—21no—
31#11719188—21no—
32#11719188—21no—
33#11719175C2212yes—
34#11719175C2212yes—
35#11718886C2214yes—
36#11718876C2214yes—
37#11718868C2212yes—
38#11718741C2218yescomplemented
39#11718740C2214yescomplemented
40#11718739C2214yescomplemented
41#11718717C2218yescomplemented
42#11718716C2214yescomplemented
43#11718716C2214yescomplemented
44#11718706C2218yescomplemented
45#11718705C2214yescomplemented
46#11718704C2214yescomplemented
47#11718696C2218yes—
48#11718695C2214yes—
49#11718694C2214yes—
50#11718683C2218yescomplemented
51#11718682C2214yescomplemented
52#11718681C2214yescomplemented
53#11718670C2218yescomplemented
54#11718669C2214yescomplemented
55#11718668C2214yescomplemented
56#11718661C2218yescomplemented
57#11718625C2214yes—
58#11718625C2214yes—
59#11718585C2212yes—
60C4×#6099C2212yes—
61C22×Q8×C13—21no—
62C22×Q8×C13C2311yescharacteristic
63C22×D4×C13—21no—
64C22×D4×C13C2311yescharacteristic
65C23×C4×C13—21no—
66C23×C4×C13C2311yescharacteristic
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8C2314yes—
69C13×#126—28no—
70C13×#124—28no—
71C13×#124—22no—
72C13×#124C2314yes—
73C13×#123—28no—
74C13×C22⋊Q8—22no—
75C13×C22⋊Q8—28no—
76C13×C22⋊Q8C2314yes—
77C13×#121—22no—
78C13×#121C2314yes—
79C4×Q8×C13—22no—
80C4×Q8×C13C2314yes—
81C4×D4×C13—22no—
82C4×D4×C13C2314yes—
83C13×#117D414yes—
84C13×#117C2314yes—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4D411yescharacteristic
89C2×C13×C4⋊C4D411yescharacteristic
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C4⋊C4C2311yescharacteristic
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C42×C13—21no—
100C2×C42×C13C2311yescharacteristic
101C2×C42×C13C2311yescharacteristic
102C2×C22⋊Dic13—22no—
103#88180—22no—
104#88180—22no—
105#88180C2314yes—
106#88180C2314yes—
107C2×C4⋊Dic13C2312yes—
108C2×C4⋊Dic13C2312yes—
109#88178—22no—
110#88178—22no—
111#88178—22no—
112#88178—22no—
113C2×C4×Dic13—22no—
114C2×#6099C2314yes—
115#88144—24no—
116#88144—24no—
117#88142—24no—
118#88142—24no—
119#88132—24no—
120#88132—24no—
121#88132—24no—
122#88132—24no—
123#88124C2314yes—
124#88124C2314yes—
125#88123C2312yes—
126#88123C2312yes—
127#88123C2312yes—
128#88123C2312yes—
129C4×Dic26—22no—
130C4×Dic26—22no—
131C4×Dic26—22no—
132C4×Dic26—22no—
133#88075C2318yes—
134#88075C2318yes—
135#88072C2318yes—
136#88072C2318yes—
137C22⋊#1055C2314yes—
138C22⋊#1055C2314yes—
139#88048C2318yes—
140#88048C2318yes—
141#88047C2318yes—
142#88047C2318yes—
143C4⋊#1055C2314yes—
144C4⋊#1055C2314yes—
145#88043C2314yes—
146C4×#1055C2314yes—
147#60870—131nomaximal, Sylow
148C24×C13—21no—
149C24×C13C2×D411yescharacteristic
150C2×Q8×C13—21no—
151C2×Q8×C13—24no—
152C2×Q8×C13—24no—
153C2×Q8×C13—82no—
154C2×Q8×C13C2412yes—
155C2×D4×C13—24no—
156C2×D4×C13—21no—
157C2×D4×C13—24no—
158C2×D4×C13—82no—
159C2×D4×C13C2412yes—
160C22×C4×C13—24no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—24no—
165C22×C4×C13—82no—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2412yes—
173C22×C4×C13C2411yescharacteristic
174C22×Dic13—22no—
175C22×Dic13—22no—
176C2×Dic26—22no—
177C2×Dic26—22no—
178C2×Dic26—22no—
179C2×Dic26—22no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—24no—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4C2×D414yes—
186C13×C4⋊C4C2×D414yes—
187C13×C4⋊C4C2412yes—
188C13×C4⋊C4C2412yes—
189C13×C22⋊C4—24no—
190C13×C22⋊C4—24no—
191C13×C22⋊C4—24no—
192C13×C22⋊C4—24no—
193C13×C22⋊C4—24no—
194C13×C22⋊C4C2×D414yes—
195C13×C22⋊C4C2×D414yes—
196C42×C13—24no—
197C42×C13C2×D412yes—
198C42×C13C2×D412yes—
199C42×C13C2412yes—
200C42×C13C2412yes—
201C22⋊Dic13—24no—
202C22⋊Dic13—24no—
203C4⋊Dic13—22no—
204C4⋊Dic13—22no—
205C4⋊Dic13—22no—
206C4⋊Dic13—22no—
207C4⋊Dic13—22no—
208C4⋊Dic13—22no—
209C4⋊Dic13C2414yes—
210C4⋊Dic13C2414yes—
211#6101—24no—
212#6101—24no—
213#6101—24no—
214#6101—24no—
215C4×Dic13—24no—
216C4×Dic13—24no—
217#6099—28no—
218C2×#1055C2418yes—
219#3458—131no—
220C2×#542D1311yescharacteristic
221#3244—138no—
222#3243—138no—
223#3165—132no—
224#3140—132no—
225#3095—132no—
226#3094—132no—
227#3078—132no—
228#3077—132no—
229#2921—131no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—42no—
235C23×C13—42no—
236C23×C13—42no—
237C23×C13C22×D412yes—
238C23×C13C22×D411yescharacteristic
239Q8×C13—24no—
240Q8×C13—42no—
241Q8×C13—84no—
242D4×C13—24no—
243D4×C13—42no—
244D4×C13—84no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—84no—
259C2×C4×C13C22×D412yes—
260C2×C4×C13C22×D412yes—
261C2×C4×C13C22×D412yes—
262C2×C4×C13C22×D412yes—
263C2×C4×C13C22×D412yes—
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C132−1+414yes—
266C2×C4×C13C2511yescharacteristic
267C2×Dic13—24no—
268C2×Dic13—24no—
269C2×Dic13—82no—
270C2×Dic13—82no—
271Dic26—82no—
272Dic26—82no—
273Dic26—82no—
274Dic26—82no—
275#1055—28no—
276#544—134no—
277#544—134no—
278#544—261no—
279#544—261no—
280#543—261no—
281#543—261no—
282#542—24no—
283#542C2×D1318yes—
284#533—132no—
285#533—132no—
286#533—264no—
287C2×C4⋊Q8C2×D1311yescharacteristic
288C2×#126—21no—
289C2×#124—21no—
290C2×#124C2×D1311yescharacteristic
291C2×#123—21no—
292C2×C22⋊Q8—21no—
293C2×C22⋊Q8C2×D1311yescharacteristic
294C2×#121C2×D1311yescharacteristic
295C2×C4×Q8C2×D1311yescharacteristic
296C2×C4×D4C2×D1311yescharacteristic
297C2×#117—132no—
298C2×#117C2×D1311yescharacteristic
299#501—138no—
300#500—134no—
301#498—134no—
302#489—134no—
303#489—134no—
304#488—138no—
305#485—138no—
306#484—134no—
307#483—134no—
308#482—138no—
309#481—134no—
310#480—134no—
311#479—138no—
312#478—138no—
313#477—134no—
314#476—134no—
315#475—134no—
316#474—134no—
317#433—138no—
318#428—134no—
319#428—134no—
320#423—132no—
321#419—134no—
322#418—134no—
323#407—132no—
324C4×M16—132no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13—22no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13—82no—
334C22×C13—84no—
335C22×C13#53612yes—
336C22×C13C23×D411yescharacteristic
337C4×C13—22no—
338C4×C13—22no—
339C4×C13—22no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13#53612yes—
346C4×C13C2×2−1+412yes—
347Dic13—44no—
348Dic13—44no—
349C22×Q8—21no—
350C22×Q8C22×D1311yescharacteristic
351C22×D4—21no—
352C22×D4C22×D1311yescharacteristic
353C23×C4—21no—
354C23×C4C22×D1311yescharacteristic
355C2×M16—134no—
356C4⋊Q8—22no—
357C4⋊Q8—132no—
358C4⋊Q8—132no—
359C4⋊Q8—132no—
360C4⋊Q8—132no—
361C4⋊Q8—264no—
362C4⋊Q8—264no—
363C4⋊Q8C22×D1314yes—
364#126—28no—
365#125—134no—
366#125—134no—
367#125—264no—
368#125—264no—
369#124—28no—
370#124—22no—
371#124C22×D1314yes—
372#123—28no—
373C22⋊Q8—22no—
374C22⋊Q8—28no—
375C22⋊Q8—262no—
376C22⋊Q8—262no—
377C22⋊Q8—262no—
378C22⋊Q8—262no—
379C22⋊Q8—264no—
380C22⋊Q8—264no—
381C22⋊Q8—264no—
382C22⋊Q8—264no—
383C22⋊Q8C22×D1314yes—
384#121—22no—
385#121C22×D1314yes—
386C4×Q8—22no—
387C4×Q8—262no—
388C4×Q8—262no—
389C4×Q8—262no—
390C4×Q8—262no—
391C4×Q8C22×D1314yes—
392C4×D4—22no—
393C4×D4C22×D1314yes—
394#117—134no—
395#117—134no—
396#117—262no—
397#117—262no—
398#117C22⋊D1314yes—
399#117C22×D1314yes—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—132no—
404C2×C4⋊C4—132no—
405C2×C4⋊C4C22⋊D1311yescharacteristic
406C2×C4⋊C4C22⋊D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—262no—
415C2×C22⋊C4C22⋊D1311yescharacteristic
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C42—21no—
418C2×C42—262no—
419C2×C42C22×D1311yescharacteristic
420C2×C42C22×D1311yescharacteristic
421#107—138no—
422#107—138no—
423#106—138no—
424#106—138no—
425C4⋊C8—134no—
426C4⋊C8—134no—
427#103—138no—
428#103—138no—
429#102—138no—
430#102—138no—
431C22⋊C8—134no—
432C22⋊C8—134no—
433#97—134no—
434C4×C8—134no—
435C2×C13—22no—
436C2×C13—42no—
437C2×C13—82no—
438C2×C13C2×#53611yescharacteristic
439C2×C13#358511yescharacteristic
440C2×C13#358611yescharacteristic
441C24—21no—
442C24C2×C22⋊D1311yescharacteristic
443C2×Q8—21no—
444C2×Q8—24no—
445C2×Q8—24no—
446C2×Q8—82no—
447C2×Q8—262no—
448C2×Q8—262no—
449C2×Q8—262no—
450C2×Q8—262no—
451C2×Q8C23×D1312yes—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—21no—
455C2×D4—82no—
456C2×D4C23×D1312yes—
457C22×C4—24no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—82no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4C2×C22⋊D1312yes—
466C22×C4C2×C22⋊D1311yescharacteristic
467C22×C4C2×C22⋊D1311yescharacteristic
468C22×C4C2×C22⋊D1311yescharacteristic
469C22×C4C2×C22⋊D1311yescharacteristic
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C23×D1312yes—
472C22×C4C23×D1311yescharacteristic
473M16—268no—
474C2×C8—138no—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—134no—
481C4⋊C4—134no—
482C4⋊C4—262no—
483C4⋊C4—262no—
484C4⋊C4—264no—
485C4⋊C4—264no—
486C4⋊C4—264no—
487C4⋊C4—264no—
488C4⋊C4—262no—
489C4⋊C4—262no—
490C4⋊C4—262no—
491C4⋊C4—262no—
492C4⋊C4C2×C22⋊D1314yes—
493C4⋊C4C2×C22⋊D1314yes—
494C4⋊C4C23×D1312yes—
495C4⋊C4C23×D1312yes—
496C22⋊C4—24no—
497C22⋊C4—24no—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—264no—
502C22⋊C4—264no—
503C22⋊C4C2×C22⋊D1314yes—
504C22⋊C4C2×C22⋊D1314yes—
505C42—24no—
506C42—264no—
507C42—264no—
508C42C2×C22⋊D1312yes—
509C42C2×C22⋊D1312yes—
510C42C23×D1312yes—
511C42C23×D1312yes—
512C13#6087011yescharacteristic, complemented, Sylow
513C23—22no—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23C22×C22⋊D1312yes—
521C23C22×C22⋊D1311yescharacteristic
522Q8—24no—
523Q8—42no—
524Q8—84no—
525Q8—1042no—
526Q8—1042no—
527Q8—1042no—
528Q8—1042no—
529D4—24no—
530D4—42no—
531D4—84no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—84no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—1042no—
549C2×C4—1042no—
550C2×C4#8825714yes—
551C2×C4C22×C22⋊D1312yes—
552C2×C4C22×C22⋊D1312yes—
553C2×C4C22×C22⋊D1312yes—
554C2×C4C22×C22⋊D1312yes—
555C2×C4C22×C22⋊D1312yes—
556C2×C4C22×C22⋊D1311yescharacteristic
557C2×C4C24×D1311yescharacteristic
558C8—268no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—82no—
568C22—84no—
569C22#1171953012yes—
570C22C23×C22⋊D1311yescharacteristic
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—22no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—524no—
580C4—524no—
581C4#1171953012yes—
582C4C2×#8825712yes—
583C2—22no—
584C2—42no—
585C2—82no—
586C2C2×#1171953011yescharacteristic
587C2#1312961611yescharacteristic
588C2#1312962311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#542C2
socleC22×C13C23×D4
prime radicalC2×C13×#121C22
hypercenterC2×#542D13
hypocenterC13#60870
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #13128241C2semidirect
2. #13126128C2semidirect
3. #13126113C2semidirect
4. #13125378C2semidirect
5. #13125222C2semidirect
6. #13124780C2semidirect
8. #13124641C2semidirect
9. #13124633C2semidirect
10. #13123474C2semidirect
26. #11719224C22semidirect
27. #11719224C22semidirect
38. #11718741C22semidirect
39. #11718740C22semidirect
40. #11718739C22semidirect
41. #11718717C22semidirect
42. #11718716C22semidirect
43. #11718716C22semidirect
44. #11718706C22semidirect
45. #11718705C22semidirect
46. #11718704C22semidirect
50. #11718683C22semidirect
51. #11718682C22semidirect
52. #11718681C22semidirect
53. #11718670C22semidirect
54. #11718669C22semidirect
55. #11718668C22semidirect
56. #11718661C22semidirect
512. C13#60870semidirect

Maximal subgroups

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

subgroupindex
#131282412
#131261282
#131261132
#131253782
#131252222
#131247802
#131247722
#131246412
#131246332
#131234742
C2×C13×#5422
#6087013