Finite Group Databasebeta

← #15794001

Subgroups — #15794001

Order 3328.

1342 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#13113104C212yesmaximal, complemented
2#13113098C212yesmaximal, complemented
3#13113093C212yesmaximal, complemented
4#13113089C212yesmaximal, complemented
5#13113085C212yesmaximal
6#13113081C211yesmaximal, characteristic
7#13113081C211yesmaximal, characteristic
8#13113059C212yesmaximal
9C2×C13×#385C211yesmaximal, characteristic
10C24×C4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2212yes—
12C22×C13×C22⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2212yes—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C13×#385C418yescomplemented
19C2×C13×#95C2212yes—
20C2×#88071C2212yes—
21C2×#88071C2212yes—
22C2×#88071C2212yes—
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C25×C13C2311yescharacteristic
33C23×C4×C13—41no—
34C23×C4×C13—41no—
35C23×C4×C13—42no—
36C23×C4×C13—42no—
37C23×C4×C13C2×C414yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2312yes—
41C23×C4×C13C2312yes—
42C23×Dic13C2312yes—
43C23×Dic13C2312yes—
44C23×Dic13C2312yes—
45C23×Dic13C2312yes—
46C2×C13×C4⋊C4—42no—
47C2×C13×C4⋊C4—42no—
48C2×C13×C4⋊C4C2×C418yes—
49C2×C13×C22⋊C4—22no—
50C2×C13×C22⋊C4—22no—
51C2×C13×C22⋊C4—41no—
52C2×C13×C22⋊C4—41no—
53C2×C13×C22⋊C4C2×C414yes—
54C2×C13×C22⋊C4C2×C414yes—
55C2×C22⋊Dic13—24no—
56C2×C22⋊Dic13—24no—
57C2×C22⋊Dic13—42no—
58C2×C22⋊Dic13—42no—
59C2×C22⋊Dic13—42no—
60C2×C22⋊Dic13—42no—
61C2×C4⋊Dic13—41no—
62C2×C4⋊Dic13—41no—
63C2×C4⋊Dic13—42no—
64C2×C4⋊Dic13—42no—
65C13×#95C2×C418yes—
66#88071—41no—
67#88071—41no—
68#88071—42no—
69#88071—42no—
70#88071—42no—
71#88071—42no—
72#88071—42no—
73#88071—42no—
74#88071—42no—
75#88071—42no—
76#88071—42no—
77#88071—42no—
78#14669—131nomaximal, Sylow
79C24×C13—22no—
80C24×C13—22no—
81C24×C13—22no—
82C24×C13—21no—
83C24×C13—21no—
84C24×C13—21no—
85C24×C13—21no—
86C24×C13—22no—
87C24×C13C22×C412yes—
88C24×C13#4112yes—
89C24×C13#4112yes—
90C24×C13C2411yescharacteristic
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—21no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—48no—
112C22×C4×C13—44no—
113C22×C4×C13—44no—
114C22×C4×C13—48no—
115C22×C4×C13—44no—
116C22×C4×C13C22×C412yes—
117C22×C4×C13C22×C414yes—
118C22×C4×C13C22×C414yes—
119C22×C4×C13C22×C412yes—
120C22×Dic13—22no—
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C13×C4⋊C4—48no—
149C13×C22⋊C4—28no—
150C13×C22⋊C4—44no—
151C22⋊Dic13—48no—
152C22⋊Dic13—48no—
153C4⋊Dic13—44no—
154C4⋊Dic13—44no—
155C2×#385D1311yescharacteristic
156#1445—132no—
157#1443—132no—
158#1442—132no—
159#1441—132no—
160#1440—132no—
161#1439—131no—
162#1439—131no—
163C22⋊#95—132no—
164C23×C13—22no—
165C23×C13—24no—
166C23×C13—22no—
167C23×C13—24no—
168C23×C13—24no—
169C23×C13—24no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13—22no—
173C23×C13—22no—
174C23×C13—24no—
175C23×C13—24no—
176C23×C13—41no—
177C23×C13—42no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—41no—
186C23×C13#11714yes—
187C23×C13C23×C411yescharacteristic
188C23×C13C2×#4111yescharacteristic
189C23×C13C2×#4111yescharacteristic
190C23×C13H(5,𝔽2)12yes—
191C23×C13H(5,𝔽2)12yes—
192C23×C13H(5,𝔽2)11yescharacteristic
193C23×C13H(5,𝔽2)11yescharacteristic
194C23×C13H(5,𝔽2)12yes—
195C23×C132−1+411yescharacteristic
196C23×C132−1+411yescharacteristic
197C23×C132−1+412yes—
198C2×C4×C13—24no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—24no—
202C2×C4×C13—24no—
203C2×C4×C13—24no—
204C2×C4×C13—24no—
205C2×C4×C13—24no—
206C2×C4×C13—24no—
207C2×C4×C13—24no—
208C2×C4×C13—416no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—41no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—42no—
227C2×Dic13—42no—
228C2×Dic13—42no—
229C2×Dic13—42no—
230C2×Dic13—42no—
231C2×Dic13—42no—
232C2×Dic13—42no—
233C2×Dic13—42no—
234C2×Dic13—42no—
235C2×Dic13—42no—
236C2×Dic13—42no—
237C2×Dic13—42no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—42no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C24×C4C2×D1311yescharacteristic
252C22×C4⋊C4—131no—
253C22×C4⋊C4—131no—
254C22×C4⋊C4C2×D1312yes—
255C22×C22⋊C4—132no—
256C22×C22⋊C4—132no—
257C22×C22⋊C4C2×D1311yescharacteristic
258C22×C22⋊C4C2×D1311yescharacteristic
259#385Dic1318yescomplemented
260C2×#95—132no—
261C2×#95—132no—
262C2×#95—132no—
263C2×#95—132no—
264C2×#95—132no—
265C2×#95—132no—
266C2×#95—131no—
267C2×#95—131no—
268C2×#95—132no—
269C2×#95—132no—
270C2×#95—132no—
271C2×#95—132no—
272C2×#95C2×D1312yes—
273C22×C13—24no—
274C22×C13—28no—
275C22×C13—42no—
276C22×C13—42no—
277C22×C13—44no—
278C22×C13—44no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—44no—
284C22×C13C2×#11711yescharacteristic
285C22×C13#51811yescharacteristic
286C22×C13#51812yes—
287C22×C13#51911yescharacteristic
288C22×C13#52012yes—
289C22×C13#53812yes—
290C22×C13#53812yes—
291C22×C13#53911yescharacteristic
292C22×C13#53911yescharacteristic
293C22×C13#53911yescharacteristic
294C22×C13#53911yescharacteristic
295C22×C13#53912yes—
296C22×C13#53912yes—
297C22×C13#56011yescharacteristic
298C22×C13#56012yes—
299C22×C13#56011yescharacteristic
300C22×C13H(3,𝔽4)11yescharacteristic
301C22×C13#56212yes—
302C22×C13#56212yes—
303C22×C13#56212yes—
304C22×C13#56312yes—
305C22×C13#56312yes—
306C22×C13#56311yescharacteristic
307C4×C13—44no—
308C4×C13—42no—
309C4×C13—44no—
310C4×C13—42no—
311Dic13—82no—
312Dic13—82no—
313Dic13—82no—
314Dic13—82no—
315C25C22×D1311yescharacteristic
316C23×C4—41no—
317C23×C4—41no—
318C23×C4—42no—
319C23×C4—42no—
320C23×C4—132no—
321C23×C4—132no—
322C23×C4—132no—
323C23×C4—132no—
324C23×C4C2×Dic1314yes—
325C23×C4C22×D1311yescharacteristic
326C23×C4C22×D1311yescharacteristic
327C23×C4C22×D1312yes—
328C23×C4C22×D1312yes—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—521no—
332C2×C4⋊C4—521no—
333C2×C4⋊C4—522no—
334C2×C4⋊C4—522no—
335C2×C4⋊C4C2×Dic1318yes—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—264no—
341C2×C22⋊C4—264no—
342C2×C22⋊C4—522no—
343C2×C22⋊C4—522no—
344C2×C22⋊C4—522no—
345C2×C22⋊C4—522no—
346C2×C22⋊C4C2×Dic1314yes—
347C2×C22⋊C4C2×Dic1314yes—
348#95—521no—
349#95—521no—
350#95—522no—
351#95—522no—
352#95—522no—
353#95—522no—
354#95—522no—
355#95—522no—
356#95—522no—
357#95—522no—
358#95—522no—
359#95—522no—
360#95C2×Dic1318yes—
361C2×C13—44no—
362C2×C13#231311yescharacteristic
363C2×C13#231812yes—
364C2×C13#237511yescharacteristic
365C2×C13#237611yescharacteristic
366C2×C13#237812yes—
367C2×C13#282411yescharacteristic
368C2×C13#282611yescharacteristic
369C2×C13#282712yes—
370C2×C13#282712yes—
371C2×C13#283411yescharacteristic
372C2×C13#283511yescharacteristic
373C24—21no—
374C24—21no—
375C24—22no—
376C24—22no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—22no—
381C24#612712yes—
382C24#612712yes—
383C24C22×Dic1312yes—
384C24C23×D1311yescharacteristic
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—48no—
406C22×C4—44no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—48no—
410C22×C4—262no—
411C22×C4—262no—
412C22×C4—262no—
413C22×C4—262no—
414C22×C4—262no—
415C22×C4—262no—
416C22×C4—262no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—262no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4—262no—
438C22×C4C22×Dic1312yes—
439C22×C4C22×Dic1314yes—
440C22×C4C22×Dic1314yes—
441C22×C4C22×Dic1312yes—
442C4⋊C4—48no—
443C4⋊C4—524no—
444C4⋊C4—524no—
445C22⋊C4—28no—
446C22⋊C4—44no—
447C22⋊C4—528no—
448C22⋊C4—528no—
449C13#1466911yescharacteristic, complemented, Sylow
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—24no—
456C23—22no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—41no—
470C23—41no—
471C23—42no—
472C23#8818014yes—
473C23C2×#612711yescharacteristic
474C23C2×#612711yescharacteristic
475C23#8825111yescharacteristic
476C23#8825111yescharacteristic
477C23#8825112yes—
478C23#8825112yes—
479C23#8825411yescharacteristic
480C23#8825411yescharacteristic
481C23#8825612yes—
482C23#8825712yes—
483C23C23×Dic1311yescharacteristic
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—416no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—522no—
510C2×C4—522no—
511C2×C4—522no—
512C2×C4—522no—
513C2×C4—522no—
514C2×C4—522no—
515C2×C4—522no—
516C2×C4—522no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—522no—
522C2×C4—522no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C22—28no—
538C22—24no—
539C22—42no—
540C22—42no—
541C22—44no—
542C22—42no—
543C22—42no—
544C22—44no—
545C22—44no—
546C22—42no—
547C22—42no—
548C22#1171922011yescharacteristic
549C22#1171922011yescharacteristic
550C22#1171922011yescharacteristic
551C22#1171922011yescharacteristic
552C22#1171926512yes—
553C22#1171926512yes—
554C22#1171926912yes—
555C22#1171926912yes—
556C22#1171929911yescharacteristic
557C22#1171930011yescharacteristic
558C22#1171930012yes—
559C22#1171935112yes—
560C22#1171935112yes—
561C22#1171935212yes—
562C22#1171935212yes—
563C22#1171935611yescharacteristic
564C22#1171937111yescharacteristic
565C22#1171937212yes—
566C22C2×#8818011yescharacteristic
567C22#1171950312yes—
568C22#1171950311yescharacteristic
569C22#1171951711yescharacteristic
570C22#1171953212yes—
571C4—42no—
572C4—44no—
573C4—44no—
574C4—42no—
575C4—1042no—
576C4—1042no—
577C4—1042no—
578C4—1042no—
579C2—44no—
580C2#1311743911yescharacteristic
581C2#1311746912yes—
582C2#1311797711yescharacteristic
583C2#1311798411yescharacteristic
584C2#1311800212yes—
585C2#1312291611yescharacteristic
586C2#1312292911yescharacteristic
587C2#1312293812yes—
588C2#1312294212yes—
589C2#1312301911yescharacteristic
590C2#1312302411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#385C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13#14669
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #13113104C2semidirect
2. #13113098C2semidirect
3. #13113093C2semidirect
4. #13113089C2semidirect
18. C13×#385C4semidirect
259. #385Dic13semidirect
449. C13#14669semidirect

Maximal subgroups

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

subgroupindex
#131131042
#131130982
#131130932
#131130892
#131130852
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