Finite Group Databasebeta

← #16791679

Subgroups — #16791679

Order 3328.

1326 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719082C212yesmaximal
2#13130016C212yesmaximal
3#13130015C212yesmaximal
4#13130015C212yesmaximal
5#13130013C212yesmaximal
6#13130012C211yesmaximal, characteristic
7#13130012C211yesmaximal, characteristic
8#13130011C212yesmaximal
9D13×#389C211yesmaximal, characteristic
10C22×C4⋊#261C2212yes—
11C22×C4×#261C2212yes—
12C22×C4×#261C2212yes—
13C2×C4⋊C4×D13C2212yes—
14C2×C4⋊C4×D13C2211yescharacteristic
15C2×C4⋊C4×D13C2211yescharacteristic
16C2×C42×D13C2211yescharacteristic
17C2×(C2×#261)⋊C4C2211yescharacteristic
18C2×(C2×#261)⋊C4C2212yes—
19C2×(C2×#261)⋊C4C2212yes—
20C2×(C2×#261)⋊C4C2212yes—
21C2×(C2×#261)⋊C4C2211yescharacteristic
22C2×(C2×#261)⋊C4C2212yes—
23C2×(C2×#261)⋊C4C2211yescharacteristic
24C2×(C2×#261)⋊C4C2211yescharacteristic
25C2×(C2×#261)⋊C4C2212yes—
26C2×(C2×#261)⋊C4C2212yes—
27C2×(C2×#261)⋊C4C2212yes—
28C2×(C2×#261)⋊C4C2212yes—
29C2×(C2×#261)⋊C4C2212yes—
30#11719082C4116yescomplemented
31C13×#389C411yescharacteristic, complemented
32#11718646C411yescharacteristic, complemented
33#11718634C411yescharacteristic, complemented
34#11718633C412yescomplemented
35#11718589C411yescharacteristic, complemented
36D13×#95C2212yes—
37#11718308C412yescomplemented
38C23×#261C2312yes—
39C23×#261C2312yes—
40C23×#261C2312yes—
41C23×#261C2312yes—
42C22×C4×D13C2311yescharacteristic
43C22×C4×D13C2311yescharacteristic
44C22×C4×D13C2312yes—
45C22×C4×D13C2311yescharacteristic
46C22×C4×D13C2312yes—
47C2×C4⋊#261—42no—
48C2×C4⋊#261—42no—
49C2×C4⋊#261C2×C418yes—
50C2×C4×#261—42no—
51C2×C4×#261—42no—
52C2×C4×#261—42no—
53C2×C4×#261—42no—
54C2×C4×#261—42no—
55C2×C4×#261C2×C418yes—
56C2×C13×C4⋊C4C2×C412yes—
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4C2×C411yescharacteristic
59C2×C42×C13C2×C411yescharacteristic
60C2×C4⋊Dic13C2×C412yes—
61C2×C4⋊Dic13C2×C411yescharacteristic
62C2×C4⋊Dic13C2×C411yescharacteristic
63C2×#6101C2×C412yes—
64C2×#6101C2×C412yes—
65C2×#6101C2×C412yes—
66C2×#6101C2×C412yes—
67C2×C4×Dic13C2×C411yescharacteristic
68C2×C4×Dic13C2×C411yescharacteristic
69C2×C4×Dic13C2×C411yescharacteristic
70C4⋊C4×D13—42no—
71C4⋊C4×D13—42no—
72C4⋊C4×D13—42no—
73C4⋊C4×D13C2×C418yes—
74C42×D13—42no—
75(C2×#261)⋊C4—41no—
76(C2×#261)⋊C4—41no—
77(C2×#261)⋊C4—41no—
78(C2×#261)⋊C4—41no—
79(C2×#261)⋊C4—42no—
80(C2×#261)⋊C4—42no—
81(C2×#261)⋊C4—42no—
82(C2×#261)⋊C4—42no—
83(C2×#261)⋊C4—42no—
84(C2×#261)⋊C4C2×C418yes—
85(C2×#261)⋊C4C2×C418yes—
86(C2×#261)⋊C4C2×C418yes—
87(C2×#261)⋊C4C2×C418yes—
88C13×#95C2×C412yes—
89#88071C2×C412yes—
90#88071C2×C412yes—
91#88071C2×C412yes—
92#13833—131nomaximal, Sylow
93C23×D13C2411yescharacteristic
94C22×#261—22no—
95C22×#261—22no—
96C22×#261—22no—
97C22×#261—22no—
98C22×#261—22no—
99C22×#261—22no—
100C22×#261—22no—
101C22×#261—22no—
102C22×#261—22no—
103C22×#261—22no—
104C22×#261—22no—
105C22×#261—22no—
106C22×#261—22no—
107C22×#261—22no—
108C22×#261—22no—
109C22×#261—22no—
110C22×#261—22no—
111C22×#261—22no—
112C22×#261—22no—
113C22×#261—22no—
114C22×#261—22no—
115C22×#261—22no—
116C22×#261—22no—
117C22×#261—22no—
118C22×#261C22×C414yes—
119C22×#261C22×C414yes—
120C22×#261C22×C414yes—
121C22×#261C22×C414yes—
122C22×C4×C13C22×C411yescharacteristic
123C22×C4×C13C22×C412yes—
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C412yes—
126C22×C4×C13C22×C411yescharacteristic
127C22×Dic13C22×C411yescharacteristic
128C22×Dic13C22×C412yes—
129C22×Dic13C22×C411yescharacteristic
130C22×Dic13C22×C412yes—
131C22×Dic13C22×C411yescharacteristic
132C2×C4×D13—22no—
133C2×C4×D13—22no—
134C2×C4×D13—22no—
135C2×C4×D13—22no—
136C2×C4×D13—21no—
137C2×C4×D13—21no—
138C2×C4×D13—22no—
139C2×C4×D13—21no—
140C2×C4×D13—21no—
141C2×C4×D13—22no—
142C2×C4×D13—22no—
143C2×C4×D13—22no—
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13—22no—
149C2×C4×D13—21no—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—21no—
153C2×C4×D13C22×C414yes—
154C2×C4×D13C22×C414yes—
155C2×C4×D13C22×C414yes—
156C4⋊#261—48no—
157C4×#261—48no—
158C4×#261—48no—
159C13×C4⋊C4—41no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4C4214yescomplemented
162C42×C13—41no—
163C4⋊Dic13—42no—
164C4⋊Dic13—41no—
165C4⋊Dic13C4214yescomplemented
166#6101—42no—
167#6101—42no—
168#6101—42no—
169#6101C4218yescomplemented
170C4×Dic13—41no—
171C4×Dic13—41no—
172C4×Dic13—41no—
173C2×#389—131no—
174C2×#387—132no—
175#1436—132no—
176#1436—132no—
177#1436—132no—
178C4⋊#95—132no—
179#1434—132no—
180#1434—131no—
181#1434—131no—
182C23×C13C23×C411yescharacteristic
183C22×D13C23×C412yes—
184C22×D13H(5,𝔽2)11yescharacteristic
185C22×D13H(5,𝔽2)12yes—
186C22×D13H(5,𝔽2)11yescharacteristic
187C22×D13H(5,𝔽2)12yes—
188C22×D132−1+411yescharacteristic
189C22×D132−1+412yes—
190C22×D132−1+411yescharacteristic
191C22×D132−1+411yescharacteristic
192C22×D132−1+411yescharacteristic
193C2×#261—24no—
194C2×#261—24no—
195C2×#261—24no—
196C2×#261—24no—
197C2×#261—24no—
198C2×#261—24no—
199C2×#261—24no—
200C2×#261—24no—
201C2×#261—24no—
202C2×#261—24no—
203C2×#261—24no—
204C2×#261—24no—
205C2×#261—42no—
206C2×#261—42no—
207C2×#261—42no—
208C2×#261—42no—
209C2×#261—42no—
210C2×#261—42no—
211C2×#261—42no—
212C2×#261—42no—
213C2×#261—42no—
214C2×#261—42no—
215C2×#261—42no—
216C2×#261—42no—
217C2×#261—42no—
218C2×#261—42no—
219C2×#261—42no—
220C2×#261—42no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—22no—
233C2×C4×C13—21no—
234C2×C4×C13C2×C4214yes—
235C2×C4×C13C2×C4212yes—
236C2×Dic13—21no—
237C2×Dic13—22no—
238C2×Dic13—21no—
239C2×Dic13—22no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—22no—
248C2×Dic13—21no—
249C2×Dic13C2×C4212yes—
250C2×Dic13C2×C4214yes—
251C4×D13—24no—
252C4×D13—24no—
253C4×D13—24no—
254C4×D13—24no—
255C4×D13—24no—
256C4×D13—24no—
257C4×D13—42no—
258C4×D13—42no—
259C4×D13—42no—
260C4×D13—42no—
261C4×D13—42no—
262C4×D13—42no—
263C4×D13—42no—
264C4×D13—42no—
265C22×C4⋊C4—131no—
266C22×C4⋊C4—132no—
267C22×C4⋊C4—132no—
268C22×C4⋊C4—131no—
269C22×C42—132no—
270C22×C42—131no—
271C22×C42—132no—
272#389—132no—
273#389—131no—
274#389—131no—
275#389—131no—
276#389—132no—
277#389#26111yescharacteristic, complemented
278#387—1316no—
279C2×#95—132no—
280C2×#95—132no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—131no—
285C2×#95—132no—
286C2×#95—131no—
287C2×#95—132no—
288C2×#95—132no—
289C2×#95—131no—
290C2×#95—132no—
291C2×#95—131no—
292C2×#95—132no—
293C22×C13C22×C4211yescharacteristic
294C22×C13#51811yescharacteristic
295C22×C13#51811yescharacteristic
296C22×C13#51911yescharacteristic
297C22×C13#51911yescharacteristic
298C22×C13#52011yescharacteristic
299C22×C13#52011yescharacteristic
300C2×D13#51812yes—
301C2×D13#51912yes—
302C2×D13#52012yes—
303C2×D13#52012yes—
304C2×D13#52012yes—
305C2×D13#52012yes—
306C2×D13#56012yes—
307C2×D13#56211yescharacteristic
308C2×D13#56212yes—
309C2×D13#56212yes—
310C2×D13#56312yes—
311C2×D13#56311yescharacteristic
312C2×D13#56312yes—
313C2×D13#56312yes—
314C2×D13#56311yescharacteristic
315C2×D13#56411yescharacteristic
316#261—44no—
317#261—44no—
318#261—44no—
319#261—44no—
320C4×C13—22no—
321C4×C13—24no—
322C4×C13—42no—
323C4×C13—41no—
324C4×C13—41no—
325Dic13—22no—
326Dic13—24no—
327Dic13—42no—
328Dic13—41no—
329Dic13—41no—
330C23×C4—132no—
331C23×C4—131no—
332C23×C4—132no—
333C23×C4—132no—
334C23×C4—132no—
335C23×C4—132no—
336C23×C4—132no—
337C23×C4—131no—
338C23×C4—131no—
339C2×C4⋊C4—132no—
340C2×C4⋊C4—131no—
341C2×C4⋊C4—138no—
342C2×C4⋊C4—138no—
343C2×C4⋊C4—132no—
344C2×C4⋊C4—132no—
345C2×C4⋊C4—132no—
346C2×C4⋊C4—131no—
347C2×C4⋊C4—132no—
348C2×C4⋊C4—522no—
349C2×C4⋊C4—522no—
350C2×C4⋊C4—522no—
351C2×C4⋊C4—522no—
352C2×C4⋊C4—522no—
353C2×C4⋊C4C2×#26111yescharacteristic
354C2×C4⋊C4C2×#26112yes—
355C2×C4⋊C4C2×#26111yescharacteristic
356C2×C42—138no—
357C2×C42—131no—
358C2×C42—131no—
359C2×C42—131no—
360C2×C42—522no—
361C2×C42—522no—
362C2×C42—522no—
363C2×C42—522no—
364C2×C42—522no—
365C2×C42—522no—
366C2×C42C2×#26111yescharacteristic
367#95—138no—
368#95—138no—
369#95—138no—
370#95—138no—
371#95—132no—
372#95—132no—
373#95—132no—
374#95—521no—
375#95—521no—
376#95—521no—
377#95—521no—
378#95—522no—
379#95—522no—
380#95—522no—
381#95—522no—
382#95—522no—
383#95C2×#26112yes—
384C2×C13#227411yescharacteristic
385C2×C13#227511yescharacteristic
386C2×C13#227611yescharacteristic
387C2×C13#237711yescharacteristic
388C2×C13#237811yescharacteristic
389C2×C13#238111yescharacteristic
390C2×C13#238211yescharacteristic
391D13#237612yes—
392D13#237812yes—
393D13#238212yes—
394D13#238312yes—
395C24—131no—
396C22×C4—132no—
397C22×C4—131no—
398C22×C4—134no—
399C22×C4—134no—
400C22×C4—134no—
401C22×C4—134no—
402C22×C4—134no—
403C22×C4—134no—
404C22×C4—134no—
405C22×C4—131no—
406C22×C4—132no—
407C22×C4—131no—
408C22×C4—262no—
409C22×C4—262no—
410C22×C4—262no—
411C22×C4—262no—
412C22×C4—261no—
413C22×C4—261no—
414C22×C4—262no—
415C22×C4—261no—
416C22×C4—261no—
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—261no—
427C22×C4—262no—
428C22×C4—261no—
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×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—262no—
452C22×C4—262no—
453C22×C4C22×#26111yescharacteristic
454C22×C4C22×#26112yes—
455C22×C4C22×#26111yescharacteristic
456C22×C4C22×#26112yes—
457C22×C4C22×#26111yescharacteristic
458C4⋊C4—41no—
459C4⋊C4—42no—
460C4⋊C4—138no—
461C4⋊C4—134no—
462C4⋊C4—522no—
463C4⋊C4—522no—
464C4⋊C4—522no—
465C4⋊C4—521no—
466C4⋊C4—522no—
467C4⋊C4—528no—
468C4⋊C4C4×#26114yescomplemented
469C42—41no—
470C42—521no—
471C42—521no—
472C42—521no—
473C42—528no—
474C42—528no—
475C13#1383311yescharacteristic, complemented, Sylow
476C23—132no—
477C23—132no—
478C23—132no—
479C23—131no—
480C23—131no—
481C23—132no—
482C23—131no—
483C23—131no—
484C23—131no—
485C23—131no—
486C23C23×#26111yescharacteristic
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—132no—
501C2×C4—134no—
502C2×C4—264no—
503C2×C4—264no—
504C2×C4—264no—
505C2×C4—264no—
506C2×C4—264no—
507C2×C4—264no—
508C2×C4—261no—
509C2×C4—262no—
510C2×C4—261no—
511C2×C4—262no—
512C2×C4—264no—
513C2×C4—264no—
514C2×C4—264no—
515C2×C4—264no—
516C2×C4—264no—
517C2×C4—264no—
518C2×C4—264no—
519C2×C4—264no—
520C2×C4—264no—
521C2×C4—264no—
522C2×C4—264no—
523C2×C4—264no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—261no—
530C2×C4—262no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4C2×C4×#26112yes—
558C2×C4C2×C4×#26114yes—
559C22—132no—
560C22—132no—
561C22—132no—
562C22—132no—
563C22—132no—
564C22—132no—
565C22—132no—
566C22—132no—
567C22—132no—
568C22—132no—
569C22—132no—
570C22—132no—
571C22—131no—
572C22—131no—
573C22—131no—
574C22—131no—
575C22C22×C4×#26111yescharacteristic
576C22#1171962311yescharacteristic
577C22#1171962311yescharacteristic
578C22#1171962711yescharacteristic
579C22#1171962711yescharacteristic
580C22#1171963111yescharacteristic
581C22#1171963111yescharacteristic
582C4—22no—
583C4—24no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—262no—
588C4—264no—
589C4—524no—
590C4—524no—
591C4—524no—
592C4—524no—
593C4—521no—
594C4—522no—
595C4—521no—
596C2—132no—
597C2—132no—
598C2—132no—
599C2—132no—
600C2#1313127411yescharacteristic
601C2#1313127511yescharacteristic
602C2#1313127611yescharacteristic
603C2#1313137711yescharacteristic
604C2#1313137811yescharacteristic
605C2#1313138111yescharacteristic
606C2#1313138211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#389C4
socleC23×C13C23×C4
prime radical, cosocleC23×D13C24
hypercenter#389#261
hypocenterC13#13833
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
30. #11719082C4semidirect
31. C13×#389C4semidirect
32. #11718646C4semidirect
33. #11718634C4semidirect
34. #11718633C4semidirect
35. #11718589C4semidirect
37. #11718308C4semidirect
161. C13×C4⋊C4C42semidirect
165. C4⋊Dic13C42semidirect
169. #6101C42semidirect
277. #389#261semidirect
468. C4⋊C4C4×#261semidirect
475. C13#13833semidirect

Maximal subgroups

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

subgroupindex
C2×#117190822
#131300162
#131300152
#131300132
#131300122
#131300112
D13×#3892
#1383313