Finite Group Databasebeta

← #15789578

Subgroups — #15789578

Order 3328.

1414 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
1C22×#88143C211yesmaximal, characteristic
2C2×#11718312C211yesmaximal, characteristic
3C2×C4×#6101C211yesmaximal, characteristic
4#13113102C212yesmaximal
5#13113102C212yesmaximal
6#13113088C212yesmaximal
7#13113087C212yesmaximal
8#13113071C211yesmaximal, characteristic
9#13113069C211yesmaximal, characteristic
10#13113068C211yesmaximal, characteristic
11C13×#1436C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C42×C13C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×#6101C2212yes—
16C22×#6101C2211yescharacteristic
17C22×#6101C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C2×#88143—24no—
23C2×#88143—24no—
24C2×#88143C418yescomplemented
25C2×C13×#95C2212yes—
26C2×C13×#95C2211yescharacteristic
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C4×#6101—24no—
39#11718312—24no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4C2×C414yes—
54C2×C42×C13—22no—
55C2×C42×C13—42no—
56C2×C4⋊Dic13—22no—
57C2×C4⋊Dic13—22no—
58C2×C4⋊Dic13C2×C414yes—
59C2×#6101—22no—
60C2×#6101—22no—
61C2×#6101—24no—
62C2×#6101—22no—
63C2×#6101—22no—
64C2×#6101—22no—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×#6101—22no—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101C2×C414yes—
71C2×#6101C2×C414yes—
72C2×#6101C2×C414yes—
73C2×#6101C2×C414yes—
74C2×C4×Dic13—22no—
75C2×C4×Dic13—42no—
76C2×C4×Dic13C2×C414yes—
77C2×C4×Dic13D414yes—
78C2×C4×Dic13D414yes—
79#88143—232no—
80C13×#95—22no—
81C13×#95—24no—
82C13×#95—42no—
83#88071—22no—
84#88071—24no—
85#88071—24no—
86#88071—24no—
87#88071—24no—
88#88071—24no—
89#88071—24no—
90#88071—42no—
91#88071—42no—
92#88071—42no—
93#14289—131nomaximal, Sylow
94C24×C13C2411yescharacteristic
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—22no—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13C22×C412yes—
119C22×C4×C13C22×C412yes—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C2×D412yes—
122C22×C4×C13C2×D412yes—
123C22×C4×C13#4114yes—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—22no—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
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—
148C22×Dic13—22no—
149C22×Dic13C22×C412yes—
150C22×Dic13C22×C412yes—
151C22×Dic13C22×C412yes—
152C22×Dic13C22×C412yes—
153C22×Dic13C2×D412yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D412yes—
156C22×Dic13C2×D412yes—
157C22×Dic13#4114yes—
158C13×C4⋊C4—28no—
159C42×C13—44no—
160C4⋊Dic13—28no—
161#6101—216no—
162#6101—28no—
163#6101—28no—
164#6101—28no—
165#6101—28no—
166C4×Dic13—44no—
167C4×Dic13C22⋊C4116yes—
168C22×#125—131no—
169C2×#383—131no—
170C2×C4×C4⋊C4—131no—
171#1445—132no—
172#1445—132no—
173#1441—132no—
174#1441—132no—
175#1436—131no—
176#1436—131no—
177#1436—131no—
178#1436D1311yescharacteristic
179C23×C13C23×C411yescharacteristic
180C23×C13C22×D411yescharacteristic
181C23×C13C22×D411yescharacteristic
182C23×C13C2×#4112yes—
183C23×C13C2×#4112yes—
184C23×C13H(5,𝔽2)12yes—
185C23×C132−1+412yes—
186C23×C132−1+412yes—
187C23×C132−1+412yes—
188C2×C4×C13—24no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—24no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
195C2×C4×C13—22no—
196C2×C4×C13—24no—
197C2×C4×C13—24no—
198C2×C4×C13—24no—
199C2×C4×C13—24no—
200C2×C4×C13—42no—
201C2×C4×C13—42no—
202C2×C4×C13—42no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—42no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13C2×C22⋊C414yes—
217C2×Dic13—22no—
218C2×Dic13—22no—
219C2×Dic13—24no—
220C2×Dic13—24no—
221C2×Dic13—24no—
222C2×Dic13—22no—
223C2×Dic13—24no—
224C2×Dic13—22no—
225C2×Dic13—22no—
226C2×Dic13—22no—
227C2×Dic13—22no—
228C2×Dic13—22no—
229C2×Dic13—24no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—42no—
234C2×Dic13—42no—
235C2×Dic13—42no—
236C2×Dic13—41no—
237C2×Dic13—41no—
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×Dic13C2×C22⋊C414yes—
250C2×Dic13C2×C22⋊C414yes—
251C2×#125—138no—
252C2×#125—264no—
253C2×#125—264no—
254C22×C4⋊C4—131no—
255C22×C4⋊C4—131no—
256C22×C4⋊C4—131no—
257C22×C4⋊C4—131no—
258C22×C4⋊C4—131no—
259C22×C4⋊C4—132no—
260C22×C4⋊C4C2×D1311yescharacteristic
261C22×C42—131no—
262C22×C42—131no—
263C22×C42C2×D1311yescharacteristic
264#383—264no—
265C4×C4⋊C4—264no—
266C2×#95—131no—
267C2×#95—132no—
268C2×#95—132no—
269C2×#95—132no—
270C2×#95—132no—
271C2×#95—132no—
272C2×#95—132no—
273C2×#95—132no—
274C2×#95—132no—
275C2×#95—132no—
276C2×#95C2×D1311yescharacteristic
277C2×#95C2×D1312yes—
278C2×#95C2×D1312yes—
279C22×C13C22×C22⋊C411yescharacteristic
280C22×C13C4×#4111yescharacteristic
281C22×C13C4×#4111yescharacteristic
282C22×C13#51912yes—
283C22×C13#52012yes—
284C22×C13#52512yes—
285C22×C13#53212yes—
286C22×C13#53511yescharacteristic
287C22×C13#53611yescharacteristic
288C22×C13#53612yes—
289C22×C13#53611yescharacteristic
290C22×C13#53611yescharacteristic
291C22×C13#53712yes—
292C22×C13#53912yes—
293C22×C13#53912yes—
294C22×C13#53912yes—
295C22×C13#53912yes—
296C22×C13#54112yes—
297C22×C13#54112yes—
298C22×C13#54112yes—
299C22×C13#54112yes—
300C4×C13—24no—
301C4×C13—42no—
302C4×C13—44no—
303C4×C13—42no—
304C4×C13—82no—
305Dic13—24no—
306Dic13—24no—
307Dic13—42no—
308Dic13—44no—
309Dic13—42no—
310Dic13—82no—
311C23×C4—131no—
312C23×C4—131no—
313C23×C4—131no—
314C23×C4—131no—
315C23×C4—132no—
316C23×C4—132no—
317C23×C4C22×D1312yes—
318C23×C4C22×D1311yescharacteristic
319C23×C4C22×D1311yescharacteristic
320C23×C4C22×D1312yes—
321C23×C4C22×D1311yescharacteristic
322#125—2632no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—134no—
326C2×C4⋊C4—134no—
327C2×C4⋊C4—134no—
328C2×C4⋊C4—134no—
329C2×C4⋊C4—134no—
330C2×C4⋊C4—262no—
331C2×C4⋊C4—262no—
332C2×C4⋊C4—262no—
333C2×C4⋊C4—262no—
334C2×C4⋊C4—262no—
335C2×C4⋊C4—262no—
336C2×C4⋊C4—262no—
337C2×C4⋊C4—262no—
338C2×C4⋊C4—264no—
339C2×C4⋊C4—264no—
340C2×C4⋊C4—264no—
341C2×C4⋊C4—262no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4C4×D1314yes—
344C2×C42—22no—
345C2×C42—42no—
346C2×C42—134no—
347C2×C42—134no—
348C2×C42—134no—
349C2×C42—262no—
350C2×C42—522no—
351#95—24no—
352#95—22no—
353#95—42no—
354#95—264no—
355#95—264no—
356#95—264no—
357#95—264no—
358#95—264no—
359#95—264no—
360#95—262no—
361#95—522no—
362#95—522no—
363#95—522no—
364C2×C13#229711yescharacteristic
365C2×C13#231011yescharacteristic
366C2×C13#231111yescharacteristic
367C2×C13#233612yes—
368C2×C13#233612yes—
369C2×C13#263312yes—
370C2×C13#263412yes—
371C2×C13#266412yes—
372C2×C13#266412yes—
373C24C23×D1311yescharacteristic
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—132no—
398C22×C4—132no—
399C22×C4—132no—
400C22×C4—132no—
401C22×C4—132no—
402C22×C4—132no—
403C22×C4—132no—
404C22×C4—132no—
405C22×C4—134no—
406C22×C4—262no—
407C22×C4—262no—
408C22×C4—262no—
409C22×C4—262no—
410C22×C4—262no—
411C22×C4—262no—
412C22×C4—262no—
413C22×C4—261no—
414C22×C4—261no—
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—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4C2×C4×D1312yes—
432C22×C4C2×C4×D1312yes—
433C22×C4C2×C4×D1312yes—
434C22×C4#612714yes—
435C22×C4D4×D1312yes—
436C22×C4D4×D1312yes—
437C4⋊C4—28no—
438C4⋊C4—268no—
439C4⋊C4—268no—
440C4⋊C4—268no—
441C4⋊C4—268no—
442C4⋊C4—2616no—
443C4⋊C4—268no—
444C42—44no—
445C42—1316no—
446C42—524no—
447C13#1428911yescharacteristic, complemented, Sylow
448C23C22×C4×D1311yescharacteristic
449C23C2×#612712yes—
450C23C2×D4×D1311yescharacteristic
451C23C2×D4×D1311yescharacteristic
452C23#8825112yes—
453C23#8825412yes—
454C23#41×D1312yes—
455C23#8825712yes—
456C23#8825712yes—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—134no—
486C2×C4—134no—
487C2×C4—262no—
488C2×C4—262no—
489C2×C4—262no—
490C2×C4—264no—
491C2×C4—264no—
492C2×C4—264no—
493C2×C4—264no—
494C2×C4—262no—
495C2×C4—262no—
496C2×C4—262no—
497C2×C4—262no—
498C2×C4—262no—
499C2×C4—264no—
500C2×C4—264no—
501C2×C4—264no—
502C2×C4—264no—
503C2×C4—522no—
504C2×C4—522no—
505C2×C4—522no—
506C2×C4—522no—
507C2×C4—522no—
508C2×C4—521no—
509C2×C4—522no—
510C2×C4—522no—
511C2×C4—521no—
512C2×C4—522no—
513C2×C4—522no—
514C2×C4—522no—
515C2×C4—522no—
516C2×C4—522no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4C22⋊C4×D1314yes—
520C22C4×#612711yescharacteristic
521C22C2×C22⋊C4×D1311yescharacteristic
522C22#1171922012yes—
523C22#1171922312yes—
524C22#1171922711yescharacteristic
525C22#1171925112yes—
526C22#1171925212yes—
527C22#1171925312yes—
528C22#1171926912yes—
529C22#1171927712yes—
530C22#1171928812yes—
531C22#1171929711yescharacteristic
532C22#1171930212yes—
533C22#1171933312yes—
534C22#1171934312yes—
535C22#1171935311yescharacteristic
536C22#1171936512yes—
537C22#1171938011yescharacteristic
538C22#1171940112yes—
539C22#1171940612yes—
540C22#1171942911yescharacteristic
541C4—24no—
542C4—42no—
543C4—44no—
544C4—42no—
545C4—82no—
546C4—264no—
547C4—264no—
548C4—522no—
549C4—524no—
550C4—522no—
551C4—1042no—
552C2#1311732211yescharacteristic
553C2#1311741911yescharacteristic
554C2#1311742311yescharacteristic
555C2#1311763512yes—
556C2#1311763812yes—
557C2#1312070812yes—
558C2#1312071612yes—
559C2#1312099912yes—
560C2#1312100112yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1436C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1436D13
hypocenterC13#14289
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
24. C2×#88143C4semidirect
447. C13#14289semidirect

Maximal subgroups

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

subgroupindex
C22×#881432
C2×#117183122
C2×C4×#61012
#131131022
#131130882
#131130872
#131130712
#131130692
#131130682
C13×#14362
#1428913