Finite Group Databasebeta

← #15789469

Subgroups — #15789469

Order 3328.

1406 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718633C212yesmaximal
2C2×#11718637C211yesmaximal, characteristic
3C2×#11718311C211yesmaximal, characteristic
4C2×#11718309C211yesmaximal, characteristic
5#13113100C211yesmaximal, characteristic
6#13113099C212yesmaximal
7#13113095C211yesmaximal, characteristic
8#13113094C212yesmaximal
9#13113093C211yesmaximal, characteristic
10#13113064C212yesmaximal
11C13×#1444C211yesmaximal, characteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C4⋊Dic13C2211yescharacteristic
15C22×#6101C2212yes—
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×C4×Dic13C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C2×C13×#95C2211yescharacteristic
23C2×C13×#95C2212yes—
24C2×C13×#95C2211yescharacteristic
25C2×#88071C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35#11718637—24no—
36#11718633—28no—
37#11718311C418yescomplemented
38#11718309—24no—
39C23×C4×C13C2312yes—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×Dic13C2312yes—
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C2×C13×C4⋊C4—24no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—42no—
53C2×C13×C4⋊C4—42no—
54C2×C13×C4⋊C4—42no—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13—42no—
57C2×#6101—24no—
58C2×#6101—24no—
59C2×#6101—24no—
60C2×#6101—24no—
61C2×#6101—24no—
62C2×#6101—24no—
63C2×#6101—24no—
64C2×#6101—42no—
65C2×#6101—42no—
66C2×#6101—42no—
67C2×#6101—42no—
68C2×#6101C2×C418yes—
69C2×C4×Dic13—22no—
70C2×C4×Dic13—22no—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—22no—
73C2×C4×Dic13C2×C414yes—
74C2×C4×Dic13D414yes—
75C2×C4×Dic13D414yes—
76C2×C4×Dic13Q814yes—
77C2×C4×Dic13Q814yes—
78C13×#95—22no—
79C13×#95—42no—
80C13×#95C2×C414yes—
81#88071—22no—
82#88071—22no—
83#88071—22no—
84#88071—24no—
85#88071—24no—
86#88071—42no—
87#88071—42no—
88#88071—42no—
89#88071C2×C414yes—
90#88071C2×C418yes—
91#14277—131nomaximal, Sylow
92C24×C13C2411yescharacteristic
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
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×C13C22×C414yes—
117C22×C4×C13C22×C412yes—
118C22×C4×C13C2×D412yes—
119C22×C4×C13C2×D412yes—
120C22×C4×C13C2×Q812yes—
121C22×C4×C13C2×Q812yes—
122C22×Dic13—22no—
123C22×Dic13—22no—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—22no—
127C22×Dic13—21no—
128C22×Dic13—21no—
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×Dic13C22×C414yes—
146C22×Dic13C22×C412yes—
147C22×Dic13C22×C412yes—
148C22×Dic13C2×D412yes—
149C22×Dic13C2×D412yes—
150C22×Dic13C2×D412yes—
151C22×Dic13C2×D412yes—
152C22×Dic13C2×Q812yes—
153C22×Dic13C2×Q812yes—
154C22×Dic13C2×Q812yes—
155C22×Dic13C2×Q812yes—
156C22×Dic13#4112yes—
157C22×Dic13#4112yes—
158C13×C4⋊C4—44no—
159C13×C4⋊C4—48no—
160C4⋊Dic13—44no—
161#6101—216no—
162#6101—48no—
163#6101—48no—
164#6101—48no—
165C4×Dic13—28no—
166C4×Dic13—28no—
167C4×Dic13C4⋊C4116yescomplemented
168C2×#389—132no—
169C2×#384—131no—
170C2×#382—131no—
171C2×#376—131no—
172#1444—131no—
173#1444—132no—
174#1444D1311yescharacteristic
175#1442—131no—
176#1442—132no—
177#1442—131no—
178C4⋊#95—132no—
179C23×C13C23×C411yescharacteristic
180C23×C13C22×D411yescharacteristic
181C23×C13C22×D411yescharacteristic
182C23×C13C22×Q811yescharacteristic
183C23×C13C22×Q811yescharacteristic
184C23×C13C2×#4111yescharacteristic
185C23×C13C2×#4111yescharacteristic
186C23×C13H(5,𝔽2)12yes—
187C23×C13H(5,𝔽2)12yes—
188C23×C132−1+412yes—
189C23×C132−1+412yes—
190C2×C4×C13—24no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—24no—
194C2×C4×C13—24no—
195C2×C4×C13—24no—
196C2×C4×C13—24no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—24no—
200C2×C4×C13—24no—
201C2×C4×C13—42no—
202C2×C4×C13—41no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
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×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13C2×C4⋊C414yes—
219C2×Dic13—24no—
220C2×Dic13—22no—
221C2×Dic13—22no—
222C2×Dic13—24no—
223C2×Dic13—24no—
224C2×Dic13—24no—
225C2×Dic13—24no—
226C2×Dic13—22no—
227C2×Dic13—22no—
228C2×Dic13—24no—
229C2×Dic13—24no—
230C2×Dic13—42no—
231C2×Dic13—41no—
232C2×Dic13—42no—
233C2×Dic13—41no—
234C2×Dic13—41no—
235C2×Dic13—41no—
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×Dic13C2×C4⋊C414yes—
248C2×Dic13C2×C4⋊C414yes—
249C2×Dic13C4×D414yes—
250C2×Dic13C4×Q814yes—
251C2×Dic13#12114yes—
252C2×Dic13C22⋊Q814yes—
253C2×Dic13#12514yes—
254C2×Dic13C4⋊Q814yes—
255C22×C4⋊C4—132no—
256C22×C4⋊C4—132no—
257C22×C4⋊C4—132no—
258C22×C4⋊C4—132no—
259C22×C4⋊C4—131no—
260C22×C4⋊C4C2×D1311yescharacteristic
261C22×C4⋊C4C2×D1312yes—
262C22×C42—131no—
263C22×C42—131no—
264C22×C42—131no—
265#389—268no—
266#384—264no—
267#382—138no—
268#376—264no—
269C2×#95—132no—
270C2×#95—131no—
271C2×#95—131no—
272C2×#95—131no—
273C2×#95—132no—
274C2×#95—132no—
275C2×#95—131no—
276C2×#95—132no—
277C2×#95—132no—
278C2×#95—132no—
279C2×#95C2×D1311yescharacteristic
280C2×#95C2×D1312yes—
281C2×#95C2×D1311yescharacteristic
282C22×C13C22×C4⋊C411yescharacteristic
283C22×C13C2×C4×D411yescharacteristic
284C22×C13C2×C4×Q811yescharacteristic
285C22×C13#52012yes—
286C22×C13#52012yes—
287C22×C13C2×#12111yescharacteristic
288C22×C13C2×C22⋊Q811yescharacteristic
289C22×C13C2×#12511yescharacteristic
290C22×C13C2×C4⋊Q811yescharacteristic
291C22×C13#53511yescharacteristic
292C22×C13#53512yes—
293C22×C13#53511yescharacteristic
294C22×C13#53611yescharacteristic
295C22×C13#53612yes—
296C22×C13#53611yescharacteristic
297C22×C13#54012yes—
298C22×C13#54112yes—
299C22×C13#54212yes—
300C22×C13#54212yes—
301C22×C13#54412yes—
302C22×C13#54412yes—
303C22×C13#54412yes—
304C22×C13#54412yes—
305C4×C13—24no—
306C4×C13—44no—
307C4×C13—42no—
308C4×C13—42no—
309C4×C13—82no—
310Dic13—24no—
311Dic13—44no—
312Dic13—42no—
313Dic13—42no—
314Dic13—82no—
315Dic13#38918yes—
316C23×C4—131no—
317C23×C4—131no—
318C23×C4—132no—
319C23×C4—131no—
320C23×C4—131no—
321C23×C4—132no—
322C23×C4C22×D1312yes—
323C23×C4C22×D1312yes—
324C23×C4C22×D1311yescharacteristic
325C23×C4C22×D1311yescharacteristic
326C23×C4C22×D1311yescharacteristic
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—138no—
333C2×C4⋊C4—264no—
334C2×C4⋊C4—264no—
335C2×C4⋊C4—264no—
336C2×C4⋊C4—264no—
337C2×C4⋊C4—264no—
338C2×C4⋊C4—264no—
339C2×C4⋊C4—264no—
340C2×C4⋊C4—262no—
341C2×C4⋊C4—522no—
342C2×C4⋊C4—522no—
343C2×C4⋊C4—522no—
344C2×C4⋊C4—522no—
345C2×C4⋊C4—522no—
346C2×C42—134no—
347C2×C42—134no—
348C2×C42—134no—
349C2×C42—134no—
350C2×C42—134no—
351C2×C42—262no—
352C2×C42—262no—
353C2×C42—262no—
354C2×C42—262no—
355#95—22no—
356#95—42no—
357#95—138no—
358#95—134no—
359#95—262no—
360#95—262no—
361#95—264no—
362#95—264no—
363#95—262no—
364#95—522no—
365#95—522no—
366#95—522no—
367#95C4×D1314yes—
368C2×C13C2×#38911yescharacteristic
369C2×C13#231711yescharacteristic
370C2×C13#231711yescharacteristic
371C2×C13#232612yes—
372C2×C13#233012yes—
373C2×C13#261911yescharacteristic
374C2×C13#262111yescharacteristic
375C2×C13#262811yescharacteristic
376C2×C13#262811yescharacteristic
377C2×C13#264712yes—
378C2×C13#266012yes—
379C24C23×D1311yescharacteristic
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—132no—
404C22×C4—132no—
405C22×C4—132no—
406C22×C4—132no—
407C22×C4—132no—
408C22×C4—132no—
409C22×C4—132no—
410C22×C4—132no—
411C22×C4—132no—
412C22×C4—132no—
413C22×C4—134no—
414C22×C4—132no—
415C22×C4—132no—
416C22×C4—262no—
417C22×C4—262no—
418C22×C4—261no—
419C22×C4—261no—
420C22×C4—262no—
421C22×C4—262no—
422C22×C4—262no—
423C22×C4—262no—
424C22×C4—262no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—261no—
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×C4C2×C4×D1314yes—
440C22×C4C2×C4×D1312yes—
441C22×C4D4×D1312yes—
442C22×C4D4×D1312yes—
443C22×C4Q8×D1312yes—
444C22×C4Q8×D1312yes—
445C4⋊C4—44no—
446C4⋊C4—48no—
447C4⋊C4—2616no—
448C4⋊C4—528no—
449C4⋊C4—524no—
450C4⋊C4—528no—
451C4⋊C4—528no—
452C42—1316no—
453C42—268no—
454C42—268no—
455C13#1427711yescharacteristic, complemented, Sylow
456C23C22×C4×D1311yescharacteristic
457C23C2×D4×D1311yescharacteristic
458C23C2×D4×D1311yescharacteristic
459C23#8825112yes—
460C23#8825112yes—
461C23C2×Q8×D1311yescharacteristic
462C23C2×Q8×D1311yescharacteristic
463C23#8825412yes—
464C23#41×D1311yescharacteristic
465C23#41×D1311yescharacteristic
466C23#8825712yes—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—134no—
496C2×C4—134no—
497C2×C4—134no—
498C2×C4—134no—
499C2×C4—134no—
500C2×C4—134no—
501C2×C4—134no—
502C2×C4—134no—
503C2×C4—262no—
504C2×C4—264no—
505C2×C4—264no—
506C2×C4—262no—
507C2×C4—264no—
508C2×C4—264no—
509C2×C4—264no—
510C2×C4—264no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—264no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4—522no—
517C2×C4—521no—
518C2×C4—522no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—521no—
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×C4C4⋊C4×D1314yes—
532C22C2×C4⋊C4×D1311yescharacteristic
533C22#1171920912yes—
534C22C4×D4×D1311yescharacteristic
535C22#1171925112yes—
536C22C4×Q8×D1311yescharacteristic
537C22#1171929711yescharacteristic
538C22#1171929712yes—
539C22D13×#12111yescharacteristic
540C22#1171932012yes—
541C22#1171932812yes—
542C22#1171932812yes—
543C22D13×C22⋊Q811yescharacteristic
544C22#1171933312yes—
545C22#1171934512yes—
546C22#1171935311yescharacteristic
547C22#1171936712yes—
548C22D13×#12511yescharacteristic
549C22#1171940112yes—
550C22#1171942011yescharacteristic
551C22D13×C4⋊Q811yescharacteristic
552C22#1171942911yescharacteristic
553C22#1171943412yes—
554C22#1171943412yes—
555C4—24no—
556C4—42no—
557C4—44no—
558C4—42no—
559C4—82no—
560C4—138no—
561C4—264no—
562C4—522no—
563C4—524no—
564C4—522no—
565C4—1042no—
566C2D13×#38911yescharacteristic
567C2#1311745511yescharacteristic
568C2#1311745711yescharacteristic
569C2#1311754212yes—
570C2#1311757412yes—
571C2#1312058511yescharacteristic
572C2#1312060411yescharacteristic
573C2#1312065911yescharacteristic
574C2#1312066211yescharacteristic
575C2#1312081012yes—
576C2#1312095412yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1444C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1444D13
hypocenterC13#14277
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
37. #11718311C4semidirect
167. C4×Dic13C4⋊C4semidirect
455. C13#14277semidirect

Maximal subgroups

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

subgroupindex
C2×#117186332
C2×#117186372
C2×#117183112
C2×#117183092
#131131002
#131130992
#131130952
#131130942
#131130932
#131130642
C13×#14442
#1427713