Finite Group Databasebeta

← #15788239

Subgroups — #15788239

Order 3328.

1758 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C2×#11718640C211yesmaximal, characteristic
3C2×#11718313C212yesmaximal
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic
5#13113106C211yesmaximal, characteristic
6#13113095C211yesmaximal, characteristic
7#13113070C212yesmaximal
8#13113067C212yesmaximal
9#13113067C212yesmaximal
10#13113061C211yesmaximal, characteristic
11C13×#1441C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C22×#6101C2212yes—
18C22×C4×Dic13C2211yescharacteristic
19C22×C4×Dic13C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C2×#88141—28no—
23C2×#88141—24no—
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2212yes—
26C2×C13×#95C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2212yes—
37#11718640C418yescomplemented
38C4⋊C4×Dic13—24no—
39#11718313—28no—
40C23×C4×C13C2312yes—
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×Dic26—22no—
52C22×Dic26—22no—
53C22×Dic26—24no—
54C22×Dic26—24no—
55C22×Dic26C2×C414yes—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4C2×C414yes—
61C2×C4⋊Dic13—22no—
62C2×C4⋊Dic13—22no—
63C2×C4⋊Dic13Q814yescomplemented
64C2×#6101—24no—
65C2×#6101—24no—
66C2×#6101—24no—
67C2×#6101—24no—
68C2×#6101C2×C418yes—
69C2×#6101D418yes—
70C2×C4×Dic13—24no—
71C2×C4×Dic13—22no—
72C2×C4×Dic13—24no—
73C2×C4×Dic13—24no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—24no—
78C2×C4×Dic13—22no—
79C2×C4×Dic13D414yes—
80#88141—232no—
81C13×#95—24no—
82C13×#95—24no—
83C13×#95—22no—
84#88071—24no—
85#88071—22no—
86#88071—24no—
87#88071—24no—
88#88071—22no—
89#88071—24no—
90#88071—24no—
91#88071—24no—
92#88071C2×C414yes—
93#88071C2×C418yes—
94#14174—131nomaximal, Sylow
95C24×C13C2411yescharacteristic
96C22×C4×C13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—21no—
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—21no—
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×C13—22no—
119C22×C4×C13C22×C412yes—
120C22×C4×C13C22×C412yes—
121C22×C4×C13C22×C412yes—
122C22×C4×C13C2×D414yes—
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×Q812yes—
125C22×C4×C13#4112yes—
126C22×C4×C13#4112yes—
127C22×Dic13—22no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—21no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—21no—
144C22×Dic13—22no—
145C22×Dic13—21no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13C22×C414yes—
151C22×Dic13C22×C414yes—
152C22×Dic13C2×D414yes—
153C22×Dic13C2×D414yes—
154C22×Dic13C2×D412yes—
155C22×Dic13C2×D412yes—
156C22×Dic13C2×Q812yes—
157C22×Dic13C2×Q812yes—
158C22×Dic13#4112yes—
159C22×Dic13#4114yes—
160C22×Dic13#4112yes—
161C2×Dic26—28no—
162C2×Dic26—216no—
163C2×Dic26—28no—
164C2×Dic26—28no—
165C2×Dic26—216no—
166C13×C4⋊C4—28no—
167C13×C4⋊C4—28no—
168C4⋊Dic13—28no—
169#6101—216no—
170#6101—216no—
171C4×Dic13—216no—
172C4×Dic13—28no—
173C4×Dic13—28no—
174C4×Dic13—44no—
175C22×C4×Q8—131no—
176C2×#395—131no—
177C2×#387—132no—
178C2×C4×C4⋊C4—131no—
179#1446—131no—
180#1442—131no—
181#1441D1311yescharacteristic
182#1436—132no—
183#1436—132no—
184#1436—132no—
185#1434—131no—
186C23×C13C23×C411yescharacteristic
187C23×C13C22×D411yescharacteristic
188C23×C13C22×D412yes—
189C23×C13C22×Q811yescharacteristic
190C23×C13C2×#4111yescharacteristic
191C23×C13C2×#4112yes—
192C23×C13C2×#4111yescharacteristic
193C23×C13C2×#4111yescharacteristic
194C23×C13C2×#4111yescharacteristic
195C23×C132−1+412yes—
196C23×C132−1+412yes—
197C2×C4×C13—22no—
198C2×C4×C13—24no—
199C2×C4×C13—22no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—24no—
205C2×C4×C13—22no—
206C2×C4×C13—22no—
207C2×C4×C13—24no—
208C2×C4×C13—22no—
209C2×C4×C13—24no—
210C2×C4×C13—24no—
211C2×C4×C13—24no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—41no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13C4×D414yes—
227C2×C4×C13C4×Q814yescomplemented
228C2×Dic13—24no—
229C2×Dic13—24no—
230C2×Dic13—22no—
231C2×Dic13—24no—
232C2×Dic13—22no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—24no—
236C2×Dic13—22no—
237C2×Dic13—22no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—24no—
241C2×Dic13—24no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—41no—
250C2×Dic13—41no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13C4×D418yes—
260C2×Dic13#12014yes—
261C2×Dic13C22⋊Q814yes—
262Dic26—232no—
263C23×Q8—131no—
264C2×C4×Q8—264no—
265C2×C4×Q8—268no—
266C22×C4⋊C4—132no—
267C22×C4⋊C4—132no—
268C22×C4⋊C4—131no—
269C22×C4⋊C4C2×D1311yescharacteristic
270C22×C4⋊C4C2×D1311yescharacteristic
271C22×C42—131no—
272C22×C42—132no—
273C22×C42—131no—
274C22×C42—131no—
275#395—138no—
276#387—268no—
277C4×C4⋊C4—264no—
278C2×#95—131no—
279C2×#95—132no—
280C2×#95—132no—
281C2×#95—132no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—131no—
285C2×#95—132no—
286C2×#95—132no—
287C2×#95—131no—
288C2×#95C2×D1311yescharacteristic
289C2×#95C2×D1312yes—
290C2×#95C2×D1312yes—
291C22×C13C2×C4×D411yescharacteristic
292C22×C13C2×C4×D412yes—
293C22×C13C2×C4×Q811yescharacteristic
294C22×C13C4×#4111yescharacteristic
295C22×C13#51912yes—
296C22×C13C2×#12011yescharacteristic
297C22×C13C2×C22⋊Q811yescharacteristic
298C22×C13#52511yescharacteristic
299C22×C13#52512yes—
300C22×C13#52511yescharacteristic
301C22×C13#52911yescharacteristic
302C22×C13#53311yescharacteristic
303C22×C13#53611yescharacteristic
304C22×C13#53611yescharacteristic
305C22×C13#54112yes—
306C22×C13#54712yes—
307C22×C13#54712yes—
308C22×C13#54812yes—
309C22×C13D4×Q812yes—
310C22×C13#55212yes—
311C22×C13#55612yes—
312C22×C13#55612yes—
313C22×C13#55712yes—
314C4×C13—24no—
315C4×C13—24no—
316C4×C13—44no—
317C4×C13—42no—
318C4×C13—82no—
319Dic13—24no—
320Dic13—24no—
321Dic13—28no—
322Dic13—42no—
323Dic13—44no—
324Dic13—42no—
325C22×Q8—134no—
326C22×Q8—264no—
327C22×Q8—264no—
328C22×Q8—262no—
329C22×Q8—262no—
330C23×C4—132no—
331C23×C4—131no—
332C23×C4—131no—
333C23×C4—132no—
334C23×C4—131no—
335C23×C4—131no—
336C23×C4C22×D1312yes—
337C23×C4C22×D1311yescharacteristic
338C23×C4C22×D1312yes—
339C23×C4C22×D1311yescharacteristic
340C23×C4C22×D1311yescharacteristic
341C4×Q8—2632no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—138no—
347C2×C4⋊C4—138no—
348C2×C4⋊C4—134no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—264no—
351C2×C4⋊C4—264no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—262no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4C4×D1314yes—
356C2×C42—134no—
357C2×C42—264no—
358C2×C42—264no—
359C2×C42—264no—
360C2×C42—262no—
361C2×C42—262no—
362C2×C42—264no—
363C2×C42—262no—
364C2×C42—262no—
365C2×C42—264no—
366#95—24no—
367#95—24no—
368#95—22no—
369#95—138no—
370#95—134no—
371#95—264no—
372#95—264no—
373#95—264no—
374#95—262no—
375#95—264no—
376#95—264no—
377#95—262no—
378#95—264no—
379C2×C13C4×#12011yescharacteristic
380C2×C13C4×C22⋊Q811yescharacteristic
381C2×C13#232711yescharacteristic
382C2×C13#236212yes—
383C2×C13#236512yes—
384C2×C13#240611yescharacteristic
385C2×C13#240911yescharacteristic
386C2×C13#246212yes—
387C2×C13#246912yes—
388C2×C13#258111yescharacteristic
389C2×C13#259911yescharacteristic
390C24C23×D1311yescharacteristic
391C2×Q8—2616no—
392C2×Q8—268no—
393C2×Q8—2616no—
394C2×Q8—268no—
395C2×Q8—268no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—134no—
420C22×C4—132no—
421C22×C4—134no—
422C22×C4—134no—
423C22×C4—132no—
424C22×C4—132no—
425C22×C4—132no—
426C22×C4—134no—
427C22×C4—134no—
428C22×C4—132no—
429C22×C4—132no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—262no—
433C22×C4—261no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—261no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—261no—
441C22×C4—262no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—262no—
445C22×C4—262no—
446C22×C4—262no—
447C22×C4—262no—
448C22×C4—262no—
449C22×C4—262no—
450C22×C4—262no—
451C22×C4—261no—
452C22×C4—262no—
453C22×C4C2×C4×D1312yes—
454C22×C4C2×C4×D1312yes—
455C22×C4C2×C4×D1312yes—
456C22×C4D4×D1314yes—
457C22×C4D4×D1312yes—
458C22×C4#612912yes—
459C22×C4#612912yes—
460C22×C4Q8×D1312yes—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—2616no—
464C4⋊C4—2616no—
465C4⋊C4—268no—
466C42—268no—
467C42—2616no—
468C42—268no—
469C42—524no—
470C13#1417411yescharacteristic, complemented, Sylow
471C23C22×C4×D1311yescharacteristic
472C23C2×D4×D1311yescharacteristic
473C23C2×D4×D1312yes—
474C23C2×#612911yescharacteristic
475C23C2×#612911yescharacteristic
476C23C2×Q8×D1311yescharacteristic
477C23#8825412yes—
478C23#41×D1311yescharacteristic
479C23#41×D1311yescharacteristic
480C23#41×D1312yes—
481C23#8825712yes—
482Q8—2632no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—138no—
513C2×C4—134no—
514C2×C4—134no—
515C2×C4—262no—
516C2×C4—264no—
517C2×C4—264no—
518C2×C4—264no—
519C2×C4—262no—
520C2×C4—264no—
521C2×C4—262no—
522C2×C4—264no—
523C2×C4—264no—
524C2×C4—264no—
525C2×C4—264no—
526C2×C4—264no—
527C2×C4—264no—
528C2×C4—262no—
529C2×C4—264no—
530C2×C4—264no—
531C2×C4—264no—
532C2×C4—264no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—264no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—522no—
540C2×C4—522no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4—521no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4#8813514yes—
547C2×C4#8814114yescomplemented
548C22C2×#8813511yescharacteristic
549C22C2×#8814111yescharacteristic
550C22#1171922711yescharacteristic
551C22C4×D4×D1312yes—
552C22#1171927712yes—
553C22D13×#12011yescharacteristic
554C22#1171930511yescharacteristic
555C22#1171931112yes—
556C22#1171931111yescharacteristic
557C22#1171931612yes—
558C22#1171932711yescharacteristic
559C22#1171933012yes—
560C22D13×C22⋊Q811yescharacteristic
561C22#1171933812yes—
562C22#1171934612yes—
563C22#1171936012yes—
564C22#1171936111yescharacteristic
565C22#1171938011yescharacteristic
566C22#1171939012yes—
567C22#1171939812yes—
568C22#1171940712yes—
569C22#1171942911yescharacteristic
570C22#1171943212yes—
571C4—24no—
572C4—24no—
573C4—42no—
574C4—44no—
575C4—82no—
576C4—268no—
577C4—264no—
578C4—264no—
579C4—522no—
580C4—524no—
581C4—522no—
582C2#1311734111yescharacteristic
583C2#1311736411yescharacteristic
584C2#1311755411yescharacteristic
585C2#1311785812yes—
586C2#1311788912yes—
587C2#1311816611yescharacteristic
588C2#1311819611yescharacteristic
589C2#1311881912yes—
590C2#1311891812yes—
591C2#1312019911yescharacteristic
592C2#1312041611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1441D13
hypocenterC13#14174
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
37. #11718640C4semidirect
63. C2×C4⋊Dic13Q8semidirect
227. C2×C4×C13C4×Q8semidirect
470. C13#14174semidirect
547. C2×C4#88141semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117186402
C2×#117183132
C2×C4⋊C4×Dic132
#131131062
#131130952
#131130702
#131130672
#131130612
C13×#14412
#1417413