Finite Group Databasebeta

← #15799559

Subgroups — #15799559

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718609C214yesmaximal, complemented
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718882C211yesmaximal, characteristic
4C2×#11718634C211yesmaximal, characteristic, complemented
5C2×#11718596C211yesmaximal, characteristic, complemented
6C2×C4×#6101C211yesmaximal, characteristic, complemented
7#13113081C214yesmaximal, complemented
8#13113065C211yesmaximal, characteristic, complemented
9C2×C13×#390C211yesmaximal, characteristic
10C23×D4×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C22⋊C4C2214yes—
13C22×C42×C13C2211yescharacteristic
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2214yes—
16C22×C22⋊Dic13C2212yes—
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2214yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6101C2212yes—
21C22×#6101C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C13×#390—24no—
25#11718882—24no—
26#11718882—24no—
27C2×#88071C2212yes—
28C2×#88071C2214yes—
29C2×#88071C2212yes—
30#11718634—24no—
31#11718609—216no—
32#11718596—24no—
33C4×#6101—24no—
34C25×C13C2312yes—
35C22×D4×C13—22no—
36C22×D4×C13—22no—
37C22×D4×C13—22no—
38C22×D4×C13—22no—
39C22×D4×C13—22no—
40C22×D4×C13—22no—
41C22×D4×C13Q814yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C22⋊C4—28no—
54C2×C13×C22⋊C4—28no—
55C2×C13×C22⋊C4—28no—
56C2×C42×C13—22no—
57C2×C42×C13—22no—
58C2×C42×C13D414yes—
59C2×C22⋊Dic13—28no—
60C2×C22⋊Dic13—28no—
61C2×C22⋊Dic13—28no—
62C2×C22⋊Dic13—24no—
63C2×C22⋊Dic13—24no—
64C2×C22⋊Dic13—44no—
65C2×C22⋊Dic13—44no—
66C2×C4⋊Dic13—22no—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—28no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—22no—
72C2×C4⋊Dic13—28no—
73C2×C4⋊Dic13—44no—
74C2×C4⋊Dic13D414yes—
75C2×#6101—24no—
76C2×#6101—24no—
77C2×#6101—28no—
78C2×#6101—24no—
79C2×#6101D418yescomplemented
80C2×C4×Dic13—22no—
81C2×C4×Dic13—22no—
82C2×C4×Dic13—22no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13D414yes—
86#88071—24no—
87#88071—28no—
88#88071—24no—
89#15134—131nomaximal, Sylow
90C24×C13—24no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—24no—
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—24no—
99C24×C13—24no—
100C24×C13C2×Q814yes—
101C24×C13C2411yescharacteristic
102C2×D4×C13—28no—
103C2×D4×C13—28no—
104C2×D4×C13—28no—
105C2×D4×C13—44no—
106C2×D4×C13—44no—
107C2×D4×C13—44no—
108C2×D4×C13—44no—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—24no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—24no—
117C22×C4×C13—22no—
118C22×C4×C13C2×D414yes—
119C22×C4×C13C2×D412yes—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×D414yes—
122C22×C4×C13C2×D412yes—
123C22×C4×C13C2×Q812yes—
124C22×C4×C13#4112yes—
125C22×C4×C13#4114yes—
126C22×C4×C13#4112yes—
127C22×C4×C13#4112yes—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—22no—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—24no—
136C22×Dic13—21no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—24no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—24no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—24no—
150C22×Dic13C2×D412yes—
151C22×Dic13C2×D414yes—
152C22×Dic13C2×D414yes—
153C22×Dic13C2×D412yes—
154C22×Dic13C2×D414yes—
155C13×C4⋊C4—44no—
156C13×C22⋊C4—416no—
157C42×C13—28no—
158C22⋊Dic13—416no—
159C22⋊Dic13—48no—
160C22⋊Dic13—48no—
161C4⋊Dic13—28no—
162C4⋊Dic13—416no—
163C4⋊Dic13—44no—
164#6101—216no—
165#6101—48no—
166C4×Dic13—28no—
167C4×Dic13—44no—
168C2×#396—134no—
169C2×#390—131no—
170C2×#390—131no—
171C2×#390D1311yescharacteristic
172C2×#389—131no—
173C2×#384—131no—
174C2×C4×C4⋊C4—131no—
175#1439—134no—
176C4⋊#95—131no—
177C23×C13—24no—
178C23×C13—24no—
179C23×C13—24no—
180C23×C13—28no—
181C23×C13—28no—
182C23×C13—44no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—42no—
188C23×C13—42no—
189C23×C13—44no—
190C23×C13—42no—
191C23×C13—42no—
192C23×C13—44no—
193C23×C13—44no—
194C23×C13—44no—
195C23×C13—44no—
196C23×C13—44no—
197C23×C13—44no—
198C23×C13—44no—
199C23×C13—44no—
200C23×C13C22×D411yescharacteristic
201C23×C13C22×D411yescharacteristic
202C23×C13C22×D411yescharacteristic
203C23×C13C22×D412yes—
204C23×C13C22×Q811yescharacteristic
205C23×C13C2×#4111yescharacteristic
206C23×C13C2×#4111yescharacteristic
207C23×C13C2×#4111yescharacteristic
208C23×C13C2×#4112yes—
209C23×C13H(5,𝔽2)12yes—
210C23×C132−1+412yes—
211D4×C13—416no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—24no—
218C2×C4×C13—44no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—44no—
223C2×C4×C13#12118yes—
224C2×C4×C13#12114yes—
225C2×C4×C13#12114yes—
226C2×C4×C13#12114yes—
227C2×C4×C13C22⋊Q814yes—
228C2×C4×C13C22⋊Q814yes—
229C2×C4×C13C22⋊Q814yes—
230C2×C4×C13#12614yes—
231C2×Dic13—22no—
232C2×Dic13—24no—
233C2×Dic13—22no—
234C2×Dic13—24no—
235C2×Dic13—22no—
236C2×Dic13—24no—
237C2×Dic13—24no—
238C2×Dic13—22no—
239C2×Dic13—22no—
240C2×Dic13—28no—
241C2×Dic13—24no—
242C2×Dic13—24no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—44no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—44no—
256C2×Dic13—44no—
257C2×Dic13#12714yes—
258C23×D4C2×D1311yescharacteristic
259C22×C4⋊C4—132no—
260C22×C4⋊C4—131no—
261C22×C4⋊C4—132no—
262C22×C4⋊C4—131no—
263C22×C4⋊C4—134no—
264C22×C4⋊C4C2×D1311yescharacteristic
265C22×C22⋊C4—132no—
266C22×C22⋊C4—134no—
267C22×C22⋊C4—132no—
268C22×C22⋊C4C2×D1314yes—
269C22×C42—131no—
270C22×C42—131no—
271C22×C42C2×D1311yescharacteristic
272#396—2616no—
273#390—24no—
274#390—264no—
275#390—264no—
276#389—264no—
277#384—264no—
278C4×C4⋊C4—264no—
279C2×#95—134no—
280C2×#95—132no—
281C2×#95—132no—
282C22×C13—44no—
283C22×C13—44no—
284C22×C13—48no—
285C22×C13—48no—
286C22×C13—44no—
287C22×C13—82no—
288C22×C13—82no—
289C22×C13—84no—
290C22×C13—84no—
291C22×C13—82no—
292C22×C13—82no—
293C22×C13C2×#12111yescharacteristic
294C22×C13C2×#12111yescharacteristic
295C22×C13C2×#12112yes—
296C22×C13C2×#12111yescharacteristic
297C22×C13C2×C22⋊Q811yescharacteristic
298C22×C13C2×C22⋊Q811yescharacteristic
299C22×C13C2×C22⋊Q811yescharacteristic
300C22×C13C2×#12611yescharacteristic
301C22×C13C2×#12711yescharacteristic
302C22×C13#53211yescharacteristic
303C22×C13#53212yes—
304C22×C13#53511yescharacteristic
305C22×C13#53611yescharacteristic
306C22×C13#53712yes—
307C22×C13#54212yes—
308C22×C13D4212yes—
309C22×C13#54712yes—
310C22×C13#54812yes—
311C22×C13D4×Q812yes—
312C22×C13#55012yes—
313C22×C13#55312yes—
314C22×C13#55412yes—
315C22×C13#55612yes—
316C4×C13—28no—
317C4×C13—82no—
318C4×C13#39618yescomplemented
319Dic13—24no—
320Dic13—42no—
321Dic13—44no—
322Dic13—44no—
323Dic13—82no—
324C25C22×D1312yes—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4Dic2614yes—
332C23×C4—131no—
333C23×C4—132no—
334C23×C4—132no—
335C23×C4—131no—
336C23×C4—132no—
337C23×C4C22×D1312yes—
338C23×C4C22×D1312yes—
339C23×C4C22×D1311yescharacteristic
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—138no—
344C2×C4⋊C4—134no—
345C2×C4⋊C4—262no—
346C2×C4⋊C4—262no—
347C2×C4⋊C4—264no—
348C2×C4⋊C4—264no—
349C2×C4⋊C4—264no—
350C2×C4⋊C4—268no—
351C2×C4⋊C4—268no—
352C2×C4⋊C4—262no—
353C2×C4⋊C4—262no—
354C2×C4⋊C4—262no—
355C2×C4⋊C4—268no—
356C2×C4⋊C4—524no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—264no—
361C2×C22⋊C4—268no—
362C2×C22⋊C4—264no—
363C2×C22⋊C4—268no—
364C2×C22⋊C4—268no—
365C2×C22⋊C4—524no—
366C2×C22⋊C4—524no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—134no—
370C2×C42—262no—
371C2×C42—262no—
372C2×C42—262no—
373C2×C42—262no—
374C2×C42—262no—
375C2×C42C22⋊D1314yes—
376#95—264no—
377#95—268no—
378#95—264no—
379C2×C13—84no—
380C2×C13C2×#39611yescharacteristic
381C2×C13#241612yes—
382C2×C13#245212yes—
383C2×C13#251212yes—
384C2×C13#253812yes—
385C2×C13#254111yescharacteristic
386C2×C13#254211yescharacteristic
387C2×C13#254511yescharacteristic
388C2×C13#256611yescharacteristic
389C2×C13#262011yescharacteristic
390C2×C13#285611yescharacteristic
391C24—22no—
392C24—24no—
393C24—22no—
394C24—22no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—22no—
401C24C2×Dic2614yes—
402C24C23×D1311yescharacteristic
403C2×D4—28no—
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—44no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—132no—
420C22×C4—134no—
421C22×C4—132no—
422C22×C4—134no—
423C22×C4—134no—
424C22×C4—261no—
425C22×C4—262no—
426C22×C4—261no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—262no—
430C22×C4—264no—
431C22×C4—261no—
432C22×C4—262no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—264no—
437C22×C4—262no—
438C22×C4—262no—
439C22×C4—261no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—264no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—264no—
446C22×C4C2×Dic2612yes—
447C22×C4#612712yes—
448C22×C4D4×D1314yes—
449C22×C4D4×D1312yes—
450C22×C4D4×D1312yes—
451C22×C4#612914yes—
452C22×C4#612912yes—
453C22×C4#612912yes—
454C22×C4C2×C22⋊D1314yes—
455C22×C4C2×C22⋊D1312yes—
456C4⋊C4—44no—
457C4⋊C4—268no—
458C4⋊C4—2616no—
459C4⋊C4—5216no—
460C4⋊C4—528no—
461C4⋊C4—524no—
462C22⋊C4—416no—
463C22⋊C4—528no—
464C22⋊C4—5216no—
465C22⋊C4—528no—
466C42—28no—
467C42—268no—
468C42—524no—
469C13#1513411yescharacteristic, complemented, Sylow
470C23—24no—
471C23—24no—
472C23—24no—
473C23—28no—
474C23—28no—
475C23—42no—
476C23—42no—
477C23—44no—
478C23—44no—
479C23—42no—
480C23—42no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—44no—
490C23—42no—
491C23—42no—
492C23—44no—
493C23C22×Dic2611yescharacteristic
494C23C2×#612711yescharacteristic
495C23C2×D4×D1311yescharacteristic
496C23C2×D4×D1311yescharacteristic
497C23C2×D4×D1312yes—
498C23C2×#612911yescharacteristic
499C23C2×#612911yescharacteristic
500C23C2×#612912yes—
501C23#8825612yes—
502C23#8825712yes—
503C23C22×C22⋊D1311yescharacteristic
504D4—416no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—134no—
517C2×C4—262no—
518C2×C4—264no—
519C2×C4—262no—
520C2×C4—264no—
521C2×C4—264no—
522C2×C4—262no—
523C2×C4—264no—
524C2×C4—264no—
525C2×C4—268no—
526C2×C4—264no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—522no—
530C2×C4—524no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—524no—
540C2×C4—524no—
541C2×C4—522no—
542C2×C4—522no—
543C2×C4#8813214yes—
544C2×C4#8813214yes—
545C2×C4#8813314yes—
546C2×C4#8813814yes—
547C2×C4#8817814yes—
548C2×C4#8819218yes—
549C2×C4#8819214yes—
550C2×C4#8819314yes—
551C22—48no—
552C22—44no—
553C22—44no—
554C22—44no—
555C22—48no—
556C22—82no—
557C22—84no—
558C22—82no—
559C22—82no—
560C22—82no—
561C22—84no—
562C22C2×#8813211yescharacteristic
563C22C2×#8813211yescharacteristic
564C22C2×#8813311yescharacteristic
565C22C2×#8813811yescharacteristic
566C22D4×Dic2612yes—
567C22#1171924712yes—
568C22#1171924812yes—
569C22#1171925812yes—
570C22#1171930312yes—
571C22#1171931412yes—
572C22#1171931612yes—
573C22#1171932312yes—
574C22#1171937911yescharacteristic
575C22#1171938011yescharacteristic
576C22#1171938712yes—
577C22D13×#12711yescharacteristic
578C22#1171942111yescharacteristic
579C22#1171942112yes—
580C22C2×#8817811yescharacteristic
581C22C2×#8819212yes—
582C22C2×#8819211yescharacteristic
583C22C2×#8819311yescharacteristic
584C22#1171953812yes—
585C4—28no—
586C4—82no—
587C4—264no—
588C4—524no—
589C4—524no—
590C4—522no—
591C4—1042no—
592C4#1171860918yescomplemented
593C2—84no—
594C2C2×#1171860911yescharacteristic
595C2#1311827712yes—
596C2#1311868812yes—
597C2#1311942412yes—
598C2#1311975812yes—
599C2#1311978111yescharacteristic
600C2#1311978711yescharacteristic
601C2#1311981811yescharacteristic
602C2#1312003811yescharacteristic
603C2#1312059411yescharacteristic
604C2#1312317811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#390C2
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#15134
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#11718609C2semidirect
4. C2×#11718634C2semidirect
5. C2×#11718596C2semidirect
6. C2×C4×#6101C2semidirect
7. #13113081C2semidirect
8. #13113065C2semidirect
79. C2×#6101D4semidirect
318. C4×C13#396semidirect
469. C13#15134semidirect
592. C4#11718609semidirect

Maximal subgroups

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

subgroupindex
C2×#117186092
C2×#117188822
C2×#117186342
C2×#117185962
C2×C4×#61012
#131130812
#131130652
C2×C13×#3902
#1513413