Finite Group Databasebeta

← #15793012

Subgroups — #15793012

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718608C211yesmaximal, characteristic
2C2×#11718307C212yesmaximal, complemented
3C2×#11718871C212yesmaximal
4#13113100C212yesmaximal, complemented
5#13113094C212yesmaximal, complemented
6#13113081C211yesmaximal, characteristic
7#13113073C212yesmaximal
8#13113062C212yesmaximal, complemented
9C13×C22⋊#95C211yesmaximal, characteristic
10C24×C4×C13C2211yescharacteristic
11C23×Dic26C2211yescharacteristic
12C22×C13×C22⋊C4C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic13C2212yes—
15C22×C22⋊Dic13C2212yes—
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6101C2212yes—
18C22×#6101C2212yes—
19C22×C4×Dic13C2212yes—
20C2×C13×#95C2212yes—
21C2×C13×#95C2212yes—
22#11718871—28no—
23C2×#88071C2212yes—
24C2×#88071C2212yes—
25C2×#88071C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32#11718608C418yescomplemented
33#11718307—28no—
34C25×C13C2311yescharacteristic
35C23×C4×C13—22no—
36C23×C4×C13—24no—
37C23×C4×C13—42no—
38C23×C4×C13—41no—
39C23×C4×C13—41no—
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×Dic13C2312yes—
45C23×Dic13C2312yes—
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C22×Dic26—24no—
49C22×Dic26—24no—
50C22×Dic26—41no—
51C22×Dic26—41no—
52C22×Dic26C2×C414yescomplemented
53C2×C13×C22⋊C4—41no—
54C2×C13×C22⋊C4—41no—
55C2×C13×C22⋊C4—41no—
56C2×C13×C22⋊C4—41no—
57C2×C13×C22⋊C4C2×C414yes—
58C2×C13×C22⋊C4Q814yescomplemented
59C2×C22⋊Dic13—24no—
60C2×C22⋊Dic13—24no—
61C2×C22⋊Dic13—24no—
62C2×C22⋊Dic13—24no—
63C2×C22⋊Dic13—42no—
64C2×C22⋊Dic13C2×C418yes—
65C2×C4⋊Dic13—41no—
66C2×C4⋊Dic13—42no—
67C2×#6101—24no—
68C2×#6101—24no—
69C2×#6101—24no—
70C2×#6101—42no—
71C2×#6101—42no—
72C2×#6101—42no—
73C2×C4×Dic13—24no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—42no—
76C13×#95—24no—
77C13×#95—42no—
78#88071—24no—
79#88071—24no—
80#88071—24no—
81#88071—41no—
82#88071—42no—
83#88071—42no—
84#88071C2×C414yescomplemented
85#88071C2×C418yescomplemented
86#88071D418yes—
87#14575—131nomaximal, Sylow
88C24×C13—22no—
89C24×C13—22no—
90C24×C13—22no—
91C24×C13—21no—
92C24×C13—21no—
93C24×C13—21no—
94C24×C13—21no—
95C24×C13—22no—
96C24×C13C22×C412yes—
97C24×C13C2×Q812yes—
98C24×C13#4112yes—
99C24×C13C2411yescharacteristic
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—21no—
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—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—44no—
121C22×C4×C13—48no—
122C22×C4×C13—48no—
123C22×C4×C13—44no—
124C22×C4×C13—44no—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C2×D414yes—
128C22×C4×C13C2×Q814yes—
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×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13C22×C414yes—
153C22×Dic13C22×C414yes—
154C22×Dic13C2×D414yes—
155C22×Dic13C2×D414yes—
156C22×Dic13#4114yes—
157C2×Dic26—216no—
158C2×Dic26—44no—
159C2×Dic26—44no—
160C2×Dic26—48no—
161C2×Dic26—44no—
162C13×C22⋊C4—44no—
163C13×C22⋊C4—44no—
164C22⋊Dic13—216no—
165C22⋊Dic13—48no—
166C4⋊Dic13—44no—
167#6101—48no—
168#6101—48no—
169C4×Dic13—48no—
170C2×#393—131no—
171C2×#391—132no—
172C2×#385—132no—
173#1444—132no—
174#1442—132no—
175#1439—131no—
176#1437—132no—
177#1434—132no—
178C22⋊#95D1311yescharacteristic
179C23×C13—24no—
180C23×C13—22no—
181C23×C13—22no—
182C23×C13—24no—
183C23×C13—22no—
184C23×C13—22no—
185C23×C13—22no—
186C23×C13—22no—
187C23×C13—24no—
188C23×C13—24no—
189C23×C13—24no—
190C23×C13—24no—
191C23×C13—42no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13—42no—
195C23×C13—41no—
196C23×C13—42no—
197C23×C13—41no—
198C23×C13—41no—
199C23×C13—42no—
200C23×C13—41no—
201C23×C13C4×Q814yes—
202C23×C13C23×C411yescharacteristic
203C23×C13C22×D412yes—
204C23×C13C22×Q811yescharacteristic
205C23×C13C2×#4112yes—
206C23×C13C2×#4111yescharacteristic
207C23×C13H(5,𝔽2)11yescharacteristic
208C23×C13H(5,𝔽2)11yescharacteristic
209C23×C13H(5,𝔽2)11yescharacteristic
210C23×C13H(5,𝔽2)12yes—
211C23×C132−1+411yescharacteristic
212C23×C132−1+412yes—
213C2×C4×C13—24no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—24no—
217C2×C4×C13—24no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—24no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—416no—
224C2×C4×C13—42no—
225C2×C4×C13—42no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—41no—
238C2×Dic13—24no—
239C2×Dic13—24no—
240C2×Dic13—24no—
241C2×Dic13—24no—
242C2×Dic13—24no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—24no—
246C2×Dic13—24no—
247C2×Dic13—24no—
248C2×Dic13—24no—
249C2×Dic13—24no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13C4×D418yes—
266Dic26—416no—
267C23×Q8—131no—
268C24×C4C2×D1311yescharacteristic
269C22×C4⋊C4—132no—
270C22×C4⋊C4—132no—
271C22×C4⋊C4—131no—
272C22×C22⋊C4—132no—
273C22×C22⋊C4—132no—
274C22×C22⋊C4C2×D1311yescharacteristic
275C22×C22⋊C4C2×D1311yescharacteristic
276C22×C42—132no—
277#393—138no—
278#391—268no—
279#385—268no—
280C2×#95—132no—
281C2×#95—131no—
282C2×#95—132no—
283C2×#95—132no—
284C2×#95—132no—
285C2×#95—132no—
286C2×#95—131no—
287C2×#95—132no—
288C2×#95—132no—
289C2×#95C2×D1312yes—
290C2×#95C2×D1312yes—
291C22×C13—24no—
292C22×C13—28no—
293C22×C13—44no—
294C22×C13—42no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—44no—
299C22×C13—44no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13C2×C4×D412yes—
303C22×C13C2×C4×Q811yescharacteristic
304C22×C13#51811yescharacteristic
305C22×C13#52011yescharacteristic
306C22×C13#52012yes—
307C22×C13#53512yes—
308C22×C13#53612yes—
309C22×C13#53811yescharacteristic
310C22×C13#53911yescharacteristic
311C22×C13#54212yes—
312C22×C13#54212yes—
313C22×C13#54311yescharacteristic
314C22×C13#54411yescharacteristic
315C22×C13D4211yescharacteristic
316C22×C13#54612yes—
317C22×C13#54612yes—
318C22×C13D4×Q812yes—
319C22×C13#55111yescharacteristic
320C22×C13#55212yes—
321C22×C13#55412yes—
322C22×C13H(3,𝔽4)11yescharacteristic
323C22×C13#56212yes—
324C22×C13#56311yescharacteristic
325C4×C13—42no—
326C4×C13—42no—
327C4×C13—44no—
328C4×C13—44no—
329Dic13—28no—
330Dic13—44no—
331Dic13—44no—
332Dic13—82no—
333C25C22×D1311yescharacteristic
334C22×Q8—134no—
335C22×Q8—264no—
336C22×Q8—264no—
337C22×Q8—521no—
338C22×Q8—521no—
339C23×C4—22no—
340C23×C4—24no—
341C23×C4—42no—
342C23×C4—41no—
343C23×C4—41no—
344C23×C4—132no—
345C23×C4—132no—
346C23×C4—132no—
347C23×C4—132no—
348C23×C4C22×D1312yes—
349C23×C4C22×D1311yescharacteristic
350C23×C4C22×D1311yescharacteristic
351C23×C4C22×D1312yes—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—264no—
354C2×C4⋊C4—264no—
355C2×C4⋊C4—522no—
356C2×C4⋊C4—522no—
357C2×C4⋊C4—522no—
358C2×C4⋊C4—522no—
359C2×C4⋊C4—521no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—138no—
365C2×C22⋊C4—264no—
366C2×C22⋊C4—264no—
367C2×C22⋊C4—264no—
368C2×C22⋊C4—264no—
369C2×C22⋊C4—522no—
370C2×C22⋊C4Dic2614yescomplemented
371C2×C22⋊C4C4×D1314yes—
372C2×C42—264no—
373C2×C42—264no—
374C2×C42—522no—
375#95—24no—
376#95—42no—
377#95—138no—
378#95—134no—
379#95—138no—
380#95—264no—
381#95—264no—
382#95—264no—
383#95—522no—
384#95—521no—
385#95—522no—
386C2×C13—44no—
387C2×C13#232612yes—
388C2×C13#232911yescharacteristic
389C2×C13#235811yescharacteristic
390C2×C13#236012yes—
391C2×C13#237911yescharacteristic
392C2×C13#267011yescharacteristic
393C2×C13#267711yescharacteristic
394C2×C13#268712yes—
395C2×C13#269212yes—
396C2×C13#276311yescharacteristic
397C2×C13#276411yescharacteristic
398C24—22no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24C2×Dic2612yes—
407C24C2×C4×D1312yes—
408C24#612712yes—
409C24C23×D1311yescharacteristic
410C2×Q8—2616no—
411C2×Q8—524no—
412C2×Q8—524no—
413C2×Q8—528no—
414C2×Q8—524no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—44no—
436C22×C4—48no—
437C22×C4—48no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4—134no—
441C22×C4—134no—
442C22×C4—134no—
443C22×C4—134no—
444C22×C4—134no—
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×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—262no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—262no—
468C22×C4C2×Dic2614yes—
469C22×C4C2×C4×D1312yes—
470C22×C4C2×C4×D1312yes—
471C22×C4D4×D1314yes—
472C4⋊C4—528no—
473C4⋊C4—528no—
474C4⋊C4—524no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—2616no—
478C22⋊C4—528no—
479C42—528no—
480C13#1457511yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—24no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—24no—
489C23—24no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—41no—
494C23—42no—
495C23—41no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—41no—
501C23—41no—
502C23—42no—
503C23C4×Dic2614yes—
504C23C22×Dic2611yescharacteristic
505C23C22×C4×D1311yescharacteristic
506C23C2×#612711yescharacteristic
507C23C2×D4×D1312yes—
508C23#8825111yescharacteristic
509C23#8825111yescharacteristic
510C23#8825111yescharacteristic
511C23#8825112yes—
512C23#8825411yescharacteristic
513C23#41×D1312yes—
514C23#8825712yes—
515Q8—5216no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—416no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—138no—
542C2×C4—264no—
543C2×C4—264no—
544C2×C4—264no—
545C2×C4—264no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—264no—
549C2×C4—264no—
550C2×C4—264no—
551C2×C4—264no—
552C2×C4—264no—
553C2×C4—264no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—522no—
561C2×C4—522no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4—522no—
569C22—24no—
570C22—28no—
571C22—42no—
572C22—44no—
573C22—42no—
574C22—44no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—44no—
580C22C2×C4×Dic2611yescharacteristic
581C22#1171918811yescharacteristic
582C22#1171919111yescharacteristic
583C22#1171919512yes—
584C22#1171919911yescharacteristic
585C22#1171920511yescharacteristic
586C22#1171920911yescharacteristic
587C22#1171922011yescharacteristic
588C22#1171923612yes—
589C22D4×Dic2612yes—
590C22#1171924412yes—
591C22C4×D4×D1312yes—
592C22#1171925112yes—
593C22#1171929511yescharacteristic
594C22#1171929712yes—
595C22#1171929911yescharacteristic
596C22#1171931712yes—
597C22#1171932612yes—
598C22#1171933312yes—
599C22#1171934512yes—
600C22#1171935611yescharacteristic
601C22#1171936411yescharacteristic
602C22#1171936712yes—
603C4—44no—
604C4—44no—
605C4—42no—
606C4—42no—
607C4—268no—
608C4—524no—
609C4—524no—
610C4—1042no—
611C2—44no—
612C2#1311754212yes—
613C2#1311756911yescharacteristic
614C2#1311781911yescharacteristic
615C2#1311784212yes—
616C2#1311800611yescharacteristic
617C2#1312106211yescharacteristic
618C2#1312115111yescharacteristic
619C2#1312125812yes—
620C2#1312133312yes—
621C2#1312225011yescharacteristic
622C2#1312225911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#14575
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718307C2semidirect
4. #13113100C2semidirect
5. #13113094C2semidirect
8. #13113062C2semidirect
32. #11718608C4semidirect
52. C22×Dic26C2×C4semidirect
58. C2×C13×C22⋊C4Q8semidirect
84. #88071C2×C4semidirect
85. #88071C2×C4semidirect
370. C2×C22⋊C4Dic26semidirect
480. C13#14575semidirect

Maximal subgroups

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

subgroupindex
C2×#117186082
C2×#117183072
C2×#117188712
#131131002
#131130942
#131130812
#131130732
#131130622
C13×C22⋊#952
#1457513