Finite Group Databasebeta

← #15862391

Subgroups — #15862391

Order 3328.

1514 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719227C211yesmaximal, characteristic
2C22×#88054C211yesmaximal, characteristic, complemented
3C2×#11718774C211yesmaximal, characteristic
4C2×#11718663C211yesmaximal, characteristic
5#13117239C211yesmaximal, characteristic, complemented
6#13114850C212yesmaximal, complemented
7#13114845C212yesmaximal, complemented
8#13114840C212yesmaximal, complemented
9#13114835C212yesmaximal, complemented
10#13114552C211yesmaximal, characteristic, complemented
11C13×#1735C211yesmaximal, characteristic, complemented
12C22×#6127C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C2×C13×#117C2211yescharacteristic
15C2×C13×#117C2211yescharacteristic
16C2×#88180C2211yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19#11719227—24no—
20#11719227C418yescomplemented
21C2×#88147C2211yescharacteristic
22C2×#88147C2211yescharacteristic
23C2×#88141C2211yescharacteristic
24C2×#88141C2211yescharacteristic
25C2×#88135—21no—
26C2×#88135—21no—
27C2×#88126—21no—
28C2×C42×D13—21no—
29#11718774—24no—
30C2×#88061C2212yes—
31C2×#88056C2212yes—
32C2×#88054—24no—
33C2×#88054C2212yes—
34C2×#88054C2212yes—
35#11718663—24no—
36#11718638C2212yes—
37#11718637C2212yes—
38C2×#88050C2212yes—
39C2×#88049C2212yes—
40#11718603—21no—
41#11718603—21no—
42C4×#6101—21no—
43C4×#6101—21no—
44C13×#340C2212yes—
45C13×#340C2212yes—
46#11718121C2212yes—
47#11718121C2212yes—
48C23×C4×C13C2311yescharacteristic
49C22×C22⋊D13—21no—
50C23×Dic13D411yescharacteristic
51C23×Dic13D411yescharacteristic
52C2×#6127—22no—
53C2×#6127—22no—
54C2×#6127—22no—
55C2×#6127C2×C414yes—
56C2×#6127D414yes—
57C2×#6127Q814yes—
58C22×D52C2311yescharacteristic
59C22×C4×D13—21no—
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×Dic26C2311yescharacteristic
63C22×C8×C13—22no—
64C22×C8×C13—22no—
65C22×C8×C13—22no—
66C22×C8×C13C2312yes—
67C13×#117—22no—
68C13×#117—22no—
69C13×#117—22no—
70C13×#117C2×C414yes—
71C2×C13×C4⋊C4C2312yes—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C42×C13—21no—
77C2×C42×C13—21no—
78C2×C22⋊Dic13—21no—
79C2×#6103—21no—
80C2×#6103—21no—
81#88180—22no—
82#88180—22no—
83C2×C4⋊Dic13C2312yes—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—22no—
87C2×#6101—22no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13C2×C414yes—
92C2×C4×Dic13D411yescharacteristic
93C2×C4×Dic13D411yescharacteristic
94C2×C4×Dic13D414yes—
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C22×#1055—22no—
98C22×#1055—22no—
99C22×#1055—22no—
100C22×#1055C2312yes—
101#88147—22no—
102#88147—22no—
103#88147C2×C414yes—
104#88147C2×C414yes—
105#88141—22no—
106#88141—22no—
107#88141C2×C414yes—
108#88141C2×C414yes—
109#88135—28no—
110#88135—28no—
111#88126—28no—
112C42×D13—28no—
113#88071—22no—
114#88071—22no—
115#88061—24no—
116#88056—24no—
117#88054—24no—
118#88054—24no—
119#88050—24no—
120#88049—24no—
121#20645—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C23×D13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13C22×C412yes—
128C22×C4×C13C2×D412yes—
129C22×C4×C13C2×D412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×Q812yes—
132C22×C4×C13#4112yes—
133C22×C4×C13#4112yes—
134C22×C4×C13C2411yescharacteristic
135C2×C22⋊D13—24no—
136C2×C22⋊D13—24no—
137C2×C22⋊D13—24no—
138C22×Dic13—21no—
139C22×Dic13—24no—
140C22×Dic13—22no—
141C22×Dic13—42no—
142C22×Dic13C22⋊C414yes—
143C22×Dic13C22⋊C414yes—
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146C22×Dic13C2×D411yescharacteristic
147C22×Dic13C2×D411yescharacteristic
148#6127—28no—
149#6127—28no—
150#6127—28no—
151#6127C4⋊C4116yescomplemented
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52C22×C412yes—
156C2×D52C2×D412yes—
157C2×D52C2×Q812yes—
158C2×C4×D13—24no—
159C2×C4×D13—24no—
160C2×C4×D13—24no—
161C2×C4×D13—24no—
162C2×C4×D13—24no—
163C2×C4×D13—44no—
164C2×C4×D13—44no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26C22×C412yes—
169C2×Dic26C2×D412yes—
170C2×Dic26C2×Q812yes—
171C2×C8×C13—22no—
172C2×C8×C13—22no—
173C2×C8×C13—22no—
174C2×C8×C13—44no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4C22×C412yes—
180C13×C4⋊C4C22×C412yes—
181C13×C22⋊C4—24no—
182C13×C22⋊C4—42no—
183C42×C13—24no—
184C42×C13—42no—
185C22⋊Dic13—42no—
186#6103—24no—
187#6103—24no—
188C4⋊Dic13—22no—
189C4⋊Dic13—22no—
190#6101—24no—
191#6101—24no—
192#6101—44no—
193#6101—44no—
194C4×Dic13—24no—
195C4×Dic13—24no—
196C4×Dic13—42no—
197C4×Dic13C22⋊C414yes—
198C4×Dic13C22⋊C414yes—
199C4×Dic13C22×C412yes—
200C4×Dic13C22×C412yes—
201C4×Dic13C2×D412yes—
202C4×Dic13C2×D412yes—
203C2×#1055—22no—
204C2×#1055—22no—
205C2×#1055—22no—
206C2×#1055—44no—
207C2×C4×#41—131no—
208C22×C4⋊C8—131no—
209C2×#416—131no—
210C2×#416—131no—
211#2285—131no—
212#1805—132no—
213#1804—132no—
214#1803—132no—
215#1802—132no—
216#1735—131no—
217#1735D1311yescharacteristic, complemented
218C23×C13—22no—
219C23×C13—22no—
220C23×C13C2×C22⋊C412yes—
221C23×C13#12112yes—
222C23×C13C22⋊Q812yes—
223C23×C13C22×D411yescharacteristic
224C22×D13—22no—
225C22×D13—22no—
226C22×D13—22no—
227C22×D13—42no—
228C22×D13—42no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13C2×C22⋊C412yes—
237C2×C4×C13C2×C4⋊C414yes—
238C2×C4×C13#11714yes—
239C2×C4×C13#12114yes—
240C2×C4×C13#12112yes—
241C2×C4×C13C22⋊Q814yes—
242C2×C4×C13C22⋊Q812yes—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C22×Q811yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C22⋊D13—216no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—28no—
257C2×Dic13—44no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13C2×C22⋊C412yes—
262C2×Dic13C2×C22⋊C412yes—
263C2×Dic13C2×C22⋊C412yes—
264C2×Dic13C2×C22⋊C412yes—
265C2×Dic13#13514yes—
266D52—22no—
267D52—22no—
268D52—22no—
269D52C2×C4⋊C414yes—
270C4×D13—216no—
271C4×D13—48no—
272C4×D13—48no—
273Dic26—22no—
274Dic26—22no—
275Dic26—22no—
276Dic26C2×C4⋊C414yes—
277C8×C13—42no—
278#1055—42no—
279C22×#41—131no—
280C23×C8—131no—
281C23×C8C2×D1311yescharacteristic
282C4×#41—138no—
283C4×#41—264no—
284C2×C4×Q8—131no—
285C2×C4×Q8—131no—
286C2×C4×D4—131no—
287C2×C4×D4—131no—
288C2×C4×D4—261no—
289C2×C4×D4—261no—
290C2×#117—131no—
291C2×#117—261no—
292C2×#117C2×D1311yescharacteristic
293C2×#117C2×D1311yescharacteristic
294C22×C42—131no—
295C22×C42—261no—
296C2×C4⋊C8—132no—
297C2×C4⋊C8—132no—
298C2×C4⋊C8—264no—
299#416—264no—
300#416—264no—
301C2×#103—132no—
302C2×#103—132no—
303C2×#102—132no—
304C2×#102—132no—
305#384—132no—
306#382—132no—
307#380—261no—
308#380—261no—
309C4×C4⋊C4—261no—
310C4×C4⋊C4—261no—
311#340—132no—
312#340—132no—
313#340C2×D1312yes—
314#340C2×D1312yes—
315C22×C13—24no—
316C22×C13—22no—
317C22×C13—22no—
318C22×C13—24no—
319C22×C13#38014yes—
320C22×C13C22×C22⋊C411yescharacteristic
321C22×C13C2×#12111yescharacteristic
322C22×C13C2×C22⋊Q811yescharacteristic
323C22×C13C2×#13512yes—
324C22×C13#57512yes—
325C2×D13—24no—
326C2×D13—44no—
327C2×D13—42no—
328C2×D13—42no—
329C2×D13—44no—
330C4×C13—42no—
331C4×C13—42no—
332C4×C13—82no—
333C4×C13#38014yes—
334C4×C13C22×C4⋊C411yescharacteristic
335C4×C13C2×#11711yescharacteristic
336C4×C13C2×#12111yescharacteristic
337C4×C13C2×C22⋊Q811yescharacteristic
338Dic13—22no—
339Dic13—22no—
340Dic13—22no—
341Dic13—24no—
342Dic13—82no—
343Dic13#41614yescomplemented
344C2×#41—134no—
345C2×#41—134no—
346C2×#41—134no—
347C2×#41—262no—
348C2×#41—262no—
349C2×#41—262no—
350C22×Q8—131no—
351C22×D4—131no—
352C22×D4—261no—
353C23×C4—131no—
354C23×C4—131no—
355C23×C4—261no—
356C23×C4—261no—
357C23×C4—261no—
358C23×C4C22×D1311yescharacteristic
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—132no—
363C22×C8—262no—
364C22×C8—262no—
365C22×C8—262no—
366C22×C8C22×D1312yes—
367C4×Q8—134no—
368C4×Q8—134no—
369C4×Q8—262no—
370C4×Q8—262no—
371C4×D4—134no—
372C4×D4—134no—
373C4×D4—262no—
374C4×D4—262no—
375C4×D4—268no—
376C4×D4—268no—
377#117—22no—
378#117—22no—
379#117—22no—
380#117—268no—
381#117—262no—
382#117—262no—
383#117C4×D1314yes—
384C2×C4⋊C4—132no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4C22×D1312yes—
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—134no—
400C2×C42—134no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—268no—
406C2×C42—261no—
407C2×C42—261no—
408C2×C42—261no—
409C4⋊C8—264no—
410C4⋊C8—264no—
411#103—264no—
412#103—264no—
413#102—264no—
414#102—264no—
415#95—262no—
416#95—262no—
417C2×C13—24no—
418C2×C13C2×#38011yescharacteristic
419C2×C13C2×#41611yescharacteristic
420C2×C13#289611yescharacteristic
421C2×C13#303512yes—
422C2×C13#307612yes—
423D13—44no—
424C24—261no—
425C24D4×D1311yescharacteristic
426#41—1316no—
427#41—268no—
428#41—268no—
429#41—268no—
430C2×Q8—132no—
431C2×Q8—132no—
432C2×Q8—132no—
433C2×Q8—261no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×D4—132no—
437C2×D4—132no—
438C2×D4—132no—
439C2×D4—264no—
440C2×D4—264no—
441C2×D4—264no—
442C2×D4—261no—
443C2×D4—261no—
444C2×D4—261no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—131no—
449C22×C4—134no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—134no—
454C22×C4—264no—
455C22×C4—264no—
456C22×C4—264no—
457C22×C4—261no—
458C22×C4—264no—
459C22×C4—264no—
460C22×C4—264no—
461C22×C4—262no—
462C22×C4—524no—
463C22×C4—524no—
464C22×C4—522no—
465C22×C4C2×C4×D1312yes—
466C22×C4#612712yes—
467C22×C4#612712yes—
468C22×C4D4×D1312yes—
469C22×C4D4×D1312yes—
470C22×C4D4×D1311yescharacteristic
471C22×C4Q8×D1312yes—
472C22×C4C23×D1311yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—44no—
477C2×C8—262no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—524no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—264no—
486C4⋊C4—264no—
487C4⋊C4—262no—
488C4⋊C4—262no—
489C4⋊C4—524no—
490C4⋊C4—524no—
491C4⋊C4C2×C4×D1312yes—
492C4⋊C4C2×C4×D1312yes—
493C22⋊C4—24no—
494C22⋊C4—42no—
495C22⋊C4—264no—
496C22⋊C4—264no—
497C22⋊C4—522no—
498C42—24no—
499C42—42no—
500C42—134no—
501C42—134no—
502C42—132no—
503C42—132no—
504C42—132no—
505C42—132no—
506C42—264no—
507C42—264no—
508C42—522no—
509C13#2064511yescharacteristic, complemented, Sylow
510C23—22no—
511C23—22no—
512C23—262no—
513C23—262no—
514C23—262no—
515C23—522no—
516C23—522no—
517C23C22⋊C4×D1312yes—
518C23#8813812yes—
519C23#8815012yes—
520C23C2×D4×D1311yescharacteristic
521Q8—134no—
522Q8—262no—
523Q8—262no—
524Q8—262no—
525D4—134no—
526D4—2616no—
527D4—262no—
528D4—262no—
529D4—262no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—132no—
538C2×C4—134no—
539C2×C4—132no—
540C2×C4—132no—
541C2×C4—132no—
542C2×C4—268no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—2616no—
550C2×C4—528no—
551C2×C4—528no—
552C2×C4—524no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4#8812614yes—
557C2×C4C22⋊C4×D1312yes—
558C2×C4#8813814yes—
559C2×C4#8813812yes—
560C2×C4C4⋊C4×D1314yes—
561C2×C4#8815014yes—
562C2×C4#8815012yes—
563C2×C4C22×C4×D1311yescharacteristic
564C2×C4C2×#612711yescharacteristic
565C2×C4C2×#612711yescharacteristic
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4C2×D4×D1311yescharacteristic
568C2×C4C2×Q8×D1311yescharacteristic
569C8—42no—
570C8—522no—
571C22—22no—
572C22—24no—
573C22—22no—
574C22—24no—
575C22—264no—
576C22—522no—
577C22—524no—
578C22—522no—
579C22—524no—
580C22#1171832814yes—
581C22C2×C22⋊C4×D1311yescharacteristic
582C22C2×#8813811yescharacteristic
583C22C2×#8815011yescharacteristic
584C22D13×#13512yes—
585C22#1171947312yes—
586C4—42no—
587C4—42no—
588C4—82no—
589C4—134no—
590C4—262no—
591C4—262no—
592C4—262no—
593C4—264no—
594C4—1042no—
595C4#1171832814yes—
596C4C2×#8812611yescharacteristic
597C4C2×#8813811yescharacteristic
598C4C2×C4⋊C4×D1311yescharacteristic
599C4C2×#8815011yescharacteristic
600C2—24no—
601C2—524no—
602C2C2×#1171832811yescharacteristic
603C2D13×#41611yescharacteristic
604C2#1312335111yescharacteristic
605C2#1312428912yes—
606C2#1312462212yes—
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1735C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenter#1735D13
hypocenterC13#20645
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
2. C22×#88054C2semidirect
5. #13117239C2semidirect
6. #13114850C2semidirect
7. #13114845C2semidirect
8. #13114840C2semidirect
9. #13114835C2semidirect
10. #13114552C2semidirect
11. C13×#1735C2semidirect
20. #11719227C4semidirect
151. #6127C4⋊C4semidirect
217. #1735D13semidirect
343. Dic13#416semidirect
509. C13#20645semidirect

Maximal subgroups

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

subgroupindex
C2×#117192272
C22×#880542
C2×#117187742
C2×#117186632
#131172392
#131148502
#131148452
#131148402
#131148352
#131145522
C13×#17352
#2064513