Finite Group Databasebeta

← #15890265

Subgroups — #15890265

Order 3328.

1250 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
1C2×#11718627C211yesmaximal, characteristic
2C2×#11718663C211yesmaximal, characteristic
3#13117424C211yesmaximal, characteristic
4#13115984C212yesmaximal, complemented
5#13115979C212yesmaximal, complemented
6#13115974C212yesmaximal, complemented
7#13115969C212yesmaximal, complemented
8#13114557C211yesmaximal, characteristic, complemented
9C2×#11718121C211yesmaximal, characteristic, complemented
10#13114533C211yesmaximal, characteristic, complemented
11C2×C13×#544C211yesmaximal, characteristic, complemented
12C22×#6127C2211yescharacteristic
13C13×#544—24no—
14C13×#544—24no—
15C2×C13×C4⋊Q8—21no—
16C2×C13×C4⋊Q8C2212yes—
17C2×C13×#125—21no—
18C2×C13×#125C2212yes—
19C2×C13×C22⋊Q8—22no—
20C2×C13×#117C2211yescharacteristic
21C2×C13×#117C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C23×#1055C2211yescharacteristic
26#11718663—24no—
27#11718648—21no—
28#11718648—21no—
29C2×#88050C2211yescharacteristic
30C2×#88050C2211yescharacteristic
31C2×#88050C2212yes—
32#11718627—24no—
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2212yes—
36#11718619—22no—
37#11718600C2212yes—
38#11718590C2212yes—
39#11718121C2212yes—
40#11718121C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718116C2212yes—
44#11718116C2212yes—
45C22×Q8×C13—22no—
46C23×C4×C13—21no—
47C23×C4×C13C2311yescharacteristic
48C22×C22⋊D13—21no—
49C23×Dic13—21no—
50C2×#6127—22no—
51C2×#6127—22no—
52C2×#6127—22no—
53C2×#6127—22no—
54C2×#6127—22no—
55C2×#6127Q814yescomplemented
56C22×D52C2311yescharacteristic
57C22×C4×D13—21no—
58C22×Dic26C2311yescharacteristic
59C13×C4⋊Q8—28no—
60C13×C4⋊Q8—24no—
61C13×C4⋊Q8—24no—
62C13×#125—28no—
63C13×#125—24no—
64C13×#125—24no—
65C13×C22⋊Q8—216no—
66C13×#117—22no—
67C13×#117—22no—
68C13×#117—22no—
69C13×#117D414yes—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4D414yes—
78C2×C13×C4⋊C4C2312yes—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D412yes—
83C2×C42×C13—21no—
84C2×C42×C13C2312yes—
85C2×#6103—22no—
86C2×#6103—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2312yes—
91C2×#6099—22no—
92C2×#6099—22no—
93C2×#6099—22no—
94C22×#1055—22no—
95C22×#1055—22no—
96C22×#1055—22no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2312yes—
100#88071—22no—
101#88071—22no—
102#88050—22no—
103#88050—22no—
104#88050—24no—
105#88049—22no—
106#88049—22no—
107#88049—24no—
108#23458—131nomaximal, Sylow
109C24×C13C2×D411yescharacteristic
110C23×D13—21no—
111C2×Q8×C13—28no—
112C2×Q8×C13—82no—
113C2×Q8×C13—82no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—24no—
118C22×C4×C13—81no—
119C22×C4×C13—81no—
120C22×C4×C13C2×D412yes—
121C22×C4×C13C2×D412yes—
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×D412yes—
124C22×C4×C13C2×D412yes—
125C22×C4×C13C2×Q812yes—
126C22×C4×C13#4112yes—
127C22×C4×C13#4112yes—
128C22×C4×C13#4112yes—
129C22×C4×C13C2411yescharacteristic
130C2×C22⋊D13—24no—
131C2×C22⋊D13—42no—
132C2×C22⋊D13—42no—
133C22×Dic13—21no—
134C22×Dic13—22no—
135C22×Dic13—42no—
136C22×Dic13—81no—
137C22×Dic13—81no—
138#6127—28no—
139#6127—28no—
140#6127—44no—
141#6127—44no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52C2×Q812yes—
148C2×C4×D13—24no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C2×Q812yes—
157C13×C4⋊C4—28no—
158C13×C4⋊C4—28no—
159C13×C4⋊C4—28no—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C2×D414yes—
167C13×C4⋊C4C2×D412yes—
168C13×C4⋊C4C2×D412yes—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—24no—
171C42×C13—24no—
172C42×C13—22no—
173C42×C13—22no—
174#6103—82no—
175#6103—82no—
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178C4⋊Dic13—42no—
179#6099—44no—
180C2×#1055—21no—
181C2×#1055—21no—
182C2×#1055—22no—
183C2×#1055—21no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—44no—
190C2×#544D1311yescharacteristic, complemented
191C2×#417—131no—
192C2×#416—131no—
193#2311—131no—
194#2026—132no—
195#2025—132no—
196#2024—132no—
197#2023—132no—
198#1736—131no—
199C2×#340—131no—
200#1729—131no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13#12012yes—
206C23×C13C22⋊Q812yes—
207C23×C13#12412yes—
208C23×C13C22×D411yescharacteristic
209C22×D13—22no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—41no—
216Q8×C13—88no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—42no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—84no—
233C2×C4×C13#12012yes—
234C2×C4×C13C22⋊Q814yes—
235C2×C4×C13C22⋊Q814yes—
236C2×C4×C13C22⋊Q812yes—
237C2×C4×C13#12414yes—
238C2×C4×C13#12414yes—
239C2×C4×C13#12412yes—
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C22×Q811yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C22⋊D13—48no—
247C2×Dic13—22no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—84no—
254D52—22no—
255D52—22no—
256D52—41no—
257D52—41no—
258C4×D13—48no—
259Dic26—22no—
260Dic26—22no—
261Dic26—41no—
262Dic26—41no—
263#1055—41no—
264#1055—41no—
265#1055—42no—
266C22×#41—131no—
267C22×M16—131no—
268C23×C8—131no—
269#544—24no—
270#544—24no—
271C2×C4⋊Q8—21no—
272C2×C4⋊Q8C2×D1312yes—
273C2×#125—21no—
274C2×#125C2×D1312yes—
275C2×C22⋊Q8—22no—
276C2×#117C2×D1311yescharacteristic
277C2×#117C2×D1311yescharacteristic
278C22×C4⋊C4—131no—
279C22×C4⋊C4C2×D1311yescharacteristic
280#417—264no—
281#416—264no—
282C2×#103—131no—
283C2×#103—131no—
284C2×#103—132no—
285C2×#102—131no—
286C2×#102—131no—
287C2×#102—132no—
288#391—132no—
289#390—132no—
290#386—262no—
291#380—261no—
292#380—261no—
293#340—132no—
294#340—132no—
295#340—132no—
296#340—132no—
297#336—132no—
298#336—132no—
299C22×C13—22no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13#39314yes—
306C22×C13C2×#12011yescharacteristic
307C22×C13C2×C22⋊Q811yescharacteristic
308C22×C13C2×#12411yescharacteristic
309C22×C13#57611yescharacteristic
310C22×C13#57711yescharacteristic
311C22×C13#57711yescharacteristic
312C22×C13#57811yescharacteristic
313C2×D13—42no—
314C2×D13—42no—
315C2×D13—42no—
316C2×D13—81no—
317C2×D13—81no—
318C2×D13—81no—
319C2×D13—81no—
320C4×C13—42no—
321C4×C13—44no—
322C4×C13—42no—
323C4×C13—42no—
324C4×C13—42no—
325C4×C13#39314yes—
326C4×C13C2×C22⋊Q811yescharacteristic
327C4×C13C2×C22⋊Q811yescharacteristic
328C4×C13C2×#12411yescharacteristic
329C4×C13C2×#12411yescharacteristic
330Dic13—42no—
331Dic13—82no—
332C2×#41—134no—
333C2×#41—262no—
334C2×#41—262no—
335C2×#41—262no—
336C2×#41—262no—
337C2×#41—262no—
338C22×Q8—22no—
339C22×Q8—131no—
340C22×D4—131no—
341C22×D4—261no—
342C23×C4—21no—
343C23×C4—261no—
344C23×C4—261no—
345C23×C4C22×D1311yescharacteristic
346C2×M16—262no—
347C2×M16—262no—
348C2×M16—262no—
349C22×C8—131no—
350C22×C8—131no—
351C22×C8—132no—
352C22×C8—262no—
353C22×C8—262no—
354C22×C8—262no—
355C4⋊Q8—28no—
356C4⋊Q8—24no—
357C4⋊Q8—24no—
358#125—28no—
359#125—24no—
360#125—24no—
361C22⋊Q8—216no—
362#117—22no—
363#117—22no—
364#117—22no—
365#117C22⋊D1314yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—132no—
372C2×C4⋊C4—262no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4C22⋊D1311yescharacteristic
376C2×C4⋊C4C22⋊D1311yescharacteristic
377C2×C4⋊C4C22⋊D1314yes—
378C2×C4⋊C4C22×D1312yes—
379C2×C4⋊C4C22×D1311yescharacteristic
380C2×C4⋊C4C22×D1311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—262no—
383C2×C22⋊C4—262no—
384C2×C22⋊C4C22⋊D1312yes—
385C2×C42—21no—
386C2×C42C22×D1312yes—
387#103—262no—
388#103—262no—
389#103—264no—
390#102—262no—
391#102—262no—
392#102—264no—
393#95—262no—
394#95—262no—
395C2×C13—24no—
396C2×C13C2×#39311yescharacteristic
397C2×C13#301211yescharacteristic
398C2×C13#301311yescharacteristic
399C2×C13#308311yescharacteristic
400C2×C13#308411yescharacteristic
401C2×C13#313611yescharacteristic
402C2×C13#313711yescharacteristic
403D13—82no—
404C24—261no—
405C24C2×C22⋊D1311yescharacteristic
406#41—268no—
407#41—268no—
408#41—524no—
409#41—524no—
410C2×Q8—28no—
411C2×Q8—82no—
412C2×Q8—82no—
413C2×Q8—132no—
414C2×Q8—261no—
415C2×Q8—261no—
416C2×Q8—261no—
417C2×Q8—261no—
418C2×Q8—261no—
419C2×D4—132no—
420C2×D4—264no—
421C2×D4—261no—
422C2×D4—261no—
423C2×D4—261no—
424C2×D4—261no—
425C2×D4—261no—
426C2×D4—522no—
427C2×D4—522no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4—261no—
435C22×C4—264no—
436C22×C4—262no—
437C22×C4—522no—
438C22×C4—522no—
439C22×C4—522no—
440C22×C4—1041no—
441C22×C4—1041no—
442C22×C4Q8×D1312yes—
443C22×C4#613112yes—
444C22×C4#613112yes—
445C22×C4#613112yes—
446C22×C4C2×C22⋊D1312yes—
447C22×C4C2×C22⋊D1312yes—
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C2×C22⋊D1312yes—
450C22×C4C2×C22⋊D1312yes—
451C22×C4C23×D1311yescharacteristic
452M16—524no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—262no—
458C2×C8—262no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—262no—
462C2×C8—524no—
463C4⋊C4—28no—
464C4⋊C4—28no—
465C4⋊C4—28no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—262no—
473C4⋊C4—262no—
474C4⋊C4—522no—
475C4⋊C4C2×C22⋊D1314yes—
476C4⋊C4C2×C22⋊D1312yes—
477C4⋊C4C2×C22⋊D1312yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—1042no—
481C22⋊C4—1042no—
482C42—24no—
483C42—22no—
484C42—22no—
485C13#2345811yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—262no—
491C23—521no—
492C23—521no—
493C23—521no—
494C23—521no—
495C23—521no—
496C23—521no—
497C23#8820012yes—
498C23#8820112yes—
499C23#8820712yes—
500C23C22×C22⋊D1311yescharacteristic
501Q8—88no—
502Q8—262no—
503Q8—262no—
504Q8—521no—
505Q8—521no—
506D4—262no—
507D4—262no—
508D4—528no—
509D4—521no—
510D4—521no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—84no—
527C2×C4—262no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—528no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—1044no—
535C2×C4#8820014yes—
536C2×C4#8820014yes—
537C2×C4#8820012yes—
538C2×C4#8820114yes—
539C2×C4#8820114yes—
540C2×C4#8820112yes—
541C2×C4#8820712yes—
542C2×C4C2×Q8×D1311yescharacteristic
543C2×C4C2×#613111yescharacteristic
544C2×C4C2×#613111yescharacteristic
545C2×C4C2×#613111yescharacteristic
546C2×C4C22×C22⋊D1311yescharacteristic
547C2×C4C22×C22⋊D1311yescharacteristic
548C8—521no—
549C8—521no—
550C8—522no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—522no—
558C22—522no—
559C22—522no—
560C22—1041no—
561C22—1041no—
562C22—1041no—
563C22—1041no—
564C22#1171889214yes—
565C22C2×#8820011yescharacteristic
566C22C2×#8820111yescharacteristic
567C22#1171954011yescharacteristic
568C22#1171954111yescharacteristic
569C22#1171954211yescharacteristic
570C22#1171954311yescharacteristic
571C22C2×#8820711yescharacteristic
572C4—42no—
573C4—44no—
574C4—42no—
575C4—42no—
576C4—42no—
577C4—522no—
578C4—1042no—
579C4#1171889214yes—
580C4C2×#8820011yescharacteristic
581C4C2×#8820011yescharacteristic
582C4C2×#8820111yescharacteristic
583C4C2×#8820111yescharacteristic
584C2—24no—
585C2—1042no—
586C2C2×#1171889211yescharacteristic
587C2#1312414011yescharacteristic
588C2#1312415111yescharacteristic
589C2#1312468311yescharacteristic
590C2#1312469411yescharacteristic
591C2#1312519511yescharacteristic
592C2#1312520611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
hypercenterC2×#544D13
hypocenterC13#23458
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
4. #13115984C2semidirect
5. #13115979C2semidirect
6. #13115974C2semidirect
7. #13115969C2semidirect
8. #13114557C2semidirect
9. C2×#11718121C2semidirect
10. #13114533C2semidirect
11. C2×C13×#544C2semidirect
55. C2×#6127Q8semidirect
190. C2×#544D13semidirect
485. C13#23458semidirect

Maximal subgroups

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

subgroupindex
C2×#117186272
C2×#117186632
#131174242
#131159842
#131159792
#131159742
#131159692
#131145572
C2×#117181212
#131145332
C2×C13×#5442
#2345813