Finite Group Databasebeta

← #15890269

Subgroups — #15890269

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×#11719224C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic
3C2×#11718894C211yesmaximal, characteristic
4#13115987C212yesmaximal, complemented
5#13115982C212yesmaximal, complemented
6#13115977C212yesmaximal, complemented
7#13115972C212yesmaximal, complemented
8#13114555C211yesmaximal, characteristic, complemented
9C2×#11718121C211yesmaximal, characteristic, complemented
10#13114533C211yesmaximal, characteristic, complemented
11C13×#2311C211yesmaximal, characteristic
12C22×C13×#41C2211yescharacteristic
13C2×C13×#117C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C2×#88180C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×#6099C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19#11719224—24no—
20#11719224—24no—
21C2×#88144—21no—
22C2×#88142—21no—
23C2×#88132—22no—
24C2×#88124C2212yes—
25C2×#88123C2212yes—
26C13×#391C2212yes—
27C13×#390C2212yes—
28C13×#386—22no—
29C13×#380—21no—
30C13×#380—21no—
31#11718894—24no—
32#11718893—24no—
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2212yes—
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2212yes—
39#11718121C2212yes—
40#11718121C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718116C2212yes—
44#11718116C2212yes—
45C2×C13×#41—22no—
46C2×C13×#41—22no—
47C2×C13×#41—22no—
48C2×C13×#41—22no—
49C2×C13×#41—22no—
50C2×C13×#41Q814yescomplemented
51C22×Q8×C13C2311yescharacteristic
52C22×D4×C13—21no—
53C22×D4×C13C2311yescharacteristic
54C23×C4×C13—21no—
55C23×C4×C13—21no—
56C23×C4×C13C2311yescharacteristic
57C23×Dic13—21no—
58C22×Dic26—22no—
59C13×#117—22no—
60C13×#117—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4D411yescharacteristic
65C2×C13×C4⋊C4D411yescharacteristic
66C2×C13×C4⋊C4C2312yes—
67C2×C13×C22⋊C4—22no—
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4D412yes—
70C2×C42×C13C2312yes—
71C2×C22⋊Dic13—21no—
72#88180—22no—
73#88180D414yes—
74C2×C4⋊Dic13—22no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13D414yes—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2312yes—
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—22no—
82C2×#6101—22no—
83C2×C4×Dic13—21no—
84C2×#6099—22no—
85C2×#6099—22no—
86C2×#6099—22no—
87C22×#1055—22no—
88C22×#1055—22no—
89C22×#1055—22no—
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2312yes—
93#88144—28no—
94#88142—28no—
95#88132—216no—
96#88124—24no—
97#88124—24no—
98#88123—24no—
99#88123—24no—
100C13×#95—22no—
101C13×#95—22no—
102#88075—24no—
103#88075—22no—
104#88075—22no—
105#88072—24no—
106#88072—22no—
107#88072—22no—
108#23458—131nomaximal, Sylow
109C24×C13—21no—
110C24×C13C2×D411yescharacteristic
111C13×#41—28no—
112C13×#41—28no—
113C13×#41—44no—
114C13×#41—44no—
115C2×Q8×C13—21no—
116C2×Q8×C13—21no—
117C2×Q8×C13—21no—
118C2×Q8×C13—21no—
119C2×Q8×C13—21no—
120C2×Q8×C13C2×Q812yes—
121C2×D4×C13—24no—
122C2×D4×C13—21no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—42no—
128C2×D4×C13—42no—
129C2×D4×C13C2×Q812yes—
130C22×C4×C13—21no—
131C22×C4×C13—24no—
132C22×C4×C13—22no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—81no—
137C22×C4×C13—81no—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D412yes—
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×Q812yes—
144C22×C4×C13#4112yes—
145C22×C4×C13#4112yes—
146C22×C4×C13#4112yes—
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—22no—
151C22×Dic13—24no—
152C22×Dic13—81no—
153C22×Dic13—81no—
154C2×Dic26—28no—
155C2×Dic26—82no—
156C2×Dic26—82no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—42no—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—82no—
164C13×C22⋊C4—82no—
165C42×C13—22no—
166C42×C13—22no—
167C22⋊Dic13—24no—
168C4⋊Dic13—28no—
169C4⋊Dic13—24no—
170C4⋊Dic13—21no—
171C4⋊Dic13—22no—
172C4⋊Dic13—21no—
173C4⋊Dic13C2×D412yes—
174C4⋊Dic13C2×D414yes—
175C4⋊Dic13C2×D412yes—
176#6101—28no—
177#6101—28no—
178C4×Dic13—24no—
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×#544—131no—
191C2×#417—131no—
192C2×#416—131no—
193#2311D1311yescharacteristic
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—22no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13#12012yes—
213C23×C13C22⋊Q812yes—
214C23×C13#12412yes—
215C23×C13C22×D411yescharacteristic
216Q8×C13—22no—
217Q8×C13—22no—
218Q8×C13—41no—
219Q8×C13—41no—
220D4×C13—22no—
221D4×C13—22no—
222D4×C13—48no—
223D4×C13—41no—
224D4×C13—41no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—48no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—84no—
239C2×C4×C13#12012yes—
240C2×C4×C13C22⋊Q814yes—
241C2×C4×C13C22⋊Q814yes—
242C2×C4×C13C22⋊Q812yes—
243C2×C4×C13#12414yes—
244C2×C4×C13#12414yes—
245C2×C4×C13#12412yes—
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C22×Q811yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—24no—
255C2×Dic13—41no—
256C2×Dic13—42no—
257C2×Dic13—41no—
258C2×Dic13—42no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—84no—
262Dic26—88no—
263#1055—41no—
264#1055—41no—
265#1055—42no—
266C22×#41C2×D1311yescharacteristic
267C22×M16—131no—
268C23×C8—131no—
269#544—264no—
270#544—264no—
271C2×C4⋊Q8—132no—
272C2×C4⋊Q8—261no—
273C2×#125—132no—
274C2×#125—261no—
275C2×C22⋊Q8—262no—
276C2×#117—131no—
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#391C2×D1312yes—
289#390C2×D1312yes—
290#386—22no—
291#380—21no—
292#380—21no—
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—42no—
306C22×C13—42no—
307C22×C13—42no—
308C22×C13—81no—
309C22×C13—81no—
310C22×C13—81no—
311C22×C13—81no—
312C22×C13#39314yes—
313C22×C13C2×#12011yescharacteristic
314C22×C13C2×C22⋊Q811yescharacteristic
315C22×C13C2×#12411yescharacteristic
316C22×C13#57611yescharacteristic
317C22×C13#57711yescharacteristic
318C22×C13#57711yescharacteristic
319C22×C13#57811yescharacteristic
320C4×C13—42no—
321C4×C13—42no—
322C4×C13—42no—
323C4×C13—82no—
324C4×C13#39314yes—
325C4×C13C2×C22⋊Q811yescharacteristic
326C4×C13C2×C22⋊Q811yescharacteristic
327C4×C13C2×#12411yescharacteristic
328C4×C13C2×#12411yescharacteristic
329Dic13—42no—
330Dic13—44no—
331Dic13—42no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41Dic2614yescomplemented
338C22×Q8—262no—
339C22×Q8C22×D1311yescharacteristic
340C22×D4—21no—
341C22×D4C22×D1311yescharacteristic
342C23×C4—21no—
343C23×C4—21no—
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—264no—
356C4⋊Q8—264no—
357C4⋊Q8—268no—
358#125—264no—
359#125—264no—
360#125—268no—
361C22⋊Q8—2616no—
362#117—22no—
363#117—22no—
364#117—134no—
365#117—262no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—134no—
370C2×C4⋊C4—132no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—262no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4C22⋊D1311yescharacteristic
379C2×C4⋊C4C22⋊D1311yescharacteristic
380C2×C4⋊C4C22×D1312yes—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4C22⋊D1312yes—
385C2×C42—261no—
386C2×C42C22×D1312yes—
387#103—262no—
388#103—262no—
389#103—264no—
390#102—262no—
391#102—262no—
392#102—264no—
393#95—22no—
394#95—22no—
395C2×C13—24no—
396C2×C13—82no—
397C2×C13C2×#39311yescharacteristic
398C2×C13#301211yescharacteristic
399C2×C13#301311yescharacteristic
400C2×C13#308311yescharacteristic
401C2×C13#308411yescharacteristic
402C2×C13#313611yescharacteristic
403C2×C13#313711yescharacteristic
404C24—21no—
405C24C2×C22⋊D1311yescharacteristic
406#41—28no—
407#41—28no—
408#41—44no—
409#41—44no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—268no—
416C2×Q8—1042no—
417C2×Q8—1042no—
418C2×Q8C2×Dic2612yes—
419C2×D4—24no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C2×Dic2612yes—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—261no—
437C22×C4—261no—
438C22×C4—262no—
439C22×C4—264no—
440C22×C4—1041no—
441C22×C4—1041no—
442C22×C4C2×Dic2612yes—
443C22×C4#612712yes—
444C22×C4D4×D1312yes—
445C22×C4D4×D1312yes—
446C22×C4#612912yes—
447C22×C4#612912yes—
448C22×C4C2×C22⋊D1312yes—
449C22×C4C2×C22⋊D1312yes—
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C23×D1311yescharacteristic
452M16—524no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—262no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—262no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—262no—
462C2×C8—524no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—134no—
469C4⋊C4—132no—
470C4⋊C4—132no—
471C4⋊C4—268no—
472C4⋊C4—268no—
473C4⋊C4—268no—
474C4⋊C4—264no—
475C4⋊C4—262no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C22⋊C4—24no—
479C22⋊C4—82no—
480C22⋊C4—82no—
481C22⋊C4—264no—
482C42—22no—
483C42—22no—
484C42—264no—
485C13#2345811yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23#8817812yes—
498C23#8819012yes—
499C23#8819112yes—
500C23C22×C22⋊D1311yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505Q8—1048no—
506D4—22no—
507D4—22no—
508D4—48no—
509D4—41no—
510D4—41no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—48no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—84no—
525C2×C4—262no—
526C2×C4—262no—
527C2×C4—264no—
528C2×C4—522no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—1044no—
535C2×C4#8813214yes—
536C2×C4#8813214yes—
537C2×C4#8813914yes—
538C2×C4#8813914yes—
539C2×C4#8817812yes—
540C2×C4#8819012yes—
541C2×C4#8819112yes—
542C2×C4C22×Dic2611yescharacteristic
543C2×C4C2×#612711yescharacteristic
544C2×C4C2×D4×D1311yescharacteristic
545C2×C4C2×D4×D1311yescharacteristic
546C2×C4C2×#612911yescharacteristic
547C2×C4C2×#612911yescharacteristic
548C8—521no—
549C8—521no—
550C8—522no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22#1171860814yes—
565C22C2×#8817811yescharacteristic
566C22C2×#8819011yescharacteristic
567C22C2×#8819111yescharacteristic
568C22#1171954011yescharacteristic
569C22#1171954111yescharacteristic
570C22#1171954211yescharacteristic
571C22#1171954311yescharacteristic
572C4—42no—
573C4—42no—
574C4—42no—
575C4—82no—
576C4—524no—
577C4—522no—
578C4—522no—
579C4#1171860814yes—
580C4C2×#8813211yescharacteristic
581C4C2×#8813211yescharacteristic
582C4C2×#8813911yescharacteristic
583C4C2×#8813911yescharacteristic
584C2—24no—
585C2—82no—
586C2C2×#1171860811yescharacteristic
587C2#1312413711yescharacteristic
588C2#1312414811yescharacteristic
589C2#1312468711yescharacteristic
590C2#1312469811yescharacteristic
591C2#1312519011yescharacteristic
592C2#1312520111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2311C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenter#2311D13
hypocenterC13#23458
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
1. C2×#11719224C2semidirect
4. #13115987C2semidirect
5. #13115982C2semidirect
6. #13115977C2semidirect
7. #13115972C2semidirect
8. #13114555C2semidirect
9. C2×#11718121C2semidirect
10. #13114533C2semidirect
50. C2×C13×#41Q8semidirect
337. C2×#41Dic26semidirect
485. C13#23458semidirect

Maximal subgroups

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

subgroupindex
C2×#117192242
C2×#117188932
C2×#117188942
#131159872
#131159822
#131159772
#131159722
#131145552
C2×#117181212
#131145332
C13×#23112
#2345813