Finite Group Databasebeta

← #15863923

Subgroups — #15863923

Order 3328.

1458 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718625C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic
3C2×#11718894C211yesmaximal, characteristic
4#13117452C211yesmaximal, characteristic, complemented
5#13115104C212yesmaximal, complemented
6#13115097C212yesmaximal, complemented
7#13115090C212yesmaximal, complemented
8#13115083C212yesmaximal, complemented
9C2×#11718121C211yesmaximal, characteristic, complemented
10#13114533C211yesmaximal, characteristic, complemented
11C2×C13×#520C211yesmaximal, characteristic
12C22×C13×#41C2211yescharacteristic
13C13×#520—24no—
14C13×#520—24no—
15C2×C4×Q8×C13C2212yes—
16C2×C4×D4×C13—22no—
17C2×C4×D4×C13C2212yes—
18C2×C13×#117—21no—
19C2×C13×#117C2211yescharacteristic
20C22×C13×C4⋊C4—21no—
21C22×C13×C4⋊C4C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C23×#1055C2211yescharacteristic
26#11718894—24no—
27#11718893C418yescomplemented
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2212yes—
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2212yes—
34#11718634—21no—
35#11718634—21no—
36#11718625—24no—
37C2×#88048C2212yes—
38C2×#88047C2212yes—
39#11718603—22no—
40#11718589C2212yes—
41#11718589C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44#11718116C2212yes—
45#11718116C2212yes—
46C2×C13×#41—22no—
47C2×C13×#41—22no—
48C2×C13×#41—22no—
49C2×C13×#41C2×C414yes—
50C2×C13×#41D414yes—
51C2×C13×#41Q814yes—
52C22×Q8×C13C2311yescharacteristic
53C22×D4×C13—21no—
54C22×D4×C13C2311yescharacteristic
55C23×C4×C13—21no—
56C23×C4×C13—21no—
57C23×C4×C13—22no—
58C23×C4×C13C2311yescharacteristic
59C23×Dic13—21no—
60C4×Q8×C13—24no—
61C4×Q8×C13—24no—
62C4×D4×C13—216no—
63C4×D4×C13—24no—
64C4×D4×C13—24no—
65C13×#117—28no—
66C13×#117—22no—
67C13×#117—22no—
68C2×C13×C4⋊C4—28no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4D414yes—
75C2×C13×C4⋊C4C2312yes—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4D412yes—
78C2×C42×C13—22no—
79C2×C42×C13C2312yes—
80C2×C22⋊Dic13—21no—
81#88180—22no—
82#88180—22no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13C2×C414yescomplemented
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2312yes—
89C2×#6101—22no—
90C2×#6101—22no—
91C2×C4×Dic13—21no—
92C2×#6099—22no—
93C2×#6099—22no—
94C2×#6099C2×C414yescomplemented
95C22×#1055—22no—
96C22×#1055—22no—
97C22×#1055—22no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2312yes—
101#88075—22no—
102#88075—22no—
103#88075C2×C418yescomplemented
104#88072—22no—
105#88072—22no—
106#88072C2×C418yescomplemented
107#88071—22no—
108#88071—22no—
109#88048—24no—
110#88047—24no—
111#20878—131nomaximal, Sylow
112C24×C13—21no—
113C24×C13C2×D411yescharacteristic
114C13×#41—28no—
115C13×#41—28no—
116C13×#41—28no—
117C13×#41C4⋊C4116yescomplemented
118C2×Q8×C13—21no—
119C2×Q8×C13—21no—
120C2×Q8×C13—21no—
121C2×Q8×C13C22×C412yes—
122C2×Q8×C13C2×D412yes—
123C2×Q8×C13C2×Q812yes—
124C2×D4×C13—24no—
125C2×D4×C13—24no—
126C2×D4×C13—24no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13C22×C412yes—
131C2×D4×C13C2×D412yes—
132C2×D4×C13C2×Q812yes—
133C22×C4×C13—21no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—22no—
138C22×C4×C13—28no—
139C22×C4×C13—24no—
140C22×C4×C13—82no—
141C22×C4×C13—82no—
142C22×C4×C13—81no—
143C22×C4×C13—81no—
144C22×C4×C13C22×C412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×Q812yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—22no—
155C22×Dic13—24no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—81no—
159C22×Dic13—81no—
160C13×C4⋊C4—28no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4C2×D414yes—
166C13×C22⋊C4—28no—
167C13×C22⋊C4—24no—
168C42×C13—28no—
169C42×C13—22no—
170C42×C13—22no—
171C22⋊Dic13—42no—
172C4⋊Dic13—24no—
173C4⋊Dic13—22no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13C22×C414yes—
179#6101—82no—
180#6101—82no—
181C4×Dic13—42no—
182#6099—28no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—44no—
192C2×#1055C22×C414yes—
193C2×#520D1311yescharacteristic
194C2×#428—131no—
195C2×#417—131no—
196C2×#416—131no—
197#2316—131no—
198#1865—132no—
199#1864—132no—
200#1863—132no—
201#1862—132no—
202C2×#340—131no—
203#1729—131no—
204C23×C13—21no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13C4×D412yes—
216C23×C13#12012yes—
217C23×C13C22⋊Q812yes—
218C23×C13C22×D411yescharacteristic
219Q8×C13—22no—
220Q8×C13—22no—
221Q8×C13—22no—
222Q8×C13C2×C4⋊C414yes—
223D4×C13—216no—
224D4×C13—22no—
225D4×C13—22no—
226D4×C13—22no—
227D4×C13C2×C4⋊C414yes—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—216no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—24no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—84no—
242C2×C4×C13—88no—
243C2×C4×C13C2×C4⋊C414yes—
244C2×C4×C13C4×D414yes—
245C2×C4×C13C4×D412yes—
246C2×C4×C13#12012yes—
247C2×C4×C13C22⋊Q814yes—
248C2×C4×C13C22⋊Q812yes—
249C2×C4×C13#12314yes—
250C2×C4×C13C23×C411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×Q811yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×Dic13—24no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—84no—
266#1055—24no—
267#1055—41no—
268#1055—41no—
269C22×#41C2×D1311yescharacteristic
270C22×M16—131no—
271C23×C8—131no—
272#520—24no—
273#520—24no—
274C2×C4×Q8C2×D1312yes—
275C2×C4×D4—22no—
276C2×C4×D4C2×D1312yes—
277C2×#117—21no—
278C2×#117—131no—
279C2×#117C2×D1311yescharacteristic
280C22×C4⋊C4—21no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4C2×D1311yescharacteristic
283#428—264no—
284C2×#107—132no—
285C2×#106—132no—
286#417—138no—
287#416—264no—
288C2×#103—132no—
289C2×#103—131no—
290C2×#103—131no—
291C2×#102—132no—
292C2×#102—131no—
293C2×#102—131no—
294#389—132no—
295#389—132no—
296#389—261no—
297#389—261no—
298#380—262no—
299#340—132no—
300#340—132no—
301#336—132no—
302#336—132no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—22no—
308C22×C13—22no—
309C22×C13—24no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13#38514yes—
317C22×C13C2×C4×D411yescharacteristic
318C22×C13C2×#12011yescharacteristic
319C22×C13C2×C22⋊Q811yescharacteristic
320C22×C13#57611yescharacteristic
321C22×C13#57711yescharacteristic
322C22×C13#57711yescharacteristic
323C22×C13#57811yescharacteristic
324C4×C13—24no—
325C4×C13—42no—
326C4×C13—44no—
327C4×C13—42no—
328C4×C13#38514yes—
329C4×C13C22×C4⋊C411yescharacteristic
330C4×C13C2×C4×D411yescharacteristic
331C4×C13C2×C22⋊Q811yescharacteristic
332C4×C13C2×#12311yescharacteristic
333Dic13—44no—
334Dic13—81no—
335Dic13—81no—
336C2×#41—22no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41Dic2614yes—
340C2×#41C4×D1314yes—
341C2×#41C22⋊D1314yes—
342C22×Q8C22×D1311yescharacteristic
343C22×D4—21no—
344C22×D4C22×D1311yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—22no—
348C23×C4—261no—
349C23×C4C22×D1311yescharacteristic
350C2×M16—134no—
351C2×M16—262no—
352C2×M16—262no—
353C22×C8—132no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—262no—
357C22×C8—262no—
358C22×C8—262no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×D4—216no—
362C4×D4—24no—
363C4×D4—24no—
364#117—28no—
365#117—22no—
366#117—22no—
367#117—262no—
368#117—262no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—132no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4C22⋊D1311yescharacteristic
382C2×C4⋊C4C22⋊D1311yescharacteristic
383C2×C4⋊C4C22⋊D1314yes—
384C2×C4⋊C4C22×D1312yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—261no—
387C2×C22⋊C4C22⋊D1312yes—
388C2×C42—22no—
389C2×C42—261no—
390C2×C42C22×D1312yes—
391#107—264no—
392#106—264no—
393#103—138no—
394#103—262no—
395#103—262no—
396#102—138no—
397#102—262no—
398#102—262no—
399#95—262no—
400#95—262no—
401C2×C13—24no—
402C2×C13—44no—
403C2×C13C2×#38511yescharacteristic
404C2×C13#294611yescharacteristic
405C2×C13#294711yescharacteristic
406C2×C13#301211yescharacteristic
407C2×C13#301311yescharacteristic
408C2×C13#308311yescharacteristic
409C2×C13#308411yescharacteristic
410C24—21no—
411C24C2×C22⋊D1311yescharacteristic
412#41—28no—
413#41—28no—
414#41—28no—
415#41#6101116yescomplemented
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8C2×Dic2612yes—
420C2×Q8C2×C4×D1312yes—
421C2×Q8C2×C22⋊D1312yes—
422C2×D4—24no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4C2×Dic2612yes—
429C2×D4C2×C4×D1312yes—
430C2×D4C2×C22⋊D1312yes—
431C22×C4—21no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—28no—
437C22×C4—24no—
438C22×C4—82no—
439C22×C4—82no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4—262no—
443C22×C4—264no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—1041no—
447C22×C4—1041no—
448C22×C4C2×Dic2612yes—
449C22×C4C2×C4×D1312yes—
450C22×C4#612712yes—
451C22×C4#612712yes—
452C22×C4C2×C22⋊D1312yes—
453C22×C4C2×C22⋊D1312yes—
454C22×C4C2×C22⋊D1312yes—
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1312yes—
457C22×C4C23×D1311yescharacteristic
458M16—268no—
459C2×C8—134no—
460C2×C8—262no—
461C2×C8—262no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—524no—
469C4⋊C4—28no—
470C4⋊C4—22no—
471C4⋊C4—24no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—134no—
475C4⋊C4—264no—
476C4⋊C4—262no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—1042no—
482C4⋊C4—1042no—
483C4⋊C4C2×C22⋊D1314yes—
484C22⋊C4—28no—
485C22⋊C4—24no—
486C22⋊C4—522no—
487C42—28no—
488C42—22no—
489C42—22no—
490C42—522no—
491C13#2087811yescharacteristic, complemented, Sylow
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23#8817812yes—
504C23C4×C22⋊D1312yes—
505C23#8820712yes—
506C23C22×C22⋊D1311yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—22no—
510Q8C2×#610114yes—
511D4—216no—
512D4—22no—
513D4—22no—
514D4—22no—
515D4C2×#610114yes—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—216no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—84no—
530C2×C4—88no—
531C2×C4—264no—
532C2×C4—522no—
533C2×C4—522no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—1044no—
541C2×C4C2×#610114yes—
542C2×C4#8817814yes—
543C2×C4#8817812yes—
544C2×C4C4×C22⋊D1314yes—
545C2×C4C4×C22⋊D1312yes—
546C2×C4#8818314yes—
547C2×C4#8820712yes—
548C2×C4C22×Dic2611yescharacteristic
549C2×C4C22×C4×D1311yescharacteristic
550C2×C4C2×#612711yescharacteristic
551C2×C4C2×#612711yescharacteristic
552C2×C4C22×C22⋊D1311yescharacteristic
553C2×C4C22×C22⋊D1311yescharacteristic
554C8—264no—
555C8—521no—
556C8—521no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22#1171887114yes—
571C22C2×#8817811yescharacteristic
572C22C2×C4×C22⋊D1311yescharacteristic
573C22#1171954011yescharacteristic
574C22#1171954111yescharacteristic
575C22#1171954211yescharacteristic
576C22#1171954311yescharacteristic
577C22C2×#8820711yescharacteristic
578C4—24no—
579C4—42no—
580C4—44no—
581C4—42no—
582C4—524no—
583C4—1041no—
584C4—1041no—
585C4#1171887114yes—
586C4C22×#610111yescharacteristic
587C4C2×#8817811yescharacteristic
588C4C2×C4×C22⋊D1311yescharacteristic
589C4C2×#8818311yescharacteristic
590C2—24no—
591C2—44no—
592C2C2×#1171887111yescharacteristic
593C2#1312366411yescharacteristic
594C2#1312367511yescharacteristic
595C2#1312414011yescharacteristic
596C2#1312415111yescharacteristic
597C2#1312468711yescharacteristic
598C2#1312469811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#520C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC2×#520D13
hypocenterC13#20878
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#11718625C2semidirect
4. #13117452C2semidirect
5. #13115104C2semidirect
6. #13115097C2semidirect
7. #13115090C2semidirect
8. #13115083C2semidirect
9. C2×#11718121C2semidirect
10. #13114533C2semidirect
27. #11718893C4semidirect
85. C2×C4⋊Dic13C2×C4semidirect
94. C2×#6099C2×C4semidirect
103. #88075C2×C4semidirect
106. #88072C2×C4semidirect
117. C13×#41C4⋊C4semidirect
415. #41#6101semidirect
491. C13#20878semidirect

Maximal subgroups

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

subgroupindex
C2×#117186252
C2×#117188932
C2×#117188942
#131174522
#131151042
#131150972
#131150902
#131150832
C2×#117181212
#131145332
C2×C13×#5202
#2087813