Finite Group Databasebeta

← #15896236

Subgroups — #15896236

Order 3328.

1176 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718704C211yesmaximal, characteristic, complemented
2C2×#11718694C211yesmaximal, characteristic
3C2×#11718589C211yesmaximal, characteristic, complemented
4#13116171C212yesmaximal, complemented
5#13116072C212yesmaximal, complemented
6#13115154C211yesmaximal, characteristic
7#13115144C211yesmaximal, characteristic, complemented
8#13115097C212yesmaximal, complemented
9#13115090C212yesmaximal, complemented
10#13114904C211yesmaximal, characteristic, complemented
11C2×C13×#529C211yesmaximal, characteristic
12C13×#529—24no—
13C13×#529—24no—
14C2×C13×#126—21no—
15C2×C13×#125C2211yescharacteristic
16C2×C13×#124C2211yescharacteristic
17C2×C13×#123—21no—
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×#121C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13—21no—
22C2×C4×D4×C13C2211yescharacteristic
23C2×C13×#117—21no—
24C22×C42×C13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101—21no—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30C2×#88072C2212yes—
31C2×#88072C2212yes—
32C2×#88071—21no—
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35#11718704—24no—
36#11718694—24no—
37C2×#88048C2212yes—
38C2×#88047C2212yes—
39#11718589—21no—
40#11718589—21no—
41#11718589C2212yes—
42#11718589C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718116C2212yes—
46#11718116C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13—21no—
49C22×D4×C13C2311yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×Dic13—21no—
55C23×Dic13—21no—
56C13×#126—28no—
57C13×#125—22no—
58C13×#125—22no—
59C13×#124—22no—
60C13×#124—22no—
61C13×#123—28no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8D414yes—
64C13×#121—22no—
65C13×#121D414yes—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×D4×C13—28no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C13×#117—28no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C42×C13—22no—
84C2×C42×C13—22no—
85C2×C42×C13—21no—
86C2×C42×C13D411yescharacteristic
87C2×C42×C13D411yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C42×C13C2311yescharacteristic
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—24no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13C2312yes—
96C2×C4⋊Dic13C2312yes—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—44no—
100C22×#1055C2312yes—
101C22×#1055C2312yes—
102#88075—24no—
103#88075—24no—
104#88072—24no—
105#88072—24no—
106#88071—22no—
107#88071—22no—
108C22⋊#1055—22no—
109C22⋊#1055—22no—
110#88048—24no—
111#88047—24no—
112#24066—131nomaximal, Sylow
113C24×C13—21no—
114C24×C13C2×D411yescharacteristic
115C2×Q8×C13—21no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13C2×D412yes—
119C2×D4×C13—24no—
120C2×D4×C13—21no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—42no—
124C2×D4×C13—42no—
125C2×D4×C13C2×D412yes—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—24no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—41no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—24no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—42no—
152C22×Dic13—42no—
153C22×Dic13—42no—
154C22×Dic13—42no—
155C22×Dic13—42no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4C2×D412yes—
163C13×C4⋊C4C2×D412yes—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—24no—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—24no—
169C42×C13—24no—
170C42×C13—22no—
171C42×C13—22no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C4⋊Dic13—24no—
177C4⋊Dic13—22no—
178C4⋊Dic13—22no—
179C4⋊Dic13—22no—
180C4⋊Dic13—42no—
181C4⋊Dic13#4114yes—
182#6101—44no—
183#6101—44no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#529D1311yescharacteristic
191C2×#483—131no—
192C2×#480—131no—
193C2×#389—131no—
194#2059—132no—
195#2042—132no—
196#1874—131no—
197#1872—131no—
198#1864—132no—
199#1863—132no—
200#1817—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×C13#13512yes—
214C23×C13AGL(1,ℤ/8)12yes—
215C23×C13C22×D411yescharacteristic
216Q8×C13—24no—
217Q8×C13—42no—
218D4×C13—24no—
219D4×C13—48no—
220D4×C13—42no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—44no—
240C2×C4×C13—48no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—44no—
248C2×C4×C13#12012yes—
249C2×C4×C13#13712yes—
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C2×#4112yes—
253C2×C4×C132−1+412yes—
254C2×Dic13—24no—
255C2×Dic13—48no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—84no—
262#1055—42no—
263#1055—42no—
264#529—24no—
265#529—24no—
266C2×#126—21no—
267C2×#125C2×D1311yescharacteristic
268C2×#124C2×D1311yescharacteristic
269C2×#123—21no—
270C2×C22⋊Q8C2×D1311yescharacteristic
271C2×#121C2×D1311yescharacteristic
272C2×C4×Q8C2×D1311yescharacteristic
273C2×C4×D4—21no—
274C2×C4×D4C2×D1311yescharacteristic
275C2×#117—21no—
276C22×C4⋊C4—131no—
277C22×C4⋊C4—131no—
278C22×C4⋊C4—261no—
279C22×C42C2×D1311yescharacteristic
280#483—264no—
281#480—264no—
282C2×#107—132no—
283C2×#106—132no—
284C2×#103—132no—
285C2×#103—132no—
286C2×#102—132no—
287C2×#102—132no—
288C2×C22⋊C8—131no—
289C2×C22⋊C8—131no—
290#389—132no—
291#389—132no—
292#389—261no—
293#389—261no—
294C2×#95—261no—
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#44914yes—
313C22×C13C2×#12011yescharacteristic
314C22×C13#52511yescharacteristic
315C22×C13#53611yescharacteristic
316C22×C13C2×#13511yescharacteristic
317C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C13C2×#13711yescharacteristic
319C22×C13#57511yescharacteristic
320C4×C13—22no—
321C4×C13—22no—
322C4×C13—42no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—42no—
326C4×C13—41no—
327C4×C13—42no—
328C4×C13#54712yes—
329C4×C13#54712yes—
330Dic13—44no—
331Dic13—82no—
332C22×Q8C22×D1311yescharacteristic
333C22×D4—21no—
334C22×D4C22×D1311yescharacteristic
335C23×C4—21no—
336C23×C4—261no—
337C23×C4—261no—
338C23×C4C22⋊D1311yescharacteristic
339C23×C4C22⋊D1311yescharacteristic
340C23×C4C22×D1311yescharacteristic
341C22×C8—132no—
342C22×C8—132no—
343#126—28no—
344#125—22no—
345#125—22no—
346#124—22no—
347#124—22no—
348#123—28no—
349C22⋊Q8—22no—
350C22⋊Q8C22⋊D1314yes—
351#121—22no—
352#121C22⋊D1314yes—
353C4×Q8—22no—
354C4×Q8—22no—
355C4×D4—28no—
356C4×D4—22no—
357C4×D4—22no—
358#117—28no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—132no—
365C2×C4⋊C4—264no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—261no—
370C2×C4⋊C4—262no—
371C2×C4⋊C4—262no—
372C2×C4⋊C4—524no—
373C2×C4⋊C4C22×D1311yescharacteristic
374C2×C4⋊C4C22×D1311yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C42—21no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42C22⋊D1311yescharacteristic
384C2×C42C22⋊D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386C2×C42C22×D1311yescharacteristic
387#107—264no—
388#106—264no—
389#103—264no—
390#103—264no—
391#102—264no—
392#102—264no—
393C22⋊C8—262no—
394C22⋊C8—262no—
395#95—262no—
396#95—262no—
397C2×C13—24no—
398C2×C13—82no—
399C2×C13#240611yescharacteristic
400C2×C13C2×#44911yescharacteristic
401C2×C13#300711yescharacteristic
402C2×C13#310811yescharacteristic
403C2×C13#311411yescharacteristic
404C2×C13#323211yescharacteristic
405C2×C13#323811yescharacteristic
406C24—21no—
407C24C2×C22⋊D1311yescharacteristic
408C2×Q8—21no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8C2×C22⋊D1312yes—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4C2×C22⋊D1312yes—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—41no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—264no—
434C22×C4—262no—
435C22×C4—262no—
436C22×C4—522no—
437C22×C4—522no—
438C22×C4—522no—
439C22×C4—522no—
440C22×C4—522no—
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1312yes—
447C22×C4C2×C22⋊D1312yes—
448C22×C4C23×D1311yescharacteristic
449C2×C8—262no—
450C2×C8—262no—
451C2×C8—262no—
452C2×C8—262no—
453C2×C8—262no—
454C2×C8—262no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—134no—
462C4⋊C4—264no—
463C4⋊C4—262no—
464C4⋊C4—262no—
465C4⋊C4—262no—
466C4⋊C4—524no—
467C4⋊C4—524no—
468C4⋊C4—522no—
469C4⋊C4C2×C22⋊D1312yes—
470C4⋊C4C2×C22⋊D1312yes—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C42—24no—
477C42—22no—
478C42—22no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C13#2406611yescharacteristic, complemented, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23#8820312yes—
496C23#8820412yes—
497C23#8820712yes—
498C23C22×C22⋊D1311yescharacteristic
499Q8—24no—
500Q8—42no—
501D4—24no—
502D4—48no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—44no—
523C2×C4—48no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—44no—
531C2×C4—264no—
532C2×C4—528no—
533C2×C4—522no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4—1044no—
539C2×C4#8820512yes—
540C2×C4#8820712yes—
541C2×C4#41×D1312yes—
542C2×C4#8825712yes—
543C2×C4C22×C22⋊D1311yescharacteristic
544C2×C4C22×C22⋊D1311yescharacteristic
545C8—522no—
546C8—522no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22#1171889914yes—
561C22C2×#8820311yescharacteristic
562C22C2×#8820411yescharacteristic
563C22#1171952711yescharacteristic
564C22C2×#8820511yescharacteristic
565C22#1171953011yescharacteristic
566C22#1171953311yescharacteristic
567C22C2×#8820711yescharacteristic
568C4—22no—
569C4—22no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—42no—
575C4—42no—
576C4—524no—
577C4—1042no—
578C4#1171952912yes—
579C4#1171952912yes—
580C2—24no—
581C2—82no—
582C2#1311816711yescharacteristic
583C2C2×#1171889911yescharacteristic
584C2#1312409611yescharacteristic
585C2#1312491211yescharacteristic
586C2#1312497011yescharacteristic
587C2#1312600011yescharacteristic
588C2#1312605411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#529C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#529D13
hypocenterC13#24066
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#11718704C2semidirect
3. C2×#11718589C2semidirect
4. #13116171C2semidirect
5. #13116072C2semidirect
7. #13115144C2semidirect
8. #13115097C2semidirect
9. #13115090C2semidirect
10. #13114904C2semidirect
483. C13#24066semidirect

Maximal subgroups

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

subgroupindex
C2×#117187042
C2×#117186942
C2×#117185892
#131161712
#131160722
#131151542
#131151442
#131150972
#131150902
#131149042
C2×C13×#5292
#2406613