Finite Group Databasebeta

← #15917263

Subgroups — #15917263

Order 3328.

1114 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718716C211yesmaximal, characteristic, complemented
3#13123188C211yesmaximal, characteristic, complemented
4#13116029C212yesmaximal, complemented
5#13116015C212yesmaximal
6#13115806C211yesmaximal, characteristic, complemented
7#13115653C211yesmaximal, characteristic, complemented
8#13115097C212yesmaximal, complemented
9#13115090C212yesmaximal, complemented
10#13114598C211yesmaximal, 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
25C2×#88178—21no—
26C2×#88123C2211yescharacteristic
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88072C2212yes—
30C2×#88072C2212yes—
31#11718873—21no—
32#11718873C2212yes—
33C2×C22⋊#1055C2212yes—
34#11718726—24no—
35#11718716—24no—
36C2×#88048C2212yes—
37C2×#88047C2212yes—
38#11718596C2211yescharacteristic
39#11718590—21no—
40#11718589—21no—
41#11718589C2212yes—
42C2×#88043C2211yescharacteristic
43C2×#88043C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
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
54C22×Dic26—21no—
55C13×#126—28no—
56C13×#125—22no—
57C13×#125D414yes—
58C13×#124—22no—
59C13×#124D414yes—
60C13×#123—28no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C13×#121—22no—
64C13×#121—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C4×D4×C13—28no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C13×#117—28no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13—21no—
83C2×C42×C13—22no—
84C2×C42×C13—22no—
85C2×C42×C13D411yescharacteristic
86C2×C42×C13D411yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—22no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2312yes—
94C2×C4⋊Dic13C2312yes—
95#88178—44no—
96C2×#6101—22no—
97C22×#1055C2312yes—
98C22×#1055C2312yes—
99#88123—22no—
100#88123—22no—
101#88075—24no—
102#88075—24no—
103#88072—24no—
104#88072—24no—
105#88071—22no—
106#88071—22no—
107C22⋊#1055—24no—
108#88048—24no—
109#88047—24no—
110#88043—22no—
111#88043—22no—
112#25679—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—24no—
127C22×C4×C13—22no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—41no—
139C22×C4×C13—41no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—22no—
149C22×Dic13—22no—
150C2×Dic26—42no—
151C2×Dic26—42no—
152C2×Dic26—42no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4C2×D412yes—
160C13×C4⋊C4C2×D412yes—
161C13×C22⋊C4—24no—
162C13×C22⋊C4—24no—
163C13×C22⋊C4—24no—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—24no—
166C42×C13—24no—
167C42×C13—22no—
168C42×C13—22no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13C2×D412yes—
172C42×C13C2×D412yes—
173C22⋊Dic13—44no—
174C4⋊Dic13—22no—
175C4⋊Dic13—22no—
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178C4⋊Dic13—42no—
179C4⋊Dic13—42no—
180C4⋊Dic13—42no—
181#6101—44no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#1055#4114yes—
188C2×#529D1311yescharacteristic
189C2×#501—131no—
190C2×#489—131no—
191#2857—131no—
192#2035—132no—
193#2033—132no—
194#1992—131no—
195#1959—131no—
196#1864—132no—
197#1863—132no—
198#1749—131no—
199C23×C13—21no—
200C23×C13—21no—
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×C13AGL(1,ℤ/8)12yes—
213C23×C13C22×D411yescharacteristic
214Q8×C13—24no—
215Q8×C13—42no—
216D4×C13—24no—
217D4×C13—48no—
218D4×C13—42no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—44no—
235C2×C4×C13—44no—
236C2×C4×C13—48no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13#12012yes—
246C2×C4×C13#12012yes—
247C2×C4×C13#13712yes—
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C2×#4112yes—
251C2×C4×C132−1+412yes—
252C2×Dic13—42no—
253C2×Dic13—42no—
254C2×Dic13—42no—
255C2×Dic13—42no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258Dic26—84no—
259#1055—24no—
260#1055—42no—
261C2×C4⋊Q8—131no—
262#529—24no—
263#529—24no—
264C2×#126—21no—
265C2×#125C2×D1311yescharacteristic
266C2×#124C2×D1311yescharacteristic
267C2×#123—21no—
268C2×C22⋊Q8—261no—
269C2×C22⋊Q8C2×D1311yescharacteristic
270C2×#121C2×D1311yescharacteristic
271C2×C4×Q8C2×D1311yescharacteristic
272C2×C4×D4—21no—
273C2×C4×D4C2×D1311yescharacteristic
274C2×#117—21no—
275C22×C42C2×D1311yescharacteristic
276#501—264no—
277#489—264no—
278C2×#107—132no—
279C2×#106—132no—
280C2×#103—132no—
281C2×#103—132no—
282C2×#102—132no—
283C2×#102—132no—
284C2×C22⋊C8—132no—
285C2×#97—131no—
286C2×#97—131no—
287#391—261no—
288#389—132no—
289#389—261no—
290#384—131no—
291#380—132no—
292#380—261no—
293#340—132no—
294#340—132no—
295#336—132no—
296C22×C13—22no—
297C22×C13—22no—
298C22×C13—22no—
299C22×C13—41no—
300C22×C13—41no—
301C22×C13—41no—
302C22×C13—41no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13—42no—
306C22×C13—81no—
307C22×C13—81no—
308C22×C13—81no—
309C22×C13—81no—
310C22×C13C2×#12011yescharacteristic
311C22×C13#53211yescharacteristic
312C22×C13#53611yescharacteristic
313C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C13C2×#13711yescharacteristic
315C22×C13#57511yescharacteristic
316C22×C13#57511yescharacteristic
317C4×C13—22no—
318C4×C13—22no—
319C4×C13—22no—
320C4×C13—41no—
321C4×C13—42no—
322C4×C13—41no—
323C4×C13—42no—
324C4×C13—42no—
325C4×C13#54712yes—
326C4×C13#54812yes—
327Dic13—82no—
328Dic13—82no—
329C22×Q8—261no—
330C22×Q8C22×D1311yescharacteristic
331C22×D4—21no—
332C22×D4C22×D1311yescharacteristic
333C23×C4—21no—
334C23×C4C22⋊D1311yescharacteristic
335C23×C4C22⋊D1311yescharacteristic
336C23×C4C22×D1311yescharacteristic
337C22×C8—132no—
338C22×C8—132no—
339C4⋊Q8—262no—
340C4⋊Q8—262no—
341#126—28no—
342#125—22no—
343#125C22⋊D1314yes—
344#124—22no—
345#124C22⋊D1314yes—
346#123—28no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—524no—
350#121—22no—
351#121—22no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×D4—28no—
355C4×D4—22no—
356C4×D4—22no—
357#117—28no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—132no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—262no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—262no—
376C2×C42—21no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42C22⋊D1311yescharacteristic
380C2×C42C22⋊D1311yescharacteristic
381C2×C42C22×D1311yescharacteristic
382C2×C42C22×D1311yescharacteristic
383#107—264no—
384#106—264no—
385#103—264no—
386#103—264no—
387#102—264no—
388#102—264no—
389C22⋊C8—264no—
390#97—262no—
391#97—262no—
392#95—262no—
393#95—262no—
394C2×C13—42no—
395C2×C13—82no—
396C2×C13#243211yescharacteristic
397C2×C13#300611yescharacteristic
398C2×C13#300711yescharacteristic
399C2×C13#317211yescharacteristic
400C2×C13#318011yescharacteristic
401C2×C13#323811yescharacteristic
402C2×C13#324011yescharacteristic
403C24—21no—
404C24C2×C22⋊D1311yescharacteristic
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—522no—
409C2×Q8—522no—
410C2×Q8—522no—
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—24no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—262no—
436C22×C4—262no—
437C22×C4C2×C22⋊D1311yescharacteristic
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C23×D1311yescharacteristic
443C2×C8—134no—
444C2×C8—262no—
445C2×C8—262no—
446C2×C8—262no—
447C2×C8—262no—
448C2×C8—262no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—262no—
456C4⋊C4—262no—
457C4⋊C4—262no—
458C4⋊C4—262no—
459C4⋊C4—524no—
460C4⋊C4—522no—
461C4⋊C4—522no—
462C4⋊C4—522no—
463C4⋊C4C2×C22⋊D1312yes—
464C4⋊C4C2×C22⋊D1312yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—524no—
471C42—24no—
472C42—22no—
473C42—22no—
474C42—21no—
475C42—21no—
476C42C2×C22⋊D1312yes—
477C42C2×C22⋊D1312yes—
478C13#2567911yescharacteristic, complemented, Sylow
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23#8820312yes—
493C23C22×C22⋊D1311yescharacteristic
494Q8—24no—
495Q8—42no—
496Q8—1044no—
497D4—24no—
498D4—48no—
499D4—42no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—48no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4#8820512yes—
533C2×C4#8820712yes—
534C2×C4#8820712yes—
535C2×C4#41×D1312yes—
536C2×C4#8825712yes—
537C2×C4C22×C22⋊D1311yescharacteristic
538C2×C4C22×C22⋊D1311yescharacteristic
539C8—264no—
540C8—522no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×#8820311yescharacteristic
556C22#1171952711yescharacteristic
557C22#1171952711yescharacteristic
558C22C2×#8820511yescharacteristic
559C22#1171953011yescharacteristic
560C22#1171953711yescharacteristic
561C22C2×#8820711yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—42no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—1042no—
571C4—1042no—
572C4#1171952912yes—
573C4#1171953612yes—
574C2—42no—
575C2—82no—
576C2#1311846011yescharacteristic
577C2#1312408811yescharacteristic
578C2#1312409611yescharacteristic
579C2#1312544311yescharacteristic
580C2#1312553511yescharacteristic
581C2#1312605411yescharacteristic
582C2#1312607211yescharacteristic
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#25679
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×#11718726C2semidirect
2. C2×#11718716C2semidirect
3. #13123188C2semidirect
4. #13116029C2semidirect
6. #13115806C2semidirect
7. #13115653C2semidirect
8. #13115097C2semidirect
9. #13115090C2semidirect
10. #13114598C2semidirect
478. C13#25679semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117187162
#131231882
#131160292
#131160152
#131158062
#131156532
#131150972
#131150902
#131145982
C2×C13×#5292
#2567913