Finite Group Databasebeta

← #15769387

Subgroups — #15769387

Order 3328.

1526 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
1C22×#88074C212yesmaximal
2C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
3C2×#11718118C212yesmaximal, complemented
4#13113059C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic
6C23×D4×C13C2211yescharacteristic
7C24×C4×C13C2211yescharacteristic
8C22×C13×C22⋊C4C412yescomplemented
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic13C2212yes—
11C22×C22⋊Dic13C2212yes—
12C22×C4×Dic13—21no—
13C13×#386—21no—
14C13×#386—22no—
15C13×#386—21no—
16C2×C13×#95C412yescomplemented
17C2×#88074—24no—
18C2×#88074—24no—
19C2×#88074C418yescomplemented
20C4×C22⋊Dic13—24no—
21C2×#88071—21no—
22C2×#88071—22no—
23#11718118—24no—
24C25×C13C2×C411yescharacteristic
25C25×C13C2311yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13—21no—
28C22×D4×C13—22no—
29C22×D4×C13—22no—
30C22×D4×C13—22no—
31C22×D4×C13—22no—
32C22×D4×C13—22no—
33C22×D4×C13C2×C414yes—
34C23×C4×C13—22no—
35C23×C4×C13—22no—
36C23×C4×C13—44no—
37C23×C4×C13C2×C411yescharacteristic
38C23×C4×C13C2×C412yes—
39C23×C4×C13C2×C412yes—
40C23×C4×C13D411yescharacteristic
41C23×C4×C13D412yes—
42C23×C4×C13D411yescharacteristic
43C23×Dic13—22no—
44C23×Dic13—22no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4—22no—
50C2×C13×C22⋊C4—22no—
51C2×C13×C22⋊C4—44no—
52C2×C22⋊Dic13—22no—
53C2×C22⋊Dic13—22no—
54C2×C22⋊Dic13—22no—
55C2×C22⋊Dic13—22no—
56C2×C22⋊Dic13—22no—
57C2×C22⋊Dic13—22no—
58C2×C22⋊Dic13—22no—
59C2×C22⋊Dic13—22no—
60C2×C22⋊Dic13C2×C414yes—
61C2×C22⋊Dic13C2×C414yes—
62C2×C22⋊Dic13D414yes—
63C2×C22⋊Dic13D414yes—
64C2×C4×Dic13—24no—
65C2×C4×Dic13—44no—
66C13×#95—22no—
67C13×#95—22no—
68#88074—216no—
69#88071—24no—
70#88071—44no—
71#10960—131nomaximal, Sylow
72C24×C13—21no—
73C24×C13—21no—
74C24×C13—22no—
75C24×C13—22no—
76C24×C13—42no—
77C24×C13—42no—
78C24×C13—42no—
79C24×C13—42no—
80C24×C13C4212yescomplemented
81C24×C13C22×C412yes—
82C24×C13C22×C411yescharacteristic
83C24×C13C2×D412yes—
84C24×C13C2×D412yes—
85C24×C13C2×D411yescharacteristic
86C24×C13C2×D411yescharacteristic
87C24×C13#4112yes—
88C24×C13#4112yes—
89C24×C13#4112yes—
90C2×D4×C13—24no—
91C2×D4×C13—24no—
92C2×D4×C13—24no—
93C2×D4×C13—24no—
94C2×D4×C13—24no—
95C2×D4×C13—24no—
96C2×D4×C13—41no—
97C2×D4×C13—42no—
98C2×D4×C13—42no—
99C2×D4×C13—42no—
100C2×D4×C13—42no—
101C2×D4×C13—41no—
102C2×D4×C13—42no—
103C2×D4×C13—41no—
104C2×D4×C13—42no—
105C2×D4×C13—41no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13—24no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—24no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—21no—
115C22×C4×C13—24no—
116C22×C4×C13—21no—
117C22×C4×C13—24no—
118C22×C4×C13—24no—
119C22×C4×C13—22no—
120C22×C4×C13—24no—
121C22×C4×C13—42no—
122C22×C4×C13—42no—
123C22×C4×C13—42no—
124C22×C4×C13—48no—
125C22×C4×C13—48no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13C4212yescomplemented
129C22×C4×C13C22⋊C412yes—
130C22×C4×C13C22⋊C412yes—
131C22×Dic13—24no—
132C22×Dic13—24no—
133C22×Dic13—24no—
134C22×Dic13—24no—
135C22×Dic13—44no—
136C22×Dic13—44no—
137C22×Dic13—44no—
138C22×Dic13—44no—
139C22×Dic13—42no—
140C22×Dic13—42no—
141C13×C22⋊C4—44no—
142C13×C22⋊C4—42no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—44no—
146C22⋊Dic13—24no—
147C22⋊Dic13—24no—
148C22⋊Dic13—24no—
149C22⋊Dic13—24no—
150C22⋊Dic13—24no—
151C22⋊Dic13—42no—
152C22⋊Dic13—42no—
153C22⋊Dic13C22⋊C418yescomplemented
154C4×Dic13—48no—
155C22×#99—132no—
156C2×#386D1311yescharacteristic
157C2×C4×C22⋊C4—131no—
158C2×#342—132no—
159C22⋊#95—131no—
160C23×C13—22no—
161C23×C13—22no—
162C23×C13—22no—
163C23×C13—22no—
164C23×C13—22no—
165C23×C13—22no—
166C23×C13—22no—
167C23×C13—24no—
168C23×C13—42no—
169C23×C13—42no—
170C23×C13—44no—
171C23×C13—42no—
172C23×C13—44no—
173C23×C13—42no—
174C23×C13—44no—
175C23×C13—44no—
176C23×C13—44no—
177C23×C13—44no—
178C23×C13—41no—
179C23×C13—42no—
180C23×C13—41no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—82no—
184C23×C13—82no—
185C23×C13—84no—
186C23×C13C2×C4211yescharacteristic
187C23×C13C2×C22⋊C412yes—
188C23×C13C2×C22⋊C411yescharacteristic
189C23×C13#11711yescharacteristic
190C23×C13#11712yes—
191C23×C13C4×D412yes—
192C23×C13C4×D412yes—
193C23×C13C4×D412yes—
194C23×C13C4×D412yes—
195C23×C13C4×D412yes—
196C23×C13C4×D412yes—
197C23×C13#12011yescharacteristic
198C23×C13#12112yes—
199C23×C13#12112yes—
200C23×C13#12112yes—
201C23×C13#12311yescharacteristic
202C23×C13#12312yes—
203C23×C13#12411yescharacteristic
204C23×C13#12412yes—
205C23×C13#12612yes—
206C23×C13#12711yescharacteristic
207D4×C13—44no—
208D4×C13—44no—
209D4×C13—44no—
210D4×C13—44no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—24no—
216C2×C4×C13—22no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—48no—
221C2×C4×C13—48no—
222C2×C4×C13—42no—
223C2×C4×C13—42no—
224C2×C4×C13—41no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—84no—
231C2×C4×C13#9914yescomplemented
232C2×Dic13—28no—
233C2×Dic13—44no—
234C2×Dic13—44no—
235C2×Dic13—48no—
236C2×Dic13—48no—
237C2×Dic13—48no—
238C2×Dic13—44no—
239C2×Dic13—82no—
240C2×Dic13—82no—
241C2×Dic13—84no—
242C23×D4C2×D1311yescharacteristic
243C24×C4C2×D1311yescharacteristic
244C22×C22⋊C4—132no—
245C22×C22⋊C4—132no—
246C22×C22⋊C4Dic1312yescomplemented
247C22×C22⋊C4C2×D1311yescharacteristic
248C22×C42—261no—
249C2×#99—138no—
250C2×#99—264no—
251C2×#99—264no—
252#386—21no—
253#386—22no—
254#386—21no—
255C4×C22⋊C4—264no—
256C2×#95—261no—
257C2×#95—262no—
258C2×#95Dic1312yescomplemented
259#342—264no—
260C22×C13—21no—
261C22×C13—22no—
262C22×C13—21no—
263C22×C13—22no—
264C22×C13—21no—
265C22×C13—22no—
266C22×C13—22no—
267C22×C13—21no—
268C22×C13—24no—
269C22×C13—22no—
270C22×C13—24no—
271C22×C13—22no—
272C22×C13—24no—
273C22×C13—24no—
274C22×C13—22no—
275C22×C13—22no—
276C22×C13—42no—
277C22×C13—42no—
278C22×C13—42no—
279C22×C13—42no—
280C22×C13—42no—
281C22×C13—42no—
282C22×C13—42no—
283C22×C13—42no—
284C22×C13—42no—
285C22×C13—44no—
286C22×C13—84no—
287C22×C13—84no—
288C22×C13—81no—
289C22×C13—81no—
290C22×C13—82no—
291C22×C13C4×C22⋊C412yes—
292C22×C13C4×C22⋊C411yescharacteristic
293C22×C13#38612yes—
294C22×C13#38611yescharacteristic
295C22×C13#38812yes—
296C22×C13#38812yes—
297C22×C13#38812yes—
298C22×C13#39012yes—
299C22×C13#39011yescharacteristic
300C22×C13C2×#9912yes—
301C22×C13#41012yes—
302C4×C13—24no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—82no—
306Dic13—48no—
307Dic13—84no—
308C25C2×Dic1311yescharacteristic
309C25C22×D1311yescharacteristic
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C4×D1314yes—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—44no—
321C23×C4—262no—
322C23×C4—262no—
323C23×C4C2×Dic1311yescharacteristic
324C23×C4C2×Dic1312yes—
325C23×C4C2×Dic1312yes—
326C23×C4C22⋊D1311yescharacteristic
327C23×C4C22⋊D1312yes—
328C23×C4C22⋊D1311yescharacteristic
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—134no—
337C2×C22⋊C4—134no—
338C2×C22⋊C4—134no—
339C2×C22⋊C4—134no—
340C2×C22⋊C4—262no—
341C2×C22⋊C4—262no—
342C2×C22⋊C4—262no—
343C2×C22⋊C4—262no—
344C2×C22⋊C4—262no—
345C2×C22⋊C4—262no—
346C2×C22⋊C4—262no—
347C2×C22⋊C4—262no—
348C2×C42—264no—
349C2×C42—524no—
350#99—2616no—
351#95—22no—
352#95—22no—
353#95—264no—
354#95—524no—
355C2×C13—22no—
356C2×C13—22no—
357C2×C13—22no—
358C2×C13—22no—
359C2×C13—22no—
360C2×C13—22no—
361C2×C13—82no—
362C2×C13#143711yescharacteristic
363C2×C13C4×#9912yes—
364C2×C13#189811yescharacteristic
365C2×C13#189911yescharacteristic
366C2×C13#196412yes—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—42no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24C4×Dic1312yescomplemented
376C24C2×C4×D1312yes—
377C24#612712yes—
378C24D4×D1312yes—
379C24D4×D1312yes—
380C24#612912yes—
381C24#612912yes—
382C24C22×Dic1311yescharacteristic
383C24C2×C22⋊D1311yescharacteristic
384C24C2×C22⋊D1311yescharacteristic
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—41no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—48no—
420C22×C4—48no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—264no—
424C22×C4—264no—
425C22×C4—264no—
426C22×C4—264no—
427C22×C4—524no—
428C22×C4—524no—
429C22×C4—524no—
430C22×C4—524no—
431C22×C4—522no—
432C22×C4—522no—
433C22×C4C4×Dic1312yescomplemented
434C22×C4C22⋊Dic1312yes—
435C22×C4C22⋊Dic1312yes—
436C22⋊C4—44no—
437C22⋊C4—41no—
438C22⋊C4—42no—
439C22⋊C4—41no—
440C22⋊C4—44no—
441C22⋊C4—138no—
442C22⋊C4—264no—
443C22⋊C4—264no—
444C22⋊C4—264no—
445C22⋊C4—264no—
446C22⋊C4—264no—
447C22⋊C4—522no—
448C22⋊C4—522no—
449C42—528no—
450C13#1096011yescharacteristic, complemented, Sylow
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—44no—
466C23—42no—
467C23—44no—
468C23—44no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—84no—
475C23—82no—
476C23—82no—
477C23#8813112yes—
478C23#8813312yes—
479C23C22⋊C4×D1312yes—
480C23#8813512yes—
481C23#8813512yes—
482C23#8813712yes—
483C23#8813812yes—
484C23#8813912yes—
485C23C2×C4×Dic1311yescharacteristic
486C23#8818011yescharacteristic
487C23C4×C22⋊D1312yes—
488C23C4×C22⋊D1312yes—
489C23D4×Dic1312yes—
490C23D4×Dic1312yes—
491C23#8818911yescharacteristic
492C23#8819011yescharacteristic
493C23#8819111yescharacteristic
494C23#8819212yes—
495C23#8819312yes—
496C23#8819411yescharacteristic
497C23C2×C22⋊Dic1311yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—48no—
512C2×C4—48no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—84no—
522C2×C4—268no—
523C2×C4—524no—
524C2×C4—528no—
525C2×C4—528no—
526C2×C4—524no—
527C2×C4—528no—
528C2×C4—524no—
529C2×C4—1044no—
530C2×C4—1042no—
531C2×C4—1042no—
532C2×C4#8807414yescomplemented
533C22—24no—
534C22—24no—
535C22—22no—
536C22—22no—
537C22—24no—
538C22—24no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—21no—
543C22—22no—
544C22—22no—
545C22—21no—
546C22—22no—
547C22—22no—
548C22—21no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—42no—
559C22—84no—
560C22—84no—
561C22—82no—
562C22—81no—
563C22—81no—
564C22C22⋊C4×Dic1312yes—
565C22#1171860512yes—
566C22#1171860612yes—
567C22#1171861212yes—
568C22#1171861712yes—
569C22#1171861812yes—
570C22C4×C22⋊Dic1311yescharacteristic
571C22C2×#8807412yes—
572C22#1171888111yescharacteristic
573C22#1171888211yescharacteristic
574C22#1171890112yes—
575C4—24no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—528no—
580C4—1044no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2#1311307311yescharacteristic
589C2C4×#8807412yes—
590C2#1311529011yescharacteristic
591C2#1311529511yescharacteristic
592C2#1311567312yes—
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC23×C13C2×C42
FrattiniC25C22×D13
FittingC2×C13×#386C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D4×C13C22
cosocleC25×C13C23
hypercenterC2×#386D13
hypocenterC13#10960
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic13C2semidirect
3. C2×#11718118C2semidirect
4. #13113059C2semidirect
8. C22×C13×C22⋊C4C4semidirect
16. C2×C13×#95C4semidirect
19. C2×#88074C4semidirect
80. C24×C13C42semidirect
128. C22×C4×C13C42semidirect
153. C22⋊Dic13C22⋊C4semidirect
231. C2×C4×C13#99semidirect
246. C22×C22⋊C4Dic13semidirect
258. C2×#95Dic13semidirect
375. C24C4×Dic13semidirect
433. C22×C4C4×Dic13semidirect
450. C13#10960semidirect
532. C2×C4#88074semidirect

Maximal subgroups

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

subgroupindex
C22×#880742
C2×C4×C22⋊Dic132
C2×#117181182
#131130592
C2×C13×#3862
#1096013