Finite Group Databasebeta

← #16796967

Subgroups — #16796967

Order 3328.

1834 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊#99C212yesmaximal
2#13131272C212yesmaximal, complemented
3#13130583C212yesmaximal, complemented
4C4×#88107C212yesmaximal, complemented
5#13130581C212yesmaximal, complemented
6C4×#88119C212yesmaximal, complemented
7C2×#11718289C212yesmaximal, complemented
8C2×#11719250C211yesmaximal, characteristic
9C22×D4×D13C2211yescharacteristic
10C22×C22⋊#261C2214yes—
11C2×C4×D4×C13C411yescharacteristic, complemented
12C2×D4×Dic13C411yescharacteristic, complemented
13C2×C4×C22⋊D13C411yescharacteristic, complemented
14C2×C4×C22⋊D13C2211yescharacteristic
15C22×#6103C411yescharacteristic, complemented
16C22×#6103C2211yescharacteristic
17#11719250—28no—
18C2×#88147C2211yescharacteristic
19C2×#88146C411yescharacteristic, complemented
20C2×#88135C411yescharacteristic, complemented
21C2×#88135C2211yescharacteristic
22C2×C22⋊C4×D13C411yescharacteristic, complemented
23C2×C22⋊C4×D13C2211yescharacteristic
24C2×C4×D52C2211yescharacteristic
25C2×#88126C411yescharacteristic, complemented
26C2×#88119C2214yes—
27D13⋊#99C4116yescomplemented
28C4×C22⋊#261C2214yescomplemented
29C4×C22⋊#261C2214yescomplemented
30C2×#88107C2214yes—
31C22⋊C4×#261—28no—
32#11718289C2214yescomplemented
33#11718289C2214yescomplemented
34C24×D13C2×C411yescharacteristic
35C24×D13C2311yescharacteristic
36C23×#261—24no—
37C22×D4×C13C2×C411yescharacteristic
38C23×C4×C13C2×C411yescharacteristic
39C23×C4×C13C2×C411yescharacteristic, complemented
40C22×C22⋊D13C2×C411yescharacteristic
41C22×C22⋊D13C2311yescharacteristic
42C23×Dic13C2×C411yescharacteristic
43C23×Dic13C2×C411yescharacteristic, complemented
44C2×D4×D13—24no—
45C2×D4×D13—24no—
46C2×D4×D13C2×C418yes—
47C22×D52C2311yescharacteristic
48C22×C4×D13C2×C411yescharacteristic
49C22×C4×D13C2×C411yescharacteristic, complemented
50C22×C4×D13C2×C411yescharacteristic, complemented
51C22×C4×D13C2311yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C2×C22⋊#261—24no—
54C2×C22⋊#261—28no—
55C2×C22⋊#261C2×C4116yescomplemented
56C2×C22⋊#261C2318yes—
57C2×C4×#261—24no—
58C2×C4×#261—24no—
59C4×D4×C13—24no—
60C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
61C2×C13×C22⋊C4C2×C411yescharacteristic
62C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
63C2×C42×C13C2×C411yescharacteristic, complemented
64C2×C22⋊Dic13C2×C411yescharacteristic
65C2×C22⋊Dic13C2×C411yescharacteristic, complemented
66D4×Dic13—24no—
67C4×C22⋊D13—24no—
68C4×C22⋊D13—24no—
69C2×#6103—24no—
70C2×#6103—24no—
71C2×#6103C2×C411yescharacteristic
72C2×#6103C2×C411yescharacteristic
73C2×#6103C2×C411yescharacteristic
74C2×#6103C2×C411yescharacteristic
75C2×#6103C2×C411yescharacteristic, complemented
76C2×#6103C2×C411yescharacteristic, complemented
77C2×#6103C2311yescharacteristic
78C2×#6103C2311yescharacteristic
79C2×C4⋊Dic13C2×C411yescharacteristic, complemented
80C2×#6101C2×C411yescharacteristic, complemented
81C2×#6101C2×C411yescharacteristic, complemented
82C2×C4×Dic13C2×C411yescharacteristic, complemented
83C2×C4×Dic13C2×C411yescharacteristic, complemented
84C2×C4×Dic13C2×C411yescharacteristic, complemented
85#88147—24no—
86#88146—24no—
87#88135—24no—
88#88135—24no—
89C22⋊C4×D13—24no—
90C22⋊C4×D13D418yes—
91C4×D52—24no—
92#88126—24no—
93#88119C2×C4116yescomplemented
94(C2×#261)⋊C4—24no—
95(C2×#261)⋊C4—24no—
96#88107C2×C4116yescomplemented
97#20392—131nomaximal, Sylow
98C24×C13C22×C411yescharacteristic
99C24×C13C22×C411yescharacteristic
100C23×D13—22no—
101C23×D13—22no—
102C23×D13—81no—
103C23×D13—81no—
104C23×D13—81no—
105C23×D13—81no—
106C23×D13C4214yescomplemented
107C23×D13C22×C411yescharacteristic
108C23×D13C22×C411yescharacteristic
109C23×D13C22×C414yes—
110C23×D13C2×D414yes—
111C23×D13#4114yes—
112C23×D13C2411yescharacteristic
113C22×#261—28no—
114C22×#261—216no—
115C22×#261—84no—
116C22×#261—84no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13C4214yescomplemented
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—81no—
123C22×C4×C13—81no—
124C22×C4×C13C22×C411yescharacteristic
125C22×C4×C13C22×C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C2×C22⋊D13—22no—
130C2×C22⋊D13—22no—
131C2×C22⋊D13—22no—
132C2×C22⋊D13—22no—
133C2×C22⋊D13C4214yescomplemented
134C2×C22⋊D13C22×C414yes—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—81no—
138C22×Dic13—81no—
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C22×Dic13C22×C411yescharacteristic
144D4×D13—216no—
145D4×D13—216no—
146C2×D52—22no—
147C2×D52—22no—
148C2×D52C22×C414yes—
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—22no—
153C2×C4×D13—81no—
154C2×C4×D13—81no—
155C2×C4×D13—81no—
156C2×C4×D13—81no—
157C2×C4×D13C4214yescomplemented
158C2×C4×D13C2×D414yes—
159C2×C4×D13C2×D414yes—
160C22⋊#261—216no—
161C22⋊#261—28no—
162C22⋊#261C22×C4116yes—
163C4×#261—84no—
164C4×#261—84no—
165C13×C4⋊C4—22no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4C22⋊C414yes—
168C42×C13—22no—
169C22⋊Dic13—22no—
170C22⋊Dic13C22⋊C414yes—
171#6103—22no—
172#6103—22no—
173#6103—22no—
174#6103—22no—
175#6103—22no—
176#6103—22no—
177#6103C22⋊C414yes—
178#6103C22⋊C414yes—
179C4⋊Dic13—22no—
180#6101—22no—
181#6101—22no—
182C4×Dic13—22no—
183C4×Dic13—22no—
184C4×Dic13—22no—
185C2×#518—131no—
186C22×#99—132no—
187#2273—132no—
188C4×#99—132no—
189C4×#99—132no—
190C4×#99—132no—
191C4×#99—132no—
192C2×#342—132no—
193C23×C13—21no—
194C23×C13—21no—
195C23×C13—41no—
196C23×C13—41no—
197C23×C13—41no—
198C23×C13—41no—
199C23×C13C2×C4212yes—
200C23×C13C2×C4212yes—
201C23×C13C2×C22⋊C412yes—
202C23×C13#11712yes—
203C23×C13C23×C411yescharacteristic
204C22×D13—21no—
205C22×D13—21no—
206C22×D13—28no—
207C22×D13—41no—
208C22×D13—41no—
209C22×D13—44no—
210C22×D13—44no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—41no—
215C22×D13—82no—
216C22×D13—82no—
217C22×D13—84no—
218C22×D13—84no—
219C22×D13—84no—
220C22×D13—84no—
221C22×D13C2×C4212yes—
222C22×D13C2×C4212yes—
223C22×D13C2×C22⋊C412yes—
224C22×D13#11712yes—
225C22×D13C4×D418yes—
226C22×D13C4×D418yes—
227C22×D13C23×C412yes—
228C22×D13C22×D412yes—
229C22×D13C2×#4112yes—
230C2×#261—216no—
231C2×#261—48no—
232C2×#261—48no—
233C2×#261—816no—
234D4×C13—28no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—82no—
244C2×C4×C13—82no—
245C2×C4×C13C2×C4212yes—
246C2×C4×C13C2×C22⋊C412yes—
247C2×C4×C13C2×C22⋊C412yes—
248C22⋊D13—28no—
249C22⋊D13—28no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—82no—
259C2×Dic13—82no—
260C2×Dic13C2×C4212yes—
261C2×Dic13C2×C22⋊C412yes—
262C2×Dic13C2×C22⋊C412yes—
263D52—28no—
264C4×D13—28no—
265C4×D13—44no—
266C4×D13—44no—
267C4×D13—82no—
268C4×D13—82no—
269C23×D4—131no—
270#518—268no—
271C2×C4×D4—131no—
272C2×C4×D4—131no—
273C2×C4×D4—131no—
274C2×C4×D4—131no—
275C2×C4×D4—131no—
276C2×C4×D4—131no—
277C2×C4×D4—131no—
278C2×C4×D4#26111yescharacteristic, complemented
279C2×#117—131no—
280C2×#117—131no—
281C22×C22⋊C4—131no—
282C22×C22⋊C4—134no—
283C22×C22⋊C4—131no—
284C22×C22⋊C4—131no—
285C22×C22⋊C4—131no—
286C2×#99—134no—
287C2×#99—134no—
288C2×#99—1316no—
289C4×C22⋊C4—134no—
290C4×C22⋊C4—134no—
291C4×C22⋊C4—268no—
292#342—134no—
293#342—134no—
294C22×C13—21no—
295C22×C13—21no—
296C22×C13—22no—
297C22×C13—22no—
298C22×C13—22no—
299C22×C13—42no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13C4×C22⋊C414yes—
306C22×C13C22×C4211yescharacteristic
307C22×C13C22×C22⋊C411yescharacteristic
308C22×C13C2×#11711yescharacteristic
309C2×D13—22no—
310C2×D13—22no—
311C2×D13—22no—
312C2×D13—22no—
313C2×D13—22no—
314C2×D13—48no—
315C2×D13—42no—
316C2×D13—42no—
317C2×D13—48no—
318C2×D13—42no—
319C2×D13—42no—
320C2×D13—42no—
321C2×D13—41no—
322C2×D13—41no—
323C2×D13—42no—
324C2×D13—88no—
325C2×D13C4×C22⋊C414yes—
326C2×D13C2×C4×D414yes—
327#261—416no—
328C4×C13—22no—
329C4×C13—22no—
330C4×C13—22no—
331C4×C13—41no—
332C4×C13—41no—
333Dic13—22no—
334Dic13—22no—
335Dic13—22no—
336Dic13—41no—
337Dic13—41no—
338C25—131no—
339C25—131no—
340C22×D4—131no—
341C22×D4—131no—
342C22×D4—138no—
343C22×D4—131no—
344C22×D4—264no—
345C22×D4—264no—
346C22×D4C2×#26111yescharacteristic
347C23×C4—131no—
348C23×C4—131no—
349C23×C4—131no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—264no—
355C23×C4C2×#26111yescharacteristic
356C23×C4C2×#26111yescharacteristic, complemented
357C4×D4—24no—
358C4×D4—264no—
359C4×D4—264no—
360C4×D4—264no—
361C4×D4—264no—
362C4×D4—264no—
363C4×D4—264no—
364C4×D4—264no—
365#117—264no—
366#117—264no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4C2×#26111yescharacteristic, complemented
371C2×C22⋊C4—131no—
372C2×C22⋊C4—131no—
373C2×C22⋊C4—131no—
374C2×C22⋊C4—138no—
375C2×C22⋊C4—138no—
376C2×C22⋊C4—1316no—
377C2×C22⋊C4—131no—
378C2×C22⋊C4—131no—
379C2×C22⋊C4—131no—
380C2×C22⋊C4—131no—
381C2×C22⋊C4—131no—
382C2×C22⋊C4—131no—
383C2×C22⋊C4—131no—
384C2×C22⋊C4—264no—
385C2×C22⋊C4—264no—
386C2×C22⋊C4—264no—
387C2×C22⋊C4—264no—
388C2×C22⋊C4—268no—
389C2×C22⋊C4C2×#26111yescharacteristic
390C2×C22⋊C4C2×#26111yescharacteristic, complemented
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—264no—
395C2×C42—264no—
396C2×C42C2×#26111yescharacteristic, complemented
397#99—1316no—
398#99—1316no—
399#95—264no—
400#95—264no—
401C2×C13—21no—
402C2×C13—21no—
403C2×C13—24no—
404C2×C13—42no—
405C2×C13C2×C4×C22⋊C411yescharacteristic
406C2×C13#288311yescharacteristic
407C2×C13#288311yescharacteristic
408D13—24no—
409D13—24no—
410D13—42no—
411C24—134no—
412C24—131no—
413C24—131no—
414C24—134no—
415C24—134no—
416C24—131no—
417C24—134no—
418C24—262no—
419C24—262no—
420C24—1041no—
421C24—1041no—
422C24—1041no—
423C24—1041no—
424C24C22×#26111yescharacteristic
425C24C22×#26111yescharacteristic
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—134no—
429C2×D4—134no—
430C2×D4—134no—
431C2×D4—262no—
432C2×D4—262no—
433C2×D4—2616no—
434C2×D4—2616no—
435C2×D4—262no—
436C2×D4—262no—
437C2×D4—262no—
438C2×D4—262no—
439C2×D4C4×#26114yescomplemented
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—134no—
448C22×C4—134no—
449C22×C4—134no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—262no—
453C22×C4—262no—
454C22×C4—262no—
455C22×C4—262no—
456C22×C4—268no—
457C22×C4—2616no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—1041no—
461C22×C4—1041no—
462C22×C4—1041no—
463C22×C4—1041no—
464C22×C4—1044no—
465C22×C4—1044no—
466C22×C4—1041no—
467C22×C4—1041no—
468C22×C4C22×#26111yescharacteristic
469C22×C4C22×#26111yescharacteristic
470C22×C4C22×#26111yescharacteristic
471C22×C4C22×#26111yescharacteristic
472C22×C4C22×#26111yescharacteristic
473C4⋊C4—22no—
474C4⋊C4—262no—
475C4⋊C4—262no—
476C4⋊C4—262no—
477C22⋊C4—22no—
478C22⋊C4—134no—
479C22⋊C4—134no—
480C22⋊C4—134no—
481C22⋊C4—1316no—
482C22⋊C4—262no—
483C22⋊C4—262no—
484C22⋊C4—262no—
485C22⋊C4—262no—
486C22⋊C4—262no—
487C22⋊C4—262no—
488C22⋊C4—268no—
489C22⋊C4—2616no—
490C22⋊C4—262no—
491C22⋊C4C22⋊#26114yes—
492C42—22no—
493C42—262no—
494C42—262no—
495C42—262no—
496C42—1044no—
497C42—1044no—
498C13#2039211yescharacteristic, complemented, Sylow
499C23—21no—
500C23—21no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—132no—
506C23—132no—
507C23—132no—
508C23—132no—
509C23—132no—
510C23—132no—
511C23—138no—
512C23—138no—
513C23—132no—
514C23—268no—
515C23—261no—
516C23—261no—
517C23—521no—
518C23—524no—
519C23—521no—
520C23—524no—
521C23—521no—
522C23—521no—
523C23—521no—
524C23—521no—
525C23—1042no—
526C23—1042no—
527C23—1044no—
528C23—1044no—
529C23—1044no—
530C23—1044no—
531C23C2×C4×#26112yes—
532C23C2×C4×#26112yes—
533C23#8823712yes—
534C23C2×C22⋊#26112yes—
535C23C23×#26111yescharacteristic
536D4—28no—
537D4—268no—
538D4—268no—
539D4—268no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—132no—
551C2×C4—132no—
552C2×C4—132no—
553C2×C4—268no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—2616no—
557C2×C4—261no—
558C2×C4—261no—
559C2×C4—524no—
560C2×C4—524no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—528no—
564C2×C4—528no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—1042no—
568C2×C4—1042no—
569C2×C4—1042no—
570C2×C4—1042no—
571C2×C4—10416no—
572C2×C4C2×C4×#26112yes—
573C2×C4C2×C22⋊#26112yes—
574C2×C4C2×C22⋊#26112yes—
575C22—21no—
576C22—22no—
577C22—21no—
578C22—22no—
579C22—22no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—41no—
586C22—134no—
587C22—134no—
588C22—262no—
589C22—262no—
590C22—262no—
591C22—262no—
592C22—262no—
593C22—528no—
594C22—522no—
595C22—522no—
596C22—528no—
597C22—522no—
598C22—522no—
599C22—522no—
600C22—522no—
601C22—521no—
602C22—521no—
603C22—1048no—
604C22C4×C22⋊#26114yes—
605C22C22×C4×#26111yescharacteristic
606C22C2×#8823711yescharacteristic
607C22C22×C22⋊#26111yescharacteristic
608C4—22no—
609C4—22no—
610C4—22no—
611C4—41no—
612C4—41no—
613C4—262no—
614C4—262no—
615C4—262no—
616C4—5216no—
617C4—521no—
618C4—521no—
619C2—21no—
620C2—21no—
621C2—24no—
622C2—42no—
623C2—264no—
624C2—264no—
625C2—522no—
626C2C2×C4×C22⋊#26111yescharacteristic
627C2#1313143511yescharacteristic
628C2#1313143611yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC2×C4×D4×C13C4
socleC22×C13C22×C22⋊C4
prime radicalC22×D4×D13C22
cosocleC23×D13C24
hypercenterC2×C4×D4#261
hypocenterC13#20392
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #13131272C2semidirect
3. #13130583C2semidirect
4. C4×#88107C2semidirect
5. #13130581C2semidirect
6. C4×#88119C2semidirect
7. C2×#11718289C2semidirect
11. C2×C4×D4×C13C4semidirect
12. C2×D4×Dic13C4semidirect
13. C2×C4×C22⋊D13C4semidirect
15. C22×#6103C4semidirect
19. C2×#88146C4semidirect
20. C2×#88135C4semidirect
22. C2×C22⋊C4×D13C4semidirect
25. C2×#88126C4semidirect
27. D13⋊#99C4semidirect
28. C4×C22⋊#261C22semidirect
29. C4×C22⋊#261C22semidirect
32. #11718289C22semidirect
33. #11718289C22semidirect
39. C23×C4×C13C2×C4semidirect
43. C23×Dic13C2×C4semidirect
49. C22×C4×D13C2×C4semidirect
50. C22×C4×D13C2×C4semidirect
55. C2×C22⋊#261C2×C4semidirect
60. C2×C13×C4⋊C4C2×C4semidirect
62. C2×C13×C22⋊C4C2×C4semidirect
63. C2×C42×C13C2×C4semidirect
65. C2×C22⋊Dic13C2×C4semidirect
75. C2×#6103C2×C4semidirect
76. C2×#6103C2×C4semidirect
79. C2×C4⋊Dic13C2×C4semidirect
80. C2×#6101C2×C4semidirect
81. C2×#6101C2×C4semidirect
82. C2×C4×Dic13C2×C4semidirect
83. C2×C4×Dic13C2×C4semidirect
84. C2×C4×Dic13C2×C4semidirect
93. #88119C2×C4semidirect
96. #88107C2×C4semidirect
106. C23×D13C42semidirect
119. C2×D4×C13C42semidirect
133. C2×C22⋊D13C42semidirect
157. C2×C4×D13C42semidirect
278. C2×C4×D4#261semidirect
356. C23×C4C2×#261semidirect
370. C2×C4⋊C4C2×#261semidirect
390. C2×C22⋊C4C2×#261semidirect
396. C2×C42C2×#261semidirect
439. C2×D4C4×#261semidirect
498. C13#20392semidirect

Maximal subgroups

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

subgroupindex
C2×D13⋊#992
#131312722
#131305832
C4×#881072
#131305812
C4×#881192
C2×#117182892
C2×#117192502
#2039213