Finite Group Databasebeta

← #15784744

Subgroups — #15784744

Order 3328.

1790 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718614C211yesmaximal, characteristic
2C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic13C212yesmaximal
4C2×C22⋊C4×Dic13C211yesmaximal, characteristic
5#13113105C211yesmaximal, characteristic, complemented
6#13113097C212yesmaximal, complemented
7#13113095C211yesmaximal, characteristic, complemented
8#13113083C212yesmaximal
9#95×Dic13C212yesmaximal, complemented
10#95×Dic13C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic
12C24×Dic13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C4⋊Dic13C2211yescharacteristic
19C22×C4×Dic13C2212yes—
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C2×C13×#95C2212yes—
24C2×C13×#95C2211yescharacteristic
25C2×#88071C2212yes—
26C2×#88071C2211yescharacteristic
27C2×#88071C2212yes—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C4⋊C4×Dic13—24no—
36#11718614C418yescomplemented
37C22⋊C4×Dic13—28no—
38C22⋊C4×Dic13—24no—
39C25×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×Dic13—22no—
45C23×Dic13—22no—
46C23×Dic13—24no—
47C23×Dic13—24no—
48C23×Dic13D414yes—
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2311yescharacteristic
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C22⋊C4—24no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—24no—
60C2×C13×C22⋊C4—24no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4C2×C414yes—
63C2×C22⋊Dic13—24no—
64C2×C22⋊Dic13—22no—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13—22no—
67C2×C22⋊Dic13—22no—
68C2×C22⋊Dic13C2×C418yes—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13C2×C414yescomplemented
72C2×C4×Dic13—24no—
73C2×C4×Dic13—24no—
74C2×C4×Dic13—24no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13—24no—
77C2×C4×Dic13—24no—
78C2×C4×Dic13—24no—
79C2×C4×Dic13—24no—
80C2×C4×Dic13—24no—
81C2×C4×Dic13D414yes—
82C13×#95—24no—
83C13×#95—22no—
84#88071—22no—
85#88071—24no—
86#88071—24no—
87#88071—22no—
88#88071—24no—
89#88071—24no—
90#88071—24no—
91#88071—24no—
92#88071C2×C414yescomplemented
93#88071C2×C418yescomplemented
94C4×#397—131nomaximal, Sylow
95C24×C13—21no—
96C24×C13—21no—
97C24×C13—21no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—21no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13C22×C412yes—
104C24×C13C2×D412yes—
105C24×C13#4112yes—
106C24×C13C2411yescharacteristic
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13C22×C412yes—
126C22×C4×C13C22×C412yes—
127C22×C4×C13C2×D412yes—
128C22×C4×C13#4114yes—
129C22×C4×C13#4114yes—
130C22×C4×C13#4112yes—
131C22×Dic13—21no—
132C22×Dic13—22no—
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—21no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—22no—
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—22no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—28no—
156C22×Dic13—216no—
157C22×Dic13—44no—
158C22×Dic13—44no—
159C22×Dic13—48no—
160C22×Dic13C22×C414yes—
161C22×Dic13C22×C414yes—
162C22×Dic13C2×D412yes—
163C22×Dic13C2×D412yes—
164C22×Dic13C2×D412yes—
165C22×Dic13C2×D412yes—
166C22×Dic13#4112yes—
167C22×Dic13#4112yes—
168C22×Dic13#4114yes—
169C22×Dic13#4114yes—
170C13×C4⋊C4—28no—
171C13×C22⋊C4—216no—
172C13×C22⋊C4—28no—
173C22⋊Dic13—28no—
174C22⋊Dic13—216no—
175C4⋊Dic13—28no—
176C4×Dic13—28no—
177C4×Dic13—48no—
178C4×Dic13—48no—
179C4×Dic13—44no—
180C2×#397—131no—
181C2×C4×C4⋊C4—131no—
182C2×C4×C22⋊C4—132no—
183C2×C4×C22⋊C4—131no—
184#1445—131no—
185#1443—132no—
186#1442—131no—
187#1440—132no—
188#1439D1311yescharacteristic
189C4×#95—131no—
190C4×#95—132no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—24no—
194C23×C13—24no—
195C23×C13—22no—
196C23×C13—24no—
197C23×C13—22no—
198C23×C13—24no—
199C23×C13—22no—
200C23×C13—24no—
201C23×C13—24no—
202C23×C13—22no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—41no—
213C23×C13C4×D414yes—
214C23×C13C23×C411yescharacteristic
215C23×C13C22×D411yescharacteristic
216C23×C13C22×D411yescharacteristic
217C23×C13C2×#4111yescharacteristic
218C23×C13C2×#4111yescharacteristic
219C23×C13C2×#4111yescharacteristic
220C23×C13C2×#4112yes—
221C23×C13C2×#4112yes—
222C23×C13C2×#4112yes—
223C23×C13C2×#4112yes—
224C23×C13C2×#4111yescharacteristic
225C2×C4×C13—24no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—24no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—24no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—41no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—41no—
248C2×C4×C13C4×D414yes—
249C2×Dic13—24no—
250C2×Dic13—24no—
251C2×Dic13—24no—
252C2×Dic13—24no—
253C2×Dic13—24no—
254C2×Dic13—24no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—24no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277C2×Dic13—42no—
278C2×Dic13—416no—
279C2×Dic13#12114yes—
280C2×Dic13#12314yes—
281C2×Dic13#12318yes—
282C2×Dic13#12414yes—
283C2×Dic13#12618yes—
284C24×C4—131no—
285C22×C4⋊C4—131no—
286C22×C4⋊C4C2×D1311yescharacteristic
287C22×C22⋊C4—132no—
288C22×C22⋊C4—131no—
289C22×C22⋊C4C2×D1312yes—
290C22×C22⋊C4C2×D1311yescharacteristic
291C22×C42—131no—
292C22×C42—131no—
293C22×C42—132no—
294C22×C42—132no—
295#397—138no—
296C4×C4⋊C4—264no—
297C4×C22⋊C4—264no—
298C4×C22⋊C4—268no—
299C2×#95—131no—
300C2×#95—132no—
301C2×#95—132no—
302C2×#95—132no—
303C2×#95—132no—
304C2×#95—132no—
305C2×#95—132no—
306C2×#95—131no—
307C2×#95—131no—
308C2×#95—132no—
309C2×#95C2×D1312yes—
310C2×#95C2×D1311yescharacteristic
311C22×C13—24no—
312C22×C13—28no—
313C22×C13—44no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—44no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—44no—
320C22×C13—42no—
321C22×C13—42no—
322C22×C13C2×C4×D411yescharacteristic
323C22×C13C2×C4×D411yescharacteristic
324C22×C13C4×#4111yescharacteristic
325C22×C13C4×#4112yes—
326C22×C13C4×#4112yes—
327C22×C13C2×#12111yescharacteristic
328C22×C13C2×#12311yescharacteristic
329C22×C13C2×#12312yes—
330C22×C13#52512yes—
331C22×C13#52511yescharacteristic
332C22×C13#52511yescharacteristic
333C22×C13C2×#12411yescharacteristic
334C22×C13C2×#12612yes—
335C22×C13#52912yes—
336C22×C13#52912yes—
337C22×C13#52912yes—
338C22×C13#52912yes—
339C22×C13#52912yes—
340C22×C13#52911yescharacteristic
341C22×C13#52912yes—
342C22×C13#52912yes—
343C22×C13#53211yescharacteristic
344C22×C13#53211yescharacteristic
345C4×C13—24no—
346C4×C13—44no—
347C4×C13—44no—
348C4×C13—42no—
349Dic13—42no—
350Dic13—42no—
351Dic13—42no—
352Dic13—44no—
353Dic13—44no—
354Dic13#39718yescomplemented
355C25C22×D1311yescharacteristic
356C23×C4—131no—
357C23×C4—134no—
358C23×C4—132no—
359C23×C4—132no—
360C23×C4—131no—
361C23×C4—131no—
362C23×C4—131no—
363C23×C4—262no—
364C23×C4—262no—
365C23×C4—264no—
366C23×C4—264no—
367C23×C4C22×D1311yescharacteristic
368C23×C4C22×D1312yes—
369C23×C4C22×D1312yes—
370C23×C4C22×D1311yescharacteristic
371C2×C4⋊C4—22no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—262no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—138no—
382C2×C22⋊C4—262no—
383C2×C22⋊C4—262no—
384C2×C22⋊C4—264no—
385C2×C22⋊C4—262no—
386C2×C22⋊C4—264no—
387C2×C22⋊C4C4×D1314yes—
388C2×C42—134no—
389C2×C42—264no—
390C2×C42—262no—
391C2×C42—264no—
392C2×C42—264no—
393C2×C42—264no—
394C2×C42—264no—
395C2×C42—264no—
396C2×C42—264no—
397C2×C42—264no—
398#95—24no—
399#95—22no—
400#95—134no—
401#95—138no—
402#95—264no—
403#95—264no—
404#95—264no—
405#95—262no—
406#95—264no—
407#95—262no—
408#95—264no—
409#95—264no—
410C2×C13—44no—
411C2×C13C4×#12111yescharacteristic
412C2×C13C4×#12312yes—
413C2×C13C4×#12311yescharacteristic
414C2×C13C4×#12411yescharacteristic
415C2×C13C4×#12612yes—
416C2×C13C2×#39711yescharacteristic
417C2×C13#239211yescharacteristic
418C2×C13#239512yes—
419C2×C13#239511yescharacteristic
420C2×C13#239811yescharacteristic
421C2×C13#240112yes—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24C2×C4×D1312yes—
431C24D4×D1312yes—
432C24#613112yes—
433C24C23×D1311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—134no—
456C22×C4—134no—
457C22×C4—134no—
458C22×C4—134no—
459C22×C4—132no—
460C22×C4—132no—
461C22×C4—132no—
462C22×C4—268no—
463C22×C4—2616no—
464C22×C4—261no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—261no—
468C22×C4—262no—
469C22×C4—262no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—524no—
489C22×C4—524no—
490C22×C4—528no—
491C22×C4C2×C4×D1312yes—
492C22×C4C2×C4×D1312yes—
493C22×C4D4×D1312yes—
494C22×C4#612914yes—
495C22×C4#612914yes—
496C22×C4#612912yes—
497C4⋊C4—28no—
498C4⋊C4—268no—
499C22⋊C4—216no—
500C22⋊C4—28no—
501C22⋊C4—268no—
502C22⋊C4—2616no—
503C42—268no—
504C42—528no—
505C42—528no—
506C42—524no—
507C13C4×#39711yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—41no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23#8814714yes—
531C23C22×C4×D1311yescharacteristic
532C23C2×D4×D1311yescharacteristic
533C23C2×D4×D1311yescharacteristic
534C23C2×#612911yescharacteristic
535C23C2×#612912yes—
536C23C2×#612912yes—
537C23C2×#613111yescharacteristic
538C23#41×D1311yescharacteristic
539C23#41×D1311yescharacteristic
540C23#41×D1312yes—
541C23#41×D1312yes—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—134no—
566C2×C4—134no—
567C2×C4—138no—
568C2×C4—134no—
569C2×C4—138no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—264no—
573C2×C4—264no—
574C2×C4—264no—
575C2×C4—264no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—264no—
581C2×C4—264no—
582C2×C4—262no—
583C2×C4—5216no—
584C2×C4—521no—
585C2×C4—522no—
586C2×C4—522no—
587C2×C4—522no—
588C2×C4—522no—
589C2×C4—522no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—522no—
600C2×C4#8813514yes—
601C22—24no—
602C22—28no—
603C22—42no—
604C22—42no—
605C22—44no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—44no—
610C22—42no—
611C22—44no—
612C22C2×#8813511yescharacteristic
613C22C2×#8814711yescharacteristic
614C22#1171922711yescharacteristic
615C22C4×#612912yes—
616C22C4×#612912yes—
617C22#1171929112yes—
618C22#1171929111yescharacteristic
619C22#1171930111yescharacteristic
620C22#1171930512yes—
621C22#1171930512yes—
622C22#1171930512yes—
623C22D13×#12111yescharacteristic
624C22#1171932912yes—
625C22#1171932911yescharacteristic
626C22#1171932912yes—
627C22#1171933211yescharacteristic
628C22#1171935412yes—
629C22D13×#12312yes—
630C22D13×#12311yescharacteristic
631C22D13×#12411yescharacteristic
632C22#1171938512yes—
633C22D13×#12612yes—
634C22#1171942111yescharacteristic
635C4—24no—
636C4—44no—
637C4—44no—
638C4—42no—
639C4—138no—
640C4—522no—
641C4—522no—
642C4—524no—
643C4—522no—
644C4—524no—
645C2—44no—
646C2#1311734211yescharacteristic
647C2#1311735512yes—
648C2#1311736111yescharacteristic
649C2#1311738311yescharacteristic
650C2#1311739012yes—
651C2D13×#39711yescharacteristic
652C2#1311807111yescharacteristic
653C2#1311809212yes—
654C2#1311810111yescharacteristic
655C2#1311811811yescharacteristic
656C2#1311813812yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13C4×#397
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic13C2semidirect
5. #13113105C2semidirect
6. #13113097C2semidirect
7. #13113095C2semidirect
9. #95×Dic13C2semidirect
10. #95×Dic13C2semidirect
36. #11718614C4semidirect
71. C2×C4⋊Dic13C2×C4semidirect
92. #88071C2×C4semidirect
93. #88071C2×C4semidirect
354. Dic13#397semidirect
507. C13C4×#397semidirect

Maximal subgroups

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

subgroupindex
C2×#117186142
C2×C4⋊C4×Dic132
C2×C22⋊C4×Dic132
#131131052
#131130972
#131130952
#131130832
#95×Dic132
C13×#14392
C4×#39713