Finite Group Databasebeta

← #15770751

Subgroups — #15770751

Order 3328.

866 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718627C211yesmaximal, characteristic
2C2×#11718627C211yesmaximal, characteristic
3C2×#11718771C211yesmaximal, characteristic
4C2×#11718122C211yesmaximal, characteristic, complemented
5C2×#11718122C211yesmaximal, characteristic, complemented
6C2×#11718144C211yesmaximal, characteristic, complemented
7C2×C13×#340C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×#6099C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15#11718771—22no—
16#11718771—22no—
17C2×#88060—22no—
18C2×#88050—21no—
19C2×#88050—21no—
20#11718627—22no—
21#11718627—22no—
22#11718627—22no—
23#11718627C414yescomplemented
24C2×#88049—21no—
25C2×#88049—21no—
26C13×#340—22no—
27#11718144—22no—
28#11718122—22no—
29#11718122—22no—
30C23×C4×C13—21no—
31C23×C4×C13—21no—
32C23×C4×C13C2311yescharacteristic
33C22×C22⋊D13—21no—
34C2×#6127—21no—
35C2×#6127—21no—
36C2×#6127—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127C2×C412yes—
45C2×#6127D412yes—
46C22×D52D411yescharacteristic
47C22×C4×D13—21no—
48C22×Dic26D411yescharacteristic
49C22×C8×C13—21no—
50C22×C8×C13—21no—
51C22×C8×C13—21no—
52C22×C8×C13—21no—
53C22×C8×C13—21no—
54C22×C8×C13—21no—
55C22×C8×C13D412yes—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4C2×C412yes—
67C2×C13×C4⋊C4D412yes—
68C2×#6099—21no—
69C2×#6099—21no—
70C2×#6099—21no—
71C2×#6099—21no—
72C2×#6099—21no—
73C2×#6099—21no—
74C2×#6099—21no—
75C2×#6099—21no—
76C2×#6099—21no—
77C2×#6099—21no—
78C2×#6099—21no—
79C2×#6099—21no—
80C2×#6099—21no—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099C2×C412yes—
84C2×#6099D412yes—
85C2×#6099D412yes—
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055—21no—
89#88060—28no—
90#88050—24no—
91#88050—24no—
92#88049—24no—
93#88049—24no—
94#11192—131nomaximal, Sylow
95C24×C13#4111yescharacteristic
96C23×D13—21no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—81no—
104C22×C4×C13—81no—
105C22×C4×C13—81no—
106C22×C4×C13—81no—
107C22×C4×C13C22×C411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13#4111yescharacteristic
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4111yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C22×C4×C13#4111yescharacteristic
120C22×C4×C13#4111yescharacteristic
121C2×C22⋊D13—22no—
122C2×C22⋊D13—22no—
123C2×C22⋊D13—41no—
124C2×C22⋊D13—41no—
125C2×C22⋊D13—41no—
126C2×C22⋊D13—41no—
127C22×Dic13—21no—
128#6127—22no—
129#6127—22no—
130#6127—22no—
131#6127—22no—
132#6127—22no—
133#6127—22no—
134#6127—22no—
135#6127—22no—
136#6127—41no—
137#6127—41no—
138#6127—41no—
139#6127—41no—
140#6127—41no—
141#6127—41no—
142#6127—41no—
143#6127—41no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52—21no—
148C2×D52—21no—
149C2×D52C22⋊C412yes—
150C2×C4×D13—22no—
151C2×C4×D13—22no—
152C2×C4×D13—41no—
153C2×C4×D13—41no—
154C2×C4×D13—41no—
155C2×C4×D13—41no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26C22⋊C412yes—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C2×C8×C13—41no—
166C2×C8×C13—41no—
167C2×C8×C13—41no—
168C2×C8×C13—41no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—41no—
174C13×C4⋊C4—41no—
175C13×C4⋊C4—41no—
176C13×C4⋊C4—41no—
177#6099—22no—
178#6099—22no—
179#6099—22no—
180#6099—22no—
181#6099—22no—
182#6099—22no—
183#6099—41no—
184#6099—41no—
185#6099—41no—
186#6099—41no—
187#6099—41no—
188#6099—41no—
189C2×#1055—22no—
190C2×#1055—22no—
191C2×#1055—22no—
192C2×#1055—41no—
193C2×#1055—41no—
194C2×#1055—41no—
195C2×#1055—41no—
196C2×#1055—41no—
197C2×#1055—41no—
198C2×#417—131no—
199C2×#417—131no—
200C2×#408—131no—
201C2×#343—131no—
202C2×#343—131no—
203C2×#341—131no—
204C2×#340D1311yescharacteristic, complemented
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—21no—
208C23×C13—21no—
209C23×C13C4×D411yescharacteristic
210C23×C13#12111yescharacteristic
211C23×C13#12311yescharacteristic
212C23×C13#12311yescharacteristic
213C23×C13#12411yescharacteristic
214C23×C13#12611yescharacteristic
215C23×C13#12611yescharacteristic
216C22×D13—22no—
217C22×D13—41no—
218C22×D13—41no—
219C22×D13—41no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C2×C4×C13—42no—
224C2×C4×C13—42no—
225C2×C4×C13—82no—
226C2×C4×C13—82no—
227C2×C4×C13—81no—
228C2×C4×C13—81no—
229C2×C4×C13—81no—
230C2×C4×C13—81no—
231C2×C4×C13—82no—
232C2×C4×C13—82no—
233C2×C4×C13C2×C22⋊C411yescharacteristic
234C2×C4×C13#11711yescharacteristic
235C2×C4×C13#11711yescharacteristic
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C4×D411yescharacteristic
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13#12011yescharacteristic
240C2×C4×C13#12011yescharacteristic
241C2×C4×C13#12111yescharacteristic
242C2×C4×C13#12111yescharacteristic
243C2×C4×C13#12111yescharacteristic
244C2×C4×C13#12111yescharacteristic
245C2×C4×C13#12111yescharacteristic
246C2×C4×C13#12111yescharacteristic
247C2×C4×C13#12111yescharacteristic
248C2×C4×C13#12311yescharacteristic
249C2×C4×C13#12311yescharacteristic
250C2×C4×C13#12311yescharacteristic
251C2×C4×C13#12311yescharacteristic
252C2×C4×C13#12311yescharacteristic
253C2×C4×C13#12311yescharacteristic
254C2×C4×C13#12311yescharacteristic
255C2×C4×C13#12311yescharacteristic
256C2×C4×C13#12411yescharacteristic
257C2×C4×C13#12411yescharacteristic
258C2×C4×C13#12411yescharacteristic
259C2×C4×C13#12611yescharacteristic
260C2×C4×C13#12611yescharacteristic
261C22⋊D13—42no—
262C22⋊D13—42no—
263C22⋊D13—42no—
264C22⋊D13—42no—
265C2×Dic13—22no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268D52—22no—
269D52—22no—
270D52—41no—
271D52—41no—
272C4×D13—42no—
273C4×D13—42no—
274C4×D13—42no—
275C4×D13—42no—
276Dic26—22no—
277Dic26—22no—
278Dic26—41no—
279Dic26—41no—
280C8×C13—42no—
281#1055—42no—
282#1055—42no—
283#1055—42no—
284C22×#41—131no—
285C22×M16—131no—
286C22×M16—131no—
287C22×M16—131no—
288C23×C8C2×D1311yescharacteristic
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C4⋊C4C2×D1311yescharacteristic
291#417—134no—
292#417—262no—
293#417—262no—
294#417—262no—
295C2×#103—261no—
296C2×#103—261no—
297C2×#102—261no—
298C2×#102—261no—
299#408—262no—
300#408—262no—
301C2×C22⋊C8—262no—
302#343—262no—
303#343—262no—
304#341—262no—
305#340—22no—
306C22×C13—21no—
307C22×C13—21no—
308C22×C13—21no—
309C22×C13—21no—
310C22×C13—21no—
311C22×C13—21no—
312C22×C13—21no—
313C22×C13—21no—
314C22×C13—21no—
315C22×C13—21no—
316C22×C13—21no—
317C22×C13—21no—
318C22×C13#38611yescharacteristic
319C22×C13#38811yescharacteristic
320C22×C13#38811yescharacteristic
321C22×C13#39411yescharacteristic
322C22×C13#39711yescharacteristic
323C22×C13#39711yescharacteristic
324C22×C13#39711yescharacteristic
325C22×C13#47111yescharacteristic
326C22×C13#47111yescharacteristic
327C22×C13#47211yescharacteristic
328C22×C13#47311yescharacteristic
329C2×D13—42no—
330C2×D13—42no—
331C2×D13—42no—
332C2×D13—81no—
333C2×D13—81no—
334C2×D13—81no—
335C2×D13—81no—
336C4×C13—82no—
337C4×C13—82no—
338C4×C13#38111yescharacteristic
339C4×C13#38611yescharacteristic
340C4×C13#38811yescharacteristic
341C4×C13#38811yescharacteristic
342C4×C13#39411yescharacteristic
343C4×C13#39411yescharacteristic
344C4×C13#39411yescharacteristic
345C4×C13#39711yescharacteristic
346Dic13—42no—
347C2×#41—132no—
348C2×#41—132no—
349C2×#41—261no—
350C2×#41—261no—
351C2×#41—261no—
352C2×#41—261no—
353C2×#41—261no—
354C2×#41—261no—
355C2×#41—261no—
356C2×#41—261no—
357C2×#41—261no—
358C2×#41—261no—
359C22×Q8—131no—
360C22×D4—131no—
361C22×D4—261no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—261no—
365C23×C4C22×D1311yescharacteristic
366C2×M16—132no—
367C2×M16—132no—
368C2×M16—132no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16—261no—
372C2×M16—261no—
373C2×M16—261no—
374C2×M16—261no—
375C2×M16—261no—
376C2×M16—261no—
377C2×M16—261no—
378C2×M16—261no—
379C2×M16—261no—
380C2×M16—261no—
381C2×M16—261no—
382C2×M16—261no—
383C2×M16—261no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—261no—
391C22×C8—261no—
392C22×C8—261no—
393C22×C8C22⋊D1312yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4C4×D1312yes—
405C2×C4⋊C4D5212yes—
406#103—264no—
407#103—264no—
408#102—264no—
409#102—264no—
410C22⋊C8—268no—
411C2×C13—21no—
412C2×C13—21no—
413C2×C13—21no—
414C2×C13—21no—
415C2×C13#144011yescharacteristic
416C2×C13#190711yescharacteristic
417C2×C13#190811yescharacteristic
418C2×C13#205111yescharacteristic
419C2×C13#205211yescharacteristic
420C2×C13#207811yescharacteristic
421C2×C13#207911yescharacteristic
422D13—82no—
423C24—261no—
424C24#612911yescharacteristic
425#41—262no—
426#41—262no—
427#41—262no—
428#41—262no—
429#41—262no—
430#41—262no—
431#41—262no—
432#41—262no—
433#41—521no—
434#41—521no—
435#41—521no—
436#41—521no—
437#41—521no—
438#41—521no—
439#41—521no—
440#41—521no—
441C2×Q8—132no—
442C2×Q8—261no—
443C2×Q8—261no—
444C2×Q8—261no—
445C2×Q8—261no—
446C2×Q8—261no—
447C2×D4—132no—
448C2×D4—262no—
449C2×D4—262no—
450C2×D4—261no—
451C2×D4—261no—
452C2×D4—261no—
453C2×D4—261no—
454C2×D4—261no—
455C2×D4—521no—
456C2×D4—521no—
457C2×D4—521no—
458C2×D4—521no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—81no—
466C22×C4—81no—
467C22×C4—81no—
468C22×C4—81no—
469C22×C4—261no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—521no—
473C22×C4—521no—
474C22×C4—521no—
475C22×C4—521no—
476C22×C4C2×C4×D1311yescharacteristic
477C22×C4C2×D5211yescharacteristic
478C22×C4#612711yescharacteristic
479C22×C4#612711yescharacteristic
480C22×C4#612711yescharacteristic
481C22×C4#612711yescharacteristic
482C22×C4D4×D1311yescharacteristic
483C22×C4D4×D1311yescharacteristic
484C22×C4D4×D1311yescharacteristic
485C22×C4D4×D1311yescharacteristic
486C22×C4#612911yescharacteristic
487C22×C4#613111yescharacteristic
488C22×C4#613111yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490M16—262no—
491M16—262no—
492M16—262no—
493M16—262no—
494M16—262no—
495M16—262no—
496M16—521no—
497M16—521no—
498M16—521no—
499M16—521no—
500M16—521no—
501M16—521no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—262no—
510C2×C8—262no—
511C2×C8—262no—
512C2×C8—521no—
513C2×C8—521no—
514C2×C8—521no—
515C2×C8—521no—
516C2×C8—521no—
517C2×C8—521no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C13#1119211yescharacteristic, complemented, Sylow
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—262no—
532C23—521no—
533C23—521no—
534C23—521no—
535C23—521no—
536C23—521no—
537C23—521no—
538C23#8813511yescharacteristic
539C23#8813711yescharacteristic
540C23#8813911yescharacteristic
541C23#8814011yescharacteristic
542C23#8815211yescharacteristic
543C23#8815211yescharacteristic
544C23#8819211yescharacteristic
545Q8—262no—
546Q8—262no—
547Q8—521no—
548Q8—521no—
549D4—262no—
550D4—262no—
551D4—522no—
552D4—522no—
553D4—522no—
554D4—522no—
555D4—521no—
556D4—521no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—262no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4#8812611yescharacteristic
575C2×C4C4×D5211yescharacteristic
576C2×C4#8812911yescharacteristic
577C2×C4#8813011yescharacteristic
578C2×C4C22⋊C4×D1311yescharacteristic
579C2×C4#8813611yescharacteristic
580C2×C4#8813711yescharacteristic
581C2×C4#8813711yescharacteristic
582C2×C4#8813811yescharacteristic
583C2×C4#8813811yescharacteristic
584C2×C4#8813811yescharacteristic
585C2×C4#8813911yescharacteristic
586C2×C4#8814611yescharacteristic
587C2×C4#8814711yescharacteristic
588C2×C4#8814811yescharacteristic
589C2×C4#8814811yescharacteristic
590C2×C4#8814811yescharacteristic
591C2×C4#8814811yescharacteristic
592C2×C4#8814811yescharacteristic
593C2×C4#8814911yescharacteristic
594C2×C4#8814911yescharacteristic
595C2×C4#8815211yescharacteristic
596C2×C4C4×C22⋊D1311yescharacteristic
597C2×C4#8818311yescharacteristic
598C2×C4#8818411yescharacteristic
599C2×C4#8819111yescharacteristic
600C2×C4#8819311yescharacteristic
601C2×C4#8820111yescharacteristic
602C8—42no—
603C8—522no—
604C8—522no—
605C8—522no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—522no—
619C22—522no—
620C22—522no—
621C22—1041no—
622C22—1041no—
623C22—1041no—
624C22—1041no—
625C22#1171833011yescharacteristic
626C22#1171833111yescharacteristic
627C22#1171833511yescharacteristic
628C22#1171833611yescharacteristic
629C22#1171861711yescharacteristic
630C22#1171862211yescharacteristic
631C22#1171865411yescharacteristic
632C22#1171882111yescharacteristic
633C22#1171883811yescharacteristic
634C22#1171883811yescharacteristic
635C22#1171885311yescharacteristic
636C4—82no—
637C4—82no—
638C4—522no—
639C4#1171832511yescharacteristic
640C4#1171832611yescharacteristic
641C4#1171833311yescharacteristic
642C4#1171833611yescharacteristic
643C4#1171860111yescharacteristic
644C4#1171862011yescharacteristic
645C4#1171865111yescharacteristic
646C4#1171865211yescharacteristic
647C2—21no—
648C2—21no—
649C2—21no—
650C2—21no—
651C2—1042no—
652C2#1311308411yescharacteristic
653C2#1311534711yescharacteristic
654C2#1311535411yescharacteristic
655C2#1311612911yescharacteristic
656C2#1311613611yescharacteristic
657C2#1311627711yescharacteristic
658C2#1311628211yescharacteristic
subgroupG/H
centerC23#88192
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socleC23×C13#121
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#11192
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#11718122C2semidirect
5. C2×#11718122C2semidirect
6. C2×#11718144C2semidirect
7. C2×C13×#340C2semidirect
23. #11718627C4semidirect
204. C2×#340D13semidirect
526. C13#11192semidirect

Maximal subgroups

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

subgroupindex
C2×#117186272
C2×#117187712
C2×#117181222
C2×#117181442
C2×C13×#3402
#1119213