Finite Group Databasebeta

← C2×#13115845 #15889716

Subgroups — C2×#13115845 #15889716

Order 3328.

2182 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6107C211yesmaximal, characteristic, complemented
2C22×#88151C211yesmaximal, characteristic
3C22×#88200C211yesmaximal, characteristic
4C22×#88056C211yesmaximal, characteristic, complemented
5C22×#88060C211yesmaximal, characteristic
6#13115845C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C22×C13×#103C211yesmaximal, characteristic, complemented
9C23×Q8×C13C2211yescharacteristic
10C23×C4×D13C2211yescharacteristic
11C23×Dic26C2211yescharacteristic
12C23×C8×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C2×#88200—24no—
15C2×#88200—22no—
16C2×#88200—24no—
17C2×#88200C2214yes—
18C22×#6107—24no—
19C22×#6107—24no—
20C22×#6107—24no—
21C22×#6107C2214yescomplemented
22C22×#6103—21no—
23C22×#6103—21no—
24C22×C4⋊Dic13—21no—
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101—21no—
27C23×#1055C2211yescharacteristic
28C2×#88151—22no—
29C2×#88151—24no—
30C2×#88151—24no—
31C2×#88151C2214yes—
32C2×C13×#103—24no—
33C2×C13×#103C2214yescomplemented
34C2×#88060—24no—
35C2×#88060C2214yes—
36C2×#88056—24no—
37C2×#88056C2214yescomplemented
38#11718121C2214yescomplemented
39C24×D13D411yescharacteristic
40C22×Q8×C13—22no—
41C22×Q8×C13—21no—
42C22×Q8×C13—22no—
43C22×Q8×C13—22no—
44C22×Q8×C13—22no—
45C22×Q8×C13—22no—
46C22×Q8×C13D414yes—
47C22×Q8×C13C2312yes—
48C23×C4×C13—21no—
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C23×Dic13—21no—
52C23×Dic13—21no—
53C23×Dic13D411yescharacteristic
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13—22no—
60C22×C4×D13D412yes—
61C22×C4×D13C2312yes—
62C22×Dic26—22no—
63C22×Dic26—22no—
64C22×Dic26—22no—
65C22×Dic26—22no—
66C22×Dic26—21no—
67C22×Dic26—22no—
68C22×Dic26D414yes—
69C22×Dic26C2312yes—
70C22×C8×C13—22no—
71C22×C8×C13—22no—
72C22×C8×C13—22no—
73C22×C8×C13C2312yes—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4D414yes—
77C2×C13×C4⋊C4C2312yes—
78#88200—216no—
79#88200—28no—
80#88200—28no—
81C2×#6107—232no—
82C2×#6107—28no—
83C2×#6107—28no—
84C2×#6107—28no—
85C2×#6103—28no—
86C2×#6103—28no—
87C2×#6103—24no—
88C2×#6103—24no—
89C2×C4⋊Dic13—28no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13D414yes—
94C2×C4⋊Dic13C2312yes—
95C2×#6101—28no—
96C2×#6101—24no—
97C22×#1055—22no—
98C22×#1055—22no—
99C22×#1055D414yes—
100C22×#1055C2312yes—
101#88151—216no—
102#88151—28no—
103#88151—28no—
104C13×#103—28no—
105#88060—28no—
106#88056—28no—
107C2×#2001—131nomaximal, Sylow
108C24×C13C2×D411yescharacteristic
109C23×D13—22no—
110C23×D13—22no—
111C23×D13—22no—
112C23×D13—22no—
113C23×D13—22no—
114C23×D13—22no—
115C23×D13Q1614yescomplemented
116C23×D13C2×D412yes—
117C2×Q8×C13—24no—
118C2×Q8×C13—22no—
119C2×Q8×C13—28no—
120C2×Q8×C13—28no—
121C2×Q8×C13—22no—
122C2×Q8×C13—22no—
123C2×Q8×C13—22no—
124C2×Q8×C13—22no—
125C2×Q8×C13—42no—
126C2×Q8×C13—42no—
127C2×Q8×C13—44no—
128C2×Q8×C13—44no—
129C2×Q8×C13C2×D414yes—
130C22×C4×C13—24no—
131C22×C4×C13—24no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D412yes—
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D412yes—
144C22×C4×C13#4112yes—
145C22×C4×C13C2411yescharacteristic
146C22×Dic13—22no—
147C22×Dic13—24no—
148C22×Dic13—22no—
149C22×Dic13—24no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—22no—
153C22×Dic13—42no—
154C22×Dic13—42no—
155C22×Dic13—42no—
156C22×Dic13—42no—
157C22×Dic13C2×D412yes—
158C2×C4×D13—24no—
159C2×C4×D13—24no—
160C2×C4×D13—24no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—22no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—22no—
167C2×C4×D13—44no—
168C2×C4×D13—44no—
169C2×C4×D13—44no—
170C2×C4×D13—44no—
171C2×Dic26—28no—
172C2×Dic26—28no—
173C2×Dic26—22no—
174C2×Dic26—22no—
175C2×Dic26—22no—
176C2×Dic26—22no—
177C2×Dic26—24no—
178C2×Dic26—22no—
179C2×Dic26—42no—
180C2×Dic26—44no—
181C2×Dic26—42no—
182C2×Dic26—44no—
183C2×Dic26C2×D414yes—
184C2×C8×C13—22no—
185C2×C8×C13—22no—
186C2×C8×C13—22no—
187C2×C8×C13—44no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4C2×D414yes—
191#6107—232no—
192#6103—216no—
193#6103—216no—
194C4⋊Dic13—216no—
195C4⋊Dic13—24no—
196C4⋊Dic13—22no—
197C4⋊Dic13C2×D414yes—
198#6101—216no—
199C2×#1055—28no—
200C2×#1055—22no—
201C2×#1055—22no—
202C2×#1055C2×D414yes—
203C23×Q16—131no—
204C22×C22⋊Q8—131no—
205C22×C22⋊Q8—131no—
206C22×#103—131no—
207C22×#103D1311yescharacteristic, complemented
208C22×C22⋊C8—131no—
209#2001—138no—
210C2×#340—131no—
211C23×C13#12012yes—
212C23×C13#12012yes—
213C23×C13#12112yes—
214C23×C13C2×Q1612yes—
215C23×C13#13512yes—
216C23×C13#13712yes—
217C23×C13#13712yes—
218C23×C13C22×D411yescharacteristic
219C22×D13—22no—
220C22×D13—22no—
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—22no—
224C22×D13—22no—
225C22×D13—28no—
226C22×D13—28no—
227C22×D13—28no—
228C22×D13—44no—
229C22×D13—44no—
230C22×D13—44no—
231C22×D13—44no—
232C22×D13C2×Q1614yescomplemented
233Q8×C13—24no—
234Q8×C13—24no—
235Q8×C13—42no—
236Q8×C13—42no—
237Q8×C13—48no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—48no—
245C2×C4×C13—48no—
246C2×C4×C13#12014yes—
247C2×C4×C13#12012yes—
248C2×C4×C13#12012yes—
249C2×C4×C13#12114yes—
250C2×C4×C13#12114yes—
251C2×C4×C13#12112yes—
252C2×C4×C13#12714yes—
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×Dic13—22no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—22no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—42no—
268C2×Dic13—48no—
269C2×Dic13—44no—
270C2×Dic13—48no—
271C4×D13—42no—
272C4×D13—42no—
273C4×D13—42no—
274C4×D13—42no—
275C4×D13—48no—
276Dic26—24no—
277Dic26—24no—
278Dic26—42no—
279Dic26—42no—
280Dic26—48no—
281C8×C13—42no—
282#1055—24no—
283C23×Q8—131no—
284C23×Q8C2×D1311yescharacteristic
285C24×C4—131no—
286C22×Q16—134no—
287C22×Q16—264no—
288C22×Q16—264no—
289C22×Q16—264no—
290C23×C8—131no—
291C23×C8C2×D1311yescharacteristic
292C2×C22⋊Q8—134no—
293C2×C22⋊Q8—134no—
294C2×C22⋊Q8—262no—
295C2×C22⋊Q8—264no—
296C2×C22⋊Q8—264no—
297C2×C22⋊Q8—262no—
298C2×C22⋊Q8—264no—
299C2×C22⋊Q8—264no—
300C22×C4⋊C4—131no—
301C22×C4⋊C4—261no—
302C22×C4⋊C4—261no—
303C22×C4⋊C4C2×D1311yescharacteristic
304C22×C22⋊C4—261no—
305C22×C22⋊C4—261no—
306C2×#103—24no—
307C2×#103—134no—
308C2×#103—264no—
309C2×#103C2×D1314yescomplemented
310C2×C22⋊C8—134no—
311C2×C22⋊C8—264no—
312#340—134no—
313C22×C13#39214yes—
314C22×C13#45114yes—
315C22×C13#45114yes—
316C22×C13#45214yes—
317C22×C13#45214yes—
318C22×C13#46714yes—
319C22×C13#47014yes—
320C22×C13C2×#12011yescharacteristic
321C22×C13C2×#12011yescharacteristic
322C22×C13C2×#12111yescharacteristic
323C22×C13C22×Q1611yescharacteristic
324C22×C13C2×#13511yescharacteristic
325C22×C13C2×#13711yescharacteristic
326C22×C13C2×#13711yescharacteristic
327C2×D13—24no—
328C2×D13—24no—
329C2×D13—24no—
330C2×D13—42no—
331C2×D13—42no—
332C2×D13—42no—
333C2×D13—416no—
334C2×D13—42no—
335C4×C13—44no—
336C4×C13—44no—
337C4×C13#39214yes—
338C4×C13C2×#12011yescharacteristic
339C4×C13C2×#12111yescharacteristic
340C4×C13C2×#12111yescharacteristic
341C4×C13C2×#12711yescharacteristic
342Dic13—44no—
343Dic13—42no—
344Dic13—44no—
345C25—131no—
346C22×Q8—22no—
347C22×Q8—21no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—134no—
353C22×Q8—132no—
354C22×Q8—261no—
355C22×Q8—262no—
356C22×Q8—262no—
357C22×Q8—262no—
358C22×Q8—262no—
359C22×Q8—262no—
360C22×Q8D5214yes—
361C22×Q8C22×D1312yes—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—131no—
365C23×C4—132no—
366C23×C4—132no—
367C23×C4—261no—
368C23×C4—261no—
369C23×C4—262no—
370C23×C4—262no—
371C23×C4—262no—
372C23×C4—262no—
373C23×C4—262no—
374C23×C4—262no—
375C23×C4C22×D1311yescharacteristic
376C2×Q16—268no—
377C2×Q16—268no—
378C2×Q16—2632no—
379C2×Q16—268no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—134no—
384C22×C8—132no—
385C22×C8—262no—
386C22×C8—262no—
387C22×C8C22×D1312yes—
388C22⋊Q8—268no—
389C22⋊Q8—2616no—
390C22⋊Q8—268no—
391C22⋊Q8—2616no—
392C22⋊Q8—268no—
393C22⋊Q8—268no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—134no—
397C2×C4⋊C4—132no—
398C2×C4⋊C4—264no—
399C2×C4⋊C4—264no—
400C2×C4⋊C4—268no—
401C2×C4⋊C4—268no—
402C2×C4⋊C4—262no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4C22⋊D1314yes—
405C2×C4⋊C4C22×D1312yes—
406C2×C22⋊C4—264no—
407C2×C22⋊C4—264no—
408C2×C22⋊C4—268no—
409C2×C22⋊C4—268no—
410#103—28no—
411#103—268no—
412C22⋊C8—268no—
413C2×C13#200118yescomplemented
414C2×C13C2×#39211yescharacteristic
415C2×C13C2×#45111yescharacteristic
416C2×C13C2×#45111yescharacteristic
417C2×C13C2×#45211yescharacteristic
418C2×C13C2×#45211yescharacteristic
419C2×C13C2×#46711yescharacteristic
420C2×C13C2×#47011yescharacteristic
421D13—44no—
422C24—134no—
423C24—132no—
424C24—262no—
425C24—262no—
426C24—262no—
427C24—262no—
428C24—262no—
429C24—262no—
430C24D4×D1311yescharacteristic
431C2×Q8—24no—
432C2×Q8—22no—
433C2×Q8—28no—
434C2×Q8—28no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—42no—
440C2×Q8—44no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—134no—
444C2×Q8—264no—
445C2×Q8—262no—
446C2×Q8—268no—
447C2×Q8—268no—
448C2×Q8—262no—
449C2×Q8—262no—
450C2×Q8—262no—
451C2×Q8—262no—
452C2×Q8—522no—
453C2×Q8—522no—
454C2×Q8—524no—
455C2×Q8—524no—
456C2×Q8C2×D5214yes—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—132no—
466C22×C4—264no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—264no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—264no—
474C22×C4—264no—
475C22×C4—264no—
476C22×C4—262no—
477C22×C4—262no—
478C22×C4—262no—
479C22×C4—262no—
480C22×C4—262no—
481C22×C4—262no—
482C22×C4—522no—
483C22×C4—522no—
484C22×C4—522no—
485C22×C4—522no—
486C22×C4—524no—
487C22×C4—524no—
488C22×C4—524no—
489C22×C4—524no—
490C22×C4C2×D5212yes—
491C22×C4#612712yes—
492C22×C4D4×D1311yescharacteristic
493C22×C4D4×D1312yes—
494C22×C4D4×D1312yes—
495C22×C4D4×D1312yes—
496C22×C4C2×C22⋊D1312yes—
497C22×C4C23×D1311yescharacteristic
498Q16—2632no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—44no—
503C2×C8—134no—
504C2×C8—268no—
505C2×C8—262no—
506C2×C8—262no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—134no—
510C4⋊C4—2616no—
511C4⋊C4—2616no—
512C4⋊C4—264no—
513C4⋊C4—262no—
514C4⋊C4C2×C22⋊D1314yes—
515C22⋊C4—2616no—
516C22⋊C4—2616no—
517C13C2×#200111yescharacteristic, complemented, Sylow
518C23—134no—
519C23—262no—
520C23—262no—
521C23—262no—
522C23—262no—
523C23—262no—
524C23—268no—
525C23—268no—
526C23—262no—
527C23—268no—
528C23—524no—
529C23—524no—
530C23—524no—
531C23—524no—
532C23#8813612yes—
533C23#8813812yes—
534C23#8816912yes—
535C23#8817012yes—
536C23Q16×D1312yes—
537C23#8817212yes—
538C23#8819112yes—
539C23C2×D4×D1311yescharacteristic
540Q8—24no—
541Q8—24no—
542Q8—42no—
543Q8—42no—
544Q8—48no—
545Q8—264no—
546Q8—264no—
547Q8—522no—
548Q8—522no—
549Q8—528no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—48no—
557C2×C4—48no—
558C2×C4—264no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—264no—
562C2×C4—262no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—528no—
568C2×C4—524no—
569C2×C4—528no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4—528no—
575C2×C4#8813614yes—
576C2×C4#8813612yes—
577C2×C4#8813814yes—
578C2×C4#8813812yes—
579C2×C4#8818414yes—
580C2×C4#8819112yes—
581C2×C4#8819414yes—
582C2×C4C22×D5211yescharacteristic
583C2×C4C2×#612711yescharacteristic
584C2×C4C2×D4×D1311yescharacteristic
585C2×C4C2×D4×D1311yescharacteristic
586C2×C4C2×D4×D1311yescharacteristic
587C2×C4C22×C22⋊D1311yescharacteristic
588C8—42no—
589C8—264no—
590C22—264no—
591C22—264no—
592C22—264no—
593C22—522no—
594C22—522no—
595C22—5216no—
596C22—522no—
597C22—522no—
598C22#1171846914yes—
599C22#1171847114yes—
600C22#1171847414yes—
601C22#1171847714yes—
602C22#1171862114yes—
603C22#1171883414yes—
604C22#1171884714yes—
605C22C2×#8813611yescharacteristic
606C22C2×#8813811yescharacteristic
607C22C2×#8816911yescharacteristic
608C22C2×#8817011yescharacteristic
609C22C2×Q16×D1311yescharacteristic
610C22C2×#8817211yescharacteristic
611C22C2×#8819111yescharacteristic
612C4—44no—
613C4—44no—
614C4—522no—
615C4—524no—
616C4—524no—
617C4#1171862114yes—
618C4C2×#8813611yescharacteristic
619C4C2×#8813811yescharacteristic
620C4C2×#8818411yescharacteristic
621C4C2×#8819411yescharacteristic
622C2—524no—
623C2#1311584518yesdirect product factor
624C2C2×#1171862111yescharacteristic
625C2C2×#1171884711yescharacteristic
626C2C2×#1171846911yescharacteristic
627C2C2×#1171883411yescharacteristic
628C2C2×#1171847111yescharacteristic
629C2C2×#1171847411yescharacteristic
630C2C2×#1171847711yescharacteristic
subgroupG/H
centerC24D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#103C2
socleC24×C13C2×D4
prime radicalC24×D13D4
hypercenterC22×#103D13
hypocenterC13C2×#2001
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C23×#6107C2semidirect
4. C22×#88056C2semidirect
6. #13115845C2direct (N × H)
7. C2×#11718121C2semidirect
8. C22×C13×#103C2semidirect
21. C22×#6107C22semidirect
33. C2×C13×#103C22semidirect
37. C2×#88056C22semidirect
38. #11718121C22semidirect
115. C23×D13Q16semidirect
207. C22×#103D13semidirect
232. C22×D13C2×Q16semidirect
309. C2×#103C2×D13semidirect
413. C2×C13#2001semidirect
517. C13C2×#2001semidirect
623. C2#13115845direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#61072
C22×#881512
C22×#882002
C22×#880562
C22×#880602
#131158452
C2×#117181212
C22×C13×#1032
C2×#200113