Finite Group Databasebeta

← C2×#13115844 #15889715

Subgroups — C2×#13115844 #15889715

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×#88178C211yesmaximal, characteristic
3C22×#88075C211yesmaximal, characteristic, complemented
4C22×#88050C211yesmaximal, characteristic, complemented
5C22×C22⋊#1055C211yesmaximal, characteristic
6#13115844C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C22×C13×C22⋊Q8C211yesmaximal, characteristic
9C23×Q8×C13C2211yescharacteristic
10C24×C4×C13C2211yescharacteristic
11C23×Dic26C2211yescharacteristic
12C2×C13×C22⋊Q8—24no—
13C2×C13×C22⋊Q8—22no—
14C2×C13×C22⋊Q8—24no—
15C2×C13×C22⋊Q8C2214yes—
16C22×C13×C4⋊C4—21no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4—21no—
19C22×C22⋊Dic13—21no—
20C22×#6107—24no—
21C22×#6107—24no—
22C22×#6107—24no—
23C22×#6107C2214yescomplemented
24C22×C4⋊Dic13C2211yescharacteristic
25C2×#88178—22no—
26C2×#88178—24no—
27C2×#88178—24no—
28C2×#88178C2214yes—
29C22×#6101—21no—
30C23×#1055C2211yescharacteristic
31C23×#1055C2211yescharacteristic
32C2×#88075—24no—
33C2×#88075C2214yescomplemented
34C2×C22⋊#1055—24no—
35C2×C22⋊#1055C2214yes—
36C2×#88050—24no—
37C2×#88050C2214yescomplemented
38#11718121C2214yescomplemented
39C25×C13D411yescharacteristic
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×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13D411yescharacteristic
57C23×C4×C13D412yes—
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C23×Dic13—21no—
62C22×Dic26—22no—
63C22×Dic26—22no—
64C22×Dic26—22no—
65C22×Dic26—22no—
66C22×Dic26—22no—
67C22×Dic26—21no—
68C22×Dic26D414yes—
69C22×Dic26C2312yes—
70C13×C22⋊Q8—216no—
71C13×C22⋊Q8—28no—
72C13×C22⋊Q8—28no—
73C2×C13×C4⋊C4—28no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4D414yes—
78C2×C13×C4⋊C4C2312yes—
79C2×C13×C22⋊C4—28no—
80C2×C13×C22⋊C4—24no—
81C2×C22⋊Dic13—28no—
82C2×C22⋊Dic13—24no—
83C2×#6107—232no—
84C2×#6107—28no—
85C2×#6107—28no—
86C2×#6107—28no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13D414yes—
90C2×C4⋊Dic13C2312yes—
91#88178—216no—
92#88178—28no—
93#88178—28no—
94C2×#6101—28no—
95C2×#6101—24no—
96C22×#1055—22no—
97C22×#1055—22no—
98C22×#1055—22no—
99C22×#1055—22no—
100C22×#1055—22no—
101C22×#1055D414yes—
102C22×#1055C2312yes—
103C22×#1055C2312yes—
104#88075—28no—
105C22⋊#1055—28no—
106#88050—28no—
107C2×#2001—131nomaximal, Sylow
108C24×C13—22no—
109C24×C13—22no—
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13Q1614yescomplemented
115C24×C13C2×D412yes—
116C24×C13C2×D411yescharacteristic
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—22no—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—44no—
151C22×C4×C13—44no—
152C22×C4×C13—44no—
153C22×C4×C13—44no—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13#4112yes—
162C22×C4×C13C2411yescharacteristic
163C22×Dic13—24no—
164C22×Dic13—24no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—42no—
168C22×Dic13—42no—
169C22×Dic13—42no—
170C22×Dic13—42no—
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—
184C13×C4⋊C4—216no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4C2×D414yes—
188C13×C22⋊C4—216no—
189C22⋊Dic13—216no—
190#6107—232no—
191C4⋊Dic13—24no—
192C4⋊Dic13—22no—
193C4⋊Dic13C2×D414yes—
194#6101—216no—
195C2×#1055—28no—
196C2×#1055—22no—
197C2×#1055—22no—
198C2×#1055—22no—
199C2×#1055—22no—
200C2×#1055—22no—
201C2×#1055—44no—
202C2×#1055C2×D414yes—
203C23×Q16—131no—
204C22×C22⋊Q8—131no—
205C22×C22⋊Q8D1311yescharacteristic
206C22×#103—131no—
207C22×#103—131no—
208C22×C22⋊C8—131no—
209#2001—138no—
210C2×#340—131no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—22no—
214C23×C13—22no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13—28no—
218C23×C13—28no—
219C23×C13—28no—
220C23×C13—44no—
221C23×C13—44no—
222C23×C13—44no—
223C23×C13—44no—
224C23×C13#12012yes—
225C23×C13#12012yes—
226C23×C13#12112yes—
227C23×C13C2×Q1612yes—
228C23×C13C2×Q1614yescomplemented
229C23×C13#13512yes—
230C23×C13#13712yes—
231C23×C13#13712yes—
232C23×C13C22×D411yescharacteristic
233Q8×C13—24no—
234Q8×C13—24no—
235Q8×C13—42no—
236Q8×C13—42no—
237Q8×C13—48no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—44no—
248C2×C4×C13—48no—
249C2×C4×C13—48no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—48no—
255C2×C4×C13#12014yes—
256C2×C4×C13#12012yes—
257C2×C4×C13#12012yes—
258C2×C4×C13#12114yes—
259C2×C4×C13#12114yes—
260C2×C4×C13#12112yes—
261C2×C4×C13#12714yes—
262C2×C4×C13C22×D411yescharacteristic
263C2×C4×C13C22×D411yescharacteristic
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×Dic13—24no—
269C2×Dic13—24no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—48no—
275C2×Dic13—48no—
276Dic26—24no—
277Dic26—24no—
278Dic26—42no—
279Dic26—42no—
280Dic26—48no—
281#1055—24no—
282#1055—42no—
283C23×Q8—131no—
284C23×Q8C2×D1311yescharacteristic
285C24×C4C2×D1311yescharacteristic
286C22×Q16—134no—
287C22×Q16—264no—
288C22×Q16—264no—
289C22×Q16—264no—
290C23×C8—131no—
291C23×C8—131no—
292C2×C22⋊Q8—24no—
293C2×C22⋊Q8—22no—
294C2×C22⋊Q8—24no—
295C2×C22⋊Q8—134no—
296C2×C22⋊Q8—264no—
297C2×C22⋊Q8—264no—
298C2×C22⋊Q8—262no—
299C2×C22⋊Q8C2×D1314yes—
300C22×C4⋊C4—21no—
301C22×C4⋊C4—131no—
302C22×C4⋊C4—261no—
303C22×C4⋊C4C2×D1311yescharacteristic
304C22×C22⋊C4—21no—
305C22×C22⋊C4—261no—
306C2×#103—134no—
307C2×#103—134no—
308C2×#103—264no—
309C2×#103—264no—
310C2×C22⋊C8—134no—
311C2×C22⋊C8—264no—
312#340—134no—
313C22×C13—24no—
314C22×C13—24no—
315C22×C13—24no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—416no—
320C22×C13—42no—
321C22×C13#39214yes—
322C22×C13#45114yes—
323C22×C13#45114yes—
324C22×C13#45214yes—
325C22×C13#45214yes—
326C22×C13#46714yes—
327C22×C13#47014yes—
328C22×C13C2×#12011yescharacteristic
329C22×C13C2×#12011yescharacteristic
330C22×C13C2×#12111yescharacteristic
331C22×C13C22×Q1611yescharacteristic
332C22×C13C2×#13511yescharacteristic
333C22×C13C2×#13711yescharacteristic
334C22×C13C2×#13711yescharacteristic
335C4×C13—42no—
336C4×C13—44no—
337C4×C13—44no—
338C4×C13#39214yes—
339C4×C13C2×#12011yescharacteristic
340C4×C13C2×#12111yescharacteristic
341C4×C13C2×#12111yescharacteristic
342C4×C13C2×#12711yescharacteristic
343Dic13—44no—
344Dic13—44no—
345C25C22⋊D1311yescharacteristic
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—262no—
355C22×Q8—261no—
356C22×Q8—262no—
357C22×Q8—262no—
358C22×Q8—262no—
359C22×Q8—262no—
360C22×Q8C22⋊D1314yes—
361C22×Q8C22×D1312yes—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—261no—
371C23×C4—261no—
372C23×C4C22⋊D1312yes—
373C23×C4C22⋊D1311yescharacteristic
374C23×C4C22×D1312yes—
375C23×C4C22×D1311yescharacteristic
376C2×Q16—268no—
377C2×Q16—268no—
378C2×Q16—2632no—
379C2×Q16—268no—
380C22×C8—134no—
381C22×C8—132no—
382C22×C8—132no—
383C22×C8—262no—
384C22×C8—262no—
385C22×C8—262no—
386C22×C8—262no—
387C22×C8—262no—
388C22⋊Q8—216no—
389C22⋊Q8—28no—
390C22⋊Q8—28no—
391C22⋊Q8—268no—
392C22⋊Q8—268no—
393C22⋊Q8—2616no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—134no—
399C2×C4⋊C4—132no—
400C2×C4⋊C4—268no—
401C2×C4⋊C4—262no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—264no—
404C2×C4⋊C4C22⋊D1314yes—
405C2×C4⋊C4C22×D1312yes—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—268no—
409C2×C22⋊C4—264no—
410#103—268no—
411#103—268no—
412C22⋊C8—268no—
413C2×C13—44no—
414C2×C13#200118yescomplemented
415C2×C13C2×#39211yescharacteristic
416C2×C13C2×#45111yescharacteristic
417C2×C13C2×#45111yescharacteristic
418C2×C13C2×#45211yescharacteristic
419C2×C13C2×#45211yescharacteristic
420C2×C13C2×#46711yescharacteristic
421C2×C13C2×#47011yescharacteristic
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24#610714yescomplemented
429C24C2×C22⋊D1312yes—
430C24C2×C22⋊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—524no—
454C2×Q8—524no—
455C2×Q8—522no—
456C2×Q8C2×C22⋊D1314yes—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—264no—
482C22×C4—264no—
483C22×C4—262no—
484C22×C4—262no—
485C22×C4—522no—
486C22×C4—522no—
487C22×C4—522no—
488C22×C4—522no—
489C22×C4D4×D1312yes—
490C22×C4D4×D1312yes—
491C22×C4D4×D1312yes—
492C22×C4#612912yes—
493C22×C4C2×C22⋊D1312yes—
494C22×C4C2×C22⋊D1311yescharacteristic
495C22×C4C2×C22⋊D1312yes—
496C22×C4C2×C22⋊D1312yes—
497C22×C4C23×D1311yescharacteristic
498Q16—2632no—
499C2×C8—134no—
500C2×C8—268no—
501C2×C8—262no—
502C2×C8—262no—
503C2×C8—262no—
504C2×C8—262no—
505C2×C8—262no—
506C2×C8—524no—
507C4⋊C4—216no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—134no—
511C4⋊C4—2616no—
512C4⋊C4—264no—
513C4⋊C4—262no—
514C4⋊C4C2×C22⋊D1314yes—
515C22⋊C4—216no—
516C22⋊C4—2616no—
517C13C2×#200111yescharacteristic, complemented, Sylow
518C23—28no—
519C23—28no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—28no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23#8819112yes—
532C23#8819312yes—
533C23#8819612yes—
534C23C2×#610712yes—
535C23C2×#610714yescomplemented
536C23#8820412yes—
537C23#8820512yes—
538C23#8820712yes—
539C23C22×C22⋊D1311yescharacteristic
540Q8—24no—
541Q8—24no—
542Q8—42no—
543Q8—42no—
544Q8—48no—
545Q8—264no—
546Q8—264no—
547Q8—522no—
548Q8—522no—
549Q8—528no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—44no—
560C2×C4—48no—
561C2×C4—48no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—48no—
567C2×C4—264no—
568C2×C4—264no—
569C2×C4—528no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4—528no—
575C2×C4#8819114yes—
576C2×C4#8819112yes—
577C2×C4#8819214yes—
578C2×C4#8819314yes—
579C2×C4#8819312yes—
580C2×C4#8819414yes—
581C2×C4#8820712yes—
582C2×C4C2×D4×D1311yescharacteristic
583C2×C4C2×D4×D1311yescharacteristic
584C2×C4C2×D4×D1311yescharacteristic
585C2×C4C2×#612911yescharacteristic
586C2×C4C22×C22⋊D1311yescharacteristic
587C2×C4C22×C22⋊D1311yescharacteristic
588C8—264no—
589C8—522no—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—42no—
594C22—42no—
595C22—416no—
596C22—42no—
597C22—42no—
598C22#1171870814yes—
599C22#1171871114yes—
600C22#1171871214yes—
601C22#1171871314yes—
602C22#1171888414yes—
603C22#1171888914yes—
604C22#1171890014yes—
605C22C2×#8819111yescharacteristic
606C22C2×#8819311yescharacteristic
607C22C2×#8819611yescharacteristic
608C22C22×#610711yescharacteristic
609C22C2×#8820411yescharacteristic
610C22C2×#8820511yescharacteristic
611C22C2×#8820711yescharacteristic
612C4—42no—
613C4—44no—
614C4—44no—
615C4—524no—
616C4—524no—
617C4#1171888414yes—
618C4C2×#8819111yescharacteristic
619C4C2×#8819211yescharacteristic
620C4C2×#8819311yescharacteristic
621C4C2×#8819411yescharacteristic
622C2—44no—
623C2#1311584418yesdirect product factor
624C2C2×#1171888411yescharacteristic
625C2C2×#1171871111yescharacteristic
626C2C2×#1171888911yescharacteristic
627C2C2×#1171870811yescharacteristic
628C2C2×#1171890011yescharacteristic
629C2C2×#1171871211yescharacteristic
630C2C2×#1171871311yescharacteristic
subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C2×D4
prime radicalC25×C13D4
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2001
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C23×#6107C2semidirect
3. C22×#88075C2semidirect
4. C22×#88050C2semidirect
6. #13115844C2direct (N × H)
7. C2×#11718121C2semidirect
23. C22×#6107C22semidirect
33. C2×#88075C22semidirect
37. C2×#88050C22semidirect
38. #11718121C22semidirect
114. C24×C13Q16semidirect
228. C23×C13C2×Q16semidirect
414. C2×C13#2001semidirect
428. C24#6107semidirect
517. C13C2×#2001semidirect
535. C23C2×#6107semidirect
623. C2#13115844direct (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×#881782
C22×#880752
C22×#880502
C22×C22⋊#10552
#131158442
C2×#117181212
C22×C13×C22⋊Q82
C2×#200113