Finite Group Databasebeta

← C2×#13115632 #15866501

Subgroups — C2×#13115632 #15866501

Order 3328.

2094 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D13C211yesmaximal, characteristic
2C22×#88054C211yesmaximal, characteristic, complemented
3C22×C22⋊#1055C211yesmaximal, characteristic, complemented
4C22×#88060C211yesmaximal, characteristic, complemented
5C22×#88060C211yesmaximal, characteristic, complemented
6C22×#88055C211yesmaximal, characteristic, complemented
7#13115632C218yesmaximal, direct product factor
8C22×C13×C22⋊C8C211yesmaximal, characteristic, complemented
9C24×C4×C13C2211yescharacteristic
10C23×C22⋊D13C411yescharacteristic
11C23×C4×D13C2211yescharacteristic
12C23×C8×C13C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C22×C22⋊Dic13C411yescharacteristic
15C2×C4×C22⋊D13—24no—
16C2×C4×C22⋊D13—24no—
17C2×C4×C22⋊D13C414yes—
18C2×C4×C22⋊D13C2214yes—
19C22×#6103C411yescharacteristic
20C22×#6101C411yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C23×#1055C2211yescharacteristic
24C2×C13×C22⋊C8—24no—
25C2×C13×C22⋊C8C2214yescomplemented
26C2×C22⋊#1055—24no—
27C2×C22⋊#1055C2214yescomplemented
28C2×#88060—24no—
29C2×#88060—24no—
30C2×#88060C2214yescomplemented
31C2×#88060C2214yescomplemented
32C2×#88055—24no—
33C2×#88055C2214yescomplemented
34C2×#88054—24no—
35C2×#88054C2214yescomplemented
36C25×C13C2×C411yescharacteristic
37C24×D13C2×C411yescharacteristic
38C23×C4×C13—22no—
39C23×C4×C13—22no—
40C23×C4×C13—22no—
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13C2×C411yescharacteristic
45C23×C4×C13C2×C412yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C22×C22⋊D13—24no—
49C22×C22⋊D13—24no—
50C22×C22⋊D13—24no—
51C22×C22⋊D13C2×C414yes—
52C23×Dic13C2×C411yescharacteristic
53C23×Dic13C2×C411yescharacteristic
54C23×Dic13C2×C411yescharacteristic
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13—22no—
60C22×C4×D13—22no—
61C22×C4×D13C2×C412yes—
62C22×C4×D13C2312yes—
63C22×C8×C13—22no—
64C22×C8×C13—22no—
65C22×C8×C13—22no—
66C22×C8×C13—22no—
67C22×C8×C13—22no—
68C22×C8×C13D414yescomplemented
69C22×C8×C13C2312yes—
70C22×C8×C13C2312yes—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13C2×C414yes—
73C4×C22⋊D13—216no—
74C4×C22⋊D13—28no—
75C4×C22⋊D13—28no—
76C2×#6103—24no—
77C2×#6103C2×C414yes—
78C2×#6101—24no—
79C2×#6101C2×C414yes—
80C2×C4×Dic13C2×C412yes—
81C2×C4×Dic13D414yes—
82C2×C4×Dic13D414yes—
83C2×C4×Dic13C2312yes—
84C22×#1055—22no—
85C22×#1055—22no—
86C22×#1055—22no—
87C22×#1055—22no—
88C22×#1055—22no—
89C22×#1055D414yescomplemented
90C22×#1055C2312yes—
91C22×#1055C2312yes—
92C13×C22⋊C8—28no—
93C22⋊#1055—28no—
94#88060—28no—
95#88060—28no—
96#88055—28no—
97#88054—28no—
98C2×#1955—131nomaximal, Sylow
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—22no—
104C24×C13—22no—
105C24×C13M1614yes—
106C24×C13C22×C412yes—
107C24×C13C22×C411yescharacteristic
108C23×D13—22no—
109C23×D13—22no—
110C23×D13—22no—
111C23×D13—22no—
112C23×D13—22no—
113C23×D13—22no—
114C23×D13M1614yes—
115C23×D13C22×C412yes—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—24no—
120C22×C4×C13—24no—
121C22×C4×C13—24no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—44no—
129C22×C4×C13—44no—
130C22×C4×C13—44no—
131C22×C4×C13—44no—
132C22×C4×C13C22×C412yes—
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C2×D412yes—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13#4112yes—
139C22×C4×C13#4112yes—
140C22×C4×C13C2411yescharacteristic
141C2×C22⋊D13—232no—
142C2×C22⋊D13—28no—
143C2×C22⋊D13—28no—
144C2×C22⋊D13—28no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13C22⋊C414yes—
153C22×Dic13C22⋊C414yes—
154C22×Dic13C22×C412yes—
155C22×Dic13C22×C412yes—
156C22×Dic13C22×C412yes—
157C2×C4×D13—24no—
158C2×C4×D13—24no—
159C2×C4×D13—24no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—22no—
163C2×C4×D13—22no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—44no—
167C2×C4×D13—44no—
168C2×C4×D13—44no—
169C2×C4×D13—44no—
170C2×C8×C13—28no—
171C2×C8×C13—22no—
172C2×C8×C13—22no—
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C2×C8×C13—22no—
176C2×C8×C13—44no—
177C2×C8×C13C2×D414yescomplemented
178C22⋊Dic13—28no—
179#6103—28no—
180#6101—28no—
181C4×Dic13C22⋊C418yes—
182C4×Dic13C2×D414yes—
183C4×Dic13C2×D414yes—
184C2×#1055—28no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#1055—44no—
191C2×#1055C2×D414yescomplemented
192C22×C4×D4—131no—
193C22×C4⋊C8—131no—
194C22×C22⋊C8—131no—
195C22×C22⋊C8—131no—
196C22×C22⋊C8—131no—
197C22×C22⋊C8D1311yescharacteristic, complemented
198C22×#97—131no—
199#1955—138no—
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—22no—
206C23×C13—28no—
207C23×C13—28no—
208C23×C13—28no—
209C23×C13—44no—
210C23×C13—44no—
211C23×C13—44no—
212C23×C13—44no—
213C23×C13C2×C22⋊C412yes—
214C23×C13C4×D412yes—
215C23×C13C4×D412yes—
216C23×C13C2×M1614yes—
217C23×C13C2×M1612yes—
218C23×C13C2×M1612yes—
219C23×C13#13112yes—
220C23×C13#13112yes—
221C23×C13C23×C411yescharacteristic
222C22×D13—22no—
223C22×D13—22no—
224C22×D13—22no—
225C22×D13—22no—
226C22×D13—22no—
227C22×D13—22no—
228C22×D13—28no—
229C22×D13—28no—
230C22×D13—28no—
231C22×D13—44no—
232C22×D13—44no—
233C22×D13—44no—
234C22×D13—44no—
235C22×D13C2×M1614yes—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—44no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—48no—
245C2×C4×C13C2×C22⋊C412yes—
246C2×C4×C13C4×D412yes—
247C2×C4×C13C4×D412yes—
248C2×C4×C13#12114yes—
249C2×C4×C13#12114yes—
250C2×C4×C13#12414yes—
251C2×C4×C13#12714yes—
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C22⋊D13—232no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—28no—
264C2×Dic13—28no—
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—44no—
269C2×Dic13C2×C22⋊C414yes—
270C2×Dic13C2×C22⋊C414yes—
271C4×D13—42no—
272C4×D13—42no—
273C4×D13—42no—
274C4×D13—42no—
275C4×D13—48no—
276C8×C13—24no—
277C8×C13—42no—
278#1055—24no—
279#1055—42no—
280C23×D4—131no—
281C24×C4—131no—
282C24×C4C2×D1311yescharacteristic
283C23×C8—131no—
284C23×C8—131no—
285C23×C8C2×D1311yescharacteristic
286C23×C8C2×D1311yescharacteristic
287C2×C4×D4—134no—
288C2×C4×D4—134no—
289C2×C4×D4—264no—
290C2×C4×D4—264no—
291C22×C4⋊C4—131no—
292C22×C22⋊C4—131no—
293C22×C22⋊C4—131no—
294C22×C42—131no—
295C2×C4⋊C8—134no—
296C2×C4⋊C8—264no—
297C2×C22⋊C8—24no—
298C2×C22⋊C8—134no—
299C2×C22⋊C8—134no—
300C2×C22⋊C8—134no—
301C2×C22⋊C8—264no—
302C2×C22⋊C8—264no—
303C2×C22⋊C8—264no—
304C2×C22⋊C8C2×D1314yescomplemented
305C2×#97—134no—
306C2×#97—264no—
307C22×C13—24no—
308C22×C13—24no—
309C22×C13—24no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—42no—
313C22×C13—416no—
314C22×C13—42no—
315C22×C13#39014yes—
316C22×C13#40714yes—
317C22×C13#40814yes—
318C22×C13#43514yes—
319C22×C13#43514yes—
320C22×C13#43514yes—
321C22×C13#43514yes—
322C22×C13C22×C22⋊C411yescharacteristic
323C22×C13C2×C4×D411yescharacteristic
324C22×C13C2×C4×D411yescharacteristic
325C22×C13C22×M1611yescharacteristic
326C22×C13C22×M1611yescharacteristic
327C22×C13C2×#13111yescharacteristic
328C22×C13C2×#13111yescharacteristic
329C2×D13—24no—
330C2×D13—24no—
331C2×D13—24no—
332C2×D13—42no—
333C2×D13—42no—
334C2×D13—42no—
335C2×D13—416no—
336C2×D13—42no—
337C4×C13—42no—
338C4×C13#39014yes—
339C4×C13C2×#12111yescharacteristic
340C4×C13C2×#12111yescharacteristic
341C4×C13C2×#12411yescharacteristic
342C4×C13C2×#12711yescharacteristic
343Dic13—24no—
344Dic13—24no—
345Dic13—42no—
346C25—131no—
347C25C4×D1311yescharacteristic
348C22×D4—134no—
349C22×D4—264no—
350C22×D4—264no—
351C22×D4—264no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—131no—
359C23×C4—131no—
360C23×C4—131no—
361C23×C4—132no—
362C23×C4—132no—
363C23×C4—262no—
364C23×C4—262no—
365C23×C4—262no—
366C23×C4—262no—
367C23×C4—262no—
368C23×C4—262no—
369C23×C4C4×D1311yescharacteristic
370C23×C4C4×D1312yes—
371C23×C4C22×D1312yes—
372C23×C4C22×D1311yescharacteristic
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—134no—
379C22×C8—132no—
380C22×C8—132no—
381C22×C8—262no—
382C22×C8—262no—
383C22×C8—262no—
384C22×C8—262no—
385C22×C8—262no—
386C22×C8C22⋊D1314yescomplemented
387C22×C8C22×D1312yes—
388C22×C8C22×D1312yes—
389C4×D4—2616no—
390C4×D4—268no—
391C4×D4—268no—
392C2×C4⋊C4—134no—
393C2×C4⋊C4—264no—
394C2×C22⋊C4—134no—
395C2×C22⋊C4—134no—
396C2×C22⋊C4—264no—
397C2×C22⋊C4—264no—
398C2×C42—132no—
399C2×C42—134no—
400C2×C42—134no—
401C2×C42—132no—
402C4⋊C8—268no—
403C22⋊C8—28no—
404C22⋊C8—268no—
405C22⋊C8—268no—
406C22⋊C8—268no—
407#97—268no—
408C2×C13—44no—
409C2×C13#195518yescomplemented
410C2×C13C2×#39011yescharacteristic
411C2×C13C2×#40711yescharacteristic
412C2×C13C2×#40811yescharacteristic
413C2×C13C2×#43511yescharacteristic
414C2×C13C2×#43511yescharacteristic
415C2×C13C2×#43511yescharacteristic
416C2×C13C2×#43511yescharacteristic
417D13—44no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—134no—
425C24—132no—
426C24—262no—
427C24—262no—
428C24—262no—
429C24—262no—
430C24—262no—
431C24—262no—
432C24#609414yes—
433C24C2×C4×D1312yes—
434C24C2×C4×D1311yescharacteristic
435C2×D4—268no—
436C2×D4—268no—
437C2×D4—2632no—
438C2×D4—268no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—134no—
456C22×C4—134no—
457C22×C4—132no—
458C22×C4—132no—
459C22×C4—132no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—262no—
467C22×C4—264no—
468C22×C4—264no—
469C22×C4—264no—
470C22×C4—262no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—524no—
477C22×C4—524no—
478C22×C4—524no—
479C22×C4—524no—
480C22×C4C2×C4×D1312yes—
481C22×C4C2×C4×D1311yescharacteristic
482C22×C4#612712yes—
483C22×C4D4×D1312yes—
484C22×C4D4×D1312yes—
485C22×C4D4×D1312yes—
486C22×C4#612912yes—
487C22×C4C2×C22⋊D1312yes—
488C22×C4C23×D1311yescharacteristic
489C2×C8—28no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—44no—
496C2×C8—134no—
497C2×C8—268no—
498C2×C8—262no—
499C2×C8—262no—
500C2×C8—262no—
501C2×C8—262no—
502C2×C8—262no—
503C2×C8—524no—
504C2×C8C2×C22⋊D1314yescomplemented
505C4⋊C4—268no—
506C22⋊C4—268no—
507C22⋊C4—268no—
508C42—138no—
509C42—134no—
510C42—134no—
511C13C2×#195511yescharacteristic, complemented, Sylow
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—28no—
519C23—28no—
520C23—28no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—134no—
526C23—262no—
527C23—262no—
528C23—262no—
529C23—262no—
530C23—262no—
531C23—262no—
532C23—268no—
533C23—268no—
534C23—268no—
535C23—524no—
536C23—524no—
537C23—524no—
538C23—524no—
539C23C22⋊C4×D1312yes—
540C23#8813512yes—
541C23C2×#609414yes—
542C23C2×#609412yes—
543C23#8815512yes—
544C23M16×D1312yes—
545C23#8816112yes—
546C23C4×C22⋊D1312yes—
547C23C22×C4×D1311yescharacteristic
548D4—2632no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—48no—
558C2×C4—134no—
559C2×C4—134no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—262no—
564C2×C4—268no—
565C2×C4—268no—
566C2×C4—262no—
567C2×C4—262no—
568C2×C4—262no—
569C2×C4—524no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—522no—
573C2×C4—522no—
574C2×C4—528no—
575C2×C4C22⋊C4×D1312yes—
576C2×C4#8813512yes—
577C2×C4#8813814yes—
578C2×C4#8813914yes—
579C2×C4C4×C22⋊D1312yes—
580C2×C4#8819314yes—
581C2×C4#8819414yes—
582C2×C4C2×#612711yescharacteristic
583C2×C4C2×D4×D1311yescharacteristic
584C2×C4C2×D4×D1311yescharacteristic
585C2×C4C2×D4×D1311yescharacteristic
586C2×C4C2×#612911yescharacteristic
587C2×C4C22×C22⋊D1311yescharacteristic
588C8—24no—
589C8—42no—
590C8—264no—
591C8—522no—
592C22—24no—
593C22—24no—
594C22—24no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—416no—
600C22—264no—
601C22—264no—
602C22—264no—
603C22—522no—
604C22—522no—
605C22—522no—
606C22—522no—
607C22—5216no—
608C22#1171838714yes—
609C22#1171838814yes—
610C22#1171838914yes—
611C22#1171839114yes—
612C22#1171861814yes—
613C22#1171877214yes—
614C22#1171878814yes—
615C22C2×C22⋊C4×D1311yescharacteristic
616C22C2×#8813511yescharacteristic
617C22C22×#609411yescharacteristic
618C22C2×#8815511yescharacteristic
619C22C2×M16×D1311yescharacteristic
620C22C2×#8816111yescharacteristic
621C22C2×C4×C22⋊D1311yescharacteristic
622C4—42no—
623C4—264no—
624C4—264no—
625C4—522no—
626C4#1171861814yes—
627C4C2×#8813811yescharacteristic
628C4C2×#8813911yescharacteristic
629C4C2×#8819311yescharacteristic
630C4C2×#8819411yescharacteristic
631C2—44no—
632C2—524no—
633C2#1311563218yesdirect product factor
634C2C2×#1171861811yescharacteristic
635C2C2×#1171838711yescharacteristic
636C2C2×#1171838811yescharacteristic
637C2C2×#1171839111yescharacteristic
638C2C2×#1171878811yescharacteristic
639C2C2×#1171877211yescharacteristic
640C2C2×#1171838911yescharacteristic
subgroupG/H
centerC23×C4C22×D13
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊C8C2
socleC24×C13C22×C4
prime radicalC23×C22⋊D13C4
cosocleC22×C4×C13C24
hypercenterC22×C22⋊C8D13
hypocenterC13C2×#1955
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#88054C2semidirect
3. C22×C22⋊#1055C2semidirect
4. C22×#88060C2semidirect
5. C22×#88060C2semidirect
6. C22×#88055C2semidirect
7. #13115632C2direct (N × H)
8. C22×C13×C22⋊C8C2semidirect
25. C2×C13×C22⋊C8C22semidirect
27. C2×C22⋊#1055C22semidirect
30. C2×#88060C22semidirect
31. C2×#88060C22semidirect
33. C2×#88055C22semidirect
35. C2×#88054C22semidirect
68. C22×C8×C13D4semidirect
89. C22×#1055D4semidirect
177. C2×C8×C13C2×D4semidirect
191. C2×#1055C2×D4semidirect
197. C22×C22⋊C8D13semidirect
304. C2×C22⋊C8C2×D13semidirect
386. C22×C8C22⋊D13semidirect
409. C2×C13#1955semidirect
504. C2×C8C2×C22⋊D13semidirect
511. C13C2×#1955semidirect
633. C2#13115632direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D132
C22×#880542
C22×C22⋊#10552
C22×#880602
C22×#880552
#131156322
C22×C13×C22⋊C82
C2×#195513