Finite Group Databasebeta

← C2×#13119107 #16032683

Subgroups — C2×#13119107 #16032683

Order 3328.

4166 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88131C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic13C211yesmaximal, characteristic
3#13119107C2116yesmaximal, direct product factor
4C2×#11718610C212yesmaximal, complemented
5C2×#11718613C212yesmaximal, complemented
6C2×#11718606C212yesmaximal, complemented
7C2×#11718612C212yesmaximal, complemented
8C2×#11718611C211yesmaximal, characteristic, complemented
9C2×#11718607C211yesmaximal, characteristic, complemented
10C2×#11718604C211yesmaximal, characteristic, complemented
11C2×#11718908C211yesmaximal, characteristic
12C2×C13×#379C211yesmaximal, characteristic
13C26×C13C2211yescharacteristic
14C24×Dic13C2211yescharacteristic
15C24×Dic13C2211yescharacteristic
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2212yes—
19C22×C13×C22⋊C4C2212yes—
20C22×C22⋊Dic13—28no—
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2212yes—
24C22×C22⋊Dic13C2212yes—
25C22×C22⋊Dic13C2212yes—
26C22×C22⋊Dic13C2218yes—
27C22×C22⋊Dic13C2212yes—
28C22×C4⋊Dic13C2212yescomplemented
29C22×#6101C2211yescharacteristic, complemented
30C22×#6101C2211yescharacteristic, complemented
31C22×#6101C2212yescomplemented
32C22×C4×Dic13C2211yescharacteristic, complemented
33C22×C4×Dic13C2211yescharacteristic, complemented
34C2×#88131—28no—
35C2×#88131C2218yescomplemented
36C13×#379C2218yes—
37#11718908C2218yes—
38C2×#88071C2212yescomplemented
39C2×#88071C2212yescomplemented
40C2×#88071C2212yescomplemented
41C2×#88071C2212yescomplemented
42#11718613C22116yescomplemented
43#11718612C22116yescomplemented
44#11718611C2218yescomplemented
45#11718610C22116yescomplemented
46#11718607C2218yescomplemented
47#11718606C22116yescomplemented
48#11718604C2218yescomplemented
49C25×C13—24no—
50C25×C13—28no—
51C25×C13—24no—
52C25×C13—24no—
53C25×C13—44no—
54C25×C13C2312yes—
55C25×C13C2314yes—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2312yes—
60C23×Dic13—24no—
61C23×Dic13—24no—
62C23×Dic13—24no—
63C23×Dic13—44no—
64C23×Dic13D418yes—
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2312yes—
68C23×Dic13C2312yes—
69C23×Dic13C2314yes—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2314yes—
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—28no—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—44no—
77C2×C13×C22⋊C4C2314yes—
78C2×C13×C22⋊C4C2314yes—
79C2×C13×C22⋊C4C2318yes—
80C2×C13×C22⋊C4C2318yes—
81C2×C22⋊Dic13—24no—
82C2×C22⋊Dic13—24no—
83C2×C22⋊Dic13—28no—
84C2×C22⋊Dic13—232no—
85C2×C22⋊Dic13—28no—
86C2×C22⋊Dic13—28no—
87C2×C22⋊Dic13—44no—
88C2×C22⋊Dic13C2314yes—
89C2×C22⋊Dic13C2318yes—
90C2×C22⋊Dic13C2318yes—
91C2×C22⋊Dic13C2314yes—
92C2×C22⋊Dic13C2318yes—
93C2×C22⋊Dic13C2318yes—
94C2×C4⋊Dic13—44no—
95C2×C4⋊Dic13C2318yescomplemented
96C2×#6101—24no—
97C2×#6101—24no—
98C2×#6101—44no—
99C2×#6101C2314yescomplemented
100C2×#6101C2314yescomplemented
101C2×#6101C2318yescomplemented
102C2×C4×Dic13—24no—
103C2×C4×Dic13—24no—
104C2×C4×Dic13C2314yescomplemented
105C2×C4×Dic13C2314yescomplemented
106#88131—232no—
107#88071C2318yescomplemented
108#88071C2318yescomplemented
109#88071C2318yescomplemented
110#88071C2318yescomplemented
111C2×#2482—131nomaximal, Sylow
112C24×C13—24no—
113C24×C13—24no—
114C24×C13—232no—
115C24×C13—28no—
116C24×C13—24no—
117C24×C13—24no—
118C24×C13—216no—
119C24×C13—24no—
120C24×C13—24no—
121C24×C13—24no—
122C24×C13—24no—
123C24×C13—28no—
124C24×C13—28no—
125C24×C13—48no—
126C24×C13—432no—
127C24×C13—432no—
128C24×C13—416no—
129C24×C13—416no—
130C24×C13C2×D414yes—
131C24×C13#4114yes—
132C24×C13#4118yes—
133C24×C13#4114yes—
134C24×C13C2414yes—
135C24×C13C2412yes—
136C24×C13C2411yescharacteristic
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13—24no—
142C22×C4×C13—24no—
143C22×C4×C13—24no—
144C22×C4×C13C2414yes—
145C22×C4×C13C2412yes—
146C22×C4×C13C2412yes—
147C22×Dic13—232no—
148C22×Dic13—28no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—28no—
152C22×Dic13—22no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—28no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13—24no—
165C22×Dic13—48no—
166C22×Dic13—416no—
167C22×Dic13C2×D4116yes—
168C22×Dic13C2×D414yes—
169C22×Dic13C2×D414yes—
170C22×Dic13C2414yes—
171C22×Dic13C2412yes—
172C22×Dic13C2414yes—
173C22×Dic13C2412yes—
174C22×Dic13C2412yes—
175C22×Dic13C2412yes—
176C13×C22⋊C4—28no—
177C13×C22⋊C4—216no—
178C13×C22⋊C4—28no—
179C13×C22⋊C4—48no—
180C22⋊Dic13—28no—
181C22⋊Dic13—28no—
182C22⋊Dic13—216no—
183C22⋊Dic13—216no—
184C22⋊Dic13—216no—
185C22⋊Dic13—48no—
186C4⋊Dic13—48no—
187#6101—28no—
188#6101—28no—
189#6101—48no—
190C4×Dic13—28no—
191C4×Dic13—28no—
192C22×#117—131no—
193C23×C22⋊C4—131no—
194#2482—1316no—
195C2×#399—132no—
196C2×#397—132no—
197C2×#388—132no—
198C2×#388—132no—
199C2×#385—131no—
200C2×#385—131no—
201C2×#381—131no—
202C2×#379—131no—
203C2×#379D1311yescharacteristic
204C23×C13—28no—
205C23×C13—28no—
206C23×C13—216no—
207C23×C13—216no—
208C23×C13—24no—
209C23×C13—24no—
210C23×C13—232no—
211C23×C13—216no—
212C23×C13—216no—
213C23×C13—216no—
214C23×C13—24no—
215C23×C13—24no—
216C23×C13—24no—
217C23×C13—24no—
218C23×C13—24no—
219C23×C13—24no—
220C23×C13—432no—
221C23×C13—432no—
222C23×C13—416no—
223C23×C13—4128no—
224C23×C13—416no—
225C23×C13—48no—
226C23×C13—48no—
227C23×C13—48no—
228C23×C13—48no—
229C23×C13#123116yes—
230C23×C13C22×D414yes—
231C23×C13C22×D412yes—
232C23×C13C2×#4118yes—
233C23×C13C2×#4114yes—
234C23×C13C2×#4114yes—
235C23×C13C2×#4112yes—
236C23×C13C2×#4112yes—
237C23×C13C2×#4114yes—
238C23×C13H(5,𝔽2)14yes—
239C23×C13C2511yescharacteristic
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—44no—
248C2×C4×C13—44no—
249C2×C4×C13—48no—
250C2×Dic13—232no—
251C2×Dic13—28no—
252C2×Dic13—28no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—24no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—416no—
268C2×Dic13—44no—
269C2×Dic13—44no—
270C2×Dic13—48no—
271C2×Dic13—48no—
272C2×Dic13C22×D414yes—
273C2×Dic13C22×D414yes—
274C26C2×D1311yescharacteristic
275C24×C4—131no—
276C24×C4—131no—
277C2×#117—138no—
278C2×#117—268no—
279C22×C4⋊C4—131no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—132no—
282C22×C4⋊C4—132no—
283C22×C22⋊C4—132no—
284C22×C22⋊C4—132no—
285C22×C22⋊C4—138no—
286C22×C22⋊C4—132no—
287C22×C22⋊C4—131no—
288C22×C22⋊C4—131no—
289C22×C22⋊C4—132no—
290C22×C22⋊C4—268no—
291C22×C22⋊C4C2×D1312yes—
292C22×C22⋊C4C2×D1311yescharacteristic
293C22×C22⋊C4C2×D1311yescharacteristic
294C22×C22⋊C4C2×D1312yes—
295C22×C42—131no—
296C22×C42—131no—
297#399—1316no—
298#397—1316no—
299#388—1316no—
300#388—1316no—
301#385—138no—
302#385—138no—
303#381—138no—
304#379—138no—
305#379C2×D1318yes—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95—132no—
309C2×#95—132no—
310C22×C13—24no—
311C22×C13—24no—
312C22×C13—28no—
313C22×C13—28no—
314C22×C13—232no—
315C22×C13—28no—
316C22×C13—28no—
317C22×C13—28no—
318C22×C13—464no—
319C22×C13—44no—
320C22×C13—44no—
321C22×C13—44no—
322C22×C13—44no—
323C22×C13—432no—
324C22×C13C2×#12318yes—
325C22×C13C2×#12314yes—
326C22×C13#52514yes—
327C22×C13#53514yes—
328C22×C13#55118yes—
329C22×C13#55118yes—
330C22×C13C23×D411yescharacteristic
331C22×C13C22×#4111yescharacteristic
332C22×C13C22×#4111yescharacteristic
333C22×C13C22×#4112yes—
334C22×C13C2×H(5,𝔽2)12yes—
335C4×C13—42no—
336C4×C13—42no—
337C4×C13—44no—
338Dic13—24no—
339Dic13—24no—
340Dic13—42no—
341Dic13—42no—
342Dic13—44no—
343Dic13—44no—
344C25—24no—
345C25—28no—
346C25—24no—
347C25—24no—
348C25—44no—
349C25C22×D1312yes—
350C25C22×D1314yes—
351C25C22×D1311yescharacteristic
352C23×C4—138no—
353C23×C4—134no—
354C23×C4—131no—
355C23×C4—131no—
356C23×C4—131no—
357C23×C4—132no—
358C23×C4—131no—
359C23×C4—132no—
360C23×C4—134no—
361C23×C4—264no—
362C23×C4—264no—
363C23×C4—264no—
364C23×C4—524no—
365C23×C4C22×D1311yescharacteristic
366C23×C4C22×D1312yes—
367C23×C4C22×D1311yescharacteristic
368#117—2632no—
369C2×C4⋊C4—134no—
370C2×C4⋊C4—134no—
371C2×C4⋊C4—138no—
372C2×C4⋊C4—138no—
373C2×C4⋊C4—264no—
374C2×C4⋊C4—264no—
375C2×C4⋊C4—524no—
376C2×C4⋊C4—524no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—138no—
382C2×C22⋊C4—138no—
383C2×C22⋊C4—134no—
384C2×C22⋊C4—134no—
385C2×C22⋊C4—138no—
386C2×C22⋊C4—138no—
387C2×C22⋊C4—268no—
388C2×C22⋊C4—268no—
389C2×C22⋊C4—2632no—
390C2×C22⋊C4—264no—
391C2×C22⋊C4—264no—
392C2×C22⋊C4—268no—
393C2×C22⋊C4—524no—
394C2×C22⋊C4C22×D1314yes—
395C2×C22⋊C4C22×D1314yes—
396C2×C22⋊C4C22×D1318yes—
397C2×C22⋊C4C22×D1318yes—
398C2×C42—134no—
399C2×C42—134no—
400C2×C42—264no—
401C2×C42—264no—
402#95—138no—
403#95—138no—
404#95—138no—
405#95—138no—
406C2×C13—28no—
407C2×C13—48no—
408C2×C13#248218yescomplemented
409C2×C13C22×#12311yescharacteristic
410C2×C13C2×#52511yescharacteristic
411C2×C13C2×#53511yescharacteristic
412C2×C13C2×#55112yes—
413C2×C13C2×#55112yes—
414C24—24no—
415C24—24no—
416C24—232no—
417C24—24no—
418C24—28no—
419C24—24no—
420C24—216no—
421C24—24no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—28no—
426C24—28no—
427C24—48no—
428C24—432no—
429C24—432no—
430C24—416no—
431C24—416no—
432C24#612714yes—
433C24D4×D1314yes—
434C24#612918yes—
435C24#612914yes—
436C24C23×D1314yes—
437C24C23×D1312yes—
438C24C23×D1311yescharacteristic
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—134no—
447C22×C4—134no—
448C22×C4—1316no—
449C22×C4—132no—
450C22×C4—132no—
451C22×C4—134no—
452C22×C4—132no—
453C22×C4—134no—
454C22×C4—132no—
455C22×C4—2632no—
456C22×C4—268no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—268no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—264no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—268no—
466C22×C4—264no—
467C22×C4—264no—
468C22×C4—264no—
469C22×C4—264no—
470C22×C4—264no—
471C22×C4—264no—
472C22×C4—264no—
473C22×C4—528no—
474C22×C4—5216no—
475C22×C4C23×D1314yes—
476C22×C4C23×D1312yes—
477C22×C4C23×D1312yes—
478C4⋊C4—268no—
479C4⋊C4—268no—
480C4⋊C4—528no—
481C4⋊C4—528no—
482C22⋊C4—28no—
483C22⋊C4—216no—
484C22⋊C4—28no—
485C22⋊C4—48no—
486C22⋊C4—2616no—
487C22⋊C4—2616no—
488C22⋊C4—268no—
489C22⋊C4—268no—
490C22⋊C4—2616no—
491C22⋊C4—528no—
492C42—268no—
493C42—268no—
494C13C2×#248211yescharacteristic, complemented, Sylow
495C23—216no—
496C23—28no—
497C23—216no—
498C23—28no—
499C23—24no—
500C23—24no—
501C23—232no—
502C23—216no—
503C23—216no—
504C23—216no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—432no—
512C23—432no—
513C23—4128no—
514C23—416no—
515C23—416no—
516C23—48no—
517C23—48no—
518C23—48no—
519C23—48no—
520C23#88137116yes—
521C23C2×#612714yes—
522C23C2×#612712yes—
523C23C2×D4×D1314yes—
524C23C2×D4×D1312yes—
525C23C2×#612918yes—
526C23C2×#612914yes—
527C23C2×#612912yes—
528C23C2×#612914yes—
529C23#8825114yes—
530C23C24×D1311yescharacteristic
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—44no—
539C2×C4—48no—
540C2×C4—44no—
541C2×C4—134no—
542C2×C4—134no—
543C2×C4—2632no—
544C2×C4—268no—
545C2×C4—268no—
546C2×C4—262no—
547C2×C4—262no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—264no—
551C2×C4—262no—
552C2×C4—262no—
553C2×C4—264no—
554C2×C4—264no—
555C2×C4—264no—
556C2×C4—264no—
557C2×C4—264no—
558C2×C4—264no—
559C2×C4—264no—
560C2×C4—5216no—
561C2×C4—528no—
562C2×C4—524no—
563C2×C4—524no—
564C2×C4—528no—
565C22—232no—
566C22—24no—
567C22—28no—
568C22—28no—
569C22—24no—
570C22—28no—
571C22—28no—
572C22—28no—
573C22—464no—
574C22—432no—
575C22—44no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22C2×#8813718yes—
580C22C2×#8813714yes—
581C22#1171920018yes—
582C22#1171929114yes—
583C22#1171929218yes—
584C22#1171929714yes—
585C22C22×#612711yescharacteristic
586C22C22×D4×D1311yescharacteristic
587C22C22×#612911yescharacteristic
588C22C22×#612912yes—
589C22C2×#8825112yes—
590C4—42no—
591C4—44no—
592C4—42no—
593C4—264no—
594C4—264no—
595C4—522no—
596C4—524no—
597C4—522no—
598C4—524no—
599C2—28no—
600C2—48no—
601C2#1311910718yesdirect product factor
602C2C22×#8813711yescharacteristic
603C2C2×#1171929111yescharacteristic
604C2C2×#1171929711yescharacteristic
605C2C2×#1171920012yes—
606C2C2×#1171929212yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#379C2
socleC24×C13C24
prime radicalC26×C13C22
hypercenterC2×#379D13
hypocenterC13C2×#2482
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C22×#88131C2semidirect
3. #13119107C2direct (N × H)
4. C2×#11718610C2semidirect
5. C2×#11718613C2semidirect
6. C2×#11718606C2semidirect
7. C2×#11718612C2semidirect
8. C2×#11718611C2semidirect
9. C2×#11718607C2semidirect
10. C2×#11718604C2semidirect
28. C22×C4⋊Dic13C22semidirect
29. C22×#6101C22semidirect
30. C22×#6101C22semidirect
31. C22×#6101C22semidirect
32. C22×C4×Dic13C22semidirect
33. C22×C4×Dic13C22semidirect
35. C2×#88131C22semidirect
38. C2×#88071C22semidirect
39. C2×#88071C22semidirect
40. C2×#88071C22semidirect
41. C2×#88071C22semidirect
42. #11718613C22semidirect
43. #11718612C22semidirect
44. #11718611C22semidirect
45. #11718610C22semidirect
46. #11718607C22semidirect
47. #11718606C22semidirect
48. #11718604C22semidirect
95. C2×C4⋊Dic13C23semidirect
99. C2×#6101C23semidirect
100. C2×#6101C23semidirect
101. C2×#6101C23semidirect
104. C2×C4×Dic13C23semidirect
105. C2×C4×Dic13C23semidirect
107. #88071C23semidirect
108. #88071C23semidirect
109. #88071C23semidirect
110. #88071C23semidirect
408. C2×C13#2482semidirect
494. C13C2×#2482semidirect
601. C2#13119107direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881312
C23×C22⋊Dic132
#131191072
C2×#117186102
C2×#117186132
C2×#117186062
C2×#117186122
C2×#117186112
C2×#117186072
C2×#117186042
C2×#117189082
C2×C13×#3792
C2×#248213