Finite Group Databasebeta

← C2×#13119990 #16033294

Subgroups — C2×#13119990 #16033294

Order 3328.

4166 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88200C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D13C211yesmaximal, characteristic
3#13119990C2116yesmaximal, direct product factor
4C2×#11718335C211yesmaximal, characteristic, complemented
5C2×#11718614C211yesmaximal, characteristic, complemented
6C2×#11718892C211yesmaximal, characteristic, complemented
7C2×#11718330C212yesmaximal, complemented
8C2×#11718605C212yesmaximal, complemented
9C2×#11718325C212yesmaximal, complemented
10C2×#11718616C212yesmaximal
11C2×#11718327C211yesmaximal, characteristic, complemented
12C2×C13×#393C211yesmaximal, characteristic, complemented
13C25×D13C2211yescharacteristic
14C23×Q8×C13C2211yescharacteristic, complemented
15C23×C4×D13C2211yescharacteristic
16C23×C4×D13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C22⋊Dic13C2211yescharacteristic
21C2×#88200—28no—
22C2×#88200C2218yescomplemented
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2212yes—
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2212yes—
29C22×C4⋊Dic13C2211yescharacteristic, complemented
30C22×#6101C2212yescomplemented
31C22×C4×Dic13C2212yescomplemented
32C2×C22⋊C4×D13—28no—
33C2×C22⋊C4×D13C2218yes—
34C13×#393C2218yescomplemented
35C2×C13×#95C2212yescomplemented
36C2×C13×#95C2211yescharacteristic, complemented
37#11718892C2218yescomplemented
38C2×#88071C2212yescomplemented
39C2×#88071C2212yescomplemented
40C2×#88071C2212yescomplemented
41C2×#88071C2211yescharacteristic, complemented
42#11718616C22116yes—
43#11718614C2218yescomplemented
44#11718605C22116yescomplemented
45#11718335C2218yescomplemented
46#11718330C22116yescomplemented
47#11718327C2218yescomplemented
48#11718325C22116yescomplemented
49C25×C13C2311yescharacteristic
50C24×D13—24no—
51C24×D13—24no—
52C24×D13—24no—
53C24×D13—28no—
54C24×D13—44no—
55C24×D13C2311yescharacteristic
56C24×D13C2314yes—
57C24×D13C2311yescharacteristic
58C22×Q8×C13—24no—
59C22×Q8×C13—44no—
60C22×Q8×C13C2314yescomplemented
61C23×C4×C13C2312yes—
62C23×C4×C13C2312yes—
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13C2312yes—
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C22×C4×D13—24no—
70C22×C4×D13—28no—
71C22×C4×D13—44no—
72C22×C4×D13D418yes—
73C22×C4×D13C2314yes—
74C22×C4×D13C2314yes—
75C2×C13×C22⋊C4—24no—
76C2×C13×C22⋊C4—44no—
77C2×C13×C22⋊C4C2314yes—
78C2×C13×C22⋊C4C2318yes—
79C2×C22⋊Dic13—28no—
80C2×C22⋊Dic13—24no—
81C2×C22⋊Dic13C2314yes—
82C2×C22⋊Dic13C2318yes—
83#88200—232no—
84C2×#6103—28no—
85C2×#6103—28no—
86C2×#6103—28no—
87C2×#6103—24no—
88C2×#6103—24no—
89C2×#6103—44no—
90C2×#6103C2314yes—
91C2×#6103C2314yes—
92C2×#6103C2318yes—
93C2×#6103C2318yes—
94C2×#6103C2318yes—
95C2×#6103C2318yes—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13C2314yescomplemented
98C2×#6101—28no—
99C2×#6101C2318yescomplemented
100C2×C4×Dic13—44no—
101C2×C4×Dic13C2318yescomplemented
102C22⋊C4×D13—232no—
103C13×#95C2318yescomplemented
104C13×#95C2314yescomplemented
105#88071C2318yescomplemented
106#88071C2318yescomplemented
107#88071C2318yescomplemented
108#88071C2314yescomplemented
109C2×#2561—131nomaximal, Sylow
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—24no—
113C24×C13—24no—
114C24×C13#4114yes—
115C24×C13C2412yes—
116C24×C13C2411yescharacteristic
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—24no—
120C23×D13—232no—
121C23×D13—22no—
122C23×D13—28no—
123C23×D13—22no—
124C23×D13—24no—
125C23×D13—24no—
126C23×D13—28no—
127C23×D13—28no—
128C23×D13—216no—
129C23×D13—48no—
130C23×D13—432no—
131C23×D13—432no—
132C23×D13—416no—
133C23×D13—416no—
134C23×D13C2×D414yes—
135C23×D13#4114yes—
136C23×D13#4118yes—
137C23×D13C2412yes—
138C23×D13C2412yes—
139C2×Q8×C13—28no—
140C2×Q8×C13—48no—
141C2×Q8×C13—416no—
142C22×C4×C13—24no—
143C22×C4×C13—24no—
144C22×C4×C13—22no—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—24no—
148C22×C4×C13—24no—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13C2×D414yes—
152C22×C4×C13C2412yes—
153C22×C4×C13C2414yes—
154C22×C4×C13C2414yes—
155C22×C4×C13C2412yes—
156C22×Dic13—24no—
157C22×Dic13—24no—
158C22×Dic13—22no—
159C22×Dic13—24no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13—24no—
165C22×Dic13C2×D414yes—
166C22×Dic13C2412yes—
167C22×Dic13C2414yes—
168C22×Dic13C2414yes—
169C22×Dic13C2412yes—
170C2×C4×D13—28no—
171C2×C4×D13—216no—
172C2×C4×D13—416no—
173C2×C4×D13—48no—
174C2×C4×D13—416no—
175C2×C4×D13C2×D4116yes—
176C13×C22⋊C4—28no—
177C13×C22⋊C4—48no—
178C22⋊Dic13—216no—
179C22⋊Dic13—28no—
180#6103—216no—
181#6103—216no—
182#6103—216no—
183#6103—28no—
184#6103—28no—
185#6103—48no—
186C4⋊Dic13—28no—
187#6101—216no—
188C4×Dic13—48no—
189C22×C22⋊Q8—131no—
190C23×C22⋊C4—131no—
191#2561—1316no—
192C2×#397—131no—
193C2×#397—131no—
194C2×#393—131no—
195C2×#393D1311yescharacteristic, complemented
196C2×#388—132no—
197C2×#388—132no—
198C2×#381—132no—
199C2×#379—132no—
200C2×C4×C22⋊C4—131no—
201C23×C13—28no—
202C23×C13—216no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—24no—
206C23×C13—24no—
207C23×C13—44no—
208C23×C13—44no—
209C23×C13—48no—
210C23×C13C22×D412yes—
211C23×C13C2×#4114yes—
212C23×C13C2×#4112yes—
213C23×C13C2×#4112yes—
214C23×C13C2×#4114yes—
215C23×C13H(5,𝔽2)14yes—
216C23×C13C2511yescharacteristic
217C22×D13—28no—
218C22×D13—28no—
219C22×D13—216no—
220C22×D13—216no—
221C22×D13—22no—
222C22×D13—22no—
223C22×D13—24no—
224C22×D13—232no—
225C22×D13—28no—
226C22×D13—216no—
227C22×D13—22no—
228C22×D13—22no—
229C22×D13—24no—
230C22×D13—24no—
231C22×D13—432no—
232C22×D13—432no—
233C22×D13—4128no—
234C22×D13—416no—
235C22×D13—44no—
236C22×D13—44no—
237C22×D13—48no—
238C22×D13—416no—
239C22×D13#124116yes—
240C22×D13C22×D414yes—
241C22×D13C2×#4114yes—
242C22×D13C2×#4118yes—
243Q8×C13—416no—
244C2×C4×C13—28no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—22no—
248C2×C4×C13—24no—
249C2×C4×C13—24no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—44no—
255C2×C4×C13—48no—
256C2×C4×C13—48no—
257C2×C4×C13C22×D414yes—
258C2×Dic13—28no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—24no—
263C2×Dic13—24no—
264C2×Dic13—24no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—24no—
268C2×Dic13—48no—
269C2×Dic13—44no—
270C2×Dic13—48no—
271C2×Dic13C22×D414yes—
272C4×D13—416no—
273C4×D13—416no—
274C26—131no—
275C23×Q8C2×D1311yescharacteristic, complemented
276C24×C4—131no—
277C24×C4—131no—
278C2×C22⋊Q8—138no—
279C2×C22⋊Q8—268no—
280C22×C4⋊C4—132no—
281C22×C4⋊C4—131no—
282C22×C22⋊C4—132no—
283C22×C22⋊C4—131no—
284C22×C22⋊C4—131no—
285C22×C22⋊C4—132no—
286C22×C22⋊C4—131no—
287C22×C22⋊C4—132no—
288C22×C22⋊C4—132no—
289C22×C22⋊C4—132no—
290C22×C22⋊C4—138no—
291C22×C22⋊C4—268no—
292C22×C22⋊C4C2×D1311yescharacteristic
293C22×C22⋊C4C2×D1312yes—
294C22×C42—132no—
295#397—138no—
296#397—138no—
297#393—138no—
298#393C2×D1318yescomplemented
299#388—1316no—
300#388—1316no—
301#381—1316no—
302#379—1316no—
303C4×C22⋊C4—138no—
304C2×#95—131no—
305C2×#95—132no—
306C2×#95—132no—
307C2×#95—132no—
308C2×#95C2×D1311yescharacteristic, complemented
309C2×#95C2×D1312yescomplemented
310C22×C13—24no—
311C22×C13—28no—
312C22×C13—416no—
313C22×C13—42no—
314C22×C13—42no—
315C22×C13—44no—
316C22×C13#52514yes—
317C22×C13C2×#12414yes—
318C22×C13#53414yes—
319C22×C13#55118yes—
320C22×C13#55118yes—
321C22×C13C23×D411yescharacteristic
322C22×C13C22×#4111yescharacteristic
323C22×C13C22×#4111yescharacteristic
324C22×C13C22×#4112yes—
325C22×C13C2×H(5,𝔽2)12yes—
326C2×D13—232no—
327C2×D13—24no—
328C2×D13—24no—
329C2×D13—28no—
330C2×D13—28no—
331C2×D13—24no—
332C2×D13—28no—
333C2×D13—464no—
334C2×D13—416no—
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—44no—
338C2×D13C2×#12418yes—
339C4×C13—24no—
340C4×C13—42no—
341C4×C13—44no—
342C4×C13—44no—
343Dic13—24no—
344Dic13—44no—
345Dic13—42no—
346Dic13—44no—
347C25—131no—
348C25—131no—
349C25—134no—
350C25—264no—
351C25—264no—
352C25—268no—
353C25—264no—
354C25—524no—
355C25C22×D1311yescharacteristic
356C22×Q8—24no—
357C22×Q8—44no—
358C22×Q8C22×D1314yescomplemented
359C23×C4—131no—
360C23×C4—138no—
361C23×C4—134no—
362C23×C4—132no—
363C23×C4—132no—
364C23×C4—131no—
365C23×C4—134no—
366C23×C4—264no—
367C23×C4—268no—
368C23×C4—524no—
369C23×C4C22×D1312yes—
370C23×C4C22×D1312yes—
371C23×C4C22×D1311yescharacteristic
372C23×C4C22×D1311yescharacteristic
373C22⋊Q8—2632no—
374C2×C4⋊C4—138no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—268no—
377C2×C4⋊C4—264no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—134no—
381C2×C22⋊C4—138no—
382C2×C22⋊C4—134no—
383C2×C22⋊C4—134no—
384C2×C22⋊C4—138no—
385C2×C22⋊C4—138no—
386C2×C22⋊C4—138no—
387C2×C22⋊C4—138no—
388C2×C22⋊C4—2632no—
389C2×C22⋊C4—264no—
390C2×C22⋊C4—268no—
391C2×C22⋊C4—268no—
392C2×C22⋊C4—268no—
393C2×C22⋊C4—264no—
394C2×C22⋊C4—268no—
395C2×C22⋊C4—264no—
396C2×C22⋊C4—524no—
397C2×C22⋊C4C22×D1314yes—
398C2×C22⋊C4C22×D1318yes—
399C2×C42—138no—
400C2×C42—524no—
401#95—134no—
402#95—138no—
403#95—138no—
404#95—138no—
405#95C22×D1314yescomplemented
406#95C22×D1318yescomplemented
407C2×C13—44no—
408C2×C13#256118yescomplemented
409C2×C13C2×#52511yescharacteristic
410C2×C13C22×#12411yescharacteristic
411C2×C13C2×#53411yescharacteristic
412C2×C13C2×#55112yes—
413C2×C13C2×#55112yes—
414D13—28no—
415D13—44no—
416C24—22no—
417C24—24no—
418C24—22no—
419C24—24no—
420C24—134no—
421C24—138no—
422C24—132no—
423C24—134no—
424C24—132no—
425C24—268no—
426C24—268no—
427C24—2616no—
428C24—2632no—
429C24—264no—
430C24—262no—
431C24—262no—
432C24—262no—
433C24—264no—
434C24—268no—
435C24—262no—
436C24—264no—
437C24—528no—
438C24—5232no—
439C24—5216no—
440C24—5232no—
441C24—5216no—
442C24#613114yes—
443C24C23×D1312yes—
444C24C23×D1311yescharacteristic
445C2×Q8—28no—
446C2×Q8—48no—
447C2×Q8—416no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—134no—
458C22×C4—132no—
459C22×C4—1316no—
460C22×C4—132no—
461C22×C4—134no—
462C22×C4—134no—
463C22×C4—268no—
464C22×C4—2616no—
465C22×C4—264no—
466C22×C4—262no—
467C22×C4—264no—
468C22×C4—264no—
469C22×C4—264no—
470C22×C4—264no—
471C22×C4—264no—
472C22×C4—264no—
473C22×C4—264no—
474C22×C4—5216no—
475C22×C4—528no—
476C22×C4—5216no—
477C22×C4D4×D1314yes—
478C22×C4C23×D1312yes—
479C22×C4C23×D1314yes—
480C22×C4C23×D1314yes—
481C22×C4C23×D1312yes—
482C4⋊C4—2616no—
483C4⋊C4—268no—
484C22⋊C4—28no—
485C22⋊C4—48no—
486C22⋊C4—268no—
487C22⋊C4—2616no—
488C22⋊C4—2616no—
489C22⋊C4—2616no—
490C22⋊C4—268no—
491C22⋊C4—2616no—
492C22⋊C4—268no—
493C22⋊C4—528no—
494C42—528no—
495C13C2×#256111yescharacteristic, complemented, Sylow
496C23—28no—
497C23—216no—
498C23—22no—
499C23—24no—
500C23—24no—
501C23—22no—
502C23—44no—
503C23—44no—
504C23—48no—
505C23—1316no—
506C23—134no—
507C23—138no—
508C23—134no—
509C23—2632no—
510C23—268no—
511C23—268no—
512C23—2616no—
513C23—2616no—
514C23—264no—
515C23—262no—
516C23—262no—
517C23—268no—
518C23—262no—
519C23—2616no—
520C23—264no—
521C23—262no—
522C23—264no—
523C23—5232no—
524C23—5216no—
525C23—5232no—
526C23—5216no—
527C23—52128no—
528C23—524no—
529C23—528no—
530C23—524no—
531C23C2×D4×D1312yes—
532C23#8825114yes—
533C23C2×#613114yes—
534C23C2×#613112yes—
535C23#41×D1312yes—
536C23#41×D1314yes—
537C23C24×D1311yescharacteristic
538Q8—416no—
539C2×C4—28no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—48no—
550C2×C4—44no—
551C2×C4—48no—
552C2×C4—134no—
553C2×C4—268no—
554C2×C4—264no—
555C2×C4—262no—
556C2×C4—264no—
557C2×C4—264no—
558C2×C4—264no—
559C2×C4—264no—
560C2×C4—264no—
561C2×C4—264no—
562C2×C4—264no—
563C2×C4—5216no—
564C2×C4—5216no—
565C2×C4—528no—
566C2×C4—528no—
567C2×C4—524no—
568C2×C4C2×D4×D1314yes—
569C22—28no—
570C22—24no—
571C22—42no—
572C22—44no—
573C22—42no—
574C22—416no—
575C22—138no—
576C22—268no—
577C22—264no—
578C22—268no—
579C22—264no—
580C22—2632no—
581C22—264no—
582C22—268no—
583C22—5264no—
584C22—524no—
585C22—522no—
586C22—522no—
587C22—5216no—
588C22#1171929414yes—
589C22#1171933214yes—
590C22#1171934218yes—
591C22D13×#12414yes—
592C22#1171938418yes—
593C22C22×D4×D1311yescharacteristic
594C22C2×#8825112yes—
595C22C22×#613111yescharacteristic
596C22C2×#41×D1312yes—
597C22C2×#41×D1311yescharacteristic
598C4—24no—
599C4—42no—
600C4—44no—
601C4—44no—
602C4—264no—
603C4—524no—
604C4—524no—
605C4—522no—
606C2—44no—
607C2—268no—
608C2—524no—
609C2#1311999018yesdirect product factor
610C2C2×#1171933211yescharacteristic
611C2C2×D13×#12411yescharacteristic
612C2C2×#1171929411yescharacteristic
613C2C2×#1171934212yes—
614C2C2×#1171938412yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#393C2
socleC24×C13C24
prime radicalC25×D13C22
hypercenterC2×#393D13
hypocenterC13C2×#2561
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#88200C2semidirect
3. #13119990C2direct (N × H)
4. C2×#11718335C2semidirect
5. C2×#11718614C2semidirect
6. C2×#11718892C2semidirect
7. C2×#11718330C2semidirect
8. C2×#11718605C2semidirect
9. C2×#11718325C2semidirect
11. C2×#11718327C2semidirect
12. C2×C13×#393C2semidirect
14. C23×Q8×C13C22semidirect
22. C2×#88200C22semidirect
29. C22×C4⋊Dic13C22semidirect
30. C22×#6101C22semidirect
31. C22×C4×Dic13C22semidirect
34. C13×#393C22semidirect
35. C2×C13×#95C22semidirect
36. C2×C13×#95C22semidirect
37. #11718892C22semidirect
38. C2×#88071C22semidirect
39. C2×#88071C22semidirect
40. C2×#88071C22semidirect
41. C2×#88071C22semidirect
43. #11718614C22semidirect
44. #11718605C22semidirect
45. #11718335C22semidirect
46. #11718330C22semidirect
47. #11718327C22semidirect
48. #11718325C22semidirect
60. C22×Q8×C13C23semidirect
97. C2×C4⋊Dic13C23semidirect
99. C2×#6101C23semidirect
101. C2×C4×Dic13C23semidirect
103. C13×#95C23semidirect
104. C13×#95C23semidirect
105. #88071C23semidirect
106. #88071C23semidirect
107. #88071C23semidirect
108. #88071C23semidirect
195. C2×#393D13semidirect
275. C23×Q8C2×D13semidirect
298. #393C2×D13semidirect
308. C2×#95C2×D13semidirect
309. C2×#95C2×D13semidirect
358. C22×Q8C22×D13semidirect
405. #95C22×D13semidirect
406. #95C22×D13semidirect
408. C2×C13#2561semidirect
495. C13C2×#2561semidirect
609. C2#13119990direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C22×C22⋊C4×D132
#131199902
C2×#117183352
C2×#117186142
C2×#117188922
C2×#117183302
C2×#117186052
C2×#117183252
C2×#117186162
C2×#117183272
C2×C13×#3932
C2×#256113