Finite Group Databasebeta

← C2×#13120579 #16029283

Subgroups — C2×#13120579 #16029283

Order 3328.

3718 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88148C212yesmaximal, complemented
2C22×#88149C211yesmaximal, characteristic
3C22×C4⋊C4×D13C211yesmaximal, characteristic, complemented
4#13120579C2116yesmaximal, direct product factor
5C2×#11718641C211yesmaximal, characteristic, complemented
6C2×#11718337C212yesmaximal, complemented
7C2×#11718655C212yesmaximal, complemented
8C2×#11718333C211yesmaximal, characteristic, complemented
9C2×#11718652C211yesmaximal, characteristic, complemented
10C2×#11718326C212yesmaximal, complemented
11C2×#11718328C211yesmaximal, characteristic, complemented
12C2×C13×#398C211yesmaximal, characteristic, complemented
13C23×D52C2212yes—
14C23×D52C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C23×C4×D13C2211yescharacteristic
17C23×C4×D13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2212yes—
26C22×#6103C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2212yes—
31C22×#6101C2212yes—
32C2×#88149—28no—
33C2×#88149C2218yes—
34C2×#88148—216no—
35C2×#88148C22116yescomplemented
36C2×C4⋊C4×D13—28no—
37C2×C4⋊C4×D13C2218yescomplemented
38C13×#398C2218yescomplemented
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2212yes—
41C2×#88071C2211yescharacteristic
42C2×#88071C2212yes—
43#11718655C22116yescomplemented
44#11718652C2218yescomplemented
45#11718641C2218yescomplemented
46#11718337C22116yescomplemented
47#11718333C2218yescomplemented
48#11718328C2218yescomplemented
49#11718326C22116yescomplemented
50C24×D13C2312yes—
51C24×D13C2311yescharacteristic
52C23×C4×C13C2312yes—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2312yes—
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×Dic13C2312yes—
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C22×D52—28no—
62C22×D52—28no—
63C22×D52—28no—
64C22×D52—24no—
65C22×D52—44no—
66C22×D52C2318yes—
67C22×D52C2314yes—
68C22×C4×D13—24no—
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13—44no—
72C22×C4×D13—44no—
73C22×C4×D13D418yes—
74C22×C4×D13D418yescomplemented
75C22×C4×D13C2314yes—
76C22×C4×D13C2314yes—
77C22×C4×D13C2314yes—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4—28no—
80C2×C13×C4⋊C4—24no—
81C2×C13×C4⋊C4C2314yes—
82C2×C13×C4⋊C4C2318yes—
83C2×C13×C4⋊C4C2314yes—
84C2×#6103—28no—
85C2×#6103—28no—
86C2×#6103—28no—
87C2×#6103—28no—
88C2×#6103—44no—
89C2×#6103—44no—
90C2×#6103C2318yes—
91C2×#6103C2318yes—
92C2×#6103C2318yes—
93C2×#6103C2318yes—
94C2×#6103C2318yes—
95C2×#6103C2318yes—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13C2314yes—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101—28no—
101C2×#6101—44no—
102C2×#6101C2314yes—
103C2×#6101C2314yes—
104C2×#6101C2318yes—
105C2×#6101C2318yes—
106#88149—232no—
107#88148—264no—
108C4⋊C4×D13—232no—
109C13×#95C2318yes—
110C13×#95C2314yes—
111#88071C2318yes—
112#88071C2314yes—
113C2×#2618—131nomaximal, Sylow
114C24×C13C2411yescharacteristic
115C23×D13—24no—
116C23×D13—24no—
117C23×D13—24no—
118C23×D13—24no—
119C23×D13—24no—
120C23×D13—24no—
121C23×D13—24no—
122C23×D13—24no—
123C23×D13—24no—
124C23×D13C2×D414yes—
125C23×D13C2×D414yes—
126C23×D13#4114yes—
127C23×D13C2414yes—
128C23×D13C2412yes—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—24no—
132C22×C4×C13—22no—
133C22×C4×C13—24no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13C2×D414yes—
141C22×C4×C13C2×D414yes—
142C22×C4×C13C2414yes—
143C22×C4×C13C2414yes—
144C22×C4×C13C2412yes—
145C22×C4×C13C2412yes—
146C22×C4×C13C2412yes—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—24no—
150C22×Dic13—22no—
151C22×Dic13—24no—
152C22×Dic13—24no—
153C22×Dic13—24no—
154C22×Dic13—24no—
155C22×Dic13C2×D414yes—
156C22×Dic13C2×D414yes—
157C22×Dic13C2414yes—
158C22×Dic13C2412yes—
159C22×Dic13C2412yes—
160C22×Dic13C2412yes—
161C2×D52—216no—
162C2×D52—216no—
163C2×D52—216no—
164C2×D52—28no—
165C2×D52—48no—
166C2×D52—416no—
167C2×D52—432no—
168C2×C4×D13—232no—
169C2×C4×D13—28no—
170C2×C4×D13—28no—
171C2×C4×D13—28no—
172C2×C4×D13—416no—
173C2×C4×D13—48no—
174C2×C4×D13—48no—
175C2×C4×D13—416no—
176C2×C4×D13C2×D4116yes—
177C2×C4×D13C2×D4116yescomplemented
178C13×C4⋊C4—28no—
179C13×C4⋊C4—216no—
180C13×C4⋊C4—28no—
181#6103—216no—
182#6103—216no—
183#6103—216no—
184#6103—216no—
185#6103—48no—
186#6103—48no—
187C4⋊Dic13—28no—
188#6101—28no—
189#6101—28no—
190#6101—216no—
191#6101—48no—
192C22×#123—132no—
193C22×#121—131no—
194C23×C4⋊C4—131no—
195#2618—1316no—
196C2×#398—131no—
197C2×#398D1311yescharacteristic, complemented
198C2×#396—132no—
199C2×#396—132no—
200C2×#394—131no—
201C2×#394—131no—
202C2×#386—132no—
203C2×#380—131no—
204C23×C13C22×D412yes—
205C23×C13C22×D412yes—
206C23×C13C2×#4112yes—
207C23×C13H(5,𝔽2)14yes—
208C23×C132−1+414yes—
209C23×C13C2511yescharacteristic
210C22×D13—28no—
211C22×D13—28no—
212C22×D13—216no—
213C22×D13—216no—
214C22×D13—24no—
215C22×D13—24no—
216C22×D13—24no—
217C22×D13—24no—
218C22×D13—24no—
219C22×D13—24no—
220C22×D13—24no—
221C22×D13—24no—
222C22×D13—24no—
223C22×D13—48no—
224C22×D13—48no—
225C22×D13—48no—
226C22×D13—48no—
227C22×D13—48no—
228C22×D13—48no—
229C22×D13—48no—
230C22×D13#121116yes—
231C22×D13C22×D414yes—
232C22×D13C22×D414yes—
233C22×D13C2×#4114yes—
234C2×C4×C13—28no—
235C2×C4×C13—28no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—24no—
247C2×C4×C13—48no—
248C2×C4×C13—44no—
249C2×C4×C13—48no—
250C2×C4×C13C22×D414yes—
251C2×C4×C13C22×D414yes—
252C2×Dic13—28no—
253C2×Dic13—28no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—24no—
257C2×Dic13—22no—
258C2×Dic13—24no—
259C2×Dic13—24no—
260C2×Dic13—24no—
261C2×Dic13—24no—
262C2×Dic13—44no—
263C2×Dic13—48no—
264C2×Dic13C22×D414yes—
265C2×Dic13C22×D414yes—
266D52—416no—
267D52—432no—
268C4×D13—232no—
269C4×D13—416no—
270C4×D13—416no—
271C23×D4—132no—
272C23×D4—131no—
273C24×C4—131no—
274C24×C4—131no—
275C24×C4—131no—
276C2×#123—1316no—
277C2×#123—2616no—
278C2×#121—138no—
279C2×#121—268no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4—132no—
283C22×C4⋊C4—131no—
284C22×C4⋊C4—132no—
285C22×C4⋊C4—138no—
286C22×C4⋊C4—268no—
287C22×C4⋊C4C2×D1311yescharacteristic
288C22×C4⋊C4C2×D1312yes—
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C22⋊C4—132no—
291C22×C22⋊C4—132no—
292C22×C22⋊C4—132no—
293C22×C22⋊C4—132no—
294C22×C22⋊C4—132no—
295C22×C22⋊C4—132no—
296#398—138no—
297#398C2×D1318yescomplemented
298#396—1316no—
299#396—1316no—
300#394—138no—
301#394—138no—
302#386—1316no—
303#380—138no—
304C2×#95—131no—
305C2×#95—132no—
306C2×#95C2×D1311yescharacteristic
307C2×#95C2×D1312yes—
308C22×C13C2×#12114yes—
309C22×C13#53414yes—
310C22×C13#53614yes—
311C22×C13#53718yes—
312C22×C13#53918yes—
313C22×C13C23×D411yescharacteristic
314C22×C13C23×D411yescharacteristic
315C22×C13C22×#4111yescharacteristic
316C22×C13C2×H(5,𝔽2)12yes—
317C22×C13C2×2−1+412yes—
318C2×D13—232no—
319C2×D13—24no—
320C2×D13—24no—
321C2×D13—28no—
322C2×D13—28no—
323C2×D13—44no—
324C2×D13—44no—
325C2×D13—44no—
326C2×D13—44no—
327C2×D13—44no—
328C2×D13—44no—
329C2×D13—44no—
330C2×D13—816no—
331C2×D13C2×#12118yes—
332C4×C13—24no—
333C4×C13—24no—
334C4×C13—44no—
335C4×C13—42no—
336C4×C13—44no—
337Dic13—24no—
338Dic13—24no—
339Dic13—42no—
340Dic13—44no—
341C25—131no—
342C25—132no—
343C22×D4—138no—
344C22×D4—134no—
345C22×D4—268no—
346C22×D4—268no—
347C22×D4—268no—
348C22×D4—264no—
349C22×D4—524no—
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—138no—
353C23×C4—134no—
354C23×C4—138no—
355C23×C4—134no—
356C23×C4—132no—
357C23×C4—131no—
358C23×C4—134no—
359C23×C4—264no—
360C23×C4—264no—
361C23×C4—264no—
362C23×C4—524no—
363C23×C4—524no—
364C23×C4C22×D1312yes—
365C23×C4C22×D1311yescharacteristic
366C23×C4C22×D1312yes—
367C23×C4C22×D1311yescharacteristic
368C23×C4C22×D1311yescharacteristic
369#123—2664no—
370#121—2632no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—134no—
375C2×C4⋊C4—134no—
376C2×C4⋊C4—134no—
377C2×C4⋊C4—138no—
378C2×C4⋊C4—138no—
379C2×C4⋊C4—2632no—
380C2×C4⋊C4—264no—
381C2×C4⋊C4—264no—
382C2×C4⋊C4—268no—
383C2×C4⋊C4—264no—
384C2×C4⋊C4—524no—
385C2×C4⋊C4C22×D1314yes—
386C2×C4⋊C4C22×D1314yes—
387C2×C4⋊C4C22×D1318yes—
388C2×C22⋊C4—138no—
389C2×C22⋊C4—138no—
390C2×C22⋊C4—138no—
391C2×C22⋊C4—138no—
392C2×C22⋊C4—138no—
393C2×C22⋊C4—138no—
394C2×C22⋊C4—268no—
395C2×C22⋊C4—268no—
396C2×C22⋊C4—268no—
397C2×C22⋊C4—268no—
398C2×C22⋊C4—524no—
399C2×C22⋊C4—524no—
400#95—134no—
401#95—138no—
402#95C22×D1314yes—
403#95C22×D1318yes—
404C2×C13#261818yescomplemented
405C2×C13C22×#12111yescharacteristic
406C2×C13C2×#53411yescharacteristic
407C2×C13C2×#53611yescharacteristic
408C2×C13C2×#53712yes—
409C2×C13C2×#53912yes—
410D13—28no—
411D13—84no—
412C24—134no—
413C24—134no—
414C24—134no—
415C24—132no—
416C24—134no—
417C24—264no—
418C24—264no—
419C24—264no—
420C24—264no—
421C24—264no—
422C24—264no—
423C24—264no—
424C24—264no—
425C24—264no—
426C24C23×D1311yescharacteristic
427C2×D4—2616no—
428C2×D4—2616no—
429C2×D4—2616no—
430C2×D4—268no—
431C2×D4—528no—
432C2×D4—5216no—
433C2×D4—5232no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—134no—
446C22×C4—134no—
447C22×C4—132no—
448C22×C4—132no—
449C22×C4—1316no—
450C22×C4—1316no—
451C22×C4—134no—
452C22×C4—132no—
453C22×C4—268no—
454C22×C4—2632no—
455C22×C4—268no—
456C22×C4—268no—
457C22×C4—262no—
458C22×C4—262no—
459C22×C4—264no—
460C22×C4—264no—
461C22×C4—262no—
462C22×C4—264no—
463C22×C4—264no—
464C22×C4—264no—
465C22×C4—5216no—
466C22×C4—528no—
467C22×C4—528no—
468C22×C4—5216no—
469C22×C4D4×D1314yes—
470C22×C4D4×D1314yes—
471C22×C4C23×D1314yes—
472C22×C4C23×D1314yes—
473C22×C4C23×D1312yes—
474C22×C4C23×D1312yes—
475C22×C4C23×D1312yes—
476C4⋊C4—28no—
477C4⋊C4—28no—
478C4⋊C4—216no—
479C4⋊C4—268no—
480C4⋊C4—268no—
481C4⋊C4—2616no—
482C4⋊C4—268no—
483C4⋊C4—528no—
484C22⋊C4—2616no—
485C22⋊C4—2616no—
486C22⋊C4—2616no—
487C22⋊C4—2616no—
488C22⋊C4—528no—
489C22⋊C4—528no—
490C13C2×#261811yescharacteristic, complemented, Sylow
491C23—1316no—
492C23—134no—
493C23—134no—
494C23—134no—
495C23—268no—
496C23—2616no—
497C23—268no—
498C23—264no—
499C23—264no—
500C23—2616no—
501C23—264no—
502C23—264no—
503C23—264no—
504C23—264no—
505C23—264no—
506C23—264no—
507C23—264no—
508C23—528no—
509C23—528no—
510C23—528no—
511C23—528no—
512C23—528no—
513C23—528no—
514C23—528no—
515C23C2×D4×D1312yes—
516C23C2×D4×D1312yes—
517C23#8825414yes—
518C23#41×D1312yes—
519C23#8825614yes—
520C23C24×D1311yescharacteristic
521D4—5216no—
522D4—5232no—
523C2×C4—28no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—48no—
537C2×C4—48no—
538C2×C4—44no—
539C2×C4—134no—
540C2×C4—134no—
541C2×C4—2632no—
542C2×C4—268no—
543C2×C4—268no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—264no—
547C2×C4—264no—
548C2×C4—262no—
549C2×C4—264no—
550C2×C4—264no—
551C2×C4—264no—
552C2×C4—5216no—
553C2×C4—5216no—
554C2×C4—528no—
555C2×C4—524no—
556C2×C4C2×D4×D1314yes—
557C2×C4C2×D4×D1314yes—
558C22—138no—
559C22—2632no—
560C22—264no—
561C22—264no—
562C22—268no—
563C22—268no—
564C22—524no—
565C22—524no—
566C22—524no—
567C22—524no—
568C22—524no—
569C22—524no—
570C22—524no—
571C22—10416no—
572C22D13×#12114yes—
573C22#1171933418yes—
574C22#1171935814yes—
575C22#1171939718yes—
576C22#1171942914yes—
577C22C22×D4×D1311yescharacteristic
578C22C22×D4×D1311yescharacteristic
579C22C2×#8825412yes—
580C22C2×#41×D1311yescharacteristic
581C22C2×#8825612yes—
582C4—24no—
583C4—24no—
584C4—44no—
585C4—42no—
586C4—44no—
587C4—264no—
588C4—264no—
589C4—522no—
590C4—524no—
591C2—268no—
592C2—1044no—
593C2#1312057918yesdirect product factor
594C2C2×D13×#12111yescharacteristic
595C2C2×#1171935811yescharacteristic
596C2C2×#1171942911yescharacteristic
597C2C2×#1171933412yes—
598C2C2×#1171939712yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#398C2
socleC24×C13C24
prime radicalC22×#88149C2
hypercenterC2×#398D13
hypocenterC13C2×#2618
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#88148C2semidirect
3. C22×C4⋊C4×D13C2semidirect
4. #13120579C2direct (N × H)
5. C2×#11718641C2semidirect
6. C2×#11718337C2semidirect
7. C2×#11718655C2semidirect
8. C2×#11718333C2semidirect
9. C2×#11718652C2semidirect
10. C2×#11718326C2semidirect
11. C2×#11718328C2semidirect
12. C2×C13×#398C2semidirect
35. C2×#88148C22semidirect
37. C2×C4⋊C4×D13C22semidirect
38. C13×#398C22semidirect
43. #11718655C22semidirect
44. #11718652C22semidirect
45. #11718641C22semidirect
46. #11718337C22semidirect
47. #11718333C22semidirect
48. #11718328C22semidirect
49. #11718326C22semidirect
74. C22×C4×D13D4semidirect
177. C2×C4×D13C2×D4semidirect
197. C2×#398D13semidirect
297. #398C2×D13semidirect
404. C2×C13#2618semidirect
490. C13C2×#2618semidirect
593. C2#13120579direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881482
C22×#881492
C22×C4⋊C4×D132
#131205792
C2×#117186412
C2×#117183372
C2×#117186552
C2×#117183332
C2×#117186522
C2×#117183262
C2×#117183282
C2×C13×#3982
C2×#261813