Finite Group Databasebeta

← C2×#13113380 #15830175

Subgroups — C2×#13113380 #15830175

Order 3328.

1510 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2C2×#11718873C211yesmaximal, characteristic, complemented
3#13113380C218yesmaximal, direct product factor
4C2×#11718059C212yesmaximal, complemented
5C2×#11718062C212yesmaximal, complemented
6C2×C13×#407C211yesmaximal, characteristic, complemented
7C24×C4×C13C2211yescharacteristic
8C22×#6127C411yescharacteristic, complemented
9C22×C13×M16—21no—
10C2×#88207—21no—
11C22×C22⋊Dic13—21no—
12#11719496—22no—
13#11719496—22no—
14#11719496C414yescomplemented
15#11719496C2214yes—
16C2×#88184C411yescharacteristic, complemented
17C2×#88184C2211yescharacteristic
18C2×#88183—21no—
19C2×C4×C22⋊D13—21no—
20C2×C4×C22⋊D13—21no—
21C2×#88180C411yescharacteristic, complemented
22C22×C4⋊Dic13—21no—
23C2×#88178C411yescharacteristic, complemented
24C2×#88178C2211yescharacteristic
25C13×#407—22no—
26C13×#407C2214yescomplemented
27C2×C13×C22⋊C8—21no—
28C2×C13×C22⋊C8C2212yes—
29#11718873—22no—
30#11718873C2214yescomplemented
31C2×#88071C2212yes—
32#11718062C2218yescomplemented
33#11718059C2218yescomplemented
34C25×C13D411yescharacteristic
35C23×C4×C13—44no—
36C23×C4×C13C2×C411yescharacteristic
37C23×C4×C13C2×C411yescharacteristic
38C23×C4×C13C2×C412yes—
39C23×C4×C13D411yescharacteristic
40C23×C4×C13D412yes—
41C23×C4×C13D411yescharacteristic
42C23×C4×C13D411yescharacteristic
43C23×C4×C13D412yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C22×C22⋊D13—21no—
47C22×C22⋊D13—21no—
48C22×C22⋊D13—21no—
49C23×Dic13—22no—
50C2×#6127—22no—
51C2×#6127—44no—
52C2×#6127C2×C414yescomplemented
53C22×D52C2×C411yescharacteristic
54C22×C4×D13—21no—
55C22×Dic26C2×C411yescharacteristic
56C2×C13×M16—24no—
57C2×C13×M16—44no—
58C22×C8×C13—22no—
59#88207—24no—
60#88207—24no—
61C2×C22⋊Dic13—21no—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13—21no—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—44no—
66#88184—22no—
67#88184—21no—
68#88184—21no—
69#88184C2×C412yes—
70#88184C2×C414yescomplemented
71#88184C2312yes—
72#88183—24no—
73#88183—24no—
74C4×C22⋊D13—24no—
75C4×C22⋊D13—24no—
76C4×C22⋊D13—24no—
77C4×C22⋊D13—24no—
78C2×#6103—21no—
79C2×#6103—21no—
80#88180—22no—
81#88180C2×C414yescomplemented
82C2×C4⋊Dic13—24no—
83C2×C4⋊Dic13—44no—
84C2×C4⋊Dic13C2×C411yescharacteristic
85C2×C4⋊Dic13C2×C411yescharacteristic
86#88178—22no—
87#88178—21no—
88#88178—21no—
89#88178C2×C412yes—
90#88178C2×C414yescomplemented
91#88178C2312yes—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C13×C22⋊C8—24no—
96C13×C22⋊C8—22no—
97C13×C22⋊C8C2314yes—
98#88071—22no—
99#88071C2314yes—
100C2×#1513—131nomaximal, Sylow
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—42no—
104C24×C13—42no—
105C24×C13C22⋊C411yescharacteristic
106C24×C13C22⋊C411yescharacteristic
107C24×C13C22⋊C412yes—
108C24×C13C2×D411yescharacteristic
109C24×C13C2×D412yes—
110C23×D13—21no—
111C22×C4×C13—24no—
112C22×C4×C13—24no—
113C22×C4×C13—24no—
114C22×C4×C13—44no—
115C22×C4×C13—44no—
116C22×C4×C13—44no—
117C22×C4×C13—44no—
118C22×C4×C13—42no—
119C22×C4×C13—42no—
120C22×C4×C13—42no—
121C22×C4×C13C22⋊C411yescharacteristic
122C22×C4×C13C22⋊C412yes—
123C22×C4×C13C22⋊C412yes—
124C22×C4×C13C22⋊C412yes—
125C22×C4×C13C22⋊C412yes—
126C22×C4×C13C22⋊C412yes—
127C22×C4×C13C22⋊C411yescharacteristic
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C22×C412yes—
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C412yes—
132C22×C4×C13C2×D412yes—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2411yescharacteristic
139C2×C22⋊D13—22no—
140C2×C22⋊D13—24no—
141C2×C22⋊D13—24no—
142C2×C22⋊D13—22no—
143C2×C22⋊D13—44no—
144C2×C22⋊D13—44no—
145C2×C22⋊D13—42no—
146C2×C22⋊D13—42no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—24no—
151C22×Dic13—44no—
152C22×Dic13—44no—
153C22×Dic13—44no—
154#6127—48no—
155#6127—48no—
156C2×D52—21no—
157C2×D52—42no—
158C2×D52C22×C412yes—
159C2×C4×D13—24no—
160C2×C4×D13—44no—
161C2×Dic26—21no—
162C2×Dic26—42no—
163C2×Dic26C22×C412yes—
164C13×M16—48no—
165C2×C8×C13—24no—
166C2×C8×C13—44no—
167C22⋊Dic13—22no—
168C22⋊Dic13—24no—
169C22⋊Dic13—24no—
170C22⋊Dic13—22no—
171C22⋊Dic13—48no—
172#6103—22no—
173#6103—24no—
174#6103—22no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—48no—
178C4⋊Dic13C22×C412yes—
179C4⋊Dic13C22×C412yes—
180#6101—22no—
181#6101—24no—
182#6101—22no—
183C4×Dic13—24no—
184C2×#525—131no—
185C2×#407D1311yescharacteristic, complemented
186C2×#380—131no—
187#1513—138no—
188C2×#328—132no—
189C2×#327—132no—
190C23×C13—22no—
191C23×C13—22no—
192C23×C13—22no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—24no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—48no—
206C23×C13—48no—
207C23×C13C2×C22⋊C412yes—
208C23×C13C2×C22⋊C412yes—
209C23×C13C2×C22⋊C411yescharacteristic
210C23×C13C2×C22⋊C411yescharacteristic
211C23×C13AGL(1,ℤ/8)12yes—
212C23×C13#13712yes—
213C23×C13C22×D411yescharacteristic
214C22×D13—22no—
215C22×D13—42no—
216C22×D13—42no—
217C22×D13—42no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—24no—
224C2×C4×C13—24no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—41no—
230C2×C4×C13—42no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13#9914yes—
236C2×C4×C13C2×C22⋊C411yescharacteristic
237C2×C4×C13C2×C22⋊C412yes—
238C2×C4×C13C2×C22⋊C411yescharacteristic
239C2×C4×C13C2×C22⋊C412yes—
240C2×C4×C13C23×C411yescharacteristic
241C2×C4×C13C22×D411yescharacteristic
242C22⋊D13—48no—
243C22⋊D13—48no—
244C22⋊D13—42no—
245C22⋊D13—42no—
246C22⋊D13—44no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—44no—
254C2×Dic13—44no—
255C2×Dic13—44no—
256C2×Dic13—88no—
257D52—42no—
258D52—42no—
259C4×D13—48no—
260Dic26—42no—
261Dic26—42no—
262C8×C13—44no—
263C22×#41—131no—
264C24×C4C2×D1311yescharacteristic
265C22×M16—21no—
266#525—134no—
267#525—134no—
268#525—262no—
269#525—262no—
270C2×#123—261no—
271C2×C22⋊Q8—131no—
272C2×C22⋊Q8—131no—
273C2×#121—131no—
274C2×#121—131no—
275C2×#120—261no—
276C2×C4×D4—261no—
277C2×C4×D4—261no—
278C2×#117—131no—
279C22×C4⋊C4—261no—
280C22×C22⋊C4—261no—
281#407—22no—
282#407C2×D1314yescomplemented
283C2×C22⋊C8—21no—
284C2×C22⋊C8C2×D1312yes—
285#380—134no—
286#380—262no—
287C2×#95—132no—
288#328—138no—
289#327—138no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—21no—
294C22×C13—24no—
295C22×C13—24no—
296C22×C13—22no—
297C22×C13—22no—
298C22×C13—22no—
299C22×C13—22no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—44no—
303C22×C13—44no—
304C22×C13—48no—
305C22×C13—44no—
306C22×C13—44no—
307C22×C13C2×#9912yes—
308C22×C13#41712yes—
309C22×C13#41712yes—
310C22×C13#42112yes—
311C22×C13C22×C22⋊C411yescharacteristic
312C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C13C2×#13711yescharacteristic
314C2×D13—42no—
315C2×D13—42no—
316C2×D13—42no—
317C2×D13—84no—
318C4×C13—21no—
319C4×C13—21no—
320C4×C13—21no—
321C4×C13—21no—
322C4×C13—22no—
323C4×C13C2×#9914yes—
324Dic13—42no—
325Dic13—42no—
326Dic13—42no—
327Dic13—84no—
328C25D5211yescharacteristic
329C2×#41—134no—
330C2×#41—262no—
331C2×#41—524no—
332C22×Q8—131no—
333C22×D4—131no—
334C22×D4—261no—
335C22×D4—261no—
336C22×D4—261no—
337C23×C4—44no—
338C23×C4—261no—
339C23×C4—262no—
340C23×C4C4×D1311yescharacteristic
341C23×C4C4×D1311yescharacteristic
342C23×C4C4×D1312yes—
343C23×C4D5211yescharacteristic
344C23×C4D5212yes—
345C23×C4C22⋊D1311yescharacteristic
346C23×C4C22⋊D1311yescharacteristic
347C23×C4C22⋊D1312yes—
348C23×C4C22×D1311yescharacteristic
349C23×C4C22×D1312yes—
350C2×M16—24no—
351C2×M16—44no—
352C22×C8—22no—
353#123—264no—
354#123—264no—
355C22⋊Q8—132no—
356C22⋊Q8—134no—
357C22⋊Q8—132no—
358C22⋊Q8—262no—
359C22⋊Q8—261no—
360C22⋊Q8—261no—
361#121—132no—
362#121—134no—
363#121—132no—
364#121—262no—
365#121—261no—
366#121—261no—
367#120—264no—
368#120—264no—
369C4×D4—264no—
370C4×D4—264no—
371C4×D4—264no—
372C4×D4—264no—
373#117—134no—
374#117—262no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—264no—
380C2×C4⋊C4—524no—
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—264no—
387C2×C22⋊C4—524no—
388C2×C42—261no—
389C22⋊C8—24no—
390C22⋊C8—22no—
391C22⋊C8C22×D1314yes—
392#95—134no—
393#95—262no—
394C2×C13—21no—
395C2×C13—21no—
396C2×C13—22no—
397C2×C13—42no—
398C2×C13—42no—
399C2×C13#151314yescomplemented
400C2×C13C22×#9911yescharacteristic
401C2×C13C2×#41711yescharacteristic
402C2×C13C2×#42111yescharacteristic
403D13—82no—
404C24—22no—
405C24—22no—
406C24—42no—
407C24—42no—
408C24—261no—
409C24#610311yescharacteristic
410C24#610311yescharacteristic
411C24#610312yes—
412C24C2×D5211yescharacteristic
413C24C2×D5212yes—
414#41—528no—
415#41—528no—
416C2×Q8—132no—
417C2×Q8—261no—
418C2×Q8—522no—
419C2×D4—132no—
420C2×D4—264no—
421C2×D4—262no—
422C2×D4—264no—
423C2×D4—262no—
424C2×D4—261no—
425C2×D4—522no—
426C2×D4—524no—
427C2×D4—524no—
428C2×D4—522no—
429C2×D4—522no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—264no—
444C22×C4—264no—
445C22×C4—524no—
446C22×C4—524no—
447C22×C4—524no—
448C22×C4—524no—
449C22×C4#610312yes—
450C22×C4#610312yes—
451C22×C4#610312yes—
452C22×C4#610311yescharacteristic
453C22×C4#610312yes—
454C22×C4#610312yes—
455C22×C4#610311yescharacteristic
456C22×C4C2×C4×D1312yes—
457C22×C4C2×C4×D1311yescharacteristic
458C22×C4C2×C4×D1312yes—
459C22×C4C2×C4×D1311yescharacteristic
460C22×C4C2×D5212yes—
461C22×C4C2×D5211yescharacteristic
462C22×C4C2×C22⋊D1312yes—
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C2×C22⋊D1311yescharacteristic
465C22×C4C2×C22⋊D1312yes—
466C22×C4C23×D1311yescharacteristic
467M16—48no—
468C2×C8—24no—
469C2×C8—44no—
470C4⋊C4—132no—
471C4⋊C4—132no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—264no—
475C4⋊C4—262no—
476C4⋊C4—262no—
477C4⋊C4—528no—
478C22⋊C4—264no—
479C22⋊C4—264no—
480C22⋊C4—262no—
481C22⋊C4—262no—
482C22⋊C4—264no—
483C22⋊C4—262no—
484C22⋊C4—262no—
485C22⋊C4—528no—
486C42—264no—
487C13C2×#151311yescharacteristic, complemented, Sylow
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—48no—
504C23—48no—
505C23—262no—
506C23—522no—
507C23—522no—
508C23—522no—
509C23#8816212yes—
510C23#8816312yes—
511C23C2×#610312yes—
512C23C2×#610312yes—
513C23C2×#610311yescharacteristic
514C23C2×#610311yescharacteristic
515C23C22×D5211yescharacteristic
516Q8—522no—
517Q8—522no—
518D4—522no—
519D4—522no—
520D4—528no—
521D4—528no—
522D4—522no—
523D4—522no—
524D4—524no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—262no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—522no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—528no—
549C2×C4—524no—
550C2×C4—524no—
551C2×C4—524no—
552C2×C4—1048no—
553C2×C4#8804614yes—
554C2×C4C2×#610311yescharacteristic
555C2×C4C2×#610312yes—
556C2×C4C2×#610311yescharacteristic
557C2×C4C2×#610312yes—
558C2×C4C22×C4×D1311yescharacteristic
559C2×C4C22×C22⋊D1311yescharacteristic
560C8—44no—
561C22—24no—
562C22—24no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—44no—
574C22—44no—
575C22—48no—
576C22—44no—
577C22—44no—
578C22—522no—
579C22—522no—
580C22—522no—
581C22—1044no—
582C22C2×#8804612yes—
583C22#1171879412yes—
584C22#1171879412yes—
585C22#1171880012yes—
586C22C2×#8816211yescharacteristic
587C22C2×#8816311yescharacteristic
588C22C22×#610311yescharacteristic
589C4—21no—
590C4—21no—
591C4—22no—
592C4—21no—
593C4—21no—
594C4—522no—
595C4—522no—
596C4—522no—
597C4—1044no—
598C4C2×#8804614yes—
599C2—21no—
600C2—21no—
601C2—22no—
602C2—42no—
603C2—42no—
604C2—1042no—
605C2#1311338014yesdirect product factor
606C2C22×#8804611yescharacteristic
607C2C2×#1171879411yescharacteristic
608C2C2×#1171880011yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#407C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC2×#407D13
hypocenterC13C2×#1513
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#11718873C2semidirect
3. #13113380C2direct (N × H)
4. C2×#11718059C2semidirect
5. C2×#11718062C2semidirect
6. C2×C13×#407C2semidirect
8. C22×#6127C4semidirect
14. #11719496C4semidirect
16. C2×#88184C4semidirect
21. C2×#88180C4semidirect
23. C2×#88178C4semidirect
26. C13×#407C22semidirect
30. #11718873C22semidirect
32. #11718062C22semidirect
33. #11718059C22semidirect
52. C2×#6127C2×C4semidirect
70. #88184C2×C4semidirect
81. #88180C2×C4semidirect
90. #88178C2×C4semidirect
185. C2×#407D13semidirect
282. #407C2×D13semidirect
399. C2×C13#1513semidirect
487. C13C2×#1513semidirect
605. C2#13113380direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194962
C2×#117188732
#131133802
C2×#117180592
C2×#117180622
C2×C13×#4072
C2×#151313