Finite Group Databasebeta

← C2×#13113393 #15830254

Subgroups — C2×#13113393 #15830254

Order 3328.

1498 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2C2×#11718872C211yesmaximal, characteristic, complemented
3#13113393C218yesmaximal, direct product factor
4C2×#11718059C212yesmaximal, complemented
5C2×#11718062C212yesmaximal, complemented
6C22×C13×C22⋊C8C211yesmaximal, characteristic, complemented
7C24×C4×C13C2211yescharacteristic
8C22×#6127C411yescharacteristic, complemented
9C23×C8×C13—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
22C2×#88178C411yescharacteristic, complemented
23C2×#88178C2211yescharacteristic
24C2×C13×C22⋊C8—22no—
25C2×C13×C22⋊C8—21no—
26C2×C13×C22⋊C8C2212yes—
27C2×C13×C22⋊C8C2214yescomplemented
28#11718872—22no—
29#11718872C2214yescomplemented
30C2×#88071—21no—
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
56C22×C8×C13—22no—
57C22×C8×C13—24no—
58C22×C8×C13—44no—
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⋊Dic13C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84#88178—22no—
85#88178—21no—
86#88178—21no—
87#88178C2×C412yes—
88#88178C2×C414yescomplemented
89#88178C2312yes—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×C4×Dic13—21no—
93C13×C22⋊C8—22no—
94C13×C22⋊C8—24no—
95C13×C22⋊C8C2314yes—
96#88071—24no—
97#88071—22no—
98#88071C2314yes—
99C2×#1516—131nomaximal, Sylow
100C24×C13—24no—
101C24×C13—24no—
102C24×C13—42no—
103C24×C13C22⋊C411yescharacteristic
104C24×C13C22⋊C412yes—
105C24×C13C22⋊C411yescharacteristic
106C24×C13C2×D412yes—
107C24×C13C2×D411yescharacteristic
108C23×D13—21no—
109C22×C4×C13—24no—
110C22×C4×C13—24no—
111C22×C4×C13—42no—
112C22×C4×C13—44no—
113C22×C4×C13—42no—
114C22×C4×C13—44no—
115C22×C4×C13—42no—
116C22×C4×C13—44no—
117C22×C4×C13—42no—
118C22×C4×C13—44no—
119C22×C4×C13C22⋊C411yescharacteristic
120C22×C4×C13C22⋊C411yescharacteristic
121C22×C4×C13C22⋊C412yes—
122C22×C4×C13C22⋊C412yes—
123C22×C4×C13C22⋊C412yes—
124C22×C4×C13C22⋊C412yes—
125C22×C4×C13C22⋊C412yes—
126C22×C4×C13C22×C411yescharacteristic
127C22×C4×C13C22×C412yes—
128C22×C4×C13C22×C411yescharacteristic
129C22×C4×C13C22×C412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D412yes—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2411yescharacteristic
137C2×C22⋊D13—22no—
138C2×C22⋊D13—24no—
139C2×C22⋊D13—24no—
140C2×C22⋊D13—22no—
141C2×C22⋊D13—44no—
142C2×C22⋊D13—44no—
143C2×C22⋊D13—44no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—24no—
148C22×Dic13—44no—
149C22×Dic13—44no—
150C22×Dic13—44no—
151#6127—48no—
152#6127—48no—
153C2×D52—21no—
154C2×D52—42no—
155C2×D52C22×C412yes—
156C2×C4×D13—24no—
157C2×C4×D13—44no—
158C2×Dic26—21no—
159C2×Dic26—42no—
160C2×Dic26C22×C412yes—
161C2×C8×C13—24no—
162C2×C8×C13—44no—
163C2×C8×C13—48no—
164C22⋊Dic13—22no—
165C22⋊Dic13—24no—
166C22⋊Dic13—24no—
167C22⋊Dic13—22no—
168C22⋊Dic13—48no—
169#6103—22no—
170#6103—24no—
171#6103—22no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13C22×C412yes—
175C4⋊Dic13C22×C412yes—
176#6101—22no—
177#6101—24no—
178#6101—22no—
179C4×Dic13—24no—
180C2×#525—131no—
181C22×C22⋊C8D1311yescharacteristic, complemented
182C2×#381—131no—
183#1516—138no—
184C2×#328—132no—
185C2×#327—132no—
186C23×C13—22no—
187C23×C13—22no—
188C23×C13—22no—
189C23×C13—22no—
190C23×C13—24no—
191C23×C13—24no—
192C23×C13—24no—
193C23×C13—22no—
194C23×C13—24no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—42no—
198C23×C13—42no—
199C23×C13—416no—
200C23×C13#9914yes—
201C23×C13C2×C22⋊C412yes—
202C23×C13C2×C22⋊C412yes—
203C23×C13C2×C22⋊C411yescharacteristic
204C23×C13C2×C22⋊C411yescharacteristic
205C23×C13#13514yes—
206C23×C13C22×D411yescharacteristic
207C22×D13—22no—
208C22×D13—42no—
209C22×D13—42no—
210C22×D13—42no—
211C2×C4×C13—24no—
212C2×C4×C13—22no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—24no—
218C2×C4×C13—22no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—41no—
223C2×C4×C13—42no—
224C2×C4×C13—41no—
225C2×C4×C13—42no—
226C2×C4×C13—41no—
227C2×C4×C13—42no—
228C2×C4×C13—41no—
229C2×C4×C13C2×C22⋊C412yes—
230C2×C4×C13C2×C22⋊C411yescharacteristic
231C2×C4×C13C2×C22⋊C412yes—
232C2×C4×C13C2×C22⋊C411yescharacteristic
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C22⋊D13—48no—
236C22⋊D13—44no—
237C22⋊D13—48no—
238C22⋊D13—44no—
239C2×Dic13—22no—
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13—42no—
245C2×Dic13—44no—
246C2×Dic13—44no—
247C2×Dic13—44no—
248C2×Dic13—88no—
249D52—42no—
250D52—42no—
251C4×D13—48no—
252Dic26—42no—
253Dic26—42no—
254C8×C13—44no—
255C22×#41—131no—
256C24×C4C2×D1311yescharacteristic
257C23×C8—21no—
258#525—134no—
259#525—134no—
260#525—262no—
261#525—262no—
262C2×#123—261no—
263C2×C22⋊Q8—131no—
264C2×C22⋊Q8—131no—
265C2×#121—131no—
266C2×#121—131no—
267C2×#120—261no—
268C2×C4×D4—261no—
269C2×C4×D4—261no—
270C2×#117—131no—
271C22×C22⋊C4—261no—
272C2×C22⋊C8—22no—
273C2×C22⋊C8—21no—
274C2×C22⋊C8C2×D1312yes—
275C2×C22⋊C8C2×D1314yescomplemented
276#381—134no—
277#381—262no—
278C2×#95—132no—
279C2×#95—261no—
280#328—138no—
281#327—138no—
282C22×C13—21no—
283C22×C13—21no—
284C22×C13—22no—
285C22×C13—21no—
286C22×C13—22no—
287C22×C13—21no—
288C22×C13—28no—
289C22×C13—28no—
290C22×C13—22no—
291C22×C13—22no—
292C22×C13—22no—
293C22×C13—48no—
294C22×C13—48no—
295C22×C13—44no—
296C22×C13C2×#9914yes—
297C22×C13C2×#9912yes—
298C22×C13#41612yes—
299C22×C13#41612yes—
300C22×C13#42112yes—
301C22×C13C22×C22⋊C411yescharacteristic
302C22×C13C2×#13512yes—
303C2×D13—42no—
304C2×D13—42no—
305C2×D13—42no—
306C2×D13—84no—
307C4×C13—21no—
308C4×C13—21no—
309C4×C13—21no—
310C4×C13—22no—
311C4×C13—22no—
312C4×C13—21no—
313Dic13—42no—
314Dic13—42no—
315Dic13—42no—
316Dic13—84no—
317C25D5211yescharacteristic
318C2×#41—134no—
319C2×#41—262no—
320C2×#41—524no—
321C22×Q8—131no—
322C22×D4—131no—
323C22×D4—261no—
324C22×D4—261no—
325C22×D4—261no—
326C23×C4—44no—
327C23×C4—261no—
328C23×C4—262no—
329C23×C4C4×D1311yescharacteristic
330C23×C4C4×D1311yescharacteristic
331C23×C4C4×D1312yes—
332C23×C4D5211yescharacteristic
333C23×C4D5212yes—
334C23×C4C22⋊D1311yescharacteristic
335C23×C4C22⋊D1311yescharacteristic
336C23×C4C22⋊D1312yes—
337C23×C4C22×D1311yescharacteristic
338C23×C4C22×D1312yes—
339C22×C8—22no—
340C22×C8—24no—
341C22×C8—44no—
342#123—264no—
343#123—264no—
344C22⋊Q8—132no—
345C22⋊Q8—134no—
346C22⋊Q8—132no—
347C22⋊Q8—262no—
348C22⋊Q8—261no—
349C22⋊Q8—261no—
350#121—132no—
351#121—134no—
352#121—132no—
353#121—262no—
354#121—261no—
355#121—261no—
356#120—264no—
357#120—264no—
358C4×D4—264no—
359C4×D4—264no—
360C4×D4—264no—
361C4×D4—264no—
362#117—134no—
363#117—262no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C22⋊C4—261no—
369C2×C22⋊C4—261no—
370C2×C22⋊C4—261no—
371C2×C22⋊C4—261no—
372C2×C22⋊C4—261no—
373C2×C22⋊C4—264no—
374C2×C22⋊C4—524no—
375C2×C42—261no—
376C22⋊C8—22no—
377C22⋊C8—24no—
378C22⋊C8C22×D1314yes—
379#95—134no—
380#95—262no—
381#95—264no—
382C2×C13—22no—
383C2×C13—24no—
384C2×C13—22no—
385C2×C13—42no—
386C2×C13#151614yescomplemented
387C2×C13C22×#9911yescharacteristic
388C2×C13C2×#41611yescharacteristic
389C2×C13C2×#42111yescharacteristic
390D13—82no—
391C24—24no—
392C24—24no—
393C24—42no—
394C24—261no—
395C24#610311yescharacteristic
396C24#610312yes—
397C24#610311yescharacteristic
398C24C2×D5212yes—
399C24C2×D5211yescharacteristic
400#41—528no—
401#41—528no—
402C2×Q8—132no—
403C2×Q8—261no—
404C2×Q8—522no—
405C2×D4—132no—
406C2×D4—264no—
407C2×D4—262no—
408C2×D4—264no—
409C2×D4—262no—
410C2×D4—261no—
411C2×D4—522no—
412C2×D4—524no—
413C2×D4—524no—
414C2×D4—524no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—42no—
418C22×C4—44no—
419C22×C4—42no—
420C22×C4—44no—
421C22×C4—42no—
422C22×C4—44no—
423C22×C4—42no—
424C22×C4—44no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—261no—
428C22×C4—264no—
429C22×C4—264no—
430C22×C4—524no—
431C22×C4—524no—
432C22×C4—524no—
433C22×C4—524no—
434C22×C4#610312yes—
435C22×C4#610312yes—
436C22×C4#610311yescharacteristic
437C22×C4#610311yescharacteristic
438C22×C4#610312yes—
439C22×C4#610312yes—
440C22×C4#610312yes—
441C22×C4C2×C4×D1312yes—
442C22×C4C2×C4×D1311yescharacteristic
443C22×C4C2×C4×D1312yes—
444C22×C4C2×C4×D1311yescharacteristic
445C22×C4C2×D5212yes—
446C22×C4C2×D5211yescharacteristic
447C22×C4C2×C22⋊D1312yes—
448C22×C4C2×C22⋊D1311yescharacteristic
449C22×C4C2×C22⋊D1312yes—
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C23×D1311yescharacteristic
452C2×C8—24no—
453C2×C8—44no—
454C2×C8—48no—
455C4⋊C4—132no—
456C4⋊C4—132no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—264no—
460C4⋊C4—262no—
461C4⋊C4—262no—
462C22⋊C4—264no—
463C22⋊C4—264no—
464C22⋊C4—262no—
465C22⋊C4—262no—
466C22⋊C4—264no—
467C22⋊C4—262no—
468C22⋊C4—262no—
469C22⋊C4—528no—
470C42—264no—
471C13C2×#151611yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—24no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—416no—
486C23—262no—
487C23—522no—
488C23—522no—
489C23—522no—
490C23#8804614yes—
491C23#8815814yes—
492C23C2×#610312yes—
493C23C2×#610311yescharacteristic
494C23C2×#610312yes—
495C23C2×#610311yescharacteristic
496C23C22×D5211yescharacteristic
497Q8—522no—
498Q8—522no—
499D4—522no—
500D4—522no—
501D4—528no—
502D4—524no—
503D4—524no—
504D4—528no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—528no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—522no—
530C2×C4—524no—
531C2×C4—524no—
532C2×C4—524no—
533C2×C4—1048no—
534C2×C4C2×#610312yes—
535C2×C4C2×#610311yescharacteristic
536C2×C4C2×#610312yes—
537C2×C4C2×#610311yescharacteristic
538C2×C4C22×C4×D1311yescharacteristic
539C2×C4C22×C22⋊D1311yescharacteristic
540C8—44no—
541C22—22no—
542C22—28no—
543C22—28no—
544C22—21no—
545C22—21no—
546C22—22no—
547C22—21no—
548C22—21no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—48no—
553C22—48no—
554C22—44no—
555C22—522no—
556C22—522no—
557C22—522no—
558C22—1044no—
559C22C2×#8804614yes—
560C22C2×#8804612yes—
561C22#1171877412yes—
562C22#1171877412yes—
563C22#1171880012yes—
564C22C2×#8815812yes—
565C22C22×#610311yescharacteristic
566C4—21no—
567C4—22no—
568C4—22no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—522no—
573C4—522no—
574C4—522no—
575C4—1044no—
576C2—22no—
577C2—22no—
578C2—24no—
579C2—42no—
580C2—1042no—
581C2#1311339314yesdirect product factor
582C2C22×#8804611yescharacteristic
583C2C2×#1171877411yescharacteristic
584C2C2×#1171880011yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊C8C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC22×C22⋊C8D13
hypocenterC13C2×#1516
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#11718872C2semidirect
3. #13113393C2direct (N × H)
4. C2×#11718059C2semidirect
5. C2×#11718062C2semidirect
6. C22×C13×C22⋊C8C2semidirect
8. C22×#6127C4semidirect
14. #11719496C4semidirect
16. C2×#88184C4semidirect
21. C2×#88180C4semidirect
22. C2×#88178C4semidirect
27. C2×C13×C22⋊C8C22semidirect
29. #11718872C22semidirect
32. #11718062C22semidirect
33. #11718059C22semidirect
52. C2×#6127C2×C4semidirect
70. #88184C2×C4semidirect
81. #88180C2×C4semidirect
88. #88178C2×C4semidirect
181. C22×C22⋊C8D13semidirect
275. C2×C22⋊C8C2×D13semidirect
386. C2×C13#1516semidirect
471. C13C2×#1516semidirect
581. C2#13113393direct (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×#117188722
#131133932
C2×#117180592
C2×#117180622
C22×C13×C22⋊C82
C2×#151613