Finite Group Databasebeta

← C2×#13124917 #16731003

Subgroups — C2×#13124917 #16731003

Order 3328.

2170 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×#11719329C211yesmaximal, characteristic
2C22×Q8×Dic13C211yesmaximal, characteristic, complemented
3#13124917C2116yesmaximal, direct product factor
4C2×#11718704C211yesmaximal, characteristic, complemented
5C2×#11718397C211yesmaximal, characteristic
6C2×#11718457C212yesmaximal, complemented
7C2×#11718846C212yesmaximal, complemented
8C2×#11718888C211yesmaximal, characteristic
9C2×Q16×Dic13C212yesmaximal, complemented
10C2×#11718449C212yesmaximal, complemented
11C2×#11718379C211yesmaximal, characteristic, complemented
12C2×C13×#451C211yesmaximal, characteristic, complemented
13C23×Q8×C13C2211yescharacteristic
14C22×C13×Q16C2212yes—
15C2×C13×C22⋊Q8C2211yescharacteristic
16C2×#88201C2211yescharacteristic
17C2×Q8×Dic13—21no—
18C2×Q8×Dic13—21no—
19C2×Q8×Dic13—24no—
20C2×Q8×Dic13C2212yes—
21C2×Q8×Dic13C2212yes—
22C2×Q8×Dic13C2211yescharacteristic
23C2×Q8×Dic13C2218yescomplemented
24C22×#6106C2212yes—
25C2×#88184C2211yescharacteristic
26C22×C4⋊Dic13—21no—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4×Dic13—21no—
29C22×C4×Dic13C2211yescharacteristic
30#11719329—24no—
31#11719329C2218yes—
32C2×#88152—21no—
33C2×#88147C2211yescharacteristic
34C2×#88146—21no—
35C2×#88144C2211yescharacteristic
36C2×#88140—21no—
37C2×#88135—21no—
38C13×#451C2218yescomplemented
39C2×C13×#103C2212yes—
40C2×C13×C22⋊C8C2211yescharacteristic
41#11718888C2218yes—
42C2×#88075C2212yes—
43C2×#88075C2212yes—
44C2×C22⋊#1055C2211yescharacteristic
45#11718846C22116yescomplemented
46Q16×Dic13C22116yescomplemented
47C2×#88061C2212yes—
48C2×#88058C2212yes—
49C2×#88054C2212yes—
50C2×C8×Dic13C2212yes—
51#11718704C2218yescomplemented
52C2×#88048C2212yes—
53#11718457C22116yescomplemented
54#11718449C22116yescomplemented
55#11718397C2218yes—
56#11718379C2218yescomplemented
57C22×Q8×C13—28no—
58C22×Q8×C13—21no—
59C22×Q8×C13—22no—
60C22×Q8×C13C2314yes—
61C22×Q8×C13C2311yescharacteristic
62C22×Q8×C13C2312yes—
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C22×C22⋊D13—21no—
66C23×Dic13—21no—
67C23×Dic13D411yescharacteristic
68C23×Dic13D411yescharacteristic
69C22×D52C2311yescharacteristic
70C22×C4×D13—21no—
71C2×C13×Q16—28no—
72C2×C13×Q16C2318yes—
73C22×C8×C13C2312yes—
74C13×C22⋊Q8—22no—
75C13×C22⋊Q8C2314yes—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79#88201—22no—
80#88201C2314yes—
81Q8×Dic13—24no—
82Q8×Dic13—24no—
83Q8×Dic13—28no—
84Q8×Dic13—28no—
85Q8×Dic13—22no—
86Q8×Dic13C2318yes—
87Q8×Dic13C2318yes—
88Q8×Dic13C2314yes—
89C2×#6106—28no—
90C2×#6106C2318yes—
91#88184—22no—
92#88184C2314yes—
93C2×#6103—21no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×#6103—21no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—21no—
100C2×C4⋊Dic13—21no—
101C2×C4⋊Dic13—22no—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—28no—
104C2×C4⋊Dic13C2311yescharacteristic
105C2×C4⋊Dic13C2314yes—
106C2×C4⋊Dic13C2312yes—
107C2×#6101—21no—
108C2×C4×Dic13—21no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—28no—
112C2×C4×Dic13D411yescharacteristic
113C2×C4×Dic13D411yescharacteristic
114C2×C4×Dic13D414yes—
115C2×C4×Dic13C2311yescharacteristic
116C2×C4×Dic13C2311yescharacteristic
117C2×C4×Dic13C2314yes—
118C22×#1055C2312yes—
119#88152—28no—
120#88147—22no—
121#88147C2314yes—
122#88146—28no—
123#88144—22no—
124#88144C2314yes—
125#88140—28no—
126#88135—28no—
127C13×#103C2318yes—
128C13×C22⋊C8C2314yes—
129#88075C2318yes—
130#88075C2318yes—
131C22⋊#1055C2314yes—
132#88061C2318yes—
133#88058C2318yes—
134#88054C2318yes—
135C8×Dic13C2318yes—
136#88048C2318yes—
137C2×#3108—131nomaximal, Sylow
138C24×C13C2×D411yescharacteristic
139C23×D13—21no—
140C2×Q8×C13—216no—
141C2×Q8×C13—28no—
142C2×Q8×C13—216no—
143C2×Q8×C13—24no—
144C2×Q8×C13—22no—
145C2×Q8×C13—21no—
146C2×Q8×C13—24no—
147C2×Q8×C13—24no—
148C2×Q8×C13#4118yes—
149C2×Q8×C13C2412yes—
150C2×Q8×C13C2414yes—
151C22×C4×C13—28no—
152C22×C4×C13—24no—
153C22×C4×C13—22no—
154C22×C4×C13—24no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2412yes—
160C22×C4×C13C2411yescharacteristic
161C2×C22⋊D13—24no—
162C2×C22⋊D13—44no—
163C22×Dic13—24no—
164C22×Dic13—24no—
165C22×Dic13—24no—
166C22×Dic13—22no—
167C22×Dic13—21no—
168C22×Dic13—44no—
169C22×Dic13C2×D414yes—
170C22×Dic13C2×D414yes—
171C22×Dic13C2×D411yescharacteristic
172C22×Dic13C2×D411yescharacteristic
173C22×Dic13C2×D411yescharacteristic
174C22×Dic13C2×D411yescharacteristic
175C2×D52—24no—
176C2×D52—21no—
177C2×D52C2412yes—
178C2×C4×D13—24no—
179C2×C4×D13—44no—
180C13×Q16—216no—
181C2×C8×C13—24no—
182C2×C8×C13C2414yes—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4C2412yes—
186C13×C22⋊C4—24no—
187#6106—216no—
188#6103—24no—
189#6103—24no—
190#6103—24no—
191#6103—24no—
192C4⋊Dic13—21no—
193C4⋊Dic13—24no—
194C4⋊Dic13—22no—
195C4⋊Dic13—24no—
196C4⋊Dic13—24no—
197C4⋊Dic13—28no—
198C4⋊Dic13—28no—
199C4⋊Dic13C2412yes—
200C4⋊Dic13C2414yes—
201#6101—24no—
202C4×Dic13—24no—
203C4×Dic13—28no—
204C4×Dic13—28no—
205C4×Dic13C2×D412yes—
206C4×Dic13C2×D414yes—
207C4×Dic13C2×D412yes—
208C4×Dic13C2×D414yes—
209C4×Dic13C2412yes—
210C4×Dic13C2412yes—
211C2×#1055—24no—
212C2×#1055C2414yes—
213C2×#529—131no—
214C22×C4×Q8—131no—
215#3108—1316no—
216C2×#483—131no—
217C2×#480—131no—
218C2×#479—132no—
219C2×#464—132no—
220C2×#451D1311yescharacteristic, complemented
221C2×#448—131no—
222C2×C4×Q16—132no—
223C2×C4×SD16—132no—
224C2×#431—131no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13#13514yes—
228C23×C13C22×D412yes—
229C23×C13C22×D411yescharacteristic
230C22×D13—22no—
231C22×D13—42no—
232C22×D13—42no—
233C22×D13—42no—
234Q8×C13—216no—
235Q8×C13—28no—
236Q8×C13—24no—
237Q8×C13—24no—
238Q8×C13—42no—
239Q8×C13C2×#4118yes—
240C2×C4×C13—216no—
241C2×C4×C13—28no—
242C2×C4×C13—22no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13C22×D412yes—
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C2×#4114yes—
253C2×C4×C13C2511yescharacteristic
254C22⋊D13—48no—
255C2×Dic13—28no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—28no—
260C2×Dic13—24no—
261C2×Dic13—22no—
262C2×Dic13—48no—
263C2×Dic13—44no—
264C2×Dic13—42no—
265C2×Dic13#13714yes—
266C2×Dic13C22×D412yes—
267C2×Dic13C22×D412yes—
268C2×Dic13C22×D412yes—
269C2×Dic13C22×D412yes—
270D52—24no—
271D52—42no—
272C4×D13—48no—
273C8×C13—24no—
274#1055—24no—
275C23×Q8C2×D1311yescharacteristic
276C22×Q16C2×D1312yes—
277C22×SD16—132no—
278#529—138no—
279#529—264no—
280C2×#126—261no—
281C2×#125—131no—
282C2×#124—131no—
283C2×#123—261no—
284C2×C22⋊Q8C2×D1311yescharacteristic
285C2×#121—131no—
286C2×C4×Q8—132no—
287C2×C4×Q8—138no—
288C2×C4×Q8—132no—
289C2×C4×Q8—131no—
290C2×C4×Q8—261no—
291C2×C4×Q8—261no—
292C2×C4×Q8—264no—
293C2×C4×D4—131no—
294C2×C4×D4—261no—
295C2×#117—261no—
296C22×C4⋊C4—131no—
297C22×C4⋊C4—261no—
298C22×C42—131no—
299C22×C42—261no—
300#483—138no—
301#480—138no—
302#479—1316no—
303#464—1316no—
304#451C2×D1318yescomplemented
305#448—138no—
306C4×Q16—1316no—
307C4×SD16—1316no—
308#431—138no—
309C2×#107—132no—
310C2×#106—132no—
311C2×C4⋊C8—132no—
312C2×#103—132no—
313C2×#103—132no—
314C2×#103C2×D1312yes—
315C2×#102—132no—
316C2×C22⋊C8—131no—
317C2×C22⋊C8C2×D1311yescharacteristic
318C2×C4×C8—132no—
319C22×C13—28no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13#52512yes—
323C22×C13C2×#13514yes—
324C22×C13C2×#13512yes—
325C22×C13C2×#13712yes—
326C22×C13C23×D411yescharacteristic
327C2×D13—42no—
328C2×D13—42no—
329C2×D13—42no—
330C2×D13—84no—
331C4×C13—28no—
332C4×C13—22no—
333C4×C13—42no—
334C4×C13—42no—
335C4×C13#52512yes—
336C4×C13C22×#4112yes—
337Dic13—22no—
338Dic13—22no—
339Dic13—22no—
340Dic13—44no—
341Dic13—42no—
342Dic13C2×#13714yes—
343C22×Q8—28no—
344C22×Q8—22no—
345C22×Q8—21no—
346C22×Q8C22×D1314yes—
347C22×Q8C22×D1311yescharacteristic
348C22×Q8C22×D1312yes—
349C22×D4—131no—
350C22×D4—261no—
351C23×C4—21no—
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—261no—
355C23×C4—261no—
356C23×C4C22×D1311yescharacteristic
357C2×Q16—28no—
358C2×Q16C22×D1318yes—
359C2×SD16—138no—
360C2×SD16—268no—
361C22×C8—132no—
362C22×C8C22×D1312yes—
363#126—268no—
364#125—134no—
365#125—262no—
366#124—134no—
367#124—262no—
368#123—268no—
369C22⋊Q8—22no—
370C22⋊Q8C22×D1314yes—
371#121—134no—
372#121—262no—
373C4×Q8—138no—
374C4×Q8—138no—
375C4×Q8—134no—
376C4×Q8—268no—
377C4×Q8—264no—
378C4×Q8—264no—
379C4×Q8—268no—
380C4×Q8—262no—
381C4×D4—134no—
382C4×D4—262no—
383C4×D4—268no—
384#117—268no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—132no—
387C2×C4⋊C4—134no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—268no—
390C2×C4⋊C4—262no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—262no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4C22×D1311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—261no—
400C2×C22⋊C4—261no—
401C2×C22⋊C4—261no—
402C2×C22⋊C4—261no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—134no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—134no—
409C2×C42—261no—
410C2×C42—268no—
411C2×C42—262no—
412C2×C42—262no—
413#107—138no—
414#106—138no—
415C4⋊C8—138no—
416#103—138no—
417#103—138no—
418#103C22×D1318yes—
419#102—138no—
420C22⋊C8—134no—
421C22⋊C8C22×D1314yes—
422C4×C8—138no—
423C2×C13—24no—
424C2×C13#310814yescomplemented
425C2×C13C2×#52511yescharacteristic
426C2×C13C22×#13511yescharacteristic
427C2×C13C22×#13711yescharacteristic
428D13—82no—
429C24—261no—
430C24D4×D1311yescharacteristic
431C2×Q8—216no—
432C2×Q8—28no—
433C2×Q8—216no—
434C2×Q8—24no—
435C2×Q8—22no—
436C2×Q8—21no—
437C2×Q8—24no—
438C2×Q8—24no—
439C2×Q8#612918yes—
440C2×Q8C23×D1312yes—
441C2×Q8C23×D1314yes—
442C2×D4—132no—
443C2×D4—264no—
444C2×D4—261no—
445C2×D4—264no—
446C2×D4—524no—
447C22×C4—28no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—131no—
454C22×C4—134no—
455C22×C4—134no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—264no—
460C22×C4—264no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4—262no—
464C22×C4—261no—
465C22×C4—524no—
466C22×C4—524no—
467C22×C4D4×D1312yes—
468C22×C4D4×D1311yescharacteristic
469C22×C4C23×D1312yes—
470C22×C4C23×D1311yescharacteristic
471Q16—216no—
472SD16—2616no—
473C2×C8—24no—
474C2×C8—134no—
475C2×C8—264no—
476C2×C8C23×D1314yes—
477C4⋊C4—24no—
478C4⋊C4—21no—
479C4⋊C4—134no—
480C4⋊C4—132no—
481C4⋊C4—268no—
482C4⋊C4—268no—
483C4⋊C4—264no—
484C4⋊C4—264no—
485C4⋊C4—264no—
486C4⋊C4—264no—
487C4⋊C4—262no—
488C4⋊C4—261no—
489C4⋊C4C23×D1312yes—
490C22⋊C4—24no—
491C22⋊C4—264no—
492C22⋊C4—264no—
493C22⋊C4—264no—
494C22⋊C4—264no—
495C42—134no—
496C42—132no—
497C42—132no—
498C42—134no—
499C42—132no—
500C42—132no—
501C42—268no—
502C42—268no—
503C42—264no—
504C13C2×#310811yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—262no—
508C23—522no—
509C23—522no—
510C23—522no—
511C23#8817314yes—
512C23C2×D4×D1312yes—
513C23C2×D4×D1311yescharacteristic
514Q8—216no—
515Q8—28no—
516Q8—24no—
517Q8—24no—
518Q8—42no—
519Q8C2×#612918yes—
520D4—264no—
521D4—528no—
522D4—522no—
523C2×C4—216no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—134no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—268no—
539C2×C4—268no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—264no—
544C2×C4—262no—
545C2×C4—528no—
546C2×C4—528no—
547C2×C4—524no—
548C2×C4—522no—
549C2×C4C2×D4×D1312yes—
550C2×C4C2×D4×D1311yescharacteristic
551C2×C4C2×#612914yes—
552C2×C4C24×D1311yescharacteristic
553C8—24no—
554C8—264no—
555C22—28no—
556C22—22no—
557C22—22no—
558C22—522no—
559C22—522no—
560C22—522no—
561C22—1044no—
562C22#1171929112yes—
563C22C2×#8817314yes—
564C22C2×#8817312yes—
565C22D13×#13712yes—
566C22C22×D4×D1311yescharacteristic
567C4—28no—
568C4—22no—
569C4—42no—
570C4—42no—
571C4—134no—
572C4—262no—
573C4—262no—
574C4—262no—
575C4—524no—
576C4—522no—
577C4#1171929112yes—
578C4C22×#612912yes—
579C2—24no—
580C2—1042no—
581C2#1312491714yesdirect product factor
582C2C2×#1171929111yescharacteristic
583C2C22×#8817311yescharacteristic
584C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#451C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#451D13
hypocenterC13C2×#3108
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic13C2semidirect
3. #13124917C2direct (N × H)
4. C2×#11718704C2semidirect
6. C2×#11718457C2semidirect
7. C2×#11718846C2semidirect
9. C2×Q16×Dic13C2semidirect
10. C2×#11718449C2semidirect
11. C2×#11718379C2semidirect
12. C2×C13×#451C2semidirect
23. C2×Q8×Dic13C22semidirect
38. C13×#451C22semidirect
45. #11718846C22semidirect
46. Q16×Dic13C22semidirect
51. #11718704C22semidirect
53. #11718457C22semidirect
54. #11718449C22semidirect
56. #11718379C22semidirect
220. C2×#451D13semidirect
304. #451C2×D13semidirect
424. C2×C13#3108semidirect
504. C13C2×#3108semidirect
581. C2#13124917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193292
C22×Q8×Dic132
#131249172
C2×#117187042
C2×#117183972
C2×#117184572
C2×#117188462
C2×#117188882
C2×Q16×Dic132
C2×#117184492
C2×#117183792
C2×C13×#4512
C2×#310813