Finite Group Databasebeta

← C2×#13124913 #16730999

Subgroups — C2×#13124913 #16730999

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×#11719305C211yesmaximal, characteristic
2C22×#88141C211yesmaximal, characteristic, complemented
3#13124913C2116yesmaximal, direct product factor
4C2×#11718632C211yesmaximal, characteristic, complemented
5C2×#11718538C212yesmaximal, complemented
6C2×#11718428C212yesmaximal, complemented
7C2×#11718400C211yesmaximal, characteristic, complemented
8C2×#11718701C211yesmaximal, characteristic
9C2×#11718534C212yesmaximal, complemented
10C2×#11718419C212yesmaximal, complemented
11C2×#11718379C211yesmaximal, characteristic, complemented
12C2×C13×#480C211yesmaximal, characteristic
13C23×Dic26C2211yescharacteristic
14C2×C13×#121C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C2×#88190C2211yescharacteristic
17C2×#88189—21no—
18C2×D4×Dic13—21no—
19C2×D4×Dic13C2211yescharacteristic
20C22×#6105C2212yes—
21C2×#88178C2211yescharacteristic
22C22×#6101—21no—
23C22×C4×Dic13—21no—
24C22×C4×Dic13C2211yescharacteristic
25C22×Dic52C2212yes—
26#11719305—24no—
27#11719305C2218yes—
28C2×#88144C2211yescharacteristic
29C2×#88141—24no—
30C2×#88141—21no—
31C2×#88141—21no—
32C2×#88141C2212yes—
33C2×#88141C2212yes—
34C2×#88141C2211yescharacteristic
35C2×#88141C2218yescomplemented
36C2×#88133—21no—
37C2×#88131—21no—
38C13×#480C2218yes—
39C2×C13×#107C2212yes—
40C2×C13×#102C2212yes—
41C2×C13×C22⋊C8C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43C2×#88056C2212yes—
44C2×#88054C2212yes—
45C2×C8×Dic13C2212yes—
46#11718701C2218yes—
47#11718632C2218yescomplemented
48C2×#88050C2212yes—
49C2×#88050C2212yes—
50C2×#88048C2212yes—
51#11718538C22116yescomplemented
52#11718534C22116yescomplemented
53#11718428C22116yescomplemented
54#11718419C22116yescomplemented
55#11718400C2218yescomplemented
56#11718379C2218yescomplemented
57C22×D4×C13—21no—
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C23×Dic13—21no—
63C23×Dic13D411yescharacteristic
64C23×Dic13D411yescharacteristic
65C22×Dic26—21no—
66C22×Dic26—22no—
67C22×Dic26—28no—
68C22×Dic26C2314yes—
69C22×Dic26C2311yescharacteristic
70C22×Dic26C2312yes—
71C22×C8×C13C2312yes—
72C13×#121—22no—
73C13×#121C2314yes—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4C2312yes—
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2314yes—
79C2×C13×C22⋊C4—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84#88190—22no—
85#88190C2314yes—
86#88189—28no—
87D4×Dic13—28no—
88D4×Dic13—22no—
89D4×Dic13C2314yes—
90C2×#6105—28no—
91C2×#6105C2318yes—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2311yescharacteristic
94#88178—22no—
95#88178C2314yes—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—28no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—28no—
106C2×C4×Dic13D411yescharacteristic
107C2×C4×Dic13D411yescharacteristic
108C2×C4×Dic13D414yes—
109C2×C4×Dic13C2311yescharacteristic
110C2×C4×Dic13C2311yescharacteristic
111C2×C4×Dic13C2314yes—
112C22×#1055C2312yes—
113C2×Dic52—28no—
114C2×Dic52C2318yes—
115#88144—22no—
116#88144C2314yes—
117#88141—24no—
118#88141—24no—
119#88141—28no—
120#88141—28no—
121#88141—22no—
122#88141C2318yes—
123#88141C2318yes—
124#88141C2314yes—
125#88133—28no—
126#88131—28no—
127C13×#107C2318yes—
128C13×#102C2318yes—
129C13×C22⋊C8C2314yes—
130C22⋊#1055C2314yes—
131#88056C2318yes—
132#88054C2318yes—
133C8×Dic13C2318yes—
134#88050C2318yes—
135#88050C2318yes—
136#88048C2318yes—
137C2×#3108—131nomaximal, Sylow
138C24×C13—21no—
139C24×C13C2×D411yescharacteristic
140C2×D4×C13—24no—
141C2×D4×C13—21no—
142C2×D4×C13—24no—
143C2×D4×C13—44no—
144C2×D4×C13C2412yes—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—44no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2412yes—
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—28no—
155C22×Dic13—24no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—24no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—24no—
162C22×Dic13—44no—
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D414yes—
165C22×Dic13C2×D411yescharacteristic
166C22×Dic13C2×D411yescharacteristic
167C22×Dic13C2×D414yes—
168C22×Dic13C2×D411yescharacteristic
169C2×Dic26—28no—
170C2×Dic26—216no—
171C2×Dic26—24no—
172C2×Dic26—22no—
173C2×Dic26—24no—
174C2×Dic26—216no—
175C2×Dic26—24no—
176C2×Dic26—21no—
177C2×Dic26#4118yes—
178C2×Dic26C2412yes—
179C2×Dic26C2414yes—
180C2×C8×C13—24no—
181C2×C8×C13C2414yes—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4C2414yes—
186C13×C4⋊C4C2412yes—
187C13×C22⋊C4—24no—
188C22⋊Dic13—24no—
189C22⋊Dic13—24no—
190C22⋊Dic13—24no—
191C22⋊Dic13—24no—
192#6105—216no—
193C4⋊Dic13—21no—
194C4⋊Dic13—24no—
195C4⋊Dic13C2412yes—
196#6101—24no—
197#6101—24no—
198#6101—24no—
199#6101—28no—
200#6101—28no—
201C4×Dic13—24no—
202C4×Dic13—28no—
203C4×Dic13—28no—
204C4×Dic13C2×D414yes—
205C4×Dic13C2×D414yes—
206C4×Dic13C2×D412yes—
207C4×Dic13C2×D412yes—
208C4×Dic13C2412yes—
209C4×Dic13C2412yes—
210C2×#1055—24no—
211C2×#1055C2414yes—
212Dic52—216no—
213C2×#529—131no—
214C22×C4×Q8—131no—
215#3108—1316no—
216C2×#483—131no—
217C2×#480D1311yescharacteristic
218C2×#479—132no—
219C2×#464—132no—
220C2×#451—131no—
221C2×#448—131no—
222C2×C4×Q16—132no—
223C2×C4×SD16—132no—
224C2×#431—131no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—42no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13#13514yes—
232C23×C13C22×D412yes—
233C23×C13C22×D411yescharacteristic
234D4×C13—24no—
235D4×C13—48no—
236D4×C13—42no—
237C2×C4×C13—22no—
238C2×C4×C13—24no—
239C2×C4×C13—24no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—48no—
243C2×C4×C13—44no—
244C2×C4×C13—42no—
245C2×C4×C13C22×D412yes—
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C2×#4114yes—
248C2×C4×C13C2511yescharacteristic
249C2×Dic13—216no—
250C2×Dic13—28no—
251C2×Dic13—28no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—24no—
256C2×Dic13—28no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261C2×Dic13—48no—
262C2×Dic13#13714yes—
263C2×Dic13C22×D412yes—
264C2×Dic13C22×D412yes—
265C2×Dic13C22×D412yes—
266C2×Dic13C22×D412yes—
267Dic26—216no—
268Dic26—28no—
269Dic26—24no—
270Dic26—24no—
271Dic26—42no—
272Dic26C2×#4118yes—
273C8×C13—24no—
274#1055—24no—
275C23×Q8—131no—
276C22×Q16—132no—
277C22×SD16—132no—
278#529—138no—
279#529—264no—
280C2×#126—261no—
281C2×#125—131no—
282C2×#124—131no—
283C2×#123—261no—
284C2×C22⋊Q8—131no—
285C2×#121C2×D1311yescharacteristic
286C2×C4×Q8—132no—
287C2×C4×Q8—132no—
288C2×C4×Q8—131no—
289C2×C4×Q8—138no—
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—261no—
297C22×C4⋊C4C2×D1311yescharacteristic
298C22×C42—131no—
299C22×C42—261no—
300#483—138no—
301#480C2×D1318yes—
302#479—1316no—
303#464—1316no—
304#451—138no—
305#448—138no—
306C4×Q16—1316no—
307C4×SD16—1316no—
308#431—138no—
309C2×#107C2×D1312yes—
310C2×#106—132no—
311C2×C4⋊C8—132no—
312C2×#103—132no—
313C2×#103—132no—
314C2×#103—132no—
315C2×#102C2×D1312yes—
316C2×C22⋊C8—131no—
317C2×C22⋊C8C2×D1311yescharacteristic
318C2×C4×C8—132no—
319C22×C13—28no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—84no—
326C22×C13#52512yes—
327C22×C13C2×#13514yes—
328C22×C13C2×#13512yes—
329C22×C13C2×#13712yes—
330C22×C13C23×D411yescharacteristic
331C4×C13—22no—
332C4×C13—44no—
333C4×C13—42no—
334C4×C13#52512yes—
335C4×C13C22×#4112yes—
336Dic13—28no—
337Dic13—22no—
338Dic13—22no—
339Dic13—22no—
340Dic13—42no—
341Dic13—42no—
342Dic13C2×#13714yes—
343C22×Q8—132no—
344C22×Q8—134no—
345C22×Q8—131no—
346C22×Q8—268no—
347C22×Q8—262no—
348C22×Q8—261no—
349C22×D4—21no—
350C22×D4C22×D1311yescharacteristic
351C23×C4—21no—
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—261no—
355C23×C4—261no—
356C23×C4C22×D1311yescharacteristic
357C2×Q16—138no—
358C2×Q16—268no—
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—134no—
370C22⋊Q8—262no—
371#121—22no—
372#121C22×D1314yes—
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—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—268no—
389C2×C4⋊C4—262no—
390C2×C4⋊C4—262no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4C22×D1312yes—
396C2×C4⋊C4C22×D1314yes—
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#107C22×D1318yes—
414#106—138no—
415C4⋊C8—138no—
416#103—138no—
417#103—138no—
418#103—138no—
419#102C22×D1318yes—
420C22⋊C8—134no—
421C22⋊C8C22×D1314yes—
422C4×C8—138no—
423C2×C13—24no—
424C2×C13—82no—
425C2×C13#310814yescomplemented
426C2×C13C2×#52511yescharacteristic
427C2×C13C22×#13511yescharacteristic
428C2×C13C22×#13711yescharacteristic
429C24—21no—
430C24D4×D1311yescharacteristic
431C2×Q8—138no—
432C2×Q8—134no—
433C2×Q8—132no—
434C2×Q8—2616no—
435C2×Q8—268no—
436C2×Q8—2616no—
437C2×Q8—264no—
438C2×Q8—262no—
439C2×Q8—261no—
440C2×Q8—264no—
441C2×Q8—264no—
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—24no—
445C2×D4—44no—
446C2×D4C23×D1312yes—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—44no—
452C22×C4—131no—
453C22×C4—134no—
454C22×C4—134no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—264no—
459C22×C4—264no—
460C22×C4—268no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4—262no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—524no—
467C22×C4D4×D1312yes—
468C22×C4D4×D1311yescharacteristic
469C22×C4C23×D1312yes—
470C22×C4C23×D1311yescharacteristic
471Q16—2616no—
472SD16—2616no—
473C2×C8—24no—
474C2×C8—134no—
475C2×C8—264no—
476C2×C8C23×D1314yes—
477C4⋊C4—24no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—132no—
481C4⋊C4—268no—
482C4⋊C4—268no—
483C4⋊C4—264no—
484C4⋊C4—264no—
485C4⋊C4—264no—
486C4⋊C4—261no—
487C4⋊C4—264no—
488C4⋊C4C23×D1314yes—
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—22no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23#8816614yes—
512C23C2×D4×D1312yes—
513C23C2×D4×D1311yescharacteristic
514Q8—138no—
515Q8—2616no—
516Q8—268no—
517Q8—264no—
518Q8—264no—
519Q8—522no—
520D4—24no—
521D4—48no—
522D4—42no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—48no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—134no—
532C2×C4—132no—
533C2×C4—132no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—268no—
537C2×C4—2616no—
538C2×C4—268no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—268no—
543C2×C4—264no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—528no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4C2×D4×D1312yes—
550C2×C4C2×D4×D1311yescharacteristic
551C2×C4#41×D1314yes—
552C2×C4C24×D1311yescharacteristic
553C8—24no—
554C8—264no—
555C22—28no—
556C22—22no—
557C22—22no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—84no—
562C22#1171936112yes—
563C22C2×#8816614yes—
564C22C2×#8816612yes—
565C22D13×#13712yes—
566C22C22×D4×D1311yescharacteristic
567C4—22no—
568C4—44no—
569C4—42no—
570C4—134no—
571C4—262no—
572C4—262no—
573C4—262no—
574C4—268no—
575C4—522no—
576C4—522no—
577C4#1171936112yes—
578C4C2×#41×D1312yes—
579C2—24no—
580C2—82no—
581C2#1312491314yesdirect product factor
582C2C2×#1171936111yescharacteristic
583C2C22×#8816611yescharacteristic
584C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#480C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#480D13
hypocenterC13C2×#3108
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×#88141C2semidirect
3. #13124913C2direct (N × H)
4. C2×#11718632C2semidirect
5. C2×#11718538C2semidirect
6. C2×#11718428C2semidirect
7. C2×#11718400C2semidirect
9. C2×#11718534C2semidirect
10. C2×#11718419C2semidirect
11. C2×#11718379C2semidirect
35. C2×#88141C22semidirect
47. #11718632C22semidirect
51. #11718538C22semidirect
52. #11718534C22semidirect
53. #11718428C22semidirect
54. #11718419C22semidirect
55. #11718400C22semidirect
56. #11718379C22semidirect
425. C2×C13#3108semidirect
504. C13C2×#3108semidirect
581. C2#13124913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193052
C22×#881412
#131249132
C2×#117186322
C2×#117185382
C2×#117184282
C2×#117184002
C2×#117187012
C2×#117185342
C2×#117184192
C2×#117183792
C2×C13×#4802
C2×#310813