Finite Group Databasebeta

← C2×#13124642 #16730440

Subgroups — C2×#13124642 #16730440

Order 3328.

2098 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2C2×C4×Q8×D13C211yesmaximal, characteristic
3#13124642C2116yesmaximal, direct product factor
4C2×#11718538C212yesmaximal, complemented
5C2×#11718460C212yesmaximal, complemented
6C2×#11718752C211yesmaximal, characteristic, complemented
7C2×#11718512C211yesmaximal, characteristic, complemented
8C2×#11718681C211yesmaximal, characteristic, complemented
9C2×#11718542C212yesmaximal
10C2×#11718498C211yesmaximal, characteristic
11C2×#11718463C212yesmaximal
12C2×C13×#477C211yesmaximal, characteristic, complemented
13C22×Q8×D13C2211yescharacteristic
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C13C2211yescharacteristic
16C2×#88200—21no—
17C2×Q8×Dic13—21no—
18C2×Q8×Dic13C2211yescharacteristic
19C22×#6094C2212yes—
20#11719433—24no—
21#11719433C2218yes—
22C4×Q8×D13—24no—
23C4×Q8×D13C2218yes—
24C2×#88151—21no—
25C2×#88146C2212yes—
26C2×C4⋊C4×D13—21no—
27C2×C4⋊C4×D13C2211yescharacteristic
28C2×#88144C2212yes—
29C2×#88141—21no—
30C2×#88141—21no—
31C2×#88141C2211yescharacteristic
32C2×C42×D13—21no—
33C2×C42×D13C2211yescharacteristic
34C2×#88123C2211yescharacteristic
35C2×C4×Dic26—21no—
36C2×C4×Dic26C2211yescharacteristic
37C13×#477C2218yescomplemented
38C2×C13×#107C2212yes—
39C2×C13×C4⋊C8C2211yescharacteristic
40C2×C13×#103C2212yes—
41C2×#88075C2212yes—
42C2×#88057C2212yes—
43C2×#88056C2212yes—
44C2×#88054C2212yes—
45#11718752C2218yescomplemented
46#11718681C2218yescomplemented
47C2×#88050C2212yes—
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51#11718542C22116yes—
52#11718538C22116yescomplemented
53#11718512C2218yescomplemented
54#11718498C2218yes—
55#11718463C22116yes—
56#11718460C22116yescomplemented
57C22×Q8×C13—21no—
58C22×Q8×C13C2311yescharacteristic
59C2×Q8×D13—22no—
60C2×Q8×D13—24no—
61C2×Q8×D13Q818yescomplemented
62C2×Q8×D13C2314yes—
63C22×C4×D13—21no—
64C22×C4×D13—21no—
65C22×C4×D13D411yescharacteristic
66C22×C4×D13D411yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×Dic26—21no—
69C22×Dic26—21no—
70C22×Dic26C2311yescharacteristic
71C22×C8×C13C2312yes—
72C13×C4⋊Q8—22no—
73C13×C4⋊Q8C2314yes—
74C4×Q8×C13—22no—
75C4×Q8×C13C2314yes—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2312yes—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82#88200—28no—
83Q8×Dic13—28no—
84Q8×Dic13—22no—
85Q8×Dic13C2314yes—
86C2×#6103—22no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2312yes—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—22no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13D411yescharacteristic
101C2×C4×Dic13D411yescharacteristic
102C2×C4×Dic13C2311yescharacteristic
103C22×#1055C2312yes—
104C2×#6094—28no—
105C2×#6094C2318yes—
106#88151—28no—
107#88146—24no—
108#88146C2318yes—
109C4⋊C4×D13—28no—
110C4⋊C4×D13—22no—
111C4⋊C4×D13C2314yes—
112#88144—24no—
113#88144C2318yes—
114#88141—28no—
115#88141—28no—
116#88141—22no—
117#88141C2314yes—
118C42×D13—28no—
119C42×D13D414yes—
120C42×D13C2314yes—
121#88123—22no—
122#88123C2314yes—
123C4×Dic26—22no—
124C4×Dic26—28no—
125C4×Dic26C2314yes—
126C13×#107C2318yes—
127C13×C4⋊C8C2314yes—
128C13×#103C2318yes—
129#88075C2318yes—
130#88057C2318yes—
131#88056C2318yes—
132#88054C2318yes—
133#88050C2318yes—
134#88048C2318yes—
135#88047C2318yes—
136C4⋊#1055C2314yes—
137C2×#3078—131nomaximal, Sylow
138C23×D13C2×D411yescharacteristic
139C2×Q8×C13—21no—
140C2×Q8×C13—24no—
141C2×Q8×C13—22no—
142C2×Q8×C13—44no—
143C2×Q8×C13C2×Q814yes—
144C2×Q8×C13C2412yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—22no—
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C22×Dic13C2×D411yescharacteristic
157Q8×D13—216no—
158Q8×D13—28no—
159Q8×D13C2×Q8116yescomplemented
160C2×C4×D13—28no—
161C2×C4×D13—24no—
162C2×C4×D13—24no—
163C2×C4×D13—24no—
164C2×C4×D13—42no—
165C2×C4×D13—44no—
166C2×C4×D13C2×D414yes—
167C2×C4×D13C2×D414yes—
168C2×C4×D13C2×D412yes—
169C2×C4×D13C2×Q814yes—
170C2×C4×D13#4114yes—
171C2×C4×D13C2412yes—
172C2×Dic26—21no—
173C2×Dic26—22no—
174C2×Dic26—28no—
175C2×Dic26—24no—
176C2×Dic26—24no—
177C2×Dic26—44no—
178C2×Dic26C2×Q814yes—
179C2×Dic26C2412yes—
180C2×C8×C13—24no—
181C2×C8×C13C2414yes—
182C13×C4⋊C4—24no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4C2414yes—
187C13×C4⋊C4C2412yes—
188C42×C13—24no—
189C42×C13C2×D412yes—
190C42×C13C2412yes—
191#6103—28no—
192C4⋊Dic13—21no—
193C4⋊Dic13—22no—
194C4⋊Dic13—24no—
195C4⋊Dic13—24no—
196C4⋊Dic13—28no—
197C4⋊Dic13C2414yes—
198C4⋊Dic13C2412yes—
199#6101—24no—
200#6101—24no—
201#6101—24no—
202#6101—28no—
203C4×Dic13—24no—
204C4×Dic13—24no—
205C4×Dic13—24no—
206C4×Dic13—28no—
207C4×Dic13C2×D414yes—
208C4×Dic13C2×D412yes—
209C4×Dic13C2×D414yes—
210C4×Dic13C2412yes—
211C2×#1055—24no—
212C2×#1055C2414yes—
213#6094—216no—
214C2×#533—131no—
215C22×C4×Q8—131no—
216#3078—1316no—
217C2×#479—132no—
218C2×#479—132no—
219C2×#477—131no—
220C2×#477D1311yescharacteristic, complemented
221C2×#475—131no—
222C2×#475—131no—
223C2×#428—132no—
224C2×#423—131no—
225C2×#419—132no—
226C23×C13C22×D411yescharacteristic
227C22×D13—22no—
228C22×D13—22no—
229C22×D13C22⋊Q814yes—
230C22×D13C22×D412yes—
231Q8×C13—24no—
232Q8×C13—22no—
233Q8×C13—48no—
234Q8×C13C22×Q814yes—
235C2×C4×C13—24no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—42no—
241C2×C4×C13—44no—
242C2×C4×C13#13714yes—
243C2×C4×C13C22×D412yes—
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D412yes—
246C2×C4×C13C22×Q812yes—
247C2×C4×C13C2×#4112yes—
248C2×C4×C13C2511yescharacteristic
249C2×Dic13—24no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—24no—
255C2×Dic13—44no—
256C2×Dic13—42no—
257C2×Dic13C22⋊Q814yes—
258C2×Dic13C22×D412yes—
259C2×Dic13C22×D412yes—
260C2×Dic13C22×D412yes—
261C4×D13—216no—
262C4×D13—28no—
263C4×D13—44no—
264C4×D13—48no—
265C4×D13C22⋊Q818yes—
266C4×D13C22×Q814yes—
267C4×D13C2×#4114yes—
268Dic26—24no—
269Dic26—22no—
270Dic26—216no—
271Dic26—48no—
272Dic26C22×Q814yes—
273C8×C13—24no—
274#1055—24no—
275C23×Q8—131no—
276C22×M16—132no—
277#533—138no—
278#533—264no—
279C2×C4⋊Q8—131no—
280C2×C4⋊Q8C2×D1311yescharacteristic
281C2×#125—132no—
282C2×C22⋊Q8—261no—
283C2×C22⋊Q8—261no—
284C2×C4×Q8—131no—
285C2×C4×Q8—138no—
286C2×C4×Q8—131no—
287C2×C4×Q8—131no—
288C2×C4×Q8—261no—
289C2×C4×Q8—261no—
290C2×C4×Q8—261no—
291C2×C4×Q8—264no—
292C2×C4×Q8—261no—
293C2×C4×Q8C2×D1311yescharacteristic
294C2×#117—132no—
295C22×C4⋊C4—131no—
296C22×C4⋊C4—261no—
297C22×C42—131no—
298C22×C42—261no—
299#479—1316no—
300#479—1316no—
301#477—138no—
302#477C2×D1318yescomplemented
303#475—138no—
304#475—138no—
305#428—1316no—
306C2×#107—132no—
307C2×#107C2×D1312yes—
308C2×#106—132no—
309C2×#106—132no—
310#423—138no—
311C2×C4⋊C8—132no—
312C2×C4⋊C8—131no—
313C2×C4⋊C8C2×D1311yescharacteristic
314#419—1316no—
315C2×#103—132no—
316C2×#103—132no—
317C2×#103—132no—
318C2×#103C2×D1312yes—
319C22×C13C2×C22⋊Q812yes—
320C22×C13C2×#13712yes—
321C22×C13#57512yes—
322C22×C13C23×D411yescharacteristic
323C2×D13—28no—
324C2×D13—22no—
325C2×D13—22no—
326C2×D13C2×C22⋊Q814yes—
327C4×C13—24no—
328C4×C13—22no—
329C4×C13—42no—
330C4×C13—44no—
331C4×C13C2×C22⋊Q812yes—
332C4×C13C2×#13714yes—
333C4×C13C23×Q811yescharacteristic
334C4×C13C22×#4111yescharacteristic
335Dic13—24no—
336Dic13—22no—
337Dic13—22no—
338Dic13—44no—
339Dic13—42no—
340Dic13C2×C22⋊Q814yes—
341C22×Q8—21no—
342C22×Q8—138no—
343C22×Q8—134no—
344C22×Q8—131no—
345C22×Q8—261no—
346C22×Q8—262no—
347C22×Q8—264no—
348C22×Q8—261no—
349C22×Q8C22×D1311yescharacteristic
350C23×C4—131no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—261no—
354C23×C4—261no—
355C2×M16—138no—
356C2×M16—268no—
357C22×C8—132no—
358C22×C8C22×D1312yes—
359C4⋊Q8—22no—
360C4⋊Q8—134no—
361C4⋊Q8—262no—
362C4⋊Q8C22×D1314yes—
363#125—138no—
364#125—264no—
365C22⋊Q8—268no—
366C22⋊Q8—268no—
367C4×Q8—22no—
368C4×Q8—134no—
369C4×Q8—134no—
370C4×Q8—134no—
371C4×Q8—268no—
372C4×Q8—268no—
373C4×Q8—262no—
374C4×Q8—268no—
375C4×Q8—262no—
376C4×Q8—268no—
377C4×Q8—262no—
378C4×Q8C22×D1314yes—
379#117—138no—
380#117—264no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—132no—
385C2×C4⋊C4—134no—
386C2×C4⋊C4—262no—
387C2×C4⋊C4—268no—
388C2×C4⋊C4—261no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—262no—
392C2×C4⋊C4—262no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C4⋊C4C22×D1312yes—
397C2×C22⋊C4—262no—
398C2×C42—21no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—134no—
403C2×C42—134no—
404C2×C42—268no—
405C2×C42—262no—
406C2×C42—261no—
407C2×C42—261no—
408C2×C42—261no—
409C2×C42C22×D1311yescharacteristic
410#107—138no—
411#107C22×D1318yes—
412#106—138no—
413#106—138no—
414C4⋊C8—138no—
415C4⋊C8—134no—
416C4⋊C8C22×D1314yes—
417#103—138no—
418#103—138no—
419#103—138no—
420#103C22×D1318yes—
421C2×C13#307814yescomplemented
422C2×C13C22×C22⋊Q811yescharacteristic
423C2×C13C22×#13711yescharacteristic
424C2×C13C2×#57511yescharacteristic
425D13—24no—
426C24—131no—
427C2×Q8—21no—
428C2×Q8—24no—
429C2×Q8—22no—
430C2×Q8—44no—
431C2×Q8—1316no—
432C2×Q8—134no—
433C2×Q8—132no—
434C2×Q8—264no—
435C2×Q8—268no—
436C2×Q8—2616no—
437C2×Q8—268no—
438C2×Q8—261no—
439C2×Q8—264no—
440C2×Q8—262no—
441C2×Q8—524no—
442C2×Q8Q8×D1314yes—
443C2×Q8C23×D1312yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—131no—
448C22×C4—132no—
449C22×C4—134no—
450C22×C4—134no—
451C22×C4—132no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—134no—
455C22×C4—134no—
456C22×C4—264no—
457C22×C4—268no—
458C22×C4—264no—
459C22×C4—261no—
460C22×C4—264no—
461C22×C4—261no—
462C22×C4—262no—
463C22×C4—522no—
464C22×C4—524no—
465C22×C4D4×D1311yescharacteristic
466C22×C4D4×D1311yescharacteristic
467C22×C4C23×D1311yescharacteristic
468M16—2616no—
469C2×C8—24no—
470C2×C8—134no—
471C2×C8—264no—
472C2×C8C23×D1314yes—
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—134no—
478C4⋊C4—132no—
479C4⋊C4—264no—
480C4⋊C4—264no—
481C4⋊C4—264no—
482C4⋊C4—268no—
483C4⋊C4—268no—
484C4⋊C4—261no—
485C4⋊C4—262no—
486C4⋊C4—264no—
487C4⋊C4—264no—
488C4⋊C4C23×D1314yes—
489C4⋊C4C23×D1312yes—
490C22⋊C4—268no—
491C42—24no—
492C42—134no—
493C42—134no—
494C42—132no—
495C42—132no—
496C42—264no—
497C42—264no—
498C42—268no—
499C42—264no—
500C42D4×D1312yes—
501C42C23×D1312yes—
502C13C2×#307811yescharacteristic, complemented, Sylow
503C23—134no—
504C23—132no—
505C23—262no—
506C23—262no—
507C23C2×D4×D1311yescharacteristic
508Q8—24no—
509Q8—22no—
510Q8—48no—
511Q8—134no—
512Q8—2616no—
513Q8—264no—
514Q8—262no—
515Q8—528no—
516Q8C2×Q8×D1314yes—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—134no—
525C2×C4—132no—
526C2×C4—138no—
527C2×C4—134no—
528C2×C4—134no—
529C2×C4—132no—
530C2×C4—132no—
531C2×C4—2616no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—264no—
535C2×C4—262no—
536C2×C4—268no—
537C2×C4—262no—
538C2×C4—264no—
539C2×C4—524no—
540C2×C4—528no—
541C2×C4—524no—
542C2×C4—522no—
543C2×C4#8817214yes—
544C2×C4C2×D4×D1312yes—
545C2×C4C2×D4×D1312yes—
546C2×C4C2×D4×D1311yescharacteristic
547C2×C4C2×Q8×D1312yes—
548C2×C4#41×D1312yes—
549C2×C4C24×D1311yescharacteristic
550C8—24no—
551C8—264no—
552C22—134no—
553C22—268no—
554C22—262no—
555C22—262no—
556C22D13×C22⋊Q812yes—
557C22C2×#8817212yes—
558C22#1171947812yes—
559C22C22×D4×D1311yescharacteristic
560C4—22no—
561C4—24no—
562C4—42no—
563C4—44no—
564C4—134no—
565C4—262no—
566C4—262no—
567C4—264no—
568C4—524no—
569C4—522no—
570C4D13×C22⋊Q812yes—
571C4C2×#8817214yes—
572C4C22×Q8×D1311yescharacteristic
573C4C2×#41×D1311yescharacteristic
574C2—264no—
575C2#1312464214yesdirect product factor
576C2C2×D13×C22⋊Q811yescharacteristic
577C2C22×#8817211yescharacteristic
578C2C2×#1171947811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#477C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#477D13
hypocenterC13C2×#3078
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13124642C2direct (N × H)
4. C2×#11718538C2semidirect
5. C2×#11718460C2semidirect
6. C2×#11718752C2semidirect
7. C2×#11718512C2semidirect
8. C2×#11718681C2semidirect
12. C2×C13×#477C2semidirect
37. C13×#477C22semidirect
45. #11718752C22semidirect
46. #11718681C22semidirect
52. #11718538C22semidirect
53. #11718512C22semidirect
56. #11718460C22semidirect
61. C2×Q8×D13Q8semidirect
159. Q8×D13C2×Q8semidirect
220. C2×#477D13semidirect
302. #477C2×D13semidirect
421. C2×C13#3078semidirect
502. C13C2×#3078semidirect
575. C2#13124642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×C4×Q8×D132
#131246422
C2×#117185382
C2×#117184602
C2×#117187522
C2×#117185122
C2×#117186812
C2×#117185422
C2×#117184982
C2×#117184632
C2×C13×#4772
C2×#307813