Finite Group Databasebeta

← C2×#13126175 #16735726

Subgroups — C2×#13126175 #16735726

Order 3328.

1930 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic, complemented
2C2×#11719262C211yesmaximal, characteristic
3#13126175C2116yesmaximal, direct product factor
4C2×#11718538C212yesmaximal, complemented
5C2×#11718755C211yesmaximal, characteristic, complemented
6C2×#11718548C212yesmaximal, complemented
7C2×#11718439C212yesmaximal
8C2×#11718428C212yesmaximal, complemented
9C2×#11718510C211yesmaximal, characteristic, complemented
10C2×#11718680C211yesmaximal, characteristic, complemented
11C2×D13×C4⋊C8C211yesmaximal, characteristic, complemented
12C2×C13×#474C211yesmaximal, characteristic, complemented
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C13C2211yescharacteristic
15C2×#88200—21no—
16C2×Q8×Dic13—21no—
17C2×#88192C2211yescharacteristic
18C2×#88190C2211yescharacteristic
19C22×#6105C2212yes—
20C2×C4×C22⋊D13—21no—
21C2×#88180—21no—
22C22×Dic52C2212yes—
23C22×C8×D13C2212yes—
24#11719433—24no—
25#11719433C2218yescomplemented
26#11719262—24no—
27#11719262C2218yes—
28C2×#88151C2212yes—
29C2×#88151C2211yescharacteristic
30C2×#88146—21no—
31C2×#88144—21no—
32C2×#88144C2211yescharacteristic
33C2×#88141C2212yes—
34C2×#88137—21no—
35C2×#88133—21no—
36C2×C42×D13C2211yescharacteristic
37C2×#88123C2211yescharacteristic
38C2×C4×Dic26C2211yescharacteristic
39C13×#474C2218yescomplemented
40C2×C13×#107C2212yes—
41C2×C13×C4⋊C8C2211yescharacteristic
42C2×C13×#102C2212yes—
43C2×#88056C2212yes—
44C2×#88054C2212yes—
45#11718755C2218yescomplemented
46#11718680C2218yescomplemented
47C2×#88050C2212yes—
48C2×#88050C2212yes—
49C2×#88048C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51#11718548C22116yescomplemented
52#11718538C22116yescomplemented
53#11718510C2218yescomplemented
54D13×C4⋊C8C2218yescomplemented
55#11718439C22116yes—
56#11718428C22116yescomplemented
57C22×Q8×C13—21no—
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C22×C22⋊D13—21no—
61C22×C4×D13D411yescharacteristic
62C22×C4×D13D411yescharacteristic
63C22×C4×D13C2311yescharacteristic
64C22×Dic26C2311yescharacteristic
65C22×Dic26C2312yes—
66C22×C8×C13C2312yes—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8C2314yes—
69C4×D4×C13—22no—
70C4×D4×C13C2314yes—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79#88200—28no—
80Q8×Dic13—28no—
81#88192—22no—
82#88192C2314yes—
83#88190—22no—
84#88190C2314yes—
85C2×#6105—44no—
86C2×#6105C2318yes—
87C4×C22⋊D13—28no—
88C2×#6103—21no—
89C2×#6103—22no—
90#88180—28no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—22no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13D411yescharacteristic
103C2×C4×Dic13D411yescharacteristic
104C2×C4×Dic13C2311yescharacteristic
105C22×#1055C2312yes—
106C2×Dic52—44no—
107C2×Dic52C2318yes—
108C2×C8×D13—44no—
109C2×C8×D13C2318yes—
110#88151—24no—
111#88151—22no—
112#88151C2318yes—
113#88151C2314yes—
114#88146—28no—
115#88144—28no—
116#88144—22no—
117#88144C2314yes—
118#88141—24no—
119#88141C2318yes—
120#88137—28no—
121#88133—28no—
122C42×D13D414yes—
123C42×D13C2314yes—
124#88123—22no—
125#88123C2314yes—
126C4×Dic26—22no—
127C4×Dic26C2314yes—
128C13×#107C2318yes—
129C13×C4⋊C8C2314yes—
130C13×#102C2318yes—
131#88056C2318yes—
132#88054C2318yes—
133#88050C2318yes—
134#88050C2318yes—
135#88048C2318yes—
136C4⋊#1055C2314yes—
137C2×#3248—131nomaximal, Sylow
138C24×C13—21no—
139C23×D13C2×D411yescharacteristic
140C2×Q8×C13—24no—
141C2×Q8×C13—44no—
142C2×D4×C13—21no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13C2412yes—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—24no—
149C22×C4×C13—44no—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C2×C22⋊D13—24no—
154C2×C22⋊D13—44no—
155C22×Dic13—21no—
156C22×Dic13—22no—
157C22×Dic13—21no—
158C22×Dic13C2×D411yescharacteristic
159C22×Dic13C2×D411yescharacteristic
160C22×Dic13C2×D411yescharacteristic
161C2×C4×D13—24no—
162C2×C4×D13—24no—
163C2×C4×D13—22no—
164C2×C4×D13—22no—
165C2×C4×D13C2×D412yes—
166C2×C4×D13C2×D414yes—
167C2×C4×D13C2×D414yes—
168C2×C4×D13C2412yes—
169C2×Dic26—22no—
170C2×Dic26—24no—
171C2×Dic26—22no—
172C2×Dic26—24no—
173C2×Dic26—21no—
174C2×Dic26—22no—
175C2×Dic26C2412yes—
176C2×Dic26C2414yes—
177C2×C8×C13—24no—
178C2×C8×C13C2414yes—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4C2414yes—
183C13×C4⋊C4C2412yes—
184C13×C22⋊C4—24no—
185C42×C13C2×D412yes—
186C42×C13C2412yes—
187C22⋊Dic13—24no—
188C22⋊Dic13—24no—
189C22⋊Dic13—24no—
190#6105—48no—
191#6103—24no—
192#6103—28no—
193C4⋊Dic13—21no—
194C4⋊Dic13—24no—
195C4⋊Dic13—24no—
196C4⋊Dic13—24no—
197C4⋊Dic13—24no—
198C4⋊Dic13—28no—
199C4⋊Dic13C2412yes—
200#6101—24no—
201#6101—24no—
202#6101—28no—
203C4×Dic13—24no—
204C4×Dic13—28no—
205C4×Dic13C2×D412yes—
206C4×Dic13C2×D414yes—
207C4×Dic13C2×D414yes—
208C4×Dic13C2412yes—
209C2×#1055—24no—
210C2×#1055C2414yes—
211Dic52—48no—
212C8×D13—48no—
213C2×#533—131no—
214C2×#529—131no—
215#3248—1316no—
216C2×#479—132no—
217C2×#475—131no—
218C2×#474D1311yescharacteristic, complemented
219C2×#467—132no—
220C2×#465—132no—
221C2×#464—132no—
222C2×#462—131no—
223C2×#461—131no—
224C22×C4⋊C8—131no—
225C23×C13—22no—
226C23×C13—42no—
227C23×C13—42no—
228C23×C13—42no—
229C23×C13C22×D411yescharacteristic
230C22×D13—22no—
231C22×D13—22no—
232C22×D13#13714yes—
233C22×D13C22×D412yes—
234Q8×C13—48no—
235D4×C13—22no—
236D4×C13—22no—
237D4×C13—42no—
238C2×C4×C13—22no—
239C2×C4×C13—24no—
240C2×C4×C13—22no—
241C2×C4×C13—42no—
242C2×C4×C13—44no—
243C2×C4×C13—48no—
244C2×C4×C13#13514yes—
245C2×C4×C13C22×D412yes—
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C22×D412yes—
248C2×C4×C13H(5,𝔽2)12yes—
249C2×C4×C132−1+412yes—
250C2×C4×C13C2511yescharacteristic
251C22⋊D13—48no—
252C2×Dic13—22no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—24no—
257C2×Dic13—22no—
258C2×Dic13—42no—
259C2×Dic13—44no—
260C2×Dic13—42no—
261C2×Dic13C22×D412yes—
262C2×Dic13C22×D412yes—
263C2×Dic13C22×D412yes—
264C4×D13—28no—
265C4×D13—24no—
266C4×D13—28no—
267C4×D13—22no—
268C4×D13—22no—
269Dic26—22no—
270Dic26—24no—
271Dic26—22no—
272Dic26—24no—
273Dic26—42no—
274Dic26—44no—
275C8×C13—24no—
276#1055—24no—
277C22×Q16—132no—
278C22×SD16—132no—
279C23×C8—132no—
280#533—138no—
281#533—264no—
282C2×C4⋊Q8—131no—
283C2×C4⋊Q8C2×D1311yescharacteristic
284#529—138no—
285#529—264no—
286C2×#126—261no—
287C2×#125—131no—
288C2×#125—261no—
289C2×#124—131no—
290C2×#123—261no—
291C2×C22⋊Q8—131no—
292C2×C22⋊Q8—132no—
293C2×C22⋊Q8—261no—
294C2×#121—131no—
295C2×C4×Q8—132no—
296C2×C4×Q8—131no—
297C2×C4×Q8—261no—
298C2×C4×D4—261no—
299C2×C4×D4C2×D1311yescharacteristic
300C2×#117—261no—
301C2×#117—261no—
302C22×C42—131no—
303#479—1316no—
304#475—138no—
305#474C2×D1318yescomplemented
306#467—1316no—
307#465—1316no—
308#464—1316no—
309#462—138no—
310#461—138no—
311C2×#107C2×D1312yes—
312C2×#106—132no—
313C2×C4⋊C8—132no—
314C2×C4⋊C8—131no—
315C2×C4⋊C8—138no—
316C2×C4⋊C8C2×D1311yescharacteristic
317C2×#103—132no—
318C2×#103—132no—
319C2×#103—132no—
320C2×#102C2×D1312yes—
321C22×C13—42no—
322C22×C13—42no—
323C22×C13—42no—
324C22×C13—84no—
325C22×C13#53712yes—
326C22×C13C2×#13512yes—
327C22×C13C2×#13712yes—
328C22×C13C23×D411yescharacteristic
329C2×D13—22no—
330C2×D13—28no—
331C2×D13—22no—
332C2×D13C2×#13714yes—
333C4×C13—22no—
334C4×C13—42no—
335C4×C13—44no—
336C4×C13#53712yes—
337C4×C13C2×#13514yes—
338C4×C13C2×H(5,𝔽2)11yescharacteristic
339C4×C13C2×2−1+411yescharacteristic
340Dic13—22no—
341Dic13—22no—
342Dic13—22no—
343Dic13—42no—
344Dic13—44no—
345Dic13—42no—
346C22×Q8—21no—
347C22×Q8—131no—
348C22×Q8—132no—
349C22×D4—261no—
350C22×D4C22×D1311yescharacteristic
351C23×C4—21no—
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—131no—
355C2×Q16—138no—
356C2×Q16—524no—
357C2×SD16—138no—
358C2×SD16—524no—
359C22×C8—132no—
360C22×C8—138no—
361C22×C8—524no—
362C22×C8C22×D1312yes—
363C4⋊Q8—22no—
364C4⋊Q8—134no—
365C4⋊Q8—262no—
366C4⋊Q8C22×D1314yes—
367#126—268no—
368#125—134no—
369#125—262no—
370#125—268no—
371#124—134no—
372#124—262no—
373#123—268no—
374C22⋊Q8—134no—
375C22⋊Q8—138no—
376C22⋊Q8—262no—
377C22⋊Q8—264no—
378C22⋊Q8—268no—
379#121—134no—
380#121—262no—
381C4×Q8—138no—
382C4×Q8—134no—
383C4×Q8—264no—
384C4×Q8—268no—
385C4×Q8—262no—
386C4×D4—22no—
387C4×D4—268no—
388C4×D4C22×D1314yes—
389#117—268no—
390#117—268no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—262no—
397C2×C4⋊C4—262no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C4⋊C4C22×D1312yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—262no—
405C2×C22⋊C4—261no—
406C2×C22⋊C4—261no—
407C2×C22⋊C4—261no—
408C2×C22⋊C4—261no—
409C2×C42—131no—
410C2×C42—131no—
411C2×C42—131no—
412C2×C42—134no—
413C2×C42—134no—
414C2×C42—262no—
415C2×C42—261no—
416C2×C42C22×D1311yescharacteristic
417#107C22×D1318yes—
418#106—138no—
419C4⋊C8—138no—
420C4⋊C8—134no—
421C4⋊C8C22×D1314yes—
422#103—138no—
423#103—138no—
424#103—138no—
425#102C22×D1318yes—
426C2×C13—82no—
427C2×C13#324814yescomplemented
428C2×C13C2×#53711yescharacteristic
429C2×C13C22×#13511yescharacteristic
430C2×C13C22×#13711yescharacteristic
431D13—24no—
432C24—21no—
433C24—131no—
434C2×Q8—24no—
435C2×Q8—44no—
436C2×Q8—132no—
437C2×Q8—134no—
438C2×Q8—261no—
439C2×Q8—262no—
440C2×Q8—262no—
441C2×Q8—264no—
442C2×Q8—264no—
443C2×Q8—262no—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—264no—
448C2×D4—524no—
449C2×D4C23×D1312yes—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—44no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—134no—
458C22×C4—134no—
459C22×C4—132no—
460C22×C4—132no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—262no—
468C22×C4D4×D1311yescharacteristic
469C22×C4D4×D1311yescharacteristic
470C22×C4C23×D1311yescharacteristic
471Q16—528no—
472SD16—528no—
473C2×C8—24no—
474C2×C8—134no—
475C2×C8—264no—
476C2×C8—528no—
477C2×C8C23×D1314yes—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—132no—
482C4⋊C4—264no—
483C4⋊C4—264no—
484C4⋊C4—264no—
485C4⋊C4—268no—
486C4⋊C4—268no—
487C4⋊C4—261no—
488C4⋊C4—264no—
489C4⋊C4—264no—
490C4⋊C4—264no—
491C4⋊C4C23×D1314yes—
492C4⋊C4C23×D1312yes—
493C22⋊C4—24no—
494C22⋊C4—268no—
495C22⋊C4—264no—
496C22⋊C4—264no—
497C22⋊C4—264no—
498C22⋊C4—264no—
499C42—134no—
500C42—132no—
501C42—134no—
502C42—132no—
503C42—268no—
504C42—264no—
505C42D4×D1312yes—
506C42C23×D1312yes—
507C13C2×#324811yescharacteristic, complemented, Sylow
508C23—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—134no—
513C23—132no—
514C23—262no—
515C23—262no—
516C23C2×D4×D1311yescharacteristic
517Q8—48no—
518Q8—262no—
519Q8—264no—
520Q8—264no—
521Q8—262no—
522Q8—522no—
523Q8—524no—
524D4—22no—
525D4—22no—
526D4—42no—
527D4—528no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—48no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—268no—
538C2×C4—262no—
539C2×C4—262no—
540C2×C4—262no—
541C2×C4—268no—
542C2×C4—264no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—262no—
546C2×C4—262no—
547C2×C4—264no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—524no—
551C2×C4#8816614yes—
552C2×C4C2×D4×D1312yes—
553C2×C4C2×D4×D1312yes—
554C2×C4C2×D4×D1311yescharacteristic
555C2×C4#8825412yes—
556C2×C4#8825612yes—
557C2×C4C24×D1311yescharacteristic
558C8—24no—
559C8—264no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—84no—
564C22—134no—
565C22—268no—
566C22—262no—
567C22—262no—
568C22#1171933412yes—
569C22C2×#8816612yes—
570C22D13×#13712yes—
571C22C22×D4×D1311yescharacteristic
572C4—22no—
573C4—42no—
574C4—44no—
575C4—262no—
576C4—262no—
577C4—262no—
578C4—522no—
579C4—522no—
580C4—524no—
581C4#1171933412yes—
582C4C2×#8816614yes—
583C4C2×#8825411yescharacteristic
584C4C2×#8825611yescharacteristic
585C2—82no—
586C2—264no—
587C2#1312617514yesdirect product factor
588C2C2×#1171933411yescharacteristic
589C2C22×#8816611yescharacteristic
590C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#474C2
socleC23×C13C22×D4
prime radicalC2×#88192C22
hypercenterC2×#474D13
hypocenterC13C2×#3248
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#11719433C2semidirect
3. #13126175C2direct (N × H)
4. C2×#11718538C2semidirect
5. C2×#11718755C2semidirect
6. C2×#11718548C2semidirect
8. C2×#11718428C2semidirect
9. C2×#11718510C2semidirect
10. C2×#11718680C2semidirect
11. C2×D13×C4⋊C8C2semidirect
12. C2×C13×#474C2semidirect
25. #11719433C22semidirect
39. C13×#474C22semidirect
45. #11718755C22semidirect
46. #11718680C22semidirect
51. #11718548C22semidirect
52. #11718538C22semidirect
53. #11718510C22semidirect
54. D13×C4⋊C8C22semidirect
56. #11718428C22semidirect
218. C2×#474D13semidirect
305. #474C2×D13semidirect
427. C2×C13#3248semidirect
507. C13C2×#3248semidirect
587. C2#13126175direct (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×#117192622
#131261752
C2×#117185382
C2×#117187552
C2×#117185482
C2×#117184392
C2×#117184282
C2×#117185102
C2×#117186802
C2×D13×C4⋊C82
C2×C13×#4742
C2×#324813