Finite Group Databasebeta

← C2×#13126049 #16735070

Subgroups — C2×#13126049 #16735070

Order 3328.

1758 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2C2×#11719283C211yesmaximal, characteristic
3#13126049C2116yesmaximal, direct product factor
4C2×#11718517C212yesmaximal, complemented
5C2×#11718458C212yesmaximal, complemented
6C2×#11718528C212yesmaximal
7C2×#11718475C212yesmaximal
8C2×#11718511C211yesmaximal, characteristic, complemented
9C2×#11718682C211yesmaximal, characteristic, complemented
10C2×#11718755C211yesmaximal, characteristic, complemented
11C2×#11718496C211yesmaximal, characteristic
12C2×C13×#475C211yesmaximal, characteristic, complemented
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C13C2211yescharacteristic
15C2×#88200—21no—
16C2×#88200C2211yescharacteristic
17C2×Q8×Dic13—21no—
18C2×#88198C2211yescharacteristic
19#11719433—24no—
20#11719433C2218yes—
21#11719283—24no—
22#11719283C2218yes—
23C2×#88151—21no—
24C2×#88151C2211yescharacteristic
25C2×#88150—21no—
26C2×#88146C2212yes—
27C2×#88144C2212yes—
28C2×#88143—21no—
29C2×#88142C2211yescharacteristic
30C2×#88141—21no—
31C2×#88126—21no—
32C2×C42×D13C2211yescharacteristic
33C2×#88123C2211yescharacteristic
34C2×C4×Dic26—21no—
35C2×C4×Dic26C2211yescharacteristic
36C13×#475C2218yescomplemented
37C2×C13×#106C2212yes—
38C2×C13×C4⋊C8C2211yescharacteristic
39C2×C13×#103C2212yes—
40C2×#88075C2212yes—
41C2×#88060C2212yes—
42C2×#88058C2212yes—
43C2×#88056C2212yes—
44C2×#88055C2212yes—
45#11718755C2218yescomplemented
46#11718682C2218yescomplemented
47C2×#88050C2212yes—
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51#11718528C22116yes—
52#11718517C22116yescomplemented
53#11718511C2218yescomplemented
54#11718496C2218yes—
55#11718475C22116yes—
56#11718458C22116yescomplemented
57C22×Q8×C13—21no—
58C22×Q8×C13C2311yescharacteristic
59C22×C4×D13D411yescharacteristic
60C22×C4×D13D411yescharacteristic
61C22×C4×D13C2311yescharacteristic
62C22×Dic26—21no—
63C22×Dic26—21no—
64C22×Dic26C2311yescharacteristic
65C22×C8×C13C2312yes—
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8C2314yes—
68C4×Q8×C13—22no—
69C4×Q8×C13C2314yes—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2312yes—
74C2×C42×C13—21no—
75C2×C42×C13C2311yescharacteristic
76#88200—28no—
77#88200—22no—
78#88200C2314yes—
79Q8×Dic13—28no—
80#88198—22no—
81#88198C2314yes—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—22no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2312yes—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—22no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13D411yescharacteristic
99C2×C4×Dic13D411yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055C2312yes—
102#88151—28no—
103#88151—22no—
104#88151C2314yes—
105#88150—28no—
106#88146—24no—
107#88146C2318yes—
108#88144—24no—
109#88144C2318yes—
110#88143—28no—
111#88142—22no—
112#88142C2314yes—
113#88141—28no—
114#88126—28no—
115C42×D13D414yes—
116C42×D13C2314yes—
117#88123—22no—
118#88123C2314yes—
119C4×Dic26—22no—
120C4×Dic26—28no—
121C4×Dic26C2314yes—
122C13×#106C2318yes—
123C13×C4⋊C8C2314yes—
124C13×#103C2318yes—
125#88075C2318yes—
126#88060C2318yes—
127#88058C2318yes—
128#88056C2318yes—
129#88055C2318yes—
130#88050C2318yes—
131#88048C2318yes—
132#88047C2318yes—
133C4⋊#1055C2314yes—
134C2×#3237—131nomaximal, Sylow
135C23×D13C2×D411yescharacteristic
136C2×Q8×C13—21no—
137C2×Q8×C13—24no—
138C2×Q8×C13—22no—
139C2×Q8×C13—22no—
140C2×Q8×C13—44no—
141C2×Q8×C13C2412yes—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—22no—
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C2×C4×D13—24no—
155C2×C4×D13—22no—
156C2×C4×D13—22no—
157C2×C4×D13—42no—
158C2×C4×D13C2×D412yes—
159C2×C4×D13C2×D414yes—
160C2×C4×D13C2×D414yes—
161C2×C4×D13C2412yes—
162C2×Dic26—22no—
163C2×Dic26—22no—
164C2×Dic26—21no—
165C2×Dic26—24no—
166C2×Dic26—24no—
167C2×Dic26—44no—
168C2×Dic26—44no—
169C2×Dic26C2412yes—
170C2×C8×C13—24no—
171C2×C8×C13C2414yes—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4C2414yes—
177C13×C4⋊C4C2412yes—
178C42×C13—24no—
179C42×C13C2×D412yes—
180C42×C13C2412yes—
181#6103—24no—
182#6103—24no—
183#6103—28no—
184C4⋊Dic13—21no—
185C4⋊Dic13—22no—
186C4⋊Dic13—24no—
187C4⋊Dic13—24no—
188C4⋊Dic13—28no—
189C4⋊Dic13C2414yes—
190C4⋊Dic13C2412yes—
191#6101—24no—
192#6101—24no—
193#6101—24no—
194#6101—24no—
195#6101—24no—
196#6101—28no—
197C4×Dic13—24no—
198C4×Dic13—28no—
199C4×Dic13C2×D414yes—
200C4×Dic13C2×D412yes—
201C4×Dic13C2×D414yes—
202C4×Dic13C2412yes—
203C2×#1055—24no—
204C2×#1055C2414yes—
205C2×#533—131no—
206C2×#533—131no—
207#3237—1316no—
208C2×#501—132no—
209C2×#491—132no—
210C2×#485—132no—
211C2×#485—132no—
212C2×#477—131no—
213C2×#477—131no—
214C2×#475—131no—
215C2×#475D1311yescharacteristic, complemented
216C2×#432—131no—
217C23×C13C22×D411yescharacteristic
218C22×D13—22no—
219C22×D13—22no—
220C22×D13—22no—
221C22×D13C22×D412yes—
222Q8×C13—22no—
223Q8×C13—22no—
224Q8×C13—42no—
225Q8×C13—48no—
226C2×C4×C13—22no—
227C2×C4×C13—24no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—42no—
231C2×C4×C13—44no—
232C2×C4×C13—42no—
233C2×C4×C13#13714yes—
234C2×C4×C13C22×D412yes—
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C22×D412yes—
237C2×C4×C132−1+412yes—
238C2×C4×C132−1+412yes—
239C2×C4×C13C2511yescharacteristic
240C2×Dic13—22no—
241C2×Dic13—22no—
242C2×Dic13—22no—
243C2×Dic13—22no—
244C2×Dic13—22no—
245C2×Dic13—24no—
246C2×Dic13—42no—
247C2×Dic13—42no—
248C2×Dic13—44no—
249C2×Dic13C22×D412yes—
250C2×Dic13C22×D412yes—
251C2×Dic13C22×D412yes—
252C4×D13—24no—
253C4×D13—28no—
254C4×D13—22no—
255C4×D13—22no—
256C4×D13—44no—
257Dic26—22no—
258Dic26—22no—
259Dic26—48no—
260Dic26—48no—
261Dic26—42no—
262C8×C13—24no—
263#1055—24no—
264#533—138no—
265#533—138no—
266#533—264no—
267#533—264no—
268C2×C4⋊Q8—131no—
269C2×C4⋊Q8—131no—
270C2×C4⋊Q8—131no—
271C2×C4⋊Q8C2×D1311yescharacteristic
272C2×#125—132no—
273C2×#125—261no—
274C2×C22⋊Q8—131no—
275C2×C22⋊Q8—131no—
276C2×C22⋊Q8—261no—
277C2×C22⋊Q8—261no—
278C2×C22⋊Q8—261no—
279C2×C4×Q8—131no—
280C2×C4×Q8—261no—
281C2×C4×Q8—261no—
282C2×C4×Q8—261no—
283C2×C4×Q8C2×D1311yescharacteristic
284C2×#117—132no—
285C2×#117—261no—
286C22×C42—131no—
287#501—1316no—
288#491—1316no—
289#485—1316no—
290#485—1316no—
291#477—138no—
292#477—138no—
293#475—138no—
294#475C2×D1318yescomplemented
295#432—138no—
296C2×#107—132no—
297C2×#107—132no—
298C2×#106—132no—
299C2×#106C2×D1312yes—
300C2×C4⋊C8—131no—
301C2×C4⋊C8C2×D1311yescharacteristic
302C2×#103—132no—
303C2×#103—132no—
304C2×#103—132no—
305C2×#103C2×D1312yes—
306C2×C22⋊C8—132no—
307C2×#97—132no—
308C22×C13#53612yes—
309C22×C13C2×#13712yes—
310C22×C13#57512yes—
311C22×C13C23×D411yescharacteristic
312C2×D13—22no—
313C2×D13—22no—
314C2×D13—22no—
315C2×D13—44no—
316C4×C13—22no—
317C4×C13—42no—
318C4×C13—44no—
319C4×C13—42no—
320C4×C13#53612yes—
321C4×C13C2×#13714yes—
322C4×C13C2×2−1+411yescharacteristic
323C4×C13C2×2−1+411yescharacteristic
324Dic13—22no—
325Dic13—22no—
326Dic13—22no—
327Dic13—42no—
328Dic13—42no—
329Dic13—44no—
330C22×Q8—21no—
331C22×Q8—131no—
332C22×Q8—261no—
333C22×Q8—261no—
334C22×Q8C22×D1311yescharacteristic
335C23×C4—131no—
336C23×C4—131no—
337C23×C4—131no—
338C22×C8—132no—
339C22×C8C22×D1312yes—
340C4⋊Q8—22no—
341C4⋊Q8—134no—
342C4⋊Q8—134no—
343C4⋊Q8—134no—
344C4⋊Q8—262no—
345C4⋊Q8—262no—
346C4⋊Q8—262no—
347C4⋊Q8C22×D1314yes—
348#125—138no—
349#125—264no—
350#125—268no—
351C22⋊Q8—134no—
352C22⋊Q8—134no—
353C22⋊Q8—262no—
354C22⋊Q8—268no—
355C22⋊Q8—268no—
356C22⋊Q8—262no—
357C22⋊Q8—268no—
358C4×Q8—22no—
359C4×Q8—134no—
360C4×Q8—268no—
361C4×Q8—268no—
362C4×Q8—268no—
363C4×Q8—262no—
364C4×Q8C22×D1314yes—
365#117—138no—
366#117—268no—
367#117—264no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—132no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4C22×D1312yes—
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C22⋊C4—262no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C42—21no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—134no—
391C2×C42—134no—
392C2×C42—262no—
393C2×C42—261no—
394C2×C42C22×D1311yescharacteristic
395#107—138no—
396#107—138no—
397#106—138no—
398#106C22×D1318yes—
399C4⋊C8—134no—
400C4⋊C8C22×D1314yes—
401#103—138no—
402#103—138no—
403#103—138no—
404#103C22×D1318yes—
405C22⋊C8—138no—
406#97—138no—
407C2×C13#323714yescomplemented
408C2×C13C2×#53611yescharacteristic
409C2×C13C22×#13711yescharacteristic
410C2×C13C2×#57511yescharacteristic
411D13—42no—
412C24—131no—
413C2×Q8—21no—
414C2×Q8—24no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—44no—
418C2×Q8—132no—
419C2×Q8—264no—
420C2×Q8—264no—
421C2×Q8—261no—
422C2×Q8—262no—
423C2×Q8—262no—
424C2×Q8—524no—
425C2×Q8—524no—
426C2×Q8C23×D1312yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—132no—
434C22×C4—134no—
435C22×C4—132no—
436C22×C4—134no—
437C22×C4—264no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—261no—
442C22×C4—261no—
443C22×C4—522no—
444C22×C4D4×D1311yescharacteristic
445C22×C4D4×D1311yescharacteristic
446C22×C4C23×D1311yescharacteristic
447C2×C8—24no—
448C2×C8—134no—
449C2×C8—264no—
450C2×C8C23×D1314yes—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—134no—
456C4⋊C4—132no—
457C4⋊C4—264no—
458C4⋊C4—264no—
459C4⋊C4—264no—
460C4⋊C4—264no—
461C4⋊C4—268no—
462C4⋊C4—268no—
463C4⋊C4—264no—
464C4⋊C4—262no—
465C4⋊C4—261no—
466C4⋊C4—264no—
467C4⋊C4—264no—
468C4⋊C4C23×D1314yes—
469C4⋊C4C23×D1312yes—
470C22⋊C4—268no—
471C22⋊C4—264no—
472C22⋊C4—264no—
473C42—24no—
474C42—134no—
475C42—134no—
476C42—132no—
477C42—132no—
478C42—268no—
479C42—264no—
480C42D4×D1312yes—
481C42C23×D1312yes—
482C13C2×#323711yescharacteristic, complemented, Sylow
483C23—132no—
484C23—262no—
485C23—262no—
486C23—262no—
487C23C2×D4×D1311yescharacteristic
488Q8—22no—
489Q8—22no—
490Q8—48no—
491Q8—42no—
492Q8—262no—
493Q8—262no—
494Q8—528no—
495Q8—528no—
496Q8—522no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—132no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—262no—
508C2×C4—262no—
509C2×C4—262no—
510C2×C4—268no—
511C2×C4—264no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—264no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—524no—
518C2×C4—524no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4#8816914yes—
522C2×C4C2×D4×D1312yes—
523C2×C4C2×D4×D1312yes—
524C2×C4C2×D4×D1311yescharacteristic
525C2×C4#8825412yes—
526C2×C4#8825712yes—
527C2×C4C24×D1311yescharacteristic
528C8—24no—
529C8—264no—
530C22—262no—
531C22—262no—
532C22—262no—
533C22—524no—
534C22#1171933312yes—
535C22C2×#8816912yes—
536C22#1171948212yes—
537C22C22×D4×D1311yescharacteristic
538C4—22no—
539C4—44no—
540C4—42no—
541C4—42no—
542C4—262no—
543C4—262no—
544C4—262no—
545C4—524no—
546C4—522no—
547C4—522no—
548C4#1171933312yes—
549C4C2×#8816914yes—
550C4C2×#8825411yescharacteristic
551C4C2×#8825711yescharacteristic
552C2—522no—
553C2#1312604914yesdirect product factor
554C2C2×#1171933311yescharacteristic
555C2C22×#8816911yescharacteristic
556C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#475C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#475D13
hypocenterC13C2×#3237
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13126049C2direct (N × H)
4. C2×#11718517C2semidirect
5. C2×#11718458C2semidirect
8. C2×#11718511C2semidirect
9. C2×#11718682C2semidirect
10. C2×#11718755C2semidirect
12. C2×C13×#475C2semidirect
36. C13×#475C22semidirect
45. #11718755C22semidirect
46. #11718682C22semidirect
52. #11718517C22semidirect
53. #11718511C22semidirect
56. #11718458C22semidirect
215. C2×#475D13semidirect
294. #475C2×D13semidirect
407. C2×C13#3237semidirect
482. C13C2×#3237semidirect
553. C2#13126049direct (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×#117192832
#131260492
C2×#117185172
C2×#117184582
C2×#117185282
C2×#117184752
C2×#117185112
C2×#117186822
C2×#117187552
C2×#117184962
C2×C13×#4752
C2×#323713