Finite Group Databasebeta

← C2×#13124841 #16730920

Subgroups — C2×#13124841 #16730920

Order 3328.

2570 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719327C211yesmaximal, characteristic, complemented
2C22×#88147C211yesmaximal, characteristic
3#13124841C2116yesmaximal, direct product factor
4C2×#11718632C211yesmaximal, characteristic, complemented
5C2×#11718531C212yesmaximal, complemented
6C2×#11718479C212yesmaximal, complemented
7C2×#11718392C211yesmaximal, characteristic
8C2×#11718707C211yesmaximal, characteristic
9C2×#11718513C212yesmaximal, complemented
10C2×#11718449C212yesmaximal, complemented
11C2×#11718379C211yesmaximal, characteristic, complemented
12C2×C13×#483C211yesmaximal, characteristic, complemented
13C23×D52C2211yescharacteristic
14C23×C4×D13—21no—
15C2×C13×C22⋊Q8C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic, complemented
18C2×#88198C2211yescharacteristic, complemented
19C22×#6106C2212yes—
20C22×#6103—21no—
21C2×#88178C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C22×#6095C2212yes—
24#11719327—24no—
25#11719327C2218yescomplemented
26C2×#88147—21no—
27C2×#88147—21no—
28C2×#88147—24no—
29C2×#88147C2212yes—
30C2×#88147C2212yes—
31C2×#88147C2218yes—
32C2×#88143—21no—
33C2×#88142C2211yescharacteristic, complemented
34C2×#88141—21no—
35C2×#88141C2211yescharacteristic, complemented
36C2×#88132—21no—
37C2×#88131—21no—
38C13×#483C2218yescomplemented
39C2×C13×#106C2212yescomplemented
40C2×C13×#103C2212yescomplemented
41C2×C13×C22⋊C8C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43C2×#88061C2212yes—
44C2×#88054C2212yescomplemented
45C2×C8×Dic13C2212yescomplemented
46#11718707C2218yes—
47#11718632C2218yescomplemented
48C2×#88050C2212yescomplemented
49C2×#88049C2212yes—
50C2×#88048C2212yescomplemented
51#11718531C22116yescomplemented
52#11718513C22116yescomplemented
53#11718479C22116yescomplemented
54#11718449C22116yescomplemented
55#11718392C2218yes—
56#11718379C2218yescomplemented
57C24×D13—21no—
58C22×Q8×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13D411yescharacteristic
62C23×Dic13D411yescharacteristic
63C22×D52—21no—
64C22×D52—22no—
65C22×D52—28no—
66C22×D52C2314yes—
67C22×D52C2312yes—
68C22×C4×D13—22no—
69C22×C4×D13—22no—
70C22×C4×D13—28no—
71C22×C4×D13—48no—
72C22×Dic26—21no—
73C22×Dic26C2311yescharacteristic
74C22×C8×C13C2312yes—
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8C2314yes—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2312yes—
82C2×C13×C4⋊C4C2314yes—
83C2×C13×C22⋊C4—21no—
84C2×C22⋊Dic13—21no—
85Q8×Dic13—22no—
86Q8×Dic13C2314yescomplemented
87#88198—22no—
88#88198C2314yescomplemented
89C2×#6106—28no—
90C2×#6106C2318yes—
91C2×#6103—22no—
92C2×#6103—22no—
93C2×#6103—28no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13C2311yescharacteristic
96#88178—22no—
97#88178C2314yes—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6101—21no—
102C2×#6101—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13—21no—
105C2×C4×Dic13D411yescharacteristic
106C2×C4×Dic13D411yescharacteristic
107C2×C4×Dic13D414yes—
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2311yescharacteristic
110C2×C4×Dic13C2314yes—
111C22×#1055C2312yes—
112C2×#6095—28no—
113C2×#6095C2318yes—
114#88147—28no—
115#88147—24no—
116#88147—24no—
117#88147—28no—
118#88147C2318yes—
119#88147C2318yes—
120#88143—28no—
121#88142—22no—
122#88142C2314yescomplemented
123#88141—28no—
124#88141—22no—
125#88141C2314yescomplemented
126#88132—28no—
127#88131—28no—
128C13×#106C2318yescomplemented
129C13×#103C2318yescomplemented
130C13×C22⋊C8C2314yes—
131C22⋊#1055C2314yes—
132#88061C2318yes—
133#88054C2318yescomplemented
134C8×Dic13C2318yescomplemented
135#88050C2318yescomplemented
136#88049C2318yes—
137#88048C2318yescomplemented
138C2×#3101—131nomaximal, Sylow
139C24×C13C2×D411yescharacteristic
140C23×D13—28no—
141C23×D13—24no—
142C23×D13—22no—
143C23×D13—44no—
144C23×D13—44no—
145C2×Q8×C13—21no—
146C2×Q8×C13—24no—
147C2×Q8×C13C2412yes—
148C22×C4×C13—24no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—24no—
152C22×C4×C13—22no—
153C22×C4×C13—44no—
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2412yes—
157C22×C4×C13C2411yescharacteristic
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—42no—
161C22×Dic13SD1618yescomplemented
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13C2×D411yescharacteristic
164C22×Dic13C2×D414yes—
165C22×Dic13C2×D411yescharacteristic
166C22×Dic13C2×D411yescharacteristic
167C22×Dic13C2×D414yes—
168C2×D52—28no—
169C2×D52—216no—
170C2×D52—24no—
171C2×D52—22no—
172C2×D52—24no—
173C2×D52—216no—
174C2×D52#4118yes—
175C2×D52C2414yes—
176C2×C4×D13—28no—
177C2×C4×D13—28no—
178C2×C4×D13—48no—
179C2×C4×D13—48no—
180C2×C4×D13—432no—
181C2×Dic26—24no—
182C2×Dic26—21no—
183C2×Dic26—24no—
184C2×Dic26—44no—
185C2×Dic26C2412yes—
186C2×C8×C13—24no—
187C2×C8×C13C2414yes—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—24no—
190C13×C4⋊C4—24no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4C2414yes—
193C13×C4⋊C4C2412yes—
194C13×C22⋊C4—24no—
195C22⋊Dic13—24no—
196#6106—216no—
197#6103—28no—
198#6103—28no—
199C4⋊Dic13—21no—
200C4⋊Dic13—24no—
201C4⋊Dic13C2412yes—
202#6101—24no—
203#6101—24no—
204#6101—24no—
205#6101—24no—
206#6101—24no—
207C4×Dic13—24no—
208C4×Dic13—24no—
209C4×Dic13C2×D414yes—
210C4×Dic13C2×D412yes—
211C4×Dic13C2×D412yes—
212C4×Dic13C2×D414yes—
213C4×Dic13C2412yes—
214C4×Dic13C2412yes—
215C2×#1055—24no—
216C2×#1055C2414yes—
217#6095—216no—
218C2×#533—131no—
219C22×C4×D4—131no—
220#3101—1316no—
221C2×#483—131no—
222C2×#483D1311yescharacteristic, complemented
223C2×#476—132no—
224C2×#461—132no—
225C2×#450—131no—
226C2×#450—131no—
227C2×C4×SD16—132no—
228C2×C4×SD16—132no—
229C2×#431—131no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13C2×SD1614yes—
233C23×C13C22×D412yes—
234C23×C13C22×D411yescharacteristic
235C22×D13—216no—
236C22×D13—28no—
237C22×D13—24no—
238C22×D13—432no—
239C22×D13—48no—
240C22×D13—48no—
241C22×D13—44no—
242C22×D13—44no—
243Q8×C13—24no—
244Q8×C13—42no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—24no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—24no—
251C2×C4×C13—42no—
252C2×C4×C13—48no—
253C2×C4×C13—44no—
254C2×C4×C13—42no—
255C2×C4×C13C22×D412yes—
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C2×#4114yes—
258C2×C4×C13C2511yescharacteristic
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—44no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13C2×SD1614yes—
267C2×Dic13C2×SD1614yes—
268C2×Dic13C2×SD16116yescomplemented
269C2×Dic13C22×D412yes—
270C2×Dic13C22×D412yes—
271C2×Dic13C22×D412yes—
272C2×Dic13C22×D412yes—
273D52—216no—
274D52—28no—
275D52—24no—
276D52C2×#4118yes—
277C4×D13—416no—
278C4×D13—416no—
279Dic26—24no—
280Dic26—48no—
281Dic26—42no—
282C8×C13—24no—
283#1055—24no—
284C23×D4—131no—
285C24×C4—261no—
286C22×SD16—132no—
287C22×SD16—132no—
288#533—138no—
289#533—264no—
290C2×C4⋊Q8—131no—
291C2×C4⋊Q8—131no—
292C2×#125—261no—
293C2×C22⋊Q8—131no—
294C2×C22⋊Q8—261no—
295C2×C22⋊Q8C2×D1311yescharacteristic
296C2×C4×Q8—131no—
297C2×C4×Q8—131no—
298C2×C4×Q8—261no—
299C2×C4×D4—138no—
300C2×C4×D4—132no—
301C2×C4×D4—132no—
302C2×C4×D4—261no—
303C2×C4×D4—261no—
304C2×C4×D4—264no—
305C2×#117—261no—
306C22×C4⋊C4C2×D1311yescharacteristic
307C22×C22⋊C4—261no—
308C22×C42—131no—
309#483—138no—
310#483C2×D1318yescomplemented
311#476—1316no—
312#461—1316no—
313#450—138no—
314#450—138no—
315C4×SD16—1316no—
316C4×SD16—1316no—
317#431—138no—
318C2×#106—132no—
319C2×#106C2×D1312yescomplemented
320C2×C4⋊C8—132no—
321C2×#103—132no—
322C2×#103C2×D1312yescomplemented
323C2×#102—132no—
324C2×#102—132no—
325C2×C22⋊C8—131no—
326C2×C22⋊C8C2×D1311yescharacteristic
327C2×C4×C8—132no—
328C22×C13—28no—
329C22×C13—22no—
330C22×C13—22no—
331C22×C13#52512yes—
332C22×C13C22×SD1614yes—
333C22×C13C22×SD1612yes—
334C22×C13#57512yes—
335C22×C13C23×D411yescharacteristic
336C2×D13—28no—
337C2×D13—432no—
338C2×D13—416no—
339C2×D13—44no—
340C2×D13—44no—
341C4×C13—22no—
342C4×C13—42no—
343C4×C13—44no—
344C4×C13—42no—
345C4×C13#52512yes—
346C4×C13C22×#4112yes—
347Dic13—22no—
348Dic13—22no—
349Dic13—42no—
350Dic13—42no—
351Dic13C22×SD1614yes—
352Dic13C22×SD1614yes—
353C25—261no—
354C22×Q8—131no—
355C22×Q8—261no—
356C22×Q8C22×D1311yescharacteristic
357C22×D4—132no—
358C22×D4—134no—
359C22×D4—268no—
360C22×D4—262no—
361C22×D4—261no—
362C23×C4—21no—
363C23×C4—131no—
364C23×C4—131no—
365C23×C4—268no—
366C23×C4—262no—
367C23×C4—262no—
368C23×C4—528no—
369C23×C4C22×D1311yescharacteristic
370C2×SD16—138no—
371C2×SD16—138no—
372C2×SD16—268no—
373C2×SD16—268no—
374C22×C8—132no—
375C22×C8C22×D1312yes—
376C4⋊Q8—134no—
377C4⋊Q8—134no—
378C4⋊Q8—262no—
379C4⋊Q8—262no—
380#125—268no—
381C22⋊Q8—22no—
382C22⋊Q8—134no—
383C22⋊Q8—268no—
384C22⋊Q8—262no—
385C22⋊Q8C22×D1314yes—
386C4×Q8—134no—
387C4×Q8—134no—
388C4×Q8—262no—
389C4×Q8—268no—
390C4×Q8—262no—
391C4×D4—138no—
392C4×D4—138no—
393C4×D4—268no—
394C4×D4—264no—
395C4×D4—268no—
396C4×D4—264no—
397#117—268no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4C22×D1312yes—
409C2×C4⋊C4C22×D1314yes—
410C2×C4⋊C4C22×D1311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—268no—
413C2×C22⋊C4—262no—
414C2×C22⋊C4—262no—
415C2×C22⋊C4—261no—
416C2×C42—131no—
417C2×C42—131no—
418C2×C42—134no—
419C2×C42—131no—
420C2×C42—131no—
421C2×C42—134no—
422C2×C42—261no—
423C2×C42—261no—
424#106—138no—
425#106C22×D1318yescomplemented
426C4⋊C8—138no—
427#103—138no—
428#103C22×D1318yescomplemented
429#102—138no—
430#102—138no—
431C22⋊C8—134no—
432C22⋊C8C22×D1314yes—
433C4×C8—138no—
434C2×C13—24no—
435C2×C13#310114yescomplemented
436C2×C13C2×#52511yescharacteristic
437C2×C13C23×SD1611yescharacteristic
438C2×C13C2×#57511yescharacteristic
439D13—48no—
440C24—268no—
441C24—264no—
442C24—262no—
443C24—524no—
444C24—524no—
445C24D4×D1311yescharacteristic
446C2×Q8—21no—
447C2×Q8—24no—
448C2×Q8—132no—
449C2×Q8—264no—
450C2×Q8—261no—
451C2×Q8—264no—
452C2×Q8—524no—
453C2×Q8C23×D1312yes—
454C2×D4—138no—
455C2×D4—134no—
456C2×D4—2616no—
457C2×D4—268no—
458C2×D4—2616no—
459C2×D4—264no—
460C2×D4—262no—
461C2×D4—264no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—44no—
468C22×C4—138no—
469C22×C4—134no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—134no—
475C22×C4—268no—
476C22×C4—268no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—528no—
480C22×C4—528no—
481C22×C4—5232no—
482C22×C4—522no—
483C22×C4D4×D1312yes—
484C22×C4D4×D1311yescharacteristic
485C22×C4C23×D1312yes—
486C22×C4C23×D1311yescharacteristic
487SD16—2616no—
488SD16—2616no—
489C2×C8—24no—
490C2×C8—134no—
491C2×C8—264no—
492C2×C8C23×D1314yes—
493C4⋊C4—24no—
494C4⋊C4—22no—
495C4⋊C4—24no—
496C4⋊C4—21no—
497C4⋊C4—132no—
498C4⋊C4—264no—
499C4⋊C4—264no—
500C4⋊C4—264no—
501C4⋊C4—264no—
502C4⋊C4—264no—
503C4⋊C4—261no—
504C4⋊C4—264no—
505C4⋊C4C23×D1312yes—
506C4⋊C4C23×D1314yes—
507C22⋊C4—24no—
508C22⋊C4—268no—
509C22⋊C4—268no—
510C22⋊C4—264no—
511C42—132no—
512C42—134no—
513C42—134no—
514C42—132no—
515C42—132no—
516C42—132no—
517C42—264no—
518C42—264no—
519C13C2×#310111yescharacteristic, complemented, Sylow
520C23—22no—
521C23—22no—
522C23—2616no—
523C23—268no—
524C23—264no—
525C23—528no—
526C23—5232no—
527C23—528no—
528C23—524no—
529C23—524no—
530C23SD16×D1314yes—
531C23C2×D4×D1312yes—
532C23C2×D4×D1311yescharacteristic
533Q8—24no—
534Q8—42no—
535Q8—264no—
536Q8—528no—
537Q8—522no—
538D4—138no—
539D4—2616no—
540D4—268no—
541D4—264no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—48no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—134no—
553C2×C4—134no—
554C2×C4—1316no—
555C2×C4—132no—
556C2×C4—132no—
557C2×C4—132no—
558C2×C4—132no—
559C2×C4—262no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—5216no—
564C2×C4—5216no—
565C2×C4—524no—
566C2×C4—522no—
567C2×C4—522no—
568C2×C4C2×D4×D1312yes—
569C2×C4C2×D4×D1311yescharacteristic
570C2×C4#41×D1314yes—
571C2×C4C24×D1311yescharacteristic
572C8—24no—
573C8—264no—
574C22—22no—
575C22—22no—
576C22—28no—
577C22—268no—
578C22—5232no—
579C22—524no—
580C22—524no—
581C22—5216no—
582C22#1171936112yes—
583C22C2×SD16×D1314yes—
584C22C2×SD16×D1312yes—
585C22#1171948212yes—
586C22C22×D4×D1311yescharacteristic
587C4—22no—
588C4—44no—
589C4—42no—
590C4—42no—
591C4—134no—
592C4—134no—
593C4—262no—
594C4—262no—
595C4—522no—
596C4—522no—
597C4#1171936112yes—
598C4C2×#41×D1312yes—
599C2—24no—
600C2—528no—
601C2#1312484114yesdirect product factor
602C2C2×#1171936111yescharacteristic
603C2C22×SD16×D1311yescharacteristic
604C2C2×#1171948211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#483C2
socleC23×C13C22×D4
prime radicalC23×D52C22
hypercenterC2×#483D13
hypocenterC13C2×#3101
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#11719327C2semidirect
3. #13124841C2direct (N × H)
4. C2×#11718632C2semidirect
5. C2×#11718531C2semidirect
6. C2×#11718479C2semidirect
9. C2×#11718513C2semidirect
10. C2×#11718449C2semidirect
11. C2×#11718379C2semidirect
12. C2×C13×#483C2semidirect
17. C2×Q8×Dic13C22semidirect
18. C2×#88198C22semidirect
25. #11719327C22semidirect
33. C2×#88142C22semidirect
35. C2×#88141C22semidirect
38. C13×#483C22semidirect
39. C2×C13×#106C22semidirect
40. C2×C13×#103C22semidirect
44. C2×#88054C22semidirect
45. C2×C8×Dic13C22semidirect
47. #11718632C22semidirect
48. C2×#88050C22semidirect
50. C2×#88048C22semidirect
51. #11718531C22semidirect
52. #11718513C22semidirect
53. #11718479C22semidirect
54. #11718449C22semidirect
56. #11718379C22semidirect
86. Q8×Dic13C23semidirect
88. #88198C23semidirect
122. #88142C23semidirect
125. #88141C23semidirect
128. C13×#106C23semidirect
129. C13×#103C23semidirect
133. #88054C23semidirect
134. C8×Dic13C23semidirect
135. #88050C23semidirect
137. #88048C23semidirect
161. C22×Dic13SD16semidirect
222. C2×#483D13semidirect
268. C2×Dic13C2×SD16semidirect
310. #483C2×D13semidirect
319. C2×#106C2×D13semidirect
322. C2×#103C2×D13semidirect
425. #106C22×D13semidirect
428. #103C22×D13semidirect
435. C2×C13#3101semidirect
519. C13C2×#3101semidirect
601. C2#13124841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193272
C22×#881472
#131248412
C2×#117186322
C2×#117185312
C2×#117184792
C2×#117183922
C2×#117187072
C2×#117185132
C2×#117184492
C2×#117183792
C2×C13×#4832
C2×#310113