Finite Group Databasebeta

← C2×#13125955 #16734930

Subgroups — C2×#13125955 #16734930

Order 3328.

2286 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×#11719301C211yesmaximal, characteristic
2C22×#88142C211yesmaximal, characteristic, complemented
3#13125955C2116yesmaximal, direct product factor
4C2×#11718535C212yesmaximal, complemented
5C2×#11718421C212yesmaximal, complemented
6C2×#11718397C211yesmaximal, characteristic, complemented
7C2×#11718628C211yesmaximal, characteristic, complemented
8C2×#11718694C211yesmaximal, characteristic, complemented
9C2×#11718551C212yesmaximal, complemented
10C2×#11718420C212yesmaximal, complemented
11C2×#11718379C211yesmaximal, characteristic, complemented
12C2×C13×#480C211yesmaximal, characteristic, complemented
13C22×#6129—21no—
14C23×Dic26—21no—
15C2×C13×#121C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88194C2211yescharacteristic
18C2×#88193—21no—
19C2×D4×Dic13C2211yescharacteristic
20C2×#88184C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101—21no—
23C22×C4×Dic13C2211yescharacteristic
24#11719301—24no—
25#11719301C2218yes—
26C2×#88147C2211yescharacteristic
27C2×#88142—24no—
28C2×#88142—21no—
29C2×#88142—21no—
30C2×#88142C2212yes—
31C2×#88142C2212yes—
32C2×#88142C2211yescharacteristic
33C2×#88142C2218yescomplemented
34C2×#88139—21no—
35C2×#88135—21no—
36C13×#480C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×#102C2212yes—
39C2×C13×C22⋊C8C2211yescharacteristic
40C2×#88072C2212yes—
41C2×C22⋊#1055C2211yescharacteristic
42C2×#88061C2212yes—
43C2×#88058C2212yes—
44C2×#88054C2212yes—
45C2×C8×Dic13C2212yes—
46#11718694C2218yescomplemented
47#11718628C2218yescomplemented
48C2×#88049C2212yes—
49C2×#88047C2212yes—
50C2×#88047C2212yes—
51#11718551C22116yescomplemented
52#11718535C22116yescomplemented
53#11718421C22116yescomplemented
54#11718420C22116yescomplemented
55#11718397C2218yescomplemented
56#11718379C2218yescomplemented
57C22×D4×C13—21no—
58C22×D4×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C22×C22⋊D13—21no—
62C22×C22⋊D13—21no—
63C22×C22⋊D13—21no—
64C23×Dic13—21no—
65C23×Dic13—21no—
66C23×Dic13D411yescharacteristic
67C23×Dic13D411yescharacteristic
68C2×#6129—28no—
69C2×#6129—48no—
70C22×D52C2311yescharacteristic
71C22×C4×D13—21no—
72C22×Dic26—21no—
73C22×Dic26—22no—
74C22×Dic26—22no—
75C22×Dic26—28no—
76C22×Dic26—48no—
77C22×C8×C13C2312yes—
78C13×#121—22no—
79C13×#121C2314yes—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2314yes—
85C2×C13×C22⋊C4—21no—
86C2×C22⋊Dic13—21no—
87#88194—22no—
88#88194C2314yes—
89#88193—28no—
90D4×Dic13—22no—
91D4×Dic13C2314yes—
92#88184—22no—
93#88184C2314yes—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13C2312yes—
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2314yes—
101C2×#6101—21no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—28no—
105C2×C4×Dic13D411yescharacteristic
106C2×C4×Dic13D411yescharacteristic
107C2×C4×Dic13D414yes—
108C2×C4×Dic13C2311yescharacteristic
109C2×C4×Dic13C2311yescharacteristic
110C2×C4×Dic13C2314yes—
111C22×#1055C2312yes—
112#88147—22no—
113#88147C2314yes—
114#88142—24no—
115#88142—24no—
116#88142—28no—
117#88142—28no—
118#88142—22no—
119#88142C2318yes—
120#88142C2318yes—
121#88142C2314yes—
122#88139—28no—
123#88135—28no—
124C13×#107C2318yes—
125C13×#102C2318yes—
126C13×C22⋊C8C2314yes—
127#88072C2318yes—
128C22⋊#1055C2314yes—
129#88061C2318yes—
130#88058C2318yes—
131#88054C2318yes—
132C8×Dic13C2318yes—
133#88049C2318yes—
134#88047C2318yes—
135#88047C2318yes—
136C2×#3226—131nomaximal, Sylow
137C24×C13—21no—
138C24×C13C2×D411yescharacteristic
139C23×D13—21no—
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
154C2×C22⋊D13—24no—
155C2×C22⋊D13—24no—
156C2×C22⋊D13—24no—
157C2×C22⋊D13—44no—
158C2×C22⋊D13—44no—
159C2×C22⋊D13—44no—
160C22×Dic13—24no—
161C22×Dic13—24no—
162C22×Dic13—22no—
163C22×Dic13—21no—
164C22×Dic13—24no—
165C22×Dic13—44no—
166C22×Dic13—44no—
167C22×Dic13D818yes—
168C22×Dic13C2×D411yescharacteristic
169C22×Dic13C2×D414yes—
170C22×Dic13C2×D411yescharacteristic
171C22×Dic13C2×D411yescharacteristic
172C22×Dic13C2×D414yes—
173C22×Dic13C2×D411yescharacteristic
174#6129—432no—
175C2×D52—24no—
176C2×D52—21no—
177C2×D52C2412yes—
178C2×C4×D13—24no—
179C2×C4×D13—44no—
180C2×Dic26—24no—
181C2×Dic26—28no—
182C2×Dic26—28no—
183C2×Dic26—48no—
184C2×Dic26—48no—
185C2×Dic26—432no—
186C2×Dic26—44no—
187C2×C8×C13—24no—
188C2×C8×C13C2414yes—
189C13×C4⋊C4—24no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4C2414yes—
193C13×C4⋊C4C2412yes—
194C13×C22⋊C4—24no—
195C22⋊Dic13—24no—
196#6103—24no—
197#6103—24no—
198C4⋊Dic13—24no—
199C4⋊Dic13—22no—
200C4⋊Dic13—21no—
201C4⋊Dic13C2414yes—
202C4⋊Dic13C2412yes—
203#6101—24no—
204#6101—28no—
205#6101—28no—
206C4×Dic13C2×D414yes—
207C4×Dic13C2×D414yes—
208C4×Dic13C2×D412yes—
209C4×Dic13C2×D412yes—
210C4×Dic13C2412yes—
211C4×Dic13C2412yes—
212C2×#1055—24no—
213C2×#1055C2414yes—
214C2×#532—131no—
215C22×C4⋊Q8—131no—
216#3226—1316no—
217C2×#500—132no—
218C2×#486—132no—
219C2×#480—131no—
220C2×#480—131no—
221C2×#480—131no—
222C2×#480D1311yescharacteristic, complemented
223C2×#474—132no—
224C2×#474—132no—
225C2×#431—131no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13C2×D814yes—
233C23×C13C22×D412yes—
234C23×C13C22×D411yescharacteristic
235C22×D13—22no—
236C22×D13—42no—
237C22×D13—42no—
238C22×D13—42no—
239D4×C13—24no—
240D4×C13—48no—
241D4×C13—42no—
242C2×C4×C13—22no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—24no—
246C2×C4×C13—22no—
247C2×C4×C13—48no—
248C2×C4×C13—44no—
249C2×C4×C13—42no—
250C2×C4×C13C22×D412yes—
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C132−1+414yes—
253C2×C4×C13C2511yescharacteristic
254C22⋊D13—48no—
255C22⋊D13—48no—
256C22⋊D13—48no—
257C2×Dic13—22no—
258C2×Dic13—28no—
259C2×Dic13—24no—
260C2×Dic13—22no—
261C2×Dic13—48no—
262C2×Dic13—44no—
263C2×Dic13—42no—
264C2×Dic13—48no—
265C2×Dic13C2×D814yes—
266C2×Dic13C2×D814yes—
267C2×Dic13C2×D8116yes—
268C2×Dic13#13714yes—
269C2×Dic13C22×D412yes—
270C2×Dic13C22×D412yes—
271C2×Dic13C22×D412yes—
272C2×Dic13C22×D412yes—
273D52—24no—
274D52—42no—
275C4×D13—48no—
276Dic26—416no—
277Dic26—416no—
278Dic26—48no—
279C8×C13—24no—
280#1055—24no—
281C22×#41—261no—
282C23×Q8—261no—
283#532—138no—
284#532—264no—
285C2×C4⋊Q8—132no—
286C2×C4⋊Q8—131no—
287C2×C4⋊Q8—132no—
288C2×C4⋊Q8—138no—
289C2×C4⋊Q8—261no—
290C2×C4⋊Q8—261no—
291C2×C4⋊Q8—264no—
292C2×#127—131no—
293C2×#124—261no—
294C2×#121—131no—
295C2×#121—261no—
296C2×#121C2×D1311yescharacteristic
297C2×C4×D4—131no—
298C2×C4×D4—131no—
299C2×C4×D4—261no—
300C22×C4⋊C4—131no—
301C22×C4⋊C4—261no—
302C22×C4⋊C4C2×D1311yescharacteristic
303C22×C42—131no—
304#500—1316no—
305#486—1316no—
306#480—138no—
307#480—138no—
308#480—138no—
309#480C2×D1318yescomplemented
310#474—1316no—
311#474—1316no—
312#431—138no—
313C2×#107—132no—
314C2×#107—132no—
315C2×#107—132no—
316C2×#107C2×D1312yes—
317C2×C4⋊C8—132no—
318C2×#102—132no—
319C2×#102—132no—
320C2×#102—132no—
321C2×#102C2×D1312yes—
322C2×C22⋊C8—131no—
323C2×C22⋊C8C2×D1311yescharacteristic
324C2×C4×C8—132no—
325C22×C13—22no—
326C22×C13—28no—
327C22×C13—22no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—84no—
332C22×C13#53612yes—
333C22×C13C22×D814yes—
334C22×C13C22×D812yes—
335C22×C13C2×#13712yes—
336C22×C13C23×D411yescharacteristic
337C2×D13—42no—
338C2×D13—42no—
339C2×D13—42no—
340C2×D13—84no—
341C4×C13—22no—
342C4×C13—44no—
343C4×C13—42no—
344C4×C13#53612yes—
345C4×C13C2×2−1+412yes—
346Dic13—22no—
347Dic13—44no—
348Dic13—42no—
349Dic13C22×D814yes—
350Dic13C22×D814yes—
351Dic13C2×#13714yes—
352C2×#41—268no—
353C2×#41—528no—
354C22×Q8—261no—
355C22×Q8—268no—
356C22×Q8—262no—
357C22×Q8—262no—
358C22×Q8—528no—
359C22×D4—21no—
360C22×D4—131no—
361C22×D4—261no—
362C22×D4—261no—
363C22×D4—261no—
364C22×D4C22×D1311yescharacteristic
365C23×C4—21no—
366C23×C4—131no—
367C23×C4—131no—
368C23×C4—261no—
369C23×C4—261no—
370C23×C4—261no—
371C23×C4C22×D1311yescharacteristic
372C22×C8—132no—
373C22×C8C22×D1312yes—
374C4⋊Q8—138no—
375C4⋊Q8—138no—
376C4⋊Q8—134no—
377C4⋊Q8—264no—
378C4⋊Q8—268no—
379C4⋊Q8—268no—
380C4⋊Q8—264no—
381C4⋊Q8—262no—
382#127—134no—
383#127—262no—
384#124—268no—
385#121—22no—
386#121—134no—
387#121—268no—
388#121—262no—
389#121C22×D1314yes—
390C4×D4—134no—
391C4×D4—134no—
392C4×D4—268no—
393C4×D4—262no—
394C4×D4—262no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—132no—
398C2×C4⋊C4—134no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—268no—
401C2×C4⋊C4—262no—
402C2×C4⋊C4—262no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—262no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4C22×D1312yes—
407C2×C4⋊C4C22×D1314yes—
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—261no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C42—131no—
414C2×C42—131no—
415C2×C42—134no—
416C2×C42—131no—
417C2×C42—131no—
418C2×C42—134no—
419#107—138no—
420#107—138no—
421#107—138no—
422#107C22×D1318yes—
423C4⋊C8—138no—
424#102—138no—
425#102—138no—
426#102—138no—
427#102C22×D1318yes—
428C22⋊C8—134no—
429C22⋊C8C22×D1314yes—
430C4×C8—138no—
431C2×C13—24no—
432C2×C13—82no—
433C2×C13#322614yescomplemented
434C2×C13C2×#53611yescharacteristic
435C2×C13C23×D811yescharacteristic
436C2×C13C22×#13711yescharacteristic
437D13—82no—
438C24—21no—
439C24—261no—
440C24D4×D1311yescharacteristic
441#41—5232no—
442C2×Q8—264no—
443C2×Q8—268no—
444C2×Q8—268no—
445C2×Q8—528no—
446C2×Q8—528no—
447C2×Q8—5232no—
448C2×Q8—524no—
449C2×D4—24no—
450C2×D4—21no—
451C2×D4—24no—
452C2×D4—44no—
453C2×D4—132no—
454C2×D4—264no—
455C2×D4—264no—
456C2×D4—264no—
457C2×D4—261no—
458C2×D4—264no—
459C2×D4—524no—
460C2×D4—524no—
461C2×D4—524no—
462C2×D4C23×D1312yes—
463C22×C4—24no—
464C22×C4—24no—
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—134no—
474C22×C4—131no—
475C22×C4—264no—
476C22×C4—264no—
477C22×C4—264no—
478C22×C4—264no—
479C22×C4—261no—
480C22×C4—262no—
481C22×C4—524no—
482C22×C4—524no—
483C22×C4—524no—
484C22×C4D4×D1312yes—
485C22×C4D4×D1311yescharacteristic
486C22×C4C23×D1312yes—
487C22×C4C23×D1311yescharacteristic
488C2×C8—24no—
489C2×C8—134no—
490C2×C8—264no—
491C2×C8C23×D1314yes—
492C4⋊C4—24no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—134no—
496C4⋊C4—132no—
497C4⋊C4—268no—
498C4⋊C4—268no—
499C4⋊C4—264no—
500C4⋊C4—264no—
501C4⋊C4—262no—
502C4⋊C4—261no—
503C4⋊C4C23×D1314yes—
504C4⋊C4C23×D1312yes—
505C22⋊C4—24no—
506C22⋊C4—264no—
507C22⋊C4—264no—
508C22⋊C4—264no—
509C42—134no—
510C42—132no—
511C42—134no—
512C42—132no—
513C42—132no—
514C42—132no—
515C13C2×#322611yescharacteristic, complemented, Sylow
516C23—22no—
517C23—22no—
518C23—22no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—262no—
523C23—522no—
524C23—522no—
525C23—522no—
526C23D8×D1314yes—
527C23C2×D4×D1312yes—
528C23C2×D4×D1311yescharacteristic
529Q8—5216no—
530Q8—5216no—
531Q8—528no—
532D4—24no—
533D4—48no—
534D4—42no—
535D4—264no—
536D4—528no—
537D4—528no—
538D4—528no—
539D4—522no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—48no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—134no—
549C2×C4—134no—
550C2×C4—1316no—
551C2×C4—134no—
552C2×C4—132no—
553C2×C4—132no—
554C2×C4—132no—
555C2×C4—132no—
556C2×C4—268no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—264no—
560C2×C4—528no—
561C2×C4—528no—
562C2×C4—522no—
563C2×C4—528no—
564C2×C4—524no—
565C2×C4C2×D4×D1312yes—
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4#8825714yes—
568C2×C4C24×D1311yescharacteristic
569C8—24no—
570C8—264no—
571C22—28no—
572C22—22no—
573C22—22no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—84no—
578C22—522no—
579C22—522no—
580C22—522no—
581C22—1044no—
582C22#1171935312yes—
583C22C2×D8×D1314yes—
584C22C2×D8×D1312yes—
585C22D13×#13712yes—
586C22C22×D4×D1311yescharacteristic
587C4—22no—
588C4—44no—
589C4—42no—
590C4—134no—
591C4—134no—
592C4—134no—
593C4—262no—
594C4—522no—
595C4—524no—
596C4#1171935312yes—
597C4C2×#8825712yes—
598C2—24no—
599C2—82no—
600C2—1042no—
601C2#1312595514yesdirect product factor
602C2C2×#1171935311yescharacteristic
603C2C22×D8×D1311yescharacteristic
604C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#480C2
socleC23×C13C22×D4
prime radicalC2×#11719301C2
hypercenterC2×#480D13
hypocenterC13C2×#3226
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×#88142C2semidirect
3. #13125955C2direct (N × H)
4. C2×#11718535C2semidirect
5. C2×#11718421C2semidirect
6. C2×#11718397C2semidirect
7. C2×#11718628C2semidirect
8. C2×#11718694C2semidirect
9. C2×#11718551C2semidirect
10. C2×#11718420C2semidirect
11. C2×#11718379C2semidirect
12. C2×C13×#480C2semidirect
33. C2×#88142C22semidirect
36. C13×#480C22semidirect
46. #11718694C22semidirect
47. #11718628C22semidirect
51. #11718551C22semidirect
52. #11718535C22semidirect
53. #11718421C22semidirect
54. #11718420C22semidirect
55. #11718397C22semidirect
56. #11718379C22semidirect
222. C2×#480D13semidirect
309. #480C2×D13semidirect
433. C2×C13#3226semidirect
515. C13C2×#3226semidirect
601. C2#13125955direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193012
C22×#881422
#131259552
C2×#117185352
C2×#117184212
C2×#117183972
C2×#117186282
C2×#117186942
C2×#117185512
C2×#117184202
C2×#117183792
C2×C13×#4802
C2×#322613