Finite Group Databasebeta

← C2×#13125993 #16734985

Subgroups — C2×#13125993 #16734985

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719222C211yesmaximal, characteristic
2C2×#11719327C211yesmaximal, characteristic
3#13125993C2116yesmaximal, direct product factor
4C2×#11718535C211yesmaximal, characteristic, complemented
5C2×#11718516C211yesmaximal, characteristic, complemented
6C2×#11718453C211yesmaximal, characteristic, complemented
7C2×#11718453C211yesmaximal, characteristic, complemented
8C2×#11718384C211yesmaximal, characteristic
9C2×#11718657C211yesmaximal, characteristic
10C2×#11718706C211yesmaximal, characteristic
11C2×#11718518C211yesmaximal, characteristic, complemented
12C2×#11718457C211yesmaximal, characteristic, complemented
13C2×#11718538C211yesmaximal, characteristic, complemented
14C2×#11718460C211yesmaximal, characteristic, complemented
15C2×#11718379C211yesmaximal, characteristic
16C2×C13×#485C211yesmaximal, characteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×Q8×Dic13C2211yescharacteristic
20C2×#88198C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C2×#88178C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24#11719327—24no—
25#11719327C2218yes—
26#11719222—24no—
27#11719222C2218yes—
28C2×#88144C2211yescharacteristic
29C2×#88144C2211yescharacteristic
30C2×#88143—21no—
31C2×#88142C2211yescharacteristic
32C2×#88142C2211yescharacteristic
33C2×#88142C2211yescharacteristic
34C2×#88141—21no—
35C2×#88141C2211yescharacteristic
36C2×#88132—21no—
37C2×#88132—21no—
38C2×#88132—21no—
39C2×#88131—21no—
40C2×C4×Dic26—21no—
41C2×C4×Dic26—21no—
42C13×#485C2218yes—
43C2×C13×#107C2211yescharacteristic
44C2×C13×#106C2211yescharacteristic
45C2×C13×#103C2211yescharacteristic
46C2×C13×#103C2211yescharacteristic
47C2×C13×C22⋊C8C2211yescharacteristic
48C2×#88075C2211yescharacteristic
49C2×#88075C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×#88058C2211yescharacteristic
52C2×#88057C2211yescharacteristic
53C2×#88056C2211yescharacteristic
54C2×#88056C2211yescharacteristic
55C2×#88054C2211yescharacteristic
56C2×#88054C2211yescharacteristic
57C2×C8×Dic13C2211yescharacteristic
58C2×C8×Dic13C2211yescharacteristic
59#11718706C2218yes—
60#11718657C2218yes—
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88048C2211yescharacteristic
64C2×#88048C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×#88047C2211yescharacteristic
67#11718538C2218yescomplemented
68#11718535C2218yescomplemented
69#11718518C2218yescomplemented
70#11718516C2218yescomplemented
71#11718460C2218yescomplemented
72#11718457C2218yescomplemented
73#11718453C2218yescomplemented
74#11718453C2218yescomplemented
75#11718384C2218yes—
76#11718379C2218yes—
77C22×Q8×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×Dic13D411yescharacteristic
80C23×Dic13D411yescharacteristic
81C22×Dic26—21no—
82C22×Dic26—21no—
83C22×Dic26—21no—
84C22×Dic26C2311yescharacteristic
85C22×C8×C13C2311yescharacteristic
86C22×C8×C13C2311yescharacteristic
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8C2314yes—
89C13×#117—22no—
90C13×#117C2314yes—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C42×C13—21no—
98C2×C22⋊Dic13—21no—
99C2×C22⋊Dic13—21no—
100Q8×Dic13—22no—
101Q8×Dic13C2314yes—
102#88198—22no—
103#88198C2314yes—
104#88180—22no—
105#88180C2314yes—
106C2×C4⋊Dic13—21no—
107C2×C4⋊Dic13—21no—
108C2×C4⋊Dic13—21no—
109C2×C4⋊Dic13C2311yescharacteristic
110C2×C4⋊Dic13C2311yescharacteristic
111C2×C4⋊Dic13C2311yescharacteristic
112#88178—22no—
113#88178C2314yes—
114C2×#6101—21no—
115C2×#6101—21no—
116C2×#6101—21no—
117C2×#6101—21no—
118C2×#6101—21no—
119C2×#6101—21no—
120C2×#6101—21no—
121C2×#6101—21no—
122C2×#6101—21no—
123C2×C4×Dic13—21no—
124C2×C4×Dic13—21no—
125C2×C4×Dic13—21no—
126C2×C4×Dic13D411yescharacteristic
127C2×C4×Dic13D411yescharacteristic
128C2×C4×Dic13D414yes—
129C2×C4×Dic13C2311yescharacteristic
130C2×C4×Dic13C2311yescharacteristic
131C2×C4×Dic13C2314yes—
132C22×#1055C2311yescharacteristic
133C22×#1055C2311yescharacteristic
134#88144—22no—
135#88144—22no—
136#88144C2314yes—
137#88144C2314yes—
138#88143—28no—
139#88142—22no—
140#88142—22no—
141#88142—22no—
142#88142C2314yes—
143#88142C2314yes—
144#88142C2314yes—
145#88141—28no—
146#88141—22no—
147#88141C2314yes—
148#88132—28no—
149#88132—28no—
150#88132—28no—
151#88131—28no—
152C4×Dic26—28no—
153C4×Dic26—28no—
154C13×#107C2314yes—
155C13×#106C2314yes—
156C13×#103C2314yes—
157C13×#103C2314yes—
158C13×C22⋊C8C2314yes—
159#88075C2314yes—
160#88075C2314yes—
161C22⋊#1055C2314yes—
162#88058C2314yes—
163#88057C2314yes—
164#88056C2314yes—
165#88056C2314yes—
166#88054C2314yes—
167#88054C2314yes—
168C8×Dic13C2314yes—
169C8×Dic13C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88048C2314yes—
173#88048C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176C2×#3231—131nomaximal, Sylow
177C24×C13C2×D411yescharacteristic
178C2×Q8×C13—21no—
179C2×Q8×C13—22no—
180C2×Q8×C13—22no—
181C2×Q8×C13C2412yes—
182C22×C4×C13—22no—
183C22×C4×C13—22no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D412yes—
190C22×C4×C13C2412yes—
191C22×C4×C13C2411yescharacteristic
192C22×Dic13—24no—
193C22×Dic13—24no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13C2×D414yes—
199C22×Dic13C2×D414yes—
200C22×Dic13C2×D411yescharacteristic
201C22×Dic13C2×D411yescharacteristic
202C22×Dic13C2×D411yescharacteristic
203C22×Dic13C2×D411yescharacteristic
204C2×Dic26—22no—
205C2×Dic26—22no—
206C2×Dic26—21no—
207C2×Dic26—24no—
208C2×Dic26—24no—
209C2×Dic26—24no—
210C2×Dic26—44no—
211C2×Dic26—44no—
212C2×Dic26—44no—
213C2×Dic26C2412yes—
214C2×C8×C13—22no—
215C2×C8×C13—22no—
216C2×C8×C13C2412yes—
217C2×C8×C13C2412yes—
218C13×C4⋊C4—21no—
219C13×C4⋊C4—24no—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4C2412yes—
223C13×C4⋊C4C2412yes—
224C13×C4⋊C4C2412yes—
225C13×C22⋊C4—24no—
226C13×C22⋊C4—24no—
227C42×C13—24no—
228C22⋊Dic13—24no—
229C22⋊Dic13—24no—
230C4⋊Dic13—21no—
231C4⋊Dic13—21no—
232C4⋊Dic13—21no—
233C4⋊Dic13—24no—
234C4⋊Dic13—24no—
235C4⋊Dic13—24no—
236C4⋊Dic13C2412yes—
237C4⋊Dic13C2412yes—
238C4⋊Dic13C2412yes—
239#6101—24no—
240#6101—24no—
241#6101—24no—
242#6101—24no—
243#6101—24no—
244#6101—24no—
245#6101—24no—
246#6101—24no—
247#6101—24no—
248C4×Dic13—24no—
249C4×Dic13—24no—
250C4×Dic13—24no—
251C4×Dic13C2×D414yes—
252C4×Dic13C2×D414yes—
253C4×Dic13C2×D412yes—
254C4×Dic13C2×D412yes—
255C4×Dic13C2412yes—
256C4×Dic13C2412yes—
257C2×#1055—22no—
258C2×#1055—22no—
259C2×#1055C2412yes—
260C2×#1055C2412yes—
261C2×#533—131no—
262C2×#533—131no—
263#3231—1316no—
264C2×#500—131no—
265C2×#498—131no—
266C2×#487—131no—
267C2×#487—131no—
268C2×#485—131no—
269C2×#485—131no—
270C2×#485—131no—
271C2×#485D1311yescharacteristic
272C2×#479—131no—
273C2×#479—131no—
274C2×#479—131no—
275C2×#479—131no—
276C2×#431—131no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13C22×D412yes—
281C23×C13C22×D411yescharacteristic
282Q8×C13—22no—
283Q8×C13—22no—
284Q8×C13—42no—
285C2×C4×C13—22no—
286C2×C4×C13—24no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13C22×D412yes—
298C2×C4×C13C22×D411yescharacteristic
299C2×C4×C132−1+412yes—
300C2×C4×C132−1+412yes—
301C2×C4×C13C2511yescharacteristic
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—28no—
305C2×Dic13—28no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—42no—
311C2×Dic13—42no—
312C2×Dic13—42no—
313C2×Dic13—42no—
314C2×Dic13#13514yes—
315C2×Dic13#13714yes—
316C2×Dic13C22×D412yes—
317C2×Dic13C22×D412yes—
318C2×Dic13C22×D412yes—
319C2×Dic13C22×D412yes—
320Dic26—22no—
321Dic26—22no—
322Dic26—42no—
323Dic26—48no—
324Dic26—48no—
325Dic26—48no—
326C8×C13—22no—
327C8×C13—22no—
328#1055—22no—
329#1055—22no—
330#533—138no—
331#533—138no—
332#533—264no—
333#533—264no—
334C2×C4⋊Q8—131no—
335C2×C4⋊Q8—131no—
336C2×C4⋊Q8—131no—
337C2×C4⋊Q8—131no—
338C2×#125—131no—
339C2×#125—131no—
340C2×#125—261no—
341C2×C22⋊Q8—131no—
342C2×C22⋊Q8—261no—
343C2×C22⋊Q8—261no—
344C2×C22⋊Q8—261no—
345C2×C22⋊Q8C2×D1311yescharacteristic
346C2×C4×Q8—131no—
347C2×C4×Q8—131no—
348C2×C4×Q8—261no—
349C2×C4×Q8—261no—
350C2×C4×Q8—261no—
351C2×#117—131no—
352C2×#117—261no—
353C2×#117C2×D1311yescharacteristic
354C22×C42—131no—
355#500—138no—
356#498—138no—
357#487—138no—
358#487—138no—
359#485—138no—
360#485—138no—
361#485—138no—
362#485C2×D1318yes—
363#479—138no—
364#479—138no—
365#479—138no—
366#479—138no—
367#431—138no—
368C2×#107—131no—
369C2×#107—131no—
370C2×#107—131no—
371C2×#107C2×D1311yescharacteristic
372C2×#106—131no—
373C2×#106—131no—
374C2×#106—131no—
375C2×#106C2×D1311yescharacteristic
376C2×C4⋊C8—131no—
377C2×C4⋊C8—131no—
378C2×#103—131no—
379C2×#103—131no—
380C2×#103—131no—
381C2×#103—131no—
382C2×#103—131no—
383C2×#103—131no—
384C2×#103C2×D1311yescharacteristic
385C2×#103C2×D1311yescharacteristic
386C2×C22⋊C8—131no—
387C2×C22⋊C8C2×D1311yescharacteristic
388C2×C4×C8—131no—
389C2×C4×C8—131no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—44no—
394C22×C13#53612yes—
395C22×C13C2×#13512yes—
396C22×C13C2×#13712yes—
397C22×C13C23×D411yescharacteristic
398C4×C13—22no—
399C4×C13—42no—
400C4×C13—42no—
401C4×C13—42no—
402C4×C13—42no—
403C4×C13#53612yes—
404C4×C13C2×2−1+411yescharacteristic
405C4×C13C2×2−1+411yescharacteristic
406Dic13—22no—
407Dic13—22no—
408Dic13—42no—
409Dic13—42no—
410Dic13—42no—
411Dic13—42no—
412Dic13C2×#13514yes—
413Dic13C2×#13714yes—
414C22×Q8—131no—
415C22×Q8—261no—
416C22×Q8—261no—
417C22×Q8—261no—
418C22×Q8C22×D1311yescharacteristic
419C23×C4—131no—
420C23×C4—131no—
421C23×C4C22×D1311yescharacteristic
422C22×C8—131no—
423C22×C8—131no—
424C22×C8C22×D1311yescharacteristic
425C22×C8C22×D1311yescharacteristic
426C4⋊Q8—134no—
427C4⋊Q8—134no—
428C4⋊Q8—134no—
429C4⋊Q8—134no—
430C4⋊Q8—262no—
431C4⋊Q8—262no—
432C4⋊Q8—262no—
433C4⋊Q8—262no—
434#125—134no—
435#125—134no—
436#125—262no—
437#125—262no—
438#125—268no—
439C22⋊Q8—22no—
440C22⋊Q8—134no—
441C22⋊Q8—268no—
442C22⋊Q8—268no—
443C22⋊Q8—268no—
444C22⋊Q8—262no—
445C22⋊Q8C22×D1314yes—
446C4×Q8—134no—
447C4×Q8—134no—
448C4×Q8—268no—
449C4×Q8—268no—
450C4×Q8—262no—
451C4×Q8—268no—
452C4×Q8—262no—
453#117—22no—
454#117—134no—
455#117—268no—
456#117—262no—
457#117C22×D1314yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—131no—
461C2×C4⋊C4—131no—
462C2×C4⋊C4—261no—
463C2×C4⋊C4—261no—
464C2×C4⋊C4—261no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—261no—
467C2×C4⋊C4—261no—
468C2×C4⋊C4—261no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4—261no—
471C2×C4⋊C4—261no—
472C2×C4⋊C4—261no—
473C2×C4⋊C4—261no—
474C2×C4⋊C4C22×D1311yescharacteristic
475C2×C4⋊C4C22×D1311yescharacteristic
476C2×C4⋊C4C22×D1311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C42—21no—
482C2×C42—131no—
483C2×C42—131no—
484C2×C42—134no—
485C2×C42—131no—
486C2×C42—131no—
487C2×C42—134no—
488C2×C42—261no—
489C2×C42—261no—
490C2×C42—261no—
491#107—134no—
492#107—134no—
493#107—134no—
494#107C22×D1314yes—
495#106—134no—
496#106—134no—
497#106—134no—
498#106C22×D1314yes—
499C4⋊C8—134no—
500C4⋊C8—134no—
501#103—134no—
502#103—134no—
503#103—134no—
504#103—134no—
505#103—134no—
506#103—134no—
507#103C22×D1314yes—
508#103C22×D1314yes—
509C22⋊C8—134no—
510C22⋊C8C22×D1314yes—
511C4×C8—134no—
512C4×C8—134no—
513C2×C13—42no—
514C2×C13#323114yescomplemented
515C2×C13C2×#53611yescharacteristic
516C2×C13C22×#13511yescharacteristic
517C2×C13C22×#13711yescharacteristic
518C24D4×D1311yescharacteristic
519C2×Q8—21no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—132no—
523C2×Q8—264no—
524C2×Q8—264no—
525C2×Q8—264no—
526C2×Q8—261no—
527C2×Q8—262no—
528C2×Q8—262no—
529C2×Q8—524no—
530C2×Q8—524no—
531C2×Q8—524no—
532C2×Q8C23×D1312yes—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—131no—
540C22×C4—131no—
541C22×C4—134no—
542C22×C4—134no—
543C22×C4—131no—
544C22×C4—131no—
545C22×C4—264no—
546C22×C4—264no—
547C22×C4—261no—
548C22×C4—261no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4D4×D1312yes—
552C22×C4D4×D1311yescharacteristic
553C22×C4C23×D1312yes—
554C22×C4C23×D1311yescharacteristic
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—132no—
558C2×C8—132no—
559C2×C8—262no—
560C2×C8—262no—
561C2×C8C23×D1312yes—
562C2×C8C23×D1312yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—132no—
568C4⋊C4—132no—
569C4⋊C4—132no—
570C4⋊C4—264no—
571C4⋊C4—264no—
572C4⋊C4—264no—
573C4⋊C4—264no—
574C4⋊C4—264no—
575C4⋊C4—264no—
576C4⋊C4—264no—
577C4⋊C4—264no—
578C4⋊C4—264no—
579C4⋊C4—264no—
580C4⋊C4—264no—
581C4⋊C4—261no—
582C4⋊C4—261no—
583C4⋊C4—261no—
584C4⋊C4—264no—
585C4⋊C4C23×D1312yes—
586C4⋊C4C23×D1312yes—
587C4⋊C4C23×D1312yes—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—264no—
591C22⋊C4—264no—
592C42—24no—
593C42—134no—
594C42—134no—
595C42—132no—
596C42—132no—
597C42—132no—
598C42—132no—
599C42—264no—
600C42—264no—
601C42—264no—
602C13C2×#323111yescharacteristic, complemented, Sylow
603C23—22no—
604C23—22no—
605C23—22no—
606C23C2×D4×D1312yes—
607C23C2×D4×D1311yescharacteristic
608Q8—22no—
609Q8—22no—
610Q8—42no—
611Q8—262no—
612Q8—262no—
613Q8—528no—
614Q8—528no—
615Q8—528no—
616Q8—522no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—134no—
630C2×C4—134no—
631C2×C4—132no—
632C2×C4—132no—
633C2×C4—132no—
634C2×C4—132no—
635C2×C4—268no—
636C2×C4—268no—
637C2×C4—262no—
638C2×C4—262no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—262no—
642C2×C4—262no—
643C2×C4—522no—
644C2×C4—522no—
645C2×C4—522no—
646C2×C4—522no—
647C2×C4C2×D4×D1312yes—
648C2×C4C2×D4×D1311yescharacteristic
649C2×C4#8825712yes—
650C2×C4#8825712yes—
651C2×C4C24×D1311yescharacteristic
652C8—22no—
653C8—22no—
654C8—262no—
655C8—262no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—44no—
660C22#1171935312yes—
661C22D13×#13512yes—
662C22D13×#13712yes—
663C22C22×D4×D1311yescharacteristic
664C4—22no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4—134no—
670C4—134no—
671C4—262no—
672C4—262no—
673C4—522no—
674C4—522no—
675C4—522no—
676C4—522no—
677C4#1171935312yes—
678C4C2×#8825711yescharacteristic
679C4C2×#8825711yescharacteristic
680C2—42no—
681C2#1312599314yesdirect product factor
682C2C2×#1171935311yescharacteristic
683C2C2×D13×#13511yescharacteristic
684C2C2×D13×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#485C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#485D13
hypocenterC13C2×#3231
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #13125993C2direct (N × H)
4. C2×#11718535C2semidirect
5. C2×#11718516C2semidirect
6. C2×#11718453C2semidirect
7. C2×#11718453C2semidirect
11. C2×#11718518C2semidirect
12. C2×#11718457C2semidirect
13. C2×#11718538C2semidirect
14. C2×#11718460C2semidirect
67. #11718538C22semidirect
68. #11718535C22semidirect
69. #11718518C22semidirect
70. #11718516C22semidirect
71. #11718460C22semidirect
72. #11718457C22semidirect
73. #11718453C22semidirect
74. #11718453C22semidirect
514. C2×C13#3231semidirect
602. C13C2×#3231semidirect
681. C2#13125993direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192222
C2×#117193272
#131259932
C2×#117185352
C2×#117185162
C2×#117184532
C2×#117183842
C2×#117186572
C2×#117187062
C2×#117185182
C2×#117184572
C2×#117185382
C2×#117184602
C2×#117183792
C2×C13×#4852
C2×#323113