Finite Group Databasebeta

← C2×#13124781 #16730722

Subgroups — C2×#13124781 #16730722

Order 3328.

2326 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C22⋊Q8C211yesmaximal, characteristic
2C22×#88146C211yesmaximal, characteristic
3#13124781C2116yesmaximal, direct product factor
4C2×#11718631C211yesmaximal, characteristic, complemented
5C2×#11718549C212yesmaximal, complemented
6C2×#11718476C212yesmaximal, complemented
7C2×#11718382C211yesmaximal, characteristic, complemented
8C2×#11718704C211yesmaximal, characteristic, complemented
9C2×#11718542C212yesmaximal, complemented
10C2×#11718463C212yesmaximal, complemented
11C2×#11718387C211yesmaximal, characteristic
12C2×C13×#484C211yesmaximal, characteristic, complemented
13C22×Q8×D13C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C2×C13×C22⋊Q8C2211yescharacteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88200C2211yescharacteristic
18C22×#6103—21no—
19C22×C4⋊Dic13C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C22×C4×Dic13—21no—
22C22×#6094C2212yes—
23D13×C22⋊Q8—24no—
24D13×C22⋊Q8C2218yes—
25C2×#88151C2211yescharacteristic
26C2×#88150—21no—
27C2×#88146—21no—
28C2×#88146—21no—
29C2×#88146—24no—
30C2×#88146C2212yes—
31C2×#88146C2212yes—
32C2×#88146C2218yes—
33C2×C4⋊C4×D13—21no—
34C2×C4⋊C4×D13C2211yescharacteristic
35C2×C22⋊C4×D13—21no—
36C2×#88132—21no—
37C13×#484C2218yescomplemented
38C2×C13×#107C2212yescomplemented
39C2×C13×#103C2212yescomplemented
40C2×C13×C22⋊C8C2211yescharacteristic
41C2×#88075C2212yescomplemented
42C2×C22⋊#1055C2211yescharacteristic
43C2×#88060C2212yes—
44C2×#88057C2212yescomplemented
45C2×#88056C2212yescomplemented
46#11718704C2218yescomplemented
47#11718631C2218yescomplemented
48C2×#88050C2212yescomplemented
49C2×#88048C2212yescomplemented
50C2×#88047C2212yescomplemented
51#11718549C22116yescomplemented
52#11718542C22116yescomplemented
53#11718476C22116yescomplemented
54#11718463C22116yescomplemented
55#11718387C2218yes—
56#11718382C2218yescomplemented
57C24×D13D411yescharacteristic
58C22×Q8×C13C2311yescharacteristic
59C23×C4×C13—21no—
60C23×C4×C13C2311yescharacteristic
61C23×Dic13—21no—
62C23×Dic13D411yescharacteristic
63C2×Q8×D13—22no—
64C2×Q8×D13—28no—
65C2×Q8×D13C2314yes—
66C22×C4×D13—28no—
67C22×C4×D13—21no—
68C22×C4×D13—21no—
69C22×C4×D13D411yescharacteristic
70C22×C4×D13D411yescharacteristic
71C22×C4×D13D414yes—
72C22×C4×D13C2311yescharacteristic
73C22×C4×D13C2314yes—
74C22×C4×D13C2311yescharacteristic
75C22×Dic26—21no—
76C22×Dic26C2311yescharacteristic
77C22×C8×C13C2312yes—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8C2314yes—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4C2312yes—
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2314yes—
86C2×C13×C22⋊C4—21no—
87C2×C22⋊Dic13—21no—
88#88200—22no—
89#88200C2314yes—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—22no—
93C2×#6103—28no—
94C2×#6103—22no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2314yes—
100C2×C4⋊Dic13C2312yes—
101#88178—22no—
102#88178C2314yes—
103C2×#6101—21no—
104C2×#6101—21no—
105C2×#6101—21no—
106C2×C4×Dic13—28no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C22×#1055C2312yes—
110C2×#6094—28no—
111C2×#6094C2318yes—
112#88151—22no—
113#88151C2314yes—
114#88150—28no—
115#88146—28no—
116#88146—28no—
117#88146—24no—
118#88146—24no—
119#88146C2318yes—
120#88146C2318yes—
121C4⋊C4×D13—28no—
122C4⋊C4×D13—22no—
123C4⋊C4×D13C2314yes—
124C22⋊C4×D13—28no—
125#88132—28no—
126C13×#107C2318yescomplemented
127C13×#103C2318yescomplemented
128C13×C22⋊C8C2314yes—
129#88075C2318yescomplemented
130C22⋊#1055C2314yes—
131#88060C2318yes—
132#88057C2318yescomplemented
133#88056C2318yescomplemented
134#88050C2318yescomplemented
135#88048C2318yescomplemented
136#88047C2318yescomplemented
137C2×#3095—131nomaximal, Sylow
138C24×C13C2×D411yescharacteristic
139C23×D13—24no—
140C23×D13—24no—
141C23×D13—42no—
142C23×D13C2×D411yescharacteristic
143C23×D13C2×D414yes—
144C23×D13C2×D411yescharacteristic
145C2×Q8×C13—21no—
146C2×Q8×C13—24no—
147C2×Q8×C13C2412yes—
148C22×C4×C13—24no—
149C22×C4×C13—24no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—44no—
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2412yes—
157C22×C4×C13C2411yescharacteristic
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—22no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—44no—
164C22×Dic13C2×D414yes—
165C22×Dic13C2×D411yescharacteristic
166C22×Dic13C2×D411yescharacteristic
167Q8×D13—216no—
168Q8×D13—48no—
169C2×C4×D13—24no—
170C2×C4×D13—24no—
171C2×C4×D13—24no—
172C2×C4×D13—216no—
173C2×C4×D13—216no—
174C2×C4×D13—24no—
175C2×C4×D13—24no—
176C2×C4×D13—44no—
177C2×C4×D13—44no—
178C2×C4×D13C2×D414yes—
179C2×C4×D13C2×D414yes—
180C2×C4×D13C2×D412yes—
181C2×C4×D13C2×D412yes—
182C2×C4×D13#4118yes—
183C2×C4×D13C2412yes—
184C2×C4×D13C2412yes—
185C2×Dic26—24no—
186C2×Dic26—21no—
187C2×Dic26—24no—
188C2×Dic26—44no—
189C2×Dic26C2412yes—
190C2×C8×C13—24no—
191C2×C8×C13C2414yes—
192C13×C4⋊C4—24no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—24no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4C2414yes—
197C13×C4⋊C4C2412yes—
198C13×C22⋊C4—24no—
199C22⋊Dic13—24no—
200#6103—24no—
201#6103—24no—
202#6103—28no—
203#6103—28no—
204C4⋊Dic13—21no—
205C4⋊Dic13—24no—
206C4⋊Dic13—22no—
207C4⋊Dic13—24no—
208C4⋊Dic13C2414yes—
209C4⋊Dic13C2412yes—
210#6101—24no—
211#6101—24no—
212#6101—24no—
213C4×Dic13—28no—
214C4×Dic13—28no—
215C2×#1055—24no—
216C2×#1055C2414yes—
217#6094—216no—
218C22×C22⋊Q8—131no—
219C22×#117—131no—
220#3095—1316no—
221C2×#484—131no—
222C2×#484D1311yescharacteristic, complemented
223C2×#485—132no—
224C2×#485—132no—
225C2×#483—131no—
226C2×#483—131no—
227C2×#428—132no—
228C2×#419—132no—
229C2×#407—131no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13#13714yes—
233C23×C13C22×D412yes—
234C23×C13C22×D411yescharacteristic
235C22×D13—22no—
236C22×D13—22no—
237C22×D13—22no—
238C22×D13—28no—
239C22×D13—22no—
240C22×D13—22no—
241C22×D13—28no—
242C22×D13—44no—
243C22×D13—416no—
244C22×D13#12314yes—
245C22×D13C22×D412yes—
246C22×D13C22×D412yes—
247Q8×C13—24no—
248Q8×C13—42no—
249C2×C4×C13—22no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—48no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—44no—
259C2×C4×C13C22×D412yes—
260C2×C4×C13C22×D411yescharacteristic
261C2×C4×C13C2×#4114yes—
262C2×C4×C13C2511yescharacteristic
263C2×Dic13—22no—
264C2×Dic13—28no—
265C2×Dic13—24no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—42no—
269C2×Dic13—48no—
270C2×Dic13—44no—
271C2×Dic13—42no—
272C2×Dic13#12314yes—
273C2×Dic13C22×D412yes—
274C2×Dic13C22×D412yes—
275C4×D13—28no—
276C4×D13—24no—
277C4×D13—24no—
278C4×D13—28no—
279C4×D13—48no—
280C4×D13—48no—
281C4×D13#12318yes—
282C4×D13C2×#4118yes—
283Dic26—24no—
284Dic26—42no—
285Dic26—48no—
286C8×C13—24no—
287#1055—24no—
288C23×Q8—131no—
289C24×C4—131no—
290C22×M16—132no—
291C2×C22⋊Q8—131no—
292C2×C22⋊Q8—131no—
293C2×C22⋊Q8—138no—
294C2×C22⋊Q8—131no—
295C2×C22⋊Q8—261no—
296C2×C22⋊Q8—261no—
297C2×C22⋊Q8—264no—
298C2×C22⋊Q8C2×D1311yescharacteristic
299C2×#117—132no—
300C2×#117—138no—
301C2×#117—132no—
302C2×#117—261no—
303C2×#117—264no—
304C2×#117—261no—
305C22×C4⋊C4—131no—
306C22×C4⋊C4—131no—
307C22×C4⋊C4—261no—
308C22×C4⋊C4C2×D1311yescharacteristic
309C22×C22⋊C4—261no—
310C22×C22⋊C4—261no—
311C22×C42—261no—
312#485—1316no—
313#485—1316no—
314#484—138no—
315#484C2×D1318yescomplemented
316#483—138no—
317#483—138no—
318#428—1316no—
319C2×#107—132no—
320C2×#107C2×D1312yescomplemented
321C2×#106—132no—
322C2×#106—132no—
323#419—1316no—
324C2×#103—132no—
325C2×#103—132no—
326C2×#103—132no—
327C2×#103C2×D1312yescomplemented
328#407—138no—
329C2×C22⋊C8—131no—
330C2×C22⋊C8—132no—
331C2×C22⋊C8C2×D1311yescharacteristic
332C22×C13—28no—
333C22×C13—22no—
334C22×C13—22no—
335C22×C13C2×#12312yes—
336C22×C13C2×#13714yes—
337C22×C13C2×#13712yes—
338C22×C13#57512yes—
339C22×C13C23×D411yescharacteristic
340C2×D13—28no—
341C2×D13—22no—
342C2×D13—22no—
343C2×D13—22no—
344C2×D13—22no—
345C2×D13—22no—
346C2×D13—416no—
347C2×D13—44no—
348C2×D13C2×#12314yes—
349C4×C13—22no—
350C4×C13—42no—
351C4×C13—42no—
352C4×C13—44no—
353C4×C13C2×#12312yes—
354C4×C13C22×#4112yes—
355Dic13—22no—
356Dic13—42no—
357Dic13—44no—
358Dic13—42no—
359Dic13C2×#12314yes—
360C25—131no—
361C22×Q8—134no—
362C22×Q8—131no—
363C22×Q8—261no—
364C22×Q8—262no—
365C22×Q8—268no—
366C22×Q8C22×D1311yescharacteristic
367C23×C4—21no—
368C23×C4—131no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—134no—
373C23×C4—131no—
374C23×C4—134no—
375C23×C4—268no—
376C23×C4—261no—
377C23×C4—261no—
378C23×C4—261no—
379C23×C4C22×D1311yescharacteristic
380C2×M16—138no—
381C2×M16—268no—
382C22×C8—132no—
383C22×C8C22×D1312yes—
384C22⋊Q8—22no—
385C22⋊Q8—134no—
386C22⋊Q8—134no—
387C22⋊Q8—134no—
388C22⋊Q8—268no—
389C22⋊Q8—268no—
390C22⋊Q8—262no—
391C22⋊Q8—262no—
392C22⋊Q8—262no—
393C22⋊Q8C22×D1314yes—
394#117—138no—
395#117—138no—
396#117—264no—
397#117—268no—
398#117—264no—
399#117—268no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—132no—
404C2×C4⋊C4—134no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—134no—
407C2×C4⋊C4—262no—
408C2×C4⋊C4—268no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—262no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C4⋊C4C22×D1312yes—
417C2×C4⋊C4C22×D1314yes—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—268no—
420C2×C22⋊C4—268no—
421C2×C22⋊C4—262no—
422C2×C22⋊C4—262no—
423C2×C22⋊C4—261no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4—261no—
426C2×C42—268no—
427C2×C42—262no—
428C2×C42—262no—
429#107—138no—
430#107C22×D1318yescomplemented
431#106—138no—
432#106—138no—
433#103—138no—
434#103—138no—
435#103—138no—
436#103C22×D1318yescomplemented
437C22⋊C8—134no—
438C22⋊C8—138no—
439C22⋊C8C22×D1314yes—
440C2×C13—24no—
441C2×C13#309514yescomplemented
442C2×C13C22×#12311yescharacteristic
443C2×C13C22×#13711yescharacteristic
444C2×C13C2×#57511yescharacteristic
445D13—24no—
446D13—42no—
447C24—131no—
448C24—131no—
449C24—134no—
450C24—264no—
451C24—264no—
452C24—522no—
453C24D4×D1311yescharacteristic
454C2×Q8—21no—
455C2×Q8—24no—
456C2×Q8—132no—
457C2×Q8—264no—
458C2×Q8—2616no—
459C2×Q8—261no—
460C2×Q8—264no—
461C2×Q8—524no—
462C2×Q8—528no—
463C2×Q8C23×D1312yes—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—44no—
470C22×C4—131no—
471C22×C4—132no—
472C22×C4—138no—
473C22×C4—132no—
474C22×C4—134no—
475C22×C4—131no—
476C22×C4—134no—
477C22×C4—134no—
478C22×C4—132no—
479C22×C4—132no—
480C22×C4—264no—
481C22×C4—2616no—
482C22×C4—2616no—
483C22×C4—264no—
484C22×C4—264no—
485C22×C4—264no—
486C22×C4—264no—
487C22×C4—264no—
488C22×C4—264no—
489C22×C4—262no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—524no—
493C22×C4—524no—
494C22×C4—524no—
495C22×C4D4×D1312yes—
496C22×C4D4×D1311yescharacteristic
497C22×C4C23×D1312yes—
498C22×C4C23×D1311yescharacteristic
499M16—2616no—
500C2×C8—24no—
501C2×C8—134no—
502C2×C8—264no—
503C2×C8C23×D1314yes—
504C4⋊C4—24no—
505C4⋊C4—22no—
506C4⋊C4—24no—
507C4⋊C4—21no—
508C4⋊C4—134no—
509C4⋊C4—132no—
510C4⋊C4—264no—
511C4⋊C4—264no—
512C4⋊C4—264no—
513C4⋊C4—264no—
514C4⋊C4—262no—
515C4⋊C4—261no—
516C4⋊C4—264no—
517C4⋊C4C23×D1314yes—
518C4⋊C4C23×D1312yes—
519C22⋊C4—24no—
520C22⋊C4—268no—
521C22⋊C4—268no—
522C22⋊C4—264no—
523C22⋊C4—264no—
524C22⋊C4—264no—
525C42—268no—
526C42—268no—
527C13C2×#309511yescharacteristic, complemented, Sylow
528C23—22no—
529C23—22no—
530C23—134no—
531C23—132no—
532C23—132no—
533C23—268no—
534C23—262no—
535C23—262no—
536C23—268no—
537C23—262no—
538C23—262no—
539C23—262no—
540C23—524no—
541C23—5216no—
542C23#8817214yes—
543C23C2×D4×D1312yes—
544C23C2×D4×D1311yescharacteristic
545Q8—24no—
546Q8—42no—
547Q8—264no—
548Q8—528no—
549Q8—522no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—48no—
557C2×C4—44no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—134no—
561C2×C4—132no—
562C2×C4—138no—
563C2×C4—138no—
564C2×C4—132no—
565C2×C4—268no—
566C2×C4—268no—
567C2×C4—268no—
568C2×C4—262no—
569C2×C4—264no—
570C2×C4—264no—
571C2×C4—264no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—528no—
575C2×C4—528no—
576C2×C4—528no—
577C2×C4—524no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4C2×D4×D1312yes—
581C2×C4C2×D4×D1311yescharacteristic
582C2×C4#41×D1314yes—
583C2×C4C24×D1311yescharacteristic
584C8—24no—
585C8—264no—
586C22—22no—
587C22—22no—
588C22—28no—
589C22—134no—
590C22—262no—
591C22—262no—
592C22—268no—
593C22—262no—
594C22—262no—
595C22—262no—
596C22—5216no—
597C22—524no—
598C22D13×#12312yes—
599C22C2×#8817214yes—
600C22C2×#8817212yes—
601C22#1171947812yes—
602C22C22×D4×D1311yescharacteristic
603C4—22no—
604C4—44no—
605C4—42no—
606C4—42no—
607C4—134no—
608C4—262no—
609C4—524no—
610C4—522no—
611C4—522no—
612C4D13×#12312yes—
613C4C2×#41×D1312yes—
614C2—24no—
615C2—264no—
616C2—522no—
617C2#1312478114yesdirect product factor
618C2C2×D13×#12311yescharacteristic
619C2C22×#8817211yescharacteristic
620C2C2×#1171947811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#484C2
socleC23×C13C22×D4
prime radicalC24×D13D4
hypercenterC2×#484D13
hypocenterC13C2×#3095
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #13124781C2direct (N × H)
4. C2×#11718631C2semidirect
5. C2×#11718549C2semidirect
6. C2×#11718476C2semidirect
7. C2×#11718382C2semidirect
8. C2×#11718704C2semidirect
9. C2×#11718542C2semidirect
10. C2×#11718463C2semidirect
12. C2×C13×#484C2semidirect
37. C13×#484C22semidirect
38. C2×C13×#107C22semidirect
39. C2×C13×#103C22semidirect
41. C2×#88075C22semidirect
44. C2×#88057C22semidirect
45. C2×#88056C22semidirect
46. #11718704C22semidirect
47. #11718631C22semidirect
48. C2×#88050C22semidirect
49. C2×#88048C22semidirect
50. C2×#88047C22semidirect
51. #11718549C22semidirect
52. #11718542C22semidirect
53. #11718476C22semidirect
54. #11718463C22semidirect
56. #11718382C22semidirect
126. C13×#107C23semidirect
127. C13×#103C23semidirect
129. #88075C23semidirect
132. #88057C23semidirect
133. #88056C23semidirect
134. #88050C23semidirect
135. #88048C23semidirect
136. #88047C23semidirect
222. C2×#484D13semidirect
315. #484C2×D13semidirect
320. C2×#107C2×D13semidirect
327. C2×#103C2×D13semidirect
430. #107C22×D13semidirect
436. #103C22×D13semidirect
441. C2×C13#3095semidirect
527. C13C2×#3095semidirect
617. C2#13124781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13×C22⋊Q82
C22×#881462
#131247812
C2×#117186312
C2×#117185492
C2×#117184762
C2×#117183822
C2×#117187042
C2×#117185422
C2×#117184632
C2×#117183872
C2×C13×#4842
C2×#309513