Finite Group Databasebeta

← C2×#13126107 #16735127

Subgroups — C2×#13126107 #16735127

Order 3328.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719394C211yesmaximal, characteristic
2C2×#11719402C211yesmaximal, characteristic
3#13126107C2116yesmaximal, direct product factor
4C2×#11718726C211yesmaximal, characteristic, complemented
5C2×#11718730C211yesmaximal, characteristic, complemented
6C2×#11718342C211yesmaximal, characteristic, complemented
7C2×#11718545C211yesmaximal, characteristic
8C2×#11718528C211yesmaximal, characteristic
9C2×#11718549C211yesmaximal, characteristic
10C2×#11718523C211yesmaximal, characteristic
11C2×#11718518C211yesmaximal, characteristic, complemented
12C2×#11718538C211yesmaximal, characteristic, complemented
13C2×#11718536C211yesmaximal, characteristic, complemented
14C2×#11718515C211yesmaximal, characteristic, complemented
15C2×#11718351C211yesmaximal, characteristic
16C2×C13×#499C211yesmaximal, characteristic, complemented
17C2×C13×#125C2211yescharacteristic
18C2×C13×#125C2211yescharacteristic
19#11719402—24no—
20#11719402C2218yes—
21#11719394—24no—
22#11719394C2218yes—
23C2×#88152—21no—
24C2×#88152—21no—
25C2×#88151—21no—
26C2×#88151C2211yescharacteristic
27C2×#88151C2211yescharacteristic
28C2×#88150—21no—
29C2×#88146C2211yescharacteristic
30C2×C4⋊C4×D13C2211yescharacteristic
31C2×#88144—21no—
32C2×#88144—21no—
33C2×#88144C2211yescharacteristic
34C2×#88143—21no—
35C2×#88142—21no—
36C2×#88142C2211yescharacteristic
37C2×#88141C2211yescharacteristic
38C2×#88141C2211yescharacteristic
39C2×#88126C2211yescharacteristic
40C2×#88123C2211yescharacteristic
41C2×#88123C2211yescharacteristic
42C13×#499C2218yescomplemented
43C2×C13×#107C2211yescharacteristic
44C2×C13×#107C2211yescharacteristic
45C2×C13×#106C2211yescharacteristic
46C2×C13×#106C2211yescharacteristic
47C2×C4×C8×C13C2211yescharacteristic
48C2×#88060C2211yescharacteristic
49C2×#88060C2211yescharacteristic
50C2×#88056C2211yescharacteristic
51C2×#88056C2211yescharacteristic
52C2×#88056C2211yescharacteristic
53C2×#88056C2211yescharacteristic
54C2×#88054C2211yescharacteristic
55C2×#88054C2211yescharacteristic
56#11718730C2218yescomplemented
57#11718726C2218yescomplemented
58C2×#88050C2211yescharacteristic
59C2×#88050C2211yescharacteristic
60C2×#88050C2211yescharacteristic
61C2×#88050C2211yescharacteristic
62C2×#88048C2211yescharacteristic
63C2×#88048C2211yescharacteristic
64C2×#88047C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×#88043C2211yescharacteristic
67#11718549C2218yes—
68#11718545C2218yes—
69#11718538C2218yescomplemented
70#11718536C2218yescomplemented
71#11718528C2218yes—
72#11718523C2218yes—
73#11718518C2218yescomplemented
74#11718515C2218yescomplemented
75#11718351C2218yes—
76#11718342C2218yescomplemented
77C22×C4×D13—21no—
78C22×C4×D13C2311yescharacteristic
79C22×Dic26—21no—
80C22×Dic26—21no—
81C22×Dic26C2311yescharacteristic
82C22×Dic26C2311yescharacteristic
83C22×C8×C13C2311yescharacteristic
84C22×C8×C13C2311yescharacteristic
85C13×#125—22no—
86C13×#125—22no—
87C13×#125C2314yes—
88C13×#125C2314yes—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C2×#6103—21no—
99C2×#6103—21no—
100C2×#6103—21no—
101C2×#6103D411yescharacteristic
102C2×#6103D411yescharacteristic
103C2×C4⋊Dic13—21no—
104C2×C4⋊Dic13—21no—
105C2×C4⋊Dic13—21no—
106C2×C4⋊Dic13—21no—
107C2×C4⋊Dic13—21no—
108C2×C4⋊Dic13—21no—
109C2×C4⋊Dic13C2311yescharacteristic
110C2×C4⋊Dic13C2311yescharacteristic
111C2×#6101—21no—
112C2×#6101—21no—
113C2×#6101—21no—
114C2×#6101—21no—
115C2×#6101—21no—
116C2×#6101D411yescharacteristic
117C2×#6101D411yescharacteristic
118C2×C4×Dic13—21no—
119C2×C4×Dic13—21no—
120C2×C4×Dic13—21no—
121C2×C4×Dic13C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123C22×#1055C2311yescharacteristic
124#88152—28no—
125#88152—28no—
126#88151—22no—
127#88151—22no—
128#88151—28no—
129#88151C2314yes—
130#88151C2314yes—
131#88150—28no—
132#88146—22no—
133#88146C2314yes—
134C4⋊C4×D13—22no—
135C4⋊C4×D13C2314yes—
136#88144—28no—
137#88144—28no—
138#88144—22no—
139#88144C2314yes—
140#88143—28no—
141#88142—28no—
142#88142—22no—
143#88142C2314yes—
144#88141—22no—
145#88141—22no—
146#88141C2314yes—
147#88141C2314yes—
148#88126D414yes—
149#88126C2314yes—
150#88123—22no—
151#88123—22no—
152#88123C2314yes—
153#88123C2314yes—
154C13×#107C2314yes—
155C13×#107C2314yes—
156C13×#106C2314yes—
157C13×#106C2314yes—
158C4×C8×C13C2314yes—
159#88060C2314yes—
160#88060C2314yes—
161#88056C2314yes—
162#88056C2314yes—
163#88056C2314yes—
164#88056C2314yes—
165#88054C2314yes—
166#88054C2314yes—
167#88050C2314yes—
168#88050C2314yes—
169#88050C2314yes—
170#88050C2314yes—
171#88048C2314yes—
172#88048C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88043C2314yes—
176C2×#3242—131nomaximal, Sylow
177C23×D13C2×D411yescharacteristic
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2411yescharacteristic
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13C2×D411yescharacteristic
190C22×Dic13C2×D411yescharacteristic
191C22×Dic13C2×D411yescharacteristic
192C2×C4×D13—22no—
193C2×C4×D13—22no—
194C2×C4×D13—24no—
195C2×C4×D13—82no—
196C2×C4×D13C2×D412yes—
197C2×C4×D13C2412yes—
198C2×Dic26—22no—
199C2×Dic26—22no—
200C2×Dic26—22no—
201C2×Dic26—22no—
202C2×Dic26—21no—
203C2×Dic26—21no—
204C2×Dic26—24no—
205C2×Dic26—24no—
206C2×Dic26—82no—
207C2×Dic26—82no—
208C2×Dic26C2412yes—
209C2×Dic26C2412yes—
210C2×C8×C13—22no—
211C2×C8×C13—22no—
212C2×C8×C13C2412yes—
213C2×C8×C13C2412yes—
214C13×C4⋊C4—21no—
215C13×C4⋊C4—21no—
216C13×C4⋊C4—21no—
217C13×C4⋊C4—24no—
218C13×C4⋊C4—24no—
219C13×C4⋊C4—21no—
220C13×C4⋊C4—24no—
221C13×C4⋊C4—24no—
222C13×C4⋊C4C2412yes—
223C13×C4⋊C4C2412yes—
224C13×C4⋊C4C2412yes—
225C13×C4⋊C4C2412yes—
226C42×C13C2×D412yes—
227C42×C13C2412yes—
228#6103—24no—
229#6103—24no—
230#6103—24no—
231#6103C2×D414yes—
232#6103C2×D414yes—
233C4⋊Dic13—21no—
234C4⋊Dic13—21no—
235C4⋊Dic13—24no—
236C4⋊Dic13—24no—
237C4⋊Dic13—24no—
238C4⋊Dic13—24no—
239C4⋊Dic13—24no—
240C4⋊Dic13—24no—
241C4⋊Dic13C2412yes—
242C4⋊Dic13C2412yes—
243#6101—24no—
244#6101—24no—
245#6101—24no—
246#6101—24no—
247#6101—24no—
248#6101C2×D414yes—
249#6101C2×D414yes—
250C4×Dic13—24no—
251C4×Dic13—24no—
252C4×Dic13—24no—
253C4×Dic13C2×D412yes—
254C4×Dic13C2412yes—
255C2×#1055—22no—
256C2×#1055—22no—
257C2×#1055C2412yes—
258C2×#1055C2412yes—
259C2×#544—131no—
260C2×#541—131no—
261#3242—1316no—
262C2×#501—131no—
263C2×#499D1311yescharacteristic, complemented
264C2×#491—131no—
265C2×#487—131no—
266C2×#484—131no—
267C2×#485—131no—
268C2×#485—131no—
269C2×#483—131no—
270C2×#479—131no—
271C2×#479—131no—
272C2×#477—131no—
273C2×#475—131no—
274C2×#433—131no—
275C23×C13C22×D411yescharacteristic
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—22no—
279C22×D13C22×D412yes—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13C22×D412yes—
291C2×C4×C13C22×D412yes—
292C2×C4×C13C22×D411yescharacteristic
293C2×C4×C132−1+412yes—
294C2×C4×C132−1+412yes—
295C2×C4×C13C2511yescharacteristic
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—22no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—42no—
304C2×Dic13—42no—
305C2×Dic13—42no—
306C2×Dic13—42no—
307C2×Dic13C22×D412yes—
308C2×Dic13C22×D412yes—
309C2×Dic13C22×D412yes—
310C4×D13—24no—
311C4×D13—22no—
312C4×D13—22no—
313C4×D13—84no—
314Dic26—22no—
315Dic26—22no—
316Dic26—22no—
317Dic26—22no—
318Dic26—42no—
319Dic26—42no—
320Dic26—84no—
321Dic26—84no—
322C8×C13—22no—
323C8×C13—22no—
324#1055—22no—
325#1055—22no—
326#544—138no—
327#544—264no—
328#541—138no—
329#541—264no—
330C2×C4⋊Q8—131no—
331C2×C4⋊Q8—131no—
332C2×C4⋊Q8—131no—
333C2×C4⋊Q8—261no—
334C2×#126—261no—
335C2×#126—261no—
336C2×#125—131no—
337C2×#125—261no—
338C2×#125—261no—
339C2×#125—261no—
340C2×#125C2×D1311yescharacteristic
341C2×#125C2×D1311yescharacteristic
342C2×C22⋊Q8—131no—
343C2×C22⋊Q8—131no—
344C2×C22⋊Q8—261no—
345C2×C22⋊Q8—261no—
346C2×C4×Q8—131no—
347C2×C4×Q8—131no—
348C2×#117—131no—
349C2×#117—131no—
350C22×C4⋊C4—131no—
351#501—138no—
352#499C2×D1318yescomplemented
353#491—138no—
354#487—138no—
355#485—138no—
356#485—138no—
357#484—138no—
358#483—138no—
359#479—138no—
360#479—138no—
361#477—138no—
362#475—138no—
363#433—138no—
364C2×#107—131no—
365C2×#107—131no—
366C2×#107C2×D1311yescharacteristic
367C2×#107C2×D1311yescharacteristic
368C2×#106—131no—
369C2×#106—131no—
370C2×#106C2×D1311yescharacteristic
371C2×#106C2×D1311yescharacteristic
372C2×C4⋊C8—131no—
373C2×C4⋊C8—131no—
374C2×#103—131no—
375C2×#103—131no—
376C2×#103—131no—
377C2×#103—131no—
378C2×#103—131no—
379C2×#103—131no—
380C2×#103—131no—
381C2×#103—131no—
382C2×C22⋊C8—131no—
383C2×C22⋊C8—131no—
384C2×#97—131no—
385C2×C4×C8C2×D1311yescharacteristic
386C22×C13#53612yes—
387C22×C13#57712yes—
388C22×C13#57812yes—
389C22×C13C23×D411yescharacteristic
390C2×D13—22no—
391C2×D13—22no—
392C2×D13—22no—
393C2×D13—44no—
394C4×C13—22no—
395C4×C13—22no—
396C4×C13—42no—
397C4×C13—42no—
398C4×C13—42no—
399C4×C13—42no—
400C4×C13#53612yes—
401C4×C13C2×2−1+411yescharacteristic
402C4×C13C2×2−1+411yescharacteristic
403Dic13—22no—
404Dic13—22no—
405Dic13—22no—
406Dic13—42no—
407Dic13—42no—
408Dic13—42no—
409Dic13—42no—
410C22×Q8—131no—
411C22×Q8—131no—
412C22×Q8—261no—
413C22×Q8—261no—
414C23×C4—131no—
415C23×C4—261no—
416C22×C8—131no—
417C22×C8—131no—
418C22×C8C22×D1311yescharacteristic
419C22×C8C22×D1311yescharacteristic
420C4⋊Q8—134no—
421C4⋊Q8—134no—
422C4⋊Q8—134no—
423C4⋊Q8—262no—
424C4⋊Q8—268no—
425C4⋊Q8—262no—
426C4⋊Q8—262no—
427#126—268no—
428#126—268no—
429#125—22no—
430#125—22no—
431#125—134no—
432#125—262no—
433#125—268no—
434#125—268no—
435#125—268no—
436#125C22×D1314yes—
437#125C22×D1314yes—
438C22⋊Q8—134no—
439C22⋊Q8—134no—
440C22⋊Q8—268no—
441C22⋊Q8—268no—
442C22⋊Q8—262no—
443C22⋊Q8—262no—
444C4×Q8—134no—
445C4×Q8—134no—
446C4×Q8—262no—
447C4×Q8—262no—
448#117—134no—
449#117—134no—
450#117—134no—
451#117—262no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—134no—
461C2×C4⋊C4—262no—
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⋊C4C22×D1311yescharacteristic
474C2×C4⋊C4C22×D1311yescharacteristic
475C2×C4⋊C4C22×D1311yescharacteristic
476C2×C4⋊C4C22×D1311yescharacteristic
477C2×C22⋊C4—131no—
478C2×C22⋊C4—131no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C22⋊C4—261no—
482C2×C42—131no—
483C2×C42—261no—
484C2×C42—261no—
485C2×C42—261no—
486C2×C42C22×D1311yescharacteristic
487#107—134no—
488#107—134no—
489#107C22×D1314yes—
490#107C22×D1314yes—
491#106—134no—
492#106—134no—
493#106C22×D1314yes—
494#106C22×D1314yes—
495C4⋊C8—134no—
496C4⋊C8—134no—
497#103—134no—
498#103—134no—
499#103—134no—
500#103—134no—
501#103—134no—
502#103—134no—
503#103—134no—
504#103—134no—
505C22⋊C8—134no—
506C22⋊C8—134no—
507#97—134no—
508C4×C8C22×D1314yes—
509C2×C13#324214yescomplemented
510C2×C13C2×#53611yescharacteristic
511C2×C13C2×#57711yescharacteristic
512C2×C13C2×#57811yescharacteristic
513D13—42no—
514C24—131no—
515C2×Q8—132no—
516C2×Q8—132no—
517C2×Q8—264no—
518C2×Q8—261no—
519C2×Q8—261no—
520C2×Q8—264no—
521C2×Q8—262no—
522C2×Q8—262no—
523C2×Q8—262no—
524C2×Q8—262no—
525C2×Q8—1042no—
526C2×Q8—1042no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—131no—
532C22×C4—131no—
533C22×C4—131no—
534C22×C4—132no—
535C22×C4—132no—
536C22×C4—264no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—261no—
540C22×C4—261no—
541C22×C4—261no—
542C22×C4—261no—
543C22×C4—1042no—
544C22×C4D4×D1311yescharacteristic
545C22×C4D4×D1311yescharacteristic
546C22×C4C23×D1311yescharacteristic
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—132no—
550C2×C8—132no—
551C2×C8—262no—
552C2×C8—262no—
553C2×C8C23×D1312yes—
554C2×C8C23×D1312yes—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—134no—
564C4⋊C4—134no—
565C4⋊C4—132no—
566C4⋊C4—132no—
567C4⋊C4—264no—
568C4⋊C4—264no—
569C4⋊C4—264no—
570C4⋊C4—264no—
571C4⋊C4—264no—
572C4⋊C4—264no—
573C4⋊C4—264no—
574C4⋊C4—264no—
575C4⋊C4—261no—
576C4⋊C4—261no—
577C4⋊C4—264no—
578C4⋊C4—264no—
579C4⋊C4—264no—
580C4⋊C4C23×D1312yes—
581C4⋊C4C23×D1312yes—
582C4⋊C4C23×D1312yes—
583C4⋊C4C23×D1312yes—
584C22⋊C4—134no—
585C22⋊C4—134no—
586C22⋊C4—264no—
587C22⋊C4—264no—
588C22⋊C4—264no—
589C42—132no—
590C42—132no—
591C42—264no—
592C42—264no—
593C42—264no—
594C42D4×D1312yes—
595C42C23×D1312yes—
596C13C2×#324211yescharacteristic, complemented, Sylow
597C23—132no—
598C23—262no—
599C23—262no—
600C23—262no—
601C23C2×D4×D1311yescharacteristic
602Q8—262no—
603Q8—262no—
604Q8—262no—
605Q8—262no—
606Q8—522no—
607Q8—522no—
608Q8—1044no—
609Q8—1044no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—132no—
621C2×C4—132no—
622C2×C4—132no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—264no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—262no—
630C2×C4—262no—
631C2×C4—262no—
632C2×C4—262no—
633C2×C4—522no—
634C2×C4—522no—
635C2×C4—522no—
636C2×C4—522no—
637C2×C4—1044no—
638C2×C4C2×D4×D1312yes—
639C2×C4C2×D4×D1312yes—
640C2×C4C2×D4×D1311yescharacteristic
641C2×C4#8825412yes—
642C2×C4#8825412yes—
643C2×C4C24×D1311yescharacteristic
644C8—22no—
645C8—22no—
646C8—262no—
647C8—262no—
648C22—262no—
649C22—262no—
650C22—262no—
651C22—524no—
652C22#1171942912yes—
653C22#1171947512yes—
654C22#1171947612yes—
655C22C22×D4×D1311yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—42no—
662C4—262no—
663C4—262no—
664C4—262no—
665C4—522no—
666C4—522no—
667C4—522no—
668C4—522no—
669C4#1171942912yes—
670C4C2×#8825411yescharacteristic
671C4C2×#8825411yescharacteristic
672C2—522no—
673C2#1312610714yesdirect product factor
674C2C2×#1171942911yescharacteristic
675C2C2×#1171947511yescharacteristic
676C2C2×#1171947611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#499C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenterC2×#499D13
hypocenterC13C2×#3242
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
3. #13126107C2direct (N × H)
4. C2×#11718726C2semidirect
5. C2×#11718730C2semidirect
6. C2×#11718342C2semidirect
11. C2×#11718518C2semidirect
12. C2×#11718538C2semidirect
13. C2×#11718536C2semidirect
14. C2×#11718515C2semidirect
16. C2×C13×#499C2semidirect
42. C13×#499C22semidirect
56. #11718730C22semidirect
57. #11718726C22semidirect
69. #11718538C22semidirect
70. #11718536C22semidirect
73. #11718518C22semidirect
74. #11718515C22semidirect
76. #11718342C22semidirect
263. C2×#499D13semidirect
352. #499C2×D13semidirect
509. C2×C13#3242semidirect
596. C13C2×#3242semidirect
673. C2#13126107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193942
C2×#117194022
#131261072
C2×#117187262
C2×#117187302
C2×#117183422
C2×#117185452
C2×#117185282
C2×#117185492
C2×#117185232
C2×#117185182
C2×#117185382
C2×#117185362
C2×#117185152
C2×#117183512
C2×C13×#4992
C2×#324213