Finite Group Databasebeta

← C2×#13129232 #16770711

Subgroups — C2×#13129232 #16770711

Order 3328.

7810 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129232C2132yesmaximal, direct product factor
2C2×#11719405C211yesmaximal, characteristic, complemented
3C2×#11719389C212yesmaximal, complemented
4C2×#11719341C214yesmaximal, complemented
5C2×#11719304C214yesmaximal, complemented
6C2×#11719360C214yesmaximal, complemented
7C2×#11719368C214yesmaximal, complemented
8C2×#11719334C214yesmaximal, complemented
9C2×#11719302C214yesmaximal, complemented
10C2×#11719393C211yesmaximal, characteristic, complemented
11C2×#11719373C212yesmaximal, complemented
12C2×C13×#562C211yesmaximal, characteristic, complemented
13C22×#6131C2212yes—
14C22×#6129C2214yes—
15C22×#6129C2212yes—
16C22×#6127C2214yes—
17C13×#562C22116yescomplemented
18C2×C13×#125C2211yescharacteristic
19C2×C13×#124C2212yes—
20C2×C13×#123C2214yes—
21C2×C13×C22⋊Q8C2214yes—
22C2×C13×#121C2214yes—
23C2×#88200C2214yes—
24C2×#88198C2212yes—
25C2×#88194C2214yes—
26C2×#88194C2212yes—
27C2×#88193C2214yes—
28C2×#88193C2214yes—
29C2×#88193C2214yes—
30C2×#88184C2214yes—
31C2×C4×C22⋊D13C2214yes—
32C22×#6101C2214yes—
33#11719405C22116yescomplemented
34#11719393C22116yescomplemented
35#11719389C22132yescomplemented
36#11719373C22132yescomplemented
37#11719368C22164yescomplemented
38#11719360C22164yescomplemented
39#11719341C22164yescomplemented
40#11719334C22164yescomplemented
41#11719304C22164yescomplemented
42#11719302C22164yescomplemented
43C2×#88150C2214yes—
44C2×#88150C2214yes—
45C2×#88150C2214yes—
46C2×#88149C2214yes—
47C2×#88149C2214yes—
48C2×#88148C2214yes—
49C2×#88146C2212yes—
50C2×C4⋊C4×D13C2214yes—
51C2×#88143C2214yes—
52C2×#88142C2212yes—
53C2×#88141C2214yes—
54C2×#88140C2214yes—
55C2×#88138C2214yes—
56C2×#88138C2214yes—
57C2×#88138C2214yes—
58C2×#88138C2214yes—
59C2×#88138C2214yes—
60C2×#88137C2214yes—
61C2×#88135C2214yes—
62C2×#88135C2214yes—
63C2×#88135C2214yes—
64C2×#88132C2214yes—
65C2×#88132C2214yes—
66C2×#88129C2212yes—
67C2×C42×D13C2211yescharacteristic
68C2×#88124C2211yescharacteristic
69C22×Q8×C13C2312yes—
70C22×D4×C13C2314yes—
71C22×D4×C13C2312yes—
72C23×C4×C13C2314yes—
73C22×C22⋊D13C2314yes—
74C22×C22⋊D13C2314yes—
75C22×C22⋊D13C2314yes—
76C22×C22⋊D13C2314yes—
77C22×C22⋊D13C2314yes—
78C23×Dic13C2314yes—
79C23×Dic13C2314yes—
80C2×#6131—48no—
81C2×#6131C23116yes—
82C2×#6129—416no—
83C2×#6129—48no—
84C2×#6129C23116yes—
85C2×#6129C23132yes—
86C2×#6127—416no—
87C2×#6127C23132yes—
88C22×D52C2312yes—
89C22×D52C2314yes—
90C22×D52C2314yes—
91C22×C4×D13C2311yescharacteristic
92C22×C4×D13C2312yes—
93C22×C4×D13C2314yes—
94C22×C4×D13C2314yes—
95C22×C4×D13C2314yes—
96C22×Dic26C2314yes—
97C22×Dic26C2312yes—
98C13×#125C2318yes—
99C13×#124C23116yes—
100C13×#123C23132yes—
101C13×C22⋊Q8C23132yes—
102C13×#121C23132yes—
103C2×C13×C4⋊C4C2314yes—
104C2×C13×C4⋊C4C2312yes—
105C2×C13×C4⋊C4C2314yes—
106C2×C13×C22⋊C4C2314yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2314yes—
109C2×C42×C13C2311yescharacteristic
110C2×C22⋊Dic13C2314yes—
111#88200C23132yes—
112#88198C23116yes—
113#88194C23132yes—
114#88194C23116yes—
115#88193C23132yes—
116#88193C23132yes—
117#88193C23132yes—
118#88184C23132yes—
119C4×C22⋊D13C23132yes—
120C2×#6103C2314yes—
121C2×#6103C2314yes—
122C2×#6103C2314yes—
123C2×#6103C2314yes—
124C2×#6103C2314yes—
125C2×C4⋊Dic13C2312yes—
126C2×C4⋊Dic13C2314yes—
127C2×#6101C2314yes—
128C2×#6101C2314yes—
129C2×#6101C2314yes—
130C2×#6101C2314yes—
131C2×#6101C2314yes—
132C2×#6101C2314yes—
133C2×#6101C23132yes—
134C2×C4×Dic13C2311yescharacteristic
135C2×C4×Dic13C2312yes—
136C2×C4×Dic13C2314yes—
137#88150C23132yes—
138#88150C23132yes—
139#88150C23132yes—
140#88149C23132yes—
141#88149C23132yes—
142#88148C23132yes—
143#88146C23116yes—
144C4⋊C4×D13C23132yes—
145#88143C23132yes—
146#88142C23116yes—
147#88141C23132yes—
148#88140C23132yes—
149#88138C23132yes—
150#88138C23132yes—
151#88138C23132yes—
152#88138C23132yes—
153#88138C23132yes—
154#88137C23132yes—
155#88135C23132yes—
156#88135C23132yes—
157#88135C23132yes—
158#88132C23132yes—
159#88132C23132yes—
160#88129C23116yes—
161C42×D13C2318yes—
162#88124C2318yes—
163C2×#3548—131nomaximal, Sylow
164C24×C13C2414yes—
165C23×D13C2414yes—
166C23×D13C2411yescharacteristic
167C2×Q8×C13—44no—
168C2×Q8×C13C2418yes—
169C2×D4×C13—48no—
170C2×D4×C13—44no—
171C2×D4×C13C24116yes—
172C2×D4×C13C2418yes—
173C22×C4×C13—48no—
174C22×C4×C13C2412yes—
175C22×C4×C13C2414yes—
176C22×C4×C13C2411yescharacteristic
177C22×C4×C13C2414yes—
178C22×C4×C13C24116yes—
179C2×C22⋊D13—216no—
180C2×C22⋊D13—216no—
181C2×C22⋊D13—48no—
182C2×C22⋊D13—48no—
183C2×C22⋊D13—48no—
184C2×C22⋊D13C24116yes—
185C2×C22⋊D13C24116yes—
186C2×C22⋊D13C24116yes—
187C2×C22⋊D13C24116yes—
188C2×C22⋊D13C24116yes—
189C22×Dic13—216no—
190C22×Dic13—48no—
191C22×Dic13C24116yes—
192C22×Dic13C2414yes—
193C22×Dic13C2414yes—
194C22×Dic13C24116yes—
195C22×Dic13C2412yes—
196C22×Dic13C2411yescharacteristic
197#6131—432no—
198#6129—464no—
199#6129—432no—
200#6127—464no—
201C2×D52—48no—
202C2×D52—44no—
203C2×D52—48no—
204C2×D52C2418yes—
205C2×D52C24116yes—
206C2×D52C24116yes—
207C2×C4×D13—216no—
208C2×C4×D13—28no—
209C2×C4×D13—24no—
210C2×C4×D13—48no—
211C2×C4×D13—48no—
212C2×C4×D13C2414yes—
213C2×C4×D13C2418yes—
214C2×C4×D13C24116yes—
215C2×C4×D13C24116yes—
216C2×C4×D13C24116yes—
217C2×Dic26—216no—
218C2×Dic26—44no—
219C2×Dic26C24116yes—
220C2×Dic26C2418yes—
221C13×C4⋊C4C24116yes—
222C13×C4⋊C4C2418yes—
223C13×C4⋊C4C24116yes—
224C13×C22⋊C4C24116yes—
225C13×C22⋊C4C24116yes—
226C13×C22⋊C4C24116yes—
227C42×C13C2414yes—
228C22⋊Dic13C24116yes—
229#6103C24116yes—
230#6103C24116yes—
231#6103C24116yes—
232#6103C24116yes—
233#6103C24116yes—
234C4⋊Dic13C2418yes—
235C4⋊Dic13C24116yes—
236#6101C24116yes—
237#6101C24116yes—
238#6101C24116yes—
239#6101C24116yes—
240#6101C24116yes—
241#6101C24116yes—
242C4×Dic13C2414yes—
243C4×Dic13C2418yes—
244C4×Dic13C24116yes—
245#3548—1332no—
246C2×#562—131no—
247C2×#562—132no—
248C2×#562D1311yescharacteristic, complemented
249C2×#554—134no—
250C2×#550—134no—
251C2×#547—134no—
252C2×#540—134no—
253C2×#537—134no—
254C2×#537—134no—
255C2×#533—131no—
256C2×#532—132no—
257C23×C13—28no—
258C23×C13—28no—
259C23×C13—28no—
260C23×C13C2518yes—
261C23×C13C2511yescharacteristic
262C22×D13—28no—
263C22×D13—24no—
264C22×D13—28no—
265C22×D13—22no—
266C22×D13—28no—
267C22×D13C2518yes—
268C22×D13C2512yes—
269Q8×C13—48no—
270D4×C13—416no—
271D4×C13—48no—
272C2×C4×C13—28no—
273C2×C4×C13—24no—
274C2×C4×C13—28no—
275C2×C4×C13—22no—
276C2×C4×C13—416no—
277C2×C4×C13C2514yes—
278C2×C4×C13C2518yes—
279C2×C4×C13C2512yes—
280C2×C4×C13C2518yes—
281C22⋊D13—232no—
282C22⋊D13—232no—
283C22⋊D13—416no—
284C22⋊D13—416no—
285C22⋊D13—416no—
286C2×Dic13—28no—
287C2×Dic13—28no—
288C2×Dic13—232no—
289C2×Dic13—416no—
290C2×Dic13H(5,𝔽2)18yes—
291C2×Dic132−1+414yes—
292C2×Dic13C2518yes—
293C2×Dic13C2518yes—
294C2×Dic13C2514yes—
295C2×Dic13C2512yes—
296D52—416no—
297D52—48no—
298D52—416no—
299C4×D13—232no—
300C4×D13—216no—
301C4×D13—28no—
302C4×D13—416no—
303C4×D13—416no—
304Dic26—232no—
305Dic26—48no—
306C22×#41—132no—
307C22×#41—132no—
308C22×#41—134no—
309C22×#41—134no—
310#562—1316no—
311#562—1332no—
312#562C2×D13116yescomplemented
313#554—1364no—
314#550—1364no—
315#547—1364no—
316#540—1364no—
317#537—1364no—
318#537—1364no—
319#533—1316no—
320#532—1332no—
321C2×C4⋊Q8—132no—
322C2×C4⋊Q8—132no—
323C2×#127—132no—
324C2×#127—134no—
325C2×#125—134no—
326C2×#125—131no—
327C2×#125C2×D1311yescharacteristic
328C2×#124—132no—
329C2×#124C2×D1312yes—
330C2×#123—134no—
331C2×#123—134no—
332C2×#123—134no—
333C2×#123C2×D1314yes—
334C2×C22⋊Q8—134no—
335C2×C22⋊Q8—134no—
336C2×C22⋊Q8—134no—
337C2×C22⋊Q8—134no—
338C2×C22⋊Q8—134no—
339C2×C22⋊Q8—134no—
340C2×C22⋊Q8C2×D1314yes—
341C2×#121—134no—
342C2×#121—134no—
343C2×#121—134no—
344C2×#121—134no—
345C2×#121—134no—
346C2×#121—134no—
347C2×#121—134no—
348C2×#121—134no—
349C2×#121—134no—
350C2×#121—134no—
351C2×#121—134no—
352C2×#121C2×D1314yes—
353C2×C4×Q8—134no—
354C2×C4×D4—134no—
355C2×C4×D4—134no—
356C2×C4×D4—134no—
357C2×C4×D4—134no—
358C2×#117—132no—
359C22×C4⋊C4—134no—
360C22×C4⋊C4—134no—
361C22×C42—131no—
362C22×C13—28no—
363C22×C13—28no—
364C22×C13—28no—
365C22×C13—416no—
366C22×C13C2×H(5,𝔽2)14yes—
367C22×C13C2×2−1+412yes—
368C22×C13C2611yescharacteristic
369C2×D13—28no—
370C2×D13—24no—
371C2×D13—28no—
372C2×D13—22no—
373C2×D13—28no—
374C2×D13—416no—
375C2×D13—44no—
376C4×C13—28no—
377C4×C13—24no—
378C4×C13—28no—
379C4×C13—22no—
380Dic13—28no—
381Dic13—28no—
382Dic13C2×H(5,𝔽2)18yes—
383Dic13C2×2−1+414yes—
384C2×#41—1316no—
385C2×#41—1316no—
386C2×#41—1332no—
387C2×#41—1332no—
388C2×#41—5216no—
389C2×#41—528no—
390C2×#41—528no—
391C2×#41—5216no—
392C22×Q8—134no—
393C22×Q8—132no—
394C22×Q8C22×D1312yes—
395C22×D4—134no—
396C22×D4—134no—
397C22×D4—134no—
398C22×D4—134no—
399C22×D4—134no—
400C22×D4—134no—
401C22×D4—134no—
402C22×D4—132no—
403C22×D4C22×D1314yes—
404C22×D4C22×D1312yes—
405C23×C4—134no—
406C23×C4—134no—
407C23×C4—134no—
408C23×C4—131no—
409C23×C4—132no—
410C23×C4—134no—
411C23×C4—134no—
412C23×C4C22×D1314yes—
413C4⋊Q8—1316no—
414C4⋊Q8—1316no—
415#127—1316no—
416#127—1332no—
417#125—1332no—
418#125—138no—
419#125C22×D1318yes—
420#124—1316no—
421#124C22×D13116yes—
422#123—1332no—
423#123—1332no—
424#123—1332no—
425#123C22×D13132yes—
426C22⋊Q8—1332no—
427C22⋊Q8—1332no—
428C22⋊Q8—1332no—
429C22⋊Q8—1332no—
430C22⋊Q8—1332no—
431C22⋊Q8—1332no—
432C22⋊Q8C22×D13132yes—
433#121—1332no—
434#121—1332no—
435#121—1332no—
436#121—1332no—
437#121—1332no—
438#121—1332no—
439#121—1332no—
440#121—1332no—
441#121—1332no—
442#121—1332no—
443#121—1332no—
444#121C22×D13132yes—
445C4×Q8—1332no—
446C4×D4—1332no—
447C4×D4—1332no—
448C4×D4—1332no—
449C4×D4—1332no—
450#117—1316no—
451C2×C4⋊C4—134no—
452C2×C4⋊C4—134no—
453C2×C4⋊C4—134no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—134no—
456C2×C4⋊C4—1332no—
457C2×C4⋊C4—132no—
458C2×C4⋊C4—134no—
459C2×C4⋊C4—134no—
460C2×C4⋊C4—1332no—
461C2×C4⋊C4C22×D1314yes—
462C2×C4⋊C4C22×D1312yes—
463C2×C4⋊C4C22×D1314yes—
464C2×C22⋊C4—134no—
465C2×C22⋊C4—134no—
466C2×C22⋊C4—134no—
467C2×C22⋊C4—134no—
468C2×C22⋊C4—134no—
469C2×C22⋊C4—134no—
470C2×C22⋊C4C22×D1314yes—
471C2×C22⋊C4C22×D1314yes—
472C2×C22⋊C4C22×D1314yes—
473C2×C42—134no—
474C2×C42—131no—
475C2×C42—132no—
476C2×C42—138no—
477C2×C42C22×D1311yescharacteristic
478C2×C13—48no—
479C2×C13#354814yescomplemented
480C2×C13C22×H(5,𝔽2)12yes—
481C2×C13C22×2−1+411yescharacteristic
482D13—48no—
483D13—42no—
484C24—131no—
485C24—134no—
486C24C23×D1314yes—
487#41—5264no—
488#41—5232no—
489#41—5232no—
490#41—5264no—
491C2×Q8—44no—
492C2×Q8—1316no—
493C2×Q8—138no—
494C2×Q8—2616no—
495C2×Q8—524no—
496C2×Q8C23×D1318yes—
497C2×D4—48no—
498C2×D4—44no—
499C2×D4—1316no—
500C2×D4—1316no—
501C2×D4—1316no—
502C2×D4—1316no—
503C2×D4—1316no—
504C2×D4—1316no—
505C2×D4—1316no—
506C2×D4—138no—
507C2×D4—2616no—
508C2×D4—2616no—
509C2×D4—528no—
510C2×D4—528no—
511C2×D4—524no—
512C2×D4—528no—
513C2×D4—528no—
514C2×D4—528no—
515C2×D4C23×D13116yes—
516C2×D4C23×D1318yes—
517C22×C4—48no—
518C22×C4—131no—
519C22×C4—132no—
520C22×C4—1316no—
521C22×C4—134no—
522C22×C4—134no—
523C22×C4—1316no—
524C22×C4—134no—
525C22×C4—138no—
526C22×C4—1316no—
527C22×C4—1316no—
528C22×C4—1316no—
529C22×C4—2616no—
530C22×C4—268no—
531C22×C4—264no—
532C22×C4—2616no—
533C22×C4—528no—
534C22×C4—528no—
535C22×C4—528no—
536C22×C4C23×D1311yescharacteristic
537C22×C4C23×D1312yes—
538C22×C4C23×D1314yes—
539C22×C4C23×D1314yes—
540C22×C4C23×D13116yes—
541C4⋊C4—1316no—
542C4⋊C4—1316no—
543C4⋊C4—1316no—
544C4⋊C4—1316no—
545C4⋊C4—1316no—
546C4⋊C4—138no—
547C4⋊C4—1316no—
548C4⋊C4—1316no—
549C4⋊C4C23×D13116yes—
550C4⋊C4C23×D1318yes—
551C4⋊C4C23×D13116yes—
552C22⋊C4—1316no—
553C22⋊C4—1316no—
554C22⋊C4—1316no—
555C22⋊C4—1316no—
556C22⋊C4—1316no—
557C22⋊C4—1316no—
558C22⋊C4C23×D13116yes—
559C22⋊C4C23×D13116yes—
560C22⋊C4C23×D13116yes—
561C42—134no—
562C42—138no—
563C42—1316no—
564C42C23×D1314yes—
565C13C2×#354811yescharacteristic, complemented, Sylow
566C23—28no—
567C23—28no—
568C23—28no—
569C23—132no—
570C23—138no—
571C23—268no—
572C23—264no—
573C23—268no—
574C23—262no—
575C23—268no—
576C23C24×D1318yes—
577C23C24×D1311yescharacteristic
578Q8—48no—
579Q8—2632no—
580Q8—528no—
581D4—416no—
582D4—48no—
583D4—2632no—
584D4—2632no—
585D4—5216no—
586D4—5216no—
587D4—528no—
588D4—5216no—
589D4—5216no—
590D4—5216no—
591C2×C4—28no—
592C2×C4—28no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—416no—
596C2×C4—138no—
597C2×C4—134no—
598C2×C4—132no—
599C2×C4—134no—
600C2×C4—138no—
601C2×C4—138no—
602C2×C4—268no—
603C2×C4—2632no—
604C2×C4—2616no—
605C2×C4—2632no—
606C2×C4—268no—
607C2×C4—268no—
608C2×C4—5216no—
609C2×C4—5216no—
610C2×C4—5216no—
611C2×C4C24×D1312yes—
612C2×C4C24×D1314yes—
613C2×C4C24×D1318yes—
614C2×C4C24×D1318yes—
615C22—28no—
616C22—28no—
617C22—28no—
618C22—416no—
619C22—268no—
620C22—264no—
621C22—268no—
622C22—262no—
623C22—268no—
624C22—524no—
625C22—5216no—
626C22D13×H(5,𝔽2)14yes—
627C22D13×2−1+412yes—
628C22C25×D1311yescharacteristic
629C4—28no—
630C4—28no—
631C4—24no—
632C4—22no—
633C4—138no—
634C4—134no—
635C4—268no—
636C4—268no—
637C2—48no—
638C2—522no—
639C2—528no—
640C2#1312923214yesdirect product factor
641C2C2×D13×H(5,𝔽2)12yes—
642C2C2×D13×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#562C2
socleC23×C13C25
hypercenterC2×#562D13
hypocenterC13C2×#3548
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13129232C2direct (N × H)
2. C2×#11719405C2semidirect
3. C2×#11719389C2semidirect
4. C2×#11719341C2semidirect
5. C2×#11719304C2semidirect
6. C2×#11719360C2semidirect
7. C2×#11719368C2semidirect
8. C2×#11719334C2semidirect
9. C2×#11719302C2semidirect
10. C2×#11719393C2semidirect
11. C2×#11719373C2semidirect
12. C2×C13×#562C2semidirect
17. C13×#562C22semidirect
33. #11719405C22semidirect
34. #11719393C22semidirect
35. #11719389C22semidirect
36. #11719373C22semidirect
37. #11719368C22semidirect
38. #11719360C22semidirect
39. #11719341C22semidirect
40. #11719334C22semidirect
41. #11719304C22semidirect
42. #11719302C22semidirect
248. C2×#562D13semidirect
312. #562C2×D13semidirect
479. C2×C13#3548semidirect
565. C13C2×#3548semidirect
640. C2#13129232direct (N × H)

Maximal subgroups

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

subgroupindex
#131292322
C2×#117194052
C2×#117193892
C2×#117193412
C2×#117193042
C2×#117193602
C2×#117193682
C2×#117193342
C2×#117193022
C2×#117193932
C2×#117193732
C2×C13×#5622
C2×#354813