Finite Group Databasebeta

← C2×#13118263 #16031332

Subgroups — C2×#13118263 #16031332

Order 3328.

3526 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic, complemented
2C22×#88151C211yesmaximal, characteristic, complemented
3C22×C4×D52C211yesmaximal, characteristic
4C22×#88146C211yesmaximal, characteristic, complemented
5#13118263C2116yesmaximal, direct product factor
6C2×#11718335C212yesmaximal, complemented
7C2×#11718652C212yesmaximal
8C2×#11718590C211yesmaximal, characteristic, complemented
9C2×#11718646C212yesmaximal, complemented
10C2×#11718331C212yesmaximal, complemented
11C2×#11718648C211yesmaximal, characteristic, complemented
12C2×C13×#389C211yesmaximal, characteristic, complemented
13C23×D52C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C23×Dic26C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2212yes—
26C22×#6103C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2212yes—
30C22×C4⋊Dic13C2212yes—
31C22×C4×Dic13C2212yes—
32C2×#88151—28no—
33C2×#88151—28no—
34C2×#88151C2218yescomplemented
35C2×#88151C2218yescomplemented
36C2×#88146—28no—
37C2×#88146C2218yescomplemented
38C2×C4×D52—28no—
39C2×C4×D52C2218yes—
40C13×#389C2218yescomplemented
41C2×C13×#95C2212yes—
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44C2×#88071C2212yes—
45#11718652C22116yes—
46#11718648C2218yescomplemented
47#11718646C22116yescomplemented
48#11718590C2218yescomplemented
49#11718335C22116yescomplemented
50#11718331C22116yescomplemented
51C24×D13C2311yescharacteristic
52C24×D13C2311yescharacteristic
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×Dic13C2312yes—
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2312yes—
61C23×Dic13C2311yescharacteristic
62C22×D52—24no—
63C22×D52—24no—
64C22×D52—24no—
65C22×D52C2314yes—
66C22×C4×D13—24no—
67C22×C4×D13—24no—
68C22×C4×D13—24no—
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13D418yes—
72C22×C4×D13C2314yes—
73C22×C4×D13C2314yes—
74C22×Dic26—24no—
75C22×Dic26—24no—
76C22×Dic26—24no—
77C22×Dic26C2314yes—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4—28no—
80C2×C13×C4⋊C4D418yescomplemented
81C2×C13×C4⋊C4C2314yes—
82C2×C13×C4⋊C4C2318yes—
83C2×C13×C4⋊C4C2314yes—
84C2×C42×C13—24no—
85C2×C42×C13C2314yes—
86C2×#6103—24no—
87C2×#6103—28no—
88C2×#6103—28no—
89C2×#6103—28no—
90C2×#6103—28no—
91C2×#6103—24no—
92C2×#6103C2314yes—
93C2×#6103C2314yes—
94C2×#6103C2318yes—
95C2×#6103C2318yes—
96C2×#6103C2318yes—
97C2×#6103C2318yes—
98C2×C4⋊Dic13—24no—
99C2×C4⋊Dic13—28no—
100C2×C4⋊Dic13—24no—
101C2×C4⋊Dic13—28no—
102C2×C4⋊Dic13C2314yes—
103C2×C4⋊Dic13C2314yes—
104C2×C4⋊Dic13C2318yes—
105C2×C4⋊Dic13C2318yes—
106C2×C4×Dic13—28no—
107C2×C4×Dic13C2318yes—
108#88151—232no—
109#88151—232no—
110#88146—232no—
111C4×D52—232no—
112C13×#95C2318yes—
113#88071C2318yes—
114#88071C2318yes—
115#88071C2318yes—
116C2×#2415—131nomaximal, Sylow
117C24×C13C2411yescharacteristic
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—22no—
128C23×D13—22no—
129C23×D13—22no—
130C23×D13C2×D414yes—
131C23×D13#4114yes—
132C23×D13C2412yes—
133C23×D13C2412yes—
134C22×C4×C13—22no—
135C22×C4×C13—24no—
136C22×C4×C13—22no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—22no—
140C22×C4×C13—24no—
141C22×C4×C13—24no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13C2×D418yes—
145C22×C4×C13C2×D414yes—
146C22×C4×C13C2×D414yes—
147C22×C4×C13#4114yes—
148C22×C4×C13#4114yes—
149C22×C4×C13C2412yes—
150C22×C4×C13C2414yes—
151C22×C4×C13C2414yes—
152C22×C4×C13C2412yes—
153C22×C4×C13C2412yes—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—24no—
157C22×Dic13—22no—
158C22×Dic13—24no—
159C22×Dic13—24no—
160C22×Dic13—22no—
161C22×Dic13—24no—
162C22×Dic13—24no—
163C22×Dic13—22no—
164C22×Dic13—24no—
165C22×Dic13C2×D414yes—
166C22×Dic13C2414yes—
167C22×Dic13C2412yes—
168C22×Dic13C2414yes—
169C22×Dic13C2412yes—
170C2×D52—232no—
171C2×D52—28no—
172C2×D52—28no—
173C2×D52—28no—
174C2×C4×D13—232no—
175C2×C4×D13—28no—
176C2×C4×D13—28no—
177C2×C4×D13—28no—
178C2×C4×D13—28no—
179C2×C4×D13—28no—
180C2×C4×D13—416no—
181C2×C4×D13C2×D4116yes—
182C2×Dic26—28no—
183C2×Dic26—28no—
184C2×Dic26—28no—
185C2×Dic26—416no—
186C13×C4⋊C4—28no—
187C13×C4⋊C4—216no—
188C13×C4⋊C4C2×D4116yescomplemented
189C42×C13—28no—
190#6103—28no—
191#6103—216no—
192#6103—216no—
193#6103—216no—
194#6103—216no—
195#6103—28no—
196C4⋊Dic13—28no—
197C4⋊Dic13—216no—
198C4⋊Dic13—28no—
199C4⋊Dic13—216no—
200C4×Dic13—216no—
201C22×C22⋊Q8—131no—
202C22×C22⋊Q8—131no—
203C22×C4×D4—131no—
204C22×#117—131no—
205#2415—1316no—
206C2×#397—132no—
207C2×#394—132no—
208C2×#391—131no—
209C2×#389—132no—
210C2×#389D1311yescharacteristic, complemented
211C2×#388—132no—
212C2×#380—131no—
213C23×C13C22×D412yes—
214C23×C13C22×D412yes—
215C23×C13C2×#4112yes—
216C23×C13C2×#4112yes—
217C23×C13C2×#4112yes—
218C23×C132−1+412yes—
219C23×C132−1+412yes—
220C23×C13C2511yescharacteristic
221C22×D13—28no—
222C22×D13—28no—
223C22×D13—28no—
224C22×D13—28no—
225C22×D13—28no—
226C22×D13—28no—
227C22×D13—22no—
228C22×D13—22no—
229C22×D13—22no—
230C22×D13—22no—
231C22×D13—22no—
232C22×D13—22no—
233C22×D13—22no—
234C22×D13—22no—
235C22×D13—22no—
236C22×D13—22no—
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—44no—
240C22×D13—44no—
241C22×D13—44no—
242C22×D13—44no—
243C22×D13—44no—
244C22×D13—44no—
245C22×D13—44no—
246C22×D13—44no—
247C22×D13C22×D414yes—
248C22×D13C2×#4114yes—
249C2×C4×C13—28no—
250C2×C4×C13—216no—
251C2×C4×C13—22no—
252C2×C4×C13—24no—
253C2×C4×C13—22no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—22no—
257C2×C4×C13—24no—
258C2×C4×C13—24no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—48no—
262C2×C4×C13—44no—
263C2×C4×C13#121116yes—
264C2×C4×C13C22×D418yes—
265C2×C4×C13C22×D414yes—
266C2×C4×C13C22×D414yes—
267C2×C4×C13C2×#4114yes—
268C2×C4×C13C2×#4114yes—
269C2×Dic13—28no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—24no—
273C2×Dic13—22no—
274C2×Dic13—24no—
275C2×Dic13—24no—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—24no—
279C2×Dic13—22no—
280C2×Dic13—24no—
281C2×Dic13—48no—
282C2×Dic13—44no—
283C2×Dic13—48no—
284C2×Dic13C22×D414yes—
285D52—232no—
286C4×D13—232no—
287C4×D13—416no—
288Dic26—416no—
289C23×Q8—131no—
290C23×D4—131no—
291C24×C4—131no—
292C24×C4—131no—
293C2×C22⋊Q8—138no—
294C2×C22⋊Q8—138no—
295C2×C22⋊Q8—268no—
296C2×C22⋊Q8—268no—
297C2×C4×D4—138no—
298C2×C4×D4—268no—
299C2×#117—138no—
300C2×#117—268no—
301C22×C4⋊C4—132no—
302C22×C4⋊C4—131no—
303C22×C4⋊C4—131no—
304C22×C4⋊C4—132no—
305C22×C4⋊C4C2×D1312yes—
306C22×C4⋊C4C2×D1311yescharacteristic
307C22×C4⋊C4C2×D1311yescharacteristic
308C22×C22⋊C4—132no—
309C22×C22⋊C4—132no—
310C22×C22⋊C4—132no—
311C22×C22⋊C4—132no—
312C22×C22⋊C4—131no—
313C22×C22⋊C4—131no—
314C22×C42—132no—
315C22×C42C2×D1311yescharacteristic
316#397—1316no—
317#394—1316no—
318#391—138no—
319#389—1316no—
320#389C2×D1318yescomplemented
321#388—1316no—
322#380—138no—
323C2×#95—132no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95C2×D1312yes—
327C22×C13C2×#12114yes—
328C22×C13#52514yes—
329C22×C13#53614yes—
330C22×C13#54714yes—
331C22×C13#54814yes—
332C22×C13#55214yes—
333C22×C13#55614yes—
334C22×C13C23×D411yescharacteristic
335C22×C13C23×D411yescharacteristic
336C22×C13C22×#4111yescharacteristic
337C22×C13C22×#4111yescharacteristic
338C22×C13C22×#4111yescharacteristic
339C22×C13C2×2−1+411yescharacteristic
340C22×C13C2×2−1+411yescharacteristic
341C2×D13—24no—
342C2×D13—24no—
343C2×D13—24no—
344C2×D13—24no—
345C2×D13—24no—
346C2×D13—24no—
347C2×D13—42no—
348C2×D13—416no—
349C2×D13—416no—
350C2×D13—42no—
351C2×D13—42no—
352C2×D13—42no—
353C2×D13—42no—
354C2×D13—42no—
355C2×D13—42no—
356C2×D13—42no—
357C4×C13—24no—
358C4×C13—28no—
359C4×C13—44no—
360C4×C13—42no—
361C4×C13C2×#12118yes—
362Dic13—24no—
363Dic13—44no—
364Dic13—42no—
365Dic13—44no—
366C25—131no—
367C25—131no—
368C22×Q8—134no—
369C22×Q8—264no—
370C22×Q8—264no—
371C22×Q8—264no—
372C22×D4—134no—
373C22×D4—264no—
374C22×D4—264no—
375C22×D4—264no—
376C23×C4—131no—
377C23×C4—138no—
378C23×C4—134no—
379C23×C4—132no—
380C23×C4—132no—
381C23×C4—131no—
382C23×C4—134no—
383C23×C4—264no—
384C23×C4—264no—
385C23×C4—264no—
386C23×C4—264no—
387C23×C4—264no—
388C23×C4C22×D1312yes—
389C23×C4C22×D1311yescharacteristic
390C23×C4C22×D1312yes—
391C23×C4C22×D1311yescharacteristic
392C23×C4C22×D1311yescharacteristic
393C22⋊Q8—2632no—
394C22⋊Q8—2632no—
395C4×D4—2632no—
396#117—2632no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—28no—
399C2×C4⋊C4—134no—
400C2×C4⋊C4—134no—
401C2×C4⋊C4—138no—
402C2×C4⋊C4—138no—
403C2×C4⋊C4—264no—
404C2×C4⋊C4—268no—
405C2×C4⋊C4—264no—
406C2×C4⋊C4—268no—
407C2×C4⋊C4D5218yescomplemented
408C2×C4⋊C4C22×D1314yes—
409C2×C4⋊C4C22×D1318yes—
410C2×C4⋊C4C22×D1314yes—
411C2×C22⋊C4—138no—
412C2×C22⋊C4—134no—
413C2×C22⋊C4—134no—
414C2×C22⋊C4—138no—
415C2×C22⋊C4—138no—
416C2×C22⋊C4—138no—
417C2×C22⋊C4—264no—
418C2×C22⋊C4—264no—
419C2×C22⋊C4—268no—
420C2×C22⋊C4—268no—
421C2×C22⋊C4—268no—
422C2×C22⋊C4—268no—
423C2×C42—24no—
424C2×C42—138no—
425C2×C42—268no—
426C2×C42C22×D1314yes—
427#95—138no—
428#95—138no—
429#95—138no—
430#95C22×D1318yes—
431C2×C13#241518yescomplemented
432C2×C13C22×#12111yescharacteristic
433C2×C13C2×#52511yescharacteristic
434C2×C13C2×#53611yescharacteristic
435C2×C13C2×#54711yescharacteristic
436C2×C13C2×#54811yescharacteristic
437C2×C13C2×#55211yescharacteristic
438C2×C13C2×#55611yescharacteristic
439D13—44no—
440D13—44no—
441C24—134no—
442C24—134no—
443C24—132no—
444C24—132no—
445C24—262no—
446C24—262no—
447C24—262no—
448C24—262no—
449C24—262no—
450C24—262no—
451C24—262no—
452C24—262no—
453C24—262no—
454C24—262no—
455C24—262no—
456C24—262no—
457C24C23×D1311yescharacteristic
458C2×Q8—268no—
459C2×Q8—268no—
460C2×Q8—268no—
461C2×Q8—5216no—
462C2×D4—268no—
463C2×D4—268no—
464C2×D4—2632no—
465C2×D4—268no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—134no—
477C22×C4—132no—
478C22×C4—1316no—
479C22×C4—134no—
480C22×C4—134no—
481C22×C4—132no—
482C22×C4—262no—
483C22×C4—262no—
484C22×C4—2632no—
485C22×C4—268no—
486C22×C4—268no—
487C22×C4—264no—
488C22×C4—264no—
489C22×C4—262no—
490C22×C4—262no—
491C22×C4—264no—
492C22×C4—262no—
493C22×C4—264no—
494C22×C4—264no—
495C22×C4—264no—
496C22×C4—268no—
497C22×C4—268no—
498C22×C4—268no—
499C22×C4—5216no—
500C22×C4C2×D5218yes—
501C22×C4C2×D5214yes—
502C22×C4D4×D1314yes—
503C22×C4#612914yes—
504C22×C4#613114yes—
505C22×C4C23×D1312yes—
506C22×C4C23×D1314yes—
507C22×C4C23×D1314yes—
508C22×C4C23×D1312yes—
509C22×C4C23×D1312yes—
510C4⋊C4—28no—
511C4⋊C4—216no—
512C4⋊C4—268no—
513C4⋊C4—2616no—
514C4⋊C4—268no—
515C4⋊C4—2616no—
516C4⋊C4C2×D52116yescomplemented
517C22⋊C4—268no—
518C22⋊C4—268no—
519C22⋊C4—2616no—
520C22⋊C4—2616no—
521C22⋊C4—2616no—
522C22⋊C4—2616no—
523C42—28no—
524C42—2616no—
525C13C2×#241511yescharacteristic, complemented, Sylow
526C23—134no—
527C23—134no—
528C23—268no—
529C23—268no—
530C23—268no—
531C23—268no—
532C23—268no—
533C23—262no—
534C23—262no—
535C23—262no—
536C23—262no—
537C23—262no—
538C23—262no—
539C23—262no—
540C23—262no—
541C23—262no—
542C23—262no—
543C23—262no—
544C23—262no—
545C23—268no—
546C23—524no—
547C23—524no—
548C23—524no—
549C23—524no—
550C23—524no—
551C23—524no—
552C23—524no—
553C23—524no—
554C23C22×D5212yes—
555C23C2×D4×D1312yes—
556C23C2×#612912yes—
557C23C2×#613112yes—
558C23#8825412yes—
559C23#41×D1312yes—
560C23#8825712yes—
561C23C24×D1311yescharacteristic
562Q8—5216no—
563D4—2632no—
564C2×C4—216no—
565C2×C4—28no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—48no—
577C2×C4—44no—
578C2×C4—134no—
579C2×C4—268no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—2632no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—264no—
588C2×C4—262no—
589C2×C4—264no—
590C2×C4—264no—
591C2×C4—264no—
592C2×C4—524no—
593C2×C4—528no—
594C2×C4—528no—
595C2×C4—5216no—
596C2×C4#88149116yes—
597C2×C4C22×D5218yes—
598C2×C4C22×D5214yes—
599C2×C4C2×D4×D1314yes—
600C2×C4C2×#612914yes—
601C2×C4C2×#613114yes—
602C22—264no—
603C22—264no—
604C22—264no—
605C22—264no—
606C22—264no—
607C22—264no—
608C22—5216no—
609C22—5216no—
610C22—522no—
611C22—522no—
612C22—522no—
613C22—522no—
614C22—522no—
615C22—522no—
616C22—522no—
617C22—522no—
618C22C2×#8814914yes—
619C22#1171926014yes—
620C22#1171928114yes—
621C22#1171931114yes—
622C22#1171933314yes—
623C22#1171939914yes—
624C22#1171943714yes—
625C22C23×D5211yescharacteristic
626C22C22×D4×D1311yescharacteristic
627C22C22×#612911yescharacteristic
628C22C22×#613111yescharacteristic
629C22C2×#8825411yescharacteristic
630C22C2×#41×D1311yescharacteristic
631C22C2×#8825711yescharacteristic
632C4—28no—
633C4—24no—
634C4—44no—
635C4—42no—
636C4—264no—
637C4—524no—
638C4—522no—
639C4—524no—
640C4C2×#8814918yes—
641C2—524no—
642C2—524no—
643C2#1311826318yesdirect product factor
644C2C22×#8814911yescharacteristic
645C2C2×#1171931111yescharacteristic
646C2C2×#1171933311yescharacteristic
647C2C2×#1171926011yescharacteristic
648C2C2×#1171928111yescharacteristic
649C2C2×#1171939911yescharacteristic
650C2C2×#1171943711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#389C2
socleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13C2×#2415
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#88151C2semidirect
2. C22×#88151C2semidirect
4. C22×#88146C2semidirect
5. #13118263C2direct (N × H)
6. C2×#11718335C2semidirect
8. C2×#11718590C2semidirect
9. C2×#11718646C2semidirect
10. C2×#11718331C2semidirect
11. C2×#11718648C2semidirect
12. C2×C13×#389C2semidirect
34. C2×#88151C22semidirect
35. C2×#88151C22semidirect
37. C2×#88146C22semidirect
40. C13×#389C22semidirect
46. #11718648C22semidirect
47. #11718646C22semidirect
48. #11718590C22semidirect
49. #11718335C22semidirect
50. #11718331C22semidirect
80. C2×C13×C4⋊C4D4semidirect
188. C13×C4⋊C4C2×D4semidirect
210. C2×#389D13semidirect
320. #389C2×D13semidirect
407. C2×C4⋊C4D52semidirect
431. C2×C13#2415semidirect
516. C4⋊C4C2×D52semidirect
525. C13C2×#2415semidirect
643. C2#13118263direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881512
C22×C4×D522
C22×#881462
#131182632
C2×#117183352
C2×#117186522
C2×#117185902
C2×#117186462
C2×#117183312
C2×#117186482
C2×C13×#3892
C2×#241513