Finite Group Databasebeta

← C2×#13119743 #16034185

Subgroups — C2×#13119743 #16034185

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×#88200C211yesmaximal, characteristic, complemented
2C22×Q8×Dic13C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D13C211yesmaximal, characteristic
4#13119743C2116yesmaximal, direct product factor
5C2×#11718645C212yesmaximal, complemented
6C2×#11718622C212yesmaximal
7C2×#11718606C212yesmaximal, complemented
8C2×#11718651C212yesmaximal, complemented
9C2×#11718638C211yesmaximal, characteristic, complemented
10C2×#11718873C211yesmaximal, characteristic, complemented
11C2×#11718648C211yesmaximal, characteristic, complemented
12C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
13C23×Q8×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C23×C22⋊D13C2211yescharacteristic
16C23×C4×D13C2211yescharacteristic
17C2×C13×C22⋊Q8—28no—
18C2×C13×C22⋊Q8C2218yescomplemented
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2212yes—
21C22×C13×C22⋊C4C2212yes—
22C22×C22⋊Dic13C2212yes—
23C22×C22⋊Dic13C2211yescharacteristic
24C2×#88200—28no—
25C2×#88200C2218yescomplemented
26C2×Q8×Dic13—28no—
27C2×Q8×Dic13C2218yescomplemented
28C2×C4×C22⋊D13—28no—
29C2×C4×C22⋊D13C2218yes—
30C22×#6103C2212yes—
31C22×#6103C2211yescharacteristic
32C22×#6103C2212yes—
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2212yes—
36C22×#6101C2211yescharacteristic
37C22×#6101C2212yes—
38C22×C4×Dic13C2212yes—
39C22×C4×Dic13C2211yescharacteristic
40#11718873C2218yescomplemented
41C2×#88071C2212yes—
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44C2×#88071C2212yes—
45#11718651C22116yescomplemented
46#11718648C2218yescomplemented
47#11718645C22116yescomplemented
48#11718638C2218yescomplemented
49#11718622C22116yes—
50#11718606C22116yescomplemented
51C25×C13C2311yescharacteristic
52C24×D13C2311yescharacteristic
53C22×Q8×C13—24no—
54C22×Q8×C13—24no—
55C22×Q8×C13D418yescomplemented
56C22×Q8×C13C2314yes—
57C23×C4×C13—24no—
58C23×C4×C13—24no—
59C23×C4×C13—24no—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2312yes—
62C23×C4×C13C2314yes—
63C23×C4×C13C2312yes—
64C23×C4×C13C2311yescharacteristic
65C22×C22⋊D13—24no—
66C22×C22⋊D13—24no—
67C22×C22⋊D13—24no—
68C22×C22⋊D13C2314yes—
69C23×Dic13C2312yes—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2312yes—
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C22×C4×D13—24no—
75C22×C4×D13—24no—
76C22×C4×D13—24no—
77C22×C4×D13C2314yes—
78C13×C22⋊Q8—232no—
79C2×C13×C4⋊C4—24no—
80C2×C13×C4⋊C4—28no—
81C2×C13×C4⋊C4C2314yes—
82C2×C13×C4⋊C4C2318yes—
83C2×C13×C22⋊C4—28no—
84C2×C13×C22⋊C4C2318yes—
85C2×C22⋊Dic13—28no—
86C2×C22⋊Dic13—24no—
87C2×C22⋊Dic13C2314yes—
88C2×C22⋊Dic13C2318yes—
89#88200—232no—
90Q8×Dic13—232no—
91C4×C22⋊D13—232no—
92C2×#6103—28no—
93C2×#6103—28no—
94C2×#6103—24no—
95C2×#6103C2314yes—
96C2×#6103C2318yes—
97C2×#6103C2318yes—
98C2×C4⋊Dic13—24no—
99C2×C4⋊Dic13—24no—
100C2×C4⋊Dic13—28no—
101C2×C4⋊Dic13C2314yes—
102C2×C4⋊Dic13C2318yes—
103C2×C4⋊Dic13C2314yes—
104C2×#6101—28no—
105C2×#6101—24no—
106C2×#6101C2314yes—
107C2×#6101C2318yes—
108C2×C4×Dic13—28no—
109C2×C4×Dic13D418yes—
110C2×C4×Dic13C2318yes—
111C2×C4×Dic13C2314yes—
112#88071C2318yes—
113#88071C2318yes—
114#88071C2318yes—
115#88071C2318yes—
116C2×#2536—131nomaximal, Sylow
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—22no—
122C24×C13—22no—
123C24×C13#4114yes—
124C24×C13C2412yes—
125C24×C13C2411yescharacteristic
126C23×D13—22no—
127C23×D13—22no—
128C23×D13—22no—
129C23×D13—22no—
130C23×D13—22no—
131C23×D13—22no—
132C23×D13#4114yes—
133C23×D13C2412yes—
134C2×Q8×C13—232no—
135C2×Q8×C13—28no—
136C2×Q8×C13—28no—
137C2×Q8×C13C2×D4116yescomplemented
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13—22no—
141C22×C4×C13—24no—
142C22×C4×C13—22no—
143C22×C4×C13—24no—
144C22×C4×C13—22no—
145C22×C4×C13—24no—
146C22×C4×C13—28no—
147C22×C4×C13—28no—
148C22×C4×C13—28no—
149C22×C4×C13—416no—
150C22×C4×C13C2×D414yes—
151C22×C4×C13C2×D418yes—
152C22×C4×C13C2×D414yes—
153C22×C4×C13#4114yes—
154C22×C4×C13C2414yes—
155C22×C4×C13C2412yes—
156C22×C4×C13C2414yes—
157C22×C4×C13C2412yes—
158C2×C22⋊D13—232no—
159C2×C22⋊D13—28no—
160C2×C22⋊D13—28no—
161C2×C22⋊D13—28no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—24no—
167C22×Dic13—22no—
168C22×Dic13—24no—
169C22×Dic13—22no—
170C22×Dic13—24no—
171C22×Dic13—24no—
172C22×Dic13—24no—
173C22×Dic13—22no—
174C22×Dic13—24no—
175C22×Dic13C2×D414yes—
176C22×Dic13C2×D414yes—
177C22×Dic13C2414yes—
178C22×Dic13C2414yes—
179C22×Dic13C2412yes—
180C22×Dic13C2412yes—
181C22×Dic13C2412yes—
182C2×C4×D13—28no—
183C2×C4×D13—28no—
184C2×C4×D13—28no—
185C2×C4×D13—416no—
186C13×C4⋊C4—28no—
187C13×C4⋊C4—216no—
188C13×C22⋊C4—216no—
189C22⋊Dic13—216no—
190C22⋊Dic13—28no—
191#6103—216no—
192#6103—216no—
193#6103—28no—
194C4⋊Dic13—28no—
195C4⋊Dic13—28no—
196C4⋊Dic13—216no—
197#6101—216no—
198#6101—28no—
199C4×Dic13—216no—
200C4×Dic13C2×D4116yes—
201C22×C22⋊Q8—131no—
202C22×C22⋊Q8D1311yescharacteristic, complemented
203C22×C4×Q8—131no—
204C22×C4×D4—131no—
205#2536—1316no—
206C2×#398—132no—
207C2×#394—132no—
208C2×#388—132no—
209C2×#388—132no—
210C2×#382—131no—
211C2×#380—131no—
212C2×#380—131no—
213C23×C13—28no—
214C23×C13—28no—
215C23×C13—28no—
216C23×C13—22no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—44no—
223C23×C13—44no—
224C23×C13—44no—
225C23×C13—44no—
226C23×C13C22×D412yes—
227C23×C13C22×D412yes—
228C23×C13C2×#4114yes—
229C23×C13C2×#4112yes—
230C23×C13C2×#4112yes—
231C23×C13C2×#4112yes—
232C23×C132−1+412yes—
233C23×C132−1+412yes—
234C23×C13C2511yescharacteristic
235C22×D13—28no—
236C22×D13—28no—
237C22×D13—28no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—22no—
241C22×D13—22no—
242C22×D13—22no—
243C22×D13—22no—
244C22×D13—44no—
245C22×D13—44no—
246C22×D13—44no—
247C22×D13—44no—
248C22×D13C2×#4114yes—
249Q8×C13—232no—
250C2×C4×C13—216no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—22no—
254C2×C4×C13—24no—
255C2×C4×C13—22no—
256C2×C4×C13—24no—
257C2×C4×C13—22no—
258C2×C4×C13—24no—
259C2×C4×C13—44no—
260C2×C4×C13—48no—
261C2×C4×C13—416no—
262C2×C4×C13#121116yes—
263C2×C4×C13C22×D418yes—
264C2×C4×C13C22×D414yes—
265C2×C4×C13C22×D414yes—
266C2×C4×C13C2×#4114yes—
267C22⋊D13—232no—
268C2×Dic13—28no—
269C2×Dic13—28no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—24no—
275C2×Dic13—22no—
276C2×Dic13—24no—
277C2×Dic13—22no—
278C2×Dic13—24no—
279C2×Dic13—24no—
280C2×Dic13—24no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—44no—
284C2×Dic13—48no—
285C2×Dic13—48no—
286C2×Dic13C22×D414yes—
287C2×Dic13C22×D414yes—
288C4×D13—416no—
289C23×Q8C2×D1311yescharacteristic
290C23×D4—131no—
291C24×C4—131no—
292C24×C4C2×D1311yescharacteristic
293C2×C22⋊Q8—28no—
294C2×C22⋊Q8—138no—
295C2×C22⋊Q8—268no—
296C2×C22⋊Q8C2×D1318yescomplemented
297C2×C4×Q8—138no—
298C2×C4×Q8—268no—
299C2×C4×D4—138no—
300C2×C4×D4—268no—
301C22×C4⋊C4—131no—
302C22×C4⋊C4—132no—
303C22×C4⋊C4—132no—
304C22×C4⋊C4—131no—
305C22×C4⋊C4—131no—
306C22×C4⋊C4C2×D1312yes—
307C22×C4⋊C4C2×D1311yescharacteristic
308C22×C22⋊C4—132no—
309C22×C22⋊C4—131no—
310C22×C22⋊C4—132no—
311C22×C22⋊C4—132no—
312C22×C22⋊C4—131no—
313C22×C22⋊C4C2×D1312yes—
314C22×C42—131no—
315C22×C42—132no—
316#398—1316no—
317#394—1316no—
318#388—1316no—
319#388—1316no—
320#382—138no—
321#380—138no—
322#380—138no—
323C2×#95—132no—
324C2×#95—132no—
325C2×#95—132no—
326C2×#95—132no—
327C22×C13—24no—
328C22×C13—24no—
329C22×C13—24no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13—42no—
334C22×C13—416no—
335C22×C13C2×#12114yes—
336C22×C13#52514yes—
337C22×C13#53614yes—
338C22×C13#54814yes—
339C22×C13#54814yes—
340C22×C13#55214yes—
341C22×C13#55214yes—
342C22×C13C23×D411yescharacteristic
343C22×C13C23×D411yescharacteristic
344C22×C13C22×#4111yescharacteristic
345C22×C13C22×#4111yescharacteristic
346C22×C13C22×#4111yescharacteristic
347C22×C13C2×2−1+411yescharacteristic
348C22×C13C2×2−1+411yescharacteristic
349C2×D13—24no—
350C2×D13—24no—
351C2×D13—24no—
352C2×D13—42no—
353C2×D13—42no—
354C2×D13—42no—
355C2×D13—42no—
356C2×D13—416no—
357C4×C13—28no—
358C4×C13—42no—
359C4×C13—44no—
360C4×C13C2×#12118yes—
361Dic13—24no—
362Dic13—24no—
363Dic13—42no—
364Dic13—44no—
365Dic13—44no—
366C25—131no—
367C25C22×D1311yescharacteristic
368C22×Q8—24no—
369C22×Q8—24no—
370C22×Q8C22⋊D1318yescomplemented
371C22×Q8C22×D1314yes—
372C22×D4—134no—
373C22×D4—264no—
374C22×D4—264no—
375C22×D4—264no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—131no—
380C23×C4—131no—
381C23×C4—132no—
382C23×C4—132no—
383C23×C4—131no—
384C23×C4—134no—
385C23×C4—264no—
386C23×C4—264no—
387C23×C4—264no—
388C23×C4C22×D1314yes—
389C23×C4C22×D1312yes—
390C23×C4C22×D1311yescharacteristic
391C23×C4C22×D1312yes—
392C23×C4C22×D1311yescharacteristic
393C22⋊Q8—232no—
394C22⋊Q8—2632no—
395C4×Q8—2632no—
396C4×D4—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—134no—
404C2×C4⋊C4—264no—
405C2×C4⋊C4—268no—
406C2×C4⋊C4—264no—
407C2×C4⋊C4—268no—
408C2×C4⋊C4—264no—
409C2×C4⋊C4C22×D1314yes—
410C2×C4⋊C4C22×D1318yes—
411C2×C22⋊C4—28no—
412C2×C22⋊C4—134no—
413C2×C22⋊C4—138no—
414C2×C22⋊C4—134no—
415C2×C22⋊C4—138no—
416C2×C22⋊C4—138no—
417C2×C22⋊C4—264no—
418C2×C22⋊C4—268no—
419C2×C22⋊C4—264no—
420C2×C22⋊C4—268no—
421C2×C22⋊C4—268no—
422C2×C22⋊C4C22×D1318yes—
423C2×C42—138no—
424C2×C42—134no—
425C2×C42—138no—
426C2×C42—268no—
427#95—138no—
428#95—138no—
429#95—138no—
430#95—138no—
431C2×C13—44no—
432C2×C13#253618yescomplemented
433C2×C13C22×#12111yescharacteristic
434C2×C13C2×#52511yescharacteristic
435C2×C13C2×#53611yescharacteristic
436C2×C13C2×#54811yescharacteristic
437C2×C13C2×#54811yescharacteristic
438C2×C13C2×#55211yescharacteristic
439C2×C13C2×#55211yescharacteristic
440D13—44no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—134no—
448C24—132no—
449C24—262no—
450C24—262no—
451C24—262no—
452C24—262no—
453C24—262no—
454C24—262no—
455C24#613114yes—
456C24C23×D1312yes—
457C24C23×D1311yescharacteristic
458C2×Q8—232no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8C2×C22⋊D13116yescomplemented
462C2×D4—268no—
463C2×D4—268no—
464C2×D4—2632no—
465C2×D4—268no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—416no—
478C22×C4—134no—
479C22×C4—134no—
480C22×C4—132no—
481C22×C4—132no—
482C22×C4—134no—
483C22×C4—134no—
484C22×C4—132no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—262no—
488C22×C4—262no—
489C22×C4—264no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—264no—
493C22×C4—264no—
494C22×C4—264no—
495C22×C4—264no—
496C22×C4—264no—
497C22×C4—262no—
498C22×C4—268no—
499C22×C4—268no—
500C22×C4—268no—
501C22×C4—5216no—
502C22×C4D4×D1314yes—
503C22×C4#612914yes—
504C22×C4C2×C22⋊D1318yes—
505C22×C4C2×C22⋊D1314yes—
506C22×C4C23×D1314yes—
507C22×C4C23×D1312yes—
508C22×C4C23×D1314yes—
509C22×C4C23×D1312yes—
510C4⋊C4—28no—
511C4⋊C4—216no—
512C4⋊C4—268no—
513C4⋊C4—2616no—
514C4⋊C4—268no—
515C4⋊C4—2616no—
516C4⋊C4—268no—
517C22⋊C4—216no—
518C22⋊C4—268no—
519C22⋊C4—2616no—
520C22⋊C4—268no—
521C22⋊C4—2616no—
522C22⋊C4—2616no—
523C42—1316no—
524C42—2616no—
525C13C2×#253611yescharacteristic, complemented, Sylow
526C23—28no—
527C23—28no—
528C23—28no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—22no—
535C23—44no—
536C23—44no—
537C23—44no—
538C23—44no—
539C23—134no—
540C23—268no—
541C23—268no—
542C23—268no—
543C23—262no—
544C23—262no—
545C23—262no—
546C23—262no—
547C23—262no—
548C23—262no—
549C23—524no—
550C23—524no—
551C23—524no—
552C23—524no—
553C23C2×D4×D1312yes—
554C23C2×#612912yes—
555C23C2×#613114yes—
556C23C2×#613112yes—
557C23#8825412yes—
558C23#41×D1312yes—
559C23#8825712yes—
560C23C22×C22⋊D1312yes—
561C23C24×D1311yescharacteristic
562Q8—232no—
563D4—2632no—
564C2×C4—216no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—44no—
574C2×C4—48no—
575C2×C4—416no—
576C2×C4—134no—
577C2×C4—134no—
578C2×C4—268no—
579C2×C4—268no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—262no—
584C2×C4—264no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—264no—
588C2×C4—264no—
589C2×C4—264no—
590C2×C4—264no—
591C2×C4—264no—
592C2×C4—262no—
593C2×C4—524no—
594C2×C4—528no—
595C2×C4—528no—
596C2×C4—5216no—
597C2×C4#88193116yes—
598C2×C4C2×D4×D1314yes—
599C2×C4C2×#612914yes—
600C2×C4C22×C22⋊D1318yes—
601C2×C4C22×C22⋊D1314yes—
602C22—24no—
603C22—24no—
604C22—24no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—416no—
610C22—264no—
611C22—264no—
612C22—264no—
613C22—522no—
614C22—522no—
615C22—522no—
616C22—522no—
617C22—5216no—
618C22#1171933214yes—
619C22#1171933314yes—
620C22#1171934414yes—
621C22#1171934714yes—
622C22C2×#8819314yes—
623C22#1171952214yes—
624C22#1171953614yes—
625C22C22×D4×D1311yescharacteristic
626C22C22×#612911yescharacteristic
627C22C22×#613111yescharacteristic
628C22C2×#8825411yescharacteristic
629C22C2×#41×D1311yescharacteristic
630C22C2×#8825711yescharacteristic
631C22C23×C22⋊D1311yescharacteristic
632C4—28no—
633C4—44no—
634C4—42no—
635C4—264no—
636C4—264no—
637C4—524no—
638C4—522no—
639C4—524no—
640C4C2×#8819318yes—
641C2—44no—
642C2—524no—
643C2#1311974318yesdirect product factor
644C2C22×#8819311yescharacteristic
645C2C2×#1171933211yescharacteristic
646C2C2×#1171933311yescharacteristic
647C2C2×#1171953611yescharacteristic
648C2C2×#1171952211yescharacteristic
649C2C2×#1171934411yescharacteristic
650C2C2×#1171934711yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×C22⋊Q8C2
socleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#2536
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#88200C2semidirect
2. C22×Q8×Dic13C2semidirect
4. #13119743C2direct (N × H)
5. C2×#11718645C2semidirect
7. C2×#11718606C2semidirect
8. C2×#11718651C2semidirect
9. C2×#11718638C2semidirect
10. C2×#11718873C2semidirect
11. C2×#11718648C2semidirect
12. C22×C13×C22⋊Q8C2semidirect
18. C2×C13×C22⋊Q8C22semidirect
25. C2×#88200C22semidirect
27. C2×Q8×Dic13C22semidirect
40. #11718873C22semidirect
45. #11718651C22semidirect
46. #11718648C22semidirect
47. #11718645C22semidirect
48. #11718638C22semidirect
50. #11718606C22semidirect
55. C22×Q8×C13D4semidirect
137. C2×Q8×C13C2×D4semidirect
202. C22×C22⋊Q8D13semidirect
296. C2×C22⋊Q8C2×D13semidirect
370. C22×Q8C22⋊D13semidirect
432. C2×C13#2536semidirect
461. C2×Q8C2×C22⋊D13semidirect
525. C13C2×#2536semidirect
643. C2#13119743direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882002
C22×Q8×Dic132
C22×C4×C22⋊D132
#131197432
C2×#117186452
C2×#117186222
C2×#117186062
C2×#117186512
C2×#117186382
C2×#117188732
C2×#117186482
C22×C13×C22⋊Q82
C2×#253613