Finite Group Databasebeta

← C2×#13119305 #16031976

Subgroups — C2×#13119305 #16031976

Order 3328.

4222 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88140C211yesmaximal, characteristic, complemented
2C22×#88183C211yesmaximal, characteristic, complemented
3C22×#88189C211yesmaximal, characteristic, complemented
4C22×#88193C211yesmaximal, characteristic
5C23×#6101C211yesmaximal, characteristic, complemented
6#13119305C2116yesmaximal, direct product factor
7C2×#11718610C212yesmaximal, complemented
8C2×#11718653C212yesmaximal, complemented
9C2×#11718618C212yesmaximal, complemented
10C2×#11718637C212yesmaximal, complemented
11C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
12C22×C13×#123C211yesmaximal, characteristic, complemented
13C23×D4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C23×C22⋊D13C2211yescharacteristic
16C23×C22⋊D13C2211yescharacteristic
17C24×Dic13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C2×C13×#123—28no—
20C2×C13×#123C2218yescomplemented
21C22×C13×C4⋊C4C2212yes—
22C22×C13×C22⋊C4C2212yes—
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic13C2212yes—
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C2×#88193—28no—
28C2×#88193C2218yes—
29C2×#88189—28no—
30C2×#88189C2218yescomplemented
31C2×#88183—28no—
32C2×#88183C2218yescomplemented
33C22×#6103C2212yes—
34C22×#6103C2212yes—
35C22×#6103C2211yescharacteristic
36C22×C4⋊Dic13C2212yes—
37C22×#6101—28no—
38C22×#6101C2211yescharacteristic
39C22×#6101C2212yes—
40C22×#6101C2212yes—
41C22×#6101C2212yes—
42C22×#6101C2212yes—
43C22×#6101C2218yescomplemented
44C22×C4×Dic13C2212yes—
45C2×#88140—28no—
46C2×#88140C2218yescomplemented
47C2×#88071C2212yes—
48#11718653C22116yescomplemented
49#11718637C22116yescomplemented
50#11718618C22116yescomplemented
51#11718610C22116yescomplemented
52C22⋊C4×Dic13C2218yescomplemented
53C25×C13C2311yescharacteristic
54C25×C13C2311yescharacteristic
55C24×D13C2311yescharacteristic
56C22×D4×C13—24no—
57C22×D4×C13—24no—
58C22×D4×C13—24no—
59C22×D4×C13C2314yes—
60C23×C4×C13—24no—
61C23×C4×C13—24no—
62C23×C4×C13—24no—
63C23×C4×C13C2312yes—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2314yes—
66C23×C4×C13C2312yes—
67C22×C22⋊D13—24no—
68C22×C22⋊D13—24no—
69C22×C22⋊D13—24no—
70C22×C22⋊D13—24no—
71C22×C22⋊D13—28no—
72C22×C22⋊D13C2314yes—
73C22×C22⋊D13C2314yes—
74C23×Dic13—28no—
75C23×Dic13—24no—
76C23×Dic13—24no—
77C23×Dic13—24no—
78C23×Dic13D418yes—
79C23×Dic13C2314yes—
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2312yes—
82C23×Dic13C2312yes—
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2314yes—
85C23×Dic13C2311yescharacteristic
86C13×#123—232no—
87C2×C13×C4⋊C4—28no—
88C2×C13×C4⋊C4C2318yes—
89C2×C13×C22⋊C4—28no—
90C2×C13×C22⋊C4D418yescomplemented
91C2×C13×C22⋊C4C2318yes—
92C2×C13×C22⋊C4C2314yes—
93C2×C22⋊Dic13—28no—
94C2×C22⋊Dic13—24no—
95C2×C22⋊Dic13D418yescomplemented
96C2×C22⋊Dic13C2318yes—
97C2×C22⋊Dic13C2314yes—
98C2×C22⋊Dic13C2314yes—
99#88193—232no—
100#88189—232no—
101#88183—232no—
102C2×#6103—28no—
103C2×#6103—28no—
104C2×#6103—24no—
105C2×#6103C2318yes—
106C2×#6103C2318yes—
107C2×#6103C2314yes—
108C2×C4⋊Dic13—28no—
109C2×C4⋊Dic13C2318yes—
110C2×#6101—28no—
111C2×#6101—28no—
112C2×#6101—232no—
113C2×#6101—28no—
114C2×#6101—28no—
115C2×#6101—24no—
116C2×#6101C2318yes—
117C2×#6101C2318yes—
118C2×#6101C2318yes—
119C2×#6101C2318yes—
120C2×#6101C2314yes—
121C2×C4×Dic13—28no—
122C2×C4×Dic13C2318yes—
123#88140—232no—
124#88071C2318yes—
125C2×#2501—131nomaximal, Sylow
126C24×C13—24no—
127C24×C13—24no—
128C24×C13—22no—
129C24×C13—22no—
130C24×C13—22no—
131C24×C13—24no—
132C24×C13—24no—
133C24×C13C2×D414yes—
134C24×C13C2×D414yes—
135C24×C13C2×D414yes—
136C24×C13C2412yes—
137C24×C13C2412yes—
138C24×C13C2411yescharacteristic
139C23×D13—22no—
140C23×D13—22no—
141C23×D13—22no—
142C23×D13—24no—
143C23×D13—24no—
144C23×D13C2412yes—
145C2×D4×C13—28no—
146C2×D4×C13—28no—
147C2×D4×C13—28no—
148C2×D4×C13—416no—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13—28no—
152C22×C4×C13—24no—
153C22×C4×C13—22no—
154C22×C4×C13—24no—
155C22×C4×C13—22no—
156C22×C4×C13—28no—
157C22×C4×C13—24no—
158C22×C4×C13—22no—
159C22×C4×C13—28no—
160C22×C4×C13—416no—
161C22×C4×C13C2×D418yes—
162C22×C4×C13C2414yes—
163C22×C4×C13C2412yes—
164C22×C4×C13C2414yes—
165C2×C22⋊D13—28no—
166C2×C22⋊D13—28no—
167C2×C22⋊D13—28no—
168C2×C22⋊D13—28no—
169C2×C22⋊D13—216no—
170C2×C22⋊D13—416no—
171C2×C22⋊D13—416no—
172C22×Dic13—24no—
173C22×Dic13—24no—
174C22×Dic13—24no—
175C22×Dic13—232no—
176C22×Dic13—216no—
177C22×Dic13—28no—
178C22×Dic13—28no—
179C22×Dic13—24no—
180C22×Dic13—22no—
181C22×Dic13—24no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—24no—
185C22×Dic13—28no—
186C22×Dic13—416no—
187C22×Dic13C2×D418yes—
188C22×Dic13C2×D414yes—
189C22×Dic13C2×D4116yes—
190C22×Dic13C2×D414yes—
191C22×Dic13#4118yes—
192C22×Dic13C2412yes—
193C22×Dic13C2414yes—
194C22×Dic13C2412yes—
195C22×Dic13C2414yes—
196C22×Dic13C2412yes—
197C13×C4⋊C4—216no—
198C13×C22⋊C4—216no—
199C13×C22⋊C4C2×D4116yescomplemented
200C22⋊Dic13—216no—
201C22⋊Dic13—28no—
202C22⋊Dic13C2×D4116yescomplemented
203#6103—216no—
204#6103—216no—
205#6103—28no—
206C4⋊Dic13—216no—
207#6101—216no—
208#6101—216no—
209#6101—216no—
210#6101—216no—
211#6101—28no—
212C4×Dic13—216no—
213C22×#123—131no—
214C22×#123—131no—
215C22×#123—131no—
216C22×#123D1311yescharacteristic, complemented
217C22×#121—131no—
218C23×C4⋊C4—131no—
219#2501—1316no—
220C2×#399—132no—
221C2×#399—132no—
222C2×#390—132no—
223C2×#384—132no—
224C2×C4×C22⋊C4—131no—
225C23×C13—28no—
226C23×C13—28no—
227C23×C13—216no—
228C23×C13—216no—
229C23×C13—24no—
230C23×C13—24no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—24no—
235C23×C13—24no—
236C23×C13—44no—
237C23×C13—44no—
238C23×C13—44no—
239C23×C13—48no—
240C23×C13—48no—
241C23×C13#127116yes—
242C23×C13C22×D414yes—
243C23×C13C22×D414yes—
244C23×C13C22×D414yes—
245C23×C13C22×D412yes—
246C23×C13C22×D412yes—
247C23×C13C22×D412yes—
248C23×C13C2×#4114yes—
249C23×C132−1+414yes—
250C23×C13C2511yescharacteristic
251C22×D13—22no—
252C22×D13—22no—
253C22×D13—22no—
254C22×D13—24no—
255C22×D13—24no—
256C22×D13—44no—
257C22×D13—44no—
258C22×D13—44no—
259C22×D13—48no—
260C22×D13—48no—
261D4×C13—416no—
262C2×C4×C13—216no—
263C2×C4×C13—24no—
264C2×C4×C13—24no—
265C2×C4×C13—24no—
266C2×C4×C13—22no—
267C2×C4×C13—24no—
268C2×C4×C13—22no—
269C2×C4×C13—24no—
270C2×C4×C13—22no—
271C2×C4×C13—416no—
272C2×C4×C13—48no—
273C2×C4×C13—44no—
274C2×C4×C13C22×D418yes—
275C22⋊D13—416no—
276C22⋊D13—416no—
277C2×Dic13—28no—
278C2×Dic13—216no—
279C2×Dic13—24no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—232no—
283C2×Dic13—24no—
284C2×Dic13—22no—
285C2×Dic13—24no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—24no—
289C2×Dic13—416no—
290C2×Dic13—48no—
291C2×Dic13—44no—
292C2×Dic13#123116yescomplemented
293C2×Dic13C22×D418yes—
294C2×Dic13C22×D414yes—
295C2×Dic13C22×D414yes—
296C2×Dic13C2×#4118yes—
297C23×D4—131no—
298C23×D4—131no—
299C23×D4C2×D1311yescharacteristic
300C24×C4—131no—
301C24×C4—131no—
302C24×C4C2×D1311yescharacteristic
303C2×#123—28no—
304C2×#123—138no—
305C2×#123—138no—
306C2×#123—138no—
307C2×#123—268no—
308C2×#123—268no—
309C2×#123—268no—
310C2×#123C2×D1318yescomplemented
311C2×#121—138no—
312C2×#121—268no—
313C22×C4⋊C4—132no—
314C22×C4⋊C4—132no—
315C22×C4⋊C4—132no—
316C22×C4⋊C4—132no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4—138no—
319C22×C4⋊C4—132no—
320C22×C4⋊C4—268no—
321C22×C4⋊C4C2×D1312yes—
322C22×C22⋊C4—131no—
323C22×C22⋊C4—131no—
324C22×C22⋊C4—132no—
325C22×C22⋊C4—131no—
326C22×C22⋊C4—132no—
327C22×C22⋊C4—132no—
328C22×C22⋊C4C2×D1312yes—
329C22×C22⋊C4C2×D1311yescharacteristic
330C22×C42—132no—
331#399—1316no—
332#399—1316no—
333#390—1316no—
334#384—1316no—
335C4×C22⋊C4—138no—
336C2×#95—132no—
337C22×C13—24no—
338C22×C13—24no—
339C22×C13—28no—
340C22×C13—28no—
341C22×C13—232no—
342C22×C13—42no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—44no—
346C22×C13—44no—
347C22×C13—88no—
348C22×C13C2×#12314yes—
349C22×C13C2×#12718yes—
350C22×C13C2×#12714yes—
351C22×C13#53614yes—
352C22×C13#54718yes—
353C22×C13#54718yes—
354C22×C13C23×D411yescharacteristic
355C22×C13C23×D411yescharacteristic
356C22×C13C23×D411yescharacteristic
357C22×C13C22×#4112yes—
358C22×C13C2×2−1+412yes—
359C2×D13—42no—
360C2×D13—42no—
361C2×D13—42no—
362C2×D13—44no—
363C2×D13—44no—
364C2×D13—88no—
365C4×C13—28no—
366C4×C13—44no—
367C4×C13—42no—
368Dic13—24no—
369Dic13—28no—
370Dic13—44no—
371Dic13—42no—
372Dic13C2×#12318yescomplemented
373C25—131no—
374C25C22×D1311yescharacteristic
375C25C22×D1311yescharacteristic
376C22×D4—24no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—134no—
380C22×D4—134no—
381C22×D4—264no—
382C22×D4—268no—
383C22×D4—264no—
384C22×D4—264no—
385C22×D4—264no—
386C22×D4C22×D1314yes—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—131no—
391C23×C4—138no—
392C23×C4—134no—
393C23×C4—132no—
394C23×C4—131no—
395C23×C4—134no—
396C23×C4—132no—
397C23×C4—131no—
398C23×C4—268no—
399C23×C4—264no—
400C23×C4—264no—
401C23×C4—264no—
402C23×C4C22×D1314yes—
403C23×C4C22×D1312yes—
404C23×C4C22×D1311yescharacteristic
405C23×C4C22×D1312yes—
406#123—232no—
407#123—2632no—
408#123—2632no—
409#123—2632no—
410#121—2632no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—138no—
413C2×C4⋊C4—138no—
414C2×C4⋊C4—134no—
415C2×C4⋊C4—138no—
416C2×C4⋊C4—138no—
417C2×C4⋊C4—138no—
418C2×C4⋊C4—268no—
419C2×C4⋊C4—268no—
420C2×C4⋊C4—2632no—
421C2×C4⋊C4—264no—
422C2×C4⋊C4—268no—
423C2×C4⋊C4—268no—
424C2×C4⋊C4—268no—
425C2×C4⋊C4C22×D1318yes—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—138no—
428C2×C22⋊C4—134no—
429C2×C22⋊C4—134no—
430C2×C22⋊C4—138no—
431C2×C22⋊C4—134no—
432C2×C22⋊C4—138no—
433C2×C22⋊C4—138no—
434C2×C22⋊C4—264no—
435C2×C22⋊C4—268no—
436C2×C22⋊C4—264no—
437C2×C22⋊C4—268no—
438C2×C22⋊C4—268no—
439C2×C22⋊C4C22⋊D1318yescomplemented
440C2×C22⋊C4C22×D1318yes—
441C2×C22⋊C4C22×D1314yes—
442C2×C42—138no—
443C2×C42—268no—
444#95—138no—
445C2×C13—28no—
446C2×C13—82no—
447C2×C13#250118yescomplemented
448C2×C13C22×#12311yescharacteristic
449C2×C13C22×#12711yescharacteristic
450C2×C13C2×#53611yescharacteristic
451C2×C13C2×#54712yes—
452C2×C13C2×#54712yes—
453D13—82no—
454C24—24no—
455C24—24no—
456C24—22no—
457C24—22no—
458C24—24no—
459C24—24no—
460C24—22no—
461C24—132no—
462C24—262no—
463C24—262no—
464C24—264no—
465C24—264no—
466C24—262no—
467C24D4×D1314yes—
468C24D4×D1314yes—
469C24C2×C22⋊D1314yes—
470C24C23×D1312yes—
471C24C23×D1312yes—
472C24C23×D1311yescharacteristic
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—416no—
477C2×D4—268no—
478C2×D4—2616no—
479C2×D4—268no—
480C2×D4—268no—
481C2×D4—268no—
482C2×D4—5216no—
483C2×D4—5216no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—28no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—28no—
495C22×C4—416no—
496C22×C4—134no—
497C22×C4—138no—
498C22×C4—132no—
499C22×C4—138no—
500C22×C4—134no—
501C22×C4—1316no—
502C22×C4—132no—
503C22×C4—134no—
504C22×C4—134no—
505C22×C4—132no—
506C22×C4—2632no—
507C22×C4—2616no—
508C22×C4—264no—
509C22×C4—264no—
510C22×C4—264no—
511C22×C4—264no—
512C22×C4—262no—
513C22×C4—268no—
514C22×C4—264no—
515C22×C4—262no—
516C22×C4—268no—
517C22×C4—264no—
518C22×C4—262no—
519C22×C4—268no—
520C22×C4—5216no—
521C22×C4C2×C22⋊D1318yes—
522C22×C4C23×D1314yes—
523C22×C4C23×D1312yes—
524C22×C4C23×D1314yes—
525C4⋊C4—216no—
526C4⋊C4—2616no—
527C4⋊C4—2616no—
528C4⋊C4—268no—
529C4⋊C4—2616no—
530C4⋊C4—2616no—
531C4⋊C4—2616no—
532C22⋊C4—216no—
533C22⋊C4—1316no—
534C22⋊C4—268no—
535C22⋊C4—2616no—
536C22⋊C4—268no—
537C22⋊C4—2616no—
538C22⋊C4—2616no—
539C22⋊C4C2×C22⋊D13116yescomplemented
540C42—2616no—
541C13C2×#250111yescharacteristic, complemented, Sylow
542C23—216no—
543C23—28no—
544C23—28no—
545C23—216no—
546C23—24no—
547C23—24no—
548C23—22no—
549C23—22no—
550C23—24no—
551C23—24no—
552C23—22no—
553C23—44no—
554C23—48no—
555C23—44no—
556C23—44no—
557C23—48no—
558C23—262no—
559C23—262no—
560C23—264no—
561C23—264no—
562C23—262no—
563C23—524no—
564C23—528no—
565C23—524no—
566C23—524no—
567C23—528no—
568C23#88194116yes—
569C23C2×D4×D1314yes—
570C23C2×D4×D1314yes—
571C23C2×D4×D1312yes—
572C23C2×D4×D1312yes—
573C23#41×D1314yes—
574C23#8825714yes—
575C23C22×C22⋊D1314yes—
576C23C22×C22⋊D1312yes—
577C23C24×D1311yescharacteristic
578D4—416no—
579D4—5216no—
580D4—5216no—
581C2×C4—216no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—416no—
591C2×C4—48no—
592C2×C4—44no—
593C2×C4—1316no—
594C2×C4—134no—
595C2×C4—138no—
596C2×C4—138no—
597C2×C4—134no—
598C2×C4—2632no—
599C2×C4—268no—
600C2×C4—2616no—
601C2×C4—264no—
602C2×C4—264no—
603C2×C4—264no—
604C2×C4—264no—
605C2×C4—262no—
606C2×C4—264no—
607C2×C4—262no—
608C2×C4—264no—
609C2×C4—262no—
610C2×C4—5216no—
611C2×C4—528no—
612C2×C4—524no—
613C2×C4C22×C22⋊D1318yes—
614C22—232no—
615C22—28no—
616C22—28no—
617C22—24no—
618C22—24no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—88no—
625C22—524no—
626C22—524no—
627C22—522no—
628C22—522no—
629C22—522no—
630C22—1048no—
631C22#1171935314yes—
632C22D13×#12314yes—
633C22#1171936018yes—
634C22C2×#8819418yes—
635C22C2×#8819414yes—
636C22#1171952918yes—
637C22C22×D4×D1311yescharacteristic
638C22C22×D4×D1311yescharacteristic
639C22C2×#41×D1312yes—
640C22C2×#8825712yes—
641C22C23×C22⋊D1311yescharacteristic
642C4—28no—
643C4—44no—
644C4—42no—
645C4—138no—
646C4—268no—
647C4—264no—
648C4—524no—
649C4—522no—
650C2—28no—
651C2—82no—
652C2—1042no—
653C2#1311930518yesdirect product factor
654C2C2×D13×#12311yescharacteristic
655C2C22×#8819411yescharacteristic
656C2C2×#1171935311yescharacteristic
657C2C2×#1171936012yes—
658C2C2×#1171952912yes—
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC22×C13×#123C2
socleC24×C13C24
prime radicalC22×#88193C2
hypercenterC22×#123D13
hypocenterC13C2×#2501
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#88140C2semidirect
2. C22×#88183C2semidirect
3. C22×#88189C2semidirect
5. C23×#6101C2semidirect
6. #13119305C2direct (N × H)
7. C2×#11718610C2semidirect
8. C2×#11718653C2semidirect
9. C2×#11718618C2semidirect
10. C2×#11718637C2semidirect
11. C2×C22⋊C4×Dic13C2semidirect
12. C22×C13×#123C2semidirect
20. C2×C13×#123C22semidirect
30. C2×#88189C22semidirect
32. C2×#88183C22semidirect
43. C22×#6101C22semidirect
46. C2×#88140C22semidirect
48. #11718653C22semidirect
49. #11718637C22semidirect
50. #11718618C22semidirect
51. #11718610C22semidirect
52. C22⋊C4×Dic13C22semidirect
90. C2×C13×C22⋊C4D4semidirect
95. C2×C22⋊Dic13D4semidirect
199. C13×C22⋊C4C2×D4semidirect
202. C22⋊Dic13C2×D4semidirect
216. C22×#123D13semidirect
292. C2×Dic13#123semidirect
310. C2×#123C2×D13semidirect
372. Dic13C2×#123semidirect
439. C2×C22⋊C4C22⋊D13semidirect
447. C2×C13#2501semidirect
539. C22⋊C4C2×C22⋊D13semidirect
541. C13C2×#2501semidirect
653. C2#13119305direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881402
C22×#881832
C22×#881892
C22×#881932
C23×#61012
#131193052
C2×#117186102
C2×#117186532
C2×#117186182
C2×#117186372
C2×C22⋊C4×Dic132
C22×C13×#1232
C2×#250113